%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU690^1 : 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 : n008.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 09:36:25 AM UTC 2026
% Result : Theorem 50.18s 8.41s
% Output : Refutation 50.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 18
% Syntax : Number of formulae : 118 ( 12 unt; 0 typ; 8 def)
% Number of atoms : 6113 (1612 equ; 0 cnn)
% Maximal formula atoms : 217 ( 51 avg)
% Number of connectives : 4439 ( 426 ~; 404 |; 914 &;1786 @)
% ( 14 <=>; 895 =>; 0 <=; 0 <~>)
% Maximal formula depth : 225 ( 21 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 396 ( 393 usr; 226 con; 0-4 aty)
% Number of variables : 278 ( 0 ^; 228 !; 50 ?; 278 :)
% 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_260,type,
sP3: $o > $i > $i > $i > $o ).
thf(func_def_262,type,
sP5: $i > $i > $o ).
thf(func_def_263,type,
sP6: $i > $o ).
thf(func_def_264,type,
sP7: $i > $i > $o ).
thf(func_def_265,type,
sP8: $i > $i > $o ).
thf(func_def_281,type,
sK24: $i > $o ).
thf(func_def_282,type,
sK25: $i > $o ).
thf(func_def_283,type,
sK26: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_284,type,
sK27: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_294,type,
sK37: $i > $o ).
thf(func_def_295,type,
sK38: $i > $i ).
thf(func_def_296,type,
sK39: ( $i > $o ) > $i ).
thf(func_def_298,type,
sK41: $i > $o ).
thf(func_def_302,type,
sK45: ( $i > $o ) > $i ).
thf(func_def_303,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_304,type,
sK47: $i > $o ).
thf(func_def_311,type,
sK54: $i > $o ).
thf(func_def_313,type,
sK56: ( $i > $o ) > $i > $i ).
thf(func_def_321,type,
sK64: ( $i > $o ) > $i ).
thf(func_def_322,type,
sK65: $i > $o ).
thf(func_def_325,type,
sK68: $i > $o ).
thf(func_def_335,type,
sK78: $i > $o ).
thf(func_def_337,type,
sK80: ( $i > $o ) > $i > $i ).
thf(func_def_338,type,
sK81: ( $i > $o ) > $i > $i ).
thf(func_def_344,type,
sK87: $i > $i ).
thf(func_def_347,type,
sK90: $i > $i > $i ).
thf(func_def_349,type,
sK92: $i > $o ).
thf(func_def_351,type,
sK94: ( $i > $o ) > $i > $i ).
thf(func_def_352,type,
sK95: ( $i > $o ) > $i > $i ).
thf(func_def_355,type,
sK98: $i > $o ).
thf(func_def_387,type,
sK130: $i > $i ).
thf(func_def_391,type,
sK134: $i > $i > $o ).
thf(func_def_407,type,
sK150: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_408,type,
sK151: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_412,type,
sK155: $i > $o ).
thf(func_def_420,type,
sK163: $i > $i > $o ).
thf(func_def_429,type,
sK172: $i > $o ).
thf(func_def_434,type,
sK177: $i > $o ).
thf(func_def_437,type,
sK180: $i > ( $i > $o ) > $i ).
thf(func_def_438,type,
sK181: $i > $o ).
thf(func_def_450,type,
sK193: $i > ( $i > $o ) > $i ).
thf(func_def_451,type,
sK194: $i > $o ).
thf(func_def_454,type,
sK197: $i > $i > $o ).
thf(func_def_466,type,
sK209: $i > $o ).
thf(func_def_471,type,
sK214: $i > $i ).
thf(func_def_478,type,
sK221: $i > $i > $i > $i > $i ).
thf(func_def_482,type,
sK225: $i > $o ).
thf(func_def_484,type,
sK227: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_485,type,
sK228: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_492,type,
sK235: $i > $i > $i ).
thf(func_def_497,type,
sK240: $i > $o ).
thf(func_def_500,type,
sK243: $i > $i > $o ).
thf(func_def_515,type,
sK258: $i > $o ).
thf(func_def_519,type,
sK262: $i > $i > $i ).
thf(func_def_520,type,
sK263: $i > $i > $i ).
thf(func_def_534,type,
sK277: $i > $o ).
thf(func_def_535,type,
sK278: $i > $i ).
thf(func_def_536,type,
sK279: ( $i > $o ) > $i ).
thf(func_def_540,type,
sK283: $i > $i > $i ).
thf(func_def_548,type,
sK291: $i > $o ).
thf(func_def_555,type,
sK298: $i > $i > $o ).
thf(func_def_585,type,
sK328: $i > $i ).
thf(func_def_587,type,
sK330: $i > $i ).
thf(func_def_593,type,
sK336: $i > $i > $i ).
thf(func_def_605,type,
sK348: $i > $i > $o ).
thf(func_def_618,type,
sK361: $i > ( $i > $i ) > $i > $i ).
thf(func_def_620,type,
sK363: $i > $i ).
thf(func_def_630,type,
sK373: ( $i > $i ) > $i > $i > $i ).
thf(func_def_633,type,
sK376: $i > $i ).
thf(func_def_641,type,
sK384: $i > $o ).
thf(func_def_646,type,
sK389: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_647,type,
sK390: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_650,type,
sK393: $i > $o ).
thf(func_def_651,type,
sK394: $i > $o ).
thf(func_def_652,type,
sK395: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_653,type,
sK396: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_654,type,
sK397: $i > $o ).
thf(func_def_655,type,
sK398: $i > $o ).
thf(func_def_665,type,
sK408: $i > $i > $i > $i > $i ).
thf(func_def_666,type,
sK409: $i > $i > $i > $i > $i ).
thf(func_def_672,type,
sK415: $i > $o ).
thf(func_def_674,type,
sK417: $i > ( $i > $o ) > $i > $i ).
thf(func_def_676,type,
sK419: $i > $i > $o ).
thf(func_def_677,type,
sK420: $i > $i ).
thf(func_def_678,type,
sK421: $i > $i ).
thf(func_def_679,type,
sK422: ( $i > $i > $o ) > $i > $i ).
thf(func_def_680,type,
sK423: ( $i > $i > $o ) > $i > $i ).
thf(func_def_681,type,
sK424: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_684,type,
sK427: $i > $i > $i ).
thf(func_def_685,type,
sK428: $i > $i > $i ).
thf(func_def_686,type,
sK429: $i > $i > $i ).
thf(func_def_687,type,
sK430: $i > $i > $i ).
thf(func_def_688,type,
sK431: $i > $i > $i ).
thf(func_def_689,type,
sK432: $i > $i > $i > $i ).
thf(func_def_690,type,
sK433: $i > $i ).
thf(func_def_691,type,
sK434: $i > $i ).
thf(func_def_692,type,
sK435: $i > $i ).
thf(func_def_693,type,
sK436: $i > $i ).
thf(func_def_694,type,
sK437: $i > $i > $i ).
thf(func_def_695,type,
sK438: $i > $i > $i > $i ).
thf(func_def_696,type,
sK439: $i > $i > $i > $i ).
thf(func_def_697,type,
sK440: $i > $i > $i ).
thf(func_def_698,type,
sK441: $i > $i > $i ).
thf(func_def_699,type,
sK442: $i > $i ).
thf(func_def_701,type,
sK444: $i > $i ).
thf(func_def_702,type,
sK445: $i > $i ).
thf(func_def_712,type,
sK455: $i > $i > $i > $i ).
thf(func_def_713,type,
sK456: $i > $i > $i > $i ).
thf(func_def_726,type,
sK469: $i > $o ).
thf(func_def_734,type,
sK477: $i > $i > $i ).
thf(func_def_738,type,
sK481: $i > ( $i > $o ) > $i ).
thf(func_def_739,type,
sK482: $i > $o ).
thf(func_def_760,type,
sK503: $i > $o ).
thf(func_def_778,type,
sK521: $o > $i > $i > $i ).
thf(func_def_783,type,
sK526: $i > $i ).
thf(func_def_794,type,
sK537: ( $i > $o ) > $i > $i ).
thf(func_def_796,type,
sK539: $i > $o ).
thf(func_def_797,type,
sK540: $i > $o ).
thf(func_def_800,type,
sK543: $i > ( $i > $o ) > $i ).
thf(func_def_802,type,
sK545: $i > $o ).
thf(func_def_809,type,
sK552: $i > $i ).
thf(func_def_812,type,
sK555: $i > $i > $i ).
thf(func_def_813,type,
sK556: $i > ( $i > $o ) > $i ).
thf(func_def_814,type,
sK557: $i > $o ).
thf(func_def_822,type,
sK565: $i > $i ).
thf(func_def_823,type,
sK566: ( $i > $i ) > $i > $i > $i ).
thf(func_def_853,type,
sK596: $i > ( $i > $o ) > $i ).
thf(func_def_854,type,
sK597: $i > $o ).
thf(func_def_864,type,
sK607: $i > $i > $i ).
thf(func_def_869,type,
sK612: $i > $i > $o ).
thf(func_def_875,type,
sK618: $i > $i > $i ).
thf(func_def_882,type,
sK625: $i > $o ).
thf(func_def_884,type,
sK627: $i > ( $i > $o ) > $i ).
thf(func_def_886,type,
ph629:
!>[X0: $tType] : X0 ).
thf(f19683,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3475,f3505,f6076,f6567,f6602,f11308,f19450,f19477,f19678]) ).
thf(f19678,plain,
( ~ spl628_122
| spl628_8
| ~ spl628_18 ),
inference(avatar_split_clause,[status(thm)],[f19677,f6600,f3469,f11305]) ).
thf(f11305,definition,
( spl628_122
<=> ( $true
= ( breln @ sK204 @ sK205 @ sK207 ) ) ),
introduced(definition,[new_symbols(naming,[spl628_122])],[avatar_definition]) ).
thf(f3469,definition,
( spl628_8
<=> ( ( subset @ sK206 @ sK207 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl628_8])],[avatar_definition]) ).
thf(f6600,definition,
( spl628_18
<=> ! [X0: $i] :
( ( ( in @ ( sK408 @ sK207 @ X0 @ sK205 @ sK206 ) @ sK204 )
!= $true )
| ( $true
!= ( breln @ X0 @ sK205 @ sK207 ) )
| ( ( breln @ X0 @ sK205 @ sK206 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl628_18])],[avatar_definition]) ).
thf(f19677,plain,
( ( ( subset @ sK206 @ sK207 )
= $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ~ spl628_18 ),
inference(trivial_inequality_removal,[status(thm)],[f19676]) ).
thf(f19676,plain,
( ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( $true != $true )
| ~ spl628_18 ),
inference(forward_demodulation,[status(thm)],[f19675,f2269]) ).
thf(f2269,plain,
( $true
= ( breln @ sK204 @ sK205 @ sK206 ) ),
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f1213,plain,
( ( subsetemptysetimpeq = $true )
& ( nonemptyI1 = $true )
& ( setminusSubset1 = $true )
& ( binintersectLsub = $true )
& ( notequalI1 = $true )
& ( exu__Cong = $true )
& ( setukpairinjL2 = $true )
& ( emptyinunitempty = $true )
& ( exuE2 = $true )
& ( upairset2IR = $true )
& ( subset2powerset = $true )
& ( omegaIndAx = $true )
& ( subsetTrans = $true )
& ( powerset__Cong = $true )
& ( setminusIRneg = $true )
& ( powersetI = $true )
& ( symdiffIneg2 = $true )
& ( setminusELneg = $true )
& ( lam2p = $true )
& ( binunionE = $true )
& ( cartprodpairsurjEq = $true )
& ( bs114d = $true )
& ( subsetE = $true )
& ( lamp = $true )
& ( dpsetconstrI = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan4 = $true )
& ( funcextLem = $true )
& ( kpairiskpair = $true )
& ( setminusLsub = $true )
& ( symdiffIneg1 = $true )
& ( singletonsuniq = $true )
& ( infuncsetfunc = $true )
& ( subPowSU = $true )
& ( setextAx = $true )
& ( cartprodsndin = $true )
& ( setadjoinIL = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( upairsubunion = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( cartprodmempair1 = $true )
& ( symdiffI2 = $true )
& ( dsetconstrEL = $true )
& ( exuI2 = $true )
& ( quantDeMorgan3 = $true )
& ( setextsub = $true )
& ( descr__Cong = $true )
& ( descrp = $true )
& ( cartprodpairmemEL = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinE = $true )
& ( eqimpsubset2 = $true )
& ( in__Cong = $true )
& ( setukpairinjL1 = $true )
& ( wellorderingAx = $true )
& ( prop2setE = $true )
& ( lamProp = $true )
& ( cartprodpairin = $true )
& ( dpsetconstrEL2 = $true )
& ( setukpairIR = $true )
& ( binintersectRsub = $true )
& ( setext = $true )
& ( setminusILneg = $true )
& ( cartprodfstpairEq = $true )
& ( omega0Ax = $true )
& ( disjointsetsI1 = $true )
& ( kpairp = $true )
& ( binintersectSubset2 = $true )
& ( $true
= ( breln @ sK204 @ sK205 @ sK206 ) )
& ( $true
= ( breln @ sK204 @ sK205 @ sK207 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ sK206 ) )
| ( ( in @ X5 @ sK205 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK207 ) ) )
| ( $true
!= ( in @ X4 @ sK204 ) ) )
& ! [X6: $i] :
( ( ( in @ X6 @ sK204 )
!= $true )
| ! [X7: $i] :
( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ sK207 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ sK206 ) )
| ( $true
!= ( in @ X7 @ sK205 ) ) ) )
& ( sK206 != sK207 )
& ( dsetconstrER = $true )
& ( cartprodfstin = $true )
& ( notequalI2 = $true )
& ( binunionRsub = $true )
& ( quantDeMorgan2 = $true )
& ( setunionI = $true )
& ( emptysetE = $true )
& ( brelnall2 = $true )
& ( setunionsingleton = $true )
& ( binintersectER = $true )
& ( funcGraphProp4 = $true )
& ( singletoninpowerset = $true )
& ( exuE3u = $true )
& ( setOfPairsIsBReln = $true )
& ( kfstsingleton = $true )
& ( ubforcartprodlem1 = $true )
& ( setoftrueEq = $true )
& ( setadjoinSub = $true )
& ( setadjoinIR = $true )
& ( binunionIL = $true )
& ( setunionAx = $true )
& ( cartprodpairmemER = $true )
& ( binintersectEL = $true )
& ( funcGraphProp1 = $true )
& ( ex1E1 = $true )
& ( ksndsingleton = $true )
& ( upairsetIL = $true )
& ( setukpairinjL = $true )
& ( theprop = $true )
& ( sepSubset = $true )
& ( setukpairIL = $true )
& ( emptyset__Cong = $true )
& ( binintersectSubset1 = $true )
& ( ap2p = $true )
& ( setminusEL = $true )
& ( subsetI1 = $true )
& ( upairset2E = $true )
& ( funcinfuncset = $true )
& ( nonemptyE1 = $true )
& ( inCongP = $true )
& ( subbreln = $true )
& ( prop2setI = $true )
& ( cartprodsndpairEq = $true )
& ( upairinpowunion = $true )
& ( singletonprop = $true )
& ( notsubsetI = $true )
& ( notinsingleton = $true )
& ( setbeta = $true )
& ( setadjoinOr = $true )
& ( noeltsimpempty = $true )
& ( omegaSAx = $true )
& ( setukpairinjR11 = $true )
& ( dpsetconstrERa = $true )
& ( setunionE = $true )
& ( dpsetconstrEL1 = $true )
& ( setminusER = $true )
& ( apProp = $true )
& ( singletoninpowunion = $true )
& ( sepInPowerset = $true )
& ( foundationAx = $true )
& ( setminusI = $true )
& ( upairsetIR = $true )
& ( upairequniteq = $true )
& ( emptyInPowerset = $true )
& ( setminusERneg = $true )
& ( notdexE = $true )
& ( emptyI = $true )
& ( binintersectSubset3 = $true )
& ( setunion__Cong = $true )
& ( ubforcartprodlem3 = $true )
& ( notdallE = $true )
& ( emptysetimpfalse = $true )
& ( setadjoin__Cong = $true )
& ( ex1I2 = $true )
& ( exuI1 = $true )
& ( emptysetsubset = $true )
& ( setukpairinjR2 = $true )
& ( omega__Cong = $true )
& ( setukpairinjR1 = $true )
& ( vacuousDall = $true )
& ( binintersectSubset5 = $true )
& ( eqinunit = $true )
& ( singletonsubset = $true )
& ( powersetsubset = $true )
& ( symdiffE = $true )
& ( dpsetconstrER = $true )
& ( secondinupair = $true )
& ( setunionsingleton1 = $true )
& ( funcImageSingleton = $true )
& ( exuI3 = $true )
& ( setukpairinjR12 = $true )
& ( funcGraphProp2 = $true )
& ( dsetconstr__Cong = $true )
& ( powersetE = $true )
& ( binunionEcases = $true )
& ( binintersectSubset4 = $true )
& ( powersetI1 = $true )
& ( ex1E2 = $true )
& ( cartprodmempair = $true )
& ( ubforcartprodlem2 = $true )
& ( dpsetconstrSub = $true )
& ( cartprodmempaircEq = $true )
& ( subsetRefl = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan1 = $true )
& ( subsetE2 = $true )
& ( setadjoinSub2 = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyI = $true )
& ( ksndpairEq = $true )
& ( upairsetE = $true )
& ( setadjoinAx = $true )
& ( kfstpairEq = $true )
& ( ex1I = $true )
& ( setunionE2 = $true )
& ( subsetI2 = $true )
& ( notinemptyset = $true )
& ( setminusSubset2 = $true )
& ( kpairsurjEq = $true )
& ( singletonsswitch = $true )
& ( binunionIR = $true )
& ( funcGraphProp3 = $true )
& ( exuEu = $true )
& ( binunionLsub = $true )
& ( setukpairinjR = $true )
& ( symdiffI1 = $true )
& ( uniqinunit = $true )
& ( emptyE1 = $true )
& ( app = $true )
& ( powersetE1 = $true )
& ( emptyinPowerset = $true )
& ( brelnall1 = $true )
& ( binintersectI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK204,sK205,sK206,sK207])],[f1210,f1212,f1211]) ).
