%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU687^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n031.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 09:36:24 AM UTC 2026
% Result : Theorem 92.68s 14.54s
% Output : Refutation 92.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 13
% Syntax : Number of formulae : 60 ( 15 unt; 0 typ; 1 def)
% Number of atoms : 4164 (1099 equ; 0 cnn)
% Maximal formula atoms : 211 ( 69 avg)
% Number of connectives : 2812 ( 140 ~; 110 |; 707 &; 982 @)
% ( 6 <=>; 867 =>; 0 <=; 0 <~>)
% Maximal formula depth : 221 ( 31 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 388 ( 385 usr; 221 con; 0-4 aty)
% Number of variables : 198 ( 0 ^; 133 !; 65 ?; 198 :)
% 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_255,type,
sP1: $o > $i > $i > $i > $o ).
thf(func_def_256,type,
sP2: $i > $i > $o ).
thf(func_def_257,type,
sP3: $i > $o ).
thf(func_def_258,type,
sP4: $i > $i > $o ).
thf(func_def_259,type,
sP5: $i > $i > $o ).
thf(func_def_273,type,
sK19: $i > $i > $i ).
thf(func_def_286,type,
sK32: $i > $i > $o ).
thf(func_def_291,type,
sK37: $i > $i ).
thf(func_def_303,type,
sK49: $i > $i > $o ).
thf(func_def_306,type,
sK52: $i > $i ).
thf(func_def_312,type,
sK58: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_313,type,
sK59: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_316,type,
sK62: $i > $o ).
thf(func_def_317,type,
sK63: $i > $o ).
thf(func_def_318,type,
sK64: $i > $o ).
thf(func_def_319,type,
sK65: $i > $i ).
thf(func_def_320,type,
sK66: ( $i > $o ) > $i ).
thf(func_def_322,type,
sK68: $i > $i > $o ).
thf(func_def_332,type,
sK78: $i > $o ).
thf(func_def_334,type,
sK80: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_335,type,
sK81: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_338,type,
sK84: $i > $i > $i ).
thf(func_def_346,type,
sK92: $i > $i > $o ).
thf(func_def_347,type,
sK93: $i > $i ).
thf(func_def_348,type,
sK94: $i > $i ).
thf(func_def_349,type,
sK95: ( $i > $i > $o ) > $i > $i ).
thf(func_def_350,type,
sK96: ( $i > $i > $o ) > $i > $i ).
thf(func_def_351,type,
sK97: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_355,type,
sK101: $i > $o ).
thf(func_def_367,type,
sK113: $i > $i > $i ).
thf(func_def_368,type,
sK114: $i > $i > $i ).
thf(func_def_383,type,
sK129: $o > $i > $i > $i ).
thf(func_def_406,type,
sK152: $i > $i > $o ).
thf(func_def_411,type,
sK157: ( $i > $o ) > $i > $i ).
thf(func_def_413,type,
sK159: $i > $o ).
thf(func_def_415,type,
sK161: ( $i > $o ) > $i ).
thf(func_def_416,type,
sK162: $i > $o ).
thf(func_def_417,type,
sK163: $i > $i ).
thf(func_def_418,type,
sK164: ( $i > $o ) > $i ).
thf(func_def_419,type,
sK165: ( $i > $o ) > $i ).
thf(func_def_420,type,
sK166: $i > $o ).
thf(func_def_424,type,
sK170: $i > $o ).
thf(func_def_431,type,
sK177: $i > $i > $i ).
thf(func_def_432,type,
sK178: $i > $i > $i ).
thf(func_def_433,type,
sK179: $i > $i > $i ).
thf(func_def_434,type,
sK180: $i > $i > $i ).
thf(func_def_435,type,
sK181: $i > $i > $i ).
thf(func_def_436,type,
sK182: $i > $i > $i > $i ).
thf(func_def_437,type,
sK183: $i > $i ).
thf(func_def_438,type,
sK184: $i > $i ).
thf(func_def_439,type,
sK185: $i > $i ).
thf(func_def_440,type,
sK186: $i > $i ).
thf(func_def_441,type,
sK187: $i > $i > $i ).
thf(func_def_442,type,
sK188: $i > $i > $i > $i ).
thf(func_def_443,type,
sK189: $i > $i > $i > $i ).
thf(func_def_444,type,
sK190: $i > $i > $i ).
thf(func_def_445,type,
sK191: $i > $i > $i ).
thf(func_def_447,type,
sK193: $i > $i ).
thf(func_def_448,type,
sK194: $i > $i ).
thf(func_def_449,type,
sK195: $i > $i ).
thf(func_def_457,type,
sK203: $i > $o ).
thf(func_def_473,type,
sK219: $i > $o ).
thf(func_def_478,type,
sK224: $i > $o ).
thf(func_def_481,type,
sK227: $i > ( $i > $o ) > $i ).
thf(func_def_482,type,
sK228: $i > ( $i > $o ) > $i ).
thf(func_def_483,type,
sK229: $i > $i > $i > $i ).
thf(func_def_484,type,
sK230: $i > $i > $i > $i ).
thf(func_def_504,type,
sK250: $i > $i > $i ).
thf(func_def_510,type,
sK256: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_511,type,
sK257: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_512,type,
sK258: $i > $o ).
thf(func_def_513,type,
sK259: $i > $o ).
thf(func_def_520,type,
sK266: $i > ( $i > $o ) > $i ).
thf(func_def_521,type,
sK267: $i > $o ).
thf(func_def_534,type,
sK280: ( $i > $i ) > $i > $i > $i ).
thf(func_def_537,type,
sK283: $i > $i ).
thf(func_def_547,type,
sK293: $i > $i > $i ).
thf(func_def_570,type,
sK316: $i > $i ).
thf(func_def_572,type,
sK318: $i > $i ).
thf(func_def_573,type,
sK319: $i > $o ).
thf(func_def_587,type,
sK333: ( $i > $o ) > $i > $i ).
thf(func_def_589,type,
sK335: $i > $o ).
thf(func_def_609,type,
sK355: ( $i > $o ) > $i > $i ).
thf(func_def_611,type,
sK357: $i > $o ).
thf(func_def_620,type,
sK366: $i > $i ).
thf(func_def_626,type,
sK372: $i > $i ).
thf(func_def_628,type,
sK374: $i > ( $i > $i ) > $i > $i ).
thf(func_def_633,type,
sK379: $i > $o ).
thf(func_def_637,type,
sK383: $i > $i > $i ).
thf(func_def_644,type,
sK390: $i > $i > $o ).
thf(func_def_653,type,
sK399: ( $i > $o ) > $i ).
thf(func_def_654,type,
sK400: $i > $o ).
thf(func_def_660,type,
sK406: $i > $i > $i ).
thf(func_def_667,type,
sK413: $i > $i > $i ).
thf(func_def_675,type,
sK421: $i > $o ).
thf(func_def_677,type,
sK423: $i > ( $i > $o ) > $i > $i ).
thf(func_def_694,type,
sK440: $i > $i > $o ).
thf(func_def_698,type,
sK444: $i > $o ).
thf(func_def_700,type,
sK446: $i > ( $i > $o ) > $i ).
thf(func_def_701,type,
sK447: $i > $o ).
thf(func_def_705,type,
sK451: $i > $i > $i ).
thf(func_def_709,type,
sK455: $i > $o ).
thf(func_def_712,type,
sK458: $i > $o ).
thf(func_def_716,type,
sK462: $i > $o ).
thf(func_def_718,type,
sK464: ( $i > $o ) > $i > $i ).
thf(func_def_719,type,
sK465: ( $i > $o ) > $i > $i ).
thf(func_def_735,type,
sK481: $i > $o ).
thf(func_def_736,type,
sK482: $i > $o ).
thf(func_def_737,type,
sK483: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_738,type,
sK484: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_739,type,
sK485: $i > $i > $o ).
thf(func_def_744,type,
sK490: $i > $o ).
thf(func_def_745,type,
sK491: ( $i > $o ) > $i > $i ).
thf(func_def_747,type,
sK493: $i > $o ).
thf(func_def_756,type,
sK502: $i > $o ).
thf(func_def_758,type,
sK504: $i > ( $i > $o ) > $i ).
thf(func_def_769,type,
sK515: $i > $o ).
thf(func_def_772,type,
sK518: $i > $i ).
thf(func_def_775,type,
sK521: $i > $i > ( $i > $i ) > $i ).
thf(func_def_778,type,
sK524: $i > $o ).
thf(func_def_781,type,
sK527: $i > ( $i > $o ) > $i ).
thf(func_def_783,type,
sK529: $i > $o ).
thf(func_def_795,type,
sK541: $i > $o ).
thf(func_def_798,type,
sK544: $i > ( $i > $o ) > $i ).
thf(func_def_800,type,
sK546: $i > $o ).
thf(func_def_804,type,
sK550: $i > $i ).
thf(func_def_806,type,
sK552: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_807,type,
sK553: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_811,type,
sK557: $i > $o ).
thf(func_def_842,type,
sK588: $i > $i ).
thf(func_def_866,type,
ph612:
!>[X0: $tType] : X0 ).
thf(f17577,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f14624,f17573]) ).
thf(f17573,plain,
~ spl611_583,
inference(avatar_contradiction_clause,[status(thm)],[f17572]) ).
thf(f17572,plain,
( $false
| ~ spl611_583 ),
inference(subsumption_resolution,[status(thm)],[f17571,f2262]) ).
thf(f2262,plain,
( $true
= ( in @ ( kpair @ sK264 @ sK265 ) @ sK263 ) ),
inference(cnf_transformation,[status(thm)],[f1280]) ).
thf(f1280,plain,
( ( exuI1 = $true )
& ( quantDeMorgan4 = $true )
& ( binunionLsub = $true )
& ( in__Cong = $true )
& ( symdiffE = $true )
& ( subsetTrans = $true )
& ( ex1E2 = $true )
& ( subsetemptysetimpeq = $true )
& ( subsetE2 = $true )
& ( singletonsswitch = $true )
& ( singletoninpowerset = $true )
& ( binintersectSubset1 = $true )
& ( cartprodmempair = $true )
& ( emptyinPowerset = $true )
& ( setukpairinjR = $true )
& ( ex1I2 = $true )
& ( prop2set2propI = $true )
& ( symdiffIneg1 = $true )
& ( setminusLsub = $true )
& ( powersetI = $true )
& ( exuI2 = $true )
& ( setminusER = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( binintersectEL = $true )
& ( uniqinunit = $true )
& ( powerset__Cong = $true )
& ( setminusIRneg = $true )
& ( ubforcartprodlem3 = $true )
& ( kfstsingleton = $true )
& ( cartprodpairmemEL = $true )
& ( sepInPowerset = $true )
& ( setunionsingleton2 = $true )
& ( eqinunit = $true )
& ( setunionAx = $true )
& ( binintersectSubset3 = $true )
& ( descrp = $true )
& ( subsetI1 = $true )
& ( nonemptyI = $true )
& ( kpairp = $true )
& ( cartprodmempair1 = $true )
& ( ex1E1 = $true )
& ( binintersectRsub = $true )
& ( setunion__Cong = $true )
& ( descr__Cong = $true )
& ( binunionEcases = $true )
& ( apProp = $true )
& ( setukpairinjR1 = $true )
& ( funcGraphProp1 = $true )
& ( disjointsetsI1 = $true )
& ( noeltsimpempty = $true )
& ( cartprodsndin = $true )
& ( cartprodfstin = $true )
& ( setukpairinjL2 = $true )
& ( setadjoinSub2 = $true )
& ( ap2p = $true )
& ( dpsetconstrER = $true )
& ( setextAx = $true )
& ( setextsub = $true )
& ( dsetconstrI = $true )
& ( emptysetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( eqimpsubset2 = $true )
& ( notinsingleton = $true )
& ( setukpairinjL1 = $true )
& ( setminusEL = $true )
& ( singletonsubset = $true )
& ( powersetAx = $true )
& ( dsetconstr__Cong = $true )
& ( binintersectSubset4 = $true )
& ( omegaSAx = $true )
& ( nonemptyI1 = $true )
& ( inPowerset = $true )
& ( setminusI = $true )
& ( notdallE = $true )
& ( ksndpairEq = $true )
& ( upairsetIL = $true )
& ( notinemptyset = $true )
& ( setminusSubset1 = $true )
& ( binintersectSubset5 = $true )
& ( symdiffI2 = $true )
& ( dpsetconstrSub = $true )
& ( setoftrueEq = $true )
& ( setukpairinjL = $true )
& ( eqimpsubset1 = $true )
& ( dpsetconstrI = $true )
& ( secondinupair = $true )
& ( binintersectER = $true )
& ( quantDeMorgan2 = $true )
& ( exuE1 = $true )
& ( upairset2IR = $true )
& ( setOfPairsIsBReln = $true )
& ( singletonsuniq = $true )
& ( subsetRefl = $true )
& ( nonemptyImpWitness = $true )
& ( binunionE = $true )
& ( cartprodpairmemER = $true )
& ( symdiffIneg2 = $true )
& ( exuE2 = $true )
& ( ex1I = $true )
& ( setadjoinIL = $true )
& ( setminusELneg = $true )
& ( kfstpairEq = $true )
& ( upairsetIR = $true )
& ( cartprodpairin = $true )
& ( exuE3e = $true )
& ( emptyInPowerset = $true )
& ( binunionRsub = $true )
& ( cartprodmempaircEq = $true )
& ( brelnall1 = $true )
& ( binunionIR = $true )
& ( brelnall2 = $true )
& ( emptyinunitempty = $true )
& ( setunionI = $true )
& ( upairequniteq = $true )
& ( lamp = $true )
& ( kpairsurjEq = $true )
& ( notequalI2 = $true )
& ( vacuousDall = $true )
& ( omega0Ax = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusILneg = $true )
& ( setadjoinIR = $true )
& ( setext = $true )
& ( setukpairIR = $true )
& ( exu__Cong = $true )
& ( dsetconstrEL = $true )
& ( setunionsingleton = $true )
& ( setukpairIL = $true )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK261 ) )
| ( ( ap @ sK261 @ sK262 @ sK260 @ X4 )
= ( ap @ sK261 @ sK262 @ sK263 @ X4 ) ) )
& ( $true
= ( in @ sK264 @ sK261 ) )
& ( $true
= ( in @ sK265 @ sK262 ) )
& ( $true
= ( in @ ( kpair @ sK264 @ sK265 ) @ sK263 ) )
& ( $true
!= ( in @ ( kpair @ sK264 @ sK265 ) @ sK260 ) )
& ( $true
= ( func @ sK261 @ sK262 @ sK263 ) )
& ( $true
= ( func @ sK261 @ sK262 @ sK260 ) )
& ( foundationAx = $true )
& ( emptysetAx = $true )
& ( subsetI2 = $true )
& ( emptyE1 = $true )
& ( infuncsetfunc = $true )
& ( prop2setE = $true )
& ( setunionsingleton1 = $true )
& ( inCongP = $true )
& ( replAx = $true )
& ( sepSubset = $true )
& ( notsubsetI = $true )
& ( binintersectSubset2 = $true )
& ( ubforcartprodlem1 = $true )
& ( subsetE = $true )
& ( binintersectI = $true )
& ( funcinfuncset = $true )
& ( powersetE = $true )
& ( setukpairinjR2 = $true )
& ( subset2powerset = $true )
& ( emptyI = $true )
& ( ksndsingleton = $true )
& ( setunionE2 = $true )
& ( upairsubunion = $true )
& ( setukpairinjR12 = $true )
& ( nonemptyE1 = $true )
& ( setminusERneg = $true )
& ( dsetconstrER = $true )
& ( subPowSU = $true )
& ( upairinpowunion = $true )
& ( exuI3 = $true )
& ( kpairiskpair = $true )
& ( powersetI1 = $true )
& ( setadjoinE = $true )
& ( emptysetimpfalse = $true )
& ( setukpairinjR11 = $true )
& ( binunionIL = $true )
& ( theprop = $true )
& ( funcGraphProp3 = $true )
& ( powersetE1 = $true )
& ( dpsetconstrERa = $true )
& ( funcGraphProp2 = $true )
& ( dpsetconstrEL1 = $true )
& ( cartprodpairsurjEq = $true )
& ( wellorderingAx = $true )
& ( funcImageSingleton = $true )
& ( notequalI1 = $true )
& ( emptyset__Cong = $true )
& ( lam2p = $true )
& ( cartprodfstpairEq = $true )
& ( setbeta = $true )
& ( notdexE = $true )
& ( quantDeMorgan1 = $true )
& ( setminusSubset2 = $true )
& ( upairsetE = $true )
& ( bs114d = $true )
& ( setadjoin__Cong = $true )
& ( singletonprop = $true )
& ( lamProp = $true )
& ( cartprodsndpairEq = $true )
& ( omegaIndAx = $true )
& ( setunionE = $true )
& ( dpsetconstrEL2 = $true )
& ( exuEu = $true )
& ( binintersectLsub = $true )
& ( powersetsubset = $true )
& ( setadjoinAx = $true )
& ( exuE3u = $true )
& ( symdiffI1 = $true )
& ( setadjoinSub = $true )
& ( setadjoinOr = $true )
& ( prop2setI = $true )
& ( emptysetE = $true )
& ( omega__Cong = $true )
& ( app = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK260,sK261,sK262,sK263,sK264,sK265])],[f801,f1279,f1278,f1277,f1276]) ).
thf(f1276,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X1 ) )
| ( ( ap @ X1 @ X2 @ X0 @ X4 )
= ( ap @ X1 @ X2 @ X3 @ X4 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ X1 ) )
& ? [X6: $i] :
( ( $true
= ( in @ X6 @ X2 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ X3 ) )
& ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ X0 ) ) ) )
& ( $true
= ( func @ X1 @ X2 @ X3 ) ) )
& ( $true
= ( func @ X1 @ X2 @ X0 ) ) )
=> ( ? [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK261 ) )
| ( ( ap @ sK261 @ sK262 @ sK260 @ X4 )
= ( ap @ sK261 @ sK262 @ X3 @ X4 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ sK261 ) )
& ? [X6: $i] :
( ( $true
= ( in @ X6 @ sK262 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ X3 ) )
& ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK260 ) ) ) )
& ( $true
= ( func @ sK261 @ sK262 @ X3 ) ) )
& ( $true
= ( func @ sK261 @ sK262 @ sK260 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1277,plain,
( ? [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK261 ) )
| ( ( ap @ sK261 @ sK262 @ sK260 @ X4 )
= ( ap @ sK261 @ sK262 @ X3 @ X4 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ sK261 ) )
& ? [X6: $i] :
( ( $true
= ( in @ X6 @ sK262 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ X3 ) )
& ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK260 ) ) ) )
& ( $true
= ( func @ sK261 @ sK262 @ X3 ) ) )
=> ( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK261 ) )
| ( ( ap @ sK261 @ sK262 @ sK260 @ X4 )
= ( ap @ sK261 @ sK262 @ sK263 @ X4 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ sK261 ) )
& ? [X6: $i] :
( ( $true
= ( in @ X6 @ sK262 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ sK263 ) )
& ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK260 ) ) ) )
& ( $true
= ( func @ sK261 @ sK262 @ sK263 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1278,plain,
( ? [X5: $i] :
( ( $true
= ( in @ X5 @ sK261 ) )
& ? [X6: $i] :
( ( $true
= ( in @ X6 @ sK262 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ sK263 ) )
& ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ sK260 ) ) ) )
=> ( ( $true
= ( in @ sK264 @ sK261 ) )
& ? [X6: $i] :
( ( $true
= ( in @ X6 @ sK262 ) )
& ( $true
= ( in @ ( kpair @ sK264 @ X6 ) @ sK263 ) )
& ( $true
!= ( in @ ( kpair @ sK264 @ X6 ) @ sK260 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1279,plain,
( ? [X6: $i] :
( ( $true
= ( in @ X6 @ sK262 ) )
& ( $true
= ( in @ ( kpair @ sK264 @ X6 ) @ sK263 ) )
& ( $true
!= ( in @ ( kpair @ sK264 @ X6 ) @ sK260 ) ) )
=> ( ( $true
= ( in @ sK265 @ sK262 ) )
& ( $true
= ( in @ ( kpair @ sK264 @ sK265 ) @ sK263 ) )
& ( $true
!= ( in @ ( kpair @ sK264 @ sK265 ) @ sK260 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f801,plain,
( ( exuI1 = $true )
& ( quantDeMorgan4 = $true )
& ( binunionLsub = $true )
& ( in__Cong = $true )
& ( symdiffE = $true )
& ( subsetTrans = $true )
& ( ex1E2 = $true )
& ( subsetemptysetimpeq = $true )
& ( subsetE2 = $true )
& ( singletonsswitch = $true )
& ( singletoninpowerset = $true )
& ( binintersectSubset1 = $true )
& ( cartprodmempair = $true )
& ( emptyinPowerset = $true )
& ( setukpairinjR = $true )
& ( ex1I2 = $true )
& ( prop2set2propI = $true )
& ( symdiffIneg1 = $true )
& ( setminusLsub = $true )
& ( powersetI = $true )
& ( exuI2 = $true )
& ( setminusER = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( binintersectEL = $true )
& ( uniqinunit = $true )
& ( powerset__Cong = $true )
& ( setminusIRneg = $true )
& ( ubforcartprodlem3 = $true )
& ( kfstsingleton = $true )
& ( cartprodpairmemEL = $true )
& ( sepInPowerset = $true )
& ( setunionsingleton2 = $true )
& ( eqinunit = $true )
& ( setunionAx = $true )
& ( binintersectSubset3 = $true )
& ( descrp = $true )
& ( subsetI1 = $true )
& ( nonemptyI = $true )
& ( kpairp = $true )
& ( cartprodmempair1 = $true )
& ( ex1E1 = $true )
& ( binintersectRsub = $true )
& ( setunion__Cong = $true )
& ( descr__Cong = $true )
& ( binunionEcases = $true )
& ( apProp = $true )
& ( setukpairinjR1 = $true )
& ( funcGraphProp1 = $true )
& ( disjointsetsI1 = $true )
& ( noeltsimpempty = $true )
& ( cartprodsndin = $true )
& ( cartprodfstin = $true )
& ( setukpairinjL2 = $true )
& ( setadjoinSub2 = $true )
& ( ap2p = $true )
& ( dpsetconstrER = $true )
& ( setextAx = $true )
& ( setextsub = $true )
& ( dsetconstrI = $true )
& ( emptysetsubset = $true )
& ( quantDeMorgan3 = $true )
& ( eqimpsubset2 = $true )
& ( notinsingleton = $true )
& ( setukpairinjL1 = $true )
& ( setminusEL = $true )
& ( singletonsubset = $true )
& ( powersetAx = $true )
& ( dsetconstr__Cong = $true )
& ( binintersectSubset4 = $true )
& ( omegaSAx = $true )
& ( nonemptyI1 = $true )
& ( inPowerset = $true )
& ( setminusI = $true )
& ( notdallE = $true )
& ( ksndpairEq = $true )
& ( upairsetIL = $true )
& ( notinemptyset = $true )
& ( setminusSubset1 = $true )
& ( binintersectSubset5 = $true )
& ( symdiffI2 = $true )
& ( dpsetconstrSub = $true )
& ( setoftrueEq = $true )
& ( setukpairinjL = $true )
& ( eqimpsubset1 = $true )
& ( dpsetconstrI = $true )
& ( secondinupair = $true )
& ( binintersectER = $true )
& ( quantDeMorgan2 = $true )
& ( exuE1 = $true )
& ( upairset2IR = $true )
& ( setOfPairsIsBReln = $true )
& ( singletonsuniq = $true )
& ( subsetRefl = $true )
& ( nonemptyImpWitness = $true )
& ( binunionE = $true )
& ( cartprodpairmemER = $true )
& ( symdiffIneg2 = $true )
& ( exuE2 = $true )
& ( ex1I = $true )
& ( setadjoinIL = $true )
& ( setminusELneg = $true )
& ( kfstpairEq = $true )
& ( upairsetIR = $true )
& ( cartprodpairin = $true )
& ( exuE3e = $true )
& ( emptyInPowerset = $true )
& ( binunionRsub = $true )
& ( cartprodmempaircEq = $true )
& ( brelnall1 = $true )
& ( binunionIR = $true )
& ( brelnall2 = $true )
& ( emptyinunitempty = $true )
& ( setunionI = $true )
& ( upairequniteq = $true )
& ( lamp = $true )
& ( kpairsurjEq = $true )
& ( notequalI2 = $true )
& ( vacuousDall = $true )
& ( omega0Ax = $true )
& ( ubforcartprodlem2 = $true )
& ( setminusILneg = $true )
& ( setadjoinIR = $true )
& ( setext = $true )
& ( setukpairIR = $true )
& ( exu__Cong = $true )
& ( dsetconstrEL = $true )
& ( setunionsingleton = $true )
& ( setukpairIL = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X1 ) )
| ( ( ap @ X1 @ X2 @ X0 @ X4 )
= ( ap @ X1 @ X2 @ X3 @ X4 ) ) )
& ? [X5: $i] :
( ( $true
= ( in @ X5 @ X1 ) )
& ? [X6: $i] :
( ( $true
= ( in @ X6 @ X2 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ X3 ) )
& ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ X0 ) ) ) )
& ( $true
= ( func @ X1 @ X2 @ X3 ) ) )
& ( $true
= ( func @ X1 @ X2 @ X0 ) ) )
& ( foundationAx = $true )
& ( emptysetAx = $true )
& ( subsetI2 = $true )
& ( emptyE1 = $true )
& ( infuncsetfunc = $true )
& ( prop2setE = $true )
& ( setunionsingleton1 = $true )
& ( inCongP = $true )
& ( replAx = $true )
& ( sepSubset = $true )
& ( notsubsetI = $true )
& ( binintersectSubset2 = $true )
& ( ubforcartprodlem1 = $true )
& ( subsetE = $true )
& ( binintersectI = $true )
& ( funcinfuncset = $true )
& ( powersetE = $true )
& ( setukpairinjR2 = $true )
& ( subset2powerset = $true )
& ( emptyI = $true )
& ( ksndsingleton = $true )
& ( setunionE2 = $true )
& ( upairsubunion = $true )
& ( setukpairinjR12 = $true )
& ( nonemptyE1 = $true )
& ( setminusERneg = $true )
& ( dsetconstrER = $true )
& ( subPowSU = $true )
& ( upairinpowunion = $true )
& ( exuI3 = $true )
& ( kpairiskpair = $true )
& ( powersetI1 = $true )
& ( setadjoinE = $true )
& ( emptysetimpfalse = $true )
& ( setukpairinjR11 = $true )
& ( binunionIL = $true )
& ( theprop = $true )
& ( funcGraphProp3 = $true )
& ( powersetE1 = $true )
& ( dpsetconstrERa = $true )
& ( funcGraphProp2 = $true )
& ( dpsetconstrEL1 = $true )
& ( cartprodpairsurjEq = $true )
& ( wellorderingAx = $true )
& ( funcImageSingleton = $true )
& ( notequalI1 = $true )
& ( emptyset__Cong = $true )
& ( lam2p = $true )
& ( cartprodfstpairEq = $true )
& ( setbeta = $true )
& ( notdexE = $true )
& ( quantDeMorgan1 = $true )
& ( setminusSubset2 = $true )
& ( upairsetE = $true )
& ( bs114d = $true )
& ( setadjoin__Cong = $true )
& ( singletonprop = $true )
& ( lamProp = $true )
& ( cartprodsndpairEq = $true )
& ( omegaIndAx = $true )
& ( setunionE = $true )
& ( dpsetconstrEL2 = $true )
& ( exuEu = $true )
& ( binintersectLsub = $true )
& ( powersetsubset = $true )
& ( setadjoinAx = $true )
& ( exuE3u = $true )
& ( symdiffI1 = $true )
& ( setadjoinSub = $true )
& ( setadjoinOr = $true )
& ( prop2setI = $true )
& ( emptysetE = $true )
& ( omega__Cong = $true )
& ( app = $true ) ),
inference(flattening,[status(thm)],[f800]) ).
thf(f800,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X5: $i] :
( ? [X6: $i] :
( ( $true
!= ( in @ ( kpair @ X5 @ X6 ) @ X0 ) )
& ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ X3 ) )
& ( $true
= ( in @ X6 @ X2 ) ) )
& ( $true
= ( in @ X5 @ X1 ) ) )
& ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X1 ) )
| ( ( ap @ X1 @ X2 @ X0 @ X4 )
= ( ap @ X1 @ X2 @ X3 @ X4 ) ) )
& ( $true
= ( func @ X1 @ X2 @ X3 ) ) )
& ( $true
= ( func @ X1 @ X2 @ X0 ) ) )
& ( 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)],[f271]) ).
thf(f271,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X1 @ X2 @ X0 ) )
=> ! [X3: $i] :
( ( $true
= ( func @ X1 @ X2 @ X3 ) )
=> ( ! [X4: $i] :
( ( $true
= ( in @ X4 @ X1 ) )
=> ( ( ap @ X1 @ X2 @ X0 @ X4 )
= ( ap @ X1 @ X2 @ X3 @ X4 ) ) )
=> ! [X5: $i] :
( ( $true
= ( in @ X5 @ X1 ) )
=> ! [X6: $i] :
( ( $true
= ( in @ X6 @ X2 ) )
=> ( ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ X3 ) )
=> ( $true
= ( in @ ( kpair @ X5 @ X6 ) @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f270]) ).
thf(f270,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( func @ X1 @ X2 @ X0 )
=> ! [X3: $i] :
( ( func @ X1 @ X2 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X1 )
=> ( ( ap @ X1 @ X2 @ X0 @ X4 )
= ( ap @ X1 @ X2 @ X3 @ X4 ) ) )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ! [X6: $i] :
( ( in @ X6 @ X2 )
=> ( ( in @ ( kpair @ X5 @ X6 ) @ X3 )
=> ( in @ ( kpair @ X5 @ X6 ) @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f212]) ).
thf(f212,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
=> ! [X13: $i,X3: $i,X4: $i] :
( ( func @ X3 @ X4 @ X13 )
=> ! [X14: $i] :
( ( func @ X3 @ X4 @ X14 )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( ap @ X3 @ X4 @ X13 @ X1 )
= ( ap @ X3 @ X4 @ X14 @ X1 ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X14 )
=> ( in @ ( kpair @ X1 @ X2 ) @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f211]) ).
thf(f211,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
=> ! [X13: $i,X3: $i,X4: $i] :
( ( func @ X3 @ X4 @ X13 )
=> ! [X14: $i] :
( ( func @ X3 @ X4 @ X14 )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( ap @ X3 @ X4 @ X13 @ X1 )
= ( ap @ X3 @ X4 @ X14 @ X1 ) ) )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X14 )
=> ( in @ ( kpair @ X1 @ X2 ) @ X13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.pJgJnm9BBC/DTF2THF_23745.p',funcextLem) ).
thf(f17571,plain,
( ( $true
!= ( in @ ( kpair @ sK264 @ sK265 ) @ sK263 ) )
| ~ spl611_583 ),
inference(subsumption_resolution,[status(thm)],[f17570,f2263]) ).
thf(f2263,plain,
( $true
= ( in @ sK265 @ sK262 ) ),
inference(cnf_transformation,[status(thm)],[f1280]) ).
thf(f17570,plain,
( ( $true
!= ( in @ sK265 @ sK262 ) )
| ( $true
!= ( in @ ( kpair @ sK264 @ sK265 ) @ sK263 ) )
| ~ spl611_583 ),
inference(subsumption_resolution,[status(thm)],[f17545,f2264]) ).
thf(f2264,plain,
( $true
= ( in @ sK264 @ sK261 ) ),
inference(cnf_transformation,[status(thm)],[f1280]) ).
thf(f17545,plain,
( ( $true
!= ( in @ sK264 @ sK261 ) )
| ( $true
!= ( in @ sK265 @ sK262 ) )
| ( $true
!= ( in @ ( kpair @ sK264 @ sK265 ) @ sK263 ) )
| ~ spl611_583 ),
inference(trivial_inequality_removal,[status(thm)],[f17537]) ).
thf(f17537,plain,
( ( $true
!= ( in @ sK264 @ sK261 ) )
| ( $true
!= ( in @ ( kpair @ sK264 @ sK265 ) @ sK263 ) )
| ( $true
!= ( in @ sK265 @ sK262 ) )
| ( $true != $true )
| ~ spl611_583 ),
inference(superposition,[status(thm)],[f2261,f14617]) ).
thf(f14617,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sK260 ) )
| ( $true
!= ( in @ ( kpair @ X0 @ X1 ) @ sK263 ) )
| ( $true
!= ( in @ X1 @ sK262 ) )
| ( $true
!= ( in @ X0 @ sK261 ) ) )
| ~ spl611_583 ),
inference(avatar_component_clause,[status(thm)],[f14616]) ).
thf(f14616,definition,
( spl611_583
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ X0 @ X1 ) @ sK263 ) )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sK260 ) )
| ( $true
!= ( in @ X0 @ sK261 ) )
| ( $true
!= ( in @ X1 @ sK262 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl611_583])],[avatar_definition]) ).
thf(f2261,plain,
( $true
!= ( in @ ( kpair @ sK264 @ sK265 ) @ sK260 ) ),
inference(cnf_transformation,[status(thm)],[f1280]) ).
thf(f14624,plain,
spl611_583,
inference(avatar_split_clause,[status(thm)],[f14623,f14616]) ).
thf(f14623,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ sK261 ) )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sK260 ) )
| ( $true
!= ( in @ X1 @ sK262 ) )
| ( $true
!= ( in @ ( kpair @ X0 @ X1 ) @ sK263 ) ) ),
inference(subsumption_resolution,[status(thm)],[f14622,f2346]) ).
thf(f2346,plain,
funcGraphProp1 = $true,
inference(cnf_transformation,[status(thm)],[f1280]) ).
thf(f14622,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ X0 @ X1 ) @ sK263 ) )
| ( $true
!= ( in @ X1 @ sK262 ) )
| ( $true
!= ( in @ X0 @ sK261 ) )
| ( funcGraphProp1 != $true )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sK260 ) ) ),
inference(subsumption_resolution,[status(thm)],[f14603,f2259]) ).
thf(f2259,plain,
( $true
= ( func @ sK261 @ sK262 @ sK260 ) ),
inference(cnf_transformation,[status(thm)],[f1280]) ).
thf(f14603,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ sK261 ) )
| ( $true
!= ( in @ X1 @ sK262 ) )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sK260 ) )
| ( $true
!= ( func @ sK261 @ sK262 @ sK260 ) )
| ( $true
!= ( in @ ( kpair @ X0 @ X1 ) @ sK263 ) )
| ( funcGraphProp1 != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f14601]) ).
thf(f14601,plain,
! [X0: $i,X1: $i] :
( ( funcGraphProp1 != $true )
| ( $true
!= ( in @ ( kpair @ X0 @ X1 ) @ sK263 ) )
| ( $true
!= ( in @ X1 @ sK262 ) )
| ( $true
!= ( func @ sK261 @ sK262 @ sK260 ) )
| ( $true
= ( in @ ( kpair @ X0 @ X1 ) @ sK260 ) )
| ( $true
!= ( in @ X0 @ sK261 ) )
| ( $true
!= ( in @ X0 @ sK261 ) ) ),
inference(superposition,[status(thm)],[f1883,f8146]) ).
thf(f8146,plain,
! [X0: $i,X1: $i] :
( ( ( ap @ sK261 @ sK262 @ sK260 @ X0 )
= X1 )
| ( $true
!= ( in @ X0 @ sK261 ) )
| ( $true
!= ( in @ ( kpair @ X0 @ X1 ) @ sK263 ) )
| ( $true
!= ( in @ X1 @ sK262 ) ) ),
inference(subsumption_resolution,[status(thm)],[f8145,f2260]) ).
thf(f2260,plain,
( $true
= ( func @ sK261 @ sK262 @ sK263 ) ),
inference(cnf_transformation,[status(thm)],[f1280]) ).
thf(f8145,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ sK262 ) )
| ( ( ap @ sK261 @ sK262 @ sK260 @ X0 )
= X1 )
| ( $true
!= ( in @ ( kpair @ X0 @ X1 ) @ sK263 ) )
| ( $true
!= ( func @ sK261 @ sK262 @ sK263 ) )
| ( $true
!= ( in @ X0 @ sK261 ) ) ),
inference(subsumption_resolution,[status(thm)],[f8128,f2218]) ).
thf(f2218,plain,
funcGraphProp2 = $true,
inference(cnf_transformation,[status(thm)],[f1280]) ).
thf(f8128,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ X1 @ sK262 ) )
| ( funcGraphProp2 != $true )
| ( $true
!= ( in @ ( kpair @ X0 @ X1 ) @ sK263 ) )
| ( $true
!= ( func @ sK261 @ sK262 @ sK263 ) )
| ( $true
!= ( in @ X0 @ sK261 ) )
| ( ( ap @ sK261 @ sK262 @ sK260 @ X0 )
= X1 ) ),
inference(duplicate_literal_removal,[status(thm)],[f8120]) ).
thf(f8120,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ X0 @ X1 ) @ sK263 ) )
| ( $true
!= ( in @ X0 @ sK261 ) )
| ( $true
!= ( in @ X1 @ sK262 ) )
| ( $true
!= ( func @ sK261 @ sK262 @ sK263 ) )
| ( funcGraphProp2 != $true )
| ( ( ap @ sK261 @ sK262 @ sK260 @ X0 )
= X1 )
| ( $true
!= ( in @ X0 @ sK261 ) ) ),
inference(superposition,[status(thm)],[f2265,f2505]) ).
thf(f2505,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( func @ X1 @ X2 @ X0 ) )
| ( $true
!= ( in @ X4 @ X2 ) )
| ( funcGraphProp2 != $true )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f1413]) ).
thf(f1413,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X1 @ X2 @ X0 ) )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ! [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ X4 @ X2 ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) ) ) )
| ( funcGraphProp2 != $true ) )
& ( ( funcGraphProp2 = $true )
| ( ( $true
= ( func @ sK346 @ sK347 @ sK345 ) )
& ( $true
= ( in @ sK348 @ sK346 ) )
& ( ( ap @ sK346 @ sK347 @ sK345 @ sK348 )
!= sK349 )
& ( $true
= ( in @ sK349 @ sK347 ) )
& ( $true
= ( in @ ( kpair @ sK348 @ sK349 ) @ sK345 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK345,sK346,sK347,sK348,sK349])],[f1409,f1412,f1411,f1410]) ).
thf(f1410,plain,
( ? [X5: $i,X6: $i,X7: $i] :
( ( $true
= ( func @ X6 @ X7 @ X5 ) )
& ? [X8: $i] :
( ( $true
= ( in @ X8 @ X6 ) )
& ? [X9: $i] :
( ( ( ap @ X6 @ X7 @ X5 @ X8 )
!= X9 )
& ( $true
= ( in @ X9 @ X7 ) )
& ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ X5 ) ) ) ) )
=> ( ( $true
= ( func @ sK346 @ sK347 @ sK345 ) )
& ? [X8: $i] :
( ( $true
= ( in @ X8 @ sK346 ) )
& ? [X9: $i] :
( ( ( ap @ sK346 @ sK347 @ sK345 @ X8 )
!= X9 )
& ( $true
= ( in @ X9 @ sK347 ) )
& ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ sK345 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1411,plain,
( ? [X8: $i] :
( ( $true
= ( in @ X8 @ sK346 ) )
& ? [X9: $i] :
( ( ( ap @ sK346 @ sK347 @ sK345 @ X8 )
!= X9 )
& ( $true
= ( in @ X9 @ sK347 ) )
& ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ sK345 ) ) ) )
=> ( ( $true
= ( in @ sK348 @ sK346 ) )
& ? [X9: $i] :
( ( ( ap @ sK346 @ sK347 @ sK345 @ sK348 )
!= X9 )
& ( $true
= ( in @ X9 @ sK347 ) )
& ( $true
= ( in @ ( kpair @ sK348 @ X9 ) @ sK345 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1412,plain,
( ? [X9: $i] :
( ( ( ap @ sK346 @ sK347 @ sK345 @ sK348 )
!= X9 )
& ( $true
= ( in @ X9 @ sK347 ) )
& ( $true
= ( in @ ( kpair @ sK348 @ X9 ) @ sK345 ) ) )
=> ( ( ( ap @ sK346 @ sK347 @ sK345 @ sK348 )
!= sK349 )
& ( $true
= ( in @ sK349 @ sK347 ) )
& ( $true
= ( in @ ( kpair @ sK348 @ sK349 ) @ sK345 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1409,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X1 @ X2 @ X0 ) )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ! [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ X4 @ X2 ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) ) ) )
| ( funcGraphProp2 != $true ) )
& ( ( funcGraphProp2 = $true )
| ? [X5: $i,X6: $i,X7: $i] :
( ( $true
= ( func @ X6 @ X7 @ X5 ) )
& ? [X8: $i] :
( ( $true
= ( in @ X8 @ X6 ) )
& ? [X9: $i] :
( ( ( ap @ X6 @ X7 @ X5 @ X8 )
!= X9 )
& ( $true
= ( in @ X9 @ X7 ) )
& ( $true
= ( in @ ( kpair @ X8 @ X9 ) @ X5 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1408]) ).
thf(f1408,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X1 @ X2 @ X0 ) )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ! [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ X4 @ X2 ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) ) ) )
| ( funcGraphProp2 != $true ) )
& ( ( funcGraphProp2 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X1 @ X2 @ X0 ) )
& ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ? [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
!= X4 )
& ( $true
= ( in @ X4 @ X2 ) )
& ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f718]) ).
thf(f718,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( func @ X1 @ X2 @ X0 ) )
| ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ! [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ X4 @ X2 ) )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) ) ) ) )
<=> ( funcGraphProp2 = $true ) ),
inference(flattening,[status(thm)],[f717]) ).
thf(f717,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 )
| ( $true
!= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
| ( $true
!= ( in @ X4 @ X2 ) ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
| ( $true
!= ( func @ X1 @ X2 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f221]) ).
thf(f221,plain,
( ( funcGraphProp2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X1 @ X2 @ X0 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ( ( $true
= ( in @ ( kpair @ X3 @ X4 ) @ X0 ) )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f220]) ).
thf(f220,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X2 @ X0 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ( ( in @ ( kpair @ X3 @ X4 ) @ X0 )
=> ( ( ap @ X1 @ X2 @ X0 @ X3 )
= X4 ) ) ) ) )
= funcGraphProp2 ),
inference(rectify,[status(thm)],[f210]) ).
thf(f210,axiom,
! [X13: $i,X3: $i,X4: $i] :
( ( ( func @ X3 @ X4 @ X13 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X13 )
=> ( ( ap @ X3 @ X4 @ X13 @ X1 )
= X2 ) ) ) ) )
= funcGraphProp2 ),
file('/export/starexec/sandbox/tmp/tmp.pJgJnm9BBC/DTF2THF_23745.p',funcGraphProp2) ).
thf(f2265,plain,
! [X4: $i] :
( ( ( ap @ sK261 @ sK262 @ sK260 @ X4 )
= ( ap @ sK261 @ sK262 @ sK263 @ X4 ) )
| ( $true
!= ( in @ X4 @ sK261 ) ) ),
inference(cnf_transformation,[status(thm)],[f1280]) ).
thf(f1883,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) )
| ( $true
!= ( func @ X1 @ X0 @ X2 ) )
| ( funcGraphProp1 != $true )
| ( $true
!= ( in @ X3 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f942]) ).
thf(f942,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) ) )
| ( $true
!= ( func @ X1 @ X0 @ X2 ) ) )
| ( funcGraphProp1 != $true ) )
& ( ( funcGraphProp1 = $true )
| ( ( $true
= ( in @ sK43 @ sK41 ) )
& ( $true
!= ( in @ ( kpair @ sK43 @ ( ap @ sK41 @ sK40 @ sK42 @ sK43 ) ) @ sK42 ) )
& ( $true
= ( func @ sK41 @ sK40 @ sK42 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42,sK43])],[f939,f941,f940]) ).
thf(f940,plain,
( ? [X4: $i,X5: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ ( kpair @ X7 @ ( ap @ X5 @ X4 @ X6 @ X7 ) ) @ X6 ) ) )
& ( $true
= ( func @ X5 @ X4 @ X6 ) ) )
=> ( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK41 ) )
& ( $true
!= ( in @ ( kpair @ X7 @ ( ap @ sK41 @ sK40 @ sK42 @ X7 ) ) @ sK42 ) ) )
& ( $true
= ( func @ sK41 @ sK40 @ sK42 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f941,plain,
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ sK41 ) )
& ( $true
!= ( in @ ( kpair @ X7 @ ( ap @ sK41 @ sK40 @ sK42 @ X7 ) ) @ sK42 ) ) )
=> ( ( $true
= ( in @ sK43 @ sK41 ) )
& ( $true
!= ( in @ ( kpair @ sK43 @ ( ap @ sK41 @ sK40 @ sK42 @ sK43 ) ) @ sK42 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f939,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) ) )
| ( $true
!= ( func @ X1 @ X0 @ X2 ) ) )
| ( funcGraphProp1 != $true ) )
& ( ( funcGraphProp1 = $true )
| ? [X4: $i,X5: $i,X6: $i] :
( ? [X7: $i] :
( ( $true
= ( in @ X7 @ X5 ) )
& ( $true
!= ( in @ ( kpair @ X7 @ ( ap @ X5 @ X4 @ X6 @ X7 ) ) @ X6 ) ) )
& ( $true
= ( func @ X5 @ X4 @ X6 ) ) ) ) ),
inference(rectify,[status(thm)],[f938]) ).
thf(f938,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) ) )
| ( $true
!= ( func @ X1 @ X0 @ X2 ) ) )
| ( funcGraphProp1 != $true ) )
& ( ( funcGraphProp1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
& ( $true
!= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) ) )
& ( $true
= ( func @ X1 @ X0 @ X2 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f803]) ).
thf(f803,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
!= ( in @ X3 @ X1 ) )
| ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) ) )
| ( $true
!= ( func @ X1 @ X0 @ X2 ) ) )
<=> ( funcGraphProp1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f545]) ).
thf(f545,plain,
( ( funcGraphProp1 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( func @ X1 @ X0 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ X1 ) )
=> ( $true
= ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f544]) ).
thf(f544,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( func @ X1 @ X0 @ X2 )
=> ! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( in @ ( kpair @ X3 @ ( ap @ X1 @ X0 @ X2 @ X3 ) ) @ X2 ) ) )
= funcGraphProp1 ),
inference(rectify,[status(thm)],[f208]) ).
thf(f208,axiom,
! [X4: $i,X3: $i,X13: $i] :
( ( ( func @ X3 @ X4 @ X13 )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( in @ ( kpair @ X1 @ ( ap @ X3 @ X4 @ X13 @ X1 ) ) @ X13 ) ) )
= funcGraphProp1 ),
file('/export/starexec/sandbox/tmp/tmp.pJgJnm9BBC/DTF2THF_23745.p',funcGraphProp1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU687^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n031.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 12:32:03 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SEU687^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.47 % Domain : Set Theory
% 0.30/0.47 % Problem : Functions - Extensionality and Beta Reduction
% 0.30/0.47 % Version : Especial.
% 0.30/0.47 % English : (! A:i.! B:i.! f:i.func A B f -> (! g:i.func A B g ->
% 0.30/0.47 % (! x:i.in x A -> ap A B f x = ap A B g x) -> (! x:i.in x A ->
% 0.30/0.47 % (! y:i.in y B -> in (kpair x y) g -> in (kpair x y) f))))
% 0.30/0.47
% 0.30/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.47 % Source : [Bro08]
% 0.30/0.47 % Names : ZFC189g [Bro08]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.50 v8.2.0, 0.69 v8.1.0, 0.73 v7.5.0, 0.71 v7.4.0, 0.56 v7.3.0, 0.67 v7.2.0, 0.62 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 1.00 v3.7.0
% 0.30/0.47 % Syntax : Number of formulae : 451 ( 210 unt; 240 typ; 210 def)
% 0.30/0.47 % Number of atoms : 1133 ( 308 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 211 ( 5 avg)
% 0.30/0.47 % Number of connectives : 2112 ( 47 ~; 7 |; 36 &;1494 @)
% 0.30/0.47 % ( 14 <=>; 514 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 220 ( 2 avg)
% 0.30/0.47 % Number of types : 2 ( 0 usr)
% 0.30/0.47 % Number of type conns : 126 ( 126 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 243 ( 240 usr; 207 con; 0-4 aty)
% 0.30/0.47 % Number of variables : 678 ( 73 ^; 569 !; 36 ?; 678 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : http://mathgate.info/detsetitem.php?id=414
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(in_type,type,
% 0.30/0.47 in: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(exu_type,type,
% 0.30/0.47 exu: ( $i > $o ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(exu,definition,
% 0.30/0.47 ( exu
% 0.30/0.47 = ( ^ [Xphi: $i > $o] :
% 0.30/0.47 ? [Xx: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 & ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setextAx_type,type,
% 0.30/0.47 setextAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setextAx,definition,
% 0.30/0.47 ( setextAx
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 <=> ( in @ Xx @ B ) )
% 0.30/0.47 => ( A = B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyset_type,type,
% 0.30/0.47 emptyset: $i ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetAx_type,type,
% 0.30/0.47 emptysetAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetAx,definition,
% 0.30/0.47 ( emptysetAx
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoin_type,type,
% 0.30/0.47 setadjoin: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinAx_type,type,
% 0.30/0.47 setadjoinAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinAx,definition,
% 0.30/0.47 ( setadjoinAx
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.47 <=> ( ( Xy = Xx )
% 0.30/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powerset_type,type,
% 0.30/0.47 powerset: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(powersetAx_type,type,
% 0.30/0.47 powersetAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetAx,definition,
% 0.30/0.47 ( powersetAx
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.47 <=> ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunion_type,type,
% 0.30/0.47 setunion: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(setunionAx_type,type,
% 0.30/0.47 setunionAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionAx,definition,
% 0.30/0.47 ( setunionAx
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.47 <=> ? [B: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(omega_type,type,
% 0.30/0.47 omega: $i ).
% 0.30/0.47
% 0.30/0.47 thf(omega0Ax_type,type,
% 0.30/0.47 omega0Ax: $o ).
% 0.30/0.47
% 0.30/0.47 thf(omega0Ax,definition,
% 0.30/0.47 ( omega0Ax
% 0.30/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(omegaSAx_type,type,
% 0.30/0.47 omegaSAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(omegaSAx,definition,
% 0.30/0.47 ( omegaSAx
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ omega )
% 0.30/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(omegaIndAx_type,type,
% 0.30/0.47 omegaIndAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(omegaIndAx,definition,
% 0.30/0.47 ( omegaIndAx
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( ( in @ emptyset @ A )
% 0.30/0.47 & ! [Xx: $i] :
% 0.30/0.47 ( ( ( in @ Xx @ omega )
% 0.30/0.47 & ( in @ Xx @ A ) )
% 0.30/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ omega )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(replAx_type,type,
% 0.30/0.47 replAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(replAx,definition,
% 0.30/0.47 ( replAx
% 0.30/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( exu
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.47 => ? [B: $i] :
% 0.30/0.47 ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 <=> ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(foundationAx_type,type,
% 0.30/0.47 foundationAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(foundationAx,definition,
% 0.30/0.47 ( foundationAx
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.47 => ? [B: $i] :
% 0.30/0.47 ( ( in @ B @ A )
% 0.30/0.47 & ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(wellorderingAx_type,type,
% 0.30/0.47 wellorderingAx: $o ).