thf(f1211,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X3 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
| ( $true
!= ( in @ X5 @ X1 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ! [X6: $i] :
( ( $true
!= ( in @ X6 @ X0 ) )
| ! [X7: $i] :
( ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
= $true )
| ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
!= $true )
| ( $true
!= ( in @ X7 @ X1 ) ) ) )
& ( X2 != X3 ) ) )
=> ( ( $true
= ( breln @ sK204 @ sK205 @ sK206 ) )
& ? [X3: $i] :
( ( $true
= ( breln @ sK204 @ sK205 @ X3 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ sK206 ) )
| ( ( in @ X5 @ sK205 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
| ( $true
!= ( in @ X4 @ sK204 ) ) )
& ! [X6: $i] :
( ( ( in @ X6 @ sK204 )
!= $true )
| ! [X7: $i] :
( ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ sK206 ) )
| ( $true
!= ( in @ X7 @ sK205 ) ) ) )
& ( sK206 != X3 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1212,plain,
( ? [X3: $i] :
( ( $true
= ( breln @ sK204 @ sK205 @ X3 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ sK206 ) )
| ( ( in @ X5 @ sK205 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
| ( $true
!= ( in @ X4 @ sK204 ) ) )
& ! [X6: $i] :
( ( ( in @ X6 @ sK204 )
!= $true )
| ! [X7: $i] :
( ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ sK206 ) )
| ( $true
!= ( in @ X7 @ sK205 ) ) ) )
& ( sK206 != X3 ) )
=> ( ( $true
= ( breln @ sK204 @ sK205 @ sK207 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ sK206 ) )
| ( ( in @ X5 @ sK205 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK207 ) ) )
| ( $true
!= ( in @ X4 @ sK204 ) ) )
& ! [X6: $i] :
( ( ( in @ X6 @ sK204 )
!= $true )
| ! [X7: $i] :
( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ sK207 ) )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ sK206 ) )
| ( $true
!= ( in @ X7 @ sK205 ) ) ) )
& ( sK206 != sK207 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1210,plain,
( ( subsetemptysetimpeq = $true )
& ( nonemptyI1 = $true )
& ( setminusSubset1 = $true )
& ( binintersectLsub = $true )
& ( notequalI1 = $true )
& ( exu__Cong = $true )
& ( setukpairinjL2 = $true )
& ( emptyinunitempty = $true )
& ( exuE2 = $true )
& ( upairset2IR = $true )
& ( subset2powerset = $true )
& ( omegaIndAx = $true )
& ( subsetTrans = $true )
& ( powerset__Cong = $true )
& ( setminusIRneg = $true )
& ( powersetI = $true )
& ( symdiffIneg2 = $true )
& ( setminusELneg = $true )
& ( lam2p = $true )
& ( binunionE = $true )
& ( cartprodpairsurjEq = $true )
& ( bs114d = $true )
& ( subsetE = $true )
& ( lamp = $true )
& ( dpsetconstrI = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan4 = $true )
& ( funcextLem = $true )
& ( kpairiskpair = $true )
& ( setminusLsub = $true )
& ( symdiffIneg1 = $true )
& ( singletonsuniq = $true )
& ( infuncsetfunc = $true )
& ( subPowSU = $true )
& ( setextAx = $true )
& ( cartprodsndin = $true )
& ( setadjoinIL = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( upairsubunion = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( cartprodmempair1 = $true )
& ( symdiffI2 = $true )
& ( dsetconstrEL = $true )
& ( exuI2 = $true )
& ( quantDeMorgan3 = $true )
& ( setextsub = $true )
& ( descr__Cong = $true )
& ( descrp = $true )
& ( cartprodpairmemEL = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinE = $true )
& ( eqimpsubset2 = $true )
& ( in__Cong = $true )
& ( setukpairinjL1 = $true )
& ( wellorderingAx = $true )
& ( prop2setE = $true )
& ( lamProp = $true )
& ( cartprodpairin = $true )
& ( dpsetconstrEL2 = $true )
& ( setukpairIR = $true )
& ( binintersectRsub = $true )
& ( setext = $true )
& ( setminusILneg = $true )
& ( cartprodfstpairEq = $true )
& ( omega0Ax = $true )
& ( disjointsetsI1 = $true )
& ( kpairp = $true )
& ( binintersectSubset2 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X3 ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
| ( $true
!= ( in @ X5 @ X1 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ! [X6: $i] :
( ( $true
!= ( in @ X6 @ X0 ) )
| ! [X7: $i] :
( ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
= $true )
| ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
!= $true )
| ( $true
!= ( in @ X7 @ X1 ) ) ) )
& ( X2 != X3 ) ) )
& ( dsetconstrER = $true )
& ( cartprodfstin = $true )
& ( notequalI2 = $true )
& ( binunionRsub = $true )
& ( quantDeMorgan2 = $true )
& ( setunionI = $true )
& ( emptysetE = $true )
& ( brelnall2 = $true )
& ( setunionsingleton = $true )
& ( binintersectER = $true )
& ( funcGraphProp4 = $true )
& ( singletoninpowerset = $true )
& ( exuE3u = $true )
& ( setOfPairsIsBReln = $true )
& ( kfstsingleton = $true )
& ( ubforcartprodlem1 = $true )
& ( setoftrueEq = $true )
& ( setadjoinSub = $true )
& ( setadjoinIR = $true )
& ( binunionIL = $true )
& ( setunionAx = $true )
& ( cartprodpairmemER = $true )
& ( binintersectEL = $true )
& ( funcGraphProp1 = $true )
& ( ex1E1 = $true )
& ( ksndsingleton = $true )
& ( upairsetIL = $true )
& ( setukpairinjL = $true )
& ( theprop = $true )
& ( sepSubset = $true )
& ( setukpairIL = $true )
& ( emptyset__Cong = $true )
& ( binintersectSubset1 = $true )
& ( ap2p = $true )
& ( setminusEL = $true )
& ( subsetI1 = $true )
& ( upairset2E = $true )
& ( funcinfuncset = $true )
& ( nonemptyE1 = $true )
& ( inCongP = $true )
& ( subbreln = $true )
& ( prop2setI = $true )
& ( cartprodsndpairEq = $true )
& ( upairinpowunion = $true )
& ( singletonprop = $true )
& ( notsubsetI = $true )
& ( notinsingleton = $true )
& ( setbeta = $true )
& ( setadjoinOr = $true )
& ( noeltsimpempty = $true )
& ( omegaSAx = $true )
& ( setukpairinjR11 = $true )
& ( dpsetconstrERa = $true )
& ( setunionE = $true )
& ( dpsetconstrEL1 = $true )
& ( setminusER = $true )
& ( apProp = $true )
& ( singletoninpowunion = $true )
& ( sepInPowerset = $true )
& ( foundationAx = $true )
& ( setminusI = $true )
& ( upairsetIR = $true )
& ( upairequniteq = $true )
& ( emptyInPowerset = $true )
& ( setminusERneg = $true )
& ( notdexE = $true )
& ( emptyI = $true )
& ( binintersectSubset3 = $true )
& ( setunion__Cong = $true )
& ( ubforcartprodlem3 = $true )
& ( notdallE = $true )
& ( emptysetimpfalse = $true )
& ( setadjoin__Cong = $true )
& ( ex1I2 = $true )
& ( exuI1 = $true )
& ( emptysetsubset = $true )
& ( setukpairinjR2 = $true )
& ( omega__Cong = $true )
& ( setukpairinjR1 = $true )
& ( vacuousDall = $true )
& ( binintersectSubset5 = $true )
& ( eqinunit = $true )
& ( singletonsubset = $true )
& ( powersetsubset = $true )
& ( symdiffE = $true )
& ( dpsetconstrER = $true )
& ( secondinupair = $true )
& ( setunionsingleton1 = $true )
& ( funcImageSingleton = $true )
& ( exuI3 = $true )
& ( setukpairinjR12 = $true )
& ( funcGraphProp2 = $true )
& ( dsetconstr__Cong = $true )
& ( powersetE = $true )
& ( binunionEcases = $true )
& ( binintersectSubset4 = $true )
& ( powersetI1 = $true )
& ( ex1E2 = $true )
& ( cartprodmempair = $true )
& ( ubforcartprodlem2 = $true )
& ( dpsetconstrSub = $true )
& ( cartprodmempaircEq = $true )
& ( subsetRefl = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan1 = $true )
& ( subsetE2 = $true )
& ( setadjoinSub2 = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyI = $true )
& ( ksndpairEq = $true )
& ( upairsetE = $true )
& ( setadjoinAx = $true )
& ( kfstpairEq = $true )
& ( ex1I = $true )
& ( setunionE2 = $true )
& ( subsetI2 = $true )
& ( notinemptyset = $true )
& ( setminusSubset2 = $true )
& ( kpairsurjEq = $true )
& ( singletonsswitch = $true )
& ( binunionIR = $true )
& ( funcGraphProp3 = $true )
& ( exuEu = $true )
& ( binunionLsub = $true )
& ( setukpairinjR = $true )
& ( symdiffI1 = $true )
& ( uniqinunit = $true )
& ( emptyE1 = $true )
& ( app = $true )
& ( powersetE1 = $true )
& ( emptyinPowerset = $true )
& ( brelnall1 = $true )
& ( binintersectI = $true ) ),
inference(rectify,[status(thm)],[f864]) ).
thf(f864,plain,
( ( subsetemptysetimpeq = $true )
& ( nonemptyI1 = $true )
& ( setminusSubset1 = $true )
& ( binintersectLsub = $true )
& ( notequalI1 = $true )
& ( exu__Cong = $true )
& ( setukpairinjL2 = $true )
& ( emptyinunitempty = $true )
& ( exuE2 = $true )
& ( upairset2IR = $true )
& ( subset2powerset = $true )
& ( omegaIndAx = $true )
& ( subsetTrans = $true )
& ( powerset__Cong = $true )
& ( setminusIRneg = $true )
& ( powersetI = $true )
& ( symdiffIneg2 = $true )
& ( setminusELneg = $true )
& ( lam2p = $true )
& ( binunionE = $true )
& ( cartprodpairsurjEq = $true )
& ( bs114d = $true )
& ( subsetE = $true )
& ( lamp = $true )
& ( dpsetconstrI = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan4 = $true )
& ( funcextLem = $true )
& ( kpairiskpair = $true )
& ( setminusLsub = $true )
& ( symdiffIneg1 = $true )
& ( singletonsuniq = $true )
& ( infuncsetfunc = $true )
& ( subPowSU = $true )
& ( setextAx = $true )
& ( cartprodsndin = $true )
& ( setadjoinIL = $true )
& ( inPowerset = $true )
& ( replAx = $true )
& ( upairsubunion = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( cartprodmempair1 = $true )
& ( symdiffI2 = $true )
& ( dsetconstrEL = $true )
& ( exuI2 = $true )
& ( quantDeMorgan3 = $true )
& ( setextsub = $true )
& ( descr__Cong = $true )
& ( descrp = $true )
& ( cartprodpairmemEL = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinE = $true )
& ( eqimpsubset2 = $true )
& ( in__Cong = $true )
& ( setukpairinjL1 = $true )
& ( wellorderingAx = $true )
& ( prop2setE = $true )
& ( lamProp = $true )
& ( cartprodpairin = $true )
& ( dpsetconstrEL2 = $true )
& ( setukpairIR = $true )
& ( binintersectRsub = $true )
& ( setext = $true )
& ( setminusILneg = $true )
& ( cartprodfstpairEq = $true )
& ( omega0Ax = $true )
& ( disjointsetsI1 = $true )
& ( kpairp = $true )
& ( binintersectSubset2 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X2 ) )
& ? [X3: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X3 ) )
& ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
= $true )
| ( $true
!= ( in @ X7 @ X1 ) )
| ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
!= $true ) )
| ( $true
!= ( in @ X6 @ X0 ) ) )
& ! [X4: $i] :
( ( ( in @ X4 @ X0 )
!= $true )
| ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( $true
!= ( in @ X5 @ X1 ) ) ) )
& ( X2 != X3 ) ) )
& ( dsetconstrER = $true )
& ( cartprodfstin = $true )
& ( notequalI2 = $true )
& ( binunionRsub = $true )
& ( quantDeMorgan2 = $true )
& ( setunionI = $true )
& ( emptysetE = $true )
& ( brelnall2 = $true )
& ( setunionsingleton = $true )
& ( binintersectER = $true )
& ( funcGraphProp4 = $true )
& ( singletoninpowerset = $true )
& ( exuE3u = $true )
& ( setOfPairsIsBReln = $true )
& ( kfstsingleton = $true )
& ( ubforcartprodlem1 = $true )
& ( setoftrueEq = $true )
& ( setadjoinSub = $true )
& ( setadjoinIR = $true )
& ( binunionIL = $true )
& ( setunionAx = $true )
& ( cartprodpairmemER = $true )
& ( binintersectEL = $true )
& ( funcGraphProp1 = $true )
& ( ex1E1 = $true )
& ( ksndsingleton = $true )
& ( upairsetIL = $true )
& ( setukpairinjL = $true )
& ( theprop = $true )
& ( sepSubset = $true )
& ( setukpairIL = $true )
& ( emptyset__Cong = $true )
& ( binintersectSubset1 = $true )
& ( ap2p = $true )
& ( setminusEL = $true )
& ( subsetI1 = $true )
& ( upairset2E = $true )
& ( funcinfuncset = $true )
& ( nonemptyE1 = $true )
& ( inCongP = $true )
& ( subbreln = $true )
& ( prop2setI = $true )
& ( cartprodsndpairEq = $true )
& ( upairinpowunion = $true )
& ( singletonprop = $true )
& ( notsubsetI = $true )
& ( notinsingleton = $true )
& ( setbeta = $true )
& ( setadjoinOr = $true )
& ( noeltsimpempty = $true )
& ( omegaSAx = $true )
& ( setukpairinjR11 = $true )
& ( dpsetconstrERa = $true )
& ( setunionE = $true )
& ( dpsetconstrEL1 = $true )
& ( setminusER = $true )
& ( apProp = $true )
& ( singletoninpowunion = $true )
& ( sepInPowerset = $true )
& ( foundationAx = $true )
& ( setminusI = $true )
& ( upairsetIR = $true )
& ( upairequniteq = $true )
& ( emptyInPowerset = $true )
& ( setminusERneg = $true )
& ( notdexE = $true )
& ( emptyI = $true )
& ( binintersectSubset3 = $true )
& ( setunion__Cong = $true )
& ( ubforcartprodlem3 = $true )
& ( notdallE = $true )
& ( emptysetimpfalse = $true )
& ( setadjoin__Cong = $true )
& ( ex1I2 = $true )
& ( exuI1 = $true )
& ( emptysetsubset = $true )
& ( setukpairinjR2 = $true )
& ( omega__Cong = $true )
& ( setukpairinjR1 = $true )
& ( vacuousDall = $true )
& ( binintersectSubset5 = $true )
& ( eqinunit = $true )
& ( singletonsubset = $true )
& ( powersetsubset = $true )
& ( symdiffE = $true )
& ( dpsetconstrER = $true )
& ( secondinupair = $true )
& ( setunionsingleton1 = $true )
& ( funcImageSingleton = $true )
& ( exuI3 = $true )
& ( setukpairinjR12 = $true )
& ( funcGraphProp2 = $true )
& ( dsetconstr__Cong = $true )
& ( powersetE = $true )
& ( binunionEcases = $true )
& ( binintersectSubset4 = $true )
& ( powersetI1 = $true )
& ( ex1E2 = $true )
& ( cartprodmempair = $true )
& ( ubforcartprodlem2 = $true )
& ( dpsetconstrSub = $true )
& ( cartprodmempaircEq = $true )
& ( subsetRefl = $true )
& ( eqimpsubset1 = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan1 = $true )
& ( subsetE2 = $true )
& ( setadjoinSub2 = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyI = $true )
& ( ksndpairEq = $true )
& ( upairsetE = $true )
& ( setadjoinAx = $true )
& ( kfstpairEq = $true )
& ( ex1I = $true )
& ( setunionE2 = $true )
& ( subsetI2 = $true )
& ( notinemptyset = $true )
& ( setminusSubset2 = $true )
& ( kpairsurjEq = $true )
& ( singletonsswitch = $true )
& ( binunionIR = $true )
& ( funcGraphProp3 = $true )
& ( exuEu = $true )
& ( binunionLsub = $true )
& ( setukpairinjR = $true )
& ( symdiffI1 = $true )
& ( uniqinunit = $true )
& ( emptyE1 = $true )
& ( app = $true )
& ( powersetE1 = $true )
& ( emptyinPowerset = $true )
& ( brelnall1 = $true )
& ( binintersectI = $true ) ),
inference(flattening,[status(thm)],[f863]) ).
thf(f863,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ( X2 != X3 )
& ! [X6: $i] :
( ! [X7: $i] :
( ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
= $true )
| ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
!= $true )
| ( $true
!= ( in @ X7 @ X1 ) ) )
| ( $true
!= ( in @ X6 @ X0 ) ) )
& ! [X4: $i] :
( ! [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
| ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
!= $true )
| ( $true
!= ( in @ X5 @ X1 ) ) )
| ( ( in @ X4 @ X0 )
!= $true ) )
& ( $true
= ( breln @ X0 @ X1 @ X3 ) ) )
& ( $true
= ( breln @ X0 @ X1 @ X2 ) ) )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f600]) ).
thf(f600,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X2 ) )
=> ! [X3: $i] :
( ( $true
= ( breln @ X0 @ X1 @ X3 ) )
=> ( ! [X4: $i] :
( ( ( in @ X4 @ X0 )
= $true )
=> ! [X5: $i] :
( ( $true
= ( in @ X5 @ X1 ) )
=> ( ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
= $true )
=> ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) )
=> ( ! [X6: $i] :
( ( $true
= ( in @ X6 @ X0 ) )
=> ! [X7: $i] :
( ( $true
= ( in @ X7 @ X1 ) )
=> ( ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
= $true )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X2 )
= $true ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f599]) ).
thf(f599,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X0 @ X1 @ X2 )
=> ! [X3: $i] :
( ( breln @ X0 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X0 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X2 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( ! [X6: $i] :
( ( in @ X6 @ X0 )
=> ! [X7: $i] :
( ( in @ X7 @ X1 )
=> ( ( in @ ( kpair @ X6 @ X7 ) @ X3 )
=> ( in @ ( kpair @ X6 @ X7 ) @ X2 ) ) ) )
=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f215]) ).
thf(f215,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ! [X3: $i,X4: $i,X12: $i] :
( ( breln @ X3 @ X4 @ X12 )
=> ! [X15: $i] :
( ( breln @ X3 @ X4 @ X15 )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X12 )
=> ( in @ ( kpair @ X1 @ X2 ) @ X15 ) ) ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X15 )
=> ( in @ ( kpair @ X1 @ X2 ) @ X12 ) ) ) )
=> ( X12 = X15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f214]) ).
thf(f214,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ! [X3: $i,X4: $i,X12: $i] :
( ( breln @ X3 @ X4 @ X12 )
=> ! [X15: $i] :
( ( breln @ X3 @ X4 @ X15 )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X12 )
=> ( in @ ( kpair @ X1 @ X2 ) @ X15 ) ) ) )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X15 )
=> ( in @ ( kpair @ X1 @ X2 ) @ X12 ) ) ) )
=> ( X12 = X15 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rJod2NOsaw/DTF2THF_5039.p',eqbreln) ).
thf(f19675,plain,
( ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ~ spl628_18 ),
inference(trivial_inequality_removal,[status(thm)],[f19674]) ).
thf(f19674,plain,
( ( $true != $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ~ spl628_18 ),
inference(forward_demodulation,[status(thm)],[f19669,f2224]) ).
thf(f2224,plain,
subbreln = $true,
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f19669,plain,
( ( ( subset @ sK206 @ sK207 )
= $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( subbreln != $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ~ spl628_18 ),
inference(trivial_inequality_removal,[status(thm)],[f19668]) ).
thf(f19668,plain,
( ( subbreln != $true )
| ( $true != $true )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ~ spl628_18 ),
inference(duplicate_literal_removal,[status(thm)],[f19661]) ).
thf(f19661,plain,
( ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( subbreln != $true )
| ( $true != $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ~ spl628_18 ),
inference(superposition,[status(thm)],[f6601,f2600]) ).
thf(f2600,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ X2 )
= $true )
| ( $true
= ( subset @ X0 @ X3 ) )
| ( ( breln @ X2 @ X1 @ X3 )
!= $true )
| ( $true
!= ( breln @ X2 @ X1 @ X0 ) )
| ( subbreln != $true ) ),
inference(cnf_transformation,[status(thm)],[f1524]) ).
thf(f1524,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( breln @ X2 @ X1 @ X0 ) )
| ! [X3: $i] :
( ( ( ( in @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ X2 )
= $true )
& ( $true
= ( in @ ( kpair @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ ( sK409 @ X3 @ X2 @ X1 @ X0 ) ) @ X0 ) )
& ( $true
!= ( in @ ( kpair @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ ( sK409 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 ) )
& ( ( in @ ( sK409 @ X3 @ X2 @ X1 @ X0 ) @ X1 )
= $true ) )
| ( ( breln @ X2 @ X1 @ X3 )
!= $true )
| ( $true
= ( subset @ X0 @ X3 ) ) ) )
| ( subbreln != $true ) )
& ( ( subbreln = $true )
| ( ( $true
= ( breln @ sK412 @ sK411 @ sK410 ) )
& ! [X10: $i] :
( ( $true
!= ( in @ X10 @ sK412 ) )
| ! [X11: $i] :
( ( ( in @ ( kpair @ X10 @ X11 ) @ sK410 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ sK413 )
= $true )
| ( ( in @ X11 @ sK411 )
!= $true ) ) )
& ( $true
= ( breln @ sK412 @ sK411 @ sK413 ) )
& ( $true
!= ( subset @ sK410 @ sK413 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK408,sK409,sK410,sK411,sK412,sK413])],[f1519,f1523,f1522,f1521,f1520]) ).
thf(f1520,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
& ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
& ( $true
= ( in @ X5 @ X1 ) ) ) )
=> ( ( ( in @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ X2 )
= $true )
& ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ X5 ) @ X0 ) )
& ( ( in @ ( kpair @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ X5 ) @ X3 )
!= $true )
& ( $true
= ( in @ X5 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1521,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ X5 ) @ X0 ) )
& ( ( in @ ( kpair @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ X5 ) @ X3 )
!= $true )
& ( $true
= ( in @ X5 @ X1 ) ) )
=> ( ( $true
= ( in @ ( kpair @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ ( sK409 @ X3 @ X2 @ X1 @ X0 ) ) @ X0 ) )
& ( $true
!= ( in @ ( kpair @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ ( sK409 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 ) )
& ( ( in @ ( sK409 @ X3 @ X2 @ X1 @ X0 ) @ X1 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1522,plain,
( ? [X6: $i,X7: $i,X8: $i] :
( ( $true
= ( breln @ X8 @ X7 @ X6 ) )
& ? [X9: $i] :
( ! [X10: $i] :
( ( ( in @ X10 @ X8 )
!= $true )
| ! [X11: $i] :
( ( ( in @ ( kpair @ X10 @ X11 ) @ X6 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ X9 )
= $true )
| ( $true
!= ( in @ X11 @ X7 ) ) ) )
& ( ( breln @ X8 @ X7 @ X9 )
= $true )
& ( ( subset @ X6 @ X9 )
!= $true ) ) )
=> ( ( $true
= ( breln @ sK412 @ sK411 @ sK410 ) )
& ? [X9: $i] :
( ! [X10: $i] :
( ( $true
!= ( in @ X10 @ sK412 ) )
| ! [X11: $i] :
( ( ( in @ ( kpair @ X10 @ X11 ) @ sK410 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ X9 )
= $true )
| ( ( in @ X11 @ sK411 )
!= $true ) ) )
& ( ( breln @ sK412 @ sK411 @ X9 )
= $true )
& ( ( subset @ sK410 @ X9 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1523,plain,
( ? [X9: $i] :
( ! [X10: $i] :
( ( $true
!= ( in @ X10 @ sK412 ) )
| ! [X11: $i] :
( ( ( in @ ( kpair @ X10 @ X11 ) @ sK410 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ X9 )
= $true )
| ( ( in @ X11 @ sK411 )
!= $true ) ) )
& ( ( breln @ sK412 @ sK411 @ X9 )
= $true )
& ( ( subset @ sK410 @ X9 )
!= $true ) )
=> ( ! [X10: $i] :
( ( $true
!= ( in @ X10 @ sK412 ) )
| ! [X11: $i] :
( ( ( in @ ( kpair @ X10 @ X11 ) @ sK410 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ sK413 )
= $true )
| ( ( in @ X11 @ sK411 )
!= $true ) ) )
& ( $true
= ( breln @ sK412 @ sK411 @ sK413 ) )
& ( $true
!= ( subset @ sK410 @ sK413 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1519,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( breln @ X2 @ X1 @ X0 ) )
| ! [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
& ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
& ( $true
= ( in @ X5 @ X1 ) ) ) )
| ( ( breln @ X2 @ X1 @ X3 )
!= $true )
| ( $true
= ( subset @ X0 @ X3 ) ) ) )
| ( subbreln != $true ) )
& ( ( subbreln = $true )
| ? [X6: $i,X7: $i,X8: $i] :
( ( $true
= ( breln @ X8 @ X7 @ X6 ) )
& ? [X9: $i] :
( ! [X10: $i] :
( ( ( in @ X10 @ X8 )
!= $true )
| ! [X11: $i] :
( ( ( in @ ( kpair @ X10 @ X11 ) @ X6 )
!= $true )
| ( ( in @ ( kpair @ X10 @ X11 ) @ X9 )
= $true )
| ( $true
!= ( in @ X11 @ X7 ) ) ) )
& ( ( breln @ X8 @ X7 @ X9 )
= $true )
& ( ( subset @ X6 @ X9 )
!= $true ) ) ) ) ),
inference(rectify,[status(thm)],[f1518]) ).
thf(f1518,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( breln @ X2 @ X1 @ X0 ) )
| ! [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
& ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
& ( $true
= ( in @ X5 @ X1 ) ) ) )
| ( ( breln @ X2 @ X1 @ X3 )
!= $true )
| ( $true
= ( subset @ X0 @ X3 ) ) ) )
| ( subbreln != $true ) )
& ( ( subbreln = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X2 @ X1 @ X0 ) )
& ? [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ X2 ) )
| ! [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
| ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
| ( $true
!= ( in @ X5 @ X1 ) ) ) )
& ( ( breln @ X2 @ X1 @ X3 )
= $true )
& ( $true
!= ( subset @ X0 @ X3 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f804]) ).
thf(f804,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( breln @ X2 @ X1 @ X0 ) )
| ! [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
& ? [X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
& ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
& ( $true
= ( in @ X5 @ X1 ) ) ) )
| ( ( breln @ X2 @ X1 @ X3 )
!= $true )
| ( $true
= ( subset @ X0 @ X3 ) ) ) )
<=> ( subbreln = $true ) ),
inference(flattening,[status(thm)],[f803]) ).
thf(f803,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ( $true
= ( subset @ X0 @ X3 ) )
| ? [X4: $i] :
( ? [X5: $i] :
( ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) )
& ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
& ( $true
= ( in @ X5 @ X1 ) ) )
& ( $true
= ( in @ X4 @ X2 ) ) )
| ( ( breln @ X2 @ X1 @ X3 )
!= $true ) )
| ( $true
!= ( breln @ X2 @ X1 @ X0 ) ) )
<=> ( subbreln = $true ) ),
inference(ennf_transformation,[status(thm)],[f622]) ).
thf(f622,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( breln @ X2 @ X1 @ X0 ) )
=> ! [X3: $i] :
( ( ( breln @ X2 @ X1 @ X3 )
= $true )
=> ( ! [X4: $i] :
( ( $true
= ( in @ X4 @ X2 ) )
=> ! [X5: $i] :
( ( $true
= ( in @ X5 @ X1 ) )
=> ( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X0 ) )
=> ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) ) )
=> ( $true
= ( subset @ X0 @ X3 ) ) ) ) )
<=> ( subbreln = $true ) ),
inference(fool_elimination,[status(thm)],[f621]) ).
thf(f621,plain,
( subbreln
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( breln @ X2 @ X1 @ X0 )
=> ! [X3: $i] :
( ( breln @ X2 @ X1 @ X3 )
=> ( ! [X4: $i] :
( ( in @ X4 @ X2 )
=> ! [X5: $i] :
( ( in @ X5 @ X1 )
=> ( ( in @ ( kpair @ X4 @ X5 ) @ X0 )
=> ( in @ ( kpair @ X4 @ X5 ) @ X3 ) ) ) )
=> ( subset @ X0 @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f213]) ).
thf(f213,axiom,
( subbreln
= ( ! [X12: $i,X4: $i,X3: $i] :
( ( breln @ X3 @ X4 @ X12 )
=> ! [X15: $i] :
( ( breln @ X3 @ X4 @ X15 )
=> ( ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ! [X2: $i] :
( ( in @ X2 @ X4 )
=> ( ( in @ ( kpair @ X1 @ X2 ) @ X12 )
=> ( in @ ( kpair @ X1 @ X2 ) @ X15 ) ) ) )
=> ( subset @ X12 @ X15 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rJod2NOsaw/DTF2THF_5039.p',subbreln) ).
thf(f6601,plain,
( ! [X0: $i] :
( ( ( in @ ( sK408 @ sK207 @ X0 @ sK205 @ sK206 ) @ sK204 )
!= $true )
| ( $true
!= ( breln @ X0 @ sK205 @ sK207 ) )
| ( ( breln @ X0 @ sK205 @ sK206 )
!= $true ) )
| ~ spl628_18 ),
inference(avatar_component_clause,[status(thm)],[f6600]) ).
thf(f19477,plain,
( spl628_12
| ~ spl628_8
| ~ spl628_11 ),
inference(avatar_split_clause,[status(thm)],[f19476,f3502,f3469,f3511]) ).
thf(f3511,definition,
( spl628_12
<=> ( sK206 = sK207 ) ),
introduced(definition,[new_symbols(naming,[spl628_12])],[avatar_definition]) ).
thf(f3502,definition,
( spl628_11
<=> ( $true
= ( subset @ sK207 @ sK206 ) ) ),
introduced(definition,[new_symbols(naming,[spl628_11])],[avatar_definition]) ).
thf(f19476,plain,
( ( ( subset @ sK206 @ sK207 )
!= $true )
| ( sK206 = sK207 )
| ~ spl628_11 ),
inference(trivial_inequality_removal,[status(thm)],[f19475]) ).
thf(f19475,plain,
( ( ( subset @ sK206 @ sK207 )
!= $true )
| ( $true != $true )
| ( sK206 = sK207 )
| ~ spl628_11 ),
inference(forward_demodulation,[status(thm)],[f19474,f2292]) ).
thf(f2292,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f19474,plain,
( ( setextsub != $true )
| ( ( subset @ sK206 @ sK207 )
!= $true )
| ( sK206 = sK207 )
| ~ spl628_11 ),
inference(trivial_inequality_removal,[status(thm)],[f19473]) ).
thf(f19473,plain,
( ( setextsub != $true )
| ( $true != $true )
| ( ( subset @ sK206 @ sK207 )
!= $true )
| ( sK206 = sK207 )
| ~ spl628_11 ),
inference(superposition,[status(thm)],[f1945,f3504]) ).
thf(f3504,plain,
( ( $true
= ( subset @ sK207 @ sK206 ) )
| ~ spl628_11 ),
inference(avatar_component_clause,[status(thm)],[f3502]) ).
thf(f1945,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X3 @ X2 ) )
| ( X2 = X3 )
| ( $true
!= ( subset @ X2 @ X3 ) )
| ( setextsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f988]) ).
thf(f988,plain,
( ( ( setextsub = $true )
| ( ( $true
= ( subset @ sK62 @ sK63 ) )
& ( sK63 != sK62 )
& ( $true
= ( subset @ sK63 @ sK62 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
| ( X2 = X3 )
| ( $true
!= ( subset @ X3 @ X2 ) ) )
| ( setextsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63])],[f986,f987]) ).
thf(f987,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
& ( X0 != X1 )
& ( ( subset @ X1 @ X0 )
= $true ) )
=> ( ( $true
= ( subset @ sK62 @ sK63 ) )
& ( sK63 != sK62 )
& ( $true
= ( subset @ sK63 @ sK62 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f986,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
& ( X0 != X1 )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
| ( X2 = X3 )
| ( $true
!= ( subset @ X3 @ X2 ) ) )
| ( setextsub != $true ) ) ),
inference(rectify,[status(thm)],[f985]) ).
thf(f985,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
& ( X0 != X1 )
& ( ( subset @ X1 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( setextsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f826]) ).
thf(f826,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X0 @ X1 ) )
| ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f825]) ).
thf(f825,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true
!= ( subset @ X0 @ X1 ) )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f473]) ).
thf(f473,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( $true
= ( subset @ X0 @ X1 ) )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f472]) ).
thf(f472,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( X0 = X1 ) ) )
= setextsub ),
inference(rectify,[status(thm)],[f93]) ).
thf(f93,axiom,
! [X4: $i,X3: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X3 )
=> ( X3 = X4 ) ) )
= setextsub ),
file('/export/starexec/sandbox/tmp/tmp.rJod2NOsaw/DTF2THF_5039.p',setextsub) ).
thf(f19450,plain,
spl628_122,
inference(avatar_contradiction_clause,[status(thm)],[f19449]) ).
thf(f19449,plain,
( $false
| spl628_122 ),
inference(trivial_inequality_removal,[status(thm)],[f19448]) ).
thf(f19448,plain,
( ( $true != $true )
| spl628_122 ),
inference(superposition,[status(thm)],[f11307,f2268]) ).
thf(f2268,plain,
( $true
= ( breln @ sK204 @ sK205 @ sK207 ) ),
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f11307,plain,
( ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| spl628_122 ),
inference(avatar_component_clause,[status(thm)],[f11305]) ).
thf(f11308,plain,
( ~ spl628_122
| spl628_11
| ~ spl628_17 ),
inference(avatar_split_clause,[status(thm)],[f11303,f6074,f3502,f11305]) ).
thf(f6074,definition,
( spl628_17
<=> ! [X0: $i] :
( ( $true
!= ( in @ ( sK409 @ sK206 @ sK204 @ X0 @ sK207 ) @ sK205 ) )
| ( ( breln @ sK204 @ X0 @ sK206 )
!= $true )
| ( $true
!= ( breln @ sK204 @ X0 @ sK207 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl628_17])],[avatar_definition]) ).
thf(f11303,plain,
( ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ~ spl628_17 ),
inference(trivial_inequality_removal,[status(thm)],[f11302]) ).
thf(f11302,plain,
( ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( $true != $true )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ~ spl628_17 ),
inference(forward_demodulation,[status(thm)],[f11301,f2269]) ).
thf(f11301,plain,
( ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ~ spl628_17 ),
inference(trivial_inequality_removal,[status(thm)],[f11300]) ).
thf(f11300,plain,
( ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( $true != $true )
| ~ spl628_17 ),
inference(forward_demodulation,[status(thm)],[f11298,f2224]) ).
thf(f11298,plain,
( ( subbreln != $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ~ spl628_17 ),
inference(trivial_inequality_removal,[status(thm)],[f11297]) ).
thf(f11297,plain,
( ( $true
= ( subset @ sK207 @ sK206 ) )
| ( subbreln != $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ( $true != $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ~ spl628_17 ),
inference(duplicate_literal_removal,[status(thm)],[f11293]) ).
thf(f11293,plain,
( ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK207 ) )
| ( subbreln != $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ( $true != $true )
| ( $true
!= ( breln @ sK204 @ sK205 @ sK206 ) )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ~ spl628_17 ),
inference(superposition,[status(thm)],[f6075,f2597]) ).
thf(f2597,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( ( in @ ( sK409 @ X3 @ X2 @ X1 @ X0 ) @ X1 )
= $true )
| ( subbreln != $true )
| ( $true
= ( subset @ X0 @ X3 ) )
| ( ( breln @ X2 @ X1 @ X3 )
!= $true )
| ( $true
!= ( breln @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f1524]) ).
thf(f6075,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK409 @ sK206 @ sK204 @ X0 @ sK207 ) @ sK205 ) )
| ( ( breln @ sK204 @ X0 @ sK206 )
!= $true )
| ( $true
!= ( breln @ sK204 @ X0 @ sK207 ) ) )
| ~ spl628_17 ),
inference(avatar_component_clause,[status(thm)],[f6074]) ).
thf(f6602,plain,
( spl628_8
| spl628_18
| ~ spl628_9 ),
inference(avatar_split_clause,[status(thm)],[f6598,f3473,f6600,f3469]) ).
thf(f3473,definition,
( spl628_9
<=> ! [X0: $i,X1: $i] :
( ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( in @ ( sK408 @ sK207 @ X0 @ X1 @ sK206 ) @ sK204 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( ( in @ ( sK409 @ sK207 @ X0 @ X1 @ sK206 ) @ sK205 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl628_9])],[avatar_definition]) ).
thf(f6598,plain,
( ! [X0: $i] :
( ( ( subset @ sK206 @ sK207 )
= $true )
| ( ( in @ ( sK408 @ sK207 @ X0 @ sK205 @ sK206 ) @ sK204 )
!= $true )
| ( ( breln @ X0 @ sK205 @ sK206 )
!= $true )
| ( $true
!= ( breln @ X0 @ sK205 @ sK207 ) ) )
| ~ spl628_9 ),
inference(trivial_inequality_removal,[status(thm)],[f6597]) ).
thf(f6597,plain,
( ! [X0: $i] :
( ( ( in @ ( sK408 @ sK207 @ X0 @ sK205 @ sK206 ) @ sK204 )
!= $true )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( ( breln @ X0 @ sK205 @ sK206 )
!= $true )
| ( $true
!= ( breln @ X0 @ sK205 @ sK207 ) )
| ( $true != $true ) )
| ~ spl628_9 ),
inference(forward_demodulation,[status(thm)],[f6596,f2224]) ).
thf(f6596,plain,
( ! [X0: $i] :
( ( subbreln != $true )
| ( ( breln @ X0 @ sK205 @ sK206 )
!= $true )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( $true
!= ( breln @ X0 @ sK205 @ sK207 ) )
| ( ( in @ ( sK408 @ sK207 @ X0 @ sK205 @ sK206 ) @ sK204 )
!= $true ) )
| ~ spl628_9 ),
inference(trivial_inequality_removal,[status(thm)],[f6595]) ).