% 0.30/0.47
% 0.30/0.47 thf(wellorderingAx,definition,
% 0.30/0.47 ( wellorderingAx
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ? [B: $i] :
% 0.30/0.47 ( ! [C: $i] :
% 0.30/0.47 ( ( in @ C @ B )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ C )
% 0.30/0.47 => ( in @ Xx @ A ) ) )
% 0.30/0.47 & ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( ( in @ Xx @ A )
% 0.30/0.47 & ( in @ Xy @ A ) )
% 0.30/0.47 => ( ! [C: $i] :
% 0.30/0.47 ( ( in @ C @ B )
% 0.30/0.47 => ( ( in @ Xx @ C )
% 0.30/0.47 <=> ( in @ Xy @ C ) ) )
% 0.30/0.47 => ( Xx = Xy ) ) )
% 0.30/0.47 & ! [C: $i,D: $i] :
% 0.30/0.47 ( ( ( in @ C @ B )
% 0.30/0.47 & ( in @ D @ B ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ C )
% 0.30/0.47 => ( in @ Xx @ D ) )
% 0.30/0.47 | ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ D )
% 0.30/0.47 => ( in @ Xx @ C ) ) ) )
% 0.30/0.47 & ! [C: $i] :
% 0.30/0.47 ( ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ C )
% 0.30/0.47 => ( in @ Xx @ A ) )
% 0.30/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/0.47 => ? [D: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ D @ B )
% 0.30/0.47 & ( in @ Xx @ C )
% 0.30/0.47 & ~ ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ D )
% 0.30/0.47 & ( in @ Xy @ C ) )
% 0.30/0.47 & ! [E: $i] :
% 0.30/0.47 ( ( in @ E @ B )
% 0.30/0.47 => ( ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ E )
% 0.30/0.47 => ( in @ Xy @ D ) )
% 0.30/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(descr_type,type,
% 0.30/0.47 descr: ( $i > $o ) > $i ).
% 0.30/0.47
% 0.30/0.47 thf(descrp_type,type,
% 0.30/0.47 descrp: $o ).
% 0.30/0.47
% 0.30/0.47 thf(descrp,definition,
% 0.30/0.47 ( descrp
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ( Xphi
% 0.30/0.47 @ ( descr
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstr_type,type,
% 0.30/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrI_type,type,
% 0.30/0.47 dsetconstrI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrI,definition,
% 0.30/0.47 ( dsetconstrI
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 => ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrEL_type,type,
% 0.30/0.47 dsetconstrEL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrEL,definition,
% 0.30/0.47 ( dsetconstrEL
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrER_type,type,
% 0.30/0.47 dsetconstrER: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstrER,definition,
% 0.30/0.47 ( dsetconstrER
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuE1_type,type,
% 0.30/0.47 exuE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuE1,definition,
% 0.30/0.47 ( exuE1
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 & ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(prop2set_type,type,
% 0.30/0.47 prop2set: $o > $i ).
% 0.30/0.47
% 0.30/0.47 thf(prop2setE_type,type,
% 0.30/0.47 prop2setE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2setE,definition,
% 0.30/0.47 ( prop2setE
% 0.30/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.30/0.47 => Xphi ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetE_type,type,
% 0.30/0.47 emptysetE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetE,definition,
% 0.30/0.47 ( emptysetE
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ emptyset )
% 0.30/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetimpfalse_type,type,
% 0.30/0.47 emptysetimpfalse: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetimpfalse,definition,
% 0.30/0.47 ( emptysetimpfalse
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ emptyset )
% 0.30/0.47 => $false ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notinemptyset_type,type,
% 0.30/0.47 notinemptyset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notinemptyset,definition,
% 0.30/0.47 ( notinemptyset
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuE3e_type,type,
% 0.30/0.47 exuE3e: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuE3e,definition,
% 0.30/0.47 ( exuE3e
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setext_type,type,
% 0.30/0.47 setext: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setext,definition,
% 0.30/0.47 ( setext
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ B ) )
% 0.30/0.47 => ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ A ) )
% 0.30/0.47 => ( A = B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyI_type,type,
% 0.30/0.47 emptyI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyI,definition,
% 0.30/0.47 ( emptyI
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ~ ( in @ Xx @ A )
% 0.30/0.47 => ( A = emptyset ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(noeltsimpempty_type,type,
% 0.30/0.47 noeltsimpempty: $o ).
% 0.30/0.47
% 0.30/0.47 thf(noeltsimpempty,definition,
% 0.30/0.47 ( noeltsimpempty
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ~ ( in @ Xx @ A )
% 0.30/0.47 => ( A = emptyset ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setbeta_type,type,
% 0.30/0.47 setbeta: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setbeta,definition,
% 0.30/0.47 ( setbeta
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonempty_type,type,
% 0.30/0.47 nonempty: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonempty,definition,
% 0.30/0.47 ( nonempty
% 0.30/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyE1_type,type,
% 0.30/0.47 nonemptyE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyE1,definition,
% 0.30/0.47 ( nonemptyE1
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( nonempty @ A )
% 0.30/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyI_type,type,
% 0.30/0.47 nonemptyI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyI,definition,
% 0.30/0.47 ( nonemptyI
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 => ( nonempty
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyI1_type,type,
% 0.30/0.47 nonemptyI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyI1,definition,
% 0.30/0.47 ( nonemptyI1
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIL_type,type,
% 0.30/0.47 setadjoinIL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIL,definition,
% 0.30/0.47 ( setadjoinIL
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyinunitempty_type,type,
% 0.30/0.47 emptyinunitempty: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyinunitempty,definition,
% 0.30/0.47 ( emptyinunitempty
% 0.30/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIR_type,type,
% 0.30/0.47 setadjoinIR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinIR,definition,
% 0.30/0.47 ( setadjoinIR
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinE_type,type,
% 0.30/0.47 setadjoinE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinE,definition,
% 0.30/0.47 ( setadjoinE
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.47 => ! [Xphi: $o] :
% 0.30/0.47 ( ( ( Xy = Xx )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => ( ( ( in @ Xy @ A )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinOr_type,type,
% 0.30/0.47 setadjoinOr: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinOr,definition,
% 0.30/0.47 ( setadjoinOr
% 0.30/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.47 => ( ( Xy = Xx )
% 0.30/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setoftrueEq_type,type,
% 0.30/0.47 setoftrueEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setoftrueEq,definition,
% 0.30/0.47 ( setoftrueEq
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : $true )
% 0.30/0.47 = A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetI_type,type,
% 0.30/0.47 powersetI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetI,definition,
% 0.30/0.47 ( powersetI
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ A ) )
% 0.30/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyinPowerset_type,type,
% 0.30/0.47 emptyinPowerset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyinPowerset,definition,
% 0.30/0.47 ( emptyinPowerset
% 0.30/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyInPowerset_type,type,
% 0.30/0.47 emptyInPowerset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyInPowerset,definition,
% 0.30/0.47 ( emptyInPowerset
% 0.30/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetE_type,type,
% 0.30/0.47 powersetE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetE,definition,
% 0.30/0.47 ( powersetE
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.47 => ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionI_type,type,
% 0.30/0.47 setunionI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionI,definition,
% 0.30/0.47 ( setunionI
% 0.30/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( ( in @ B @ A )
% 0.30/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionE_type,type,
% 0.30/0.47 setunionE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionE,definition,
% 0.30/0.47 ( setunionE
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.47 => ! [Xphi: $o] :
% 0.30/0.47 ( ! [B: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( ( in @ B @ A )
% 0.30/0.47 => Xphi ) )
% 0.30/0.47 => Xphi ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subPowSU_type,type,
% 0.30/0.47 subPowSU: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subPowSU,definition,
% 0.30/0.47 ( subPowSU
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuE2_type,type,
% 0.30/0.47 exuE2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuE2,definition,
% 0.30/0.47 ( exuE2
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyImpWitness_type,type,
% 0.30/0.47 nonemptyImpWitness: $o ).
% 0.30/0.47
% 0.30/0.47 thf(nonemptyImpWitness,definition,
% 0.30/0.47 ( nonemptyImpWitness
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( nonempty @ A )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & $true ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(uniqinunit_type,type,
% 0.30/0.47 uniqinunit: $o ).
% 0.30/0.47
% 0.30/0.47 thf(uniqinunit,definition,
% 0.30/0.47 ( uniqinunit
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notinsingleton_type,type,
% 0.30/0.47 notinsingleton: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notinsingleton,definition,
% 0.30/0.47 ( notinsingleton
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx != Xy )
% 0.30/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(eqinunit_type,type,
% 0.30/0.47 eqinunit: $o ).
% 0.30/0.47
% 0.30/0.47 thf(eqinunit,definition,
% 0.30/0.47 ( eqinunit
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(singletonsswitch_type,type,
% 0.30/0.47 singletonsswitch: $o ).
% 0.30/0.47
% 0.30/0.47 thf(singletonsswitch,definition,
% 0.30/0.47 ( singletonsswitch
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetE_type,type,
% 0.30/0.47 upairsetE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetE,definition,
% 0.30/0.47 ( upairsetE
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.47 => ( ( Xz = Xx )
% 0.30/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIL_type,type,
% 0.30/0.47 upairsetIL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIL,definition,
% 0.30/0.47 ( upairsetIL
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIR_type,type,
% 0.30/0.47 upairsetIR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetIR,definition,
% 0.30/0.47 ( upairsetIR
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyE1_type,type,
% 0.30/0.47 emptyE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyE1,definition,
% 0.30/0.47 ( emptyE1
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ( ( ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 = emptyset )
% 0.30/0.47 => $false ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(vacuousDall_type,type,
% 0.30/0.47 vacuousDall: $o ).
% 0.30/0.47
% 0.30/0.47 thf(vacuousDall,definition,
% 0.30/0.47 ( vacuousDall
% 0.30/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ emptyset )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan1_type,type,
% 0.30/0.47 quantDeMorgan1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan1,definition,
% 0.30/0.47 ( quantDeMorgan1
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan2_type,type,
% 0.30/0.47 quantDeMorgan2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan2,definition,
% 0.30/0.47 ( quantDeMorgan2
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ~ ( Xphi @ Xx ) )
% 0.30/0.47 => ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan3_type,type,
% 0.30/0.47 quantDeMorgan3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan3,definition,
% 0.30/0.47 ( quantDeMorgan3
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan4_type,type,
% 0.30/0.47 quantDeMorgan4: $o ).
% 0.30/0.47
% 0.30/0.47 thf(quantDeMorgan4,definition,
% 0.30/0.47 ( quantDeMorgan4
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ~ ( Xphi @ Xx ) )
% 0.30/0.47 => ~ ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(prop2setI_type,type,
% 0.30/0.47 prop2setI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2setI,definition,
% 0.30/0.47 ( prop2setI
% 0.30/0.47 = ( ! [Xphi: $o] :
% 0.30/0.47 ( Xphi
% 0.30/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(set2prop_type,type,
% 0.30/0.47 set2prop: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2set2propI_type,type,
% 0.30/0.47 prop2set2propI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(prop2set2propI,definition,
% 0.30/0.47 ( prop2set2propI
% 0.30/0.47 = ( ! [Xphi: $o] :
% 0.30/0.47 ( Xphi
% 0.30/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notdexE_type,type,
% 0.30/0.47 notdexE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notdexE,definition,
% 0.30/0.47 ( notdexE
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notdallE_type,type,
% 0.30/0.47 notdallE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notdallE,definition,
% 0.30/0.47 ( notdallE
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ~ ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuI1_type,type,
% 0.30/0.47 exuI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuI1,definition,
% 0.30/0.47 ( exuI1
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 & ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) )
% 0.30/0.47 => ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuI3_type,type,
% 0.30/0.47 exuI3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuI3,definition,
% 0.30/0.47 ( exuI3
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.30/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 => ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) )
% 0.30/0.47 => ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuI2_type,type,
% 0.30/0.47 exuI2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuI2,definition,
% 0.30/0.47 ( exuI2
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ? [Xx: $i] :
% 0.30/0.47 ! [Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xy )
% 0.30/0.47 <=> ( Xy = Xx ) )
% 0.30/0.47 => ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(inCongP_type,type,
% 0.30/0.47 inCongP: $o ).
% 0.30/0.47
% 0.30/0.47 thf(inCongP,definition,
% 0.30/0.47 ( inCongP
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( A = B )
% 0.30/0.47 => ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(in__Cong_type,type,
% 0.30/0.47 in__Cong: $o ).
% 0.30/0.47
% 0.30/0.47 thf(in__Cong,definition,
% 0.30/0.47 ( in__Cong
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( A = B )
% 0.30/0.47 => ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( ( in @ Xx @ A )
% 0.30/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuE3u_type,type,
% 0.30/0.47 exuE3u: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuE3u,definition,
% 0.30/0.47 ( exuE3u
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 => ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exu__Cong_type,type,
% 0.30/0.47 exu__Cong: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exu__Cong,definition,
% 0.30/0.47 ( exu__Cong
% 0.30/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.47 => ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 <=> ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptyset__Cong_type,type,
% 0.30/0.47 emptyset__Cong: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptyset__Cong,definition,
% 0.30/0.47 ( emptyset__Cong
% 0.30/0.47 = ( emptyset = emptyset ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoin__Cong_type,type,
% 0.30/0.47 setadjoin__Cong: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoin__Cong,definition,
% 0.30/0.47 ( setadjoin__Cong
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ! [Xz: $i,Xu: $i] :
% 0.30/0.47 ( ( Xz = Xu )
% 0.30/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.30/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powerset__Cong_type,type,
% 0.30/0.47 powerset__Cong: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powerset__Cong,definition,
% 0.30/0.47 ( powerset__Cong
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( A = B )
% 0.30/0.47 => ( ( powerset @ A )
% 0.30/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunion__Cong_type,type,
% 0.30/0.47 setunion__Cong: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunion__Cong,definition,
% 0.30/0.47 ( setunion__Cong
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( A = B )
% 0.30/0.47 => ( ( setunion @ A )
% 0.30/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(omega__Cong_type,type,
% 0.30/0.47 omega__Cong: $o ).
% 0.30/0.47
% 0.30/0.47 thf(omega__Cong,definition,
% 0.30/0.47 ( omega__Cong
% 0.30/0.47 = ( omega = omega ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(exuEu_type,type,
% 0.30/0.47 exuEu: $o ).
% 0.30/0.47
% 0.30/0.47 thf(exuEu,definition,
% 0.30/0.47 ( exuEu
% 0.30/0.47 = ( ! [Xphi: $i > $o] :
% 0.30/0.47 ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xphi @ Xx )
% 0.30/0.47 => ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(descr__Cong_type,type,
% 0.30/0.47 descr__Cong: $o ).
% 0.30/0.47
% 0.30/0.47 thf(descr__Cong,definition,
% 0.30/0.47 ( descr__Cong
% 0.30/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.47 => ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ( ( exu
% 0.30/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.30/0.47 => ( ( descr
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 = ( descr
% 0.30/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstr__Cong_type,type,
% 0.30/0.47 dsetconstr__Cong: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dsetconstr__Cong,definition,
% 0.30/0.47 ( dsetconstr__Cong
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( A = B )
% 0.30/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( ( Xx = Xy )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.30/0.47 => ( ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 = ( dsetconstr @ B
% 0.30/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subset_type,type,
% 0.30/0.47 subset: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(disjoint_type,type,
% 0.30/0.47 disjoint: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(setsmeet_type,type,
% 0.30/0.47 setsmeet: $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(subsetI1_type,type,
% 0.30/0.47 subsetI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subsetI1,definition,
% 0.30/0.47 ( subsetI1
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ B ) )
% 0.30/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(eqimpsubset2_type,type,
% 0.30/0.47 eqimpsubset2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(eqimpsubset2,definition,
% 0.30/0.47 ( eqimpsubset2
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( A = B )
% 0.30/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(eqimpsubset1_type,type,
% 0.30/0.47 eqimpsubset1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(eqimpsubset1,definition,
% 0.30/0.47 ( eqimpsubset1
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( A = B )
% 0.30/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subsetI2_type,type,
% 0.30/0.47 subsetI2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subsetI2,definition,
% 0.30/0.47 ( subsetI2
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ B ) )
% 0.30/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetsubset_type,type,
% 0.30/0.47 emptysetsubset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(emptysetsubset,definition,
% 0.30/0.47 ( emptysetsubset
% 0.30/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subsetE_type,type,
% 0.30/0.47 subsetE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subsetE,definition,
% 0.30/0.47 ( subsetE
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( subset @ A @ B )
% 0.30/0.47 => ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subsetE2_type,type,
% 0.30/0.47 subsetE2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subsetE2,definition,
% 0.30/0.47 ( subsetE2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( subset @ A @ B )
% 0.30/0.47 => ( ~ ( in @ Xx @ B )
% 0.30/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notsubsetI_type,type,
% 0.30/0.47 notsubsetI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notsubsetI,definition,
% 0.30/0.47 ( notsubsetI
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ B )
% 0.30/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notequalI1_type,type,
% 0.30/0.47 notequalI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notequalI1,definition,
% 0.30/0.47 ( notequalI1
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ~ ( subset @ A @ B )
% 0.30/0.47 => ( A != B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(notequalI2_type,type,
% 0.30/0.47 notequalI2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(notequalI2,definition,
% 0.30/0.47 ( notequalI2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ B )
% 0.30/0.47 => ( A != B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subsetRefl_type,type,
% 0.30/0.47 subsetRefl: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subsetRefl,definition,
% 0.30/0.47 ( subsetRefl
% 0.30/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subsetTrans_type,type,
% 0.30/0.47 subsetTrans: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subsetTrans,definition,
% 0.30/0.47 ( subsetTrans
% 0.30/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.47 ( ( subset @ A @ B )
% 0.30/0.47 => ( ( subset @ B @ C )
% 0.30/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinSub_type,type,
% 0.30/0.47 setadjoinSub: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinSub,definition,
% 0.30/0.47 ( setadjoinSub
% 0.30/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinSub2_type,type,
% 0.30/0.47 setadjoinSub2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setadjoinSub2,definition,
% 0.30/0.47 ( setadjoinSub2
% 0.30/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.47 ( ( subset @ A @ B )
% 0.30/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subset2powerset_type,type,
% 0.30/0.47 subset2powerset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subset2powerset,definition,
% 0.30/0.47 ( subset2powerset
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( subset @ A @ B )
% 0.30/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setextsub_type,type,
% 0.30/0.47 setextsub: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setextsub,definition,
% 0.30/0.47 ( setextsub
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( subset @ A @ B )
% 0.30/0.47 => ( ( subset @ B @ A )
% 0.30/0.47 => ( A = B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(subsetemptysetimpeq_type,type,
% 0.30/0.47 subsetemptysetimpeq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(subsetemptysetimpeq,definition,
% 0.30/0.47 ( subsetemptysetimpeq
% 0.30/0.47 = ( ! [A: $i] :
% 0.30/0.47 ( ( subset @ A @ emptyset )
% 0.30/0.47 => ( A = emptyset ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetI1_type,type,
% 0.30/0.47 powersetI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetI1,definition,
% 0.30/0.47 ( powersetI1
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( subset @ B @ A )
% 0.30/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetE1_type,type,
% 0.30/0.47 powersetE1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetE1,definition,
% 0.30/0.47 ( powersetE1
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(inPowerset_type,type,
% 0.30/0.47 inPowerset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(inPowerset,definition,
% 0.30/0.47 ( inPowerset
% 0.30/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(powersetsubset_type,type,
% 0.30/0.47 powersetsubset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(powersetsubset,definition,
% 0.30/0.47 ( powersetsubset
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( subset @ A @ B )
% 0.30/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sepInPowerset_type,type,
% 0.30/0.47 sepInPowerset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(sepInPowerset,definition,
% 0.30/0.47 ( sepInPowerset
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( in
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(sepSubset_type,type,
% 0.30/0.47 sepSubset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(sepSubset,definition,
% 0.30/0.47 ( sepSubset
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( subset
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunion_type,type,
% 0.30/0.47 binunion: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(binunionIL_type,type,
% 0.30/0.47 binunionIL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionIL,definition,
% 0.30/0.47 ( binunionIL
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairset2IR_type,type,
% 0.30/0.47 upairset2IR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairset2IR,definition,
% 0.30/0.47 ( upairset2IR
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunionIR_type,type,
% 0.30/0.47 binunionIR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionIR,definition,
% 0.30/0.47 ( binunionIR
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunionEcases_type,type,
% 0.30/0.47 binunionEcases: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionEcases,definition,
% 0.30/0.47 ( binunionEcases
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.30/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/0.47 => ( ( ( in @ Xx @ A )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => ( ( ( in @ Xx @ B )
% 0.30/0.47 => Xphi )
% 0.30/0.47 => Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunionE_type,type,
% 0.30/0.47 binunionE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionE,definition,
% 0.30/0.47 ( binunionE
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/0.47 => ( ( in @ Xx @ A )
% 0.30/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunionLsub_type,type,
% 0.30/0.47 binunionLsub: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionLsub,definition,
% 0.30/0.47 ( binunionLsub
% 0.30/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binunionRsub_type,type,
% 0.30/0.47 binunionRsub: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binunionRsub,definition,
% 0.30/0.47 ( binunionRsub
% 0.30/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersect_type,type,
% 0.30/0.47 binintersect: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectI_type,type,
% 0.30/0.47 binintersectI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectI,definition,
% 0.30/0.47 ( binintersectI
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectSubset5_type,type,
% 0.30/0.47 binintersectSubset5: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectSubset5,definition,
% 0.30/0.47 ( binintersectSubset5
% 0.30/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.47 ( ( subset @ C @ A )
% 0.30/0.47 => ( ( subset @ C @ B )
% 0.30/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectEL_type,type,
% 0.30/0.47 binintersectEL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectEL,definition,
% 0.30/0.47 ( binintersectEL
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectLsub_type,type,
% 0.30/0.47 binintersectLsub: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectLsub,definition,
% 0.30/0.47 ( binintersectLsub
% 0.30/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectSubset2_type,type,
% 0.30/0.47 binintersectSubset2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectSubset2,definition,
% 0.30/0.47 ( binintersectSubset2
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( subset @ A @ B )
% 0.30/0.47 => ( ( binintersect @ A @ B )
% 0.30/0.47 = A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectSubset3_type,type,
% 0.30/0.47 binintersectSubset3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectSubset3,definition,
% 0.30/0.47 ( binintersectSubset3
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( ( binintersect @ A @ B )
% 0.30/0.47 = B )
% 0.30/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectER_type,type,
% 0.30/0.47 binintersectER: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectER,definition,
% 0.30/0.47 ( binintersectER
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(disjointsetsI1_type,type,
% 0.30/0.47 disjointsetsI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(disjointsetsI1,definition,
% 0.30/0.47 ( disjointsetsI1
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ~ ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( in @ Xx @ B ) )
% 0.30/0.47 => ( ( binintersect @ A @ B )
% 0.30/0.47 = emptyset ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectRsub_type,type,
% 0.30/0.47 binintersectRsub: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectRsub,definition,
% 0.30/0.47 ( binintersectRsub
% 0.30/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectSubset4_type,type,
% 0.30/0.47 binintersectSubset4: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectSubset4,definition,
% 0.30/0.47 ( binintersectSubset4
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( subset @ B @ A )
% 0.30/0.47 => ( ( binintersect @ A @ B )
% 0.30/0.47 = B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectSubset1_type,type,
% 0.30/0.47 binintersectSubset1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(binintersectSubset1,definition,
% 0.30/0.47 ( binintersectSubset1
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( ( binintersect @ A @ B )
% 0.30/0.47 = A )
% 0.30/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(bs114d_type,type,
% 0.30/0.47 bs114d: $o ).
% 0.30/0.47
% 0.30/0.47 thf(bs114d,definition,
% 0.30/0.47 ( bs114d
% 0.30/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.30/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(regular_type,type,
% 0.30/0.47 regular: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminus_type,type,
% 0.30/0.47 setminus: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(setminusI_type,type,
% 0.30/0.47 setminusI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusI,definition,
% 0.30/0.47 ( setminusI
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setminusEL_type,type,
% 0.30/0.47 setminusEL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusEL,definition,
% 0.30/0.47 ( setminusEL
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setminusER_type,type,
% 0.30/0.47 setminusER: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusER,definition,
% 0.30/0.47 ( setminusER
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setminusSubset2_type,type,
% 0.30/0.47 setminusSubset2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusSubset2,definition,
% 0.30/0.47 ( setminusSubset2
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( subset @ A @ B )
% 0.30/0.47 => ( ( setminus @ A @ B )
% 0.30/0.47 = emptyset ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setminusERneg_type,type,
% 0.30/0.47 setminusERneg: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusERneg,definition,
% 0.30/0.47 ( setminusERneg
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.47 => ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setminusELneg_type,type,
% 0.30/0.47 setminusELneg: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusELneg,definition,
% 0.30/0.47 ( setminusELneg
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.47 => ( ~ ( in @ Xx @ B )
% 0.30/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setminusILneg_type,type,
% 0.30/0.47 setminusILneg: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusILneg,definition,
% 0.30/0.47 ( setminusILneg
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ~ ( in @ Xx @ A )
% 0.30/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setminusIRneg_type,type,
% 0.30/0.47 setminusIRneg: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusIRneg,definition,
% 0.30/0.47 ( setminusIRneg
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ B )
% 0.30/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setminusLsub_type,type,
% 0.30/0.47 setminusLsub: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusLsub,definition,
% 0.30/0.47 ( setminusLsub
% 0.30/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setminusSubset1_type,type,
% 0.30/0.47 setminusSubset1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setminusSubset1,definition,
% 0.30/0.47 ( setminusSubset1
% 0.30/0.47 = ( ! [A: $i,B: $i] :
% 0.30/0.47 ( ( ( setminus @ A @ B )
% 0.30/0.47 = emptyset )
% 0.30/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(symdiff_type,type,
% 0.30/0.47 symdiff: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(symdiffE_type,type,
% 0.30/0.47 symdiffE: $o ).
% 0.30/0.47
% 0.30/0.47 thf(symdiffE,definition,
% 0.30/0.47 ( symdiffE
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.30/0.47 => ! [Xphi: $o] :
% 0.30/0.47 ( ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ B )
% 0.30/0.47 => Xphi ) )
% 0.30/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ B )
% 0.30/0.47 => Xphi ) )
% 0.30/0.47 => Xphi ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(symdiffI1_type,type,
% 0.30/0.47 symdiffI1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(symdiffI1,definition,
% 0.30/0.47 ( symdiffI1
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(symdiffI2_type,type,
% 0.30/0.47 symdiffI2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(symdiffI2,definition,
% 0.30/0.47 ( symdiffI2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ~ ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ B )
% 0.30/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(symdiffIneg1_type,type,
% 0.30/0.47 symdiffIneg1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(symdiffIneg1,definition,
% 0.30/0.47 ( symdiffIneg1
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( in @ Xx @ B )
% 0.30/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(symdiffIneg2_type,type,
% 0.30/0.47 symdiffIneg2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(symdiffIneg2,definition,
% 0.30/0.47 ( symdiffIneg2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ~ ( in @ Xx @ A )
% 0.30/0.47 => ( ~ ( in @ Xx @ B )
% 0.30/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(iskpair_type,type,
% 0.30/0.47 iskpair: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(secondinupair_type,type,
% 0.30/0.47 secondinupair: $o ).
% 0.30/0.47
% 0.30/0.47 thf(secondinupair,definition,
% 0.30/0.47 ( secondinupair
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairIL_type,type,
% 0.30/0.47 setukpairIL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairIL,definition,
% 0.30/0.47 ( setukpairIL
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairIR_type,type,
% 0.30/0.47 setukpairIR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairIR,definition,
% 0.30/0.47 ( setukpairIR
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(kpairiskpair_type,type,
% 0.30/0.47 kpairiskpair: $o ).
% 0.30/0.47
% 0.30/0.47 thf(kpairiskpair,definition,
% 0.30/0.47 ( kpairiskpair
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(kpair_type,type,
% 0.30/0.47 kpair: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(kpairp_type,type,
% 0.30/0.47 kpairp: $o ).
% 0.30/0.47
% 0.30/0.47 thf(kpairp,definition,
% 0.30/0.47 ( kpairp
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprod_type,type,
% 0.30/0.47 cartprod: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(singletonsubset_type,type,
% 0.30/0.47 singletonsubset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(singletonsubset,definition,
% 0.30/0.47 ( singletonsubset
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(singletoninpowerset_type,type,
% 0.30/0.47 singletoninpowerset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(singletoninpowerset,definition,
% 0.30/0.47 ( singletoninpowerset
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(singletoninpowunion_type,type,
% 0.30/0.47 singletoninpowunion: $o ).
% 0.30/0.47
% 0.30/0.47 thf(singletoninpowunion,definition,
% 0.30/0.47 ( singletoninpowunion
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairset2E_type,type,
% 0.30/0.47 upairset2E: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairset2E,definition,
% 0.30/0.47 ( upairset2E
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.47 => ( ( Xz = Xx )
% 0.30/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairsubunion_type,type,
% 0.30/0.47 upairsubunion: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsubunion,definition,
% 0.30/0.47 ( upairsubunion
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairinpowunion_type,type,
% 0.30/0.47 upairinpowunion: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairinpowunion,definition,
% 0.30/0.47 ( upairinpowunion
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ubforcartprodlem1_type,type,
% 0.30/0.47 ubforcartprodlem1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ubforcartprodlem1,definition,
% 0.30/0.47 ( ubforcartprodlem1
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ubforcartprodlem2_type,type,
% 0.30/0.47 ubforcartprodlem2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ubforcartprodlem2,definition,
% 0.30/0.47 ( ubforcartprodlem2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ubforcartprodlem3_type,type,
% 0.30/0.47 ubforcartprodlem3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ubforcartprodlem3,definition,
% 0.30/0.47 ( ubforcartprodlem3
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodpairin_type,type,
% 0.30/0.47 cartprodpairin: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodpairin,definition,
% 0.30/0.47 ( cartprodpairin
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodmempair1_type,type,
% 0.30/0.47 cartprodmempair1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodmempair1,definition,
% 0.30/0.47 ( cartprodmempair1
% 0.30/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ? [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 & ( Xu
% 0.30/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodmempair_type,type,
% 0.30/0.47 cartprodmempair: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodmempair,definition,
% 0.30/0.47 ( cartprodmempair
% 0.30/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionE2_type,type,
% 0.30/0.47 setunionE2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionE2,definition,
% 0.30/0.47 ( setunionE2
% 0.30/0.47 = ( ! [A: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.47 => ? [X: $i] :
% 0.30/0.47 ( ( in @ X @ A )
% 0.30/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionsingleton1_type,type,
% 0.30/0.47 setunionsingleton1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionsingleton1,definition,
% 0.30/0.47 ( setunionsingleton1
% 0.30/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionsingleton2_type,type,
% 0.30/0.47 setunionsingleton2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionsingleton2,definition,
% 0.30/0.47 ( setunionsingleton2
% 0.30/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setunionsingleton_type,type,
% 0.30/0.47 setunionsingleton: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setunionsingleton,definition,
% 0.30/0.47 ( setunionsingleton
% 0.30/0.47 = ( ! [Xx: $i] :
% 0.30/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.30/0.47 = Xx ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(singleton_type,type,
% 0.30/0.47 singleton: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(singleton,definition,
% 0.30/0.47 ( singleton
% 0.30/0.47 = ( ^ [A: $i] :
% 0.30/0.47 ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( A
% 0.30/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(singletonprop_type,type,
% 0.30/0.47 singletonprop: $o ).
% 0.30/0.47
% 0.30/0.47 thf(singletonprop,definition,
% 0.30/0.47 ( singletonprop
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 => ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) )
% 0.30/0.47 => ( ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ( singleton
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ex1_type,type,
% 0.30/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(ex1,definition,
% 0.30/0.47 ( ex1
% 0.30/0.47 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( singleton
% 0.30/0.47 @ ( dsetconstr @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ex1E1_type,type,
% 0.30/0.47 ex1E1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ex1E1,definition,
% 0.30/0.47 ( ex1E1
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ( ex1 @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ex1I_type,type,
% 0.30/0.47 ex1I: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ex1I,definition,
% 0.30/0.47 ( ex1I
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 => ( ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xy = Xx ) ) )
% 0.30/0.47 => ( ex1 @ A
% 0.30/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ex1I2_type,type,
% 0.30/0.47 ex1I2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ex1I2,definition,
% 0.30/0.47 ( ex1I2
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 => ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) )
% 0.30/0.47 => ( ? [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 & ( Xphi @ Xx ) )
% 0.30/0.47 => ( ex1 @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(singletonsuniq_type,type,
% 0.30/0.47 singletonsuniq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(singletonsuniq,definition,
% 0.30/0.47 ( singletonsuniq
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.30/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(atmost1p_type,type,
% 0.30/0.47 atmost1p: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(atleast2p_type,type,
% 0.30/0.47 atleast2p: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(atmost2p_type,type,
% 0.30/0.47 atmost2p: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairsetp_type,type,
% 0.30/0.47 upairsetp: $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjL1_type,type,
% 0.30/0.47 setukpairinjL1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjL1,definition,
% 0.30/0.47 ( setukpairinjL1
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(kfstsingleton_type,type,
% 0.30/0.47 kfstsingleton: $o ).
% 0.30/0.47
% 0.30/0.47 thf(kfstsingleton,definition,
% 0.30/0.47 ( kfstsingleton
% 0.30/0.47 = ( ! [Xu: $i] :
% 0.30/0.47 ( ( iskpair @ Xu )
% 0.30/0.47 => ( singleton
% 0.30/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(theprop_type,type,
% 0.30/0.47 theprop: $o ).
% 0.30/0.47
% 0.30/0.47 thf(theprop,definition,
% 0.30/0.47 ( theprop
% 0.30/0.47 = ( ! [X: $i] :
% 0.30/0.47 ( ( singleton @ X )
% 0.30/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(kfst_type,type,
% 0.30/0.47 kfst: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(kfstpairEq_type,type,
% 0.30/0.47 kfstpairEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(kfstpairEq,definition,
% 0.30/0.47 ( kfstpairEq
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.30/0.47 = Xx ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodfstin_type,type,
% 0.30/0.47 cartprodfstin: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodfstin,definition,
% 0.30/0.47 ( cartprodfstin
% 0.30/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjL2_type,type,
% 0.30/0.47 setukpairinjL2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjL2,definition,
% 0.30/0.47 ( setukpairinjL2
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjL_type,type,
% 0.30/0.47 setukpairinjL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjL,definition,
% 0.30/0.47 ( setukpairinjL
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.30/0.47 = ( kpair @ Xz @ Xu ) )
% 0.30/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjR11_type,type,
% 0.30/0.47 setukpairinjR11: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjR11,definition,
% 0.30/0.47 ( setukpairinjR11
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjR12_type,type,
% 0.30/0.47 setukpairinjR12: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjR12,definition,
% 0.30/0.47 ( setukpairinjR12
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xx = Xy )
% 0.30/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjR1_type,type,
% 0.30/0.47 setukpairinjR1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjR1,definition,
% 0.30/0.47 ( setukpairinjR1
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.47 => ( ( Xz = Xu )
% 0.30/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(upairequniteq_type,type,
% 0.30/0.47 upairequniteq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(upairequniteq,definition,
% 0.30/0.47 ( upairequniteq
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjR2_type,type,
% 0.30/0.47 setukpairinjR2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjR2,definition,
% 0.30/0.47 ( setukpairinjR2
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjR_type,type,
% 0.30/0.47 setukpairinjR: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setukpairinjR,definition,
% 0.30/0.47 ( setukpairinjR
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.30/0.47 = ( kpair @ Xz @ Xu ) )
% 0.30/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ksndsingleton_type,type,
% 0.30/0.47 ksndsingleton: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ksndsingleton,definition,
% 0.30/0.47 ( ksndsingleton
% 0.30/0.47 = ( ! [Xu: $i] :
% 0.30/0.47 ( ( iskpair @ Xu )
% 0.30/0.47 => ( singleton
% 0.30/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/0.47 @ ^ [Xx: $i] :
% 0.30/0.47 ( Xu
% 0.30/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ksnd_type,type,
% 0.30/0.47 ksnd: $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(ksndpairEq_type,type,
% 0.30/0.47 ksndpairEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ksndpairEq,definition,
% 0.30/0.47 ( ksndpairEq
% 0.30/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.30/0.47 = Xy ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(kpairsurjEq_type,type,
% 0.30/0.47 kpairsurjEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(kpairsurjEq,definition,
% 0.30/0.47 ( kpairsurjEq
% 0.30/0.47 = ( ! [Xu: $i] :
% 0.30/0.47 ( ( iskpair @ Xu )
% 0.30/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.30/0.47 = Xu ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodsndin_type,type,
% 0.30/0.47 cartprodsndin: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodsndin,definition,
% 0.30/0.47 ( cartprodsndin
% 0.30/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodpairmemEL_type,type,
% 0.30/0.47 cartprodpairmemEL: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodpairmemEL,definition,
% 0.30/0.47 ( cartprodpairmemEL
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodpairmemER_type,type,
% 0.30/0.47 cartprodpairmemER: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodpairmemER,definition,
% 0.30/0.47 ( cartprodpairmemER
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.30/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodmempaircEq_type,type,
% 0.30/0.47 cartprodmempaircEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodmempaircEq,definition,
% 0.30/0.47 ( cartprodmempaircEq
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( ( kpair @ Xx @ Xy )
% 0.30/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodfstpairEq_type,type,
% 0.30/0.47 cartprodfstpairEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodfstpairEq,definition,
% 0.30/0.47 ( cartprodfstpairEq
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.30/0.47 = Xx ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodsndpairEq_type,type,
% 0.30/0.47 cartprodsndpairEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodsndpairEq,definition,
% 0.30/0.47 ( cartprodsndpairEq
% 0.30/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.30/0.47 = Xy ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodpairsurjEq_type,type,
% 0.30/0.47 cartprodpairsurjEq: $o ).
% 0.30/0.47
% 0.30/0.47 thf(cartprodpairsurjEq,definition,
% 0.30/0.47 ( cartprodpairsurjEq
% 0.30/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.30/0.47 = Xu ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(breln_type,type,
% 0.30/0.47 breln: $i > $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(breln,definition,
% 0.30/0.47 ( breln
% 0.30/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstr_type,type,
% 0.30/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrI_type,type,
% 0.30/0.47 dpsetconstrI: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrI,definition,
% 0.30/0.47 ( dpsetconstrI
% 0.30/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.47 @ ( dpsetconstr @ A @ B
% 0.30/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrSub_type,type,
% 0.30/0.47 dpsetconstrSub: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrSub,definition,
% 0.30/0.47 ( dpsetconstrSub
% 0.30/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.47 ( subset
% 0.30/0.47 @ ( dpsetconstr @ A @ B
% 0.30/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.30/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(setOfPairsIsBReln_type,type,
% 0.30/0.47 setOfPairsIsBReln: $o ).
% 0.30/0.47
% 0.30/0.47 thf(setOfPairsIsBReln,definition,
% 0.30/0.47 ( setOfPairsIsBReln
% 0.30/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/0.47 ( breln @ A @ B
% 0.30/0.47 @ ( dpsetconstr @ A @ B
% 0.30/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrERa_type,type,
% 0.30/0.47 dpsetconstrERa: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrERa,definition,
% 0.30/0.47 ( dpsetconstrERa
% 0.30/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.47 @ ( dpsetconstr @ A @ B
% 0.30/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrEL1_type,type,
% 0.30/0.47 dpsetconstrEL1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrEL1,definition,
% 0.30/0.47 ( dpsetconstrEL1
% 0.30/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.47 @ ( dpsetconstr @ A @ B
% 0.30/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrEL2_type,type,
% 0.30/0.47 dpsetconstrEL2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrEL2,definition,
% 0.30/0.47 ( dpsetconstrEL2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.47 @ ( dpsetconstr @ A @ B
% 0.30/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrER_type,type,
% 0.30/0.47 dpsetconstrER: $o ).
% 0.30/0.47
% 0.30/0.47 thf(dpsetconstrER,definition,
% 0.30/0.47 ( dpsetconstrER
% 0.30/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/0.47 @ ( dpsetconstr @ A @ B
% 0.30/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(func_type,type,
% 0.30/0.47 func: $i > $i > $i > $o ).
% 0.30/0.47
% 0.30/0.47 thf(func,definition,
% 0.30/0.47 ( func
% 0.30/0.47 = ( ^ [A: $i,B: $i,R: $i] :
% 0.30/0.47 ( ( breln @ A @ B @ R )
% 0.30/0.47 & ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( ex1 @ B
% 0.30/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(funcSet_type,type,
% 0.30/0.47 funcSet: $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(funcImageSingleton_type,type,
% 0.30/0.47 funcImageSingleton: $o ).
% 0.30/0.47
% 0.30/0.47 thf(funcImageSingleton,definition,
% 0.30/0.47 ( funcImageSingleton
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( func @ A @ B @ Xf )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( singleton
% 0.30/0.47 @ ( dsetconstr @ B
% 0.30/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(apProp_type,type,
% 0.30/0.47 apProp: $o ).
% 0.30/0.47
% 0.30/0.47 thf(apProp,definition,
% 0.30/0.47 ( apProp
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( func @ A @ B @ Xf )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in
% 0.30/0.47 @ ( setunion
% 0.30/0.47 @ ( dsetconstr @ B
% 0.30/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.30/0.47 @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ap_type,type,
% 0.30/0.47 ap: $i > $i > $i > $i > $i ).
% 0.30/0.47
% 0.30/0.47 thf(app_type,type,
% 0.30/0.47 app: $o ).
% 0.30/0.47
% 0.30/0.47 thf(app,definition,
% 0.30/0.47 ( app
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( func @ A @ B @ Xf )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(infuncsetfunc_type,type,
% 0.30/0.47 infuncsetfunc: $o ).
% 0.30/0.47
% 0.30/0.47 thf(infuncsetfunc,definition,
% 0.30/0.47 ( infuncsetfunc
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ap2p_type,type,
% 0.30/0.47 ap2p: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ap2p,definition,
% 0.30/0.47 ( ap2p
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(funcinfuncset_type,type,
% 0.30/0.47 funcinfuncset: $o ).
% 0.30/0.47
% 0.30/0.47 thf(funcinfuncset,definition,
% 0.30/0.47 ( funcinfuncset
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( func @ A @ B @ Xf )
% 0.30/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(lamProp_type,type,
% 0.30/0.47 lamProp: $o ).
% 0.30/0.47
% 0.30/0.47 thf(lamProp,definition,
% 0.30/0.47 ( lamProp
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/0.47 => ( func @ A @ B
% 0.30/0.47 @ ( dpsetconstr @ A @ B
% 0.30/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xf @ Xx )
% 0.30/0.47 = Xy ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(lam_type,type,
% 0.30/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.30/0.47
% 0.30/0.47 thf(lam,definition,
% 0.30/0.47 ( lam
% 0.30/0.47 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.47 ( dpsetconstr @ A @ B
% 0.30/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.30/0.47 ( ( Xf @ Xx )
% 0.30/0.47 = Xy ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(lamp_type,type,
% 0.30/0.47 lamp: $o ).
% 0.30/0.47
% 0.30/0.47 thf(lamp,definition,
% 0.30/0.47 ( lamp
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/0.47 => ( func @ A @ B
% 0.30/0.47 @ ( lam @ A @ B
% 0.30/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(lam2p_type,type,
% 0.30/0.47 lam2p: $o ).
% 0.30/0.47
% 0.30/0.47 thf(lam2p,definition,
% 0.30/0.47 ( lam2p
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/0.47 => ( in
% 0.30/0.47 @ ( lam @ A @ B
% 0.30/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.30/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(brelnall1_type,type,
% 0.30/0.47 brelnall1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(brelnall1,definition,
% 0.30/0.47 ( brelnall1
% 0.30/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.30/0.47 ( ( breln @ A @ B @ R )
% 0.30/0.47 => ! [Xphi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ R )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(brelnall2_type,type,
% 0.30/0.47 brelnall2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(brelnall2,definition,
% 0.30/0.47 ( brelnall2
% 0.30/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.30/0.47 ( ( breln @ A @ B @ R )
% 0.30/0.47 => ! [Xphi: $i > $o] :
% 0.30/0.47 ( ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ R )
% 0.30/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(ex1E2_type,type,
% 0.30/0.47 ex1E2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(ex1E2,definition,
% 0.30/0.47 ( ex1E2
% 0.30/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.47 ( ( ex1 @ A
% 0.30/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ A )
% 0.30/0.47 => ( ( Xphi @ Xx )
% 0.30/0.47 => ( ( Xphi @ Xy )
% 0.30/0.47 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(funcGraphProp1_type,type,
% 0.30/0.47 funcGraphProp1: $o ).
% 0.30/0.47
% 0.30/0.47 thf(funcGraphProp1,definition,
% 0.30/0.47 ( funcGraphProp1
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( func @ A @ B @ Xf )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(funcGraphProp3_type,type,
% 0.30/0.47 funcGraphProp3: $o ).
% 0.30/0.47
% 0.30/0.47 thf(funcGraphProp3,definition,
% 0.30/0.47 ( funcGraphProp3
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(funcGraphProp2_type,type,
% 0.30/0.47 funcGraphProp2: $o ).