thf(f6595,plain,
( ! [X0: $i] :
( ( ( breln @ X0 @ sK205 @ sK206 )
!= $true )
| ( subbreln != $true )
| ( $true
!= ( breln @ X0 @ sK205 @ sK207 ) )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( ( in @ ( sK408 @ sK207 @ X0 @ sK205 @ sK206 ) @ sK204 )
!= $true )
| ( $true != $true ) )
| ~ spl628_9 ),
inference(duplicate_literal_removal,[status(thm)],[f6590]) ).
thf(f6590,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( breln @ X0 @ sK205 @ sK207 ) )
| ( ( breln @ X0 @ sK205 @ sK206 )
!= $true )
| ( subbreln != $true )
| ( $true
!= ( breln @ X0 @ sK205 @ sK207 ) )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( ( breln @ X0 @ sK205 @ sK206 )
!= $true )
| ( ( in @ ( sK408 @ sK207 @ X0 @ sK205 @ sK206 ) @ sK204 )
!= $true ) )
| ~ spl628_9 ),
inference(superposition,[status(thm)],[f3474,f2597]) ).
thf(f3474,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ ( sK409 @ sK207 @ X0 @ X1 @ sK206 ) @ sK205 )
!= $true )
| ( ( in @ ( sK408 @ sK207 @ X0 @ X1 @ sK206 ) @ sK204 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true ) )
| ~ spl628_9 ),
inference(avatar_component_clause,[status(thm)],[f3473]) ).
thf(f6567,plain,
~ spl628_12,
inference(avatar_contradiction_clause,[status(thm)],[f6566]) ).
thf(f6566,plain,
( $false
| ~ spl628_12 ),
inference(trivial_inequality_removal,[status(thm)],[f6557]) ).
thf(f6557,plain,
( ( sK206 != sK206 )
| ~ spl628_12 ),
inference(superposition,[status(thm)],[f2265,f3513]) ).
thf(f3513,plain,
( ( sK206 = sK207 )
| ~ spl628_12 ),
inference(avatar_component_clause,[status(thm)],[f3511]) ).
thf(f2265,plain,
sK206 != sK207,
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f6076,plain,
( spl628_17
| spl628_11
| ~ spl628_10 ),
inference(avatar_split_clause,[status(thm)],[f6072,f3499,f3502,f6074]) ).
thf(f3499,definition,
( spl628_10
<=> ! [X0: $i,X1: $i] :
( ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( $true
!= ( in @ ( sK408 @ sK206 @ X0 @ X1 @ sK207 ) @ sK204 ) )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ sK207 ) @ sK205 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl628_10])],[avatar_definition]) ).
thf(f6072,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK409 @ sK206 @ sK204 @ X0 @ sK207 ) @ sK205 ) )
| ( $true
!= ( breln @ sK204 @ X0 @ sK207 ) )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( ( breln @ sK204 @ X0 @ sK206 )
!= $true ) )
| ~ spl628_10 ),
inference(trivial_inequality_removal,[status(thm)],[f6071]) ).
thf(f6071,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ ( sK409 @ sK206 @ sK204 @ X0 @ sK207 ) @ sK205 ) )
| ( $true
!= ( breln @ sK204 @ X0 @ sK207 ) )
| ( ( breln @ sK204 @ X0 @ sK206 )
!= $true )
| ( $true != $true )
| ( $true
= ( subset @ sK207 @ sK206 ) ) )
| ~ spl628_10 ),
inference(forward_demodulation,[status(thm)],[f6069,f2224]) ).
thf(f6069,plain,
( ! [X0: $i] :
( ( subbreln != $true )
| ( ( breln @ sK204 @ X0 @ sK206 )
!= $true )
| ( $true
!= ( in @ ( sK409 @ sK206 @ sK204 @ X0 @ sK207 ) @ sK205 ) )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( $true
!= ( breln @ sK204 @ X0 @ sK207 ) ) )
| ~ spl628_10 ),
inference(trivial_inequality_removal,[status(thm)],[f6068]) ).
thf(f6068,plain,
( ! [X0: $i] :
( ( $true
!= ( breln @ sK204 @ X0 @ sK207 ) )
| ( subbreln != $true )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( $true
!= ( in @ ( sK409 @ sK206 @ sK204 @ X0 @ sK207 ) @ sK205 ) )
| ( ( breln @ sK204 @ X0 @ sK206 )
!= $true )
| ( $true != $true ) )
| ~ spl628_10 ),
inference(duplicate_literal_removal,[status(thm)],[f6060]) ).
thf(f6060,plain,
( ! [X0: $i] :
( ( $true
= ( subset @ sK207 @ sK206 ) )
| ( $true
!= ( breln @ sK204 @ X0 @ sK207 ) )
| ( $true
!= ( in @ ( sK409 @ sK206 @ sK204 @ X0 @ sK207 ) @ sK205 ) )
| ( $true
!= ( breln @ sK204 @ X0 @ sK207 ) )
| ( subbreln != $true )
| ( $true != $true )
| ( ( breln @ sK204 @ X0 @ sK206 )
!= $true )
| ( ( breln @ sK204 @ X0 @ sK206 )
!= $true ) )
| ~ spl628_10 ),
inference(superposition,[status(thm)],[f3500,f2600]) ).
thf(f3500,plain,
( ! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK408 @ sK206 @ X0 @ X1 @ sK207 ) @ sK204 ) )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ sK207 ) @ sK205 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true ) )
| ~ spl628_10 ),
inference(avatar_component_clause,[status(thm)],[f3499]) ).
thf(f3505,plain,
( spl628_10
| spl628_11 ),
inference(avatar_split_clause,[status(thm)],[f3497,f3502,f3499]) ).
thf(f3497,plain,
! [X0: $i,X1: $i] :
( ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ sK207 ) @ sK205 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( $true
!= ( in @ ( sK408 @ sK206 @ X0 @ X1 @ sK207 ) @ sK204 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3496]) ).
thf(f3496,plain,
! [X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK408 @ sK206 @ X0 @ X1 @ sK207 ) @ sK204 ) )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( $true != $true )
| ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ sK207 ) @ sK205 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f3483,f2224]) ).
thf(f3483,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( subset @ sK207 @ sK206 ) )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ sK207 ) @ sK205 )
!= $true )
| ( $true
!= ( in @ ( sK408 @ sK206 @ X0 @ X1 @ sK207 ) @ sK204 ) )
| ( subbreln != $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3482]) ).
thf(f3482,plain,
! [X0: $i,X1: $i] :
( ( subbreln != $true )
| ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ sK207 ) @ sK205 )
!= $true )
| ( $true != $true )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( $true
!= ( in @ ( sK408 @ sK206 @ X0 @ X1 @ sK207 ) @ sK204 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f3481]) ).
thf(f3481,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ sK207 ) @ sK205 )
!= $true )
| ( subbreln != $true )
| ( $true != $true )
| ( $true
!= ( in @ ( sK408 @ sK206 @ X0 @ X1 @ sK207 ) @ sK204 ) )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( $true
= ( subset @ sK207 @ sK206 ) )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true ) ),
inference(superposition,[status(thm)],[f3079,f2599]) ).
thf(f2599,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ ( kpair @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ ( sK409 @ X3 @ X2 @ X1 @ X0 ) ) @ X0 ) )
| ( ( breln @ X2 @ X1 @ X3 )
!= $true )
| ( $true
= ( subset @ X0 @ X3 ) )
| ( $true
!= ( breln @ X2 @ X1 @ X0 ) )
| ( subbreln != $true ) ),
inference(cnf_transformation,[status(thm)],[f1524]) ).
thf(f3079,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK408 @ sK206 @ X0 @ X1 @ X2 ) @ ( sK409 @ sK206 @ X0 @ X1 @ X2 ) ) @ sK207 )
!= $true )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) )
| ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ X2 ) @ sK205 )
!= $true )
| ( $true
= ( subset @ X2 @ sK206 ) )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( ( in @ ( sK408 @ sK206 @ X0 @ X1 @ X2 ) @ sK204 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3078]) ).
thf(f3078,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK408 @ sK206 @ X0 @ X1 @ X2 ) @ ( sK409 @ sK206 @ X0 @ X1 @ X2 ) ) @ sK207 )
!= $true )
| ( $true != $true )
| ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ X2 ) @ sK205 )
!= $true )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( ( in @ ( sK408 @ sK206 @ X0 @ X1 @ X2 ) @ sK204 )
!= $true )
| ( $true
= ( subset @ X2 @ sK206 ) ) ),
inference(forward_demodulation,[status(thm)],[f3077,f2224]) ).
thf(f3077,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ ( kpair @ ( sK408 @ sK206 @ X0 @ X1 @ X2 ) @ ( sK409 @ sK206 @ X0 @ X1 @ X2 ) ) @ sK207 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( $true
= ( subset @ X2 @ sK206 ) )
| ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ X2 ) @ sK205 )
!= $true )
| ( subbreln != $true )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) )
| ( ( in @ ( sK408 @ sK206 @ X0 @ X1 @ X2 ) @ sK204 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3074]) ).
thf(f3074,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( ( in @ ( kpair @ ( sK408 @ sK206 @ X0 @ X1 @ X2 ) @ ( sK409 @ sK206 @ X0 @ X1 @ X2 ) ) @ sK207 )
!= $true )
| ( $true != $true )
| ( $true
= ( subset @ X2 @ sK206 ) )
| ( ( in @ ( sK408 @ sK206 @ X0 @ X1 @ X2 ) @ sK204 )
!= $true )
| ( subbreln != $true )
| ( ( in @ ( sK409 @ sK206 @ X0 @ X1 @ X2 ) @ sK205 )
!= $true )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) ) ),
inference(superposition,[status(thm)],[f2598,f2267]) ).
thf(f2267,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( in @ ( kpair @ X4 @ X5 ) @ sK206 ) )
| ( $true
!= ( in @ ( kpair @ X4 @ X5 ) @ sK207 ) )
| ( $true
!= ( in @ X4 @ sK204 ) )
| ( ( in @ X5 @ sK205 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f1213]) ).
thf(f2598,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ ( sK408 @ X3 @ X2 @ X1 @ X0 ) @ ( sK409 @ X3 @ X2 @ X1 @ X0 ) ) @ X3 ) )
| ( $true
!= ( breln @ X2 @ X1 @ X0 ) )
| ( ( breln @ X2 @ X1 @ X3 )
!= $true )
| ( $true
= ( subset @ X0 @ X3 ) )
| ( subbreln != $true ) ),
inference(cnf_transformation,[status(thm)],[f1524]) ).
thf(f3475,plain,
( spl628_8
| spl628_9 ),
inference(avatar_split_clause,[status(thm)],[f3467,f3473,f3469]) ).
thf(f3467,plain,
! [X0: $i,X1: $i] :
( ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( ( in @ ( sK409 @ sK207 @ X0 @ X1 @ sK206 ) @ sK205 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( ( in @ ( sK408 @ sK207 @ X0 @ X1 @ sK206 ) @ sK204 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3466]) ).
thf(f3466,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ sK206 @ sK207 )
= $true )
| ( ( in @ ( sK408 @ sK207 @ X0 @ X1 @ sK206 ) @ sK204 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( $true != $true )
| ( ( in @ ( sK409 @ sK207 @ X0 @ X1 @ sK206 ) @ sK205 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f3453,f2224]) ).
thf(f3453,plain,
! [X0: $i,X1: $i] :
( ( ( in @ ( sK408 @ sK207 @ X0 @ X1 @ sK206 ) @ sK204 )
!= $true )
| ( subbreln != $true )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( in @ ( sK409 @ sK207 @ X0 @ X1 @ sK206 ) @ sK205 )
!= $true )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3452]) ).
thf(f3452,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( subbreln != $true )
| ( ( in @ ( sK408 @ sK207 @ X0 @ X1 @ sK206 ) @ sK204 )
!= $true )
| ( ( in @ ( sK409 @ sK207 @ X0 @ X1 @ sK206 ) @ sK205 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f3451]) ).
thf(f3451,plain,
! [X0: $i,X1: $i] :
( ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( ( subset @ sK206 @ sK207 )
= $true )
| ( ( in @ ( sK408 @ sK207 @ X0 @ X1 @ sK206 ) @ sK204 )
!= $true )
| ( ( in @ ( sK409 @ sK207 @ X0 @ X1 @ sK206 ) @ sK205 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( ( breln @ X0 @ X1 @ sK206 )
!= $true )
| ( subbreln != $true )
| ( $true != $true )
| ( ( subset @ sK206 @ sK207 )
= $true ) ),
inference(superposition,[status(thm)],[f3055,f2599]) ).
thf(f3055,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ ( sK408 @ sK207 @ X0 @ X1 @ X2 ) @ ( sK409 @ sK207 @ X0 @ X1 @ X2 ) ) @ sK206 ) )
| ( $true
!= ( in @ ( sK408 @ sK207 @ X0 @ X1 @ X2 ) @ sK204 ) )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) )
| ( ( subset @ X2 @ sK207 )
= $true )
| ( $true
!= ( in @ ( sK409 @ sK207 @ X0 @ X1 @ X2 ) @ sK205 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3054]) ).
thf(f3054,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ ( sK408 @ sK207 @ X0 @ X1 @ X2 ) @ ( sK409 @ sK207 @ X0 @ X1 @ X2 ) ) @ sK206 ) )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( $true != $true )
| ( $true
!= ( in @ ( sK408 @ sK207 @ X0 @ X1 @ X2 ) @ sK204 ) )
| ( $true
!= ( in @ ( sK409 @ sK207 @ X0 @ X1 @ X2 ) @ sK205 ) )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) )
| ( ( subset @ X2 @ sK207 )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f3053,f2224]) ).
thf(f3053,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( kpair @ ( sK408 @ sK207 @ X0 @ X1 @ X2 ) @ ( sK409 @ sK207 @ X0 @ X1 @ X2 ) ) @ sK206 ) )
| ( ( subset @ X2 @ sK207 )
= $true )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( $true
!= ( in @ ( sK408 @ sK207 @ X0 @ X1 @ X2 ) @ sK204 ) )
| ( subbreln != $true )
| ( $true
!= ( in @ ( sK409 @ sK207 @ X0 @ X1 @ X2 ) @ sK205 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3050]) ).
thf(f3050,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ ( sK409 @ sK207 @ X0 @ X1 @ X2 ) @ sK205 ) )
| ( $true
!= ( in @ ( sK408 @ sK207 @ X0 @ X1 @ X2 ) @ sK204 ) )
| ( $true
!= ( breln @ X0 @ X1 @ X2 ) )
| ( $true
!= ( in @ ( kpair @ ( sK408 @ sK207 @ X0 @ X1 @ X2 ) @ ( sK409 @ sK207 @ X0 @ X1 @ X2 ) ) @ sK206 ) )
| ( ( subset @ X2 @ sK207 )
= $true )
| ( ( breln @ X0 @ X1 @ sK207 )
!= $true )
| ( $true != $true )
| ( subbreln != $true ) ),
inference(superposition,[status(thm)],[f2598,f2266]) ).
thf(f2266,plain,
! [X6: $i,X7: $i] :
( ( $true
= ( in @ ( kpair @ X6 @ X7 ) @ sK207 ) )
| ( ( in @ X6 @ sK204 )
!= $true )
| ( $true
!= ( in @ ( kpair @ X6 @ X7 ) @ sK206 ) )
| ( $true
!= ( in @ X7 @ sK205 ) ) ),
inference(cnf_transformation,[status(thm)],[f1213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU690^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n008.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:31:09 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
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU690^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Functions - Extensionality and Beta Reduction
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : (! A:i.! B:i.! R:i.breln A B R -> (! S:i.breln A B S ->
% 0.29/0.46 % (! x:i.in x A -> (! y:i.in y B -> in (kpair x y) R ->
% 0.29/0.46 % in (kpair x y) S)) -> (! x:i.in x A -> (! y:i.in y B ->
% 0.29/0.46 % in (kpair x y) S -> in (kpair x y) R)) -> R = S))
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC192g [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.56 v9.1.0, 0.62 v9.0.0, 0.80 v8.2.0, 0.85 v8.1.0, 0.82 v7.5.0, 0.86 v7.4.0, 0.56 v7.2.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.71 v6.1.0, 0.86 v5.5.0, 0.83 v5.4.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 457 ( 213 unt; 243 typ; 213 def)
% 0.29/0.46 % Number of atoms : 1165 ( 313 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 217 ( 5 avg)
% 0.29/0.46 % Number of connectives : 2201 ( 47 ~; 7 |; 36 &;1560 @)
% 0.29/0.46 % ( 14 <=>; 537 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 224 ( 2 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 126 ( 126 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 246 ( 243 usr; 210 con; 0-4 aty)
% 0.29/0.46 % Number of variables : 697 ( 73 ^; 588 !; 36 ?; 697 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=244
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu_type,type,
% 0.29/0.46 exu: ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu,definition,
% 0.29/0.46 ( exu
% 0.29/0.46 = ( ^ [Xphi: $i > $o] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx_type,type,
% 0.29/0.46 setextAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx,definition,
% 0.29/0.46 ( setextAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xx @ B ) )
% 0.29/0.46 => ( A = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset_type,type,
% 0.29/0.46 emptyset: $i ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx_type,type,
% 0.29/0.46 emptysetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx,definition,
% 0.29/0.46 ( emptysetAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin_type,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx_type,type,
% 0.29/0.46 setadjoinAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx,definition,
% 0.29/0.46 ( setadjoinAx
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 <=> ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset_type,type,
% 0.29/0.46 powerset: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx_type,type,
% 0.29/0.46 powersetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx,definition,
% 0.29/0.46 ( powersetAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 <=> ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion_type,type,
% 0.29/0.46 setunion: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx_type,type,
% 0.29/0.46 setunionAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx,definition,
% 0.29/0.46 ( setunionAx
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 <=> ? [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega_type,type,
% 0.29/0.46 omega: $i ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax_type,type,
% 0.29/0.46 omega0Ax: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax,definition,
% 0.29/0.46 ( omega0Ax
% 0.29/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx_type,type,
% 0.29/0.46 omegaSAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx,definition,
% 0.29/0.46 ( omegaSAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx_type,type,
% 0.29/0.46 omegaIndAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx,definition,
% 0.29/0.46 ( omegaIndAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( ( in @ emptyset @ A )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ omega )
% 0.29/0.46 & ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(replAx_type,type,
% 0.29/0.46 replAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(replAx,definition,
% 0.29/0.46 ( replAx
% 0.29/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 <=> ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx_type,type,
% 0.29/0.46 foundationAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx,definition,
% 0.29/0.46 ( foundationAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ( ( in @ B @ A )
% 0.29/0.46 & ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx_type,type,
% 0.29/0.46 wellorderingAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx,definition,
% 0.29/0.46 ( wellorderingAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ? [B: $i] :
% 0.29/0.46 ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) ) )
% 0.29/0.46 & ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xy @ A ) )
% 0.29/0.46 => ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ( ( in @ Xx @ C )
% 0.29/0.46 <=> ( in @ Xy @ C ) ) )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 & ! [C: $i,D: $i] :
% 0.29/0.46 ( ( ( in @ C @ B )
% 0.29/0.46 & ( in @ D @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ D ) )
% 0.29/0.46 | ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ D )
% 0.29/0.46 => ( in @ Xx @ C ) ) ) )
% 0.29/0.46 & ! [C: $i] :
% 0.29/0.46 ( ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.46 => ? [D: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ D @ B )
% 0.29/0.46 & ( in @ Xx @ C )
% 0.29/0.46 & ~ ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ D )
% 0.29/0.46 & ( in @ Xy @ C ) )
% 0.29/0.46 & ! [E: $i] :
% 0.29/0.46 ( ( in @ E @ B )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ E )
% 0.29/0.46 => ( in @ Xy @ D ) )
% 0.29/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr_type,type,
% 0.29/0.46 descr: ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(descrp_type,type,
% 0.29/0.46 descrp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descrp,definition,
% 0.29/0.46 ( descrp
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 @ ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr_type,type,
% 0.29/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI_type,type,
% 0.29/0.46 dsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI,definition,
% 0.29/0.46 ( dsetconstrI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL_type,type,
% 0.29/0.46 dsetconstrEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL,definition,
% 0.29/0.46 ( dsetconstrEL
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER_type,type,
% 0.29/0.46 dsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER,definition,
% 0.29/0.46 ( dsetconstrER
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1_type,type,
% 0.29/0.46 exuE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1,definition,
% 0.29/0.46 ( exuE1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set_type,type,
% 0.29/0.46 prop2set: $o > $i ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE_type,type,
% 0.29/0.46 prop2setE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE,definition,
% 0.29/0.46 ( prop2setE
% 0.29/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE_type,type,
% 0.29/0.46 emptysetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE,definition,
% 0.29/0.46 ( emptysetE
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse_type,type,
% 0.29/0.46 emptysetimpfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse,definition,
% 0.29/0.46 ( emptysetimpfalse
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => $false ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset_type,type,
% 0.29/0.46 notinemptyset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset,definition,
% 0.29/0.46 ( notinemptyset
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e_type,type,
% 0.29/0.46 exuE3e: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e,definition,
% 0.29/0.46 ( exuE3e
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setext_type,type,
% 0.29/0.46 setext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setext,definition,
% 0.29/0.46 ( setext
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI_type,type,
% 0.29/0.46 emptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI,definition,
% 0.29/0.46 ( emptyI
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty_type,type,
% 0.29/0.46 noeltsimpempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty,definition,
% 0.29/0.46 ( noeltsimpempty
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta_type,type,
% 0.29/0.46 setbeta: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta,definition,
% 0.29/0.46 ( setbeta
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty_type,type,
% 0.29/0.46 nonempty: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty,definition,
% 0.29/0.46 ( nonempty
% 0.29/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1_type,type,
% 0.29/0.46 nonemptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1,definition,
% 0.29/0.46 ( nonemptyE1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI_type,type,
% 0.29/0.46 nonemptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI,definition,
% 0.29/0.46 ( nonemptyI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( nonempty
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1_type,type,
% 0.29/0.46 nonemptyI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1,definition,
% 0.29/0.46 ( nonemptyI1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL_type,type,
% 0.29/0.46 setadjoinIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL,definition,
% 0.29/0.46 ( setadjoinIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty_type,type,
% 0.29/0.46 emptyinunitempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty,definition,
% 0.29/0.46 ( emptyinunitempty
% 0.29/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR_type,type,
% 0.29/0.46 setadjoinIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR,definition,
% 0.29/0.46 ( setadjoinIR
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE_type,type,
% 0.29/0.46 setadjoinE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE,definition,
% 0.29/0.46 ( setadjoinE
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( Xy = Xx )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xy @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr_type,type,
% 0.29/0.46 setadjoinOr: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr,definition,
% 0.29/0.46 ( setadjoinOr
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq_type,type,
% 0.29/0.46 setoftrueEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq,definition,
% 0.29/0.46 ( setoftrueEq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : $true )
% 0.29/0.46 = A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI_type,type,
% 0.29/0.46 powersetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI,definition,
% 0.29/0.46 ( powersetI
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset_type,type,
% 0.29/0.46 emptyinPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset,definition,
% 0.29/0.46 ( emptyinPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset_type,type,
% 0.29/0.46 emptyInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset,definition,
% 0.29/0.46 ( emptyInPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE_type,type,
% 0.29/0.46 powersetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE,definition,
% 0.29/0.46 ( powersetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI_type,type,
% 0.29/0.46 setunionI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI,definition,
% 0.29/0.46 ( setunionI
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE_type,type,
% 0.29/0.46 setunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE,definition,
% 0.29/0.46 ( setunionE
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ! [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU_type,type,
% 0.29/0.46 subPowSU: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU,definition,
% 0.29/0.46 ( subPowSU
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2_type,type,
% 0.29/0.46 exuE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2,definition,
% 0.29/0.46 ( exuE2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness_type,type,
% 0.29/0.46 nonemptyImpWitness: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness,definition,
% 0.29/0.46 ( nonemptyImpWitness
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & $true ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit_type,type,
% 0.29/0.46 uniqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit,definition,
% 0.29/0.46 ( uniqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton_type,type,
% 0.29/0.46 notinsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton,definition,
% 0.29/0.46 ( notinsingleton
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx != Xy )
% 0.29/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit_type,type,
% 0.29/0.46 eqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit,definition,
% 0.29/0.46 ( eqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch_type,type,
% 0.29/0.46 singletonsswitch: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch,definition,
% 0.29/0.46 ( singletonsswitch
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE_type,type,
% 0.29/0.46 upairsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE,definition,
% 0.29/0.46 ( upairsetE
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL_type,type,
% 0.29/0.46 upairsetIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL,definition,
% 0.29/0.46 ( upairsetIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR_type,type,
% 0.29/0.46 upairsetIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR,definition,
% 0.29/0.46 ( upairsetIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1_type,type,
% 0.29/0.46 emptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1,definition,
% 0.29/0.46 ( emptyE1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => $false ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall_type,type,
% 0.29/0.46 vacuousDall: $o ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall,definition,
% 0.29/0.46 ( vacuousDall
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1_type,type,
% 0.29/0.46 quantDeMorgan1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1,definition,
% 0.29/0.46 ( quantDeMorgan1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2_type,type,
% 0.29/0.46 quantDeMorgan2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2,definition,
% 0.29/0.46 ( quantDeMorgan2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3_type,type,
% 0.29/0.46 quantDeMorgan3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3,definition,
% 0.29/0.46 ( quantDeMorgan3
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4_type,type,
% 0.29/0.46 quantDeMorgan4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4,definition,
% 0.29/0.46 ( quantDeMorgan4
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI_type,type,
% 0.29/0.46 prop2setI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI,definition,
% 0.29/0.46 ( prop2setI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(set2prop_type,type,
% 0.29/0.46 set2prop: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI_type,type,
% 0.29/0.46 prop2set2propI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI,definition,
% 0.29/0.46 ( prop2set2propI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE_type,type,
% 0.29/0.46 notdexE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE,definition,
% 0.29/0.46 ( notdexE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE_type,type,
% 0.29/0.46 notdallE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE,definition,
% 0.29/0.46 ( notdallE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1_type,type,
% 0.29/0.46 exuI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1,definition,
% 0.29/0.46 ( exuI1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3_type,type,
% 0.29/0.46 exuI3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3,definition,
% 0.29/0.46 ( exuI3
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2_type,type,
% 0.29/0.46 exuI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2,definition,
% 0.29/0.46 ( exuI2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP_type,type,
% 0.29/0.46 inCongP: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP,definition,
% 0.29/0.46 ( inCongP
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong_type,type,
% 0.29/0.46 in__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong,definition,
% 0.29/0.46 ( in__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u_type,type,
% 0.29/0.46 exuE3u: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u,definition,
% 0.29/0.46 ( exuE3u
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong_type,type,
% 0.29/0.46 exu__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong,definition,
% 0.29/0.46 ( exu__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 <=> ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong_type,type,
% 0.29/0.46 emptyset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong,definition,
% 0.29/0.46 ( emptyset__Cong
% 0.29/0.46 = ( emptyset = emptyset ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong_type,type,
% 0.29/0.46 setadjoin__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong,definition,
% 0.29/0.46 ( setadjoin__Cong
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ! [Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( Xz = Xu )
% 0.29/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong_type,type,
% 0.29/0.46 powerset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong,definition,
% 0.29/0.46 ( powerset__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( powerset @ A )
% 0.29/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong_type,type,
% 0.29/0.46 setunion__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong,definition,
% 0.29/0.46 ( setunion__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( setunion @ A )
% 0.29/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong_type,type,
% 0.29/0.46 omega__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong,definition,
% 0.29/0.46 ( omega__Cong
% 0.29/0.46 = ( omega = omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu_type,type,
% 0.29/0.46 exuEu: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu,definition,
% 0.29/0.46 ( exuEu
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong_type,type,
% 0.29/0.46 descr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong,definition,
% 0.29/0.46 ( descr__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.46 => ( ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong_type,type,
% 0.29/0.46 dsetconstr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong,definition,
% 0.29/0.46 ( dsetconstr__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset_type,type,
% 0.29/0.46 subset: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjoint_type,type,
% 0.29/0.46 disjoint: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setsmeet_type,type,
% 0.29/0.46 setsmeet: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1_type,type,
% 0.29/0.46 subsetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1,definition,
% 0.29/0.46 ( subsetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2_type,type,
% 0.29/0.46 eqimpsubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2,definition,
% 0.29/0.46 ( eqimpsubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1_type,type,
% 0.29/0.46 eqimpsubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1,definition,
% 0.29/0.46 ( eqimpsubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2_type,type,
% 0.29/0.46 subsetI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2,definition,
% 0.29/0.46 ( subsetI2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset_type,type,
% 0.29/0.46 emptysetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset,definition,
% 0.29/0.46 ( emptysetsubset
% 0.29/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE_type,type,
% 0.29/0.46 subsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE,definition,
% 0.29/0.46 ( subsetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2_type,type,
% 0.29/0.46 subsetE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2,definition,
% 0.29/0.46 ( subsetE2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI_type,type,
% 0.29/0.46 notsubsetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI,definition,
% 0.29/0.46 ( notsubsetI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1_type,type,
% 0.29/0.46 notequalI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1,definition,
% 0.29/0.46 ( notequalI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ( subset @ A @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2_type,type,
% 0.29/0.46 notequalI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2,definition,
% 0.29/0.46 ( notequalI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl_type,type,
% 0.29/0.46 subsetRefl: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl,definition,
% 0.29/0.46 ( subsetRefl
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans_type,type,
% 0.29/0.46 subsetTrans: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans,definition,
% 0.29/0.46 ( subsetTrans
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ C )
% 0.29/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub_type,type,
% 0.29/0.46 setadjoinSub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub,definition,
% 0.29/0.46 ( setadjoinSub
% 0.29/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2_type,type,
% 0.29/0.46 setadjoinSub2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2,definition,
% 0.29/0.46 ( setadjoinSub2
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset_type,type,
% 0.29/0.46 subset2powerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset,definition,
% 0.29/0.46 ( subset2powerset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub_type,type,
% 0.29/0.46 setextsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub,definition,
% 0.29/0.46 ( setextsub
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ A )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq_type,type,
% 0.29/0.46 subsetemptysetimpeq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq,definition,
% 0.29/0.46 ( subsetemptysetimpeq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( subset @ A @ emptyset )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1_type,type,
% 0.29/0.46 powersetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1,definition,
% 0.29/0.46 ( powersetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1_type,type,
% 0.29/0.46 powersetE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1,definition,
% 0.29/0.46 ( powersetE1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset_type,type,
% 0.29/0.46 inPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset,definition,
% 0.29/0.46 ( inPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset_type,type,
% 0.29/0.46 powersetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset,definition,
% 0.29/0.46 ( powersetsubset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset_type,type,
% 0.29/0.46 sepInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset,definition,
% 0.29/0.46 ( sepInPowerset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( in
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset_type,type,
% 0.29/0.46 sepSubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset,definition,
% 0.29/0.46 ( sepSubset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunion_type,type,
% 0.29/0.46 binunion: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL_type,type,
% 0.29/0.46 binunionIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIL,definition,
% 0.29/0.46 ( binunionIL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR_type,type,
% 0.29/0.46 upairset2IR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2IR,definition,
% 0.29/0.46 ( upairset2IR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR_type,type,
% 0.29/0.46 binunionIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionIR,definition,
% 0.29/0.46 ( binunionIR
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases_type,type,
% 0.29/0.46 binunionEcases: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionEcases,definition,
% 0.29/0.46 ( binunionEcases
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( ( in @ Xx @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE_type,type,
% 0.29/0.46 binunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionE,definition,
% 0.29/0.46 ( binunionE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub_type,type,
% 0.29/0.46 binunionLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionLsub,definition,
% 0.29/0.46 ( binunionLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub_type,type,
% 0.29/0.46 binunionRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binunionRsub,definition,
% 0.29/0.46 ( binunionRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersect_type,type,
% 0.29/0.46 binintersect: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI_type,type,
% 0.29/0.46 binintersectI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectI,definition,
% 0.29/0.46 ( binintersectI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5_type,type,
% 0.29/0.46 binintersectSubset5: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset5,definition,
% 0.29/0.46 ( binintersectSubset5
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ C @ A )
% 0.29/0.46 => ( ( subset @ C @ B )
% 0.29/0.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL_type,type,
% 0.29/0.46 binintersectEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectEL,definition,
% 0.29/0.46 ( binintersectEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub_type,type,
% 0.29/0.46 binintersectLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectLsub,definition,
% 0.29/0.46 ( binintersectLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2_type,type,
% 0.29/0.46 binintersectSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset2,definition,
% 0.29/0.46 ( binintersectSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3_type,type,
% 0.29/0.46 binintersectSubset3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset3,definition,
% 0.29/0.46 ( binintersectSubset3
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER_type,type,
% 0.29/0.46 binintersectER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectER,definition,
% 0.29/0.46 ( binintersectER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1_type,type,
% 0.29/0.46 disjointsetsI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjointsetsI1,definition,
% 0.29/0.46 ( disjointsetsI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xx @ B ) )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub_type,type,
% 0.29/0.46 binintersectRsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectRsub,definition,
% 0.29/0.46 ( binintersectRsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4_type,type,
% 0.29/0.46 binintersectSubset4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset4,definition,
% 0.29/0.46 ( binintersectSubset4
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( ( binintersect @ A @ B )
% 0.29/0.46 = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1_type,type,
% 0.29/0.46 binintersectSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(binintersectSubset1,definition,
% 0.29/0.46 ( binintersectSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( binintersect @ A @ B )
% 0.29/0.46 = A )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d_type,type,
% 0.29/0.46 bs114d: $o ).
% 0.29/0.46
% 0.29/0.46 thf(bs114d,definition,
% 0.29/0.46 ( bs114d
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.29/0.46 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(regular_type,type,
% 0.29/0.46 regular: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminus_type,type,
% 0.29/0.46 setminus: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI_type,type,
% 0.29/0.46 setminusI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusI,definition,
% 0.29/0.46 ( setminusI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL_type,type,
% 0.29/0.46 setminusEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusEL,definition,
% 0.29/0.46 ( setminusEL
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER_type,type,
% 0.29/0.46 setminusER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusER,definition,
% 0.29/0.46 ( setminusER
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2_type,type,
% 0.29/0.46 setminusSubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset2,definition,
% 0.29/0.46 ( setminusSubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg_type,type,
% 0.29/0.46 setminusERneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusERneg,definition,
% 0.29/0.46 ( setminusERneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg_type,type,
% 0.29/0.46 setminusELneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusELneg,definition,
% 0.29/0.46 ( setminusELneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg_type,type,
% 0.29/0.46 setminusILneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusILneg,definition,
% 0.29/0.46 ( setminusILneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg_type,type,
% 0.29/0.46 setminusIRneg: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusIRneg,definition,
% 0.29/0.46 ( setminusIRneg
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub_type,type,
% 0.29/0.46 setminusLsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusLsub,definition,
% 0.29/0.46 ( setminusLsub
% 0.29/0.46 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1_type,type,
% 0.29/0.46 setminusSubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setminusSubset1,definition,
% 0.29/0.46 ( setminusSubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( ( setminus @ A @ B )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiff_type,type,
% 0.29/0.46 symdiff: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE_type,type,
% 0.29/0.46 symdiffE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffE,definition,
% 0.29/0.46 ( symdiffE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => ( ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1_type,type,
% 0.29/0.46 symdiffI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI1,definition,
% 0.29/0.46 ( symdiffI1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2_type,type,
% 0.29/0.46 symdiffI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffI2,definition,
% 0.29/0.46 ( symdiffI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1_type,type,
% 0.29/0.46 symdiffIneg1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg1,definition,
% 0.29/0.46 ( symdiffIneg1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2_type,type,
% 0.29/0.46 symdiffIneg2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(symdiffIneg2,definition,
% 0.29/0.46 ( symdiffIneg2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ~ ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(iskpair_type,type,
% 0.29/0.46 iskpair: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair_type,type,
% 0.29/0.46 secondinupair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(secondinupair,definition,
% 0.29/0.46 ( secondinupair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL_type,type,
% 0.29/0.46 setukpairIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIL,definition,
% 0.29/0.46 ( setukpairIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR_type,type,
% 0.29/0.46 setukpairIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairIR,definition,
% 0.29/0.46 ( setukpairIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair_type,type,
% 0.29/0.46 kpairiskpair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairiskpair,definition,
% 0.29/0.46 ( kpairiskpair
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kpair_type,type,
% 0.29/0.46 kpair: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp_type,type,
% 0.29/0.46 kpairp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kpairp,definition,
% 0.29/0.46 ( kpairp
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprod_type,type,
% 0.29/0.46 cartprod: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset_type,type,
% 0.29/0.46 singletonsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsubset,definition,
% 0.29/0.46 ( singletonsubset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset_type,type,
% 0.29/0.46 singletoninpowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowerset,definition,
% 0.29/0.46 ( singletoninpowerset
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion_type,type,
% 0.29/0.46 singletoninpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletoninpowunion,definition,
% 0.29/0.46 ( singletoninpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E_type,type,
% 0.29/0.46 upairset2E: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairset2E,definition,
% 0.29/0.46 ( upairset2E
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion_type,type,
% 0.29/0.46 upairsubunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsubunion,definition,
% 0.29/0.46 ( upairsubunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion_type,type,
% 0.29/0.46 upairinpowunion: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairinpowunion,definition,
% 0.29/0.46 ( upairinpowunion
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1_type,type,
% 0.29/0.46 ubforcartprodlem1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem1,definition,
% 0.29/0.46 ( ubforcartprodlem1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem2_type,type,
% 0.29/0.46 ubforcartprodlem2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem2,definition,
% 0.29/0.46 ( ubforcartprodlem2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem3_type,type,
% 0.29/0.46 ubforcartprodlem3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ubforcartprodlem3,definition,
% 0.29/0.46 ( ubforcartprodlem3
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairin_type,type,
% 0.29/0.46 cartprodpairin: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodpairin,definition,
% 0.29/0.46 ( cartprodpairin
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair1_type,type,
% 0.29/0.46 cartprodmempair1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair1,definition,
% 0.29/0.46 ( cartprodmempair1
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 & ( Xu
% 0.29/0.46 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair_type,type,
% 0.29/0.46 cartprodmempair: $o ).