% 0.30/0.47
% 0.30/0.47 thf(funcGraphProp2,definition,
% 0.30/0.47 ( funcGraphProp2
% 0.30/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.47 ( ( func @ A @ B @ Xf )
% 0.30/0.47 => ! [Xx: $i] :
% 0.30/0.47 ( ( in @ Xx @ A )
% 0.30/0.47 => ! [Xy: $i] :
% 0.30/0.47 ( ( in @ Xy @ B )
% 0.30/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.30/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(funcextLem,conjecture,
% 0.30/0.47 ( setextAx
% 0.30/0.47 => ( emptysetAx
% 0.30/0.47 => ( setadjoinAx
% 0.30/0.47 => ( powersetAx
% 0.30/0.47 => ( setunionAx
% 0.30/0.47 => ( omega0Ax
% 0.30/0.47 => ( omegaSAx
% 0.30/0.47 => ( omegaIndAx
% 0.30/0.47 => ( replAx
% 0.30/0.47 => ( foundationAx
% 0.30/0.47 => ( wellorderingAx
% 0.30/0.47 => ( descrp
% 0.30/0.47 => ( dsetconstrI
% 0.30/0.47 => ( dsetconstrEL
% 0.30/0.47 => ( dsetconstrER
% 0.30/0.47 => ( exuE1
% 0.30/0.47 => ( prop2setE
% 0.30/0.47 => ( emptysetE
% 0.30/0.47 => ( emptysetimpfalse
% 0.30/0.47 => ( notinemptyset
% 0.30/0.47 => ( exuE3e
% 0.30/0.47 => ( setext
% 0.30/0.47 => ( emptyI
% 0.30/0.47 => ( noeltsimpempty
% 0.30/0.47 => ( setbeta
% 0.30/0.47 => ( nonemptyE1
% 0.30/0.47 => ( nonemptyI
% 0.30/0.47 => ( nonemptyI1
% 0.30/0.47 => ( setadjoinIL
% 0.30/0.47 => ( emptyinunitempty
% 0.30/0.47 => ( setadjoinIR
% 0.30/0.47 => ( setadjoinE
% 0.30/0.47 => ( setadjoinOr
% 0.30/0.47 => ( setoftrueEq
% 0.30/0.47 => ( powersetI
% 0.30/0.47 => ( emptyinPowerset
% 0.30/0.47 => ( emptyInPowerset
% 0.30/0.47 => ( powersetE
% 0.30/0.47 => ( setunionI
% 0.30/0.47 => ( setunionE
% 0.30/0.47 => ( subPowSU
% 0.30/0.47 => ( exuE2
% 0.30/0.47 => ( nonemptyImpWitness
% 0.30/0.47 => ( uniqinunit
% 0.30/0.47 => ( notinsingleton
% 0.30/0.47 => ( eqinunit
% 0.30/0.47 => ( singletonsswitch
% 0.30/0.47 => ( upairsetE
% 0.30/0.47 => ( upairsetIL
% 0.30/0.47 => ( upairsetIR
% 0.30/0.47 => ( emptyE1
% 0.30/0.47 => ( vacuousDall
% 0.30/0.47 => ( quantDeMorgan1
% 0.30/0.47 => ( quantDeMorgan2
% 0.30/0.47 => ( quantDeMorgan3
% 0.30/0.47 => ( quantDeMorgan4
% 0.30/0.47 => ( prop2setI
% 0.30/0.47 => ( prop2set2propI
% 0.30/0.47 => ( notdexE
% 0.30/0.47 => ( notdallE
% 0.30/0.47 => ( exuI1
% 0.30/0.47 => ( exuI3
% 0.30/0.47 => ( exuI2
% 0.30/0.47 => ( inCongP
% 0.30/0.47 => ( in__Cong
% 0.30/0.47 => ( exuE3u
% 0.30/0.47 => ( exu__Cong
% 0.30/0.47 => ( emptyset__Cong
% 0.30/0.47 => ( setadjoin__Cong
% 0.30/0.47 => ( powerset__Cong
% 0.30/0.47 => ( setunion__Cong
% 0.30/0.47 => ( omega__Cong
% 0.30/0.47 => ( exuEu
% 0.30/0.47 => ( descr__Cong
% 0.30/0.47 => ( dsetconstr__Cong
% 0.30/0.47 => ( subsetI1
% 0.30/0.47 => ( eqimpsubset2
% 0.30/0.47 => ( eqimpsubset1
% 0.30/0.47 => ( subsetI2
% 0.30/0.47 => ( emptysetsubset
% 0.30/0.47 => ( subsetE
% 0.30/0.47 => ( subsetE2
% 0.30/0.47 => ( notsubsetI
% 0.30/0.47 => ( notequalI1
% 0.30/0.47 => ( notequalI2
% 0.30/0.47 => ( subsetRefl
% 0.30/0.47 => ( subsetTrans
% 0.30/0.47 => ( setadjoinSub
% 0.30/0.47 => ( setadjoinSub2
% 0.30/0.47 => ( subset2powerset
% 0.30/0.47 => ( setextsub
% 0.30/0.47 => ( subsetemptysetimpeq
% 0.30/0.47 => ( powersetI1
% 0.30/0.47 => ( powersetE1
% 0.30/0.47 => ( inPowerset
% 0.30/0.47 => ( powersetsubset
% 0.30/0.47 => ( sepInPowerset
% 0.30/0.47 => ( sepSubset
% 0.30/0.47 => ( binunionIL
% 0.30/0.47 => ( upairset2IR
% 0.30/0.47 => ( binunionIR
% 0.30/0.47 => ( binunionEcases
% 0.30/0.47 => ( binunionE
% 0.30/0.47 => ( binunionLsub
% 0.30/0.47 => ( binunionRsub
% 0.30/0.47 => ( binintersectI
% 0.30/0.47 => ( binintersectSubset5
% 0.30/0.47 => ( binintersectEL
% 0.30/0.47 => ( binintersectLsub
% 0.30/0.47 => ( binintersectSubset2
% 0.30/0.47 => ( binintersectSubset3
% 0.30/0.47 => ( binintersectER
% 0.30/0.47 => ( disjointsetsI1
% 0.30/0.47 => ( binintersectRsub
% 0.30/0.47 => ( binintersectSubset4
% 0.30/0.47 => ( binintersectSubset1
% 0.30/0.47 => ( bs114d
% 0.30/0.47 => ( setminusI
% 0.30/0.47 => ( setminusEL
% 0.30/0.47 => ( setminusER
% 0.30/0.47 => ( setminusSubset2
% 0.30/0.47 => ( setminusERneg
% 0.30/0.47 => ( setminusELneg
% 0.30/0.47 => ( setminusILneg
% 0.30/0.47 => ( setminusIRneg
% 0.30/0.47 => ( setminusLsub
% 0.30/0.47 => ( setminusSubset1
% 0.30/0.47 => ( symdiffE
% 0.30/0.47 => ( symdiffI1
% 0.30/0.47 => ( symdiffI2
% 0.30/0.47 => ( symdiffIneg1
% 0.30/0.47 => ( symdiffIneg2
% 0.30/0.47 => ( secondinupair
% 0.30/0.47 => ( setukpairIL
% 0.30/0.47 => ( setukpairIR
% 0.30/0.47 => ( kpairiskpair
% 0.30/0.47 => ( kpairp
% 0.30/0.47 => ( singletonsubset
% 0.30/0.47 => ( singletoninpowerset
% 0.30/0.47 => ( singletoninpowunion
% 0.30/0.47 => ( upairset2E
% 0.30/0.47 => ( upairsubunion
% 0.30/0.47 => ( upairinpowunion
% 0.30/0.47 => ( ubforcartprodlem1
% 0.30/0.47 => ( ubforcartprodlem2
% 0.30/0.47 => ( ubforcartprodlem3
% 0.30/0.47 => ( cartprodpairin
% 0.30/0.47 => ( cartprodmempair1
% 0.30/0.47 => ( cartprodmempair
% 0.30/0.47 => ( setunionE2
% 0.30/0.47 => ( setunionsingleton1
% 0.30/0.47 => ( setunionsingleton2
% 0.30/0.47 => ( setunionsingleton
% 0.30/0.47 => ( singletonprop
% 0.30/0.47 => ( ex1E1
% 0.30/0.47 => ( ex1I
% 0.30/0.47 => ( ex1I2
% 0.30/0.47 => ( singletonsuniq
% 0.30/0.47 => ( setukpairinjL1
% 0.30/0.47 => ( kfstsingleton
% 0.30/0.47 => ( theprop
% 0.30/0.47 => ( kfstpairEq
% 0.30/0.47 => ( cartprodfstin
% 0.30/0.47 => ( setukpairinjL2
% 0.30/0.47 => ( setukpairinjL
% 0.30/0.47 => ( setukpairinjR11
% 0.30/0.47 => ( setukpairinjR12
% 0.30/0.47 => ( setukpairinjR1
% 0.30/0.47 => ( upairequniteq
% 0.30/0.47 => ( setukpairinjR2
% 0.30/0.47 => ( setukpairinjR
% 0.30/0.47 => ( ksndsingleton
% 0.30/0.47 => ( ksndpairEq
% 0.30/0.47 => ( kpairsurjEq
% 0.30/0.47 => ( cartprodsndin
% 0.30/0.47 => ( cartprodpairmemEL
% 0.30/0.47 => ( cartprodpairmemER
% 0.30/0.47 => ( cartprodmempaircEq
% 0.30/0.47 => ( cartprodfstpairEq
% 0.30/0.47 => ( cartprodsndpairEq
% 0.30/0.47 => ( cartprodpairsurjEq
% 0.30/0.47 => ( dpsetconstrI
% 0.30/0.47 => ( dpsetconstrSub
% 0.30/0.47 => ( setOfPairsIsBReln
% 0.30/0.47 => ( dpsetconstrERa
% 0.30/0.47 => ( dpsetconstrEL1
% 0.30/0.47 => ( dpsetconstrEL2
% 0.30/0.47 => ( dpsetconstrER
% 0.30/0.47 => ( funcImageSingleton
% 0.30/0.47 => ( apProp
% 0.30/0.47 => ( app
% 0.30/0.47 => ( infuncsetfunc
% 0.30/0.47 => ( ap2p
% 0.30/0.47 => ( funcinfuncset
% 0.30/0.47 => ( lamProp
% 0.30/0.47 => ( lamp
% 0.30/0.47 => ( lam2p
% 0.30/0.47 => ( brelnall1
% 0.30/0.47 => ( brelnall2
% 0.30/0.47 => ( ex1E2
% 0.30/0.48 => ( funcGraphProp1
% 0.30/0.48 => ( funcGraphProp3
% 0.30/0.48 => ( funcGraphProp2
% 0.30/0.48 => ! [A: $i,B: $i,Xf: $i] :
% 0.30/0.48 ( ( func @ A @ B @ Xf )
% 0.30/0.48 => ! [Xg: $i] :
% 0.30/0.48 ( ( func @ A @ B @ Xg )
% 0.30/0.48 => ( ! [Xx: $i] :
% 0.30/0.48 ( ( in @ Xx @ A )
% 0.30/0.48 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/0.48 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.30/0.48 => ! [Xx: $i] :
% 0.30/0.48 ( ( in @ Xx @ A )
% 0.30/0.48 => ! [Xy: $i] :
% 0.30/0.48 ( ( in @ Xy @ B )
% 0.30/0.48 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.30/0.48 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.48
% 0.30/0.48 %------------------------------------------------------------------------------
% 0.30/0.48 ------------------------
% 2.66/1.52 ---- Embedded in THF ---
% 2.66/1.52 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.66/1.52 %%% Generated on Tue Feb 24 12:32:04 EST 2026
% 2.66/1.52 %%% using '$$dhol' embedding, version 1.3.0.
% 2.66/1.52 %%% Logic specification used:
% 2.66/1.52 %%% thf(spec, logic, $$dhol).
% 2.66/1.52
% 2.66/1.52 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.pJgJnm9BBC/DTF2DTF23745.p
% See solution above
% 2.66/1.52 ------------------------
% 2.66/1.55 ---- Cleaned THF ---
% 2.66/1.55 thf(in_type,type,
% 2.66/1.55 in: $i > $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(exu_type,type,
% 2.66/1.55 exu: ( $i > $o ) > $o ).
% 2.66/1.55
% 2.66/1.55 thf(exu,definition,
% 2.66/1.55 ( exu
% 2.66/1.55 = ( ^ [Xphi: $i > $o] :
% 2.66/1.55 ? [Xx: $i] :
% 2.66/1.55 ( ( Xphi @ Xx )
% 2.66/1.55 & ! [Xy: $i] :
% 2.66/1.55 ( ( Xphi @ Xy )
% 2.66/1.55 => ( Xx = Xy ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setextAx_type,type,
% 2.66/1.55 setextAx: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setextAx,definition,
% 2.66/1.55 ( setextAx
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 <=> ( in @ Xx @ B ) )
% 2.66/1.55 => ( A = B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(emptyset_type,type,
% 2.66/1.55 emptyset: $i ).
% 2.66/1.55
% 2.66/1.55 thf(emptysetAx_type,type,
% 2.66/1.55 emptysetAx: $o ).
% 2.66/1.55
% 2.66/1.55 thf(emptysetAx,definition,
% 2.66/1.55 ( emptysetAx
% 2.66/1.55 = ( ! [Xx: $i] :
% 2.66/1.55 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoin_type,type,
% 2.66/1.55 setadjoin: $i > $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinAx_type,type,
% 2.66/1.55 setadjoinAx: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinAx,definition,
% 2.66/1.55 ( setadjoinAx
% 2.66/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.66/1.55 <=> ( ( Xy = Xx )
% 2.66/1.55 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(powerset_type,type,
% 2.66/1.55 powerset: $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(powersetAx_type,type,
% 2.66/1.55 powersetAx: $o ).
% 2.66/1.55
% 2.66/1.55 thf(powersetAx,definition,
% 2.66/1.55 ( powersetAx
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.66/1.55 <=> ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ B )
% 2.66/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setunion_type,type,
% 2.66/1.55 setunion: $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(setunionAx_type,type,
% 2.66/1.55 setunionAx: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setunionAx,definition,
% 2.66/1.55 ( setunionAx
% 2.66/1.55 = ( ! [A: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.66/1.55 <=> ? [B: $i] :
% 2.66/1.55 ( ( in @ Xx @ B )
% 2.66/1.55 & ( in @ B @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(omega_type,type,
% 2.66/1.55 omega: $i ).
% 2.66/1.55
% 2.66/1.55 thf(omega0Ax_type,type,
% 2.66/1.55 omega0Ax: $o ).
% 2.66/1.55
% 2.66/1.55 thf(omega0Ax,definition,
% 2.66/1.55 ( omega0Ax
% 2.66/1.55 = ( in @ emptyset @ omega ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(omegaSAx_type,type,
% 2.66/1.55 omegaSAx: $o ).
% 2.66/1.55
% 2.66/1.55 thf(omegaSAx,definition,
% 2.66/1.55 ( omegaSAx
% 2.66/1.55 = ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ omega )
% 2.66/1.55 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(omegaIndAx_type,type,
% 2.66/1.55 omegaIndAx: $o ).
% 2.66/1.55
% 2.66/1.55 thf(omegaIndAx,definition,
% 2.66/1.55 ( omegaIndAx
% 2.66/1.55 = ( ! [A: $i] :
% 2.66/1.55 ( ( ( in @ emptyset @ A )
% 2.66/1.55 & ! [Xx: $i] :
% 2.66/1.55 ( ( ( in @ Xx @ omega )
% 2.66/1.55 & ( in @ Xx @ A ) )
% 2.66/1.55 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ omega )
% 2.66/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(replAx_type,type,
% 2.66/1.55 replAx: $o ).
% 2.66/1.55
% 2.66/1.55 thf(replAx,definition,
% 2.66/1.55 ( replAx
% 2.66/1.55 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( exu
% 2.66/1.55 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.66/1.55 => ? [B: $i] :
% 2.66/1.55 ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ B )
% 2.66/1.55 <=> ? [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ A )
% 2.66/1.55 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(foundationAx_type,type,
% 2.66/1.55 foundationAx: $o ).
% 2.66/1.55
% 2.66/1.55 thf(foundationAx,definition,
% 2.66/1.55 ( foundationAx
% 2.66/1.55 = ( ! [A: $i] :
% 2.66/1.55 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.66/1.55 => ? [B: $i] :
% 2.66/1.55 ( ( in @ B @ A )
% 2.66/1.55 & ~ ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ B )
% 2.66/1.55 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(wellorderingAx_type,type,
% 2.66/1.55 wellorderingAx: $o ).
% 2.66/1.55
% 2.66/1.55 thf(wellorderingAx,definition,
% 2.66/1.55 ( wellorderingAx
% 2.66/1.55 = ( ! [A: $i] :
% 2.66/1.55 ? [B: $i] :
% 2.66/1.55 ( ! [C: $i] :
% 2.66/1.55 ( ( in @ C @ B )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ C )
% 2.66/1.55 => ( in @ Xx @ A ) ) )
% 2.66/1.55 & ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( ( in @ Xx @ A )
% 2.66/1.55 & ( in @ Xy @ A ) )
% 2.66/1.55 => ( ! [C: $i] :
% 2.66/1.55 ( ( in @ C @ B )
% 2.66/1.55 => ( ( in @ Xx @ C )
% 2.66/1.55 <=> ( in @ Xy @ C ) ) )
% 2.66/1.55 => ( Xx = Xy ) ) )
% 2.66/1.55 & ! [C: $i,D: $i] :
% 2.66/1.55 ( ( ( in @ C @ B )
% 2.66/1.55 & ( in @ D @ B ) )
% 2.66/1.55 => ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ C )
% 2.66/1.55 => ( in @ Xx @ D ) )
% 2.66/1.55 | ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ D )
% 2.66/1.55 => ( in @ Xx @ C ) ) ) )
% 2.66/1.55 & ! [C: $i] :
% 2.66/1.55 ( ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ C )
% 2.66/1.55 => ( in @ Xx @ A ) )
% 2.66/1.55 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.66/1.55 => ? [D: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ D @ B )
% 2.66/1.55 & ( in @ Xx @ C )
% 2.66/1.55 & ~ ? [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ D )
% 2.66/1.55 & ( in @ Xy @ C ) )
% 2.66/1.55 & ! [E: $i] :
% 2.66/1.55 ( ( in @ E @ B )
% 2.66/1.55 => ( ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ E )
% 2.66/1.55 => ( in @ Xy @ D ) )
% 2.66/1.55 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(descr_type,type,
% 2.66/1.55 descr: ( $i > $o ) > $i ).
% 2.66/1.55
% 2.66/1.55 thf(descrp_type,type,
% 2.66/1.55 descrp: $o ).
% 2.66/1.55
% 2.66/1.55 thf(descrp,definition,
% 2.66/1.55 ( descrp
% 2.66/1.55 = ( ! [Xphi: $i > $o] :
% 2.66/1.55 ( ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 => ( Xphi
% 2.66/1.55 @ ( descr
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(dsetconstr_type,type,
% 2.66/1.55 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.66/1.55
% 2.66/1.55 thf(dsetconstrI_type,type,
% 2.66/1.55 dsetconstrI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(dsetconstrI,definition,
% 2.66/1.55 ( dsetconstrI
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ( Xphi @ Xx )
% 2.66/1.55 => ( in @ Xx
% 2.66/1.55 @ ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(dsetconstrEL_type,type,
% 2.66/1.55 dsetconstrEL: $o ).
% 2.66/1.55
% 2.66/1.55 thf(dsetconstrEL,definition,
% 2.66/1.55 ( dsetconstrEL
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx
% 2.66/1.55 @ ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.66/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(dsetconstrER_type,type,
% 2.66/1.55 dsetconstrER: $o ).
% 2.66/1.55
% 2.66/1.55 thf(dsetconstrER,definition,
% 2.66/1.55 ( dsetconstrER
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx
% 2.66/1.55 @ ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.66/1.55 => ( Xphi @ Xx ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(exuE1_type,type,
% 2.66/1.55 exuE1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(exuE1,definition,
% 2.66/1.55 ( exuE1
% 2.66/1.55 = ( ! [Xphi: $i > $o] :
% 2.66/1.55 ( ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 => ? [Xx: $i] :
% 2.66/1.55 ( ( Xphi @ Xx )
% 2.66/1.55 & ! [Xy: $i] :
% 2.66/1.55 ( ( Xphi @ Xy )
% 2.66/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(prop2set_type,type,
% 2.66/1.55 prop2set: $o > $i ).
% 2.66/1.55
% 2.66/1.55 thf(prop2setE_type,type,
% 2.66/1.55 prop2setE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(prop2setE,definition,
% 2.66/1.55 ( prop2setE
% 2.66/1.55 = ( ! [Xphi: $o,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.66/1.55 => Xphi ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(emptysetE_type,type,
% 2.66/1.55 emptysetE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(emptysetE,definition,
% 2.66/1.55 ( emptysetE
% 2.66/1.55 = ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ emptyset )
% 2.66/1.55 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(emptysetimpfalse_type,type,
% 2.66/1.55 emptysetimpfalse: $o ).
% 2.66/1.55
% 2.66/1.55 thf(emptysetimpfalse,definition,
% 2.66/1.55 ( emptysetimpfalse
% 2.66/1.55 = ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ emptyset )
% 2.66/1.55 => $false ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(notinemptyset_type,type,
% 2.66/1.55 notinemptyset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(notinemptyset,definition,
% 2.66/1.55 ( notinemptyset
% 2.66/1.55 = ( ! [Xx: $i] :
% 2.66/1.55 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(exuE3e_type,type,
% 2.66/1.55 exuE3e: $o ).
% 2.66/1.55
% 2.66/1.55 thf(exuE3e,definition,
% 2.66/1.55 ( exuE3e
% 2.66/1.55 = ( ! [Xphi: $i > $o] :
% 2.66/1.55 ( ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setext_type,type,
% 2.66/1.55 setext: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setext,definition,
% 2.66/1.55 ( setext
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ Xx @ B ) )
% 2.66/1.55 => ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ B )
% 2.66/1.55 => ( in @ Xx @ A ) )
% 2.66/1.55 => ( A = B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(emptyI_type,type,
% 2.66/1.55 emptyI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(emptyI,definition,
% 2.66/1.55 ( emptyI
% 2.66/1.55 = ( ! [A: $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ~ ( in @ Xx @ A )
% 2.66/1.55 => ( A = emptyset ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(noeltsimpempty_type,type,
% 2.66/1.55 noeltsimpempty: $o ).
% 2.66/1.55
% 2.66/1.55 thf(noeltsimpempty,definition,
% 2.66/1.55 ( noeltsimpempty
% 2.66/1.55 = ( ! [A: $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ~ ( in @ Xx @ A )
% 2.66/1.55 => ( A = emptyset ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setbeta_type,type,
% 2.66/1.55 setbeta: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setbeta,definition,
% 2.66/1.55 ( setbeta
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ( in @ Xx
% 2.66/1.55 @ ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.66/1.55 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(nonempty_type,type,
% 2.66/1.55 nonempty: $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(nonempty,definition,
% 2.66/1.55 ( nonempty
% 2.66/1.55 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(nonemptyE1_type,type,
% 2.66/1.55 nonemptyE1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(nonemptyE1,definition,
% 2.66/1.55 ( nonemptyE1
% 2.66/1.55 = ( ! [A: $i] :
% 2.66/1.55 ( ( nonempty @ A )
% 2.66/1.55 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(nonemptyI_type,type,
% 2.66/1.55 nonemptyI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(nonemptyI,definition,
% 2.66/1.55 ( nonemptyI
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ( Xphi @ Xx )
% 2.66/1.55 => ( nonempty
% 2.66/1.55 @ ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(nonemptyI1_type,type,
% 2.66/1.55 nonemptyI1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(nonemptyI1,definition,
% 2.66/1.55 ( nonemptyI1
% 2.66/1.55 = ( ! [A: $i] :
% 2.66/1.55 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.66/1.55 => ( nonempty @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinIL_type,type,
% 2.66/1.55 setadjoinIL: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinIL,definition,
% 2.66/1.55 ( setadjoinIL
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(emptyinunitempty_type,type,
% 2.66/1.55 emptyinunitempty: $o ).
% 2.66/1.55
% 2.66/1.55 thf(emptyinunitempty,definition,
% 2.66/1.55 ( emptyinunitempty
% 2.66/1.55 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinIR_type,type,
% 2.66/1.55 setadjoinIR: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinIR,definition,
% 2.66/1.55 ( setadjoinIR
% 2.66/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ A )
% 2.66/1.55 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinE_type,type,
% 2.66/1.55 setadjoinE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinE,definition,
% 2.66/1.55 ( setadjoinE
% 2.66/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.66/1.55 => ! [Xphi: $o] :
% 2.66/1.55 ( ( ( Xy = Xx )
% 2.66/1.55 => Xphi )
% 2.66/1.55 => ( ( ( in @ Xy @ A )
% 2.66/1.55 => Xphi )
% 2.66/1.55 => Xphi ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinOr_type,type,
% 2.66/1.55 setadjoinOr: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinOr,definition,
% 2.66/1.55 ( setadjoinOr
% 2.66/1.55 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.66/1.55 => ( ( Xy = Xx )
% 2.66/1.55 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setoftrueEq_type,type,
% 2.66/1.55 setoftrueEq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setoftrueEq,definition,
% 2.66/1.55 ( setoftrueEq
% 2.66/1.55 = ( ! [A: $i] :
% 2.66/1.55 ( ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xx: $i] : $true )
% 2.66/1.55 = A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(powersetI_type,type,
% 2.66/1.55 powersetI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(powersetI,definition,
% 2.66/1.55 ( powersetI
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ B )
% 2.66/1.55 => ( in @ Xx @ A ) )
% 2.66/1.55 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(emptyinPowerset_type,type,
% 2.66/1.55 emptyinPowerset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(emptyinPowerset,definition,
% 2.66/1.55 ( emptyinPowerset
% 2.66/1.55 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(emptyInPowerset_type,type,
% 2.66/1.55 emptyInPowerset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(emptyInPowerset,definition,
% 2.66/1.55 ( emptyInPowerset
% 2.66/1.55 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(powersetE_type,type,
% 2.66/1.55 powersetE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(powersetE,definition,
% 2.66/1.55 ( powersetE
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.66/1.55 => ( ( in @ Xx @ B )
% 2.66/1.55 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setunionI_type,type,
% 2.66/1.55 setunionI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setunionI,definition,
% 2.66/1.55 ( setunionI
% 2.66/1.55 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.66/1.55 ( ( in @ Xx @ B )
% 2.66/1.55 => ( ( in @ B @ A )
% 2.66/1.55 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setunionE_type,type,
% 2.66/1.55 setunionE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setunionE,definition,
% 2.66/1.55 ( setunionE
% 2.66/1.55 = ( ! [A: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.66/1.55 => ! [Xphi: $o] :
% 2.66/1.55 ( ! [B: $i] :
% 2.66/1.55 ( ( in @ Xx @ B )
% 2.66/1.55 => ( ( in @ B @ A )
% 2.66/1.55 => Xphi ) )
% 2.66/1.55 => Xphi ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(subPowSU_type,type,
% 2.66/1.55 subPowSU: $o ).
% 2.66/1.55
% 2.66/1.55 thf(subPowSU,definition,
% 2.66/1.55 ( subPowSU
% 2.66/1.55 = ( ! [A: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(exuE2_type,type,
% 2.66/1.55 exuE2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(exuE2,definition,
% 2.66/1.55 ( exuE2
% 2.66/1.55 = ( ! [Xphi: $i > $o] :
% 2.66/1.55 ( ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 => ? [Xx: $i] :
% 2.66/1.55 ! [Xy: $i] :
% 2.66/1.55 ( ( Xphi @ Xy )
% 2.66/1.55 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(nonemptyImpWitness_type,type,
% 2.66/1.55 nonemptyImpWitness: $o ).
% 2.66/1.55
% 2.66/1.55 thf(nonemptyImpWitness,definition,
% 2.66/1.55 ( nonemptyImpWitness
% 2.66/1.55 = ( ! [A: $i] :
% 2.66/1.55 ( ( nonempty @ A )
% 2.66/1.55 => ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & $true ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(uniqinunit_type,type,
% 2.66/1.55 uniqinunit: $o ).
% 2.66/1.55
% 2.66/1.55 thf(uniqinunit,definition,
% 2.66/1.55 ( uniqinunit
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.66/1.55 => ( Xx = Xy ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(notinsingleton_type,type,
% 2.66/1.55 notinsingleton: $o ).
% 2.66/1.55
% 2.66/1.55 thf(notinsingleton,definition,
% 2.66/1.55 ( notinsingleton
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xx != Xy )
% 2.66/1.55 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(eqinunit_type,type,
% 2.66/1.55 eqinunit: $o ).
% 2.66/1.55
% 2.66/1.55 thf(eqinunit,definition,
% 2.66/1.55 ( eqinunit
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xx = Xy )
% 2.66/1.55 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(singletonsswitch_type,type,
% 2.66/1.55 singletonsswitch: $o ).
% 2.66/1.55
% 2.66/1.55 thf(singletonsswitch,definition,
% 2.66/1.55 ( singletonsswitch
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.66/1.55 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(upairsetE_type,type,
% 2.66/1.55 upairsetE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(upairsetE,definition,
% 2.66/1.55 ( upairsetE
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.66/1.55 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.66/1.55 => ( ( Xz = Xx )
% 2.66/1.55 | ( Xz = Xy ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(upairsetIL_type,type,
% 2.66/1.55 upairsetIL: $o ).
% 2.66/1.55
% 2.66/1.55 thf(upairsetIL,definition,
% 2.66/1.55 ( upairsetIL
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(upairsetIR_type,type,
% 2.66/1.55 upairsetIR: $o ).
% 2.66/1.55
% 2.66/1.55 thf(upairsetIR,definition,
% 2.66/1.55 ( upairsetIR
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(emptyE1_type,type,
% 2.66/1.55 emptyE1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(emptyE1,definition,
% 2.66/1.55 ( emptyE1
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ( Xphi @ Xx ) )
% 2.66/1.55 => ( ( ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 = emptyset )
% 2.66/1.55 => $false ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(vacuousDall_type,type,
% 2.66/1.55 vacuousDall: $o ).
% 2.66/1.55
% 2.66/1.55 thf(vacuousDall,definition,
% 2.66/1.55 ( vacuousDall
% 2.66/1.55 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ emptyset )
% 2.66/1.55 => ( Xphi @ Xx ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(quantDeMorgan1_type,type,
% 2.66/1.55 quantDeMorgan1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(quantDeMorgan1,definition,
% 2.66/1.55 ( quantDeMorgan1
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ~ ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( Xphi @ Xx ) )
% 2.66/1.55 => ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(quantDeMorgan2_type,type,
% 2.66/1.55 quantDeMorgan2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(quantDeMorgan2,definition,
% 2.66/1.55 ( quantDeMorgan2
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ~ ( Xphi @ Xx ) )
% 2.66/1.55 => ~ ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(quantDeMorgan3_type,type,
% 2.66/1.55 quantDeMorgan3: $o ).
% 2.66/1.55
% 2.66/1.55 thf(quantDeMorgan3,definition,
% 2.66/1.55 ( quantDeMorgan3
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ~ ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ( Xphi @ Xx ) )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(quantDeMorgan4_type,type,
% 2.66/1.55 quantDeMorgan4: $o ).
% 2.66/1.55
% 2.66/1.55 thf(quantDeMorgan4,definition,
% 2.66/1.55 ( quantDeMorgan4
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ~ ( Xphi @ Xx ) )
% 2.66/1.55 => ~ ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(prop2setI_type,type,
% 2.66/1.55 prop2setI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(prop2setI,definition,
% 2.66/1.55 ( prop2setI
% 2.66/1.55 = ( ! [Xphi: $o] :
% 2.66/1.55 ( Xphi
% 2.66/1.55 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(set2prop_type,type,
% 2.66/1.55 set2prop: $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(prop2set2propI_type,type,
% 2.66/1.55 prop2set2propI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(prop2set2propI,definition,
% 2.66/1.55 ( prop2set2propI
% 2.66/1.55 = ( ! [Xphi: $o] :
% 2.66/1.55 ( Xphi
% 2.66/1.55 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(notdexE_type,type,
% 2.66/1.55 notdexE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(notdexE,definition,
% 2.66/1.55 ( notdexE
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ~ ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ( Xphi @ Xx ) )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(notdallE_type,type,
% 2.66/1.55 notdallE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(notdallE,definition,
% 2.66/1.55 ( notdallE
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ~ ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( Xphi @ Xx ) )
% 2.66/1.55 => ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(exuI1_type,type,
% 2.66/1.55 exuI1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(exuI1,definition,
% 2.66/1.55 ( exuI1
% 2.66/1.55 = ( ! [Xphi: $i > $o] :
% 2.66/1.55 ( ? [Xx: $i] :
% 2.66/1.55 ( ( Xphi @ Xx )
% 2.66/1.55 & ! [Xy: $i] :
% 2.66/1.55 ( ( Xphi @ Xy )
% 2.66/1.55 => ( Xx = Xy ) ) )
% 2.66/1.55 => ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(exuI3_type,type,
% 2.66/1.55 exuI3: $o ).
% 2.66/1.55
% 2.66/1.55 thf(exuI3,definition,
% 2.66/1.55 ( exuI3
% 2.66/1.55 = ( ! [Xphi: $i > $o] :
% 2.66/1.55 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.66/1.55 => ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xphi @ Xx )
% 2.66/1.55 => ( ( Xphi @ Xy )
% 2.66/1.55 => ( Xx = Xy ) ) )
% 2.66/1.55 => ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(exuI2_type,type,
% 2.66/1.55 exuI2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(exuI2,definition,
% 2.66/1.55 ( exuI2
% 2.66/1.55 = ( ! [Xphi: $i > $o] :
% 2.66/1.55 ( ? [Xx: $i] :
% 2.66/1.55 ! [Xy: $i] :
% 2.66/1.55 ( ( Xphi @ Xy )
% 2.66/1.55 <=> ( Xy = Xx ) )
% 2.66/1.55 => ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(inCongP_type,type,
% 2.66/1.55 inCongP: $o ).
% 2.66/1.55
% 2.66/1.55 thf(inCongP,definition,
% 2.66/1.55 ( inCongP
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( A = B )
% 2.66/1.55 => ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xx = Xy )
% 2.66/1.55 => ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(in__Cong_type,type,
% 2.66/1.55 in__Cong: $o ).
% 2.66/1.55
% 2.66/1.55 thf(in__Cong,definition,
% 2.66/1.55 ( in__Cong
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( A = B )
% 2.66/1.55 => ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xx = Xy )
% 2.66/1.55 => ( ( in @ Xx @ A )
% 2.66/1.55 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(exuE3u_type,type,
% 2.66/1.55 exuE3u: $o ).
% 2.66/1.55
% 2.66/1.55 thf(exuE3u,definition,
% 2.66/1.55 ( exuE3u
% 2.66/1.55 = ( ! [Xphi: $i > $o] :
% 2.66/1.55 ( ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 => ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xphi @ Xx )
% 2.66/1.55 => ( ( Xphi @ Xy )
% 2.66/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(exu__Cong_type,type,
% 2.66/1.55 exu__Cong: $o ).
% 2.66/1.55
% 2.66/1.55 thf(exu__Cong,definition,
% 2.66/1.55 ( exu__Cong
% 2.66/1.55 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.66/1.55 ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xx = Xy )
% 2.66/1.55 => ( ( Xphi @ Xx )
% 2.66/1.55 <=> ( Xpsi @ Xy ) ) )
% 2.66/1.55 => ( ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 <=> ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(emptyset__Cong_type,type,
% 2.66/1.55 emptyset__Cong: $o ).
% 2.66/1.55
% 2.66/1.55 thf(emptyset__Cong,definition,
% 2.66/1.55 ( emptyset__Cong
% 2.66/1.55 = ( emptyset = emptyset ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoin__Cong_type,type,
% 2.66/1.55 setadjoin__Cong: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoin__Cong,definition,
% 2.66/1.55 ( setadjoin__Cong
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xx = Xy )
% 2.66/1.55 => ! [Xz: $i,Xu: $i] :
% 2.66/1.55 ( ( Xz = Xu )
% 2.66/1.55 => ( ( setadjoin @ Xx @ Xz )
% 2.66/1.55 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(powerset__Cong_type,type,
% 2.66/1.55 powerset__Cong: $o ).
% 2.66/1.55
% 2.66/1.55 thf(powerset__Cong,definition,
% 2.66/1.55 ( powerset__Cong
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( A = B )
% 2.66/1.55 => ( ( powerset @ A )
% 2.66/1.55 = ( powerset @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setunion__Cong_type,type,
% 2.66/1.55 setunion__Cong: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setunion__Cong,definition,
% 2.66/1.55 ( setunion__Cong
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( A = B )
% 2.66/1.55 => ( ( setunion @ A )
% 2.66/1.55 = ( setunion @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(omega__Cong_type,type,
% 2.66/1.55 omega__Cong: $o ).
% 2.66/1.55
% 2.66/1.55 thf(omega__Cong,definition,
% 2.66/1.55 ( omega__Cong
% 2.66/1.55 = ( omega = omega ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(exuEu_type,type,
% 2.66/1.55 exuEu: $o ).
% 2.66/1.55
% 2.66/1.55 thf(exuEu,definition,
% 2.66/1.55 ( exuEu
% 2.66/1.55 = ( ! [Xphi: $i > $o] :
% 2.66/1.55 ( ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 => ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xphi @ Xx )
% 2.66/1.55 => ( ( Xphi @ Xy )
% 2.66/1.55 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(descr__Cong_type,type,
% 2.66/1.55 descr__Cong: $o ).
% 2.66/1.55
% 2.66/1.55 thf(descr__Cong,definition,
% 2.66/1.55 ( descr__Cong
% 2.66/1.55 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.66/1.55 ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xx = Xy )
% 2.66/1.55 => ( ( Xphi @ Xx )
% 2.66/1.55 <=> ( Xpsi @ Xy ) ) )
% 2.66/1.55 => ( ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 => ( ( exu
% 2.66/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.66/1.55 => ( ( descr
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 = ( descr
% 2.66/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(dsetconstr__Cong_type,type,
% 2.66/1.55 dsetconstr__Cong: $o ).
% 2.66/1.55
% 2.66/1.55 thf(dsetconstr__Cong,definition,
% 2.66/1.55 ( dsetconstr__Cong
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( A = B )
% 2.66/1.55 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( ( Xx = Xy )
% 2.66/1.55 => ( ( Xphi @ Xx )
% 2.66/1.55 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.66/1.55 => ( ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 = ( dsetconstr @ B
% 2.66/1.55 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(subset_type,type,
% 2.66/1.55 subset: $i > $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(disjoint_type,type,
% 2.66/1.55 disjoint: $i > $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(setsmeet_type,type,
% 2.66/1.55 setsmeet: $i > $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(subsetI1_type,type,
% 2.66/1.55 subsetI1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(subsetI1,definition,
% 2.66/1.55 ( subsetI1
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ Xx @ B ) )
% 2.66/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(eqimpsubset2_type,type,
% 2.66/1.55 eqimpsubset2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(eqimpsubset2,definition,
% 2.66/1.55 ( eqimpsubset2
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( A = B )
% 2.66/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(eqimpsubset1_type,type,
% 2.66/1.55 eqimpsubset1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(eqimpsubset1,definition,
% 2.66/1.55 ( eqimpsubset1
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( A = B )
% 2.66/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(subsetI2_type,type,
% 2.66/1.55 subsetI2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(subsetI2,definition,
% 2.66/1.55 ( subsetI2
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ Xx @ B ) )
% 2.66/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(emptysetsubset_type,type,
% 2.66/1.55 emptysetsubset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(emptysetsubset,definition,
% 2.66/1.55 ( emptysetsubset
% 2.66/1.55 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(subsetE_type,type,
% 2.66/1.55 subsetE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(subsetE,definition,
% 2.66/1.55 ( subsetE
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( subset @ A @ B )
% 2.66/1.55 => ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(subsetE2_type,type,
% 2.66/1.55 subsetE2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(subsetE2,definition,
% 2.66/1.55 ( subsetE2
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( subset @ A @ B )
% 2.66/1.55 => ( ~ ( in @ Xx @ B )
% 2.66/1.55 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(notsubsetI_type,type,
% 2.66/1.55 notsubsetI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(notsubsetI,definition,
% 2.66/1.55 ( notsubsetI
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ~ ( in @ Xx @ B )
% 2.66/1.55 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(notequalI1_type,type,
% 2.66/1.55 notequalI1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(notequalI1,definition,
% 2.66/1.55 ( notequalI1
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ~ ( subset @ A @ B )
% 2.66/1.55 => ( A != B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(notequalI2_type,type,
% 2.66/1.55 notequalI2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(notequalI2,definition,
% 2.66/1.55 ( notequalI2
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ~ ( in @ Xx @ B )
% 2.66/1.55 => ( A != B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(subsetRefl_type,type,
% 2.66/1.55 subsetRefl: $o ).
% 2.66/1.55
% 2.66/1.55 thf(subsetRefl,definition,
% 2.66/1.55 ( subsetRefl
% 2.66/1.55 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(subsetTrans_type,type,
% 2.66/1.55 subsetTrans: $o ).
% 2.66/1.55
% 2.66/1.55 thf(subsetTrans,definition,
% 2.66/1.55 ( subsetTrans
% 2.66/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.66/1.55 ( ( subset @ A @ B )
% 2.66/1.55 => ( ( subset @ B @ C )
% 2.66/1.55 => ( subset @ A @ C ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinSub_type,type,
% 2.66/1.55 setadjoinSub: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinSub,definition,
% 2.66/1.55 ( setadjoinSub
% 2.66/1.55 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinSub2_type,type,
% 2.66/1.55 setadjoinSub2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setadjoinSub2,definition,
% 2.66/1.55 ( setadjoinSub2
% 2.66/1.55 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.66/1.55 ( ( subset @ A @ B )
% 2.66/1.55 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(subset2powerset_type,type,
% 2.66/1.55 subset2powerset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(subset2powerset,definition,
% 2.66/1.55 ( subset2powerset
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( subset @ A @ B )
% 2.66/1.55 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setextsub_type,type,
% 2.66/1.55 setextsub: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setextsub,definition,
% 2.66/1.55 ( setextsub
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( subset @ A @ B )
% 2.66/1.55 => ( ( subset @ B @ A )
% 2.66/1.55 => ( A = B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(subsetemptysetimpeq_type,type,
% 2.66/1.55 subsetemptysetimpeq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(subsetemptysetimpeq,definition,
% 2.66/1.55 ( subsetemptysetimpeq
% 2.66/1.55 = ( ! [A: $i] :
% 2.66/1.55 ( ( subset @ A @ emptyset )
% 2.66/1.55 => ( A = emptyset ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(powersetI1_type,type,
% 2.66/1.55 powersetI1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(powersetI1,definition,
% 2.66/1.55 ( powersetI1
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( subset @ B @ A )
% 2.66/1.55 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(powersetE1_type,type,
% 2.66/1.55 powersetE1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(powersetE1,definition,
% 2.66/1.55 ( powersetE1
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( in @ B @ ( powerset @ A ) )
% 2.66/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(inPowerset_type,type,
% 2.66/1.55 inPowerset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(inPowerset,definition,
% 2.66/1.55 ( inPowerset
% 2.66/1.55 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(powersetsubset_type,type,
% 2.66/1.55 powersetsubset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(powersetsubset,definition,
% 2.66/1.55 ( powersetsubset
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( subset @ A @ B )
% 2.66/1.55 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(sepInPowerset_type,type,
% 2.66/1.55 sepInPowerset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(sepInPowerset,definition,
% 2.66/1.55 ( sepInPowerset
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( in
% 2.66/1.55 @ ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 @ ( powerset @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(sepSubset_type,type,
% 2.66/1.55 sepSubset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(sepSubset,definition,
% 2.66/1.55 ( sepSubset
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( subset
% 2.66/1.55 @ ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 @ A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binunion_type,type,
% 2.66/1.55 binunion: $i > $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(binunionIL_type,type,
% 2.66/1.55 binunionIL: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binunionIL,definition,
% 2.66/1.55 ( binunionIL
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(upairset2IR_type,type,
% 2.66/1.55 upairset2IR: $o ).
% 2.66/1.55
% 2.66/1.55 thf(upairset2IR,definition,
% 2.66/1.55 ( upairset2IR
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binunionIR_type,type,
% 2.66/1.55 binunionIR: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binunionIR,definition,
% 2.66/1.55 ( binunionIR
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ B )
% 2.66/1.55 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binunionEcases_type,type,
% 2.66/1.55 binunionEcases: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binunionEcases,definition,
% 2.66/1.55 ( binunionEcases
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.66/1.55 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.66/1.55 => ( ( ( in @ Xx @ A )
% 2.66/1.55 => Xphi )
% 2.66/1.55 => ( ( ( in @ Xx @ B )
% 2.66/1.55 => Xphi )
% 2.66/1.55 => Xphi ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binunionE_type,type,
% 2.66/1.55 binunionE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binunionE,definition,
% 2.66/1.55 ( binunionE
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.66/1.55 => ( ( in @ Xx @ A )
% 2.66/1.55 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binunionLsub_type,type,
% 2.66/1.55 binunionLsub: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binunionLsub,definition,
% 2.66/1.55 ( binunionLsub
% 2.66/1.55 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binunionRsub_type,type,
% 2.66/1.55 binunionRsub: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binunionRsub,definition,
% 2.66/1.55 ( binunionRsub
% 2.66/1.55 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binintersect_type,type,
% 2.66/1.55 binintersect: $i > $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectI_type,type,
% 2.66/1.55 binintersectI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectI,definition,
% 2.66/1.55 ( binintersectI
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ( in @ Xx @ B )
% 2.66/1.55 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectSubset5_type,type,
% 2.66/1.55 binintersectSubset5: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectSubset5,definition,
% 2.66/1.55 ( binintersectSubset5
% 2.66/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.66/1.55 ( ( subset @ C @ A )
% 2.66/1.55 => ( ( subset @ C @ B )
% 2.66/1.55 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectEL_type,type,
% 2.66/1.55 binintersectEL: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectEL,definition,
% 2.66/1.55 ( binintersectEL
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.66/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectLsub_type,type,
% 2.66/1.55 binintersectLsub: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectLsub,definition,
% 2.66/1.55 ( binintersectLsub
% 2.66/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectSubset2_type,type,
% 2.66/1.55 binintersectSubset2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectSubset2,definition,
% 2.66/1.55 ( binintersectSubset2
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( subset @ A @ B )
% 2.66/1.55 => ( ( binintersect @ A @ B )
% 2.66/1.55 = A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectSubset3_type,type,
% 2.66/1.55 binintersectSubset3: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectSubset3,definition,
% 2.66/1.55 ( binintersectSubset3
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( ( binintersect @ A @ B )
% 2.66/1.55 = B )
% 2.66/1.55 => ( subset @ B @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectER_type,type,
% 2.66/1.55 binintersectER: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectER,definition,
% 2.66/1.55 ( binintersectER
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.66/1.55 => ( in @ Xx @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(disjointsetsI1_type,type,
% 2.66/1.55 disjointsetsI1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(disjointsetsI1,definition,
% 2.66/1.55 ( disjointsetsI1
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ~ ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ( in @ Xx @ B ) )
% 2.66/1.55 => ( ( binintersect @ A @ B )
% 2.66/1.55 = emptyset ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectRsub_type,type,
% 2.66/1.55 binintersectRsub: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectRsub,definition,
% 2.66/1.55 ( binintersectRsub
% 2.66/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectSubset4_type,type,
% 2.66/1.55 binintersectSubset4: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectSubset4,definition,
% 2.66/1.55 ( binintersectSubset4
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( subset @ B @ A )
% 2.66/1.55 => ( ( binintersect @ A @ B )
% 2.66/1.55 = B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectSubset1_type,type,
% 2.66/1.55 binintersectSubset1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(binintersectSubset1,definition,
% 2.66/1.55 ( binintersectSubset1
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( ( binintersect @ A @ B )
% 2.66/1.55 = A )
% 2.66/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(bs114d_type,type,
% 2.66/1.55 bs114d: $o ).
% 2.66/1.55
% 2.66/1.55 thf(bs114d,definition,
% 2.66/1.55 ( bs114d
% 2.66/1.55 = ( ! [A: $i,B: $i,C: $i] :
% 2.66/1.55 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.66/1.55 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(regular_type,type,
% 2.66/1.55 regular: $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminus_type,type,
% 2.66/1.55 setminus: $i > $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(setminusI_type,type,
% 2.66/1.55 setminusI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminusI,definition,
% 2.66/1.55 ( setminusI
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ~ ( in @ Xx @ B )
% 2.66/1.55 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setminusEL_type,type,
% 2.66/1.55 setminusEL: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminusEL,definition,
% 2.66/1.55 ( setminusEL
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.66/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setminusER_type,type,
% 2.66/1.55 setminusER: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminusER,definition,
% 2.66/1.55 ( setminusER
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.66/1.55 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setminusSubset2_type,type,
% 2.66/1.55 setminusSubset2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminusSubset2,definition,
% 2.66/1.55 ( setminusSubset2
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( subset @ A @ B )
% 2.66/1.55 => ( ( setminus @ A @ B )
% 2.66/1.55 = emptyset ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setminusERneg_type,type,
% 2.66/1.55 setminusERneg: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminusERneg,definition,
% 2.66/1.55 ( setminusERneg
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.66/1.55 => ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setminusELneg_type,type,
% 2.66/1.55 setminusELneg: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminusELneg,definition,
% 2.66/1.55 ( setminusELneg
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.66/1.55 => ( ~ ( in @ Xx @ B )
% 2.66/1.55 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setminusILneg_type,type,
% 2.66/1.55 setminusILneg: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminusILneg,definition,
% 2.66/1.55 ( setminusILneg
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ~ ( in @ Xx @ A )
% 2.66/1.55 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setminusIRneg_type,type,
% 2.66/1.55 setminusIRneg: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminusIRneg,definition,
% 2.66/1.55 ( setminusIRneg
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ B )
% 2.66/1.55 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setminusLsub_type,type,
% 2.66/1.55 setminusLsub: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminusLsub,definition,
% 2.66/1.55 ( setminusLsub
% 2.66/1.55 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setminusSubset1_type,type,
% 2.66/1.55 setminusSubset1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setminusSubset1,definition,
% 2.66/1.55 ( setminusSubset1
% 2.66/1.55 = ( ! [A: $i,B: $i] :
% 2.66/1.55 ( ( ( setminus @ A @ B )
% 2.66/1.55 = emptyset )
% 2.66/1.55 => ( subset @ A @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(symdiff_type,type,
% 2.66/1.55 symdiff: $i > $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(symdiffE_type,type,
% 2.66/1.55 symdiffE: $o ).
% 2.66/1.55
% 2.66/1.55 thf(symdiffE,definition,
% 2.66/1.55 ( symdiffE
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.66/1.55 => ! [Xphi: $o] :
% 2.66/1.55 ( ( ( in @ Xx @ A )
% 2.66/1.55 => ( ~ ( in @ Xx @ B )
% 2.66/1.55 => Xphi ) )
% 2.66/1.55 => ( ( ~ ( in @ Xx @ A )
% 2.66/1.55 => ( ( in @ Xx @ B )
% 2.66/1.55 => Xphi ) )
% 2.66/1.55 => Xphi ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(symdiffI1_type,type,
% 2.66/1.55 symdiffI1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(symdiffI1,definition,
% 2.66/1.55 ( symdiffI1
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ~ ( in @ Xx @ B )
% 2.66/1.55 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(symdiffI2_type,type,
% 2.66/1.55 symdiffI2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(symdiffI2,definition,
% 2.66/1.55 ( symdiffI2
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ~ ( in @ Xx @ A )
% 2.66/1.55 => ( ( in @ Xx @ B )
% 2.66/1.55 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(symdiffIneg1_type,type,
% 2.66/1.55 symdiffIneg1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(symdiffIneg1,definition,
% 2.66/1.55 ( symdiffIneg1
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ( in @ Xx @ B )
% 2.66/1.55 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(symdiffIneg2_type,type,
% 2.66/1.55 symdiffIneg2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(symdiffIneg2,definition,
% 2.66/1.55 ( symdiffIneg2
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ~ ( in @ Xx @ A )
% 2.66/1.55 => ( ~ ( in @ Xx @ B )
% 2.66/1.55 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(iskpair_type,type,
% 2.66/1.55 iskpair: $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(secondinupair_type,type,
% 2.66/1.55 secondinupair: $o ).
% 2.66/1.55
% 2.66/1.55 thf(secondinupair,definition,
% 2.66/1.55 ( secondinupair
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairIL_type,type,
% 2.66/1.55 setukpairIL: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairIL,definition,
% 2.66/1.55 ( setukpairIL
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairIR_type,type,
% 2.66/1.55 setukpairIR: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairIR,definition,
% 2.66/1.55 ( setukpairIR
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(kpairiskpair_type,type,
% 2.66/1.55 kpairiskpair: $o ).
% 2.66/1.55
% 2.66/1.55 thf(kpairiskpair,definition,
% 2.66/1.55 ( kpairiskpair
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(kpair_type,type,
% 2.66/1.55 kpair: $i > $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(kpairp_type,type,
% 2.66/1.55 kpairp: $o ).
% 2.66/1.55
% 2.66/1.55 thf(kpairp,definition,
% 2.66/1.55 ( kpairp
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprod_type,type,
% 2.66/1.55 cartprod: $i > $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(singletonsubset_type,type,
% 2.66/1.55 singletonsubset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(singletonsubset,definition,
% 2.66/1.55 ( singletonsubset
% 2.66/1.55 = ( ! [A: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(singletoninpowerset_type,type,
% 2.66/1.55 singletoninpowerset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(singletoninpowerset,definition,
% 2.66/1.55 ( singletoninpowerset
% 2.66/1.55 = ( ! [A: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(singletoninpowunion_type,type,
% 2.66/1.55 singletoninpowunion: $o ).
% 2.66/1.55
% 2.66/1.55 thf(singletoninpowunion,definition,
% 2.66/1.55 ( singletoninpowunion
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(upairset2E_type,type,
% 2.66/1.55 upairset2E: $o ).
% 2.66/1.55
% 2.66/1.55 thf(upairset2E,definition,
% 2.66/1.55 ( upairset2E
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.66/1.55 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.66/1.55 => ( ( Xz = Xx )
% 2.66/1.55 | ( Xz = Xy ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(upairsubunion_type,type,
% 2.66/1.55 upairsubunion: $o ).
% 2.66/1.55
% 2.66/1.55 thf(upairsubunion,definition,
% 2.66/1.55 ( upairsubunion
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(upairinpowunion_type,type,
% 2.66/1.55 upairinpowunion: $o ).
% 2.66/1.55
% 2.66/1.55 thf(upairinpowunion,definition,
% 2.66/1.55 ( upairinpowunion
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ubforcartprodlem1_type,type,
% 2.66/1.55 ubforcartprodlem1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(ubforcartprodlem1,definition,
% 2.66/1.55 ( ubforcartprodlem1
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ubforcartprodlem2_type,type,
% 2.66/1.55 ubforcartprodlem2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(ubforcartprodlem2,definition,
% 2.66/1.55 ( ubforcartprodlem2
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ubforcartprodlem3_type,type,
% 2.66/1.55 ubforcartprodlem3: $o ).