% 0.29/0.46
% 0.29/0.46 thf(cartprodmempair,definition,
% 0.29/0.46 ( cartprodmempair
% 0.29/0.46 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.46 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.46 => ( iskpair @ Xu ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2_type,type,
% 0.29/0.46 setunionE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE2,definition,
% 0.29/0.46 ( setunionE2
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ? [X: $i] :
% 0.29/0.46 ( ( in @ X @ A )
% 0.29/0.46 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1_type,type,
% 0.29/0.46 setunionsingleton1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton1,definition,
% 0.29/0.46 ( setunionsingleton1
% 0.29/0.46 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton2_type,type,
% 0.29/0.46 setunionsingleton2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton2,definition,
% 0.29/0.46 ( setunionsingleton2
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton_type,type,
% 0.29/0.46 setunionsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionsingleton,definition,
% 0.29/0.46 ( setunionsingleton
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.29/0.46 = Xx ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singleton_type,type,
% 0.29/0.46 singleton: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(singleton,definition,
% 0.29/0.46 ( singleton
% 0.29/0.46 = ( ^ [A: $i] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( A
% 0.29/0.46 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop_type,type,
% 0.29/0.46 singletonprop: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonprop,definition,
% 0.29/0.46 ( singletonprop
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1_type,type,
% 0.29/0.46 ex1: $i > ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1,definition,
% 0.29/0.46 ( ex1
% 0.29/0.46 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( singleton
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E1_type,type,
% 0.29/0.46 ex1E1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1E1,definition,
% 0.29/0.46 ( ex1E1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I_type,type,
% 0.29/0.46 ex1I: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I,definition,
% 0.29/0.46 ( ex1I
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xy = Xx ) ) )
% 0.29/0.46 => ( ex1 @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I2_type,type,
% 0.29/0.46 ex1I2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(ex1I2,definition,
% 0.29/0.46 ( ex1I2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) )
% 0.29/0.46 => ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ex1 @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsuniq_type,type,
% 0.29/0.46 singletonsuniq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsuniq,definition,
% 0.29/0.46 ( singletonsuniq
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( setadjoin @ Xx @ emptyset )
% 0.29/0.46 = ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(atmost1p_type,type,
% 0.29/0.46 atmost1p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(atleast2p_type,type,
% 0.29/0.46 atleast2p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(atmost2p_type,type,
% 0.29/0.46 atmost2p: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetp_type,type,
% 0.29/0.46 upairsetp: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL1_type,type,
% 0.29/0.46 setukpairinjL1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setukpairinjL1,definition,
% 0.29/0.46 ( setukpairinjL1
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.46 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(kfstsingleton_type,type,
% 0.29/0.46 kfstsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(kfstsingleton,definition,
% 0.29/0.46 ( kfstsingleton
% 0.29/0.46 = ( ! [Xu: $i] :
% 0.29/0.46 ( ( iskpair @ Xu )
% 0.29/0.46 => ( singleton
% 0.29/0.46 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.46 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(theprop_type,type,
% 0.29/0.46 theprop: $o ).
% 0.29/0.46
% 0.29/0.46 thf(theprop,definition,
% 0.29/0.47 ( theprop
% 0.29/0.47 = ( ! [X: $i] :
% 0.29/0.47 ( ( singleton @ X )
% 0.29/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(kfst_type,type,
% 0.29/0.47 kfst: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(kfstpairEq_type,type,
% 0.29/0.47 kfstpairEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(kfstpairEq,definition,
% 0.29/0.47 ( kfstpairEq
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.47 = Xx ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodfstin_type,type,
% 0.29/0.47 cartprodfstin: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodfstin,definition,
% 0.29/0.47 ( cartprodfstin
% 0.29/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL2_type,type,
% 0.29/0.47 setukpairinjL2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL2,definition,
% 0.29/0.47 ( setukpairinjL2
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL_type,type,
% 0.29/0.47 setukpairinjL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjL,definition,
% 0.29/0.47 ( setukpairinjL
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.47 = ( kpair @ Xz @ Xu ) )
% 0.29/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR11_type,type,
% 0.29/0.47 setukpairinjR11: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR11,definition,
% 0.29/0.47 ( setukpairinjR11
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR12_type,type,
% 0.29/0.47 setukpairinjR12: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR12,definition,
% 0.29/0.47 ( setukpairinjR12
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR1_type,type,
% 0.29/0.47 setukpairinjR1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR1,definition,
% 0.29/0.47 ( setukpairinjR1
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.47 => ( ( Xz = Xu )
% 0.29/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairequniteq_type,type,
% 0.29/0.47 upairequniteq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairequniteq,definition,
% 0.29/0.47 ( upairequniteq
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR2_type,type,
% 0.29/0.47 setukpairinjR2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR2,definition,
% 0.29/0.47 ( setukpairinjR2
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.29/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.29/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR_type,type,
% 0.29/0.47 setukpairinjR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setukpairinjR,definition,
% 0.29/0.47 ( setukpairinjR
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.29/0.47 = ( kpair @ Xz @ Xu ) )
% 0.29/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ksndsingleton_type,type,
% 0.29/0.47 ksndsingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ksndsingleton,definition,
% 0.29/0.47 ( ksndsingleton
% 0.29/0.47 = ( ! [Xu: $i] :
% 0.29/0.47 ( ( iskpair @ Xu )
% 0.29/0.47 => ( singleton
% 0.29/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.29/0.47 @ ^ [Xx: $i] :
% 0.29/0.47 ( Xu
% 0.29/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ksnd_type,type,
% 0.29/0.47 ksnd: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(ksndpairEq_type,type,
% 0.29/0.47 ksndpairEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ksndpairEq,definition,
% 0.29/0.47 ( ksndpairEq
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.47 = Xy ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(kpairsurjEq_type,type,
% 0.29/0.47 kpairsurjEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(kpairsurjEq,definition,
% 0.29/0.47 ( kpairsurjEq
% 0.29/0.47 = ( ! [Xu: $i] :
% 0.29/0.47 ( ( iskpair @ Xu )
% 0.29/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.47 = Xu ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodsndin_type,type,
% 0.29/0.47 cartprodsndin: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodsndin,definition,
% 0.29/0.47 ( cartprodsndin
% 0.29/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairmemEL_type,type,
% 0.29/0.47 cartprodpairmemEL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairmemEL,definition,
% 0.29/0.47 ( cartprodpairmemEL
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairmemER_type,type,
% 0.29/0.47 cartprodpairmemER: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairmemER,definition,
% 0.29/0.47 ( cartprodpairmemER
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempaircEq_type,type,
% 0.29/0.47 cartprodmempaircEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodmempaircEq,definition,
% 0.29/0.47 ( cartprodmempaircEq
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( kpair @ Xx @ Xy )
% 0.29/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodfstpairEq_type,type,
% 0.29/0.47 cartprodfstpairEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodfstpairEq,definition,
% 0.29/0.47 ( cartprodfstpairEq
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.29/0.47 = Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodsndpairEq_type,type,
% 0.29/0.47 cartprodsndpairEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodsndpairEq,definition,
% 0.29/0.47 ( cartprodsndpairEq
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.29/0.47 = Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairsurjEq_type,type,
% 0.29/0.47 cartprodpairsurjEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(cartprodpairsurjEq,definition,
% 0.29/0.47 ( cartprodpairsurjEq
% 0.29/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.29/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.29/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.29/0.47 = Xu ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(breln_type,type,
% 0.29/0.47 breln: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(breln,definition,
% 0.29/0.47 ( breln
% 0.29/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstr_type,type,
% 0.29/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrI_type,type,
% 0.29/0.47 dpsetconstrI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrI,definition,
% 0.29/0.47 ( dpsetconstrI
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrSub_type,type,
% 0.29/0.47 dpsetconstrSub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrSub,definition,
% 0.29/0.47 ( dpsetconstrSub
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.47 ( subset
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.29/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setOfPairsIsBReln_type,type,
% 0.29/0.47 setOfPairsIsBReln: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setOfPairsIsBReln,definition,
% 0.29/0.47 ( setOfPairsIsBReln
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.29/0.47 ( breln @ A @ B
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrERa_type,type,
% 0.29/0.47 dpsetconstrERa: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrERa,definition,
% 0.29/0.47 ( dpsetconstrERa
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrEL1_type,type,
% 0.29/0.47 dpsetconstrEL1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrEL1,definition,
% 0.29/0.47 ( dpsetconstrEL1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrEL2_type,type,
% 0.29/0.47 dpsetconstrEL2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrEL2,definition,
% 0.29/0.47 ( dpsetconstrEL2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrER_type,type,
% 0.29/0.47 dpsetconstrER: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dpsetconstrER,definition,
% 0.29/0.47 ( dpsetconstrER
% 0.29/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.29/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(func_type,type,
% 0.29/0.47 func: $i > $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(func,definition,
% 0.29/0.47 ( func
% 0.29/0.47 = ( ^ [A: $i,B: $i,R: $i] :
% 0.29/0.47 ( ( breln @ A @ B @ R )
% 0.29/0.47 & ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ex1 @ B
% 0.29/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(funcSet_type,type,
% 0.29/0.47 funcSet: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(funcImageSingleton_type,type,
% 0.29/0.47 funcImageSingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(funcImageSingleton,definition,
% 0.29/0.47 ( funcImageSingleton
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( singleton
% 0.29/0.47 @ ( dsetconstr @ B
% 0.29/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(apProp_type,type,
% 0.29/0.47 apProp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(apProp,definition,
% 0.29/0.47 ( apProp
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in
% 0.29/0.47 @ ( setunion
% 0.29/0.47 @ ( dsetconstr @ B
% 0.29/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.29/0.47 @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ap_type,type,
% 0.29/0.47 ap: $i > $i > $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(app_type,type,
% 0.29/0.47 app: $o ).
% 0.29/0.47
% 0.29/0.47 thf(app,definition,
% 0.29/0.47 ( app
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(infuncsetfunc_type,type,
% 0.29/0.47 infuncsetfunc: $o ).
% 0.29/0.47
% 0.29/0.47 thf(infuncsetfunc,definition,
% 0.29/0.47 ( infuncsetfunc
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ap2p_type,type,
% 0.29/0.47 ap2p: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ap2p,definition,
% 0.29/0.47 ( ap2p
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(funcinfuncset_type,type,
% 0.29/0.47 funcinfuncset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(funcinfuncset,definition,
% 0.29/0.47 ( funcinfuncset
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(lamProp_type,type,
% 0.29/0.47 lamProp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(lamProp,definition,
% 0.29/0.47 ( lamProp
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.47 => ( func @ A @ B
% 0.29/0.47 @ ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xf @ Xx )
% 0.29/0.47 = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(lam_type,type,
% 0.29/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.29/0.47
% 0.29/0.47 thf(lam,definition,
% 0.29/0.47 ( lam
% 0.29/0.47 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.47 ( dpsetconstr @ A @ B
% 0.29/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xf @ Xx )
% 0.29/0.47 = Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(lamp_type,type,
% 0.29/0.47 lamp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(lamp,definition,
% 0.29/0.47 ( lamp
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.47 => ( func @ A @ B
% 0.29/0.47 @ ( lam @ A @ B
% 0.29/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(lam2p_type,type,
% 0.29/0.47 lam2p: $o ).
% 0.29/0.47
% 0.29/0.47 thf(lam2p,definition,
% 0.29/0.47 ( lam2p
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.29/0.47 => ( in
% 0.29/0.47 @ ( lam @ A @ B
% 0.29/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.29/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(brelnall1_type,type,
% 0.29/0.47 brelnall1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(brelnall1,definition,
% 0.29/0.47 ( brelnall1
% 0.29/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.47 ( ( breln @ A @ B @ R )
% 0.29/0.47 => ! [Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ R )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(brelnall2_type,type,
% 0.29/0.47 brelnall2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(brelnall2,definition,
% 0.29/0.47 ( brelnall2
% 0.29/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.47 ( ( breln @ A @ B @ R )
% 0.29/0.47 => ! [Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ R )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(ex1E2_type,type,
% 0.29/0.47 ex1E2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(ex1E2,definition,
% 0.29/0.47 ( ex1E2
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ( ex1 @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(funcGraphProp1_type,type,
% 0.29/0.47 funcGraphProp1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(funcGraphProp1,definition,
% 0.29/0.47 ( funcGraphProp1
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(funcGraphProp3_type,type,
% 0.29/0.47 funcGraphProp3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(funcGraphProp3,definition,
% 0.29/0.47 ( funcGraphProp3
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(funcGraphProp2_type,type,
% 0.29/0.47 funcGraphProp2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(funcGraphProp2,definition,
% 0.29/0.47 ( funcGraphProp2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.29/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(funcextLem_type,type,
% 0.29/0.47 funcextLem: $o ).
% 0.29/0.47
% 0.29/0.47 thf(funcextLem,definition,
% 0.29/0.47 ( funcextLem
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xf )
% 0.29/0.47 => ! [Xg: $i] :
% 0.29/0.47 ( ( func @ A @ B @ Xg )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(funcGraphProp4_type,type,
% 0.29/0.47 funcGraphProp4: $o ).