% 2.66/1.55
% 2.66/1.55 thf(ubforcartprodlem3,definition,
% 2.66/1.55 ( ubforcartprodlem3
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodpairin_type,type,
% 2.66/1.55 cartprodpairin: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodpairin,definition,
% 2.66/1.55 ( cartprodpairin
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodmempair1_type,type,
% 2.66/1.55 cartprodmempair1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodmempair1,definition,
% 2.66/1.55 ( cartprodmempair1
% 2.66/1.55 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.66/1.55 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.66/1.55 => ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ? [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 & ( Xu
% 2.66/1.55 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodmempair_type,type,
% 2.66/1.55 cartprodmempair: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodmempair,definition,
% 2.66/1.55 ( cartprodmempair
% 2.66/1.55 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.66/1.55 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.66/1.55 => ( iskpair @ Xu ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setunionE2_type,type,
% 2.66/1.55 setunionE2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setunionE2,definition,
% 2.66/1.55 ( setunionE2
% 2.66/1.55 = ( ! [A: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ ( setunion @ A ) )
% 2.66/1.55 => ? [X: $i] :
% 2.66/1.55 ( ( in @ X @ A )
% 2.66/1.55 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setunionsingleton1_type,type,
% 2.66/1.55 setunionsingleton1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setunionsingleton1,definition,
% 2.66/1.55 ( setunionsingleton1
% 2.66/1.55 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setunionsingleton2_type,type,
% 2.66/1.55 setunionsingleton2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setunionsingleton2,definition,
% 2.66/1.55 ( setunionsingleton2
% 2.66/1.55 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setunionsingleton_type,type,
% 2.66/1.55 setunionsingleton: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setunionsingleton,definition,
% 2.66/1.55 ( setunionsingleton
% 2.66/1.55 = ( ! [Xx: $i] :
% 2.66/1.55 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.66/1.55 = Xx ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(singleton_type,type,
% 2.66/1.55 singleton: $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(singleton,definition,
% 2.66/1.55 ( singleton
% 2.66/1.55 = ( ^ [A: $i] :
% 2.66/1.55 ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ( A
% 2.66/1.55 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(singletonprop_type,type,
% 2.66/1.55 singletonprop: $o ).
% 2.66/1.55
% 2.66/1.55 thf(singletonprop,definition,
% 2.66/1.55 ( singletonprop
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ A )
% 2.66/1.55 => ( ( Xphi @ Xx )
% 2.66/1.55 => ( ( Xphi @ Xy )
% 2.66/1.55 => ( Xx = Xy ) ) ) ) )
% 2.66/1.55 => ( ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ( Xphi @ Xx ) )
% 2.66/1.55 => ( singleton
% 2.66/1.55 @ ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ex1_type,type,
% 2.66/1.55 ex1: $i > ( $i > $o ) > $o ).
% 2.66/1.55
% 2.66/1.55 thf(ex1,definition,
% 2.66/1.55 ( ex1
% 2.66/1.55 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( singleton
% 2.66/1.55 @ ( dsetconstr @ A
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ex1E1_type,type,
% 2.66/1.55 ex1E1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(ex1E1,definition,
% 2.66/1.55 ( ex1E1
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ( ex1 @ A
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 => ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ex1I_type,type,
% 2.66/1.55 ex1I: $o ).
% 2.66/1.55
% 2.66/1.55 thf(ex1I,definition,
% 2.66/1.55 ( ex1I
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ( Xphi @ Xx )
% 2.66/1.55 => ( ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ A )
% 2.66/1.55 => ( ( Xphi @ Xy )
% 2.66/1.55 => ( Xy = Xx ) ) )
% 2.66/1.55 => ( ex1 @ A
% 2.66/1.55 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ex1I2_type,type,
% 2.66/1.55 ex1I2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(ex1I2,definition,
% 2.66/1.55 ( ex1I2
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ A )
% 2.66/1.55 => ( ( Xphi @ Xx )
% 2.66/1.55 => ( ( Xphi @ Xy )
% 2.66/1.55 => ( Xx = Xy ) ) ) ) )
% 2.66/1.55 => ( ? [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 & ( Xphi @ Xx ) )
% 2.66/1.55 => ( ex1 @ A
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(singletonsuniq_type,type,
% 2.66/1.55 singletonsuniq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(singletonsuniq,definition,
% 2.66/1.55 ( singletonsuniq
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( ( setadjoin @ Xx @ emptyset )
% 2.66/1.55 = ( setadjoin @ Xy @ emptyset ) )
% 2.66/1.55 => ( Xx = Xy ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(atmost1p_type,type,
% 2.66/1.55 atmost1p: $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(atleast2p_type,type,
% 2.66/1.55 atleast2p: $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(atmost2p_type,type,
% 2.66/1.55 atmost2p: $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(upairsetp_type,type,
% 2.66/1.55 upairsetp: $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjL1_type,type,
% 2.66/1.55 setukpairinjL1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjL1,definition,
% 2.66/1.55 ( setukpairinjL1
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.66/1.55 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.66/1.55 => ( Xx = Xz ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(kfstsingleton_type,type,
% 2.66/1.55 kfstsingleton: $o ).
% 2.66/1.55
% 2.66/1.55 thf(kfstsingleton,definition,
% 2.66/1.55 ( kfstsingleton
% 2.66/1.55 = ( ! [Xu: $i] :
% 2.66/1.55 ( ( iskpair @ Xu )
% 2.66/1.55 => ( singleton
% 2.66/1.55 @ ( dsetconstr @ ( setunion @ Xu )
% 2.66/1.55 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(theprop_type,type,
% 2.66/1.55 theprop: $o ).
% 2.66/1.55
% 2.66/1.55 thf(theprop,definition,
% 2.66/1.55 ( theprop
% 2.66/1.55 = ( ! [X: $i] :
% 2.66/1.55 ( ( singleton @ X )
% 2.66/1.55 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(kfst_type,type,
% 2.66/1.55 kfst: $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(kfstpairEq_type,type,
% 2.66/1.55 kfstpairEq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(kfstpairEq,definition,
% 2.66/1.55 ( kfstpairEq
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.66/1.55 = Xx ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodfstin_type,type,
% 2.66/1.55 cartprodfstin: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodfstin,definition,
% 2.66/1.55 ( cartprodfstin
% 2.66/1.55 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.66/1.55 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.66/1.55 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjL2_type,type,
% 2.66/1.55 setukpairinjL2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjL2,definition,
% 2.66/1.55 ( setukpairinjL2
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.66/1.55 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.66/1.55 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.66/1.55 => ( Xx = Xz ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjL_type,type,
% 2.66/1.55 setukpairinjL: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjL,definition,
% 2.66/1.55 ( setukpairinjL
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.66/1.55 ( ( ( kpair @ Xx @ Xy )
% 2.66/1.55 = ( kpair @ Xz @ Xu ) )
% 2.66/1.55 => ( Xx = Xz ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjR11_type,type,
% 2.66/1.55 setukpairinjR11: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjR11,definition,
% 2.66/1.55 ( setukpairinjR11
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xx = Xy )
% 2.66/1.55 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.66/1.55 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjR12_type,type,
% 2.66/1.55 setukpairinjR12: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjR12,definition,
% 2.66/1.55 ( setukpairinjR12
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xx = Xy )
% 2.66/1.55 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.66/1.55 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjR1_type,type,
% 2.66/1.55 setukpairinjR1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjR1,definition,
% 2.66/1.55 ( setukpairinjR1
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.66/1.55 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.66/1.55 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.66/1.55 => ( ( Xz = Xu )
% 2.66/1.55 => ( Xy = Xu ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(upairequniteq_type,type,
% 2.66/1.55 upairequniteq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(upairequniteq,definition,
% 2.66/1.55 ( upairequniteq
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.66/1.55 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.66/1.55 = ( setadjoin @ Xz @ emptyset ) )
% 2.66/1.55 => ( Xx = Xy ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjR2_type,type,
% 2.66/1.55 setukpairinjR2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjR2,definition,
% 2.66/1.55 ( setukpairinjR2
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.66/1.55 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.66/1.55 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.66/1.55 => ( Xy = Xu ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjR_type,type,
% 2.66/1.55 setukpairinjR: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setukpairinjR,definition,
% 2.66/1.55 ( setukpairinjR
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.66/1.55 ( ( ( kpair @ Xx @ Xy )
% 2.66/1.55 = ( kpair @ Xz @ Xu ) )
% 2.66/1.55 => ( Xy = Xu ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ksndsingleton_type,type,
% 2.66/1.55 ksndsingleton: $o ).
% 2.66/1.55
% 2.66/1.55 thf(ksndsingleton,definition,
% 2.66/1.55 ( ksndsingleton
% 2.66/1.55 = ( ! [Xu: $i] :
% 2.66/1.55 ( ( iskpair @ Xu )
% 2.66/1.55 => ( singleton
% 2.66/1.55 @ ( dsetconstr @ ( setunion @ Xu )
% 2.66/1.55 @ ^ [Xx: $i] :
% 2.66/1.55 ( Xu
% 2.66/1.55 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ksnd_type,type,
% 2.66/1.55 ksnd: $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(ksndpairEq_type,type,
% 2.66/1.55 ksndpairEq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(ksndpairEq,definition,
% 2.66/1.55 ( ksndpairEq
% 2.66/1.55 = ( ! [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.66/1.55 = Xy ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(kpairsurjEq_type,type,
% 2.66/1.55 kpairsurjEq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(kpairsurjEq,definition,
% 2.66/1.55 ( kpairsurjEq
% 2.66/1.55 = ( ! [Xu: $i] :
% 2.66/1.55 ( ( iskpair @ Xu )
% 2.66/1.55 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.66/1.55 = Xu ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodsndin_type,type,
% 2.66/1.55 cartprodsndin: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodsndin,definition,
% 2.66/1.55 ( cartprodsndin
% 2.66/1.55 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.66/1.55 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.66/1.55 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodpairmemEL_type,type,
% 2.66/1.55 cartprodpairmemEL: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodpairmemEL,definition,
% 2.66/1.55 ( cartprodpairmemEL
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.66/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodpairmemER_type,type,
% 2.66/1.55 cartprodpairmemER: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodpairmemER,definition,
% 2.66/1.55 ( cartprodpairmemER
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.66/1.55 => ( in @ Xy @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodmempaircEq_type,type,
% 2.66/1.55 cartprodmempaircEq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodmempaircEq,definition,
% 2.66/1.55 ( cartprodmempaircEq
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( ( kpair @ Xx @ Xy )
% 2.66/1.55 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodfstpairEq_type,type,
% 2.66/1.55 cartprodfstpairEq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodfstpairEq,definition,
% 2.66/1.55 ( cartprodfstpairEq
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.66/1.55 = Xx ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodsndpairEq_type,type,
% 2.66/1.55 cartprodsndpairEq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodsndpairEq,definition,
% 2.66/1.55 ( cartprodsndpairEq
% 2.66/1.55 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.66/1.55 = Xy ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodpairsurjEq_type,type,
% 2.66/1.55 cartprodpairsurjEq: $o ).
% 2.66/1.55
% 2.66/1.55 thf(cartprodpairsurjEq,definition,
% 2.66/1.55 ( cartprodpairsurjEq
% 2.66/1.55 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.66/1.55 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.66/1.55 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.66/1.55 = Xu ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(breln_type,type,
% 2.66/1.55 breln: $i > $i > $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(breln,definition,
% 2.66/1.55 ( breln
% 2.66/1.55 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstr_type,type,
% 2.66/1.55 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrI_type,type,
% 2.66/1.55 dpsetconstrI: $o ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrI,definition,
% 2.66/1.55 ( dpsetconstrI
% 2.66/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( ( Xphi @ Xx @ Xy )
% 2.66/1.55 => ( in @ ( kpair @ Xx @ Xy )
% 2.66/1.55 @ ( dpsetconstr @ A @ B
% 2.66/1.55 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrSub_type,type,
% 2.66/1.55 dpsetconstrSub: $o ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrSub,definition,
% 2.66/1.55 ( dpsetconstrSub
% 2.66/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.66/1.55 ( subset
% 2.66/1.55 @ ( dpsetconstr @ A @ B
% 2.66/1.55 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.66/1.55 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(setOfPairsIsBReln_type,type,
% 2.66/1.55 setOfPairsIsBReln: $o ).
% 2.66/1.55
% 2.66/1.55 thf(setOfPairsIsBReln,definition,
% 2.66/1.55 ( setOfPairsIsBReln
% 2.66/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.66/1.55 ( breln @ A @ B
% 2.66/1.55 @ ( dpsetconstr @ A @ B
% 2.66/1.55 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrERa_type,type,
% 2.66/1.55 dpsetconstrERa: $o ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrERa,definition,
% 2.66/1.55 ( dpsetconstrERa
% 2.66/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.66/1.55 @ ( dpsetconstr @ A @ B
% 2.66/1.55 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.66/1.55 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrEL1_type,type,
% 2.66/1.55 dpsetconstrEL1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrEL1,definition,
% 2.66/1.55 ( dpsetconstrEL1
% 2.66/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ ( kpair @ Xx @ Xy )
% 2.66/1.55 @ ( dpsetconstr @ A @ B
% 2.66/1.55 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.66/1.55 => ( in @ Xx @ A ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrEL2_type,type,
% 2.66/1.55 dpsetconstrEL2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrEL2,definition,
% 2.66/1.55 ( dpsetconstrEL2
% 2.66/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ ( kpair @ Xx @ Xy )
% 2.66/1.55 @ ( dpsetconstr @ A @ B
% 2.66/1.55 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.66/1.55 => ( in @ Xy @ B ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrER_type,type,
% 2.66/1.55 dpsetconstrER: $o ).
% 2.66/1.55
% 2.66/1.55 thf(dpsetconstrER,definition,
% 2.66/1.55 ( dpsetconstrER
% 2.66/1.55 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( in @ ( kpair @ Xx @ Xy )
% 2.66/1.55 @ ( dpsetconstr @ A @ B
% 2.66/1.55 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.66/1.55 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(func_type,type,
% 2.66/1.55 func: $i > $i > $i > $o ).
% 2.66/1.55
% 2.66/1.55 thf(func,definition,
% 2.66/1.55 ( func
% 2.66/1.55 = ( ^ [A: $i,B: $i,R: $i] :
% 2.66/1.55 ( ( breln @ A @ B @ R )
% 2.66/1.55 & ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ex1 @ B
% 2.66/1.55 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(funcSet_type,type,
% 2.66/1.55 funcSet: $i > $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(funcImageSingleton_type,type,
% 2.66/1.55 funcImageSingleton: $o ).
% 2.66/1.55
% 2.66/1.55 thf(funcImageSingleton,definition,
% 2.66/1.55 ( funcImageSingleton
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.66/1.55 ( ( func @ A @ B @ Xf )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( singleton
% 2.66/1.55 @ ( dsetconstr @ B
% 2.66/1.55 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(apProp_type,type,
% 2.66/1.55 apProp: $o ).
% 2.66/1.55
% 2.66/1.55 thf(apProp,definition,
% 2.66/1.55 ( apProp
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.66/1.55 ( ( func @ A @ B @ Xf )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in
% 2.66/1.55 @ ( setunion
% 2.66/1.55 @ ( dsetconstr @ B
% 2.66/1.55 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.66/1.55 @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ap_type,type,
% 2.66/1.55 ap: $i > $i > $i > $i > $i ).
% 2.66/1.55
% 2.66/1.55 thf(app_type,type,
% 2.66/1.55 app: $o ).
% 2.66/1.55
% 2.66/1.55 thf(app,definition,
% 2.66/1.55 ( app
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.66/1.55 ( ( func @ A @ B @ Xf )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(infuncsetfunc_type,type,
% 2.66/1.55 infuncsetfunc: $o ).
% 2.66/1.55
% 2.66/1.55 thf(infuncsetfunc,definition,
% 2.66/1.55 ( infuncsetfunc
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.66/1.55 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.66/1.55 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ap2p_type,type,
% 2.66/1.55 ap2p: $o ).
% 2.66/1.55
% 2.66/1.55 thf(ap2p,definition,
% 2.66/1.55 ( ap2p
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.66/1.55 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(funcinfuncset_type,type,
% 2.66/1.55 funcinfuncset: $o ).
% 2.66/1.55
% 2.66/1.55 thf(funcinfuncset,definition,
% 2.66/1.55 ( funcinfuncset
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.66/1.55 ( ( func @ A @ B @ Xf )
% 2.66/1.55 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(lamProp_type,type,
% 2.66/1.55 lamProp: $o ).
% 2.66/1.55
% 2.66/1.55 thf(lamProp,definition,
% 2.66/1.55 ( lamProp
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.66/1.55 => ( func @ A @ B
% 2.66/1.55 @ ( dpsetconstr @ A @ B
% 2.66/1.55 @ ^ [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xf @ Xx )
% 2.66/1.55 = Xy ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(lam_type,type,
% 2.66/1.55 lam: $i > $i > ( $i > $i ) > $i ).
% 2.66/1.55
% 2.66/1.55 thf(lam,definition,
% 2.66/1.55 ( lam
% 2.66/1.55 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 2.66/1.55 ( dpsetconstr @ A @ B
% 2.66/1.55 @ ^ [Xx: $i,Xy: $i] :
% 2.66/1.55 ( ( Xf @ Xx )
% 2.66/1.55 = Xy ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(lamp_type,type,
% 2.66/1.55 lamp: $o ).
% 2.66/1.55
% 2.66/1.55 thf(lamp,definition,
% 2.66/1.55 ( lamp
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.66/1.55 => ( func @ A @ B
% 2.66/1.55 @ ( lam @ A @ B
% 2.66/1.55 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(lam2p_type,type,
% 2.66/1.55 lam2p: $o ).
% 2.66/1.55
% 2.66/1.55 thf(lam2p,definition,
% 2.66/1.55 ( lam2p
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.66/1.55 => ( in
% 2.66/1.55 @ ( lam @ A @ B
% 2.66/1.55 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.66/1.55 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(brelnall1_type,type,
% 2.66/1.55 brelnall1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(brelnall1,definition,
% 2.66/1.55 ( brelnall1
% 2.66/1.55 = ( ! [A: $i,B: $i,R: $i] :
% 2.66/1.55 ( ( breln @ A @ B @ R )
% 2.66/1.55 => ! [Xphi: $i > $o] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.66/1.55 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ R )
% 2.66/1.55 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(brelnall2_type,type,
% 2.66/1.55 brelnall2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(brelnall2,definition,
% 2.66/1.55 ( brelnall2
% 2.66/1.55 = ( ! [A: $i,B: $i,R: $i] :
% 2.66/1.55 ( ( breln @ A @ B @ R )
% 2.66/1.55 => ! [Xphi: $i > $o] :
% 2.66/1.55 ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.66/1.55 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ R )
% 2.66/1.55 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(ex1E2_type,type,
% 2.66/1.55 ex1E2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(ex1E2,definition,
% 2.66/1.55 ( ex1E2
% 2.66/1.55 = ( ! [A: $i,Xphi: $i > $o] :
% 2.66/1.55 ( ( ex1 @ A
% 2.66/1.55 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ A )
% 2.66/1.55 => ( ( Xphi @ Xx )
% 2.66/1.55 => ( ( Xphi @ Xy )
% 2.66/1.55 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(funcGraphProp1_type,type,
% 2.66/1.55 funcGraphProp1: $o ).
% 2.66/1.55
% 2.66/1.55 thf(funcGraphProp1,definition,
% 2.66/1.55 ( funcGraphProp1
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.66/1.55 ( ( func @ A @ B @ Xf )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(funcGraphProp3_type,type,
% 2.66/1.55 funcGraphProp3: $o ).
% 2.66/1.55
% 2.66/1.55 thf(funcGraphProp3,definition,
% 2.66/1.55 ( funcGraphProp3
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.66/1.55 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(funcGraphProp2_type,type,
% 2.66/1.55 funcGraphProp2: $o ).
% 2.66/1.55
% 2.66/1.55 thf(funcGraphProp2,definition,
% 2.66/1.55 ( funcGraphProp2
% 2.66/1.55 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.66/1.55 ( ( func @ A @ B @ Xf )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.66/1.55 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.66/1.55 = Xy ) ) ) ) ) ) ) ).
% 2.66/1.55
% 2.66/1.55 thf(funcextLem,conjecture,
% 2.66/1.55 ( setextAx
% 2.66/1.55 => ( emptysetAx
% 2.66/1.55 => ( setadjoinAx
% 2.66/1.55 => ( powersetAx
% 2.66/1.55 => ( setunionAx
% 2.66/1.55 => ( omega0Ax
% 2.66/1.55 => ( omegaSAx
% 2.66/1.55 => ( omegaIndAx
% 2.66/1.55 => ( replAx
% 2.66/1.55 => ( foundationAx
% 2.66/1.55 => ( wellorderingAx
% 2.66/1.55 => ( descrp
% 2.66/1.55 => ( dsetconstrI
% 2.66/1.55 => ( dsetconstrEL
% 2.66/1.55 => ( dsetconstrER
% 2.66/1.55 => ( exuE1
% 2.66/1.55 => ( prop2setE
% 2.66/1.55 => ( emptysetE
% 2.66/1.55 => ( emptysetimpfalse
% 2.66/1.55 => ( notinemptyset
% 2.66/1.55 => ( exuE3e
% 2.66/1.55 => ( setext
% 2.66/1.55 => ( emptyI
% 2.66/1.55 => ( noeltsimpempty
% 2.66/1.55 => ( setbeta
% 2.66/1.55 => ( nonemptyE1
% 2.66/1.55 => ( nonemptyI
% 2.66/1.55 => ( nonemptyI1
% 2.66/1.55 => ( setadjoinIL
% 2.66/1.55 => ( emptyinunitempty
% 2.66/1.55 => ( setadjoinIR
% 2.66/1.55 => ( setadjoinE
% 2.66/1.55 => ( setadjoinOr
% 2.66/1.55 => ( setoftrueEq
% 2.66/1.55 => ( powersetI
% 2.66/1.55 => ( emptyinPowerset
% 2.66/1.55 => ( emptyInPowerset
% 2.66/1.55 => ( powersetE
% 2.66/1.55 => ( setunionI
% 2.66/1.55 => ( setunionE
% 2.66/1.55 => ( subPowSU
% 2.66/1.55 => ( exuE2
% 2.66/1.55 => ( nonemptyImpWitness
% 2.66/1.55 => ( uniqinunit
% 2.66/1.55 => ( notinsingleton
% 2.66/1.55 => ( eqinunit
% 2.66/1.55 => ( singletonsswitch
% 2.66/1.55 => ( upairsetE
% 2.66/1.55 => ( upairsetIL
% 2.66/1.55 => ( upairsetIR
% 2.66/1.55 => ( emptyE1
% 2.66/1.55 => ( vacuousDall
% 2.66/1.55 => ( quantDeMorgan1
% 2.66/1.55 => ( quantDeMorgan2
% 2.66/1.55 => ( quantDeMorgan3
% 2.66/1.55 => ( quantDeMorgan4
% 2.66/1.55 => ( prop2setI
% 2.66/1.55 => ( prop2set2propI
% 2.66/1.55 => ( notdexE
% 2.66/1.55 => ( notdallE
% 2.66/1.55 => ( exuI1
% 2.66/1.55 => ( exuI3
% 2.66/1.55 => ( exuI2
% 2.66/1.55 => ( inCongP
% 2.66/1.55 => ( in__Cong
% 2.66/1.55 => ( exuE3u
% 2.66/1.55 => ( exu__Cong
% 2.66/1.55 => ( emptyset__Cong
% 2.66/1.55 => ( setadjoin__Cong
% 2.66/1.55 => ( powerset__Cong
% 2.66/1.55 => ( setunion__Cong
% 2.66/1.55 => ( omega__Cong
% 2.66/1.55 => ( exuEu
% 2.66/1.55 => ( descr__Cong
% 2.66/1.55 => ( dsetconstr__Cong
% 2.66/1.55 => ( subsetI1
% 2.66/1.55 => ( eqimpsubset2
% 2.66/1.55 => ( eqimpsubset1
% 2.66/1.55 => ( subsetI2
% 2.66/1.55 => ( emptysetsubset
% 2.66/1.55 => ( subsetE
% 2.66/1.55 => ( subsetE2
% 2.66/1.55 => ( notsubsetI
% 2.66/1.55 => ( notequalI1
% 2.66/1.55 => ( notequalI2
% 2.66/1.55 => ( subsetRefl
% 2.66/1.55 => ( subsetTrans
% 2.66/1.55 => ( setadjoinSub
% 2.66/1.55 => ( setadjoinSub2
% 2.66/1.55 => ( subset2powerset
% 2.66/1.55 => ( setextsub
% 2.66/1.55 => ( subsetemptysetimpeq
% 2.66/1.55 => ( powersetI1
% 2.66/1.55 => ( powersetE1
% 2.66/1.55 => ( inPowerset
% 2.66/1.55 => ( powersetsubset
% 2.66/1.55 => ( sepInPowerset
% 2.66/1.55 => ( sepSubset
% 2.66/1.55 => ( binunionIL
% 2.66/1.55 => ( upairset2IR
% 2.66/1.55 => ( binunionIR
% 2.66/1.55 => ( binunionEcases
% 2.66/1.55 => ( binunionE
% 2.66/1.55 => ( binunionLsub
% 2.66/1.55 => ( binunionRsub
% 2.66/1.55 => ( binintersectI
% 2.66/1.55 => ( binintersectSubset5
% 2.66/1.55 => ( binintersectEL
% 2.66/1.55 => ( binintersectLsub
% 2.66/1.55 => ( binintersectSubset2
% 2.66/1.55 => ( binintersectSubset3
% 2.66/1.55 => ( binintersectER
% 2.66/1.55 => ( disjointsetsI1
% 2.66/1.55 => ( binintersectRsub
% 2.66/1.55 => ( binintersectSubset4
% 2.66/1.55 => ( binintersectSubset1
% 2.66/1.55 => ( bs114d
% 2.66/1.55 => ( setminusI
% 2.66/1.55 => ( setminusEL
% 2.66/1.55 => ( setminusER
% 2.66/1.55 => ( setminusSubset2
% 2.66/1.55 => ( setminusERneg
% 2.66/1.55 => ( setminusELneg
% 2.66/1.55 => ( setminusILneg
% 2.66/1.55 => ( setminusIRneg
% 2.66/1.55 => ( setminusLsub
% 2.66/1.55 => ( setminusSubset1
% 2.66/1.55 => ( symdiffE
% 2.66/1.55 => ( symdiffI1
% 2.66/1.55 => ( symdiffI2
% 2.66/1.55 => ( symdiffIneg1
% 2.66/1.55 => ( symdiffIneg2
% 2.66/1.55 => ( secondinupair
% 2.66/1.55 => ( setukpairIL
% 2.66/1.55 => ( setukpairIR
% 2.66/1.55 => ( kpairiskpair
% 2.66/1.55 => ( kpairp
% 2.66/1.55 => ( singletonsubset
% 2.66/1.55 => ( singletoninpowerset
% 2.66/1.55 => ( singletoninpowunion
% 2.66/1.55 => ( upairset2E
% 2.66/1.55 => ( upairsubunion
% 2.66/1.55 => ( upairinpowunion
% 2.66/1.55 => ( ubforcartprodlem1
% 2.66/1.55 => ( ubforcartprodlem2
% 2.66/1.55 => ( ubforcartprodlem3
% 2.66/1.55 => ( cartprodpairin
% 2.66/1.55 => ( cartprodmempair1
% 2.66/1.55 => ( cartprodmempair
% 2.66/1.55 => ( setunionE2
% 2.66/1.55 => ( setunionsingleton1
% 2.66/1.55 => ( setunionsingleton2
% 2.66/1.55 => ( setunionsingleton
% 2.66/1.55 => ( singletonprop
% 2.66/1.55 => ( ex1E1
% 2.66/1.55 => ( ex1I
% 2.66/1.55 => ( ex1I2
% 2.66/1.55 => ( singletonsuniq
% 2.66/1.55 => ( setukpairinjL1
% 2.66/1.55 => ( kfstsingleton
% 2.66/1.55 => ( theprop
% 2.66/1.55 => ( kfstpairEq
% 2.66/1.55 => ( cartprodfstin
% 2.66/1.55 => ( setukpairinjL2
% 2.66/1.55 => ( setukpairinjL
% 2.66/1.55 => ( setukpairinjR11
% 2.66/1.55 => ( setukpairinjR12
% 2.66/1.55 => ( setukpairinjR1
% 2.66/1.55 => ( upairequniteq
% 2.66/1.55 => ( setukpairinjR2
% 2.66/1.55 => ( setukpairinjR
% 2.66/1.55 => ( ksndsingleton
% 2.66/1.55 => ( ksndpairEq
% 2.66/1.55 => ( kpairsurjEq
% 2.66/1.55 => ( cartprodsndin
% 2.66/1.55 => ( cartprodpairmemEL
% 2.66/1.55 => ( cartprodpairmemER
% 2.66/1.55 => ( cartprodmempaircEq
% 2.66/1.55 => ( cartprodfstpairEq
% 2.66/1.55 => ( cartprodsndpairEq
% 2.66/1.55 => ( cartprodpairsurjEq
% 2.66/1.55 => ( dpsetconstrI
% 2.66/1.55 => ( dpsetconstrSub
% 2.66/1.55 => ( setOfPairsIsBReln
% 2.66/1.55 => ( dpsetconstrERa
% 2.66/1.55 => ( dpsetconstrEL1
% 2.66/1.55 => ( dpsetconstrEL2
% 2.66/1.55 => ( dpsetconstrER
% 2.66/1.55 => ( funcImageSingleton
% 2.66/1.55 => ( apProp
% 2.66/1.55 => ( app
% 2.66/1.55 => ( infuncsetfunc
% 2.66/1.55 => ( ap2p
% 2.66/1.55 => ( funcinfuncset
% 2.66/1.55 => ( lamProp
% 2.66/1.55 => ( lamp
% 2.66/1.55 => ( lam2p
% 2.66/1.55 => ( brelnall1
% 2.66/1.55 => ( brelnall2
% 2.66/1.55 => ( ex1E2
% 2.66/1.55 => ( funcGraphProp1
% 2.66/1.55 => ( funcGraphProp3
% 2.66/1.55 => ( funcGraphProp2
% 2.66/1.55 => ! [A: $i,B: $i,Xf: $i] :
% 2.66/1.55 ( ( func @ A @ B @ Xf )
% 2.66/1.55 => ! [Xg: $i] :
% 2.66/1.55 ( ( func @ A @ B @ Xg )
% 2.66/1.55 => ( ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.66/1.55 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.66/1.55 => ! [Xx: $i] :
% 2.66/1.55 ( ( in @ Xx @ A )
% 2.66/1.55 => ! [Xy: $i] :
% 2.66/1.55 ( ( in @ Xy @ B )
% 2.66/1.55 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.66/1.55 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.66/1.55 ------------------------
% 2.66/1.58 % (24066)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_23745 for (2999ds/2Mi)
% 2.66/1.58 % (24063)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_23745 for (2999ds/4Mi)
% 2.66/1.58 % (24065)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/2Mi)
% 2.66/1.58 % (24065)Instruction limit reached!
% 2.66/1.58 % (24065)------------------------------
% 2.66/1.58 % (24065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.58 % (24065)Termination reason: Unknown
% 2.66/1.58 % (24065)Termination phase: shuffling
% 2.66/1.58
% 2.66/1.58 % (24065)Memory used [KB]: 1407
% 2.66/1.58 % (24065)Time elapsed: 0.002 s
% 2.66/1.58 % (24065)Instructions burned: 3 (million)
% 2.66/1.58 % (24065)------------------------------
% 2.66/1.58 % (24065)------------------------------
% 2.66/1.58 % (24066)Instruction limit reached!
% 2.66/1.58 % (24066)------------------------------
% 2.66/1.58 % (24066)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.58 % (24066)Termination reason: Unknown
% 2.66/1.58 % (24066)Termination phase: shuffling
% 2.66/1.58
% 2.66/1.58 % (24066)Memory used [KB]: 1407
% 2.66/1.58 % (24066)Time elapsed: 0.003 s
% 2.66/1.58 % (24066)Instructions burned: 5 (million)
% 2.66/1.58 % (24066)------------------------------
% 2.66/1.58 % (24066)------------------------------
% 2.66/1.58 % (24063)Instruction limit reached!
% 2.66/1.58 % (24063)------------------------------
% 2.66/1.58 % (24063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.58 % (24063)Termination reason: Unknown
% 2.66/1.58 % (24063)Termination phase: shuffling
% 2.66/1.58
% 2.66/1.58 % (24063)Memory used [KB]: 1407
% 2.66/1.58 % (24063)Time elapsed: 0.003 s
% 2.66/1.58 % (24063)Instructions burned: 7 (million)
% 2.66/1.58 % (24063)------------------------------
% 2.66/1.58 % (24063)------------------------------
% 2.66/1.59 % (24062)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/183Mi)
% 2.66/1.59 % (24064)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_23745 for (2999ds/27Mi)
% 2.66/1.59 % (24067)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_23745 for (2999ds/275Mi)
% 2.66/1.59 % (24068)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/18Mi)
% 2.66/1.59 % (24069)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/3Mi)
% 2.66/1.59 % (24070)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_23745 for (2999ds/37Mi)
% 2.66/1.59 % (24069)Instruction limit reached!
% 2.66/1.59 % (24069)------------------------------
% 2.66/1.59 % (24069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.66/1.59 % (24069)Termination reason: Unknown
% 2.66/1.59 % (24069)Termination phase: shuffling
% 2.66/1.59
% 2.66/1.59 % (24069)Memory used [KB]: 1407
% 2.66/1.59 % (24069)Time elapsed: 0.002 s
% 2.66/1.59 % (24069)Instructions burned: 3 (million)
% 2.66/1.59 % (24069)------------------------------
% 2.66/1.59 % (24069)------------------------------
% 2.66/1.59 % (24071)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_23745 for (2999ds/15Mi)
% 2.72/1.60 % (24071)Instruction limit reached!
% 2.72/1.60 % (24071)------------------------------
% 2.72/1.60 % (24071)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.60 % (24071)Termination reason: Unknown
% 2.72/1.60 % (24071)Termination phase: shuffling
% 2.72/1.60
% 2.72/1.60 % (24071)Memory used [KB]: 1663
% 2.72/1.60 % (24071)Time elapsed: 0.007 s
% 2.72/1.60 % (24071)Instructions burned: 15 (million)
% 2.72/1.60 % (24071)------------------------------
% 2.72/1.60 % (24071)------------------------------
% 2.72/1.60 % (24068)Instruction limit reached!
% 2.72/1.60 % (24068)------------------------------
% 2.72/1.60 % (24068)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.60 % (24068)Termination reason: Unknown
% 2.72/1.60 % (24068)Termination phase: shuffling
% 2.72/1.60
% 2.72/1.60 % (24068)Memory used [KB]: 1663
% 2.72/1.60 % (24068)Time elapsed: 0.014 s
% 2.72/1.60 % (24068)Instructions burned: 19 (million)
% 2.72/1.60 % (24068)------------------------------
% 2.72/1.60 % (24068)------------------------------
% 2.72/1.60 % (24070)Instruction limit reached!
% 2.72/1.60 % (24070)------------------------------
% 2.72/1.60 % (24070)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.60 % (24070)Termination reason: Unknown
% 2.72/1.60 % (24070)Termination phase: Property scanning
% 2.72/1.60
% 2.72/1.60 % (24070)Memory used [KB]: 2174
% 2.72/1.60 % (24070)Time elapsed: 0.011 s
% 2.72/1.60 % (24070)Instructions burned: 37 (million)
% 2.72/1.60 % (24070)------------------------------
% 2.72/1.60 % (24070)------------------------------
% 2.72/1.60 % (24072)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_23745 for (2999ds/3Mi)
% 2.72/1.60 % (24064)Instruction limit reached!
% 2.72/1.60 % (24064)------------------------------
% 2.72/1.60 % (24064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.60 % (24064)Termination reason: Unknown
% 2.72/1.60 % (24064)Termination phase: shuffling
% 2.72/1.60
% 2.72/1.60 % (24064)Memory used [KB]: 1918
% 2.72/1.60 % (24064)Time elapsed: 0.016 s
% 2.72/1.60 % (24064)Instructions burned: 27 (million)
% 2.72/1.60 % (24064)------------------------------
% 2.72/1.60 % (24064)------------------------------
% 2.72/1.60 % (24072)Instruction limit reached!
% 2.72/1.60 % (24072)------------------------------
% 2.72/1.60 % (24072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.60 % (24072)Termination reason: Unknown
% 2.72/1.60 % (24072)Termination phase: shuffling
% 2.72/1.60
% 2.72/1.60 % (24072)Memory used [KB]: 1407
% 2.72/1.60 % (24072)Time elapsed: 0.002 s
% 2.72/1.60 % (24072)Instructions burned: 4 (million)
% 2.72/1.60 % (24072)------------------------------
% 2.72/1.60 % (24072)------------------------------
% 2.72/1.61 % (24073)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_23745 for (2999ds/1041Mi)
% 2.72/1.61 % (24075)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/16Mi)
% 2.72/1.61 % (24077)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_23745 for (2999ds/3Mi)
% 2.72/1.61 % (24077)Instruction limit reached!
% 2.72/1.61 % (24077)------------------------------
% 2.72/1.61 % (24077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.61 % (24077)Termination reason: Unknown
% 2.72/1.61 % (24077)Termination phase: shuffling
% 2.72/1.61
% 2.72/1.61 % (24077)Memory used [KB]: 1407
% 2.72/1.61 % (24077)Time elapsed: 0.002 s
% 2.72/1.61 % (24077)Instructions burned: 3 (million)
% 2.72/1.61 % (24077)------------------------------
% 2.72/1.61 % (24077)------------------------------
% 2.72/1.62 % (24075)Instruction limit reached!
% 2.72/1.62 % (24075)------------------------------
% 2.72/1.62 % (24075)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.62 % (24075)Termination reason: Unknown
% 2.72/1.62 % (24075)Termination phase: shuffling
% 2.72/1.62
% 2.72/1.62 % (24075)Memory used [KB]: 1791
% 2.72/1.62 % (24075)Time elapsed: 0.006 s
% 2.72/1.62 % (24075)Instructions burned: 18 (million)
% 2.72/1.62 % (24075)------------------------------
% 2.72/1.62 % (24075)------------------------------
% 2.72/1.62 % (24074)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/7Mi)
% 2.72/1.62 % (24076)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_23745 for (2999ds/3Mi)
% 2.72/1.62 % (24076)Instruction limit reached!
% 2.72/1.62 % (24076)------------------------------
% 2.72/1.62 % (24076)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.62 % (24076)Termination reason: Unknown
% 2.72/1.62 % (24076)Termination phase: shuffling
% 2.72/1.62
% 2.72/1.62 % (24076)Memory used [KB]: 1407
% 2.72/1.62 % (24076)Time elapsed: 0.004 s
% 2.72/1.62 % (24076)Instructions burned: 4 (million)
% 2.72/1.62 % (24076)------------------------------
% 2.72/1.62 % (24076)------------------------------
% 2.72/1.62 % (24074)Instruction limit reached!
% 2.72/1.62 % (24074)------------------------------
% 2.72/1.62 % (24074)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.62 % (24074)Termination reason: Unknown
% 2.72/1.62 % (24074)Termination phase: shuffling
% 2.72/1.62
% 2.72/1.62 % (24074)Memory used [KB]: 1535
% 2.72/1.62 % (24074)Time elapsed: 0.006 s
% 2.72/1.62 % (24074)Instructions burned: 8 (million)
% 2.72/1.62 % (24074)------------------------------
% 2.72/1.62 % (24074)------------------------------
% 2.72/1.62 % (24078)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/7Mi)
% 2.72/1.63 % (24078)Instruction limit reached!
% 2.72/1.63 % (24078)------------------------------
% 2.72/1.63 % (24078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.63 % (24078)Termination reason: Unknown
% 2.72/1.63 % (24078)Termination phase: shuffling
% 2.72/1.63
% 2.72/1.63 % (24078)Memory used [KB]: 1407
% 2.72/1.63 % (24078)Time elapsed: 0.003 s
% 2.72/1.63 % (24078)Instructions burned: 7 (million)
% 2.72/1.63 % (24078)------------------------------
% 2.72/1.63 % (24078)------------------------------
% 2.72/1.63 % (24079)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/3Mi)
% 2.72/1.63 % (24079)Instruction limit reached!
% 2.72/1.63 % (24079)------------------------------
% 2.72/1.63 % (24079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.63 % (24079)Termination reason: Unknown
% 2.72/1.63 % (24079)Termination phase: shuffling
% 2.72/1.63
% 2.72/1.63 % (24079)Memory used [KB]: 1407
% 2.72/1.63 % (24079)Time elapsed: 0.002 s
% 2.72/1.63 % (24079)Instructions burned: 4 (million)
% 2.72/1.63 % (24079)------------------------------
% 2.72/1.63 % (24079)------------------------------
% 2.72/1.64 % (24082)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/710Mi)
% 2.72/1.64 % (24083)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/6Mi)
% 2.72/1.64 % (24083)Instruction limit reached!
% 2.72/1.64 % (24083)------------------------------
% 2.72/1.64 % (24083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.64 % (24083)Termination reason: Unknown
% 2.72/1.64 % (24083)Termination phase: shuffling
% 2.72/1.64
% 2.72/1.64 % (24083)Memory used [KB]: 1535
% 2.72/1.64 % (24083)Time elapsed: 0.003 s
% 2.72/1.64 % (24083)Instructions burned: 8 (million)
% 2.72/1.64 % (24083)------------------------------
% 2.72/1.64 % (24083)------------------------------
% 2.72/1.64 % (24080)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/4Mi)
% 2.72/1.64 % (24081)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/18Mi)
% 2.72/1.64 % (24080)Instruction limit reached!
% 2.72/1.64 % (24080)------------------------------
% 2.72/1.64 % (24080)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.64 % (24080)Termination reason: Unknown
% 2.72/1.64 % (24080)Termination phase: shuffling
% 2.72/1.64
% 2.72/1.64 % (24080)Memory used [KB]: 1407
% 2.72/1.64 % (24080)Time elapsed: 0.004 s
% 2.72/1.64 % (24080)Instructions burned: 4 (million)
% 2.72/1.64 % (24080)------------------------------
% 2.72/1.64 % (24080)------------------------------
% 2.72/1.65 % (24084)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_23745 for (2999ds/902Mi)
% 2.72/1.65 % (24081)Instruction limit reached!
% 2.72/1.65 % (24081)------------------------------
% 2.72/1.65 % (24081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.65 % (24081)Termination reason: Unknown
% 2.72/1.65 % (24081)Termination phase: shuffling
% 2.72/1.65
% 2.72/1.65 % (24081)Memory used [KB]: 1791
% 2.72/1.65 % (24081)Time elapsed: 0.011 s
% 2.72/1.65 % (24081)Instructions burned: 19 (million)
% 2.72/1.65 % (24081)------------------------------
% 2.72/1.65 % (24081)------------------------------
% 2.72/1.66 % (24085)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_23745 for (2999ds/21Mi)
% 2.72/1.66 % (24086)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/5Mi)
% 2.72/1.66 % (24085)Instruction limit reached!
% 2.72/1.66 % (24085)------------------------------
% 2.72/1.66 % (24085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.66 % (24085)Termination reason: Unknown
% 2.72/1.66 % (24085)Termination phase: shuffling
% 2.72/1.66
% 2.72/1.66 % (24085)Memory used [KB]: 1791
% 2.72/1.66 % (24085)Time elapsed: 0.009 s
% 2.72/1.66 % (24085)Instructions burned: 22 (million)
% 2.72/1.66 % (24085)------------------------------
% 2.72/1.66 % (24085)------------------------------
% 2.72/1.66 % (24086)Instruction limit reached!
% 2.72/1.66 % (24086)------------------------------
% 2.72/1.66 % (24086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.66 % (24086)Termination reason: Unknown
% 2.72/1.66 % (24086)Termination phase: shuffling
% 2.72/1.66
% 2.72/1.66 % (24086)Memory used [KB]: 1407
% 2.72/1.66 % (24086)Time elapsed: 0.003 s
% 2.72/1.66 % (24086)Instructions burned: 5 (million)
% 2.72/1.66 % (24086)------------------------------
% 2.72/1.66 % (24086)------------------------------
% 2.72/1.67 % (24087)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_23745 for (2999ds/6Mi)
% 2.72/1.68 % (24088)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_23745 for (2999ds/377Mi)
% 2.72/1.68 % (24087)Instruction limit reached!
% 2.72/1.68 % (24087)------------------------------
% 2.72/1.68 % (24087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.68 % (24087)Termination reason: Unknown
% 2.72/1.68 % (24087)Termination phase: shuffling
% 2.72/1.68
% 2.72/1.68 % (24087)Memory used [KB]: 1407
% 2.72/1.68 % (24087)Time elapsed: 0.003 s
% 2.72/1.68 % (24087)Instructions burned: 6 (million)
% 2.72/1.68 % (24087)------------------------------
% 2.72/1.68 % (24087)------------------------------
% 2.72/1.68 % (24062)Instruction limit reached!
% 2.72/1.68 % (24062)------------------------------
% 2.72/1.68 % (24062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.68 % (24062)Termination reason: Unknown
% 2.72/1.68 % (24062)Termination phase: Saturation
% 2.72/1.68
% 2.72/1.68 % (24062)Memory used [KB]: 7547
% 2.72/1.68 % (24062)Time elapsed: 0.090 s
% 2.72/1.68 % (24062)Instructions burned: 185 (million)
% 2.72/1.68 % (24062)------------------------------
% 2.72/1.68 % (24062)------------------------------
% 2.72/1.69 % (24089)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_23745 for (2998ds/779Mi)
% 2.72/1.69 % (24090)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_23745 for (2998ds/19Mi)
% 2.72/1.69 % (24090)Instruction limit reached!
% 2.72/1.69 % (24090)------------------------------
% 2.72/1.69 % (24090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.69 % (24090)Termination reason: Unknown
% 2.72/1.69 % (24090)Termination phase: shuffling
% 2.72/1.69
% 2.72/1.69 % (24090)Memory used [KB]: 1791
% 2.72/1.69 % (24090)Time elapsed: 0.007 s
% 2.72/1.69 % (24090)Instructions burned: 19 (million)
% 2.72/1.69 % (24090)------------------------------
% 2.72/1.69 % (24090)------------------------------
% 2.72/1.70 % (24067)Instruction limit reached!
% 2.72/1.70 % (24067)------------------------------
% 2.72/1.70 % (24067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.70 % (24067)Termination reason: Unknown
% 2.72/1.70 % (24067)Termination phase: Saturation
% 2.72/1.70
% 2.72/1.70 % (24067)Memory used [KB]: 8699
% 2.72/1.70 % (24067)Time elapsed: 0.109 s
% 2.72/1.70 % (24067)Instructions burned: 277 (million)
% 2.72/1.70 % (24067)------------------------------
% 2.72/1.70 % (24067)------------------------------
% 2.72/1.70 % (24091)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_23745 for (2998ds/879Mi)
% 2.72/1.71 % (24092)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_23745 for (2998ds/17Mi)
% 2.72/1.71 % (24092)Instruction limit reached!
% 2.72/1.71 % (24092)------------------------------
% 2.72/1.71 % (24092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.71 % (24092)Termination reason: Unknown
% 2.72/1.71 % (24092)Termination phase: shuffling
% 2.72/1.71
% 2.72/1.71 % (24092)Memory used [KB]: 1791
% 2.72/1.71 % (24092)Time elapsed: 0.006 s
% 2.72/1.71 % (24092)Instructions burned: 17 (million)
% 2.72/1.71 % (24092)------------------------------
% 2.72/1.71 % (24092)------------------------------
% 2.72/1.72 % (24093)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_23745 for (2998ds/3Mi)
% 2.72/1.72 % (24093)Instruction limit reached!
% 2.72/1.72 % (24093)------------------------------
% 2.72/1.72 % (24093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.72 % (24093)Termination reason: Unknown
% 2.72/1.72 % (24093)Termination phase: shuffling
% 2.72/1.72
% 2.72/1.72 % (24093)Memory used [KB]: 1407
% 2.72/1.72 % (24093)Time elapsed: 0.003 s
% 2.72/1.72 % (24093)Instructions burned: 4 (million)
% 2.72/1.72 % (24093)------------------------------
% 2.72/1.72 % (24093)------------------------------
% 2.72/1.73 % (24094)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_23745 for (2998ds/30Mi)
% 2.72/1.74 % (24094)Instruction limit reached!
% 2.72/1.74 % (24094)------------------------------
% 2.72/1.74 % (24094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.74 % (24094)Termination reason: Unknown
% 2.72/1.74 % (24094)Termination phase: shuffling
% 2.72/1.74
% 2.72/1.74 % (24094)Memory used [KB]: 1918
% 2.72/1.74 % (24094)Time elapsed: 0.011 s
% 2.72/1.74 % (24094)Instructions burned: 31 (million)
% 2.72/1.74 % (24094)------------------------------
% 2.72/1.74 % (24094)------------------------------
% 2.72/1.75 % (24095)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_23745 for (2998ds/127Mi)
% 2.72/1.79 % (24095)Instruction limit reached!
% 2.72/1.79 % (24095)------------------------------
% 2.72/1.79 % (24095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.79 % (24095)Termination reason: Unknown
% 2.72/1.79 % (24095)Termination phase: Saturation
% 2.72/1.79
% 2.72/1.79 % (24095)Memory used [KB]: 6908
% 2.72/1.79 % (24095)Time elapsed: 0.037 s
% 2.72/1.79 % (24095)Instructions burned: 128 (million)
% 2.72/1.79 % (24095)------------------------------
% 2.72/1.79 % (24095)------------------------------
% 2.72/1.79 % (24088)Instruction limit reached!
% 2.72/1.79 % (24088)------------------------------
% 2.72/1.79 % (24088)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.79 % (24088)Termination reason: Unknown
% 2.72/1.79 % (24088)Termination phase: Saturation
% 2.72/1.79
% 2.72/1.79 % (24088)Memory used [KB]: 8571
% 2.72/1.79 % (24088)Time elapsed: 0.116 s
% 2.72/1.79 % (24088)Instructions burned: 379 (million)
% 2.72/1.79 % (24088)------------------------------
% 2.72/1.79 % (24088)------------------------------
% 2.72/1.80 % (24096)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_23745 for (2997ds/100Mi)
% 2.72/1.80 % (24097)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_23745 for (2997ds/3Mi)
% 2.72/1.80 % (24097)Instruction limit reached!
% 2.72/1.80 % (24097)------------------------------
% 2.72/1.80 % (24097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.80 % (24097)Termination reason: Unknown
% 2.72/1.80 % (24097)Termination phase: shuffling
% 2.72/1.80
% 2.72/1.80 % (24097)Memory used [KB]: 1407
% 2.72/1.80 % (24097)Time elapsed: 0.002 s
% 2.72/1.80 % (24097)Instructions burned: 3 (million)
% 2.72/1.80 % (24097)------------------------------
% 2.72/1.80 % (24097)------------------------------
% 2.72/1.81 % (24098)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_23745 for (2997ds/20Mi)
% 2.72/1.82 % (24098)Instruction limit reached!
% 2.72/1.82 % (24098)------------------------------
% 2.72/1.82 % (24098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.82 % (24098)Termination reason: Unknown
% 2.72/1.82 % (24098)Termination phase: Property scanning
% 2.72/1.82
% 2.72/1.82 % (24098)Memory used [KB]: 1791
% 2.72/1.82 % (24098)Time elapsed: 0.008 s
% 2.72/1.82 % (24098)Instructions burned: 21 (million)
% 2.72/1.82 % (24098)------------------------------
% 2.72/1.82 % (24098)------------------------------
% 2.72/1.83 % (24096)Instruction limit reached!
% 2.72/1.83 % (24096)------------------------------
% 2.72/1.83 % (24096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.83 % (24096)Termination reason: Unknown
% 2.72/1.83 % (24096)Termination phase: Property scanning
% 2.72/1.83
% 2.72/1.83 % (24096)Memory used [KB]: 2302
% 2.72/1.83 % (24096)Time elapsed: 0.028 s
% 2.72/1.83 % (24096)Instructions burned: 100 (million)
% 2.72/1.83 % (24096)------------------------------
% 2.72/1.83 % (24096)------------------------------
% 2.72/1.83 % (24099)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_23745 for (2997ds/86Mi)
% 2.72/1.84 % (24100)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_23745 for (2997ds/107Mi)
% 2.72/1.85 % (24099)Instruction limit reached!
% 2.72/1.85 % (24099)------------------------------
% 2.72/1.85 % (24099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.85 % (24099)Termination reason: Unknown
% 2.72/1.85 % (24099)Termination phase: Property scanning
% 2.72/1.85
% 2.72/1.85 % (24099)Memory used [KB]: 2430
% 2.72/1.85 % (24099)Time elapsed: 0.026 s
% 2.72/1.85 % (24099)Instructions burned: 88 (million)
% 2.72/1.85 % (24099)------------------------------
% 2.72/1.85 % (24099)------------------------------
% 2.72/1.85 % (24082)Instruction limit reached!
% 2.72/1.85 % (24082)------------------------------
% 2.72/1.85 % (24082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.85 % (24082)Termination reason: Unknown
% 2.72/1.85 % (24082)Termination phase: Saturation
% 2.72/1.85
% 2.72/1.85 % (24082)Memory used [KB]: 9978
% 2.72/1.85 % (24082)Time elapsed: 0.220 s
% 2.72/1.85 % (24082)Instructions burned: 710 (million)
% 2.72/1.85 % (24082)------------------------------
% 2.72/1.85 % (24082)------------------------------
% 2.72/1.86 % (24102)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_23745 for (2997ds/448Mi)
% 2.72/1.86 % (24101)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_23745 for (2997ds/39Mi)
% 2.72/1.87 % (24100)Instruction limit reached!
% 2.72/1.87 % (24100)------------------------------
% 2.72/1.87 % (24100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.87 % (24100)Termination reason: Unknown
% 2.72/1.87 % (24100)Termination phase: Property scanning
% 2.72/1.87
% 2.72/1.87 % (24100)Memory used [KB]: 2430
% 2.72/1.87 % (24100)Time elapsed: 0.031 s
% 2.72/1.87 % (24100)Instructions burned: 107 (million)
% 2.72/1.87 % (24100)------------------------------
% 2.72/1.87 % (24100)------------------------------
% 2.72/1.88 % (24101)Instruction limit reached!
% 2.72/1.88 % (24101)------------------------------
% 2.72/1.88 % (24101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.88 % (24101)Termination reason: Unknown
% 2.72/1.88 % (24101)Termination phase: Property scanning
% 2.72/1.88
% 2.72/1.88 % (24101)Memory used [KB]: 2174
% 2.72/1.88 % (24101)Time elapsed: 0.012 s
% 2.72/1.88 % (24101)Instructions burned: 39 (million)
% 2.72/1.88 % (24101)------------------------------
% 2.72/1.88 % (24101)------------------------------
% 2.72/1.88 % (24103)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_23745 for (2997ds/46Mi)
% 2.72/1.89 % (24104)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_23745 for (2996ds/98Mi)
% 2.72/1.89 % (24103)Instruction limit reached!
% 2.72/1.89 % (24103)------------------------------
% 2.72/1.89 % (24103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.89 % (24103)Termination reason: Unknown
% 2.72/1.89 % (24103)Termination phase: Property scanning
% 2.72/1.89
% 2.72/1.89 % (24103)Memory used [KB]: 2046
% 2.72/1.89 % (24103)Time elapsed: 0.015 s
% 2.72/1.89 % (24103)Instructions burned: 47 (million)
% 2.72/1.89 % (24103)------------------------------
% 2.72/1.89 % (24103)------------------------------
% 2.72/1.89 % (24089)Instruction limit reached!
% 2.72/1.89 % (24089)------------------------------
% 2.72/1.89 % (24089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.89 % (24089)Termination reason: Unknown
% 2.72/1.89 % (24089)Termination phase: Saturation
% 2.72/1.89
% 2.72/1.89 % (24089)Memory used [KB]: 7164
% 2.72/1.89 % (24089)Time elapsed: 0.204 s
% 2.72/1.89 % (24089)Instructions burned: 780 (million)
% 2.72/1.89 % (24089)------------------------------
% 2.72/1.89 % (24089)------------------------------
% 2.72/1.89 % (24073)Instruction limit reached!
% 2.72/1.89 % (24073)------------------------------
% 2.72/1.89 % (24073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.89 % (24073)Termination reason: Unknown
% 2.72/1.89 % (24073)Termination phase: Saturation
% 2.72/1.89
% 2.72/1.89 % (24073)Memory used [KB]: 11769
% 2.72/1.89 % (24073)Time elapsed: 0.282 s
% 2.72/1.89 % (24073)Instructions burned: 1042 (million)
% 2.72/1.89 % (24073)------------------------------
% 2.72/1.89 % (24073)------------------------------
% 2.72/1.90 % (24105)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_23745 for (2996ds/507Mi)
% 2.72/1.90 % (24106)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_23745 for (2996ds/149Mi)
% 2.72/1.90 % (24107)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_23745 for (2996ds/39Mi)
% 2.72/1.91 % (24107)Instruction limit reached!
% 2.72/1.91 % (24107)------------------------------
% 2.72/1.91 % (24107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.91 % (24107)Termination reason: Unknown
% 2.72/1.91 % (24107)Termination phase: Property scanning
% 2.72/1.91
% 2.72/1.91 % (24107)Memory used [KB]: 2046
% 2.72/1.91 % (24107)Time elapsed: 0.012 s
% 2.72/1.91 % (24107)Instructions burned: 42 (million)
% 2.72/1.91 % (24107)------------------------------
% 2.72/1.91 % (24107)------------------------------
% 2.72/1.91 % (24104)Instruction limit reached!
% 2.72/1.91 % (24104)------------------------------
% 2.72/1.91 % (24104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.91 % (24104)Termination reason: Unknown
% 2.72/1.91 % (24104)Termination phase: Property scanning
% 2.72/1.91
% 2.72/1.91 % (24104)Memory used [KB]: 2302
% 2.72/1.91 % (24104)Time elapsed: 0.029 s
% 2.72/1.91 % (24104)Instructions burned: 101 (million)
% 2.72/1.91 % (24104)------------------------------
% 2.72/1.91 % (24104)------------------------------
% 2.72/1.92 % (24084)Instruction limit reached!
% 2.72/1.92 % (24084)------------------------------
% 2.72/1.92 % (24084)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.92 % (24084)Termination reason: Unknown
% 2.72/1.92 % (24084)Termination phase: Saturation
% 2.72/1.92
% 2.72/1.92 % (24084)Memory used [KB]: 10874
% 2.72/1.92 % (24084)Time elapsed: 0.273 s
% 2.72/1.92 % (24084)Instructions burned: 903 (million)
% 2.72/1.92 % (24084)------------------------------
% 2.72/1.92 % (24084)------------------------------
% 2.72/1.92 % (24108)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_23745 for (2996ds/6Mi)
% 2.72/1.92 % (24109)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_23745 for (2996ds/1087Mi)
% 2.72/1.92 % (24108)Instruction limit reached!
% 2.72/1.92 % (24108)------------------------------
% 2.72/1.92 % (24108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.92 % (24108)Termination reason: Unknown
% 2.72/1.92 % (24108)Termination phase: shuffling
% 2.72/1.92
% 2.72/1.92 % (24108)Memory used [KB]: 1535
% 2.72/1.92 % (24108)Time elapsed: 0.003 s
% 2.72/1.92 % (24108)Instructions burned: 7 (million)
% 2.72/1.92 % (24108)------------------------------
% 2.72/1.92 % (24108)------------------------------
% 2.72/1.93 % (24110)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_23745 for (2996ds/47Mi)
% 2.72/1.93 % (24111)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_23745 for (2996ds/44Mi)
% 2.72/1.94 % (24106)Instruction limit reached!
% 2.72/1.94 % (24106)------------------------------
% 2.72/1.94 % (24106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.94 % (24106)Termination reason: Unknown
% 2.72/1.94 % (24106)Termination phase: Saturation
% 2.72/1.94
% 2.72/1.94 % (24106)Memory used [KB]: 7419
% 2.72/1.94 % (24106)Time elapsed: 0.043 s
% 2.72/1.94 % (24106)Instructions burned: 149 (million)
% 2.72/1.94 % (24106)------------------------------
% 2.72/1.94 % (24106)------------------------------
% 2.72/1.94 % (24110)Instruction limit reached!
% 2.72/1.94 % (24110)------------------------------
% 2.72/1.94 % (24110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.94 % (24110)Termination reason: Unknown
% 2.72/1.94 % (24110)Termination phase: Property scanning
% 2.72/1.94
% 2.72/1.94 % (24110)Memory used [KB]: 2046
% 2.72/1.94 % (24110)Time elapsed: 0.014 s
% 2.72/1.94 % (24110)Instructions burned: 48 (million)
% 2.72/1.94 % (24110)------------------------------
% 2.72/1.94 % (24110)------------------------------
% 2.72/1.94 % (24111)Instruction limit reached!
% 2.72/1.94 % (24111)------------------------------
% 2.72/1.94 % (24111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.94 % (24111)Termination reason: Unknown
% 2.72/1.94 % (24111)Termination phase: Property scanning
% 2.72/1.94
% 2.72/1.94 % (24111)Memory used [KB]: 2174
% 2.72/1.94 % (24111)Time elapsed: 0.013 s
% 2.72/1.94 % (24111)Instructions burned: 44 (million)
% 2.72/1.94 % (24111)------------------------------
% 2.72/1.94 % (24111)------------------------------
% 2.72/1.95 % (24113)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_23745 for (2996ds/62Mi)
% 2.72/1.95 % (24112)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_23745 for (2996ds/432Mi)
% 2.72/1.95 % (24114)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_23745 for (2996ds/31Mi)
% 2.72/1.96 % (24114)Instruction limit reached!
% 2.72/1.96 % (24114)------------------------------
% 2.72/1.96 % (24114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.96 % (24114)Termination reason: Unknown
% 2.72/1.96 % (24114)Termination phase: shuffling
% 2.72/1.96
% 2.72/1.96 % (24114)Memory used [KB]: 2046
% 2.72/1.96 % (24114)Time elapsed: 0.010 s
% 2.72/1.96 % (24114)Instructions burned: 34 (million)
% 2.72/1.96 % (24114)------------------------------
% 2.72/1.96 % (24114)------------------------------
% 2.72/1.97 % (24113)Instruction limit reached!
% 2.72/1.97 % (24113)------------------------------
% 2.72/1.97 % (24113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.97 % (24113)Termination reason: Unknown
% 2.72/1.97 % (24113)Termination phase: Property scanning
% 2.72/1.97
% 2.72/1.97 % (24113)Memory used [KB]: 2174
% 2.72/1.97 % (24113)Time elapsed: 0.017 s
% 2.72/1.97 % (24113)Instructions burned: 63 (million)
% 2.72/1.97 % (24113)------------------------------
% 2.72/1.97 % (24113)------------------------------
% 2.72/1.97 % (24115)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_23745 for (2995ds/96Mi)
% 2.72/1.97 % (24102)Instruction limit reached!
% 2.72/1.97 % (24102)------------------------------
% 2.72/1.97 % (24102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/1.97 % (24102)Termination reason: Unknown
% 2.72/1.97 % (24102)Termination phase: Saturation
% 2.72/1.97
% 2.72/1.97 % (24102)Memory used [KB]: 7291
% 2.72/1.97 % (24102)Time elapsed: 0.110 s
% 2.72/1.97 % (24102)Instructions burned: 448 (million)
% 2.72/1.97 % (24102)------------------------------
% 2.72/1.97 % (24102)------------------------------
% 2.72/1.98 % (24116)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_23745 for (2995ds/453Mi)
% 2.72/1.98 % (24117)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_23745 for (2995ds/71Mi)
% 2.72/2.00 % (24091)Instruction limit reached!
% 2.72/2.00 % (24091)------------------------------
% 2.72/2.00 % (24091)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/2.00 % (24091)Termination reason: Unknown
% 2.72/2.00 % (24091)Termination phase: Saturation
% 2.72/2.00
% 2.72/2.00 % (24091)Memory used [KB]: 8699
% 2.72/2.00 % (24091)Time elapsed: 0.295 s
% 2.72/2.00 % (24115)Instruction limit reached!
% 2.72/2.00 % (24115)------------------------------
% 2.72/2.00 % (24115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/2.00 % (24115)Termination reason: Unknown
% 2.72/2.00 % (24115)Termination phase: Property scanning
% 2.72/2.00
% 2.72/2.00 % (24115)Memory used [KB]: 2302
% 2.72/2.00 % (24115)Time elapsed: 0.026 s
% 2.72/2.00 % (24115)Instructions burned: 97 (million)
% 2.72/2.00 % (24115)------------------------------
% 2.72/2.00 % (24115)------------------------------
% 2.72/2.00 % (24091)Instructions burned: 881 (million)
% 2.72/2.00 % (24091)------------------------------
% 2.72/2.00 % (24091)------------------------------
% 2.72/2.00 % (24117)Instruction limit reached!
% 2.72/2.00 % (24117)------------------------------
% 2.72/2.00 % (24117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/2.00 % (24117)Termination reason: Unknown
% 2.72/2.00 % (24117)Termination phase: Property scanning
% 2.72/2.00
% 2.72/2.00 % (24117)Memory used [KB]: 2174
% 2.72/2.00 % (24117)Time elapsed: 0.020 s
% 2.72/2.00 % (24117)Instructions burned: 72 (million)
% 2.72/2.00 % (24117)------------------------------
% 2.72/2.00 % (24117)------------------------------
% 2.72/2.01 % (24118)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_23745 for (2995ds/83Mi)
% 2.72/2.01 % (24119)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_23745 for (2995ds/11Mi)
% 2.72/2.01 % (24119)Instruction limit reached!
% 2.72/2.01 % (24119)------------------------------
% 2.72/2.01 % (24119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.72/2.01 % (24119)Termination reason: Unknown
% 2.72/2.01 % (24120)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_23745 for (2995ds/41Mi)
% 2.72/2.01 % (24119)Termination phase: shuffling
% 2.72/2.01
% 2.72/2.01 % (24119)Memory used [KB]: 1535
% 2.72/2.01 % (24119)Time elapsed: 0.004 s
% 2.72/2.01 % (24119)Instructions burned: 11 (million)
% 2.72/2.01 % (24119)------------------------------
% 2.72/2.01 % (24119)------------------------------
% 5.75/2.02 % (24121)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_23745 for (2995ds/6Mi)
% 5.75/2.02 % (24120)Instruction limit reached!
% 5.75/2.02 % (24120)------------------------------
% 5.75/2.02 % (24120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.02 % (24120)Termination reason: Unknown
% 5.75/2.02 % (24120)Termination phase: Property scanning
% 5.75/2.02
% 5.75/2.02 % (24120)Memory used [KB]: 2174
% 5.75/2.02 % (24120)Time elapsed: 0.012 s
% 5.75/2.02 % (24120)Instructions burned: 41 (million)
% 5.75/2.02 % (24120)------------------------------
% 5.75/2.02 % (24120)------------------------------
% 5.75/2.02 % (24121)Instruction limit reached!
% 5.75/2.02 % (24121)------------------------------
% 5.75/2.02 % (24121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.02 % (24121)Termination reason: Unknown
% 5.75/2.02 % (24121)Termination phase: shuffling
% 5.75/2.02
% 5.75/2.02 % (24121)Memory used [KB]: 1535
% 5.75/2.02 % (24121)Time elapsed: 0.004 s
% 5.75/2.02 % (24121)Instructions burned: 8 (million)
% 5.75/2.02 % (24121)------------------------------
% 5.75/2.02 % (24121)------------------------------
% 5.75/2.03 % (24118)Instruction limit reached!
% 5.75/2.03 % (24118)------------------------------
% 5.75/2.03 % (24118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.03 % (24118)Termination reason: Unknown
% 5.75/2.03 % (24118)Termination phase: Property scanning
% 5.75/2.03
% 5.75/2.03 % (24118)Memory used [KB]: 2174
% 5.75/2.03 % (24118)Time elapsed: 0.023 s
% 5.75/2.03 % (24118)Instructions burned: 86 (million)
% 5.75/2.03 % (24118)------------------------------
% 5.75/2.03 % (24118)------------------------------
% 5.75/2.03 % (24122)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_23745 for (2995ds/150Mi)
% 5.75/2.03 % (24123)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_23745 for (2995ds/343Mi)
% 5.75/2.04 % (24124)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_23745 for (2995ds/109Mi)
% 5.75/2.05 % (24105)Instruction limit reached!
% 5.75/2.05 % (24105)------------------------------
% 5.75/2.05 % (24105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.05 % (24105)Termination reason: Unknown
% 5.75/2.05 % (24105)Termination phase: Saturation
% 5.75/2.05
% 5.75/2.05 % (24105)Memory used [KB]: 7803
% 5.75/2.05 % (24105)Time elapsed: 0.157 s
% 5.75/2.05 % (24105)Instructions burned: 507 (million)
% 5.75/2.05 % (24105)------------------------------
% 5.75/2.05 % (24105)------------------------------
% 5.75/2.06 % (24112)Instruction limit reached!
% 5.75/2.06 % (24112)------------------------------
% 5.75/2.06 % (24112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.06 % (24112)Termination reason: Unknown
% 5.75/2.06 % (24112)Termination phase: Saturation
% 5.75/2.06
% 5.75/2.06 % (24112)Memory used [KB]: 2942
% 5.75/2.06 % (24112)Time elapsed: 0.112 s
% 5.75/2.06 % (24112)Instructions burned: 433 (million)
% 5.75/2.06 % (24112)------------------------------
% 5.75/2.06 % (24112)------------------------------
% 5.75/2.06 % (24125)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_23745 for (2995ds/253Mi)
% 5.75/2.07 % (24124)Instruction limit reached!
% 5.75/2.07 % (24124)------------------------------
% 5.75/2.07 % (24124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.07 % (24124)Termination reason: Unknown
% 5.75/2.07 % (24124)Termination phase: Property scanning
% 5.75/2.07
% 5.75/2.07 % (24124)Memory used [KB]: 2430
% 5.75/2.07 % (24124)Time elapsed: 0.029 s
% 5.75/2.07 % (24124)Instructions burned: 111 (million)
% 5.75/2.07 % (24124)------------------------------
% 5.75/2.07 % (24124)------------------------------
% 5.75/2.07 % (24122)Instruction limit reached!
% 5.75/2.07 % (24122)------------------------------
% 5.75/2.07 % (24122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.07 % (24122)Termination reason: Unknown
% 5.75/2.07 % (24122)Termination phase: Saturation
% 5.75/2.07
% 5.75/2.07 % (24122)Memory used [KB]: 8315
% 5.75/2.07 % (24122)Time elapsed: 0.043 s
% 5.75/2.07 % (24122)Instructions burned: 153 (million)
% 5.75/2.07 % (24122)------------------------------
% 5.75/2.07 % (24122)------------------------------
% 5.75/2.07 % (24126)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_23745 for (2994ds/140Mi)
% 5.75/2.08 % (24127)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_23745 for (2994ds/614Mi)
% 5.75/2.08 % (24128)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_23745 for (2994ds/202Mi)
% 5.75/2.09 % (24116)Instruction limit reached!
% 5.75/2.09 % (24116)------------------------------
% 5.75/2.09 % (24116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.09 % (24116)Termination reason: Unknown
% 5.75/2.09 % (24116)Termination phase: Saturation
% 5.75/2.09
% 5.75/2.09 % (24116)Memory used [KB]: 7291
% 5.75/2.09 % (24116)Time elapsed: 0.113 s
% 5.75/2.09 % (24116)Instructions burned: 456 (million)
% 5.75/2.09 % (24116)------------------------------
% 5.75/2.09 % (24116)------------------------------
% 5.75/2.10 % (24129)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_23745 for (2994ds/339Mi)
% 5.75/2.11 % (24126)Instruction limit reached!
% 5.75/2.11 % (24126)------------------------------
% 5.75/2.11 % (24126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.75/2.11 % (24126)Termination reason: Unknown
% 5.75/2.11 % (24126)Termination phase: Saturation
% 5.75/2.11
% 5.75/2.11 % (24126)Memory used [KB]: 7036
% 5.75/2.11 % (24126)Time elapsed: 0.038 s
% 5.75/2.11 % (24126)Instructions burned: 140 (million)
% 5.75/2.11 % (24126)------------------------------
% 5.75/2.11 % (24126)------------------------------
% 6.25/2.12 % (24130)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_23745 for (2994ds/283Mi)
% 6.25/2.13 % (24123)Instruction limit reached!
% 6.25/2.13 % (24123)------------------------------
% 6.25/2.13 % (24123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.13 % (24123)Termination reason: Unknown
% 6.25/2.13 % (24123)Termination phase: Saturation
% 6.25/2.13
% 6.25/2.13 % (24123)Memory used [KB]: 8315
% 6.25/2.13 % (24123)Time elapsed: 0.094 s
% 6.25/2.13 % (24123)Instructions burned: 344 (million)
% 6.25/2.13 % (24123)------------------------------
% 6.25/2.13 % (24123)------------------------------
% 6.25/2.14 % (24131)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_23745 for (2994ds/134Mi)
% 6.25/2.14 % (24125)Instruction limit reached!
% 6.25/2.14 % (24125)------------------------------
% 6.25/2.14 % (24125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.14 % (24125)Termination reason: Unknown
% 6.25/2.14 % (24125)Termination phase: Saturation
% 6.25/2.14
% 6.25/2.14 % (24125)Memory used [KB]: 8699
% 6.25/2.14 % (24125)Time elapsed: 0.077 s
% 6.25/2.14 % (24125)Instructions burned: 255 (million)
% 6.25/2.14 % (24125)------------------------------
% 6.25/2.14 % (24125)------------------------------
% 6.25/2.14 % (24128)Instruction limit reached!
% 6.25/2.14 % (24128)------------------------------
% 6.25/2.14 % (24128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.14 % (24128)Termination reason: Unknown
% 6.25/2.14 % (24128)Termination phase: Saturation
% 6.25/2.14
% 6.25/2.14 % (24128)Memory used [KB]: 4733
% 6.25/2.14 % (24128)Time elapsed: 0.060 s
% 6.25/2.14 % (24128)Instructions burned: 203 (million)
% 6.25/2.14 % (24128)------------------------------
% 6.25/2.14 % (24128)------------------------------
% 6.25/2.15 % (24132)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_23745 for (2994ds/298Mi)
% 6.25/2.15 % (24133)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_23745 for (2994ds/192Mi)
% 6.25/2.17 % (24131)Instruction limit reached!
% 6.25/2.17 % (24131)------------------------------
% 6.25/2.17 % (24131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.17 % (24131)Termination reason: Unknown
% 6.25/2.17 % (24131)Termination phase: Saturation
% 6.25/2.17
% 6.25/2.17 % (24131)Memory used [KB]: 7036
% 6.25/2.17 % (24131)Time elapsed: 0.037 s
% 6.25/2.17 % (24131)Instructions burned: 134 (million)
% 6.25/2.17 % (24131)------------------------------
% 6.25/2.17 % (24131)------------------------------
% 6.25/2.18 % (24134)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_23745 for (2993ds/258Mi)
% 6.25/2.19 % (24130)Instruction limit reached!
% 6.25/2.19 % (24130)------------------------------
% 6.25/2.19 % (24130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.19 % (24130)Termination reason: Unknown
% 6.25/2.19 % (24130)Termination phase: Saturation
% 6.25/2.19
% 6.25/2.19 % (24130)Memory used [KB]: 7164
% 6.25/2.19 % (24130)Time elapsed: 0.073 s
% 6.25/2.19 % (24130)Instructions burned: 283 (million)
% 6.25/2.19 % (24130)------------------------------
% 6.25/2.19 % (24130)------------------------------
% 6.25/2.19 % (24129)Instruction limit reached!
% 6.25/2.19 % (24129)------------------------------
% 6.25/2.19 % (24129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.25/2.19 % (24129)Termination reason: Unknown
% 6.25/2.19 % (24129)Termination phase: Saturation
% 6.25/2.19
% 6.25/2.19 % (24129)Memory used [KB]: 7931
% 6.25/2.19 % (24129)Time elapsed: 0.095 s
% 6.25/2.19 % (24129)Instructions burned: 340 (million)
% 6.25/2.19 % (24129)------------------------------
% 6.25/2.19 % (24129)------------------------------
% 6.83/2.20 % (24135)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_23745 for (2993ds/90Mi)
% 6.83/2.20 % (24133)Instruction limit reached!
% 6.83/2.20 % (24133)------------------------------
% 6.83/2.20 % (24133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.20 % (24133)Termination reason: Unknown
% 6.83/2.20 % (24133)Termination phase: Saturation
% 6.83/2.20
% 6.83/2.20 % (24133)Memory used [KB]: 7547
% 6.83/2.20 % (24133)Time elapsed: 0.052 s
% 6.83/2.20 % (24133)Instructions burned: 192 (million)
% 6.83/2.20 % (24133)------------------------------
% 6.83/2.20 % (24133)------------------------------
% 6.83/2.20 % (24136)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_23745 for (2993ds/231Mi)
% 6.83/2.21 % (24137)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_23745 for (2993ds/458Mi)
% 6.83/2.22 % (24135)Instruction limit reached!
% 6.83/2.22 % (24135)------------------------------
% 6.83/2.22 % (24135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.22 % (24135)Termination reason: Unknown
% 6.83/2.22 % (24135)Termination phase: Twee Goal Transformation
% 6.83/2.22
% 6.83/2.22 % (24135)Memory used [KB]: 2430
% 6.83/2.22 % (24135)Time elapsed: 0.024 s
% 6.83/2.22 % (24135)Instructions burned: 90 (million)
% 6.83/2.22 % (24135)------------------------------
% 6.83/2.22 % (24135)------------------------------
% 6.83/2.22 % (24132)Instruction limit reached!
% 6.83/2.22 % (24132)------------------------------
% 6.83/2.22 % (24132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.22 % (24132)Termination reason: Unknown
% 6.83/2.22 % (24132)Termination phase: Saturation
% 6.83/2.22
% 6.83/2.22 % (24132)Memory used [KB]: 7164
% 6.83/2.22 % (24132)Time elapsed: 0.076 s
% 6.83/2.22 % (24132)Instructions burned: 300 (million)
% 6.83/2.22 % (24132)------------------------------
% 6.83/2.22 % (24132)------------------------------
% 6.83/2.23 % (24138)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_23745 for (2993ds/31Mi)
% 6.83/2.23 % (24139)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_23745 for (2993ds/297Mi)
% 6.83/2.24 % (24138)Instruction limit reached!
% 6.83/2.24 % (24138)------------------------------
% 6.83/2.24 % (24138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.24 % (24138)Termination reason: Unknown
% 6.83/2.24 % (24138)Termination phase: shuffling
% 6.83/2.24
% 6.83/2.24 % (24138)Memory used [KB]: 2046
% 6.83/2.24 % (24138)Time elapsed: 0.010 s
% 6.83/2.24 % (24138)Instructions burned: 34 (million)
% 6.83/2.24 % (24138)------------------------------
% 6.83/2.24 % (24138)------------------------------
% 6.83/2.25 % (24134)Instruction limit reached!
% 6.83/2.25 % (24134)------------------------------
% 6.83/2.25 % (24134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.25 % (24134)Termination reason: Unknown
% 6.83/2.25 % (24134)Termination phase: Saturation
% 6.83/2.25
% 6.83/2.25 % (24134)Memory used [KB]: 7803
% 6.83/2.25 % (24134)Time elapsed: 0.068 s
% 6.83/2.25 % (24134)Instructions burned: 258 (million)
% 6.83/2.25 % (24134)------------------------------
% 6.83/2.25 % (24134)------------------------------
% 6.83/2.25 % (24140)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_23745 for (2993ds/987Mi)
% 6.83/2.26 % (24127)Instruction limit reached!
% 6.83/2.26 % (24127)------------------------------
% 6.83/2.26 % (24127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.26 % (24127)Termination reason: Unknown
% 6.83/2.26 % (24127)Termination phase: Saturation
% 6.83/2.26
% 6.83/2.26 % (24127)Memory used [KB]: 8955
% 6.83/2.26 % (24127)Time elapsed: 0.183 s
% 6.83/2.26 % (24127)Instructions burned: 615 (million)
% 6.83/2.26 % (24127)------------------------------
% 6.83/2.26 % (24127)------------------------------
% 6.83/2.26 % (24141)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_23745 for (2993ds/182Mi)
% 6.83/2.27 % (24136)Instruction limit reached!
% 6.83/2.27 % (24136)------------------------------
% 6.83/2.27 % (24136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.83/2.27 % (24136)Termination reason: Unknown
% 6.83/2.27 % (24136)Termination phase: Saturation
% 6.83/2.27
% 6.83/2.27 % (24136)Memory used [KB]: 12665
% 6.83/2.27 % (24136)Time elapsed: 0.065 s
% 6.83/2.27 % (24136)Instructions burned: 233 (million)
% 6.83/2.27 % (24136)------------------------------
% 6.83/2.27 % (24136)------------------------------
% 6.83/2.27 % (24142)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_23745 for (2993ds/182Mi)
% 6.83/2.28 % (24143)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_23745 for (2993ds/154Mi)
% 7.46/2.31 % (24141)Instruction limit reached!
% 7.46/2.31 % (24141)------------------------------
% 7.46/2.31 % (24141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.31 % (24141)Termination reason: Unknown
% 7.46/2.31 % (24141)Termination phase: Saturation
% 7.46/2.31
% 7.46/2.31 % (24141)Memory used [KB]: 7419
% 7.46/2.31 % (24141)Time elapsed: 0.049 s
% 7.46/2.31 % (24141)Instructions burned: 185 (million)
% 7.46/2.31 % (24141)------------------------------
% 7.46/2.31 % (24141)------------------------------
% 7.46/2.31 % (24139)Instruction limit reached!
% 7.46/2.31 % (24139)------------------------------
% 7.46/2.31 % (24139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.31 % (24139)Termination reason: Unknown
% 7.46/2.31 % (24139)Termination phase: Saturation
% 7.46/2.31
% 7.46/2.31 % (24139)Memory used [KB]: 7291
% 7.46/2.31 % (24139)Time elapsed: 0.074 s
% 7.46/2.31 % (24139)Instructions burned: 299 (million)
% 7.46/2.31 % (24139)------------------------------
% 7.46/2.31 % (24139)------------------------------
% 7.46/2.32 % (24143)Instruction limit reached!
% 7.46/2.32 % (24143)------------------------------
% 7.46/2.32 % (24143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.32 % (24143)Termination reason: Unknown
% 7.46/2.32 % (24143)Termination phase: Saturation
% 7.46/2.32
% 7.46/2.32 % (24143)Memory used [KB]: 6908
% 7.46/2.32 % (24143)Time elapsed: 0.039 s
% 7.46/2.32 % (24143)Instructions burned: 154 (million)
% 7.46/2.32 % (24143)------------------------------
% 7.46/2.32 % (24143)------------------------------
% 7.46/2.32 % (24144)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_23745 for (2992ds/79Mi)
% 7.46/2.32 % (24145)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_23745 for (2992ds/216Mi)
% 7.46/2.32 % (24142)Instruction limit reached!
% 7.46/2.32 % (24142)------------------------------
% 7.46/2.32 % (24142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.32 % (24142)Termination reason: Unknown
% 7.46/2.32 % (24142)Termination phase: Saturation
% 7.46/2.32
% 7.46/2.32 % (24142)Memory used [KB]: 9722
% 7.46/2.32 % (24142)Time elapsed: 0.053 s
% 7.46/2.32 % (24142)Instructions burned: 183 (million)
% 7.46/2.32 % (24142)------------------------------
% 7.46/2.32 % (24142)------------------------------
% 7.46/2.32 % (24146)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_23745 for (2992ds/114Mi)
% 7.46/2.33 % (24147)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_23745 for (2992ds/922Mi)
% 7.46/2.33 % (24109)Instruction limit reached!
% 7.46/2.33 % (24109)------------------------------
% 7.46/2.33 % (24109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.33 % (24109)Termination reason: Unknown
% 7.46/2.33 % (24109)Termination phase: Saturation
% 7.46/2.33
% 7.46/2.33 % (24109)Memory used [KB]: 10618
% 7.46/2.33 % (24109)Time elapsed: 0.412 s
% 7.46/2.33 % (24109)Instructions burned: 1088 (million)
% 7.46/2.33 % (24109)------------------------------
% 7.46/2.33 % (24109)------------------------------
% 7.46/2.34 % (24144)Instruction limit reached!
% 7.46/2.34 % (24144)------------------------------
% 7.46/2.34 % (24144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.34 % (24144)Termination reason: Unknown
% 7.46/2.34 % (24144)Termination phase: Function definition elimination
% 7.46/2.34
% 7.46/2.34 % (24144)Memory used [KB]: 2302
% 7.46/2.34 % (24144)Time elapsed: 0.022 s
% 7.46/2.34 % (24144)Instructions burned: 81 (million)
% 7.46/2.34 % (24144)------------------------------
% 7.46/2.34 % (24144)------------------------------
% 7.46/2.34 % (24137)Instruction limit reached!
% 7.46/2.34 % (24137)------------------------------
% 7.46/2.34 % (24137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.34 % (24137)Termination reason: Unknown
% 7.46/2.34 % (24137)Termination phase: Saturation
% 7.46/2.34
% 7.46/2.34 % (24137)Memory used [KB]: 8699
% 7.46/2.34 % (24137)Time elapsed: 0.129 s
% 7.46/2.34 % (24137)Instructions burned: 458 (million)
% 7.46/2.34 % (24137)------------------------------
% 7.46/2.34 % (24137)------------------------------
% 7.46/2.34 % (24148)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_23745 for (2992ds/182Mi)
% 7.46/2.35 % (24149)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_23745 for (2992ds/164Mi)
% 7.46/2.35 % (24150)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_23745 for (2992ds/50Mi)
% 7.46/2.35 % (24146)Instruction limit reached!
% 7.46/2.35 % (24146)------------------------------
% 7.46/2.35 % (24146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.35 % (24146)Termination reason: Unknown
% 7.46/2.35 % (24146)Termination phase: Saturation
% 7.46/2.35
% 7.46/2.35 % (24146)Memory used [KB]: 6908
% 7.46/2.35 % (24146)Time elapsed: 0.030 s
% 7.46/2.35 % (24146)Instructions burned: 114 (million)
% 7.46/2.35 % (24146)------------------------------
% 7.46/2.35 % (24146)------------------------------
% 7.46/2.36 % (24150)Instruction limit reached!
% 7.46/2.36 % (24150)------------------------------
% 7.46/2.36 % (24150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.36 % (24150)Termination reason: Unknown
% 7.46/2.36 % (24150)Termination phase: Property scanning
% 7.46/2.36
% 7.46/2.36 % (24150)Memory used [KB]: 2174
% 7.46/2.36 % (24150)Time elapsed: 0.014 s
% 7.46/2.36 % (24150)Instructions burned: 50 (million)
% 7.46/2.36 % (24150)------------------------------
% 7.46/2.36 % (24150)------------------------------
% 7.46/2.36 % (24151)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_23745 for (2991ds/368Mi)
% 7.46/2.37 % (24145)Instruction limit reached!
% 7.46/2.37 % (24145)------------------------------
% 7.46/2.37 % (24145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.37 % (24145)Termination reason: Unknown
% 7.46/2.37 % (24145)Termination phase: Saturation
% 7.46/2.37
% 7.46/2.37 % (24145)Memory used [KB]: 7291
% 7.46/2.37 % (24145)Time elapsed: 0.055 s
% 7.46/2.37 % (24145)Instructions burned: 220 (million)
% 7.46/2.37 % (24145)------------------------------
% 7.46/2.37 % (24145)------------------------------
% 7.46/2.37 % (24152)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_23745 for (2991ds/1021Mi)
% 7.46/2.38 % (24153)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_23745 for (2991ds/267Mi)
% 7.46/2.39 % (24149)Instruction limit reached!
% 7.46/2.39 % (24149)------------------------------
% 7.46/2.39 % (24149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.39 % (24149)Termination reason: Unknown
% 7.46/2.39 % (24149)Termination phase: Saturation
% 7.46/2.39
% 7.46/2.39 % (24149)Memory used [KB]: 2558
% 7.46/2.39 % (24149)Time elapsed: 0.043 s
% 7.46/2.39 % (24149)Instructions burned: 166 (million)
% 7.46/2.39 % (24149)------------------------------
% 7.46/2.39 % (24149)------------------------------
% 7.46/2.39 % (24148)Instruction limit reached!
% 7.46/2.39 % (24148)------------------------------
% 7.46/2.39 % (24148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.46/2.39 % (24148)Termination reason: Unknown
% 7.46/2.39 % (24148)Termination phase: Saturation
% 7.46/2.39
% 7.46/2.39 % (24148)Memory used [KB]: 6908
% 7.46/2.39 % (24148)Time elapsed: 0.050 s
% 7.46/2.39 % (24148)Instructions burned: 183 (million)
% 7.46/2.39 % (24148)------------------------------
% 7.46/2.39 % (24148)------------------------------
% 8.16/2.40 % (24154)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_23745 for (2991ds/204Mi)
% 8.16/2.40 % (24155)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_23745 for (2991ds/26Mi)
% 8.16/2.41 % (24155)Instruction limit reached!
% 8.16/2.41 % (24155)------------------------------
% 8.16/2.41 % (24155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.41 % (24155)Termination reason: Unknown
% 8.16/2.41 % (24155)Termination phase: shuffling
% 8.16/2.41
% 8.16/2.41 % (24155)Memory used [KB]: 1918
% 8.16/2.41 % (24155)Time elapsed: 0.010 s
% 8.16/2.41 % (24155)Instructions burned: 28 (million)
% 8.16/2.41 % (24155)------------------------------
% 8.16/2.41 % (24155)------------------------------
% 8.16/2.42 % (24156)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_23745 for (2991ds/53Mi)
% 8.16/2.44 % (24156)Instruction limit reached!
% 8.16/2.44 % (24156)------------------------------
% 8.16/2.44 % (24156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.44 % (24156)Termination reason: Unknown
% 8.16/2.44 % (24156)Termination phase: Property scanning
% 8.16/2.44
% 8.16/2.44 % (24156)Memory used [KB]: 2174
% 8.16/2.44 % (24156)Time elapsed: 0.017 s
% 8.16/2.44 % (24156)Instructions burned: 55 (million)
% 8.16/2.44 % (24156)------------------------------
% 8.16/2.44 % (24156)------------------------------
% 8.16/2.45 % (24153)Instruction limit reached!
% 8.16/2.45 % (24153)------------------------------
% 8.16/2.45 % (24153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.45 % (24153)Termination reason: Unknown
% 8.16/2.45 % (24153)Termination phase: Saturation
% 8.16/2.45
% 8.16/2.45 % (24153)Memory used [KB]: 7164
% 8.16/2.45 % (24153)Time elapsed: 0.068 s
% 8.16/2.45 % (24153)Instructions burned: 271 (million)
% 8.16/2.45 % (24153)------------------------------
% 8.16/2.45 % (24153)------------------------------
% 8.16/2.45 % (24157)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_23745 for (2991ds/4436Mi)
% 8.16/2.45 % (24154)Instruction limit reached!
% 8.16/2.45 % (24154)------------------------------
% 8.16/2.45 % (24154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.45 % (24154)Termination reason: Unknown
% 8.16/2.45 % (24154)Termination phase: Saturation
% 8.16/2.45
% 8.16/2.45 % (24154)Memory used [KB]: 7547
% 8.16/2.45 % (24154)Time elapsed: 0.054 s
% 8.16/2.45 % (24154)Instructions burned: 206 (million)
% 8.16/2.45 % (24154)------------------------------
% 8.16/2.45 % (24154)------------------------------
% 8.16/2.46 % (24158)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_23745 for (2991ds/1539Mi)
% 8.16/2.46 % (24159)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_23745 for (2991ds/408Mi)
% 8.16/2.47 % (24151)Instruction limit reached!
% 8.16/2.47 % (24151)------------------------------
% 8.16/2.47 % (24151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.16/2.47 % (24151)Termination reason: Unknown
% 8.16/2.47 % (24151)Termination phase: Saturation
% 8.16/2.47
% 8.16/2.47 % (24151)Memory used [KB]: 8443
% 8.16/2.47 % (24151)Time elapsed: 0.106 s
% 8.16/2.47 % (24151)Instructions burned: 370 (million)
% 8.16/2.47 % (24151)------------------------------
% 8.16/2.47 % (24151)------------------------------
% 8.16/2.48 % (24160)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_23745 for (2990ds/5205Mi)
% 8.46/2.50 % (24140)Instruction limit reached!
% 8.46/2.50 % (24140)------------------------------
% 8.46/2.50 % (24140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.50 % (24140)Termination reason: Unknown
% 8.46/2.50 % (24140)Termination phase: Saturation
% 8.46/2.50
% 8.46/2.50 % (24140)Memory used [KB]: 11769
% 8.46/2.50 % (24140)Time elapsed: 0.246 s
% 8.46/2.50 % (24140)Instructions burned: 987 (million)
% 8.46/2.50 % (24140)------------------------------
% 8.46/2.50 % (24140)------------------------------
% 8.46/2.51 % (24161)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_23745 for (2990ds/1913Mi)
% 8.46/2.58 % (24159)Instruction limit reached!
% 8.46/2.58 % (24159)------------------------------
% 8.46/2.58 % (24159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.46/2.58 % (24159)Termination reason: Unknown
% 8.46/2.58 % (24159)Termination phase: Saturation
% 8.46/2.58
% 8.46/2.58 % (24159)Memory used [KB]: 10106
% 8.46/2.58 % (24159)Time elapsed: 0.126 s
% 8.46/2.58 % (24159)Instructions burned: 409 (million)
% 8.46/2.58 % (24159)------------------------------
% 8.46/2.58 % (24159)------------------------------
% 8.46/2.60 % (24162)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_23745 for (2989ds/4350Mi)
% 8.85/2.62 % (24147)Instruction limit reached!
% 8.85/2.62 % (24147)------------------------------
% 8.85/2.62 % (24147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.62 % (24147)Termination reason: Unknown
% 8.85/2.62 % (24147)Termination phase: Saturation
% 8.85/2.62
% 8.85/2.62 % (24147)Memory used [KB]: 10490
% 8.85/2.62 % (24147)Time elapsed: 0.288 s
% 8.85/2.62 % (24147)Instructions burned: 924 (million)
% 8.85/2.62 % (24147)------------------------------
% 8.85/2.62 % (24147)------------------------------
% 8.85/2.63 % (24163)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_23745 for (2989ds/68Mi)
% 8.85/2.64 % (24163)Instruction limit reached!
% 8.85/2.64 % (24163)------------------------------
% 8.85/2.64 % (24163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.64 % (24163)Termination reason: Unknown
% 8.85/2.64 % (24163)Termination phase: SInE selection
% 8.85/2.64
% 8.85/2.64 % (24163)Memory used [KB]: 2046
% 8.85/2.64 % (24163)Time elapsed: 0.018 s
% 8.85/2.64 % (24163)Instructions burned: 68 (million)
% 8.85/2.64 % (24163)------------------------------
% 8.85/2.64 % (24163)------------------------------
% 8.85/2.65 % (24164)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_23745 for (2989ds/358Mi)
% 8.85/2.69 % (24152)Instruction limit reached!
% 8.85/2.69 % (24152)------------------------------
% 8.85/2.69 % (24152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.85/2.69 % (24152)Termination reason: Unknown
% 8.85/2.69 % (24152)Termination phase: Saturation
% 8.85/2.69
% 8.85/2.69 % (24152)Memory used [KB]: 11129
% 8.85/2.69 % (24152)Time elapsed: 0.318 s
% 8.85/2.69 % (24152)Instructions burned: 1023 (million)
% 8.85/2.69 % (24152)------------------------------
% 8.85/2.69 % (24152)------------------------------
% 9.51/2.70 % (24165)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_23745 for (2988ds/31Mi)
% 9.51/2.71 % (24165)Instruction limit reached!
% 9.51/2.71 % (24165)------------------------------
% 9.51/2.71 % (24165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.71 % (24165)Termination reason: Unknown
% 9.51/2.71 % (24165)Termination phase: shuffling
% 9.51/2.71
% 9.51/2.71 % (24165)Memory used [KB]: 2046
% 9.51/2.71 % (24165)Time elapsed: 0.010 s
% 9.51/2.71 % (24165)Instructions burned: 33 (million)
% 9.51/2.71 % (24165)------------------------------
% 9.51/2.71 % (24165)------------------------------
% 9.51/2.72 % (24166)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_23745 for (2988ds/279Mi)
% 9.51/2.75 % (24164)Instruction limit reached!
% 9.51/2.75 % (24164)------------------------------
% 9.51/2.75 % (24164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.75 % (24164)Termination reason: Unknown
% 9.51/2.75 % (24164)Termination phase: Saturation
% 9.51/2.75
% 9.51/2.75 % (24164)Memory used [KB]: 8315
% 9.51/2.75 % (24164)Time elapsed: 0.100 s
% 9.51/2.75 % (24164)Instructions burned: 358 (million)
% 9.51/2.75 % (24164)------------------------------
% 9.51/2.75 % (24164)------------------------------
% 9.51/2.76 % (24167)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_23745 for (2988ds/258Mi)
% 9.51/2.79 % (24166)Instruction limit reached!
% 9.51/2.79 % (24166)------------------------------
% 9.51/2.79 % (24166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.79 % (24166)Termination reason: Unknown
% 9.51/2.79 % (24166)Termination phase: Saturation
% 9.51/2.79
% 9.51/2.79 % (24166)Memory used [KB]: 7291
% 9.51/2.79 % (24166)Time elapsed: 0.071 s
% 9.51/2.79 % (24166)Instructions burned: 279 (million)
% 9.51/2.79 % (24166)------------------------------
% 9.51/2.79 % (24166)------------------------------
% 9.72/2.80 % (24168)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_23745 for (2987ds/26Mi)
% 9.72/2.80 % (24168)Instruction limit reached!
% 9.72/2.80 % (24168)------------------------------
% 9.72/2.80 % (24168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.80 % (24168)Termination reason: Unknown
% 9.72/2.80 % (24168)Termination phase: shuffling
% 9.72/2.80
% 9.72/2.80 % (24168)Memory used [KB]: 1918
% 9.72/2.80 % (24168)Time elapsed: 0.008 s
% 9.72/2.80 % (24168)Instructions burned: 27 (million)
% 9.72/2.80 % (24168)------------------------------
% 9.72/2.80 % (24168)------------------------------
% 9.72/2.81 % (24169)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_23745 for (2987ds/995Mi)
% 9.72/2.83 % (24167)Instruction limit reached!
% 9.72/2.83 % (24167)------------------------------
% 9.72/2.83 % (24167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.72/2.83 % (24167)Termination reason: Unknown
% 9.72/2.83 % (24167)Termination phase: Saturation
% 9.72/2.83
% 9.72/2.83 % (24167)Memory used [KB]: 8315
% 9.72/2.83 % (24167)Time elapsed: 0.070 s
% 9.72/2.83 % (24167)Instructions burned: 258 (million)
% 9.72/2.83 % (24167)------------------------------
% 9.72/2.83 % (24167)------------------------------
% 9.72/2.84 % (24170)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_23745 for (2987ds/373Mi)
% 9.81/2.94 % (24158)Instruction limit reached!
% 9.81/2.94 % (24158)------------------------------
% 9.81/2.94 % (24158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.81/2.94 % (24158)Termination reason: Unknown
% 9.81/2.94 % (24158)Termination phase: Saturation
% 9.81/2.94
% 9.81/2.94 % (24158)Memory used [KB]: 9466
% 9.81/2.94 % (24158)Time elapsed: 0.480 s
% 9.81/2.94 % (24158)Instructions burned: 1540 (million)
% 9.81/2.94 % (24158)------------------------------
% 9.81/2.94 % (24158)------------------------------
% 9.81/2.95 % (24171)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_23745 for (2986ds/253Mi)
% 9.81/2.95 % (24170)Instruction limit reached!
% 9.81/2.95 % (24170)------------------------------
% 9.81/2.95 % (24170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.81/2.95 % (24170)Termination reason: Unknown
% 9.81/2.95 % (24170)Termination phase: Saturation
% 9.81/2.95
% 9.81/2.95 % (24170)Memory used [KB]: 8443
% 9.81/2.95 % (24170)Time elapsed: 0.110 s
% 9.81/2.95 % (24170)Instructions burned: 374 (million)
% 9.81/2.95 % (24170)------------------------------
% 9.81/2.95 % (24170)------------------------------
% 9.81/2.96 % (24172)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_23745 for (2986ds/832Mi)
% 9.81/3.01 % (24171)Instruction limit reached!
% 9.81/3.01 % (24171)------------------------------
% 9.81/3.01 % (24171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.81/3.01 % (24171)Termination reason: Unknown
% 9.81/3.01 % (24171)Termination phase: Saturation
% 9.81/3.01
% 9.81/3.01 % (24171)Memory used [KB]: 7164
% 9.81/3.01 % (24171)Time elapsed: 0.065 s
% 9.81/3.01 % (24171)Instructions burned: 256 (million)
% 9.81/3.01 % (24171)------------------------------
% 9.81/3.01 % (24171)------------------------------
% 9.81/3.02 % (24173)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_23745 for (2985ds/668Mi)
% 12.84/3.06 % (24169)Instruction limit reached!
% 12.84/3.06 % (24169)------------------------------
% 12.84/3.06 % (24169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.84/3.06 % (24169)Termination reason: Unknown
% 12.84/3.06 % (24169)Termination phase: Saturation
% 12.84/3.06
% 12.84/3.06 % (24169)Memory used [KB]: 11257
% 12.84/3.06 % (24169)Time elapsed: 0.250 s
% 12.84/3.06 % (24169)Instructions burned: 996 (million)
% 12.84/3.06 % (24169)------------------------------
% 12.84/3.06 % (24169)------------------------------
% 12.84/3.07 % (24174)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_23745 for (2984ds/40Mi)
% 12.84/3.08 % (24174)Instruction limit reached!
% 12.84/3.08 % (24174)------------------------------
% 12.84/3.08 % (24174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.84/3.08 % (24174)Termination reason: Unknown
% 12.84/3.08 % (24174)Termination phase: Property scanning
% 12.84/3.08
% 12.84/3.08 % (24174)Memory used [KB]: 2174
% 12.84/3.08 % (24174)Time elapsed: 0.013 s
% 12.84/3.08 % (24174)Instructions burned: 42 (million)
% 12.84/3.08 % (24174)------------------------------
% 12.84/3.08 % (24174)------------------------------
% 12.84/3.09 % (24175)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_23745 for (2984ds/294Mi)
% 12.84/3.10 % (24161)Instruction limit reached!