% 0.29/0.47
% 0.29/0.47 thf(funcGraphProp4,definition,
% 0.29/0.47 ( funcGraphProp4
% 0.29/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.29/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.29/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.29/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subbreln_type,type,
% 0.29/0.47 subbreln: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subbreln,definition,
% 0.29/0.47 ( subbreln
% 0.29/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.29/0.47 ( ( breln @ A @ B @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln @ A @ B @ S )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqbreln,conjecture,
% 0.29/0.47 ( setextAx
% 0.29/0.47 => ( emptysetAx
% 0.29/0.47 => ( setadjoinAx
% 0.29/0.47 => ( powersetAx
% 0.29/0.47 => ( setunionAx
% 0.29/0.47 => ( omega0Ax
% 0.29/0.47 => ( omegaSAx
% 0.29/0.47 => ( omegaIndAx
% 0.29/0.47 => ( replAx
% 0.29/0.47 => ( foundationAx
% 0.29/0.47 => ( wellorderingAx
% 0.29/0.47 => ( descrp
% 0.29/0.47 => ( dsetconstrI
% 0.29/0.47 => ( dsetconstrEL
% 0.29/0.47 => ( dsetconstrER
% 0.29/0.47 => ( exuE1
% 0.29/0.47 => ( prop2setE
% 0.29/0.47 => ( emptysetE
% 0.29/0.47 => ( emptysetimpfalse
% 0.29/0.47 => ( notinemptyset
% 0.29/0.47 => ( exuE3e
% 0.29/0.47 => ( setext
% 0.29/0.47 => ( emptyI
% 0.29/0.47 => ( noeltsimpempty
% 0.29/0.47 => ( setbeta
% 0.29/0.47 => ( nonemptyE1
% 0.29/0.47 => ( nonemptyI
% 0.29/0.47 => ( nonemptyI1
% 0.29/0.47 => ( setadjoinIL
% 0.29/0.47 => ( emptyinunitempty
% 0.29/0.47 => ( setadjoinIR
% 0.29/0.47 => ( setadjoinE
% 0.29/0.47 => ( setadjoinOr
% 0.29/0.47 => ( setoftrueEq
% 0.29/0.47 => ( powersetI
% 0.29/0.47 => ( emptyinPowerset
% 0.29/0.47 => ( emptyInPowerset
% 0.29/0.47 => ( powersetE
% 0.29/0.47 => ( setunionI
% 0.29/0.47 => ( setunionE
% 0.29/0.47 => ( subPowSU
% 0.29/0.47 => ( exuE2
% 0.29/0.47 => ( nonemptyImpWitness
% 0.29/0.47 => ( uniqinunit
% 0.29/0.47 => ( notinsingleton
% 0.29/0.47 => ( eqinunit
% 0.29/0.47 => ( singletonsswitch
% 0.29/0.47 => ( upairsetE
% 0.29/0.47 => ( upairsetIL
% 0.29/0.47 => ( upairsetIR
% 0.29/0.47 => ( emptyE1
% 0.29/0.47 => ( vacuousDall
% 0.29/0.47 => ( quantDeMorgan1
% 0.29/0.47 => ( quantDeMorgan2
% 0.29/0.47 => ( quantDeMorgan3
% 0.29/0.47 => ( quantDeMorgan4
% 0.29/0.47 => ( prop2setI
% 0.29/0.47 => ( prop2set2propI
% 0.29/0.47 => ( notdexE
% 0.29/0.47 => ( notdallE
% 0.29/0.47 => ( exuI1
% 0.29/0.47 => ( exuI3
% 0.29/0.47 => ( exuI2
% 0.29/0.47 => ( inCongP
% 0.29/0.47 => ( in__Cong
% 0.29/0.47 => ( exuE3u
% 0.29/0.47 => ( exu__Cong
% 0.29/0.47 => ( emptyset__Cong
% 0.29/0.47 => ( setadjoin__Cong
% 0.29/0.47 => ( powerset__Cong
% 0.29/0.47 => ( setunion__Cong
% 0.29/0.47 => ( omega__Cong
% 0.29/0.47 => ( exuEu
% 0.29/0.47 => ( descr__Cong
% 0.29/0.47 => ( dsetconstr__Cong
% 0.29/0.47 => ( subsetI1
% 0.29/0.47 => ( eqimpsubset2
% 0.29/0.47 => ( eqimpsubset1
% 0.29/0.47 => ( subsetI2
% 0.29/0.47 => ( emptysetsubset
% 0.29/0.47 => ( subsetE
% 0.29/0.47 => ( subsetE2
% 0.29/0.47 => ( notsubsetI
% 0.29/0.47 => ( notequalI1
% 0.29/0.47 => ( notequalI2
% 0.29/0.47 => ( subsetRefl
% 0.29/0.47 => ( subsetTrans
% 0.29/0.47 => ( setadjoinSub
% 0.29/0.47 => ( setadjoinSub2
% 0.29/0.47 => ( subset2powerset
% 0.29/0.47 => ( setextsub
% 0.29/0.47 => ( subsetemptysetimpeq
% 0.29/0.47 => ( powersetI1
% 0.29/0.47 => ( powersetE1
% 0.29/0.47 => ( inPowerset
% 0.29/0.47 => ( powersetsubset
% 0.29/0.47 => ( sepInPowerset
% 0.29/0.47 => ( sepSubset
% 0.29/0.47 => ( binunionIL
% 0.29/0.47 => ( upairset2IR
% 0.29/0.47 => ( binunionIR
% 0.29/0.47 => ( binunionEcases
% 0.29/0.47 => ( binunionE
% 0.29/0.47 => ( binunionLsub
% 0.29/0.47 => ( binunionRsub
% 0.29/0.47 => ( binintersectI
% 0.29/0.47 => ( binintersectSubset5
% 0.29/0.47 => ( binintersectEL
% 0.29/0.47 => ( binintersectLsub
% 0.29/0.47 => ( binintersectSubset2
% 0.29/0.47 => ( binintersectSubset3
% 0.29/0.47 => ( binintersectER
% 0.29/0.47 => ( disjointsetsI1
% 0.29/0.47 => ( binintersectRsub
% 0.29/0.47 => ( binintersectSubset4
% 0.29/0.47 => ( binintersectSubset1
% 0.29/0.47 => ( bs114d
% 0.29/0.47 => ( setminusI
% 0.29/0.47 => ( setminusEL
% 0.29/0.47 => ( setminusER
% 0.29/0.47 => ( setminusSubset2
% 0.29/0.47 => ( setminusERneg
% 0.29/0.47 => ( setminusELneg
% 0.29/0.47 => ( setminusILneg
% 0.29/0.47 => ( setminusIRneg
% 0.29/0.47 => ( setminusLsub
% 0.29/0.47 => ( setminusSubset1
% 0.29/0.47 => ( symdiffE
% 0.29/0.47 => ( symdiffI1
% 0.29/0.47 => ( symdiffI2
% 0.29/0.47 => ( symdiffIneg1
% 0.29/0.47 => ( symdiffIneg2
% 0.29/0.47 => ( secondinupair
% 0.29/0.47 => ( setukpairIL
% 0.29/0.47 => ( setukpairIR
% 0.29/0.47 => ( kpairiskpair
% 0.29/0.47 => ( kpairp
% 0.29/0.47 => ( singletonsubset
% 0.29/0.47 => ( singletoninpowerset
% 0.29/0.47 => ( singletoninpowunion
% 0.29/0.47 => ( upairset2E
% 0.29/0.47 => ( upairsubunion
% 0.29/0.47 => ( upairinpowunion
% 0.29/0.47 => ( ubforcartprodlem1
% 0.29/0.47 => ( ubforcartprodlem2
% 0.29/0.47 => ( ubforcartprodlem3
% 0.29/0.47 => ( cartprodpairin
% 0.29/0.47 => ( cartprodmempair1
% 0.29/0.47 => ( cartprodmempair
% 0.29/0.47 => ( setunionE2
% 0.29/0.47 => ( setunionsingleton1
% 0.29/0.47 => ( setunionsingleton2
% 0.29/0.47 => ( setunionsingleton
% 0.29/0.47 => ( singletonprop
% 0.29/0.47 => ( ex1E1
% 0.29/0.47 => ( ex1I
% 0.29/0.47 => ( ex1I2
% 0.29/0.47 => ( singletonsuniq
% 0.29/0.47 => ( setukpairinjL1
% 0.29/0.47 => ( kfstsingleton
% 0.29/0.47 => ( theprop
% 0.29/0.47 => ( kfstpairEq
% 0.29/0.47 => ( cartprodfstin
% 0.29/0.47 => ( setukpairinjL2
% 0.29/0.47 => ( setukpairinjL
% 0.29/0.47 => ( setukpairinjR11
% 0.29/0.47 => ( setukpairinjR12
% 0.29/0.47 => ( setukpairinjR1
% 0.29/0.47 => ( upairequniteq
% 0.29/0.47 => ( setukpairinjR2
% 0.29/0.47 => ( setukpairinjR
% 0.29/0.47 => ( ksndsingleton
% 0.29/0.47 => ( ksndpairEq
% 0.29/0.47 => ( kpairsurjEq
% 0.29/0.47 => ( cartprodsndin
% 0.29/0.47 => ( cartprodpairmemEL
% 0.29/0.47 => ( cartprodpairmemER
% 0.29/0.47 => ( cartprodmempaircEq
% 0.29/0.47 => ( cartprodfstpairEq
% 0.29/0.47 => ( cartprodsndpairEq
% 0.29/0.47 => ( cartprodpairsurjEq
% 0.29/0.47 => ( dpsetconstrI
% 0.29/0.47 => ( dpsetconstrSub
% 0.29/0.47 => ( setOfPairsIsBReln
% 0.29/0.47 => ( dpsetconstrERa
% 0.29/0.47 => ( dpsetconstrEL1
% 0.29/0.47 => ( dpsetconstrEL2
% 0.29/0.47 => ( dpsetconstrER
% 0.29/0.47 => ( funcImageSingleton
% 0.29/0.47 => ( apProp
% 0.29/0.47 => ( app
% 0.29/0.47 => ( infuncsetfunc
% 0.29/0.47 => ( ap2p
% 0.29/0.47 => ( funcinfuncset
% 0.29/0.47 => ( lamProp
% 0.29/0.47 => ( lamp
% 0.29/0.47 => ( lam2p
% 0.29/0.47 => ( brelnall1
% 0.29/0.47 => ( brelnall2
% 0.29/0.47 => ( ex1E2
% 0.29/0.47 => ( funcGraphProp1
% 0.29/0.47 => ( funcGraphProp3
% 0.29/0.47 => ( funcGraphProp2
% 0.29/0.47 => ( funcextLem
% 0.29/0.47 => ( funcGraphProp4
% 0.29/0.47 => ( subbreln
% 0.29/0.47 => ! [A: $i,B: $i,R: $i] :
% 0.29/0.47 ( ( breln @ A @ B @ R )
% 0.29/0.47 => ! [S: $i] :
% 0.29/0.47 ( ( breln @ A @ B @ S )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.29/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.29/0.47 => ( R = S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 0.30/1.51 ---- Embedded in THF ---
% 0.30/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.30/1.51 %%% Generated on Tue Feb 24 12:31:10 EST 2026
% 0.30/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 0.30/1.51 %%% Logic specification used:
% 0.30/1.51 %%% thf(spec, logic, $$dhol).
% 0.30/1.51
% 0.30/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rJod2NOsaw/DTF2DTF5039.p
% See solution above
% 0.30/1.51 ------------------------
% 0.30/1.54 ---- Cleaned THF ---
% 0.30/1.54 thf(in_type,type,
% 0.30/1.54 in: $i > $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(exu_type,type,
% 0.30/1.54 exu: ( $i > $o ) > $o ).
% 0.30/1.54
% 0.30/1.54 thf(exu,definition,
% 0.30/1.54 ( exu
% 0.30/1.54 = ( ^ [Xphi: $i > $o] :
% 0.30/1.54 ? [Xx: $i] :
% 0.30/1.54 ( ( Xphi @ Xx )
% 0.30/1.54 & ! [Xy: $i] :
% 0.30/1.54 ( ( Xphi @ Xy )
% 0.30/1.54 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setextAx_type,type,
% 0.30/1.54 setextAx: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setextAx,definition,
% 0.30/1.54 ( setextAx
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 <=> ( in @ Xx @ B ) )
% 0.30/1.54 => ( A = B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(emptyset_type,type,
% 0.30/1.54 emptyset: $i ).
% 0.30/1.54
% 0.30/1.54 thf(emptysetAx_type,type,
% 0.30/1.54 emptysetAx: $o ).
% 0.30/1.54
% 0.30/1.54 thf(emptysetAx,definition,
% 0.30/1.54 ( emptysetAx
% 0.30/1.54 = ( ! [Xx: $i] :
% 0.30/1.54 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoin_type,type,
% 0.30/1.54 setadjoin: $i > $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinAx_type,type,
% 0.30/1.54 setadjoinAx: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinAx,definition,
% 0.30/1.54 ( setadjoinAx
% 0.30/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/1.54 <=> ( ( Xy = Xx )
% 0.30/1.54 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(powerset_type,type,
% 0.30/1.54 powerset: $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(powersetAx_type,type,
% 0.30/1.54 powersetAx: $o ).
% 0.30/1.54
% 0.30/1.54 thf(powersetAx,definition,
% 0.30/1.54 ( powersetAx
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( in @ B @ ( powerset @ A ) )
% 0.30/1.54 <=> ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ B )
% 0.30/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setunion_type,type,
% 0.30/1.54 setunion: $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(setunionAx_type,type,
% 0.30/1.54 setunionAx: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setunionAx,definition,
% 0.30/1.54 ( setunionAx
% 0.30/1.54 = ( ! [A: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/1.54 <=> ? [B: $i] :
% 0.30/1.54 ( ( in @ Xx @ B )
% 0.30/1.54 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(omega_type,type,
% 0.30/1.54 omega: $i ).
% 0.30/1.54
% 0.30/1.54 thf(omega0Ax_type,type,
% 0.30/1.54 omega0Ax: $o ).
% 0.30/1.54
% 0.30/1.54 thf(omega0Ax,definition,
% 0.30/1.54 ( omega0Ax
% 0.30/1.54 = ( in @ emptyset @ omega ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(omegaSAx_type,type,
% 0.30/1.54 omegaSAx: $o ).
% 0.30/1.54
% 0.30/1.54 thf(omegaSAx,definition,
% 0.30/1.54 ( omegaSAx
% 0.30/1.54 = ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ omega )
% 0.30/1.54 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(omegaIndAx_type,type,
% 0.30/1.54 omegaIndAx: $o ).
% 0.30/1.54
% 0.30/1.54 thf(omegaIndAx,definition,
% 0.30/1.54 ( omegaIndAx
% 0.30/1.54 = ( ! [A: $i] :
% 0.30/1.54 ( ( ( in @ emptyset @ A )
% 0.30/1.54 & ! [Xx: $i] :
% 0.30/1.54 ( ( ( in @ Xx @ omega )
% 0.30/1.54 & ( in @ Xx @ A ) )
% 0.30/1.54 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ omega )
% 0.30/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(replAx_type,type,
% 0.30/1.54 replAx: $o ).
% 0.30/1.54
% 0.30/1.54 thf(replAx,definition,
% 0.30/1.54 ( replAx
% 0.30/1.54 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( exu
% 0.30/1.54 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/1.54 => ? [B: $i] :
% 0.30/1.54 ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ B )
% 0.30/1.54 <=> ? [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ A )
% 0.30/1.54 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(foundationAx_type,type,
% 0.30/1.54 foundationAx: $o ).
% 0.30/1.54
% 0.30/1.54 thf(foundationAx,definition,
% 0.30/1.54 ( foundationAx
% 0.30/1.54 = ( ! [A: $i] :
% 0.30/1.54 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/1.54 => ? [B: $i] :
% 0.30/1.54 ( ( in @ B @ A )
% 0.30/1.54 & ~ ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ B )
% 0.30/1.54 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(wellorderingAx_type,type,
% 0.30/1.54 wellorderingAx: $o ).
% 0.30/1.54
% 0.30/1.54 thf(wellorderingAx,definition,
% 0.30/1.54 ( wellorderingAx
% 0.30/1.54 = ( ! [A: $i] :
% 0.30/1.54 ? [B: $i] :
% 0.30/1.54 ( ! [C: $i] :
% 0.30/1.54 ( ( in @ C @ B )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ C )
% 0.30/1.54 => ( in @ Xx @ A ) ) )
% 0.30/1.54 & ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( ( in @ Xx @ A )
% 0.30/1.54 & ( in @ Xy @ A ) )
% 0.30/1.54 => ( ! [C: $i] :
% 0.30/1.54 ( ( in @ C @ B )
% 0.30/1.54 => ( ( in @ Xx @ C )
% 0.30/1.54 <=> ( in @ Xy @ C ) ) )
% 0.30/1.54 => ( Xx = Xy ) ) )
% 0.30/1.54 & ! [C: $i,D: $i] :
% 0.30/1.54 ( ( ( in @ C @ B )
% 0.30/1.54 & ( in @ D @ B ) )
% 0.30/1.54 => ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ C )
% 0.30/1.54 => ( in @ Xx @ D ) )
% 0.30/1.54 | ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ D )
% 0.30/1.54 => ( in @ Xx @ C ) ) ) )
% 0.30/1.54 & ! [C: $i] :
% 0.30/1.54 ( ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ C )
% 0.30/1.54 => ( in @ Xx @ A ) )
% 0.30/1.54 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/1.54 => ? [D: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ D @ B )
% 0.30/1.54 & ( in @ Xx @ C )
% 0.30/1.54 & ~ ? [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ D )
% 0.30/1.54 & ( in @ Xy @ C ) )
% 0.30/1.54 & ! [E: $i] :
% 0.30/1.54 ( ( in @ E @ B )
% 0.30/1.54 => ( ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ E )
% 0.30/1.54 => ( in @ Xy @ D ) )
% 0.30/1.54 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(descr_type,type,
% 0.30/1.54 descr: ( $i > $o ) > $i ).
% 0.30/1.54
% 0.30/1.54 thf(descrp_type,type,
% 0.30/1.54 descrp: $o ).
% 0.30/1.54
% 0.30/1.54 thf(descrp,definition,
% 0.30/1.54 ( descrp
% 0.30/1.54 = ( ! [Xphi: $i > $o] :
% 0.30/1.54 ( ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 => ( Xphi
% 0.30/1.54 @ ( descr
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(dsetconstr_type,type,
% 0.30/1.54 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/1.54
% 0.30/1.54 thf(dsetconstrI_type,type,
% 0.30/1.54 dsetconstrI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(dsetconstrI,definition,
% 0.30/1.54 ( dsetconstrI
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ( Xphi @ Xx )
% 0.30/1.54 => ( in @ Xx
% 0.30/1.54 @ ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(dsetconstrEL_type,type,
% 0.30/1.54 dsetconstrEL: $o ).
% 0.30/1.54
% 0.30/1.54 thf(dsetconstrEL,definition,
% 0.30/1.54 ( dsetconstrEL
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx
% 0.30/1.54 @ ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(dsetconstrER_type,type,
% 0.30/1.54 dsetconstrER: $o ).
% 0.30/1.54
% 0.30/1.54 thf(dsetconstrER,definition,
% 0.30/1.54 ( dsetconstrER
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx
% 0.30/1.54 @ ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/1.54 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(exuE1_type,type,
% 0.30/1.54 exuE1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(exuE1,definition,
% 0.30/1.54 ( exuE1
% 0.30/1.54 = ( ! [Xphi: $i > $o] :
% 0.30/1.54 ( ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 => ? [Xx: $i] :
% 0.30/1.54 ( ( Xphi @ Xx )
% 0.30/1.54 & ! [Xy: $i] :
% 0.30/1.54 ( ( Xphi @ Xy )
% 0.30/1.54 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(prop2set_type,type,
% 0.30/1.54 prop2set: $o > $i ).
% 0.30/1.54
% 0.30/1.54 thf(prop2setE_type,type,
% 0.30/1.54 prop2setE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(prop2setE,definition,
% 0.30/1.54 ( prop2setE
% 0.30/1.54 = ( ! [Xphi: $o,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.30/1.54 => Xphi ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(emptysetE_type,type,
% 0.30/1.54 emptysetE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(emptysetE,definition,
% 0.30/1.54 ( emptysetE
% 0.30/1.54 = ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ emptyset )
% 0.30/1.54 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(emptysetimpfalse_type,type,
% 0.30/1.54 emptysetimpfalse: $o ).
% 0.30/1.54
% 0.30/1.54 thf(emptysetimpfalse,definition,
% 0.30/1.54 ( emptysetimpfalse
% 0.30/1.54 = ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ emptyset )
% 0.30/1.54 => $false ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(notinemptyset_type,type,
% 0.30/1.54 notinemptyset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(notinemptyset,definition,
% 0.30/1.54 ( notinemptyset
% 0.30/1.54 = ( ! [Xx: $i] :
% 0.30/1.54 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(exuE3e_type,type,
% 0.30/1.54 exuE3e: $o ).
% 0.30/1.54
% 0.30/1.54 thf(exuE3e,definition,
% 0.30/1.54 ( exuE3e
% 0.30/1.54 = ( ! [Xphi: $i > $o] :
% 0.30/1.54 ( ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setext_type,type,
% 0.30/1.54 setext: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setext,definition,
% 0.30/1.54 ( setext
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ Xx @ B ) )
% 0.30/1.54 => ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ B )
% 0.30/1.54 => ( in @ Xx @ A ) )
% 0.30/1.54 => ( A = B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(emptyI_type,type,
% 0.30/1.54 emptyI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(emptyI,definition,
% 0.30/1.54 ( emptyI
% 0.30/1.54 = ( ! [A: $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ~ ( in @ Xx @ A )
% 0.30/1.54 => ( A = emptyset ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(noeltsimpempty_type,type,
% 0.30/1.54 noeltsimpempty: $o ).
% 0.30/1.54
% 0.30/1.54 thf(noeltsimpempty,definition,
% 0.30/1.54 ( noeltsimpempty
% 0.30/1.54 = ( ! [A: $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ~ ( in @ Xx @ A )
% 0.30/1.54 => ( A = emptyset ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setbeta_type,type,
% 0.30/1.54 setbeta: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setbeta,definition,
% 0.30/1.54 ( setbeta
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ( in @ Xx
% 0.30/1.54 @ ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/1.54 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(nonempty_type,type,
% 0.30/1.54 nonempty: $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(nonempty,definition,
% 0.30/1.54 ( nonempty
% 0.30/1.54 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(nonemptyE1_type,type,
% 0.30/1.54 nonemptyE1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(nonemptyE1,definition,
% 0.30/1.54 ( nonemptyE1
% 0.30/1.54 = ( ! [A: $i] :
% 0.30/1.54 ( ( nonempty @ A )
% 0.30/1.54 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(nonemptyI_type,type,
% 0.30/1.54 nonemptyI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(nonemptyI,definition,
% 0.30/1.54 ( nonemptyI
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ( Xphi @ Xx )
% 0.30/1.54 => ( nonempty
% 0.30/1.54 @ ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(nonemptyI1_type,type,
% 0.30/1.54 nonemptyI1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(nonemptyI1,definition,
% 0.30/1.54 ( nonemptyI1
% 0.30/1.54 = ( ! [A: $i] :
% 0.30/1.54 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/1.54 => ( nonempty @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinIL_type,type,
% 0.30/1.54 setadjoinIL: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinIL,definition,
% 0.30/1.54 ( setadjoinIL
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(emptyinunitempty_type,type,
% 0.30/1.54 emptyinunitempty: $o ).