% 12.84/3.10 % (24161)------------------------------
% 12.84/3.10 % (24161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.84/3.10 % (24161)Termination reason: Unknown
% 12.84/3.10 % (24161)Termination phase: Saturation
% 12.84/3.10
% 12.84/3.10 % (24161)Memory used [KB]: 4861
% 12.84/3.10 % (24161)Time elapsed: 0.591 s
% 12.84/3.10 % (24161)Instructions burned: 1915 (million)
% 12.84/3.10 % (24161)------------------------------
% 12.84/3.10 % (24161)------------------------------
% 12.84/3.11 % (24176)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_23745 for (2984ds/187Mi)
% 13.42/3.16 % (24176)Instruction limit reached!
% 13.42/3.16 % (24176)------------------------------
% 13.42/3.16 % (24176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.42/3.16 % (24176)Termination reason: Unknown
% 13.42/3.16 % (24176)Termination phase: Saturation
% 13.42/3.16
% 13.42/3.16 % (24176)Memory used [KB]: 7547
% 13.42/3.16 % (24176)Time elapsed: 0.050 s
% 13.42/3.16 % (24176)Instructions burned: 188 (million)
% 13.42/3.16 % (24176)------------------------------
% 13.42/3.16 % (24176)------------------------------
% 13.42/3.17 % (24177)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_23745 for (2983ds/371Mi)
% 13.42/3.17 % (24175)Instruction limit reached!
% 13.42/3.17 % (24175)------------------------------
% 13.42/3.17 % (24175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.42/3.17 % (24175)Termination reason: Unknown
% 13.42/3.17 % (24175)Termination phase: Saturation
% 13.42/3.17
% 13.42/3.17 % (24175)Memory used [KB]: 6908
% 13.42/3.17 % (24175)Time elapsed: 0.074 s
% 13.42/3.17 % (24175)Instructions burned: 295 (million)
% 13.42/3.17 % (24175)------------------------------
% 13.42/3.17 % (24175)------------------------------
% 13.42/3.18 % (24178)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_23745 for (2983ds/1827Mi)
% 13.42/3.19 % (24173)Instruction limit reached!
% 13.42/3.19 % (24173)------------------------------
% 13.42/3.19 % (24173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.42/3.19 % (24173)Termination reason: Unknown
% 13.42/3.19 % (24173)Termination phase: Saturation
% 13.42/3.19
% 13.42/3.19 % (24173)Memory used [KB]: 16247
% 13.42/3.19 % (24173)Time elapsed: 0.169 s
% 13.42/3.19 % (24173)Instructions burned: 668 (million)
% 13.42/3.19 % (24173)------------------------------
% 13.42/3.19 % (24173)------------------------------
% 14.01/3.20 % (24179)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_23745 for (2983ds/70Mi)
% 14.01/3.22 % (24179)Instruction limit reached!
% 14.01/3.22 % (24179)------------------------------
% 14.01/3.22 % (24179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.22 % (24179)Termination reason: Unknown
% 14.01/3.22 % (24179)Termination phase: Property scanning
% 14.01/3.22
% 14.01/3.22 % (24179)Memory used [KB]: 2174
% 14.01/3.22 % (24179)Time elapsed: 0.019 s
% 14.01/3.22 % (24179)Instructions burned: 72 (million)
% 14.01/3.22 % (24179)------------------------------
% 14.01/3.22 % (24179)------------------------------
% 14.01/3.22 % (24172)Instruction limit reached!
% 14.01/3.22 % (24172)------------------------------
% 14.01/3.22 % (24172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.22 % (24172)Termination reason: Unknown
% 14.01/3.22 % (24172)Termination phase: Saturation
% 14.01/3.22
% 14.01/3.22 % (24172)Memory used [KB]: 9978
% 14.01/3.22 % (24172)Time elapsed: 0.258 s
% 14.01/3.22 % (24172)Instructions burned: 832 (million)
% 14.01/3.22 % (24172)------------------------------
% 14.01/3.22 % (24172)------------------------------
% 14.01/3.22 % (24180)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_23745 for (2983ds/316Mi)
% 14.01/3.23 % (24181)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_23745 for (2983ds/932Mi)
% 14.01/3.27 % (24177)Instruction limit reached!
% 14.01/3.27 % (24177)------------------------------
% 14.01/3.27 % (24177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.01/3.27 % (24177)Termination reason: Unknown
% 14.01/3.27 % (24177)Termination phase: Saturation
% 14.01/3.27
% 14.01/3.27 % (24177)Memory used [KB]: 8571
% 14.01/3.27 % (24177)Time elapsed: 0.103 s
% 14.01/3.27 % (24177)Instructions burned: 372 (million)
% 14.01/3.27 % (24177)------------------------------
% 14.01/3.27 % (24177)------------------------------
% 14.01/3.28 % (24182)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_23745 for (2982ds/4714Mi)
% 14.48/3.30 % (24180)Instruction limit reached!
% 14.48/3.30 % (24180)------------------------------
% 14.48/3.30 % (24180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.48/3.30 % (24180)Termination reason: Unknown
% 14.48/3.30 % (24180)Termination phase: Saturation
% 14.48/3.30
% 14.48/3.30 % (24180)Memory used [KB]: 7164
% 14.48/3.30 % (24180)Time elapsed: 0.079 s
% 14.48/3.30 % (24180)Instructions burned: 317 (million)
% 14.48/3.30 % (24180)------------------------------
% 14.48/3.30 % (24180)------------------------------
% 14.48/3.31 % (24183)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_23745 for (2982ds/8250Mi)
% 14.87/3.46 % (24181)Instruction limit reached!
% 14.87/3.46 % (24181)------------------------------
% 14.87/3.46 % (24181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.87/3.46 % (24181)Termination reason: Unknown
% 14.87/3.46 % (24181)Termination phase: Saturation
% 14.87/3.46
% 14.87/3.46 % (24181)Memory used [KB]: 13048
% 14.87/3.46 % (24181)Time elapsed: 0.234 s
% 14.87/3.46 % (24181)Instructions burned: 934 (million)
% 14.87/3.46 % (24181)------------------------------
% 14.87/3.46 % (24181)------------------------------
% 14.87/3.48 % (24184)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_23745 for (2981ds/770Mi)
% 16.01/3.70 % (24178)Instruction limit reached!
% 16.01/3.70 % (24178)------------------------------
% 16.01/3.70 % (24178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.01/3.70 % (24178)Termination reason: Unknown
% 16.01/3.70 % (24178)Termination phase: Saturation
% 16.01/3.70
% 16.01/3.70 % (24178)Memory used [KB]: 18421
% 16.01/3.70 % (24178)Time elapsed: 0.528 s
% 16.01/3.70 % (24178)Instructions burned: 1830 (million)
% 16.01/3.70 % (24178)------------------------------
% 16.01/3.70 % (24178)------------------------------
% 16.01/3.71 % (24185)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_23745 for (2978ds/794Mi)
% 16.01/3.74 % (24184)Instruction limit reached!
% 16.01/3.74 % (24184)------------------------------
% 16.01/3.74 % (24184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.01/3.74 % (24184)Termination reason: Unknown
% 16.01/3.74 % (24184)Termination phase: Saturation
% 16.01/3.74
% 16.01/3.74 % (24184)Memory used [KB]: 7164
% 16.01/3.74 % (24184)Time elapsed: 0.266 s
% 16.01/3.74 % (24184)Instructions burned: 771 (million)
% 16.01/3.74 % (24184)------------------------------
% 16.01/3.74 % (24184)------------------------------
% 16.01/3.75 % (24160)Instruction limit reached!
% 16.01/3.75 % (24160)------------------------------
% 16.01/3.75 % (24160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.01/3.75 % (24160)Termination reason: Unknown
% 16.01/3.75 % (24160)Termination phase: Saturation
% 16.01/3.75
% 16.01/3.75 % (24160)Memory used [KB]: 12281
% 16.01/3.75 % (24160)Time elapsed: 1.272 s
% 16.01/3.75 % (24160)Instructions burned: 5207 (million)
% 16.01/3.75 % (24160)------------------------------
% 16.01/3.75 % (24160)------------------------------
% 16.01/3.75 % (24186)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_23745 for (2978ds/464Mi)
% 16.01/3.76 % (24187)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_23745 for (2978ds/1376Mi)
% 17.10/3.85 % (24157)Instruction limit reached!
% 17.10/3.85 % (24157)------------------------------
% 17.10/3.85 % (24157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.10/3.85 % (24157)Termination reason: Unknown
% 17.10/3.85 % (24157)Termination phase: Saturation
% 17.10/3.85
% 17.10/3.85 % (24157)Memory used [KB]: 17014
% 17.10/3.85 % (24157)Time elapsed: 1.400 s
% 17.10/3.85 % (24157)Instructions burned: 4437 (million)
% 17.10/3.85 % (24157)------------------------------
% 17.10/3.85 % (24157)------------------------------
% 17.10/3.86 % (24188)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_23745 for (2977ds/906Mi)
% 17.26/3.90 % (24186)Instruction limit reached!
% 17.26/3.90 % (24186)------------------------------
% 17.26/3.90 % (24186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.26/3.90 % (24186)Termination reason: Unknown
% 17.26/3.90 % (24186)Termination phase: Saturation
% 17.26/3.90
% 17.26/3.90 % (24186)Memory used [KB]: 8443
% 17.26/3.90 % (24186)Time elapsed: 0.146 s
% 17.26/3.90 % (24186)Instructions burned: 465 (million)
% 17.26/3.90 % (24186)------------------------------
% 17.26/3.90 % (24186)------------------------------
% 17.26/3.91 % (24189)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_23745 for (2976ds/434Mi)
% 17.26/3.93 % (24162)Instruction limit reached!
% 17.26/3.93 % (24162)------------------------------
% 17.26/3.93 % (24162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.26/3.93 % (24162)Termination reason: Unknown
% 17.26/3.93 % (24162)Termination phase: Saturation
% 17.26/3.93
% 17.26/3.93 % (24162)Memory used [KB]: 13048
% 17.26/3.93 % (24162)Time elapsed: 1.341 s
% 17.26/3.93 % (24162)Instructions burned: 4351 (million)
% 17.26/3.93 % (24162)------------------------------
% 17.26/3.93 % (24162)------------------------------
% 17.26/3.95 % (24190)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_23745 for (2976ds/865Mi)
% 17.26/3.96 % (24185)Instruction limit reached!
% 17.26/3.96 % (24185)------------------------------
% 17.26/3.96 % (24185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.26/3.96 % (24185)Termination reason: Unknown
% 17.26/3.96 % (24185)Termination phase: Saturation
% 17.26/3.96
% 17.26/3.96 % (24185)Memory used [KB]: 5245
% 17.26/3.96 % (24185)Time elapsed: 0.242 s
% 17.26/3.96 % (24185)Instructions burned: 794 (million)
% 17.26/3.96 % (24185)------------------------------
% 17.26/3.96 % (24185)------------------------------
% 17.26/3.97 % (24191)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_23745 for (2976ds/593Mi)
% 19.79/4.06 % (24189)Refutation not found, non-redundant clauses discarded% (24189)------------------------------
% 19.79/4.06 % (24189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.79/4.06 % (24189)Termination reason: Refutation not found, non-redundant clauses discarded
% 19.79/4.06
% 19.79/4.06 % (24189)Memory used [KB]: 9594
% 19.79/4.06 % (24189)Time elapsed: 0.153 s
% 19.79/4.06 % (24189)Instructions burned: 398 (million)
% 19.79/4.06 % (24189)------------------------------
% 19.79/4.06 % (24189)------------------------------
% 19.79/4.08 % (24192)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_23745 for (2974ds/443Mi)
% 19.79/4.11 % (24187)Instruction limit reached!
% 19.79/4.11 % (24187)------------------------------
% 19.79/4.11 % (24187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.79/4.11 % (24187)Termination reason: Unknown
% 19.79/4.11 % (24187)Termination phase: Saturation
% 19.79/4.11
% 19.79/4.11 % (24187)Memory used [KB]: 8827
% 19.79/4.11 % (24187)Time elapsed: 0.349 s
% 19.79/4.11 % (24187)Instructions burned: 1378 (million)
% 19.79/4.11 % (24187)------------------------------
% 19.79/4.11 % (24187)------------------------------
% 19.79/4.11 % (24191)Instruction limit reached!
% 19.79/4.11 % (24191)------------------------------
% 19.79/4.11 % (24191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.79/4.11 % (24191)Termination reason: Unknown
% 19.79/4.11 % (24191)Termination phase: Saturation
% 19.79/4.11
% 19.79/4.11 % (24191)Memory used [KB]: 7164
% 19.79/4.11 % (24191)Time elapsed: 0.147 s
% 19.79/4.11 % (24191)Instructions burned: 596 (million)
% 19.79/4.11 % (24191)------------------------------
% 19.79/4.11 % (24191)------------------------------
% 20.46/4.12 % (24193)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_23745 for (2974ds/594Mi)
% 20.46/4.12 % (24194)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_23745 for (2974ds/327Mi)
% 20.46/4.14 % (24188)Instruction limit reached!
% 20.46/4.14 % (24188)------------------------------
% 20.46/4.14 % (24188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.46/4.14 % (24188)Termination reason: Unknown
% 20.46/4.14 % (24188)Termination phase: Saturation
% 20.46/4.14
% 20.46/4.14 % (24188)Memory used [KB]: 10618
% 20.46/4.14 % (24188)Time elapsed: 0.284 s
% 20.46/4.14 % (24188)Instructions burned: 909 (million)
% 20.46/4.14 % (24188)------------------------------
% 20.46/4.14 % (24188)------------------------------
% 20.46/4.15 % (24195)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_23745 for (2974ds/5411Mi)
% 20.74/4.20 % (24190)Instruction limit reached!
% 20.74/4.20 % (24190)------------------------------
% 20.74/4.20 % (24190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.20 % (24190)Termination reason: Unknown
% 20.74/4.20 % (24190)Termination phase: Saturation
% 20.74/4.20
% 20.74/4.20 % (24190)Memory used [KB]: 9594
% 20.74/4.20 % (24190)Time elapsed: 0.259 s
% 20.74/4.20 % (24190)Instructions burned: 865 (million)
% 20.74/4.20 % (24190)------------------------------
% 20.74/4.20 % (24190)------------------------------
% 20.74/4.21 % (24192)Instruction limit reached!
% 20.74/4.21 % (24192)------------------------------
% 20.74/4.21 % (24192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.21 % (24192)Termination reason: Unknown
% 20.74/4.21 % (24192)Termination phase: Saturation
% 20.74/4.21
% 20.74/4.21 % (24192)Memory used [KB]: 8571
% 20.74/4.21 % (24192)Time elapsed: 0.135 s
% 20.74/4.21 % (24192)Instructions burned: 445 (million)
% 20.74/4.21 % (24192)------------------------------
% 20.74/4.21 % (24192)------------------------------
% 20.74/4.21 % (24196)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_23745 for (2973ds/1762Mi)
% 20.74/4.22 % (24194)Instruction limit reached!
% 20.74/4.22 % (24194)------------------------------
% 20.74/4.22 % (24194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.22 % (24194)Termination reason: Unknown
% 20.74/4.22 % (24194)Termination phase: Saturation
% 20.74/4.22
% 20.74/4.22 % (24194)Memory used [KB]: 10234
% 20.74/4.22 % (24194)Time elapsed: 0.102 s
% 20.74/4.22 % (24194)Instructions burned: 327 (million)
% 20.74/4.22 % (24194)------------------------------
% 20.74/4.22 % (24194)------------------------------
% 20.74/4.22 % (24197)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_23745 for (2973ds/96Mi)
% 20.74/4.23 % (24198)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_23745 for (2973ds/503Mi)
% 20.74/4.25 % (24197)Instruction limit reached!
% 20.74/4.25 % (24197)------------------------------
% 20.74/4.25 % (24197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.25 % (24197)Termination reason: Unknown
% 20.74/4.25 % (24197)Termination phase: Property scanning
% 20.74/4.25
% 20.74/4.25 % (24197)Memory used [KB]: 2302
% 20.74/4.25 % (24197)Time elapsed: 0.025 s
% 20.74/4.25 % (24197)Instructions burned: 98 (million)
% 20.74/4.25 % (24197)------------------------------
% 20.74/4.25 % (24197)------------------------------
% 20.74/4.26 % (24199)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_23745 for (2973ds/90Mi)
% 20.74/4.28 % (24199)Instruction limit reached!
% 20.74/4.28 % (24199)------------------------------
% 20.74/4.28 % (24199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.28 % (24199)Termination reason: Unknown
% 20.74/4.28 % (24199)Termination phase: Twee Goal Transformation
% 20.74/4.28
% 20.74/4.28 % (24199)Memory used [KB]: 2430
% 20.74/4.28 % (24199)Time elapsed: 0.025 s
% 20.74/4.28 % (24199)Instructions burned: 90 (million)
% 20.74/4.28 % (24199)------------------------------
% 20.74/4.28 % (24199)------------------------------
% 20.74/4.29 % (24200)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_23745 for (2972ds/593Mi)
% 20.74/4.29 % (24193)Instruction limit reached!
% 20.74/4.29 % (24193)------------------------------
% 20.74/4.29 % (24193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.74/4.29 % (24193)Termination reason: Unknown
% 20.74/4.29 % (24193)Termination phase: Saturation
% 20.74/4.29
% 20.74/4.29 % (24193)Memory used [KB]: 8571
% 20.74/4.29 % (24193)Time elapsed: 0.176 s
% 20.74/4.29 % (24193)Instructions burned: 597 (million)
% 20.74/4.29 % (24193)------------------------------
% 20.74/4.29 % (24193)------------------------------
% 21.47/4.30 % (24201)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_23745 for (2972ds/1512Mi)
% 21.47/4.37 % (24198)Instruction limit reached!
% 21.47/4.37 % (24198)------------------------------
% 21.47/4.37 % (24198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.47/4.37 % (24198)Termination reason: Unknown
% 21.47/4.37 % (24198)Termination phase: Saturation
% 21.47/4.37
% 21.47/4.37 % (24198)Memory used [KB]: 8827
% 21.47/4.37 % (24198)Time elapsed: 0.144 s
% 21.47/4.37 % (24198)Instructions burned: 503 (million)
% 21.47/4.37 % (24198)------------------------------
% 21.47/4.37 % (24198)------------------------------
% 21.47/4.38 % (24202)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_23745 for (2971ds/569Mi)
% 21.84/4.41 % (24182)Instruction limit reached!
% 21.84/4.41 % (24182)------------------------------
% 21.84/4.41 % (24182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.84/4.41 % (24182)Termination reason: Unknown
% 21.84/4.41 % (24182)Termination phase: Saturation
% 21.84/4.41
% 21.84/4.41 % (24182)Memory used [KB]: 7291
% 21.84/4.41 % (24182)Time elapsed: 1.131 s
% 21.84/4.41 % (24182)Instructions burned: 4715 (million)
% 21.84/4.41 % (24182)------------------------------
% 21.84/4.41 % (24182)------------------------------
% 21.84/4.42 % (24203)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_23745 for (2971ds/501Mi)
% 21.84/4.46 % (24200)Instruction limit reached!
% 21.84/4.46 % (24200)------------------------------
% 21.84/4.46 % (24200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.84/4.46 % (24200)Termination reason: Unknown
% 21.84/4.46 % (24200)Termination phase: Saturation
% 21.84/4.46
% 21.84/4.46 % (24200)Memory used [KB]: 8827
% 21.84/4.46 % (24200)Time elapsed: 0.172 s
% 21.84/4.46 % (24200)Instructions burned: 593 (million)
% 21.84/4.46 % (24200)------------------------------
% 21.84/4.46 % (24200)------------------------------
% 21.84/4.47 % (24204)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_23745 for (2971ds/562Mi)
% 22.13/4.53 % (24202)Instruction limit reached!
% 22.13/4.53 % (24202)------------------------------
% 22.13/4.53 % (24202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.13/4.53 % (24202)Termination reason: Unknown
% 22.13/4.53 % (24202)Termination phase: Saturation
% 22.13/4.53
% 22.13/4.53 % (24202)Memory used [KB]: 11513
% 22.13/4.53 % (24202)Time elapsed: 0.143 s
% 22.13/4.53 % (24202)Instructions burned: 569 (million)
% 22.13/4.53 % (24202)------------------------------
% 22.13/4.53 % (24202)------------------------------
% 22.13/4.54 % (24205)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_23745 for (2970ds/406Mi)
% 22.13/4.57 % (24203)Instruction limit reached!
% 22.13/4.57 % (24203)------------------------------
% 22.13/4.57 % (24203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.13/4.57 % (24203)Termination reason: Unknown
% 22.13/4.57 % (24203)Termination phase: Saturation
% 22.13/4.57
% 22.13/4.57 % (24203)Memory used [KB]: 9466
% 22.13/4.57 % (24203)Time elapsed: 0.151 s
% 22.13/4.57 % (24203)Instructions burned: 502 (million)
% 22.13/4.57 % (24203)------------------------------
% 22.13/4.57 % (24203)------------------------------
% 22.13/4.58 % (24206)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_23745 for (2969ds/582Mi)
% 22.55/4.64 % (24204)Instruction limit reached!
% 22.55/4.64 % (24204)------------------------------
% 22.55/4.64 % (24204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.55/4.64 % (24204)Termination reason: Unknown
% 22.55/4.64 % (24204)Termination phase: Saturation
% 22.55/4.64
% 22.55/4.64 % (24204)Memory used [KB]: 8187
% 22.55/4.64 % (24204)Time elapsed: 0.167 s
% 22.55/4.64 % (24204)Instructions burned: 562 (million)
% 22.55/4.64 % (24204)------------------------------
% 22.55/4.64 % (24204)------------------------------
% 22.55/4.65 % (24196)Instruction limit reached!
% 22.55/4.65 % (24196)------------------------------
% 22.55/4.65 % (24196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.55/4.65 % (24196)Termination reason: Unknown
% 22.55/4.65 % (24196)Termination phase: Saturation
% 22.55/4.65
% 22.55/4.65 % (24196)Memory used [KB]: 16119
% 22.55/4.65 % (24196)Time elapsed: 0.434 s
% 22.55/4.65 % (24196)Instructions burned: 1763 (million)
% 22.55/4.65 % (24196)------------------------------
% 22.55/4.65 % (24196)------------------------------
% 22.55/4.65 % (24207)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_23745 for (2969ds/456Mi)
% 22.55/4.65 % (24205)Instruction limit reached!
% 22.55/4.65 % (24205)------------------------------
% 22.55/4.65 % (24205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.55/4.65 % (24205)Termination reason: Unknown
% 22.55/4.65 % (24205)Termination phase: Saturation
% 22.55/4.65
% 22.55/4.65 % (24205)Memory used [KB]: 7291
% 22.55/4.65 % (24205)Time elapsed: 0.115 s
% 22.55/4.65 % (24205)Instructions burned: 408 (million)
% 22.55/4.65 % (24205)------------------------------
% 22.55/4.65 % (24205)------------------------------
% 22.55/4.66 % (24208)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_23745 for (2969ds/393Mi)
% 22.55/4.66 % (24209)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_23745 for (2969ds/1335Mi)
% 23.39/4.76 % (24206)Instruction limit reached!
% 23.39/4.76 % (24206)------------------------------
% 23.39/4.76 % (24206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.39/4.76 % (24206)Termination reason: Unknown
% 23.39/4.76 % (24206)Termination phase: Saturation
% 23.39/4.76
% 23.39/4.76 % (24206)Memory used [KB]: 9722
% 23.39/4.76 % (24206)Time elapsed: 0.183 s
% 23.39/4.76 % (24206)Instructions burned: 583 (million)
% 23.39/4.76 % (24206)------------------------------
% 23.39/4.76 % (24206)------------------------------
% 23.39/4.76 % (24201)Instruction limit reached!
% 23.39/4.76 % (24201)------------------------------
% 23.39/4.76 % (24201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.39/4.76 % (24201)Termination reason: Unknown
% 23.39/4.76 % (24201)Termination phase: Saturation
% 23.39/4.76
% 23.39/4.76 % (24201)Memory used [KB]: 11897
% 23.39/4.76 % (24201)Time elapsed: 0.459 s
% 23.39/4.76 % (24201)Instructions burned: 1514 (million)
% 23.39/4.76 % (24201)------------------------------
% 23.39/4.76 % (24201)------------------------------
% 23.39/4.77 % (24210)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_23745 for (2968ds/3373Mi)
% 23.39/4.77 % (24211)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_23745 for (2968ds/474Mi)
% 23.39/4.77 % (24208)Instruction limit reached!
% 23.39/4.77 % (24208)------------------------------
% 23.39/4.77 % (24208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.39/4.77 % (24208)Termination reason: Unknown
% 23.39/4.77 % (24208)Termination phase: Saturation
% 23.39/4.77
% 23.39/4.77 % (24208)Memory used [KB]: 9210
% 23.39/4.77 % (24208)Time elapsed: 0.118 s
% 23.39/4.77 % (24208)Instructions burned: 394 (million)
% 23.39/4.77 % (24208)------------------------------
% 23.39/4.77 % (24208)------------------------------
% 23.39/4.78 % (24207)Instruction limit reached!
% 23.39/4.78 % (24207)------------------------------
% 23.39/4.78 % (24207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.39/4.78 % (24207)Termination reason: Unknown
% 23.39/4.78 % (24207)Termination phase: Saturation
% 23.39/4.78
% 23.39/4.78 % (24207)Memory used [KB]: 8699
% 23.39/4.78 % (24207)Time elapsed: 0.133 s
% 23.39/4.78 % (24207)Instructions burned: 457 (million)
% 23.39/4.78 % (24207)------------------------------
% 23.39/4.78 % (24207)------------------------------
% 23.39/4.78 % (24212)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_23745 for (2967ds/157Mi)
% 23.39/4.79 % (24213)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_23745 for (2967ds/590Mi)
% 24.43/4.82 % (24212)Instruction limit reached!
% 24.43/4.82 % (24212)------------------------------
% 24.43/4.82 % (24212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.43/4.82 % (24212)Termination reason: Unknown
% 24.43/4.82 % (24212)Termination phase: Saturation
% 24.43/4.82
% 24.43/4.82 % (24212)Memory used [KB]: 6908
% 24.43/4.82 % (24212)Time elapsed: 0.040 s
% 24.43/4.82 % (24212)Instructions burned: 158 (million)
% 24.43/4.82 % (24212)------------------------------
% 24.43/4.82 % (24212)------------------------------
% 24.43/4.83 % (24214)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_23745 for (2967ds/104Mi)
% 24.43/4.86 % (24214)Instruction limit reached!
% 24.43/4.86 % (24214)------------------------------
% 24.43/4.86 % (24214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.43/4.86 % (24214)Termination reason: Unknown
% 24.43/4.86 % (24214)Termination phase: Property scanning
% 24.43/4.86
% 24.43/4.86 % (24214)Memory used [KB]: 2430
% 24.43/4.86 % (24214)Time elapsed: 0.027 s
% 24.43/4.86 % (24214)Instructions burned: 104 (million)
% 24.43/4.86 % (24214)------------------------------
% 24.43/4.86 % (24214)------------------------------
% 24.43/4.87 % (24215)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_23745 for (2967ds/414Mi)
% 24.43/4.89 % (24211)Instruction limit reached!
% 24.43/4.89 % (24211)------------------------------
% 24.43/4.89 % (24211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.43/4.89 % (24211)Termination reason: Unknown
% 24.43/4.89 % (24211)Termination phase: Saturation
% 24.43/4.89
% 24.43/4.89 % (24211)Memory used [KB]: 11513
% 24.43/4.89 % (24211)Time elapsed: 0.119 s
% 24.43/4.89 % (24211)Instructions burned: 476 (million)
% 24.43/4.89 % (24211)------------------------------
% 24.43/4.89 % (24211)------------------------------
% 24.74/4.90 % (24216)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_23745 for (2966ds/715Mi)
% 24.74/4.95 % (24213)Instruction limit reached!
% 24.74/4.95 % (24213)------------------------------
% 24.74/4.95 % (24213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.74/4.95 % (24213)Termination reason: Unknown
% 24.74/4.95 % (24213)Termination phase: Saturation
% 24.74/4.95
% 24.74/4.95 % (24213)Memory used [KB]: 8699
% 24.74/4.95 % (24213)Time elapsed: 0.159 s
% 24.74/4.95 % (24213)Instructions burned: 590 (million)
% 24.74/4.95 % (24213)------------------------------
% 24.74/4.95 % (24213)------------------------------
% 24.74/4.96 % (24217)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_23745 for (2966ds/961Mi)
% 24.74/4.97 % (24215)Instruction limit reached!
% 24.74/4.97 % (24215)------------------------------
% 24.74/4.97 % (24215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.74/4.97 % (24215)Termination reason: Unknown
% 24.74/4.97 % (24215)Termination phase: Saturation
% 24.74/4.97
% 24.74/4.97 % (24215)Memory used [KB]: 7164
% 24.74/4.97 % (24215)Time elapsed: 0.103 s
% 24.74/4.97 % (24215)Instructions burned: 417 (million)
% 24.74/4.97 % (24215)------------------------------
% 24.74/4.97 % (24215)------------------------------
% 24.74/4.98 % (24218)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_23745 for (2966ds/1213Mi)
% 26.89/5.06 % (24209)Instruction limit reached!
% 26.89/5.06 % (24209)------------------------------
% 26.89/5.06 % (24209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.89/5.06 % (24209)Termination reason: Unknown
% 26.89/5.06 % (24209)Termination phase: Saturation
% 26.89/5.06
% 26.89/5.06 % (24209)Memory used [KB]: 9594
% 26.89/5.06 % (24209)Time elapsed: 0.404 s
% 26.89/5.06 % (24209)Instructions burned: 1336 (million)
% 26.89/5.06 % (24209)------------------------------
% 26.89/5.06 % (24209)------------------------------
% 26.89/5.07 % (24219)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_23745 for (2964ds/1979Mi)
% 26.89/5.11 % (24216)Instruction limit reached!
% 26.89/5.11 % (24216)------------------------------
% 26.89/5.11 % (24216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.89/5.11 % (24216)Termination reason: Unknown
% 26.89/5.11 % (24216)Termination phase: Saturation
% 26.89/5.11
% 26.89/5.11 % (24216)Memory used [KB]: 4349
% 26.89/5.11 % (24216)Time elapsed: 0.213 s
% 26.89/5.11 % (24216)Instructions burned: 716 (million)
% 26.89/5.11 % (24216)------------------------------
% 26.89/5.11 % (24216)------------------------------
% 26.89/5.12 % (24220)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_23745 for (2964ds/481Mi)
% 27.90/5.24 % (24220)Instruction limit reached!
% 27.90/5.24 % (24220)------------------------------
% 27.90/5.24 % (24220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.90/5.24 % (24220)Termination reason: Unknown
% 27.90/5.24 % (24220)Termination phase: Saturation
% 27.90/5.24
% 27.90/5.24 % (24220)Memory used [KB]: 11129
% 27.90/5.24 % (24220)Time elapsed: 0.121 s
% 27.90/5.24 % (24220)Instructions burned: 485 (million)
% 27.90/5.24 % (24220)------------------------------
% 27.90/5.24 % (24220)------------------------------
% 27.90/5.24 % (24217)Instruction limit reached!
% 27.90/5.24 % (24217)------------------------------
% 27.90/5.24 % (24217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.90/5.24 % (24217)Termination reason: Unknown
% 27.90/5.24 % (24217)Termination phase: Saturation
% 27.90/5.24
% 27.90/5.24 % (24217)Memory used [KB]: 8955
% 27.90/5.24 % (24217)Time elapsed: 0.309 s
% 27.90/5.24 % (24217)Instructions burned: 963 (million)
% 27.90/5.24 % (24217)------------------------------
% 27.90/5.24 % (24217)------------------------------
% 27.90/5.25 % (24221)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_23745 for (2963ds/783Mi)
% 27.90/5.25 % (24222)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_23745 for (2963ds/432Mi)
% 28.48/5.35 % (24218)Instruction limit reached!
% 28.48/5.35 % (24218)------------------------------
% 28.48/5.35 % (24218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.48/5.35 % (24218)Termination reason: Unknown
% 28.48/5.35 % (24218)Termination phase: Saturation
% 28.48/5.35
% 28.48/5.35 % (24218)Memory used [KB]: 13048
% 28.48/5.35 % (24218)Time elapsed: 0.398 s
% 28.48/5.35 % (24218)Instructions burned: 1214 (million)
% 28.48/5.35 % (24218)------------------------------
% 28.48/5.35 % (24218)------------------------------
% 28.48/5.36 % (24223)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_23745 for (2962ds/1670Mi)
% 28.48/5.38 % (24222)Instruction limit reached!
% 28.48/5.38 % (24222)------------------------------
% 28.48/5.38 % (24222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.48/5.38 % (24222)Termination reason: Unknown
% 28.48/5.38 % (24222)Termination phase: Saturation
% 28.48/5.38
% 28.48/5.38 % (24222)Memory used [KB]: 8315
% 28.48/5.38 % (24222)Time elapsed: 0.130 s
% 28.48/5.38 % (24222)Instructions burned: 432 (million)
% 28.48/5.38 % (24222)------------------------------
% 28.48/5.38 % (24222)------------------------------
% 28.48/5.39 % (24224)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_23745 for (2961ds/90Mi)
% 28.99/5.41 % (24224)Instruction limit reached!
% 28.99/5.41 % (24224)------------------------------
% 28.99/5.41 % (24224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.99/5.41 % (24224)Termination reason: Unknown
% 28.99/5.41 % (24224)Termination phase: Property scanning
% 28.99/5.41
% 28.99/5.41 % (24224)Memory used [KB]: 2302
% 28.99/5.41 % (24224)Time elapsed: 0.024 s
% 28.99/5.41 % (24224)Instructions burned: 91 (million)
% 28.99/5.41 % (24224)------------------------------
% 28.99/5.41 % (24224)------------------------------
% 28.99/5.42 % (24225)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_23745 for (2961ds/346Mi)
% 29.33/5.50 % (24221)Instruction limit reached!
% 29.33/5.50 % (24221)------------------------------
% 29.33/5.50 % (24221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.33/5.50 % (24221)Termination reason: Unknown
% 29.33/5.50 % (24221)Termination phase: Saturation
% 29.33/5.50
% 29.33/5.50 % (24221)Memory used [KB]: 10746
% 29.33/5.50 % (24221)Time elapsed: 0.249 s
% 29.33/5.50 % (24221)Instructions burned: 784 (million)
% 29.33/5.50 % (24221)------------------------------
% 29.33/5.50 % (24221)------------------------------
% 29.33/5.51 % (24226)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_23745 for (2960ds/401Mi)
% 29.33/5.51 % (24225)Instruction limit reached!
% 29.33/5.51 % (24225)------------------------------
% 29.33/5.51 % (24225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.33/5.51 % (24225)Termination reason: Unknown
% 29.33/5.51 % (24225)Termination phase: Saturation
% 29.33/5.51
% 29.33/5.51 % (24225)Memory used [KB]: 7164
% 29.33/5.51 % (24225)Time elapsed: 0.089 s
% 29.33/5.51 % (24225)Instructions burned: 346 (million)
% 29.33/5.51 % (24225)------------------------------
% 29.33/5.51 % (24225)------------------------------
% 29.33/5.52 % (24227)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_23745 for (2960ds/6454Mi)
% 29.99/5.61 % (24226)Instruction limit reached!
% 29.99/5.61 % (24226)------------------------------
% 29.99/5.61 % (24226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.99/5.61 % (24226)Termination reason: Unknown
% 29.99/5.61 % (24226)Termination phase: Saturation
% 29.99/5.61
% 29.99/5.61 % (24226)Memory used [KB]: 7164
% 29.99/5.61 % (24226)Time elapsed: 0.100 s
% 29.99/5.61 % (24226)Instructions burned: 403 (million)
% 29.99/5.61 % (24226)------------------------------
% 29.99/5.61 % (24226)------------------------------
% 29.99/5.62 % (24228)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_23745 for (2959ds/283Mi)
% 29.99/5.68 % (24219)Instruction limit reached!
% 29.99/5.68 % (24219)------------------------------
% 29.99/5.68 % (24219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.99/5.68 % (24219)Termination reason: Unknown
% 29.99/5.68 % (24219)Termination phase: Saturation
% 29.99/5.68
% 29.99/5.68 % (24219)Memory used [KB]: 9722
% 29.99/5.68 % (24219)Time elapsed: 0.607 s
% 29.99/5.68 % (24219)Instructions burned: 1979 (million)
% 29.99/5.68 % (24219)------------------------------
% 29.99/5.68 % (24219)------------------------------
% 29.99/5.69 % (24229)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_23745 for (2958ds/865Mi)
% 29.99/5.69 % (24228)Instruction limit reached!
% 29.99/5.69 % (24228)------------------------------
% 29.99/5.69 % (24228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.99/5.69 % (24228)Termination reason: Unknown
% 29.99/5.69 % (24228)Termination phase: Saturation
% 29.99/5.69
% 29.99/5.69 % (24228)Memory used [KB]: 8187
% 29.99/5.69 % (24228)Time elapsed: 0.078 s
% 29.99/5.69 % (24228)Instructions burned: 285 (million)
% 29.99/5.69 % (24228)------------------------------
% 29.99/5.69 % (24228)------------------------------
% 31.10/5.70 % (24230)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_23745 for (2958ds/4528Mi)
% 31.10/5.78 % (24223)Instruction limit reached!
% 31.10/5.78 % (24223)------------------------------
% 31.10/5.78 % (24223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.10/5.78 % (24223)Termination reason: Unknown
% 31.10/5.78 % (24223)Termination phase: Saturation
% 31.10/5.78
% 31.10/5.78 % (24223)Memory used [KB]: 12665
% 31.10/5.78 % (24223)Time elapsed: 0.419 s
% 31.10/5.78 % (24223)Instructions burned: 1672 (million)
% 31.10/5.78 % (24223)------------------------------
% 31.10/5.78 % (24223)------------------------------
% 31.10/5.79 % (24231)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_23745 for (2957ds/1001Mi)
% 31.83/5.80 % (24210)Instruction limit reached!
% 31.83/5.80 % (24210)------------------------------
% 31.83/5.80 % (24210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.83/5.80 % (24210)Termination reason: Unknown
% 31.83/5.80 % (24210)Termination phase: Saturation
% 31.83/5.80
% 31.83/5.80 % (24210)Memory used [KB]: 12537
% 31.83/5.80 % (24210)Time elapsed: 1.035 s
% 31.83/5.80 % (24210)Instructions burned: 3374 (million)
% 31.83/5.80 % (24210)------------------------------
% 31.83/5.80 % (24210)------------------------------
% 31.83/5.81 % (24230)Refutation not found, incomplete strategy
% 31.83/5.81 % (24230)------------------------------
% 31.83/5.81 % (24230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.83/5.81 % (24230)Termination reason: Refutation not found, incomplete strategy
% 31.83/5.81
% 31.83/5.81
% 31.83/5.81 % (24230)Memory used [KB]: 2558
% 31.83/5.81 % (24230)Time elapsed: 0.106 s
% 31.83/5.81 % (24230)Instructions burned: 408 (million)
% 31.83/5.81 % (24230)------------------------------
% 31.83/5.81 % (24230)------------------------------
% 31.83/5.81 % (24232)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_23745 for (2957ds/102Mi)
% 31.83/5.82 % (24233)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_23745 for (2957ds/952Mi)
% 31.83/5.84 % (24232)Instruction limit reached!
% 31.83/5.84 % (24232)------------------------------
% 31.83/5.84 % (24232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.83/5.84 % (24232)Termination reason: Unknown
% 31.83/5.84 % (24232)Termination phase: Property scanning
% 31.83/5.84
% 31.83/5.84 % (24232)Memory used [KB]: 2430
% 31.83/5.84 % (24232)Time elapsed: 0.027 s
% 31.83/5.84 % (24232)Instructions burned: 103 (million)
% 31.83/5.84 % (24232)------------------------------
% 31.83/5.84 % (24232)------------------------------
% 31.83/5.85 % (24234)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_23745 for (2957ds/578Mi)
% 31.83/5.86 % (24195)Instruction limit reached!
% 31.83/5.86 % (24195)------------------------------
% 31.83/5.86 % (24195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.83/5.86 % (24195)Termination reason: Unknown
% 31.83/5.86 % (24195)Termination phase: Saturation
% 31.83/5.86
% 31.83/5.86 % (24195)Memory used [KB]: 16119
% 31.83/5.86 % (24195)Time elapsed: 1.709 s
% 31.83/5.86 % (24195)Instructions burned: 5412 (million)
% 31.83/5.86 % (24195)------------------------------
% 31.83/5.86 % (24195)------------------------------
% 31.83/5.87 % (24235)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_23745 for (2957ds/643Mi)
% 32.18/5.93 % (24229)Instruction limit reached!
% 32.18/5.93 % (24229)------------------------------
% 32.18/5.93 % (24229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.18/5.93 % (24229)Termination reason: Unknown
% 32.18/5.93 % (24229)Termination phase: Saturation
% 32.18/5.93
% 32.18/5.93 % (24229)Memory used [KB]: 8187
% 32.18/5.93 % (24229)Time elapsed: 0.239 s
% 32.18/5.93 % (24229)Instructions burned: 865 (million)
% 32.18/5.93 % (24229)------------------------------
% 32.18/5.93 % (24229)------------------------------
% 32.18/5.94 % (24236)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_23745 for (2956ds/865Mi)
% 32.18/5.96 % (24183)Instruction limit reached!
% 32.18/5.96 % (24183)------------------------------
% 32.18/5.96 % (24183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.18/5.96 % (24183)Termination reason: Unknown
% 32.18/5.96 % (24183)Termination phase: Saturation
% 32.18/5.96
% 32.18/5.96 % (24183)Memory used [KB]: 24434
% 32.18/5.96 % (24183)Time elapsed: 2.653 s
% 32.18/5.96 % (24183)Instructions burned: 8253 (million)
% 32.18/5.96 % (24183)------------------------------
% 32.18/5.96 % (24183)------------------------------
% 32.18/5.98 % (24234)Instruction limit reached!
% 32.18/5.98 % (24234)------------------------------
% 32.18/5.98 % (24234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.18/5.98 % (24234)Termination reason: Unknown
% 32.18/5.98 % (24234)Termination phase: Saturation
% 32.18/5.98
% 32.18/5.98 % (24234)Memory used [KB]: 8827
% 32.18/5.98 % (24234)Time elapsed: 0.135 s
% 32.18/5.98 % (24234)Instructions burned: 578 (million)
% 32.18/5.98 % (24234)------------------------------
% 32.18/5.98 % (24234)------------------------------
% 32.18/5.98 % (24237)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_23745 for (2955ds/1174Mi)
% 32.18/5.99 % (24238)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_23745 for (2955ds/644Mi)
% 33.91/6.03 % (24235)Instruction limit reached!
% 33.91/6.03 % (24235)------------------------------
% 33.91/6.03 % (24235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.91/6.03 % (24235)Termination reason: Unknown
% 33.91/6.03 % (24235)Termination phase: Saturation
% 33.91/6.03
% 33.91/6.03 % (24235)Memory used [KB]: 11513
% 33.91/6.03 % (24235)Time elapsed: 0.161 s
% 33.91/6.03 % (24235)Instructions burned: 644 (million)
% 33.91/6.03 % (24235)------------------------------
% 33.91/6.03 % (24235)------------------------------
% 33.91/6.04 % (24239)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_23745 for (2955ds/1201Mi)
% 33.91/6.10 % (24231)Instruction limit reached!
% 33.91/6.10 % (24231)------------------------------
% 33.91/6.10 % (24231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.91/6.10 % (24231)Termination reason: Unknown
% 33.91/6.10 % (24231)Termination phase: Saturation
% 33.91/6.10
% 33.91/6.10 % (24231)Memory used [KB]: 9850
% 33.91/6.10 % (24231)Time elapsed: 0.305 s
% 33.91/6.10 % (24231)Instructions burned: 1003 (million)
% 33.91/6.10 % (24231)------------------------------
% 33.91/6.10 % (24231)------------------------------
% 33.91/6.11 % (24233)Instruction limit reached!
% 33.91/6.11 % (24233)------------------------------
% 33.91/6.11 % (24233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.91/6.11 % (24233)Termination reason: Unknown
% 33.91/6.11 % (24233)Termination phase: Saturation
% 33.91/6.11
% 33.91/6.11 % (24233)Memory used [KB]: 9978
% 33.91/6.11 % (24233)Time elapsed: 0.289 s
% 33.91/6.11 % (24233)Instructions burned: 952 (million)
% 33.91/6.11 % (24233)------------------------------
% 33.91/6.11 % (24233)------------------------------
% 33.91/6.11 % (24240)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_23745 for (2954ds/1046Mi)
% 33.91/6.12 % (24241)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_23745 for (2954ds/222Mi)
% 34.49/6.17 % (24236)Instruction limit reached!
% 34.49/6.17 % (24236)------------------------------
% 34.49/6.17 % (24236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.49/6.17 % (24236)Termination reason: Unknown
% 34.49/6.17 % (24236)Termination phase: Saturation
% 34.49/6.17
% 34.49/6.17 % (24236)Memory used [KB]: 7419
% 34.49/6.17 % (24236)Time elapsed: 0.235 s
% 34.49/6.17 % (24236)Instructions burned: 867 (million)
% 34.49/6.17 % (24236)------------------------------
% 34.49/6.17 % (24236)------------------------------
% 34.49/6.17 % (24241)Instruction limit reached!
% 34.49/6.17 % (24241)------------------------------
% 34.49/6.17 % (24241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.49/6.17 % (24241)Termination reason: Unknown
% 34.49/6.17 % (24241)Termination phase: Saturation
% 34.49/6.17
% 34.49/6.17 % (24241)Memory used [KB]: 7164
% 34.49/6.17 % (24241)Time elapsed: 0.057 s
% 34.49/6.17 % (24241)Instructions burned: 225 (million)
% 34.49/6.17 % (24241)------------------------------
% 34.49/6.17 % (24241)------------------------------
% 34.49/6.18 % (24242)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_23745 for (2953ds/68Mi)
% 34.49/6.18 % (24243)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_23745 for (2953ds/454Mi)
% 34.49/6.18 % (24238)Instruction limit reached!
% 34.49/6.18 % (24238)------------------------------
% 34.49/6.18 % (24238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.49/6.18 % (24238)Termination reason: Unknown
% 34.49/6.18 % (24238)Termination phase: Saturation
% 34.49/6.18
% 34.49/6.18 % (24238)Memory used [KB]: 7803
% 34.49/6.18 % (24238)Time elapsed: 0.190 s
% 34.49/6.18 % (24238)Instructions burned: 647 (million)
% 34.49/6.18 % (24238)------------------------------
% 34.49/6.18 % (24238)------------------------------
% 34.49/6.19 % (24244)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_23745 for (2953ds/360Mi)
% 34.82/6.20 % (24242)Instruction limit reached!
% 34.82/6.20 % (24242)------------------------------
% 34.82/6.20 % (24242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.82/6.20 % (24242)Termination reason: Unknown
% 34.82/6.20 % (24242)Termination phase: Preprocessing 3
% 34.82/6.20
% 34.82/6.20 % (24242)Memory used [KB]: 2046
% 34.82/6.20 % (24242)Time elapsed: 0.019 s
% 34.82/6.20 % (24242)Instructions burned: 71 (million)
% 34.82/6.20 % (24242)------------------------------
% 34.82/6.20 % (24242)------------------------------
% 34.82/6.21 % (24245)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_23745 for (2953ds/157Mi)
% 34.82/6.25 % (24245)Instruction limit reached!
% 34.82/6.25 % (24245)------------------------------
% 34.82/6.25 % (24245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.82/6.25 % (24245)Termination reason: Unknown
% 34.82/6.25 % (24245)Termination phase: Saturation
% 34.82/6.25
% 34.82/6.25 % (24245)Memory used [KB]: 6908
% 34.82/6.25 % (24245)Time elapsed: 0.040 s
% 34.82/6.25 % (24245)Instructions burned: 158 (million)
% 34.82/6.25 % (24245)------------------------------
% 34.82/6.25 % (24245)------------------------------
% 34.82/6.26 % (24246)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_23745 for (2953ds/5061Mi)
% 34.82/6.28 % (24244)Instruction limit reached!
% 34.82/6.28 % (24244)------------------------------
% 34.82/6.28 % (24244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.82/6.28 % (24244)Termination reason: Unknown
% 34.82/6.28 % (24244)Termination phase: Saturation
% 34.82/6.28
% 34.82/6.28 % (24244)Memory used [KB]: 7164
% 34.82/6.28 % (24244)Time elapsed: 0.089 s
% 34.82/6.28 % (24244)Instructions burned: 360 (million)
% 34.82/6.28 % (24244)------------------------------
% 34.82/6.28 % (24244)------------------------------
% 34.82/6.29 % (24247)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_23745 for (2952ds/2401Mi)
% 34.82/6.29 % (24243)Instruction limit reached!
% 34.82/6.29 % (24243)------------------------------
% 34.82/6.29 % (24243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.82/6.29 % (24243)Termination reason: Unknown
% 34.82/6.29 % (24243)Termination phase: Saturation
% 34.82/6.29
% 34.82/6.29 % (24243)Memory used [KB]: 15991
% 34.82/6.29 % (24243)Time elapsed: 0.115 s
% 34.82/6.29 % (24243)Instructions burned: 456 (million)
% 34.82/6.29 % (24243)------------------------------
% 34.82/6.29 % (24243)------------------------------
% 35.33/6.30 % (24248)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_23745 for (2952ds/5798Mi)
% 35.33/6.35 % (24237)Instruction limit reached!
% 35.33/6.35 % (24237)------------------------------
% 35.33/6.35 % (24237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.33/6.35 % (24237)Termination reason: Unknown
% 35.33/6.35 % (24237)Termination phase: Saturation
% 35.33/6.35
% 35.33/6.35 % (24237)Memory used [KB]: 9594
% 35.33/6.35 % (24237)Time elapsed: 0.365 s
% 35.33/6.35 % (24237)Instructions burned: 1174 (million)
% 35.33/6.35 % (24237)------------------------------
% 35.33/6.35 % (24237)------------------------------
% 35.33/6.36 % (24249)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_23745 for (2952ds/346Mi)
% 35.33/6.36 % (24240)Instruction limit reached!
% 35.33/6.36 % (24240)------------------------------
% 35.33/6.36 % (24240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.33/6.36 % (24240)Termination reason: Unknown
% 35.33/6.36 % (24240)Termination phase: Saturation
% 35.33/6.36
% 35.33/6.36 % (24240)Memory used [KB]: 7291
% 35.33/6.36 % (24240)Time elapsed: 0.254 s
% 35.33/6.36 % (24240)Instructions burned: 1047 (million)
% 35.33/6.36 % (24240)------------------------------
% 35.33/6.36 % (24240)------------------------------
% 35.33/6.37 % (24250)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_23745 for (2951ds/1321Mi)
% 35.33/6.39 % (24239)Instruction limit reached!
% 35.33/6.39 % (24239)------------------------------
% 35.33/6.39 % (24239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.33/6.39 % (24239)Termination reason: Unknown
% 35.33/6.39 % (24239)Termination phase: Saturation
% 35.33/6.39
% 35.33/6.39 % (24239)Memory used [KB]: 10362
% 35.33/6.39 % (24239)Time elapsed: 0.355 s
% 35.33/6.39 % (24239)Instructions burned: 1201 (million)
% 35.33/6.39 % (24239)------------------------------
% 35.33/6.39 % (24239)------------------------------
% 36.12/6.40 % (24251)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_23745 for (2951ds/1312Mi)
% 36.12/6.44 % (24249)Instruction limit reached!
% 36.12/6.44 % (24249)------------------------------
% 36.12/6.44 % (24249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.12/6.44 % (24249)Termination reason: Unknown
% 36.12/6.44 % (24249)Termination phase: Saturation
% 36.12/6.44
% 36.12/6.44 % (24249)Memory used [KB]: 7419
% 36.12/6.44 % (24249)Time elapsed: 0.087 s
% 36.12/6.44 % (24249)Instructions burned: 348 (million)
% 36.12/6.44 % (24249)------------------------------
% 36.12/6.44 % (24249)------------------------------
% 36.12/6.45 % (24252)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_23745 for (2951ds/672Mi)
% 36.42/6.66 % (24252)Instruction limit reached!
% 36.42/6.66 % (24252)------------------------------
% 36.42/6.66 % (24252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.42/6.66 % (24252)Termination reason: Unknown
% 36.42/6.66 % (24252)Termination phase: Saturation
% 36.42/6.66
% 36.42/6.66 % (24252)Memory used [KB]: 9850
% 36.42/6.66 % (24252)Time elapsed: 0.211 s
% 36.42/6.66 % (24252)Instructions burned: 672 (million)
% 36.42/6.66 % (24252)------------------------------
% 36.42/6.66 % (24252)------------------------------
% 36.42/6.67 % (24253)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_23745 for (2948ds/1897Mi)
% 36.76/6.74 % (24251)Instruction limit reached!
% 36.76/6.74 % (24251)------------------------------
% 36.76/6.74 % (24251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.76/6.74 % (24251)Termination reason: Unknown
% 36.76/6.74 % (24251)Termination phase: Saturation
% 36.76/6.74
% 36.76/6.74 % (24251)Memory used [KB]: 11897
% 36.76/6.74 % (24251)Time elapsed: 0.343 s
% 36.76/6.74 % (24251)Instructions burned: 1312 (million)
% 36.76/6.74 % (24251)------------------------------
% 36.76/6.74 % (24251)------------------------------
% 36.76/6.75 % (24254)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_23745 for (2948ds/1202Mi)
% 36.76/6.77 % (24250)Instruction limit reached!
% 36.76/6.77 % (24250)------------------------------
% 36.76/6.77 % (24250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.76/6.77 % (24250)Termination reason: Unknown
% 36.76/6.77 % (24250)Termination phase: Saturation
% 36.76/6.77
% 36.76/6.77 % (24250)Memory used [KB]: 7036
% 36.76/6.77 % (24250)Time elapsed: 0.407 s
% 36.76/6.77 % (24250)Instructions burned: 1324 (million)
% 36.76/6.77 % (24250)------------------------------
% 36.76/6.77 % (24250)------------------------------
% 36.76/6.78 % (24255)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_23745 for (2947ds/1493Mi)
% 37.72/7.02 % (24247)Instruction limit reached!
% 37.72/7.02 % (24247)------------------------------
% 37.72/7.02 % (24247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.72/7.02 % (24247)Termination reason: Unknown
% 37.72/7.02 % (24247)Termination phase: Saturation
% 37.72/7.02
% 37.72/7.02 % (24247)Memory used [KB]: 8827
% 37.72/7.02 % (24247)Time elapsed: 0.731 s
% 37.72/7.02 % (24247)Instructions burned: 2401 (million)
% 37.72/7.02 % (24247)------------------------------
% 37.72/7.02 % (24247)------------------------------
% 40.93/7.03 % (24256)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_23745 for (2945ds/7679Mi)
% 40.93/7.10 % (24254)Instruction limit reached!
% 40.93/7.10 % (24254)------------------------------
% 40.93/7.10 % (24254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.93/7.10 % (24254)Termination reason: Unknown
% 40.93/7.10 % (24254)Termination phase: Saturation
% 40.93/7.10
% 40.93/7.10 % (24254)Memory used [KB]: 6908
% 40.93/7.10 % (24254)Time elapsed: 0.346 s
% 40.93/7.10 % (24254)Instructions burned: 1202 (million)
% 40.93/7.10 % (24254)------------------------------
% 40.93/7.10 % (24254)------------------------------
% 40.93/7.11 % (24257)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_23745 for (2944ds/340Mi)
% 41.54/7.14 % (24255)Instruction limit reached!
% 41.54/7.14 % (24255)------------------------------
% 41.54/7.14 % (24255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.54/7.14 % (24255)Termination reason: Unknown
% 41.54/7.14 % (24255)Termination phase: Saturation
% 41.54/7.14
% 41.54/7.14 % (24255)Memory used [KB]: 7291
% 41.54/7.14 % (24255)Time elapsed: 0.356 s
% 41.54/7.14 % (24255)Instructions burned: 1494 (million)
% 41.54/7.14 % (24255)------------------------------
% 41.54/7.14 % (24255)------------------------------
% 41.54/7.15 % (24258)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_23745 for (2944ds/3672Mi)
% 41.85/7.21 % (24257)Instruction limit reached!
% 41.85/7.21 % (24257)------------------------------
% 41.85/7.21 % (24257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.85/7.21 % (24257)Termination reason: Unknown
% 41.85/7.21 % (24257)Termination phase: Saturation
% 41.85/7.21
% 41.85/7.21 % (24257)Memory used [KB]: 9594
% 41.85/7.21 % (24257)Time elapsed: 0.099 s
% 41.85/7.21 % (24257)Instructions burned: 342 (million)
% 41.85/7.21 % (24257)------------------------------
% 41.85/7.21 % (24257)------------------------------
% 41.85/7.22 % (24259)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_23745 for (2943ds/1535Mi)
% 41.85/7.26 % (24253)Instruction limit reached!
% 41.85/7.26 % (24253)------------------------------
% 41.85/7.26 % (24253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.85/7.26 % (24253)Termination reason: Unknown
% 41.85/7.26 % (24253)Termination phase: Saturation
% 41.85/7.26
% 41.85/7.26 % (24253)Memory used [KB]: 12537
% 41.85/7.26 % (24253)Time elapsed: 0.590 s
% 41.85/7.26 % (24253)Instructions burned: 1899 (million)
% 41.85/7.26 % (24253)------------------------------
% 41.85/7.26 % (24253)------------------------------
% 41.85/7.27 % (24260)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_23745 for (2943ds/4637Mi)
% 42.63/7.48 % (24246)Instruction limit reached!
% 42.63/7.48 % (24246)------------------------------
% 42.63/7.48 % (24246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.63/7.48 % (24246)Termination reason: Unknown
% 42.63/7.48 % (24246)Termination phase: Saturation
% 42.63/7.48
% 42.63/7.48 % (24246)Memory used [KB]: 7803
% 42.63/7.48 % (24246)Time elapsed: 1.227 s
% 42.63/7.48 % (24246)Instructions burned: 5062 (million)
% 42.63/7.48 % (24246)------------------------------
% 42.63/7.48 % (24246)------------------------------
% 42.63/7.49 % (24261)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_23745 for (2940ds/3174Mi)
% 42.93/7.55 % (24227)Instruction limit reached!
% 42.93/7.55 % (24227)------------------------------
% 42.93/7.55 % (24227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.93/7.55 % (24227)Termination reason: Unknown
% 42.93/7.55 % (24227)Termination phase: Saturation
% 42.93/7.55
% 42.93/7.55 % (24227)Memory used [KB]: 14328
% 42.93/7.55 % (24227)Time elapsed: 2.035 s
% 42.93/7.55 % (24227)Instructions burned: 6456 (million)
% 42.93/7.55 % (24227)------------------------------
% 42.93/7.55 % (24227)------------------------------
% 42.93/7.56 % (24262)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_23745 for (2940ds/307Mi)
% 43.10/7.60 % (24259)Instruction limit reached!
% 43.10/7.60 % (24259)------------------------------
% 43.10/7.60 % (24259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.10/7.60 % (24259)Termination reason: Unknown
% 43.10/7.60 % (24259)Termination phase: Saturation
% 43.10/7.60
% 43.10/7.60 % (24259)Memory used [KB]: 11769
% 43.10/7.60 % (24259)Time elapsed: 0.384 s
% 43.10/7.60 % (24259)Instructions burned: 1535 (million)
% 43.10/7.60 % (24259)------------------------------
% 43.10/7.60 % (24259)------------------------------
% 43.10/7.61 % (24263)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_23745 for (2939ds/3619Mi)
% 43.10/7.64 % (24262)Instruction limit reached!
% 43.10/7.64 % (24262)------------------------------
% 43.10/7.64 % (24262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.10/7.64 % (24262)Termination reason: Unknown
% 43.10/7.64 % (24262)Termination phase: Saturation
% 43.10/7.64
% 43.10/7.64 % (24262)Memory used [KB]: 7164
% 43.10/7.64 % (24262)Time elapsed: 0.077 s
% 43.10/7.64 % (24262)Instructions burned: 307 (million)
% 43.10/7.64 % (24262)------------------------------
% 43.10/7.64 % (24262)------------------------------
% 43.10/7.65 % (24264)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_23745 for (2939ds/2325Mi)
% 47.92/8.12 % (24248)Instruction limit reached!
% 47.92/8.12 % (24248)------------------------------
% 47.92/8.12 % (24248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.92/8.12 % (24248)Termination reason: Unknown
% 47.92/8.12 % (24248)Termination phase: Saturation
% 47.92/8.12
% 47.92/8.12 % (24248)Memory used [KB]: 15479
% 47.92/8.12 % (24248)Time elapsed: 1.812 s
% 47.92/8.12 % (24248)Instructions burned: 5799 (million)
% 47.92/8.12 % (24248)------------------------------
% 47.92/8.12 % (24248)------------------------------
% 48.65/8.13 % (24265)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_23745 for (2934ds/2341Mi)
% 48.65/8.16 % (24264)Refutation not found, non-redundant clauses discarded% (24264)------------------------------
% 48.65/8.16 % (24264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.65/8.16 % (24264)Termination reason: Refutation not found, non-redundant clauses discarded
% 48.65/8.16
% 48.65/8.16 % (24264)Memory used [KB]: 17014
% 48.65/8.16 % (24264)Time elapsed: 0.509 s
% 48.65/8.16 % (24264)Instructions burned: 1705 (million)
% 48.65/8.16 % (24264)------------------------------
% 48.65/8.16 % (24264)------------------------------
% 48.65/8.17 % (24266)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_23745 for (2933ds/7257Mi)
% 49.07/8.29 % (24258)Instruction limit reached!
% 49.07/8.29 % (24258)------------------------------
% 49.07/8.29 % (24258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.07/8.29 % (24258)Termination reason: Unknown
% 49.07/8.29 % (24258)Termination phase: Saturation
% 49.07/8.29
% 49.07/8.29 % (24258)Memory used [KB]: 12153
% 49.07/8.29 % (24258)Time elapsed: 1.141 s
% 49.07/8.29 % (24258)Instructions burned: 3672 (million)
% 49.07/8.29 % (24258)------------------------------
% 49.07/8.29 % (24258)------------------------------
% 49.56/8.30 % (24267)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_23745 for (2932ds/3710Mi)
% 49.96/8.44 % (24261)Instruction limit reached!
% 49.96/8.44 % (24261)------------------------------
% 49.96/8.44 % (24261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.96/8.44 % (24261)Termination reason: Unknown
% 49.96/8.44 % (24261)Termination phase: Saturation
% 49.96/8.44
% 49.96/8.44 % (24261)Memory used [KB]: 19317
% 49.96/8.44 % (24261)Time elapsed: 0.951 s
% 49.96/8.44 % (24261)Instructions burned: 3175 (million)
% 49.96/8.44 % (24261)------------------------------
% 49.96/8.44 % (24261)------------------------------
% 49.96/8.45 % (24268)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_23745 for (2931ds/326Mi)
% 50.31/8.55 % (24268)Instruction limit reached!
% 50.31/8.55 % (24268)------------------------------
% 50.31/8.55 % (24268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.31/8.55 % (24268)Termination reason: Unknown
% 50.31/8.55 % (24268)Termination phase: Saturation
% 50.31/8.55
% 50.31/8.55 % (24268)Memory used [KB]: 8315
% 50.31/8.55 % (24268)Time elapsed: 0.097 s
% 50.31/8.55 % (24268)Instructions burned: 326 (million)
% 50.31/8.55 % (24268)------------------------------
% 50.31/8.55 % (24268)------------------------------
% 50.31/8.56 % (24269)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_23745 for (2930ds/1100Mi)
% 50.72/8.67 % (24263)Instruction limit reached!
% 50.72/8.67 % (24263)------------------------------
% 50.72/8.67 % (24263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.72/8.67 % (24263)Termination reason: Unknown
% 50.72/8.67 % (24263)Termination phase: Saturation
% 50.72/8.67
% 50.72/8.67 % (24263)Memory used [KB]: 17014
% 50.72/8.67 % (24263)Time elapsed: 1.064 s
% 50.72/8.67 % (24263)Instructions burned: 3619 (million)
% 50.72/8.67 % (24263)------------------------------
% 50.72/8.67 % (24263)------------------------------
% 50.72/8.68 % (24270)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_23745 for (2928ds/406Mi)
% 50.72/8.69 % (24260)Instruction limit reached!
% 50.72/8.69 % (24260)------------------------------
% 50.72/8.69 % (24260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.72/8.69 % (24260)Termination reason: Unknown
% 50.72/8.69 % (24260)Termination phase: Saturation
% 50.72/8.69
% 50.72/8.69 % (24260)Memory used [KB]: 11257
% 50.72/8.69 % (24260)Time elapsed: 1.425 s
% 50.72/8.69 % (24260)Instructions burned: 4637 (million)
% 50.72/8.69 % (24260)------------------------------
% 50.72/8.69 % (24260)------------------------------
% 51.04/8.71 % (24271)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_23745 for (2928ds/1871Mi)
% 51.14/8.80 % (24270)Instruction limit reached!
% 51.14/8.80 % (24270)------------------------------
% 51.14/8.80 % (24270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.14/8.80 % (24270)Termination reason: Unknown
% 51.14/8.80 % (24270)Termination phase: Saturation
% 51.14/8.80
% 51.14/8.80 % (24270)Memory used [KB]: 7419
% 51.14/8.80 % (24270)Time elapsed: 0.116 s
% 51.14/8.80 % (24270)Instructions burned: 409 (million)
% 51.14/8.80 % (24270)------------------------------
% 51.14/8.80 % (24270)------------------------------
% 51.14/8.81 % (24272)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_23745 for (2927ds/1194Mi)
% 51.14/8.85 % (24265)Instruction limit reached!
% 51.14/8.85 % (24265)------------------------------
% 51.14/8.85 % (24265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.14/8.85 % (24265)Termination reason: Unknown
% 51.14/8.85 % (24265)Termination phase: Saturation
% 51.14/8.85
% 51.14/8.85 % (24265)Memory used [KB]: 10490
% 51.14/8.85 % (24265)Time elapsed: 0.722 s
% 51.14/8.85 % (24265)Instructions burned: 2342 (million)
% 51.14/8.85 % (24265)------------------------------
% 51.14/8.85 % (24265)------------------------------
% 51.14/8.86 % (24273)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_23745 for (2927ds/474Mi)
% 52.09/8.90 % (24269)Instruction limit reached!
% 52.09/8.90 % (24269)------------------------------
% 52.09/8.90 % (24269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.09/8.90 % (24269)Termination reason: Unknown
% 52.09/8.90 % (24269)Termination phase: Saturation
% 52.09/8.90
% 52.09/8.90 % (24269)Memory used [KB]: 12665
% 52.09/8.90 % (24269)Time elapsed: 0.345 s
% 52.09/8.90 % (24269)Instructions burned: 1100 (million)
% 52.09/8.90 % (24269)------------------------------
% 52.09/8.90 % (24269)------------------------------
% 52.09/8.91 % (24274)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_23745 for (2926ds/3115Mi)
% 52.09/8.98 % (24273)Instruction limit reached!
% 52.09/8.98 % (24273)------------------------------
% 52.09/8.98 % (24273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.09/8.98 % (24273)Termination reason: Unknown
% 52.09/8.98 % (24273)Termination phase: Saturation
% 52.09/8.98
% 52.09/8.98 % (24273)Memory used [KB]: 11385
% 52.09/8.98 % (24273)Time elapsed: 0.120 s
% 52.09/8.98 % (24273)Instructions burned: 477 (million)
% 52.09/8.98 % (24273)------------------------------
% 52.09/8.98 % (24273)------------------------------
% 52.09/8.99 % (24275)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_23745 for (2925ds/831Mi)
% 55.70/9.18 % (24272)Instruction limit reached!
% 55.70/9.18 % (24272)------------------------------
% 55.70/9.18 % (24272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.70/9.18 % (24272)Termination reason: Unknown
% 55.70/9.18 % (24272)Termination phase: Saturation
% 55.70/9.18
% 55.70/9.18 % (24272)Memory used [KB]: 11513
% 55.70/9.18 % (24272)Time elapsed: 0.370 s
% 55.70/9.18 % (24272)Instructions burned: 1196 (million)
% 55.70/9.18 % (24272)------------------------------
% 55.70/9.18 % (24272)------------------------------
% 55.70/9.19 % (24276)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_23745 for (2923ds/1188Mi)
% 56.18/9.23 % (24267)Instruction limit reached!
% 56.18/9.23 % (24267)------------------------------
% 56.18/9.23 % (24267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.18/9.23 % (24267)Termination reason: Unknown
% 56.18/9.23 % (24267)Termination phase: Saturation
% 56.18/9.23
% 56.18/9.23 % (24267)Memory used [KB]: 13048
% 56.18/9.23 % (24267)Time elapsed: 0.934 s
% 56.18/9.23 % (24267)Instructions burned: 3710 (million)
% 56.18/9.23 % (24267)------------------------------
% 56.18/9.23 % (24267)------------------------------
% 56.18/9.24 % (24275)Instruction limit reached!
% 56.18/9.24 % (24275)------------------------------
% 56.18/9.24 % (24275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.18/9.24 % (24275)Termination reason: Unknown
% 56.18/9.24 % (24275)Termination phase: Saturation
% 56.18/9.24
% 56.18/9.24 % (24275)Memory used [KB]: 8955
% 56.18/9.24 % (24275)Time elapsed: 0.255 s
% 56.18/9.24 % (24275)Instructions burned: 832 (million)
% 56.18/9.24 % (24275)------------------------------
% 56.18/9.24 % (24275)------------------------------
% 56.18/9.24 % (24277)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_23745 for (2923ds/2868Mi)
% 56.18/9.25 % (24278)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_23745 for (2923ds/1516Mi)
% 56.18/9.29 % (24271)Instruction limit reached!
% 56.18/9.29 % (24271)------------------------------
% 56.18/9.29 % (24271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.18/9.29 % (24271)Termination reason: Unknown
% 56.18/9.29 % (24271)Termination phase: Saturation
% 56.18/9.29
% 56.18/9.29 % (24271)Memory used [KB]: 17654
% 56.18/9.29 % (24271)Time elapsed: 0.582 s
% 56.18/9.29 % (24271)Instructions burned: 1871 (million)
% 56.18/9.29 % (24271)------------------------------
% 56.18/9.29 % (24271)------------------------------
% 56.18/9.30 % (24279)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_23745 for (2922ds/2321Mi)
% 56.67/9.32 % (24256)Instruction limit reached!
% 56.67/9.32 % (24256)------------------------------
% 56.67/9.32 % (24256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.67/9.32 % (24256)Termination reason: Unknown
% 56.67/9.32 % (24256)Termination phase: Saturation
% 56.67/9.32
% 56.67/9.32 % (24256)Memory used [KB]: 17526
% 56.67/9.32 % (24256)Time elapsed: 2.293 s
% 56.67/9.32 % (24256)Instructions burned: 7680 (million)
% 56.67/9.32 % (24256)------------------------------
% 56.67/9.32 % (24256)------------------------------
% 56.67/9.33 % (24280)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_23745 for (2922ds/2812Mi)
% 56.91/9.49 % (24276)Instruction limit reached!
% 56.91/9.49 % (24276)------------------------------
% 56.91/9.49 % (24276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.91/9.49 % (24276)Termination reason: Unknown
% 56.91/9.49 % (24276)Termination phase: Saturation
% 56.91/9.49
% 56.91/9.49 % (24276)Memory used [KB]: 13304
% 56.91/9.49 % (24276)Time elapsed: 0.321 s
% 56.91/9.49 % (24276)Instructions burned: 1189 (million)
% 56.91/9.49 % (24276)------------------------------
% 56.91/9.49 % (24276)------------------------------
% 56.91/9.50 % (24281)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_23745 for (2920ds/4604Mi)
% 57.64/9.66 % (24274)Instruction limit reached!
% 57.64/9.66 % (24274)------------------------------
% 57.64/9.66 % (24274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.64/9.66 % (24274)Termination reason: Unknown
% 57.64/9.66 % (24274)Termination phase: Saturation
% 57.64/9.66
% 57.64/9.66 % (24274)Memory used [KB]: 12025
% 57.64/9.66 % (24274)Time elapsed: 0.750 s
% 57.64/9.66 % (24274)Instructions burned: 3119 (million)
% 57.64/9.66 % (24274)------------------------------
% 57.64/9.66 % (24274)------------------------------
% 57.64/9.67 % (24282)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_23745 for (2918ds/2678Mi)
% 57.81/9.71 % (24278)Instruction limit reached!
% 57.81/9.71 % (24278)------------------------------
% 57.81/9.71 % (24278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.81/9.71 % (24278)Termination reason: Unknown
% 57.81/9.71 % (24278)Termination phase: Saturation
% 57.81/9.71
% 57.81/9.71 % (24278)Memory used [KB]: 11513
% 57.81/9.71 % (24278)Time elapsed: 0.462 s
% 57.81/9.71 % (24278)Instructions burned: 1516 (million)
% 57.81/9.71 % (24278)------------------------------
% 57.81/9.71 % (24278)------------------------------
% 57.81/9.72 % (24283)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_23745 for (2918ds/643Mi)
% 58.38/9.87 % (24279)Instruction limit reached!
% 58.38/9.87 % (24279)------------------------------
% 58.38/9.87 % (24279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.38/9.87 % (24279)Termination reason: Unknown
% 58.38/9.87 % (24279)Termination phase: Saturation
% 58.38/9.87
% 58.38/9.87 % (24279)Memory used [KB]: 11513
% 58.38/9.87 % (24279)Time elapsed: 0.571 s
% 58.38/9.87 % (24279)Instructions burned: 2321 (million)
% 58.38/9.87 % (24279)------------------------------
% 58.38/9.87 % (24279)------------------------------
% 58.38/9.88 % (24284)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_23745 for (2916ds/458Mi)
% 58.38/9.88 % (24283)Instruction limit reached!
% 58.38/9.88 % (24283)------------------------------
% 58.38/9.88 % (24283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.38/9.88 % (24283)Termination reason: Unknown
% 58.38/9.88 % (24283)Termination phase: Saturation
% 58.38/9.88
% 58.38/9.88 % (24283)Memory used [KB]: 11513
% 58.38/9.88 % (24283)Time elapsed: 0.164 s
% 58.38/9.88 % (24283)Instructions burned: 646 (million)
% 58.38/9.88 % (24283)------------------------------
% 58.38/9.88 % (24283)------------------------------
% 58.38/9.89 % (24285)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_23745 for (2916ds/2546Mi)
% 59.25/9.93 % (24277)Instruction limit reached!
% 59.25/9.93 % (24277)------------------------------
% 59.25/9.93 % (24277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.25/9.93 % (24277)Termination reason: Unknown
% 59.25/9.93 % (24277)Termination phase: Saturation
% 59.25/9.93
% 59.25/9.93 % (24277)Memory used [KB]: 7291
% 59.25/9.93 % (24277)Time elapsed: 0.692 s
% 59.25/9.93 % (24277)Instructions burned: 2871 (million)
% 59.25/9.93 % (24277)------------------------------
% 59.25/9.93 % (24277)------------------------------
% 59.25/9.94 % (24286)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_23745 for (2916ds/1432Mi)
% 59.25/9.99 % (24284)Instruction limit reached!
% 59.25/9.99 % (24284)------------------------------
% 59.25/9.99 % (24284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.25/9.99 % (24284)Termination reason: Unknown
% 59.25/9.99 % (24284)Termination phase: Saturation
% 59.25/9.99
% 59.25/9.99 % (24284)Memory used [KB]: 11513
% 59.25/9.99 % (24284)Time elapsed: 0.116 s
% 59.25/9.99 % (24284)Instructions burned: 462 (million)
% 59.25/9.99 % (24284)------------------------------
% 59.25/9.99 % (24284)------------------------------
% 59.25/10.00 % (24287)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_23745 for (2915ds/386Mi)
% 62.00/10.10 % (24287)Instruction limit reached!
% 62.00/10.10 % (24287)------------------------------
% 62.00/10.10 % (24287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.00/10.10 % (24287)Termination reason: Unknown
% 62.00/10.10 % (24287)Termination phase: Saturation
% 62.00/10.10
% 62.00/10.10 % (24287)Memory used [KB]: 7164
% 62.00/10.10 % (24287)Time elapsed: 0.095 s
% 62.00/10.10 % (24287)Instructions burned: 387 (million)
% 62.00/10.10 % (24287)------------------------------
% 62.00/10.10 % (24287)------------------------------
% 62.00/10.11 % (24288)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_23745 for (2914ds/360Mi)
% 63.12/10.20 % (24288)Instruction limit reached!
% 63.12/10.20 % (24288)------------------------------
% 63.12/10.20 % (24288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.12/10.20 % (24288)Termination reason: Unknown
% 63.12/10.20 % (24288)Termination phase: Saturation
% 63.12/10.20
% 63.12/10.20 % (24288)Memory used [KB]: 7164
% 63.12/10.20 % (24288)Time elapsed: 0.094 s
% 63.12/10.20 % (24288)Instructions burned: 364 (million)
% 63.12/10.20 % (24288)------------------------------
% 63.12/10.20 % (24288)------------------------------
% 63.12/10.21 % (24280)Instruction limit reached!
% 63.12/10.21 % (24280)------------------------------
% 63.12/10.21 % (24280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.12/10.21 % (24280)Termination reason: Unknown
% 63.12/10.21 % (24280)Termination phase: Saturation
% 63.12/10.21
% 63.12/10.21 % (24280)Memory used [KB]: 11129
% 63.12/10.21 % (24280)Time elapsed: 0.875 s
% 63.12/10.21 % (24280)Instructions burned: 2812 (million)
% 63.12/10.21 % (24280)------------------------------
% 63.12/10.21 % (24280)------------------------------
% 63.12/10.21 % (24289)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_23745 for (2913ds/5446Mi)
% 63.12/10.22 % (24290)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_23745 for (2913ds/2573Mi)
% 63.12/10.29 % (24286)Instruction limit reached!
% 63.12/10.29 % (24286)------------------------------
% 63.12/10.29 % (24286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.12/10.29 % (24286)Termination reason: Unknown
% 63.12/10.29 % (24286)Termination phase: Saturation
% 63.12/10.29
% 63.12/10.29 % (24286)Memory used [KB]: 15223
% 63.12/10.29 % (24286)Time elapsed: 0.344 s
% 63.12/10.29 % (24286)Instructions burned: 1433 (million)
% 63.12/10.29 % (24286)------------------------------
% 63.12/10.29 % (24286)------------------------------
% 63.12/10.30 % (24291)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=2655:si=on:rtra=on_0 on DTF2THF_23745 for (2912ds/2655Mi)
% 63.77/10.34 % (24282)Instruction limit reached!
% 63.77/10.34 % (24282)------------------------------
% 63.77/10.34 % (24282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.77/10.34 % (24282)Termination reason: Unknown
% 63.77/10.34 % (24282)Termination phase: Saturation
% 63.77/10.34
% 63.77/10.34 % (24282)Memory used [KB]: 15863
% 63.77/10.34 % (24282)Time elapsed: 0.667 s
% 63.77/10.34 % (24282)Instructions burned: 2679 (million)
% 63.77/10.34 % (24282)------------------------------
% 63.77/10.34 % (24282)------------------------------
% 63.77/10.35 % (24292)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_23745 for (2912ds/2781Mi)
% 63.77/10.38 % (24266)Instruction limit reached!
% 63.77/10.38 % (24266)------------------------------
% 63.77/10.38 % (24266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.77/10.38 % (24266)Termination reason: Unknown
% 63.77/10.38 % (24266)Termination phase: Saturation
% 63.77/10.38
% 63.77/10.38 % (24266)Memory used [KB]: 10618
% 63.77/10.38 % (24266)Time elapsed: 2.213 s
% 63.77/10.38 % (24266)Instructions burned: 7259 (million)
% 63.77/10.38 % (24266)------------------------------
% 63.77/10.38 % (24266)------------------------------
% 63.77/10.39 % (24293)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_23745 for (2911ds/307Mi)
% 64.10/10.47 % (24293)Instruction limit reached!
% 64.10/10.47 % (24293)------------------------------
% 64.10/10.47 % (24293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.10/10.47 % (24293)Termination reason: Unknown
% 64.10/10.47 % (24293)Termination phase: Saturation
% 64.10/10.47
% 64.10/10.47 % (24293)Memory used [KB]: 7164
% 64.10/10.47 % (24293)Time elapsed: 0.077 s
% 64.10/10.47 % (24293)Instructions burned: 308 (million)
% 64.10/10.47 % (24293)------------------------------
% 64.10/10.47 % (24293)------------------------------
% 64.10/10.48 % (24294)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_23745 for (2910ds/1548Mi)
% 64.58/10.66 % (24285)Instruction limit reached!
% 64.58/10.66 % (24285)------------------------------
% 64.58/10.66 % (24285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.58/10.66 % (24285)Termination reason: Unknown
% 64.58/10.66 % (24285)Termination phase: Saturation
% 64.58/10.66
% 64.58/10.66 % (24285)Memory used [KB]: 10362
% 64.58/10.66 % (24285)Time elapsed: 0.767 s
% 64.58/10.66 % (24285)Instructions burned: 2548 (million)
% 64.58/10.66 % (24285)------------------------------
% 64.58/10.66 % (24285)------------------------------
% 64.58/10.67 % (24295)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_23745 for (2908ds/5214Mi)
% 64.86/10.86 % (24290)Instruction limit reached!
% 64.86/10.86 % (24290)------------------------------
% 64.86/10.86 % (24290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.86/10.86 % (24290)Termination reason: Unknown
% 64.86/10.86 % (24290)Termination phase: Saturation
% 64.86/10.86
% 64.86/10.86 % (24290)Memory used [KB]: 13176
% 64.86/10.86 % (24290)Time elapsed: 0.642 s
% 64.86/10.86 % (24290)Instructions burned: 2574 (million)
% 64.86/10.86 % (24290)------------------------------
% 64.86/10.86 % (24290)------------------------------
% 64.86/10.87 % (24296)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_23745 for (2907ds/3201Mi)
% 65.62/10.91 % (24281)Instruction limit reached!
% 65.62/10.91 % (24281)------------------------------
% 65.62/10.91 % (24281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.62/10.91 % (24281)Termination reason: Unknown
% 65.62/10.91 % (24281)Termination phase: Saturation
% 65.62/10.91
% 65.62/10.91 % (24281)Memory used [KB]: 14328
% 65.62/10.91 % (24281)Time elapsed: 1.416 s
% 65.62/10.91 % (24281)Instructions burned: 4604 (million)
% 65.62/10.91 % (24281)------------------------------
% 65.62/10.91 % (24281)------------------------------
% 65.62/10.92 % (24297)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_23745 for (2906ds/454Mi)
% 65.62/10.95 % (24294)Instruction limit reached!
% 65.62/10.95 % (24294)------------------------------
% 65.62/10.95 % (24294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.62/10.95 % (24294)Termination reason: Unknown
% 65.62/10.95 % (24294)Termination phase: Saturation
% 65.62/10.95
% 65.62/10.95 % (24294)Memory used [KB]: 10490
% 65.62/10.95 % (24294)Time elapsed: 0.475 s
% 65.62/10.95 % (24294)Instructions burned: 1548 (million)
% 65.62/10.95 % (24294)------------------------------
% 65.62/10.95 % (24294)------------------------------
% 65.62/10.95 % (24291)Instruction limit reached!
% 65.62/10.95 % (24291)------------------------------
% 65.62/10.95 % (24291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.62/10.95 % (24291)Termination reason: Unknown
% 65.62/10.95 % (24291)Termination phase: Saturation
% 65.62/10.95
% 65.62/10.95 % (24291)Memory used [KB]: 4861
% 65.62/10.95 % (24291)Time elapsed: 0.658 s
% 65.62/10.95 % (24291)Instructions burned: 2657 (million)
% 65.62/10.95 % (24291)------------------------------
% 65.62/10.95 % (24291)------------------------------
% 65.62/10.96 % (24298)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_23745 for (2906ds/3049Mi)
% 65.62/10.96 % (24299)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_23745 for (2906ds/7311Mi)
% 69.02/11.03 % (24297)Instruction limit reached!
% 69.02/11.03 % (24297)------------------------------
% 69.02/11.03 % (24297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.02/11.03 % (24297)Termination reason: Unknown
% 69.02/11.03 % (24297)Termination phase: Saturation
% 69.02/11.03
% 69.02/11.03 % (24297)Memory used [KB]: 15351
% 69.02/11.03 % (24297)Time elapsed: 0.114 s
% 69.02/11.03 % (24297)Instructions burned: 454 (million)
% 69.02/11.03 % (24297)------------------------------
% 69.02/11.03 % (24297)------------------------------
% 69.02/11.04 % (24300)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_23745 for (2905ds/6804Mi)
% 69.67/11.18 % (24292)Instruction limit reached!
% 69.67/11.18 % (24292)------------------------------
% 69.67/11.18 % (24292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.67/11.18 % (24292)Termination reason: Unknown
% 69.67/11.18 % (24292)Termination phase: Saturation
% 69.67/11.18
% 69.67/11.18 % (24292)Memory used [KB]: 7547
% 69.67/11.18 % (24292)Time elapsed: 0.836 s
% 69.67/11.18 % (24292)Instructions burned: 2781 (million)
% 69.67/11.18 % (24292)------------------------------
% 69.67/11.18 % (24292)------------------------------
% 69.67/11.19 % (24301)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_23745 for (2903ds/1683Mi)
% 72.10/11.69 % (24301)Instruction limit reached!
% 72.10/11.69 % (24301)------------------------------
% 72.10/11.69 % (24301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.10/11.69 % (24301)Termination reason: Unknown
% 72.10/11.69 % (24301)Termination phase: Saturation
% 72.10/11.69
% 72.10/11.69 % (24301)Memory used [KB]: 16886
% 72.10/11.69 % (24301)Time elapsed: 0.503 s
% 72.10/11.69 % (24301)Instructions burned: 1683 (million)
% 72.10/11.69 % (24301)------------------------------
% 72.10/11.69 % (24301)------------------------------
% 73.11/11.70 % (24302)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_23745 for (2898ds/4688Mi)
% 73.61/11.87 % (24296)Instruction limit reached!
% 73.61/11.87 % (24296)------------------------------
% 73.61/11.87 % (24296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.61/11.87 % (24296)Termination reason: Unknown
% 73.61/11.87 % (24296)Termination phase: Saturation
% 73.61/11.87
% 73.61/11.87 % (24296)Memory used [KB]: 11257
% 73.61/11.87 % (24296)Time elapsed: 1.005 s
% 73.61/11.87 % (24296)Instructions burned: 3203 (million)
% 73.61/11.87 % (24296)------------------------------
% 73.61/11.87 % (24296)------------------------------
% 73.61/11.88 % (24303)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_23745 for (2896ds/2207Mi)
% 74.08/11.90 % (24298)Instruction limit reached!
% 74.08/11.90 % (24298)------------------------------
% 74.08/11.90 % (24298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.08/11.90 % (24298)Termination reason: Unknown
% 74.08/11.90 % (24298)Termination phase: Saturation
% 74.08/11.90
% 74.08/11.90 % (24298)Memory used [KB]: 10874
% 74.08/11.90 % (24298)Time elapsed: 0.942 s
% 74.08/11.90 % (24298)Instructions burned: 3051 (million)
% 74.08/11.90 % (24298)------------------------------
% 74.08/11.90 % (24298)------------------------------
% 74.08/11.91 % (24304)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=8216:si=on:rtra=on_0 on DTF2THF_23745 for (2896ds/8216Mi)
% 74.08/11.94 % (24289)Instruction limit reached!
% 74.08/11.94 % (24289)------------------------------
% 74.08/11.94 % (24289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 74.08/11.94 % (24289)Termination reason: Unknown
% 74.08/11.94 % (24289)Termination phase: Saturation
% 74.08/11.94
% 74.08/11.94 % (24289)Memory used [KB]: 16502
% 74.08/11.94 % (24289)Time elapsed: 1.736 s
% 74.08/11.94 % (24289)Instructions burned: 5446 (million)
% 74.08/11.94 % (24289)------------------------------
% 74.08/11.94 % (24289)------------------------------
% 74.08/11.95 % (24305)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_23745 for (2896ds/430Mi)
% 76.04/12.06 % (24305)Instruction limit reached!
% 76.04/12.06 % (24305)------------------------------
% 76.04/12.06 % (24305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.04/12.06 % (24305)Termination reason: Unknown
% 76.04/12.06 % (24305)Termination phase: Saturation
% 76.04/12.06
% 76.04/12.06 % (24305)Memory used [KB]: 11385
% 76.04/12.06 % (24305)Time elapsed: 0.112 s
% 76.04/12.06 % (24305)Instructions burned: 430 (million)
% 76.04/12.06 % (24305)------------------------------
% 76.04/12.06 % (24305)------------------------------
% 76.04/12.07 % (24306)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_23745 for (2895ds/2012Mi)
% 77.13/12.24 % (24295)Instruction limit reached!
% 77.13/12.24 % (24295)------------------------------
% 77.13/12.24 % (24295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.13/12.24 % (24295)Termination reason: Unknown
% 77.13/12.24 % (24295)Termination phase: Saturation
% 77.13/12.24
% 77.13/12.24 % (24295)Memory used [KB]: 10490
% 77.13/12.24 % (24295)Time elapsed: 1.574 s
% 77.13/12.24 % (24295)Instructions burned: 5214 (million)
% 77.13/12.24 % (24295)------------------------------
% 77.13/12.24 % (24295)------------------------------
% 77.13/12.25 % (24307)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=631:si=on:rtra=on_0 on DTF2THF_23745 for (2893ds/631Mi)
% 78.19/12.44 % (24307)Instruction limit reached!
% 78.19/12.44 % (24307)------------------------------
% 78.19/12.44 % (24307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.19/12.44 % (24307)Termination reason: Unknown
% 78.19/12.44 % (24307)Termination phase: Saturation
% 78.19/12.44
% 78.19/12.44 % (24307)Memory used [KB]: 7803
% 78.19/12.44 % (24307)Time elapsed: 0.212 s
% 78.19/12.44 % (24307)Instructions burned: 632 (million)
% 78.19/12.44 % (24307)------------------------------
% 78.19/12.44 % (24307)------------------------------
% 78.19/12.45 % (24308)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_23745 for (2891ds/8785Mi)
% 78.89/12.56 % (24303)Instruction limit reached!
% 78.89/12.56 % (24303)------------------------------
% 78.89/12.56 % (24303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.89/12.56 % (24303)Termination reason: Unknown
% 78.89/12.56 % (24303)Termination phase: Saturation
% 78.89/12.56
% 78.89/12.56 % (24303)Memory used [KB]: 10490
% 78.89/12.56 % (24303)Time elapsed: 0.683 s
% 78.89/12.56 % (24303)Instructions burned: 2207 (million)
% 78.89/12.56 % (24303)------------------------------
% 78.89/12.56 % (24303)------------------------------
% 78.89/12.57 % (24306)Instruction limit reached!
% 78.89/12.57 % (24306)------------------------------
% 78.89/12.57 % (24306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.89/12.57 % (24306)Termination reason: Unknown
% 78.89/12.57 % (24306)Termination phase: Saturation
% 78.89/12.57
% 78.89/12.57 % (24306)Memory used [KB]: 11641
% 78.89/12.57 % (24306)Time elapsed: 0.496 s
% 78.89/12.57 % (24306)Instructions burned: 2014 (million)
% 78.89/12.57 % (24306)------------------------------
% 78.89/12.57 % (24306)------------------------------
% 78.89/12.57 % (24309)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_23745 for (2889ds/739Mi)
% 78.89/12.58 % (24310)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_23745 for (2889ds/5473Mi)
% 80.27/12.80 % (24309)Instruction limit reached!
% 80.27/12.80 % (24309)------------------------------
% 80.27/12.80 % (24309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.27/12.80 % (24309)Termination reason: Unknown
% 80.27/12.80 % (24309)Termination phase: Saturation
% 80.27/12.80
% 80.27/12.80 % (24309)Memory used [KB]: 11641
% 80.27/12.80 % (24309)Time elapsed: 0.225 s
% 80.27/12.80 % (24309)Instructions burned: 741 (million)
% 80.27/12.80 % (24309)------------------------------
% 80.27/12.80 % (24309)------------------------------
% 80.68/12.81 % (24311)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_23745 for (2887ds/43570Mi)
% 83.05/13.12 % (24302)Instruction limit reached!
% 83.05/13.12 % (24302)------------------------------
% 83.05/13.12 % (24302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.05/13.12 % (24302)Termination reason: Unknown
% 83.05/13.12 % (24302)Termination phase: Saturation
% 83.05/13.12
% 83.05/13.12 % (24302)Memory used [KB]: 13816
% 83.05/13.12 % (24302)Time elapsed: 1.413 s
% 83.05/13.12 % (24302)Instructions burned: 4689 (million)
% 83.05/13.12 % (24302)------------------------------
% 83.05/13.12 % (24302)------------------------------
% 83.77/13.13 % (24312)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_23745 for (2884ds/8382Mi)
% 83.77/13.14 % (24300)Instruction limit reached!
% 83.77/13.14 % (24300)------------------------------
% 83.77/13.14 % (24300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.77/13.14 % (24300)Termination reason: Unknown
% 83.77/13.14 % (24300)Termination phase: Saturation
% 83.77/13.14
% 83.77/13.14 % (24300)Memory used [KB]: 17142
% 83.77/13.14 % (24300)Time elapsed: 2.114 s
% 83.77/13.14 % (24300)Instructions burned: 6804 (million)
% 83.77/13.14 % (24300)------------------------------
% 83.77/13.14 % (24300)------------------------------
% 83.77/13.15 % (24313)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_23745 for (2884ds/407Mi)
% 84.18/13.26 % (24313)Instruction limit reached!
% 84.18/13.26 % (24313)------------------------------
% 84.18/13.26 % (24313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.18/13.26 % (24313)Termination reason: Unknown
% 84.18/13.26 % (24313)Termination phase: Saturation
% 84.18/13.26
% 84.18/13.26 % (24313)Memory used [KB]: 8443
% 84.18/13.26 % (24313)Time elapsed: 0.140 s
% 84.18/13.26 % (24313)Instructions burned: 408 (million)
% 84.18/13.26 % (24313)------------------------------
% 84.18/13.26 % (24313)------------------------------
% 84.18/13.27 % (24314)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_23745 for (2883ds/2971Mi)
% 84.80/13.32 % (24299)Instruction limit reached!
% 84.80/13.32 % (24299)------------------------------
% 84.80/13.32 % (24299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.80/13.32 % (24299)Termination reason: Unknown
% 84.80/13.32 % (24299)Termination phase: Saturation
% 84.80/13.32
% 84.80/13.32 % (24299)Memory used [KB]: 16886
% 84.80/13.32 % (24299)Time elapsed: 2.354 s
% 84.80/13.32 % (24299)Instructions burned: 7311 (million)
% 84.80/13.32 % (24299)------------------------------
% 84.80/13.32 % (24299)------------------------------
% 84.80/13.33 % (24315)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_23745 for (2882ds/9822Mi)
% 87.23/13.99 % (24314)Instruction limit reached!
% 87.23/13.99 % (24314)------------------------------
% 87.23/13.99 % (24314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.23/13.99 % (24314)Termination reason: Unknown
% 87.23/13.99 % (24314)Termination phase: Saturation
% 87.23/13.99
% 87.23/13.99 % (24314)Memory used [KB]: 7164
% 87.23/13.99 % (24314)Time elapsed: 0.717 s
% 87.23/13.99 % (24314)Instructions burned: 2973 (million)
% 87.23/13.99 % (24314)------------------------------
% 87.23/13.99 % (24314)------------------------------
% 87.23/14.00 % (24316)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_23745 for (2875ds/8425Mi)
% 87.23/14.00 % (24304)Instruction limit reached!
% 87.23/14.00 % (24304)------------------------------
% 87.23/14.00 % (24304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 87.23/14.00 % (24304)Termination reason: Unknown
% 87.23/14.00 % (24304)Termination phase: Saturation
% 87.23/14.00
% 87.23/14.00 % (24304)Memory used [KB]: 11257
% 87.23/14.00 % (24304)Time elapsed: 2.093 s
% 87.23/14.00 % (24304)Instructions burned: 8219 (million)
% 87.23/14.00 % (24304)------------------------------
% 87.23/14.00 % (24304)------------------------------
% 87.23/14.01 % (24317)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_23745 for (2875ds/3107Mi)
% 91.13/14.23 % (24310)Instruction limit reached!
% 91.13/14.23 % (24310)------------------------------
% 91.13/14.23 % (24310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.13/14.23 % (24310)Termination reason: Unknown
% 91.13/14.23 % (24310)Termination phase: Saturation
% 91.13/14.23
% 91.13/14.23 % (24310)Memory used [KB]: 13176
% 91.13/14.23 % (24310)Time elapsed: 1.653 s
% 91.13/14.23 % (24310)Instructions burned: 5473 (million)
% 91.13/14.23 % (24310)------------------------------
% 91.13/14.23 % (24310)------------------------------
% 91.13/14.24 % (24319)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_23745 for (2873ds/7967Mi)
% 92.68/14.53 % (24315)First to succeed.
% 92.68/14.54 % (24315)Refutation found. Thanks to Tanya!
% 92.68/14.54 % SZS status Theorem for DTF2THF_23745
% 92.68/14.54 % SZS output start Proof for DTF2THF_23745
% 92.68/14.54 thf(func_def_0, type, in: $i > $i > $o).
% 92.68/14.54 thf(func_def_1, type, exu: ($i > $o) > $o).
% 92.68/14.54 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 92.68/14.54 thf(func_def_8, type, powerset: $i > $i).
% 92.68/14.54 thf(func_def_10, type, setunion: $i > $i).
% 92.68/14.54 thf(func_def_19, type, descr: ($i > $o) > $i).
% 92.68/14.54 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_26, type, prop2set: $o > $i).
% 92.68/14.54 thf(func_def_36, type, nonempty: $i > $o).
% 92.68/14.54 thf(func_def_69, type, set2prop: $i > $o).
% 92.68/14.54 thf(func_def_88, type, subset: $i > $i > $o).
% 92.68/14.54 thf(func_def_89, type, disjoint: $i > $i > $o).
% 92.68/14.54 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 92.68/14.54 thf(func_def_114, type, binunion: $i > $i > $i).
% 92.68/14.54 thf(func_def_122, type, binintersect: $i > $i > $i).
% 92.68/14.54 thf(func_def_135, type, regular: $i > $o).
% 92.68/14.54 thf(func_def_136, type, setminus: $i > $i > $i).
% 92.68/14.54 thf(func_def_147, type, symdiff: $i > $i > $i).
% 92.68/14.54 thf(func_def_153, type, iskpair: $i > $o).
% 92.68/14.54 thf(func_def_158, type, kpair: $i > $i > $i).
% 92.68/14.54 thf(func_def_160, type, cartprod: $i > $i > $i).
% 92.68/14.54 thf(func_def_177, type, singleton: $i > $o).
% 92.68/14.54 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 92.68/14.54 thf(func_def_184, type, atmost1p: $i > $o).
% 92.68/14.54 thf(func_def_185, type, atleast2p: $i > $o).
% 92.68/14.54 thf(func_def_186, type, atmost2p: $i > $o).
% 92.68/14.54 thf(func_def_187, type, upairsetp: $i > $o).
% 92.68/14.54 thf(func_def_191, type, kfst: $i > $i).
% 92.68/14.54 thf(func_def_203, type, ksnd: $i > $i).
% 92.68/14.54 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 92.68/14.54 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 92.68/14.54 thf(func_def_222, type, func: $i > $i > $i > $o).
% 92.68/14.54 thf(func_def_223, type, funcSet: $i > $i > $i).
% 92.68/14.54 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 92.68/14.54 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 92.68/14.54 thf(func_def_255, type, sP1: $o > $i > $i > $i > $o).
% 92.68/14.54 thf(func_def_256, type, sP2: $i > $i > $o).
% 92.68/14.54 thf(func_def_257, type, sP3: $i > $o).
% 92.68/14.54 thf(func_def_258, type, sP4: $i > $i > $o).
% 92.68/14.54 thf(func_def_259, type, sP5: $i > $i > $o).
% 92.68/14.54 thf(func_def_273, type, sK19: $i > $i > $i).
% 92.68/14.54 thf(func_def_286, type, sK32: $i > $i > $o).
% 92.68/14.54 thf(func_def_291, type, sK37: $i > $i).
% 92.68/14.54 thf(func_def_303, type, sK49: $i > $i > $o).
% 92.68/14.54 thf(func_def_306, type, sK52: $i > $i).
% 92.68/14.54 thf(func_def_312, type, sK58: ($i > $o) > ($i > $o) > $i > $i > $i).
% 92.68/14.54 thf(func_def_313, type, sK59: ($i > $o) > ($i > $o) > $i > $i > $i).
% 92.68/14.54 thf(func_def_316, type, sK62: $i > $o).
% 92.68/14.54 thf(func_def_317, type, sK63: $i > $o).
% 92.68/14.54 thf(func_def_318, type, sK64: $i > $o).
% 92.68/14.54 thf(func_def_319, type, sK65: $i > $i).
% 92.68/14.54 thf(func_def_320, type, sK66: ($i > $o) > $i).
% 92.68/14.54 thf(func_def_322, type, sK68: $i > $i > $o).
% 92.68/14.54 thf(func_def_332, type, sK78: $i > $o).
% 92.68/14.54 thf(func_def_334, type, sK80: ($i > $o) > $i > $i > $i > $i).
% 92.68/14.54 thf(func_def_335, type, sK81: ($i > $o) > $i > $i > $i > $i).
% 92.68/14.54 thf(func_def_338, type, sK84: $i > $i > $i).
% 92.68/14.54 thf(func_def_346, type, sK92: $i > $i > $o).
% 92.68/14.54 thf(func_def_347, type, sK93: $i > $i).
% 92.68/14.54 thf(func_def_348, type, sK94: $i > $i).
% 92.68/14.54 thf(func_def_349, type, sK95: ($i > $i > $o) > $i > $i).
% 92.68/14.54 thf(func_def_350, type, sK96: ($i > $i > $o) > $i > $i).
% 92.68/14.54 thf(func_def_351, type, sK97: $i > ($i > $i > $o) > $i > $i).
% 92.68/14.54 thf(func_def_355, type, sK101: $i > $o).
% 92.68/14.54 thf(func_def_367, type, sK113: $i > $i > $i).
% 92.68/14.54 thf(func_def_368, type, sK114: $i > $i > $i).
% 92.68/14.54 thf(func_def_383, type, sK129: $o > $i > $i > $i).
% 92.68/14.54 thf(func_def_406, type, sK152: $i > $i > $o).
% 92.68/14.54 thf(func_def_411, type, sK157: ($i > $o) > $i > $i).
% 92.68/14.54 thf(func_def_413, type, sK159: $i > $o).
% 92.68/14.54 thf(func_def_415, type, sK161: ($i > $o) > $i).
% 92.68/14.54 thf(func_def_416, type, sK162: $i > $o).
% 92.68/14.54 thf(func_def_417, type, sK163: $i > $i).
% 92.68/14.54 thf(func_def_418, type, sK164: ($i > $o) > $i).
% 92.68/14.54 thf(func_def_419, type, sK165: ($i > $o) > $i).
% 92.68/14.54 thf(func_def_420, type, sK166: $i > $o).
% 92.68/14.54 thf(func_def_424, type, sK170: $i > $o).
% 92.68/14.54 thf(func_def_431, type, sK177: $i > $i > $i).
% 92.68/14.54 thf(func_def_432, type, sK178: $i > $i > $i).
% 92.68/14.54 thf(func_def_433, type, sK179: $i > $i > $i).
% 92.68/14.54 thf(func_def_434, type, sK180: $i > $i > $i).
% 92.68/14.54 thf(func_def_435, type, sK181: $i > $i > $i).
% 92.68/14.54 thf(func_def_436, type, sK182: $i > $i > $i > $i).
% 92.68/14.54 thf(func_def_437, type, sK183: $i > $i).
% 92.68/14.54 thf(func_def_438, type, sK184: $i > $i).
% 92.68/14.54 thf(func_def_439, type, sK185: $i > $i).
% 92.68/14.54 thf(func_def_440, type, sK186: $i > $i).
% 92.68/14.54 thf(func_def_441, type, sK187: $i > $i > $i).
% 92.68/14.54 thf(func_def_442, type, sK188: $i > $i > $i > $i).
% 92.68/14.54 thf(func_def_443, type, sK189: $i > $i > $i > $i).
% 92.68/14.54 thf(func_def_444, type, sK190: $i > $i > $i).
% 92.68/14.54 thf(func_def_445, type, sK191: $i > $i > $i).
% 92.68/14.54 thf(func_def_447, type, sK193: $i > $i).
% 92.68/14.54 thf(func_def_448, type, sK194: $i > $i).
% 92.68/14.54 thf(func_def_449, type, sK195: $i > $i).
% 92.68/14.54 thf(func_def_457, type, sK203: $i > $o).
% 92.68/14.54 thf(func_def_473, type, sK219: $i > $o).
% 92.68/14.54 thf(func_def_478, type, sK224: $i > $o).
% 92.68/14.54 thf(func_def_481, type, sK227: $i > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_482, type, sK228: $i > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_483, type, sK229: $i > $i > $i > $i).
% 92.68/14.54 thf(func_def_484, type, sK230: $i > $i > $i > $i).
% 92.68/14.54 thf(func_def_504, type, sK250: $i > $i > $i).
% 92.68/14.54 thf(func_def_510, type, sK256: ($i > $o) > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_511, type, sK257: ($i > $o) > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_512, type, sK258: $i > $o).
% 92.68/14.54 thf(func_def_513, type, sK259: $i > $o).
% 92.68/14.54 thf(func_def_520, type, sK266: $i > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_521, type, sK267: $i > $o).
% 92.68/14.54 thf(func_def_534, type, sK280: ($i > $i) > $i > $i > $i).
% 92.68/14.54 thf(func_def_537, type, sK283: $i > $i).
% 92.68/14.54 thf(func_def_547, type, sK293: $i > $i > $i).
% 92.68/14.54 thf(func_def_570, type, sK316: $i > $i).
% 92.68/14.54 thf(func_def_572, type, sK318: $i > $i).
% 92.68/14.54 thf(func_def_573, type, sK319: $i > $o).
% 92.68/14.54 thf(func_def_587, type, sK333: ($i > $o) > $i > $i).
% 92.68/14.54 thf(func_def_589, type, sK335: $i > $o).
% 92.68/14.54 thf(func_def_609, type, sK355: ($i > $o) > $i > $i).
% 92.68/14.54 thf(func_def_611, type, sK357: $i > $o).
% 92.68/14.54 thf(func_def_620, type, sK366: $i > $i).
% 92.68/14.54 thf(func_def_626, type, sK372: $i > $i).
% 92.68/14.54 thf(func_def_628, type, sK374: $i > ($i > $i) > $i > $i).
% 92.68/14.54 thf(func_def_633, type, sK379: $i > $o).
% 92.68/14.54 thf(func_def_637, type, sK383: $i > $i > $i).
% 92.68/14.54 thf(func_def_644, type, sK390: $i > $i > $o).
% 92.68/14.54 thf(func_def_653, type, sK399: ($i > $o) > $i).
% 92.68/14.54 thf(func_def_654, type, sK400: $i > $o).
% 92.68/14.54 thf(func_def_660, type, sK406: $i > $i > $i).
% 92.68/14.54 thf(func_def_667, type, sK413: $i > $i > $i).
% 92.68/14.54 thf(func_def_675, type, sK421: $i > $o).
% 92.68/14.54 thf(func_def_677, type, sK423: $i > ($i > $o) > $i > $i).
% 92.68/14.54 thf(func_def_694, type, sK440: $i > $i > $o).
% 92.68/14.54 thf(func_def_698, type, sK444: $i > $o).
% 92.68/14.54 thf(func_def_700, type, sK446: $i > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_701, type, sK447: $i > $o).
% 92.68/14.54 thf(func_def_705, type, sK451: $i > $i > $i).
% 92.68/14.54 thf(func_def_709, type, sK455: $i > $o).
% 92.68/14.54 thf(func_def_712, type, sK458: $i > $o).
% 92.68/14.54 thf(func_def_716, type, sK462: $i > $o).
% 92.68/14.54 thf(func_def_718, type, sK464: ($i > $o) > $i > $i).
% 92.68/14.54 thf(func_def_719, type, sK465: ($i > $o) > $i > $i).
% 92.68/14.54 thf(func_def_735, type, sK481: $i > $o).
% 92.68/14.54 thf(func_def_736, type, sK482: $i > $o).
% 92.68/14.54 thf(func_def_737, type, sK483: ($i > $o) > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_738, type, sK484: ($i > $o) > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_739, type, sK485: $i > $i > $o).
% 92.68/14.54 thf(func_def_744, type, sK490: $i > $o).
% 92.68/14.54 thf(func_def_745, type, sK491: ($i > $o) > $i > $i).
% 92.68/14.54 thf(func_def_747, type, sK493: $i > $o).
% 92.68/14.54 thf(func_def_756, type, sK502: $i > $o).
% 92.68/14.54 thf(func_def_758, type, sK504: $i > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_769, type, sK515: $i > $o).
% 92.68/14.54 thf(func_def_772, type, sK518: $i > $i).
% 92.68/14.54 thf(func_def_775, type, sK521: $i > $i > ($i > $i) > $i).
% 92.68/14.54 thf(func_def_778, type, sK524: $i > $o).
% 92.68/14.54 thf(func_def_781, type, sK527: $i > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_783, type, sK529: $i > $o).
% 92.68/14.54 thf(func_def_795, type, sK541: $i > $o).
% 92.68/14.54 thf(func_def_798, type, sK544: $i > ($i > $o) > $i).
% 92.68/14.54 thf(func_def_800, type, sK546: $i > $o).
% 92.68/14.54 thf(func_def_804, type, sK550: $i > $i).
% 92.68/14.54 thf(func_def_806, type, sK552: ($i > $o) > $i > $i > $i > $i).
% 92.68/14.54 thf(func_def_807, type, sK553: ($i > $o) > $i > $i > $i > $i).
% 92.68/14.54 thf(func_def_811, type, sK557: $i > $o).
% 92.68/14.54 thf(func_def_842, type, sK588: $i > $i).
% 92.68/14.54 thf(func_def_866, type, ph612: !>[X0: $tType]:(X0)).
% 92.68/14.54 thf(f17577,plain,(
% 92.68/14.54 $false),
% 92.68/14.54 inference(avatar_sat_refutation,[status(thm)],[f14624,f17573])).
% 92.68/14.54 thf(f17573,plain,(
% 92.68/14.54 ~spl611_583),
% 92.68/14.54 inference(avatar_contradiction_clause,[status(thm)],[f17572])).
% 92.68/14.54 thf(f17572,plain,(
% 92.68/14.54 $false | ~spl611_583),
% 92.68/14.54 inference(subsumption_resolution,[status(thm)],[f17571,f2262])).
% 92.68/14.54 thf(f2262,plain,(
% 92.68/14.54 ($true = (in @ (kpair @ sK264 @ sK265) @ sK263))),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f1280])).
% 92.68/14.54 thf(f1280,plain,(
% 92.68/14.54 (exuI1 = $true) & (quantDeMorgan4 = $true) & (binunionLsub = $true) & (in__Cong = $true) & (symdiffE = $true) & (subsetTrans = $true) & (ex1E2 = $true) & (subsetemptysetimpeq = $true) & (subsetE2 = $true) & (singletonsswitch = $true) & (singletoninpowerset = $true) & (binintersectSubset1 = $true) & (cartprodmempair = $true) & (emptyinPowerset = $true) & (setukpairinjR = $true) & (ex1I2 = $true) & (prop2set2propI = $true) & (symdiffIneg1 = $true) & (setminusLsub = $true) & (powersetI = $true) & (exuI2 = $true) & (setminusER = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (binintersectEL = $true) & (uniqinunit = $true) & (powerset__Cong = $true) & (setminusIRneg = $true) & (ubforcartprodlem3 = $true) & (kfstsingleton = $true) & (cartprodpairmemEL = $true) & (sepInPowerset = $true) & (setunionsingleton2 = $true) & (eqinunit = $true) & (setunionAx = $true) & (binintersectSubset3 = $true) & (descrp = $true) & (subsetI1 = $true) & (nonemptyI = $true) & (kpairp = $true) & (cartprodmempair1 = $true) & (ex1E1 = $true) & (binintersectRsub = $true) & (setunion__Cong = $true) & (descr__Cong = $true) & (binunionEcases = $true) & (apProp = $true) & (setukpairinjR1 = $true) & (funcGraphProp1 = $true) & (disjointsetsI1 = $true) & (noeltsimpempty = $true) & (cartprodsndin = $true) & (cartprodfstin = $true) & (setukpairinjL2 = $true) & (setadjoinSub2 = $true) & (ap2p = $true) & (dpsetconstrER = $true) & (setextAx = $true) & (setextsub = $true) & (dsetconstrI = $true) & (emptysetsubset = $true) & (quantDeMorgan3 = $true) & (eqimpsubset2 = $true) & (notinsingleton = $true) & (setukpairinjL1 = $true) & (setminusEL = $true) & (singletonsubset = $true) & (powersetAx = $true) & (dsetconstr__Cong = $true) & (binintersectSubset4 = $true) & (omegaSAx = $true) & (nonemptyI1 = $true) & (inPowerset = $true) & (setminusI = $true) & (notdallE = $true) & (ksndpairEq = $true) & (upairsetIL = $true) & (notinemptyset = $true) & (setminusSubset1 = $true) & (binintersectSubset5 = $true) & (symdiffI2 = $true) & (dpsetconstrSub = $true) & (setoftrueEq = $true) & (setukpairinjL = $true) & (eqimpsubset1 = $true) & (dpsetconstrI = $true) & (secondinupair = $true) & (binintersectER = $true) & (quantDeMorgan2 = $true) & (exuE1 = $true) & (upairset2IR = $true) & (setOfPairsIsBReln = $true) & (singletonsuniq = $true) & (subsetRefl = $true) & (nonemptyImpWitness = $true) & (binunionE = $true) & (cartprodpairmemER = $true) & (symdiffIneg2 = $true) & (exuE2 = $true) & (ex1I = $true) & (setadjoinIL = $true) & (setminusELneg = $true) & (kfstpairEq = $true) & (upairsetIR = $true) & (cartprodpairin = $true) & (exuE3e = $true) & (emptyInPowerset = $true) & (binunionRsub = $true) & (cartprodmempaircEq = $true) & (brelnall1 = $true) & (binunionIR = $true) & (brelnall2 = $true) & (emptyinunitempty = $true) & (setunionI = $true) & (upairequniteq = $true) & (lamp = $true) & (kpairsurjEq = $true) & (notequalI2 = $true) & (vacuousDall = $true) & (omega0Ax = $true) & (ubforcartprodlem2 = $true) & (setminusILneg = $true) & (setadjoinIR = $true) & (setext = $true) & (setukpairIR = $true) & (exu__Cong = $true) & (dsetconstrEL = $true) & (setunionsingleton = $true) & (setukpairIL = $true) & ((! [X4 : $i] : (($true != (in @ X4 @ sK261)) | ((ap @ sK261 @ sK262 @ sK260 @ X4) = (ap @ sK261 @ sK262 @ sK263 @ X4))) & (($true = (in @ sK264 @ sK261)) & (($true = (in @ sK265 @ sK262)) & ($true = (in @ (kpair @ sK264 @ sK265) @ sK263)) & ($true != (in @ (kpair @ sK264 @ sK265) @ sK260)))) & ($true = (func @ sK261 @ sK262 @ sK263))) & ($true = (func @ sK261 @ sK262 @ sK260))) & (foundationAx = $true) & (emptysetAx = $true) & (subsetI2 = $true) & (emptyE1 = $true) & (infuncsetfunc = $true) & (prop2setE = $true) & (setunionsingleton1 = $true) & (inCongP = $true) & (replAx = $true) & (sepSubset = $true) & (notsubsetI = $true) & (binintersectSubset2 = $true) & (ubforcartprodlem1 = $true) & (subsetE = $true) & (binintersectI = $true) & (funcinfuncset = $true) & (powersetE = $true) & (setukpairinjR2 = $true) & (subset2powerset = $true) & (emptyI = $true) & (ksndsingleton = $true) & (setunionE2 = $true) & (upairsubunion = $true) & (setukpairinjR12 = $true) & (nonemptyE1 = $true) & (setminusERneg = $true) & (dsetconstrER = $true) & (subPowSU = $true) & (upairinpowunion = $true) & (exuI3 = $true) & (kpairiskpair = $true) & (powersetI1 = $true) & (setadjoinE = $true) & (emptysetimpfalse = $true) & (setukpairinjR11 = $true) & (binunionIL = $true) & (theprop = $true) & (funcGraphProp3 = $true) & (powersetE1 = $true) & (dpsetconstrERa = $true) & (funcGraphProp2 = $true) & (dpsetconstrEL1 = $true) & (cartprodpairsurjEq = $true) & (wellorderingAx = $true) & (funcImageSingleton = $true) & (notequalI1 = $true) & (emptyset__Cong = $true) & (lam2p = $true) & (cartprodfstpairEq = $true) & (setbeta = $true) & (notdexE = $true) & (quantDeMorgan1 = $true) & (setminusSubset2 = $true) & (upairsetE = $true) & (bs114d = $true) & (setadjoin__Cong = $true) & (singletonprop = $true) & (lamProp = $true) & (cartprodsndpairEq = $true) & (omegaIndAx = $true) & (setunionE = $true) & (dpsetconstrEL2 = $true) & (exuEu = $true) & (binintersectLsub = $true) & (powersetsubset = $true) & (setadjoinAx = $true) & (exuE3u = $true) & (symdiffI1 = $true) & (setadjoinSub = $true) & (setadjoinOr = $true) & (prop2setI = $true) & (emptysetE = $true) & (omega__Cong = $true) & (app = $true)),
% 92.68/14.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK260,sK261,sK262,sK263,sK264,sK265])],[f801,f1279,f1278,f1277,f1276])).
% 92.68/14.54 thf(f1276,plain,(
% 92.68/14.54 ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X1)) | ((ap @ X1 @ X2 @ X0 @ X4) = (ap @ X1 @ X2 @ X3 @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ X1)) & ? [X6 : $i] : (($true = (in @ X6 @ X2)) & ($true = (in @ (kpair @ X5 @ X6) @ X3)) & ($true != (in @ (kpair @ X5 @ X6) @ X0)))) & ($true = (func @ X1 @ X2 @ X3))) & ($true = (func @ X1 @ X2 @ X0))) => (? [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ sK261)) | ((ap @ sK261 @ sK262 @ sK260 @ X4) = (ap @ sK261 @ sK262 @ X3 @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ sK261)) & ? [X6 : $i] : (($true = (in @ X6 @ sK262)) & ($true = (in @ (kpair @ X5 @ X6) @ X3)) & ($true != (in @ (kpair @ X5 @ X6) @ sK260)))) & ($true = (func @ sK261 @ sK262 @ X3))) & ($true = (func @ sK261 @ sK262 @ sK260)))),
% 92.68/14.54 introduced(definition,[],[choice_axiom])).
% 92.68/14.54 thf(f1277,plain,(
% 92.68/14.54 ? [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ sK261)) | ((ap @ sK261 @ sK262 @ sK260 @ X4) = (ap @ sK261 @ sK262 @ X3 @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ sK261)) & ? [X6 : $i] : (($true = (in @ X6 @ sK262)) & ($true = (in @ (kpair @ X5 @ X6) @ X3)) & ($true != (in @ (kpair @ X5 @ X6) @ sK260)))) & ($true = (func @ sK261 @ sK262 @ X3))) => (! [X4 : $i] : (($true != (in @ X4 @ sK261)) | ((ap @ sK261 @ sK262 @ sK260 @ X4) = (ap @ sK261 @ sK262 @ sK263 @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ sK261)) & ? [X6 : $i] : (($true = (in @ X6 @ sK262)) & ($true = (in @ (kpair @ X5 @ X6) @ sK263)) & ($true != (in @ (kpair @ X5 @ X6) @ sK260)))) & ($true = (func @ sK261 @ sK262 @ sK263)))),
% 92.68/14.54 introduced(definition,[],[choice_axiom])).
% 92.68/14.54 thf(f1278,plain,(
% 92.68/14.54 ? [X5 : $i] : (($true = (in @ X5 @ sK261)) & ? [X6 : $i] : (($true = (in @ X6 @ sK262)) & ($true = (in @ (kpair @ X5 @ X6) @ sK263)) & ($true != (in @ (kpair @ X5 @ X6) @ sK260)))) => (($true = (in @ sK264 @ sK261)) & ? [X6 : $i] : (($true = (in @ X6 @ sK262)) & ($true = (in @ (kpair @ sK264 @ X6) @ sK263)) & ($true != (in @ (kpair @ sK264 @ X6) @ sK260))))),
% 92.68/14.54 introduced(definition,[],[choice_axiom])).
% 92.68/14.54 thf(f1279,plain,(
% 92.68/14.54 ? [X6 : $i] : (($true = (in @ X6 @ sK262)) & ($true = (in @ (kpair @ sK264 @ X6) @ sK263)) & ($true != (in @ (kpair @ sK264 @ X6) @ sK260))) => (($true = (in @ sK265 @ sK262)) & ($true = (in @ (kpair @ sK264 @ sK265) @ sK263)) & ($true != (in @ (kpair @ sK264 @ sK265) @ sK260)))),
% 92.68/14.54 introduced(definition,[],[choice_axiom])).
% 92.68/14.54 thf(f801,plain,(
% 92.68/14.54 (exuI1 = $true) & (quantDeMorgan4 = $true) & (binunionLsub = $true) & (in__Cong = $true) & (symdiffE = $true) & (subsetTrans = $true) & (ex1E2 = $true) & (subsetemptysetimpeq = $true) & (subsetE2 = $true) & (singletonsswitch = $true) & (singletoninpowerset = $true) & (binintersectSubset1 = $true) & (cartprodmempair = $true) & (emptyinPowerset = $true) & (setukpairinjR = $true) & (ex1I2 = $true) & (prop2set2propI = $true) & (symdiffIneg1 = $true) & (setminusLsub = $true) & (powersetI = $true) & (exuI2 = $true) & (setminusER = $true) & (upairset2E = $true) & (singletoninpowunion = $true) & (binintersectEL = $true) & (uniqinunit = $true) & (powerset__Cong = $true) & (setminusIRneg = $true) & (ubforcartprodlem3 = $true) & (kfstsingleton = $true) & (cartprodpairmemEL = $true) & (sepInPowerset = $true) & (setunionsingleton2 = $true) & (eqinunit = $true) & (setunionAx = $true) & (binintersectSubset3 = $true) & (descrp = $true) & (subsetI1 = $true) & (nonemptyI = $true) & (kpairp = $true) & (cartprodmempair1 = $true) & (ex1E1 = $true) & (binintersectRsub = $true) & (setunion__Cong = $true) & (descr__Cong = $true) & (binunionEcases = $true) & (apProp = $true) & (setukpairinjR1 = $true) & (funcGraphProp1 = $true) & (disjointsetsI1 = $true) & (noeltsimpempty = $true) & (cartprodsndin = $true) & (cartprodfstin = $true) & (setukpairinjL2 = $true) & (setadjoinSub2 = $true) & (ap2p = $true) & (dpsetconstrER = $true) & (setextAx = $true) & (setextsub = $true) & (dsetconstrI = $true) & (emptysetsubset = $true) & (quantDeMorgan3 = $true) & (eqimpsubset2 = $true) & (notinsingleton = $true) & (setukpairinjL1 = $true) & (setminusEL = $true) & (singletonsubset = $true) & (powersetAx = $true) & (dsetconstr__Cong = $true) & (binintersectSubset4 = $true) & (omegaSAx = $true) & (nonemptyI1 = $true) & (inPowerset = $true) & (setminusI = $true) & (notdallE = $true) & (ksndpairEq = $true) & (upairsetIL = $true) & (notinemptyset = $true) & (setminusSubset1 = $true) & (binintersectSubset5 = $true) & (symdiffI2 = $true) & (dpsetconstrSub = $true) & (setoftrueEq = $true) & (setukpairinjL = $true) & (eqimpsubset1 = $true) & (dpsetconstrI = $true) & (secondinupair = $true) & (binintersectER = $true) & (quantDeMorgan2 = $true) & (exuE1 = $true) & (upairset2IR = $true) & (setOfPairsIsBReln = $true) & (singletonsuniq = $true) & (subsetRefl = $true) & (nonemptyImpWitness = $true) & (binunionE = $true) & (cartprodpairmemER = $true) & (symdiffIneg2 = $true) & (exuE2 = $true) & (ex1I = $true) & (setadjoinIL = $true) & (setminusELneg = $true) & (kfstpairEq = $true) & (upairsetIR = $true) & (cartprodpairin = $true) & (exuE3e = $true) & (emptyInPowerset = $true) & (binunionRsub = $true) & (cartprodmempaircEq = $true) & (brelnall1 = $true) & (binunionIR = $true) & (brelnall2 = $true) & (emptyinunitempty = $true) & (setunionI = $true) & (upairequniteq = $true) & (lamp = $true) & (kpairsurjEq = $true) & (notequalI2 = $true) & (vacuousDall = $true) & (omega0Ax = $true) & (ubforcartprodlem2 = $true) & (setminusILneg = $true) & (setadjoinIR = $true) & (setext = $true) & (setukpairIR = $true) & (exu__Cong = $true) & (dsetconstrEL = $true) & (setunionsingleton = $true) & (setukpairIL = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X1)) | ((ap @ X1 @ X2 @ X0 @ X4) = (ap @ X1 @ X2 @ X3 @ X4))) & ? [X5 : $i] : (($true = (in @ X5 @ X1)) & ? [X6 : $i] : (($true = (in @ X6 @ X2)) & ($true = (in @ (kpair @ X5 @ X6) @ X3)) & ($true != (in @ (kpair @ X5 @ X6) @ X0)))) & ($true = (func @ X1 @ X2 @ X3))) & ($true = (func @ X1 @ X2 @ X0))) & (foundationAx = $true) & (emptysetAx = $true) & (subsetI2 = $true) & (emptyE1 = $true) & (infuncsetfunc = $true) & (prop2setE = $true) & (setunionsingleton1 = $true) & (inCongP = $true) & (replAx = $true) & (sepSubset = $true) & (notsubsetI = $true) & (binintersectSubset2 = $true) & (ubforcartprodlem1 = $true) & (subsetE = $true) & (binintersectI = $true) & (funcinfuncset = $true) & (powersetE = $true) & (setukpairinjR2 = $true) & (subset2powerset = $true) & (emptyI = $true) & (ksndsingleton = $true) & (setunionE2 = $true) & (upairsubunion = $true) & (setukpairinjR12 = $true) & (nonemptyE1 = $true) & (setminusERneg = $true) & (dsetconstrER = $true) & (subPowSU = $true) & (upairinpowunion = $true) & (exuI3 = $true) & (kpairiskpair = $true) & (powersetI1 = $true) & (setadjoinE = $true) & (emptysetimpfalse = $true) & (setukpairinjR11 = $true) & (binunionIL = $true) & (theprop = $true) & (funcGraphProp3 = $true) & (powersetE1 = $true) & (dpsetconstrERa = $true) & (funcGraphProp2 = $true) & (dpsetconstrEL1 = $true) & (cartprodpairsurjEq = $true) & (wellorderingAx = $true) & (funcImageSingleton = $true) & (notequalI1 = $true) & (emptyset__Cong = $true) & (lam2p = $true) & (cartprodfstpairEq = $true) & (setbeta = $true) & (notdexE = $true) & (quantDeMorgan1 = $true) & (setminusSubset2 = $true) & (upairsetE = $true) & (bs114d = $true) & (setadjoin__Cong = $true) & (singletonprop = $true) & (lamProp = $true) & (cartprodsndpairEq = $true) & (omegaIndAx = $true) & (setunionE = $true) & (dpsetconstrEL2 = $true) & (exuEu = $true) & (binintersectLsub = $true) & (powersetsubset = $true) & (setadjoinAx = $true) & (exuE3u = $true) & (symdiffI1 = $true) & (setadjoinSub = $true) & (setadjoinOr = $true) & (prop2setI = $true) & (emptysetE = $true) & (omega__Cong = $true) & (app = $true)),
% 92.68/14.54 inference(flattening,[status(thm)],[f800])).
% 92.68/14.54 thf(f800,plain,(
% 92.68/14.54 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((? [X5 : $i] : (? [X6 : $i] : ((($true != (in @ (kpair @ X5 @ X6) @ X0)) & ($true = (in @ (kpair @ X5 @ X6) @ X3))) & ($true = (in @ X6 @ X2))) & ($true = (in @ X5 @ X1))) & ! [X4 : $i] : (($true != (in @ X4 @ X1)) | ((ap @ X1 @ X2 @ X0 @ X4) = (ap @ X1 @ X2 @ X3 @ X4)))) & ($true = (func @ X1 @ X2 @ X3))) & ($true = (func @ X1 @ X2 @ X0))) & (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)),
% 92.68/14.54 inference(ennf_transformation,[status(thm)],[f271])).
% 92.68/14.54 thf(f271,plain,(
% 92.68/14.54 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X1 @ X2 @ X0)) => ! [X3 : $i] : (($true = (func @ X1 @ X2 @ X3)) => (! [X4 : $i] : (($true = (in @ X4 @ X1)) => ((ap @ X1 @ X2 @ X0 @ X4) = (ap @ X1 @ X2 @ X3 @ X4))) => ! [X5 : $i] : (($true = (in @ X5 @ X1)) => ! [X6 : $i] : (($true = (in @ X6 @ X2)) => (($true = (in @ (kpair @ X5 @ X6) @ X3)) => ($true = (in @ (kpair @ X5 @ X6) @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 92.68/14.54 inference(fool_elimination,[status(thm)],[f270])).
% 92.68/14.54 thf(f270,plain,(
% 92.68/14.54 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X2 @ X0) => ! [X3 : $i] : ((func @ X1 @ X2 @ X3) => (! [X4 : $i] : ((in @ X4 @ X1) => ((ap @ X1 @ X2 @ X0 @ X4) = (ap @ X1 @ X2 @ X3 @ X4))) => ! [X5 : $i] : ((in @ X5 @ X1) => ! [X6 : $i] : ((in @ X6 @ X2) => ((in @ (kpair @ X5 @ X6) @ X3) => (in @ (kpair @ X5 @ X6) @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 92.68/14.54 inference(rectify,[status(thm)],[f212])).
% 92.68/14.54 thf(f212,negated_conjecture,(
% 92.68/14.54 ~(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 => ! [X13 : $i,X3 : $i,X4 : $i] : ((func @ X3 @ X4 @ X13) => ! [X14 : $i] : ((func @ X3 @ X4 @ X14) => (! [X1 : $i] : ((in @ X1 @ X3) => ((ap @ X3 @ X4 @ X13 @ X1) = (ap @ X3 @ X4 @ X14 @ X1))) => ! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X14) => (in @ (kpair @ X1 @ X2) @ X13))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 92.68/14.54 inference(negated_conjecture,[status(cth)],[f211])).
% 92.68/14.54 thf(f211,conjecture,(
% 92.68/14.54 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 => ! [X13 : $i,X3 : $i,X4 : $i] : ((func @ X3 @ X4 @ X13) => ! [X14 : $i] : ((func @ X3 @ X4 @ X14) => (! [X1 : $i] : ((in @ X1 @ X3) => ((ap @ X3 @ X4 @ X13 @ X1) = (ap @ X3 @ X4 @ X14 @ X1))) => ! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X14) => (in @ (kpair @ X1 @ X2) @ X13)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 92.68/14.54 file('/export/starexec/sandbox/tmp/tmp.pJgJnm9BBC/DTF2THF_23745.p',funcextLem)).
% 92.68/14.54 thf(f17571,plain,(
% 92.68/14.54 ($true != (in @ (kpair @ sK264 @ sK265) @ sK263)) | ~spl611_583),
% 92.68/14.54 inference(subsumption_resolution,[status(thm)],[f17570,f2263])).
% 92.68/14.54 thf(f2263,plain,(
% 92.68/14.54 ($true = (in @ sK265 @ sK262))),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f1280])).
% 92.68/14.54 thf(f17570,plain,(
% 92.68/14.54 ($true != (in @ sK265 @ sK262)) | ($true != (in @ (kpair @ sK264 @ sK265) @ sK263)) | ~spl611_583),
% 92.68/14.54 inference(subsumption_resolution,[status(thm)],[f17545,f2264])).
% 92.68/14.54 thf(f2264,plain,(
% 92.68/14.54 ($true = (in @ sK264 @ sK261))),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f1280])).
% 92.68/14.54 thf(f17545,plain,(
% 92.68/14.54 ($true != (in @ sK264 @ sK261)) | ($true != (in @ sK265 @ sK262)) | ($true != (in @ (kpair @ sK264 @ sK265) @ sK263)) | ~spl611_583),
% 92.68/14.54 inference(trivial_inequality_removal,[status(thm)],[f17537])).
% 92.68/14.54 thf(f17537,plain,(
% 92.68/14.54 ($true != (in @ sK264 @ sK261)) | ($true != (in @ (kpair @ sK264 @ sK265) @ sK263)) | ($true != (in @ sK265 @ sK262)) | ($true != $true) | ~spl611_583),
% 92.68/14.54 inference(superposition,[status(thm)],[f2261,f14617])).
% 92.68/14.54 thf(f14617,plain,(
% 92.68/14.54 ( ! [X0 : $i,X1 : $i] : (($true = (in @ (kpair @ X0 @ X1) @ sK260)) | ($true != (in @ (kpair @ X0 @ X1) @ sK263)) | ($true != (in @ X1 @ sK262)) | ($true != (in @ X0 @ sK261))) ) | ~spl611_583),
% 92.68/14.54 inference(avatar_component_clause,[status(thm)],[f14616])).
% 92.68/14.54 thf(f14616,definition,(
% 92.68/14.54 spl611_583 <=> ! [X0 : $i,X1 : $i] : (($true != (in @ (kpair @ X0 @ X1) @ sK263)) | ($true = (in @ (kpair @ X0 @ X1) @ sK260)) | ($true != (in @ X0 @ sK261)) | ($true != (in @ X1 @ sK262)))),
% 92.68/14.54 introduced(definition,[new_symbols(naming,[spl611_583])],[avatar_definition])).
% 92.68/14.54 thf(f2261,plain,(
% 92.68/14.54 ($true != (in @ (kpair @ sK264 @ sK265) @ sK260))),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f1280])).
% 92.68/14.54 thf(f14624,plain,(
% 92.68/14.54 spl611_583),
% 92.68/14.54 inference(avatar_split_clause,[status(thm)],[f14623,f14616])).
% 92.68/14.54 thf(f14623,plain,(
% 92.68/14.54 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ sK261)) | ($true = (in @ (kpair @ X0 @ X1) @ sK260)) | ($true != (in @ X1 @ sK262)) | ($true != (in @ (kpair @ X0 @ X1) @ sK263))) )),
% 92.68/14.54 inference(subsumption_resolution,[status(thm)],[f14622,f2346])).
% 92.68/14.54 thf(f2346,plain,(
% 92.68/14.54 (funcGraphProp1 = $true)),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f1280])).
% 92.68/14.54 thf(f14622,plain,(
% 92.68/14.54 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (kpair @ X0 @ X1) @ sK263)) | ($true != (in @ X1 @ sK262)) | ($true != (in @ X0 @ sK261)) | (funcGraphProp1 != $true) | ($true = (in @ (kpair @ X0 @ X1) @ sK260))) )),
% 92.68/14.54 inference(subsumption_resolution,[status(thm)],[f14603,f2259])).
% 92.68/14.54 thf(f2259,plain,(
% 92.68/14.54 ($true = (func @ sK261 @ sK262 @ sK260))),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f1280])).
% 92.68/14.54 thf(f14603,plain,(
% 92.68/14.54 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X0 @ sK261)) | ($true != (in @ X1 @ sK262)) | ($true = (in @ (kpair @ X0 @ X1) @ sK260)) | ($true != (func @ sK261 @ sK262 @ sK260)) | ($true != (in @ (kpair @ X0 @ X1) @ sK263)) | (funcGraphProp1 != $true)) )),
% 92.68/14.54 inference(duplicate_literal_removal,[status(thm)],[f14601])).
% 92.68/14.54 thf(f14601,plain,(
% 92.68/14.54 ( ! [X0 : $i,X1 : $i] : ((funcGraphProp1 != $true) | ($true != (in @ (kpair @ X0 @ X1) @ sK263)) | ($true != (in @ X1 @ sK262)) | ($true != (func @ sK261 @ sK262 @ sK260)) | ($true = (in @ (kpair @ X0 @ X1) @ sK260)) | ($true != (in @ X0 @ sK261)) | ($true != (in @ X0 @ sK261))) )),
% 92.68/14.54 inference(superposition,[status(thm)],[f1883,f8146])).
% 92.68/14.54 thf(f8146,plain,(
% 92.68/14.54 ( ! [X0 : $i,X1 : $i] : (((ap @ sK261 @ sK262 @ sK260 @ X0) = X1) | ($true != (in @ X0 @ sK261)) | ($true != (in @ (kpair @ X0 @ X1) @ sK263)) | ($true != (in @ X1 @ sK262))) )),
% 92.68/14.54 inference(subsumption_resolution,[status(thm)],[f8145,f2260])).
% 92.68/14.54 thf(f2260,plain,(
% 92.68/14.54 ($true = (func @ sK261 @ sK262 @ sK263))),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f1280])).
% 92.68/14.54 thf(f8145,plain,(
% 92.68/14.54 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ sK262)) | ((ap @ sK261 @ sK262 @ sK260 @ X0) = X1) | ($true != (in @ (kpair @ X0 @ X1) @ sK263)) | ($true != (func @ sK261 @ sK262 @ sK263)) | ($true != (in @ X0 @ sK261))) )),
% 92.68/14.54 inference(subsumption_resolution,[status(thm)],[f8128,f2218])).
% 92.68/14.54 thf(f2218,plain,(
% 92.68/14.54 (funcGraphProp2 = $true)),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f1280])).
% 92.68/14.54 thf(f8128,plain,(
% 92.68/14.54 ( ! [X0 : $i,X1 : $i] : (($true != (in @ X1 @ sK262)) | (funcGraphProp2 != $true) | ($true != (in @ (kpair @ X0 @ X1) @ sK263)) | ($true != (func @ sK261 @ sK262 @ sK263)) | ($true != (in @ X0 @ sK261)) | ((ap @ sK261 @ sK262 @ sK260 @ X0) = X1)) )),
% 92.68/14.54 inference(duplicate_literal_removal,[status(thm)],[f8120])).
% 92.68/14.54 thf(f8120,plain,(
% 92.68/14.54 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (kpair @ X0 @ X1) @ sK263)) | ($true != (in @ X0 @ sK261)) | ($true != (in @ X1 @ sK262)) | ($true != (func @ sK261 @ sK262 @ sK263)) | (funcGraphProp2 != $true) | ((ap @ sK261 @ sK262 @ sK260 @ X0) = X1) | ($true != (in @ X0 @ sK261))) )),
% 92.68/14.54 inference(superposition,[status(thm)],[f2265,f2505])).
% 92.68/14.54 thf(f2505,plain,(
% 92.68/14.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i,X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (func @ X1 @ X2 @ X0)) | ($true != (in @ X4 @ X2)) | (funcGraphProp2 != $true) | ($true != (in @ (kpair @ X3 @ X4) @ X0)) | ($true != (in @ X3 @ X1))) )),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f1413])).
% 92.68/14.54 thf(f1413,plain,(
% 92.68/14.54 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X1 @ X2 @ X0)) | ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ! [X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ X4 @ X2)) | ($true != (in @ (kpair @ X3 @ X4) @ X0))))) | (funcGraphProp2 != $true)) & ((funcGraphProp2 = $true) | (($true = (func @ sK346 @ sK347 @ sK345)) & (($true = (in @ sK348 @ sK346)) & (((ap @ sK346 @ sK347 @ sK345 @ sK348) != sK349) & ($true = (in @ sK349 @ sK347)) & ($true = (in @ (kpair @ sK348 @ sK349) @ sK345))))))),
% 92.68/14.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK345,sK346,sK347,sK348,sK349])],[f1409,f1412,f1411,f1410])).
% 92.68/14.54 thf(f1410,plain,(
% 92.68/14.54 ? [X5 : $i,X6 : $i,X7 : $i] : (($true = (func @ X6 @ X7 @ X5)) & ? [X8 : $i] : (($true = (in @ X8 @ X6)) & ? [X9 : $i] : (((ap @ X6 @ X7 @ X5 @ X8) != X9) & ($true = (in @ X9 @ X7)) & ($true = (in @ (kpair @ X8 @ X9) @ X5))))) => (($true = (func @ sK346 @ sK347 @ sK345)) & ? [X8 : $i] : (($true = (in @ X8 @ sK346)) & ? [X9 : $i] : (((ap @ sK346 @ sK347 @ sK345 @ X8) != X9) & ($true = (in @ X9 @ sK347)) & ($true = (in @ (kpair @ X8 @ X9) @ sK345)))))),
% 92.68/14.54 introduced(definition,[],[choice_axiom])).
% 92.68/14.54 thf(f1411,plain,(
% 92.68/14.54 ? [X8 : $i] : (($true = (in @ X8 @ sK346)) & ? [X9 : $i] : (((ap @ sK346 @ sK347 @ sK345 @ X8) != X9) & ($true = (in @ X9 @ sK347)) & ($true = (in @ (kpair @ X8 @ X9) @ sK345)))) => (($true = (in @ sK348 @ sK346)) & ? [X9 : $i] : (((ap @ sK346 @ sK347 @ sK345 @ sK348) != X9) & ($true = (in @ X9 @ sK347)) & ($true = (in @ (kpair @ sK348 @ X9) @ sK345))))),
% 92.68/14.54 introduced(definition,[],[choice_axiom])).
% 92.68/14.54 thf(f1412,plain,(
% 92.68/14.54 ? [X9 : $i] : (((ap @ sK346 @ sK347 @ sK345 @ sK348) != X9) & ($true = (in @ X9 @ sK347)) & ($true = (in @ (kpair @ sK348 @ X9) @ sK345))) => (((ap @ sK346 @ sK347 @ sK345 @ sK348) != sK349) & ($true = (in @ sK349 @ sK347)) & ($true = (in @ (kpair @ sK348 @ sK349) @ sK345)))),
% 92.68/14.54 introduced(definition,[],[choice_axiom])).
% 92.68/14.54 thf(f1409,plain,(
% 92.68/14.54 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X1 @ X2 @ X0)) | ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ! [X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ X4 @ X2)) | ($true != (in @ (kpair @ X3 @ X4) @ X0))))) | (funcGraphProp2 != $true)) & ((funcGraphProp2 = $true) | ? [X5 : $i,X6 : $i,X7 : $i] : (($true = (func @ X6 @ X7 @ X5)) & ? [X8 : $i] : (($true = (in @ X8 @ X6)) & ? [X9 : $i] : (((ap @ X6 @ X7 @ X5 @ X8) != X9) & ($true = (in @ X9 @ X7)) & ($true = (in @ (kpair @ X8 @ X9) @ X5))))))),
% 92.68/14.54 inference(rectify,[status(thm)],[f1408])).
% 92.68/14.54 thf(f1408,plain,(
% 92.68/14.54 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X1 @ X2 @ X0)) | ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ! [X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ X4 @ X2)) | ($true != (in @ (kpair @ X3 @ X4) @ X0))))) | (funcGraphProp2 != $true)) & ((funcGraphProp2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X1 @ X2 @ X0)) & ? [X3 : $i] : (($true = (in @ X3 @ X1)) & ? [X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) != X4) & ($true = (in @ X4 @ X2)) & ($true = (in @ (kpair @ X3 @ X4) @ X0))))))),
% 92.68/14.54 inference(nnf_transformation,[status(thm)],[f718])).
% 92.68/14.54 thf(f718,plain,(
% 92.68/14.54 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (func @ X1 @ X2 @ X0)) | ! [X3 : $i] : (($true != (in @ X3 @ X1)) | ! [X4 : $i] : (((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ X4 @ X2)) | ($true != (in @ (kpair @ X3 @ X4) @ X0))))) <=> (funcGraphProp2 = $true)),
% 92.68/14.54 inference(flattening,[status(thm)],[f717])).
% 92.68/14.54 thf(f717,plain,(
% 92.68/14.54 (funcGraphProp2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : ((((ap @ X1 @ X2 @ X0 @ X3) = X4) | ($true != (in @ (kpair @ X3 @ X4) @ X0))) | ($true != (in @ X4 @ X2))) | ($true != (in @ X3 @ X1))) | ($true != (func @ X1 @ X2 @ X0)))),
% 92.68/14.54 inference(ennf_transformation,[status(thm)],[f221])).
% 92.68/14.54 thf(f221,plain,(
% 92.68/14.54 (funcGraphProp2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X1 @ X2 @ X0)) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => ! [X4 : $i] : (($true = (in @ X4 @ X2)) => (($true = (in @ (kpair @ X3 @ X4) @ X0)) => ((ap @ X1 @ X2 @ X0 @ X3) = X4)))))),
% 92.68/14.54 inference(fool_elimination,[status(thm)],[f220])).
% 92.68/14.54 thf(f220,plain,(
% 92.68/14.54 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X2 @ X0) => ! [X3 : $i] : ((in @ X3 @ X1) => ! [X4 : $i] : ((in @ X4 @ X2) => ((in @ (kpair @ X3 @ X4) @ X0) => ((ap @ X1 @ X2 @ X0 @ X3) = X4))))) = funcGraphProp2)),
% 92.68/14.54 inference(rectify,[status(thm)],[f210])).
% 92.68/14.54 thf(f210,axiom,(
% 92.68/14.54 (! [X13 : $i,X3 : $i,X4 : $i] : ((func @ X3 @ X4 @ X13) => ! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X13) => ((ap @ X3 @ X4 @ X13 @ X1) = X2))))) = funcGraphProp2)),
% 92.68/14.54 file('/export/starexec/sandbox/tmp/tmp.pJgJnm9BBC/DTF2THF_23745.p',funcGraphProp2)).
% 92.68/14.54 thf(f2265,plain,(
% 92.68/14.54 ( ! [X4 : $i] : (((ap @ sK261 @ sK262 @ sK260 @ X4) = (ap @ sK261 @ sK262 @ sK263 @ X4)) | ($true != (in @ X4 @ sK261))) )),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f1280])).
% 92.68/14.54 thf(f1883,plain,(
% 92.68/14.54 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2)) | ($true != (func @ X1 @ X0 @ X2)) | (funcGraphProp1 != $true) | ($true != (in @ X3 @ X1))) )),
% 92.68/14.54 inference(cnf_transformation,[status(thm)],[f942])).
% 92.68/14.54 thf(f942,plain,(
% 92.68/14.54 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X1)) | ($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2))) | ($true != (func @ X1 @ X0 @ X2))) | (funcGraphProp1 != $true)) & ((funcGraphProp1 = $true) | ((($true = (in @ sK43 @ sK41)) & ($true != (in @ (kpair @ sK43 @ (ap @ sK41 @ sK40 @ sK42 @ sK43)) @ sK42))) & ($true = (func @ sK41 @ sK40 @ sK42))))),
% 92.68/14.54 inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42,sK43])],[f939,f941,f940])).
% 92.68/14.54 thf(f940,plain,(
% 92.68/14.54 ? [X4 : $i,X5 : $i,X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X5)) & ($true != (in @ (kpair @ X7 @ (ap @ X5 @ X4 @ X6 @ X7)) @ X6))) & ($true = (func @ X5 @ X4 @ X6))) => (? [X7 : $i] : (($true = (in @ X7 @ sK41)) & ($true != (in @ (kpair @ X7 @ (ap @ sK41 @ sK40 @ sK42 @ X7)) @ sK42))) & ($true = (func @ sK41 @ sK40 @ sK42)))),
% 92.68/14.54 introduced(definition,[],[choice_axiom])).
% 92.68/14.54 thf(f941,plain,(
% 92.68/14.54 ? [X7 : $i] : (($true = (in @ X7 @ sK41)) & ($true != (in @ (kpair @ X7 @ (ap @ sK41 @ sK40 @ sK42 @ X7)) @ sK42))) => (($true = (in @ sK43 @ sK41)) & ($true != (in @ (kpair @ sK43 @ (ap @ sK41 @ sK40 @ sK42 @ sK43)) @ sK42)))),
% 92.68/14.54 introduced(definition,[],[choice_axiom])).
% 92.68/14.54 thf(f939,plain,(
% 92.68/14.54 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X1)) | ($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2))) | ($true != (func @ X1 @ X0 @ X2))) | (funcGraphProp1 != $true)) & ((funcGraphProp1 = $true) | ? [X4 : $i,X5 : $i,X6 : $i] : (? [X7 : $i] : (($true = (in @ X7 @ X5)) & ($true != (in @ (kpair @ X7 @ (ap @ X5 @ X4 @ X6 @ X7)) @ X6))) & ($true = (func @ X5 @ X4 @ X6))))),
% 92.68/14.54 inference(rectify,[status(thm)],[f938])).
% 92.68/14.54 thf(f938,plain,(
% 92.68/14.54 (! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X1)) | ($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2))) | ($true != (func @ X1 @ X0 @ X2))) | (funcGraphProp1 != $true)) & ((funcGraphProp1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (($true = (in @ X3 @ X1)) & ($true != (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2))) & ($true = (func @ X1 @ X0 @ X2))))),
% 92.68/14.54 inference(nnf_transformation,[status(thm)],[f803])).
% 92.68/14.54 thf(f803,plain,(
% 92.68/14.54 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (($true != (in @ X3 @ X1)) | ($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2))) | ($true != (func @ X1 @ X0 @ X2))) <=> (funcGraphProp1 = $true)),
% 92.68/14.54 inference(ennf_transformation,[status(thm)],[f545])).
% 92.68/14.54 thf(f545,plain,(
% 92.68/14.54 (funcGraphProp1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (func @ X1 @ X0 @ X2)) => ! [X3 : $i] : (($true = (in @ X3 @ X1)) => ($true = (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2))))),
% 92.68/14.54 inference(fool_elimination,[status(thm)],[f544])).
% 92.68/14.54 thf(f544,plain,(
% 92.68/14.54 (! [X0 : $i,X1 : $i,X2 : $i] : ((func @ X1 @ X0 @ X2) => ! [X3 : $i] : ((in @ X3 @ X1) => (in @ (kpair @ X3 @ (ap @ X1 @ X0 @ X2 @ X3)) @ X2))) = funcGraphProp1)),
% 92.68/14.54 inference(rectify,[status(thm)],[f208])).
% 92.68/14.54 thf(f208,axiom,(
% 92.68/14.54 (! [X4 : $i,X3 : $i,X13 : $i] : ((func @ X3 @ X4 @ X13) => ! [X1 : $i] : ((in @ X1 @ X3) => (in @ (kpair @ X1 @ (ap @ X3 @ X4 @ X13 @ X1)) @ X13))) = funcGraphProp1)),
% 92.68/14.54 file('/export/starexec/sandbox/tmp/tmp.pJgJnm9BBC/DTF2THF_23745.p',funcGraphProp1)).
% 92.68/14.54 % SZS output end Proof for DTF2THF_23745
% 92.68/14.54 % (24315)------------------------------
% 92.68/14.54 % (24315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.68/14.54 % (24315)Termination reason: Refutation
% 92.68/14.54
% 92.68/14.54 % (24315)Memory used [KB]: 16886
% 92.68/14.54 % (24315)Time elapsed: 1.232 s
% 92.68/14.54 % (24315)Instructions burned: 4007 (million)
% 92.68/14.54 % (24315)------------------------------
% 92.68/14.54 % (24315)------------------------------
% 92.68/14.54 % (24061)Success in time 12.978 s
%------------------------------------------------------------------------------