% 0.30/1.54
% 0.30/1.54 thf(emptyinunitempty,definition,
% 0.30/1.54 ( emptyinunitempty
% 0.30/1.54 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinIR_type,type,
% 0.30/1.54 setadjoinIR: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinIR,definition,
% 0.30/1.54 ( setadjoinIR
% 0.30/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ A )
% 0.30/1.54 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinE_type,type,
% 0.30/1.54 setadjoinE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinE,definition,
% 0.30/1.54 ( setadjoinE
% 0.30/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/1.54 => ! [Xphi: $o] :
% 0.30/1.54 ( ( ( Xy = Xx )
% 0.30/1.54 => Xphi )
% 0.30/1.54 => ( ( ( in @ Xy @ A )
% 0.30/1.54 => Xphi )
% 0.30/1.54 => Xphi ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinOr_type,type,
% 0.30/1.54 setadjoinOr: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinOr,definition,
% 0.30/1.54 ( setadjoinOr
% 0.30/1.54 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/1.54 => ( ( Xy = Xx )
% 0.30/1.54 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setoftrueEq_type,type,
% 0.30/1.54 setoftrueEq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setoftrueEq,definition,
% 0.30/1.54 ( setoftrueEq
% 0.30/1.54 = ( ! [A: $i] :
% 0.30/1.54 ( ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xx: $i] : $true )
% 0.30/1.54 = A ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(powersetI_type,type,
% 0.30/1.54 powersetI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(powersetI,definition,
% 0.30/1.54 ( powersetI
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ B )
% 0.30/1.54 => ( in @ Xx @ A ) )
% 0.30/1.54 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(emptyinPowerset_type,type,
% 0.30/1.54 emptyinPowerset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(emptyinPowerset,definition,
% 0.30/1.54 ( emptyinPowerset
% 0.30/1.54 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(emptyInPowerset_type,type,
% 0.30/1.54 emptyInPowerset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(emptyInPowerset,definition,
% 0.30/1.54 ( emptyInPowerset
% 0.30/1.54 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(powersetE_type,type,
% 0.30/1.54 powersetE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(powersetE,definition,
% 0.30/1.54 ( powersetE
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ B @ ( powerset @ A ) )
% 0.30/1.54 => ( ( in @ Xx @ B )
% 0.30/1.54 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setunionI_type,type,
% 0.30/1.54 setunionI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setunionI,definition,
% 0.30/1.54 ( setunionI
% 0.30/1.54 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/1.54 ( ( in @ Xx @ B )
% 0.30/1.54 => ( ( in @ B @ A )
% 0.30/1.54 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setunionE_type,type,
% 0.30/1.54 setunionE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setunionE,definition,
% 0.30/1.54 ( setunionE
% 0.30/1.54 = ( ! [A: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/1.54 => ! [Xphi: $o] :
% 0.30/1.54 ( ! [B: $i] :
% 0.30/1.54 ( ( in @ Xx @ B )
% 0.30/1.54 => ( ( in @ B @ A )
% 0.30/1.54 => Xphi ) )
% 0.30/1.54 => Xphi ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(subPowSU_type,type,
% 0.30/1.54 subPowSU: $o ).
% 0.30/1.54
% 0.30/1.54 thf(subPowSU,definition,
% 0.30/1.54 ( subPowSU
% 0.30/1.54 = ( ! [A: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(exuE2_type,type,
% 0.30/1.54 exuE2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(exuE2,definition,
% 0.30/1.54 ( exuE2
% 0.30/1.54 = ( ! [Xphi: $i > $o] :
% 0.30/1.54 ( ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 => ? [Xx: $i] :
% 0.30/1.54 ! [Xy: $i] :
% 0.30/1.54 ( ( Xphi @ Xy )
% 0.30/1.54 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(nonemptyImpWitness_type,type,
% 0.30/1.54 nonemptyImpWitness: $o ).
% 0.30/1.54
% 0.30/1.54 thf(nonemptyImpWitness,definition,
% 0.30/1.54 ( nonemptyImpWitness
% 0.30/1.54 = ( ! [A: $i] :
% 0.30/1.54 ( ( nonempty @ A )
% 0.30/1.54 => ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & $true ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(uniqinunit_type,type,
% 0.30/1.54 uniqinunit: $o ).
% 0.30/1.54
% 0.30/1.54 thf(uniqinunit,definition,
% 0.30/1.54 ( uniqinunit
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/1.54 => ( Xx = Xy ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(notinsingleton_type,type,
% 0.30/1.54 notinsingleton: $o ).
% 0.30/1.54
% 0.30/1.54 thf(notinsingleton,definition,
% 0.30/1.54 ( notinsingleton
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xx != Xy )
% 0.30/1.54 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(eqinunit_type,type,
% 0.30/1.54 eqinunit: $o ).
% 0.30/1.54
% 0.30/1.54 thf(eqinunit,definition,
% 0.30/1.54 ( eqinunit
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xx = Xy )
% 0.30/1.54 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(singletonsswitch_type,type,
% 0.30/1.54 singletonsswitch: $o ).
% 0.30/1.54
% 0.30/1.54 thf(singletonsswitch,definition,
% 0.30/1.54 ( singletonsswitch
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/1.54 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(upairsetE_type,type,
% 0.30/1.54 upairsetE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(upairsetE,definition,
% 0.30/1.54 ( upairsetE
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/1.54 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/1.54 => ( ( Xz = Xx )
% 0.30/1.54 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(upairsetIL_type,type,
% 0.30/1.54 upairsetIL: $o ).
% 0.30/1.54
% 0.30/1.54 thf(upairsetIL,definition,
% 0.30/1.54 ( upairsetIL
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(upairsetIR_type,type,
% 0.30/1.54 upairsetIR: $o ).
% 0.30/1.54
% 0.30/1.54 thf(upairsetIR,definition,
% 0.30/1.54 ( upairsetIR
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(emptyE1_type,type,
% 0.30/1.54 emptyE1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(emptyE1,definition,
% 0.30/1.54 ( emptyE1
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ( Xphi @ Xx ) )
% 0.30/1.54 => ( ( ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 = emptyset )
% 0.30/1.54 => $false ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(vacuousDall_type,type,
% 0.30/1.54 vacuousDall: $o ).
% 0.30/1.54
% 0.30/1.54 thf(vacuousDall,definition,
% 0.30/1.54 ( vacuousDall
% 0.30/1.54 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ emptyset )
% 0.30/1.54 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(quantDeMorgan1_type,type,
% 0.30/1.54 quantDeMorgan1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(quantDeMorgan1,definition,
% 0.30/1.54 ( quantDeMorgan1
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ~ ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( Xphi @ Xx ) )
% 0.30/1.54 => ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(quantDeMorgan2_type,type,
% 0.30/1.54 quantDeMorgan2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(quantDeMorgan2,definition,
% 0.30/1.54 ( quantDeMorgan2
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ~ ( Xphi @ Xx ) )
% 0.30/1.54 => ~ ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(quantDeMorgan3_type,type,
% 0.30/1.54 quantDeMorgan3: $o ).
% 0.30/1.54
% 0.30/1.54 thf(quantDeMorgan3,definition,
% 0.30/1.54 ( quantDeMorgan3
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ~ ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ( Xphi @ Xx ) )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(quantDeMorgan4_type,type,
% 0.30/1.54 quantDeMorgan4: $o ).
% 0.30/1.54
% 0.30/1.54 thf(quantDeMorgan4,definition,
% 0.30/1.54 ( quantDeMorgan4
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ~ ( Xphi @ Xx ) )
% 0.30/1.54 => ~ ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(prop2setI_type,type,
% 0.30/1.54 prop2setI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(prop2setI,definition,
% 0.30/1.54 ( prop2setI
% 0.30/1.54 = ( ! [Xphi: $o] :
% 0.30/1.54 ( Xphi
% 0.30/1.54 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(set2prop_type,type,
% 0.30/1.54 set2prop: $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(prop2set2propI_type,type,
% 0.30/1.54 prop2set2propI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(prop2set2propI,definition,
% 0.30/1.54 ( prop2set2propI
% 0.30/1.54 = ( ! [Xphi: $o] :
% 0.30/1.54 ( Xphi
% 0.30/1.54 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(notdexE_type,type,
% 0.30/1.54 notdexE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(notdexE,definition,
% 0.30/1.54 ( notdexE
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ~ ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ( Xphi @ Xx ) )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(notdallE_type,type,
% 0.30/1.54 notdallE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(notdallE,definition,
% 0.30/1.54 ( notdallE
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ~ ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( Xphi @ Xx ) )
% 0.30/1.54 => ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(exuI1_type,type,
% 0.30/1.54 exuI1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(exuI1,definition,
% 0.30/1.54 ( exuI1
% 0.30/1.54 = ( ! [Xphi: $i > $o] :
% 0.30/1.54 ( ? [Xx: $i] :
% 0.30/1.54 ( ( Xphi @ Xx )
% 0.30/1.54 & ! [Xy: $i] :
% 0.30/1.54 ( ( Xphi @ Xy )
% 0.30/1.54 => ( Xx = Xy ) ) )
% 0.30/1.54 => ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(exuI3_type,type,
% 0.30/1.54 exuI3: $o ).
% 0.30/1.54
% 0.30/1.54 thf(exuI3,definition,
% 0.30/1.54 ( exuI3
% 0.30/1.54 = ( ! [Xphi: $i > $o] :
% 0.30/1.54 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.30/1.54 => ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xphi @ Xx )
% 0.30/1.54 => ( ( Xphi @ Xy )
% 0.30/1.54 => ( Xx = Xy ) ) )
% 0.30/1.54 => ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(exuI2_type,type,
% 0.30/1.54 exuI2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(exuI2,definition,
% 0.30/1.54 ( exuI2
% 0.30/1.54 = ( ! [Xphi: $i > $o] :
% 0.30/1.54 ( ? [Xx: $i] :
% 0.30/1.54 ! [Xy: $i] :
% 0.30/1.54 ( ( Xphi @ Xy )
% 0.30/1.54 <=> ( Xy = Xx ) )
% 0.30/1.54 => ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(inCongP_type,type,
% 0.30/1.54 inCongP: $o ).
% 0.30/1.54
% 0.30/1.54 thf(inCongP,definition,
% 0.30/1.54 ( inCongP
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( A = B )
% 0.30/1.54 => ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xx = Xy )
% 0.30/1.54 => ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(in__Cong_type,type,
% 0.30/1.54 in__Cong: $o ).
% 0.30/1.54
% 0.30/1.54 thf(in__Cong,definition,
% 0.30/1.54 ( in__Cong
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( A = B )
% 0.30/1.54 => ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xx = Xy )
% 0.30/1.54 => ( ( in @ Xx @ A )
% 0.30/1.54 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(exuE3u_type,type,
% 0.30/1.54 exuE3u: $o ).
% 0.30/1.54
% 0.30/1.54 thf(exuE3u,definition,
% 0.30/1.54 ( exuE3u
% 0.30/1.54 = ( ! [Xphi: $i > $o] :
% 0.30/1.54 ( ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 => ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xphi @ Xx )
% 0.30/1.54 => ( ( Xphi @ Xy )
% 0.30/1.54 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(exu__Cong_type,type,
% 0.30/1.54 exu__Cong: $o ).
% 0.30/1.54
% 0.30/1.54 thf(exu__Cong,definition,
% 0.30/1.54 ( exu__Cong
% 0.30/1.54 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/1.54 ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xx = Xy )
% 0.30/1.54 => ( ( Xphi @ Xx )
% 0.30/1.54 <=> ( Xpsi @ Xy ) ) )
% 0.30/1.54 => ( ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 <=> ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(emptyset__Cong_type,type,
% 0.30/1.54 emptyset__Cong: $o ).
% 0.30/1.54
% 0.30/1.54 thf(emptyset__Cong,definition,
% 0.30/1.54 ( emptyset__Cong
% 0.30/1.54 = ( emptyset = emptyset ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoin__Cong_type,type,
% 0.30/1.54 setadjoin__Cong: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoin__Cong,definition,
% 0.30/1.54 ( setadjoin__Cong
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xx = Xy )
% 0.30/1.54 => ! [Xz: $i,Xu: $i] :
% 0.30/1.54 ( ( Xz = Xu )
% 0.30/1.54 => ( ( setadjoin @ Xx @ Xz )
% 0.30/1.54 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(powerset__Cong_type,type,
% 0.30/1.54 powerset__Cong: $o ).
% 0.30/1.54
% 0.30/1.54 thf(powerset__Cong,definition,
% 0.30/1.54 ( powerset__Cong
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( A = B )
% 0.30/1.54 => ( ( powerset @ A )
% 0.30/1.54 = ( powerset @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setunion__Cong_type,type,
% 0.30/1.54 setunion__Cong: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setunion__Cong,definition,
% 0.30/1.54 ( setunion__Cong
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( A = B )
% 0.30/1.54 => ( ( setunion @ A )
% 0.30/1.54 = ( setunion @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(omega__Cong_type,type,
% 0.30/1.54 omega__Cong: $o ).
% 0.30/1.54
% 0.30/1.54 thf(omega__Cong,definition,
% 0.30/1.54 ( omega__Cong
% 0.30/1.54 = ( omega = omega ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(exuEu_type,type,
% 0.30/1.54 exuEu: $o ).
% 0.30/1.54
% 0.30/1.54 thf(exuEu,definition,
% 0.30/1.54 ( exuEu
% 0.30/1.54 = ( ! [Xphi: $i > $o] :
% 0.30/1.54 ( ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 => ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xphi @ Xx )
% 0.30/1.54 => ( ( Xphi @ Xy )
% 0.30/1.54 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(descr__Cong_type,type,
% 0.30/1.54 descr__Cong: $o ).
% 0.30/1.54
% 0.30/1.54 thf(descr__Cong,definition,
% 0.30/1.54 ( descr__Cong
% 0.30/1.54 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/1.54 ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xx = Xy )
% 0.30/1.54 => ( ( Xphi @ Xx )
% 0.30/1.54 <=> ( Xpsi @ Xy ) ) )
% 0.30/1.54 => ( ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 => ( ( exu
% 0.30/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.30/1.54 => ( ( descr
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 = ( descr
% 0.30/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(dsetconstr__Cong_type,type,
% 0.30/1.54 dsetconstr__Cong: $o ).
% 0.30/1.54
% 0.30/1.54 thf(dsetconstr__Cong,definition,
% 0.30/1.54 ( dsetconstr__Cong
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( A = B )
% 0.30/1.54 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( Xx = Xy )
% 0.30/1.54 => ( ( Xphi @ Xx )
% 0.30/1.54 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.30/1.54 => ( ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 = ( dsetconstr @ B
% 0.30/1.54 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(subset_type,type,
% 0.30/1.54 subset: $i > $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(disjoint_type,type,
% 0.30/1.54 disjoint: $i > $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(setsmeet_type,type,
% 0.30/1.54 setsmeet: $i > $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(subsetI1_type,type,
% 0.30/1.54 subsetI1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(subsetI1,definition,
% 0.30/1.54 ( subsetI1
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ Xx @ B ) )
% 0.30/1.54 => ( subset @ A @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(eqimpsubset2_type,type,
% 0.30/1.54 eqimpsubset2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(eqimpsubset2,definition,
% 0.30/1.54 ( eqimpsubset2
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( A = B )
% 0.30/1.54 => ( subset @ B @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(eqimpsubset1_type,type,
% 0.30/1.54 eqimpsubset1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(eqimpsubset1,definition,
% 0.30/1.54 ( eqimpsubset1
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( A = B )
% 0.30/1.54 => ( subset @ A @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(subsetI2_type,type,
% 0.30/1.54 subsetI2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(subsetI2,definition,
% 0.30/1.54 ( subsetI2
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ Xx @ B ) )
% 0.30/1.54 => ( subset @ A @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(emptysetsubset_type,type,
% 0.30/1.54 emptysetsubset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(emptysetsubset,definition,
% 0.30/1.54 ( emptysetsubset
% 0.30/1.54 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(subsetE_type,type,
% 0.30/1.54 subsetE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(subsetE,definition,
% 0.30/1.54 ( subsetE
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( subset @ A @ B )
% 0.30/1.54 => ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(subsetE2_type,type,
% 0.30/1.54 subsetE2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(subsetE2,definition,
% 0.30/1.54 ( subsetE2
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( subset @ A @ B )
% 0.30/1.54 => ( ~ ( in @ Xx @ B )
% 0.30/1.54 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(notsubsetI_type,type,
% 0.30/1.54 notsubsetI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(notsubsetI,definition,
% 0.30/1.54 ( notsubsetI
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ~ ( in @ Xx @ B )
% 0.30/1.54 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(notequalI1_type,type,
% 0.30/1.54 notequalI1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(notequalI1,definition,
% 0.30/1.54 ( notequalI1
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ~ ( subset @ A @ B )
% 0.30/1.54 => ( A != B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(notequalI2_type,type,
% 0.30/1.54 notequalI2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(notequalI2,definition,
% 0.30/1.54 ( notequalI2
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ~ ( in @ Xx @ B )
% 0.30/1.54 => ( A != B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(subsetRefl_type,type,
% 0.30/1.54 subsetRefl: $o ).
% 0.30/1.54
% 0.30/1.54 thf(subsetRefl,definition,
% 0.30/1.54 ( subsetRefl
% 0.30/1.54 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(subsetTrans_type,type,
% 0.30/1.54 subsetTrans: $o ).
% 0.30/1.54
% 0.30/1.54 thf(subsetTrans,definition,
% 0.30/1.54 ( subsetTrans
% 0.30/1.54 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/1.54 ( ( subset @ A @ B )
% 0.30/1.54 => ( ( subset @ B @ C )
% 0.30/1.54 => ( subset @ A @ C ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinSub_type,type,
% 0.30/1.54 setadjoinSub: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinSub,definition,
% 0.30/1.54 ( setadjoinSub
% 0.30/1.54 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinSub2_type,type,
% 0.30/1.54 setadjoinSub2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setadjoinSub2,definition,
% 0.30/1.54 ( setadjoinSub2
% 0.30/1.54 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/1.54 ( ( subset @ A @ B )
% 0.30/1.54 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(subset2powerset_type,type,
% 0.30/1.54 subset2powerset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(subset2powerset,definition,
% 0.30/1.54 ( subset2powerset
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( subset @ A @ B )
% 0.30/1.54 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setextsub_type,type,
% 0.30/1.54 setextsub: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setextsub,definition,
% 0.30/1.54 ( setextsub
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( subset @ A @ B )
% 0.30/1.54 => ( ( subset @ B @ A )
% 0.30/1.54 => ( A = B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(subsetemptysetimpeq_type,type,
% 0.30/1.54 subsetemptysetimpeq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(subsetemptysetimpeq,definition,
% 0.30/1.54 ( subsetemptysetimpeq
% 0.30/1.54 = ( ! [A: $i] :
% 0.30/1.54 ( ( subset @ A @ emptyset )
% 0.30/1.54 => ( A = emptyset ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(powersetI1_type,type,
% 0.30/1.54 powersetI1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(powersetI1,definition,
% 0.30/1.54 ( powersetI1
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( subset @ B @ A )
% 0.30/1.54 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(powersetE1_type,type,
% 0.30/1.54 powersetE1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(powersetE1,definition,
% 0.30/1.54 ( powersetE1
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( in @ B @ ( powerset @ A ) )
% 0.30/1.54 => ( subset @ B @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(inPowerset_type,type,
% 0.30/1.54 inPowerset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(inPowerset,definition,
% 0.30/1.54 ( inPowerset
% 0.30/1.54 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(powersetsubset_type,type,
% 0.30/1.54 powersetsubset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(powersetsubset,definition,
% 0.30/1.54 ( powersetsubset
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( subset @ A @ B )
% 0.30/1.54 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(sepInPowerset_type,type,
% 0.30/1.54 sepInPowerset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(sepInPowerset,definition,
% 0.30/1.54 ( sepInPowerset
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( in
% 0.30/1.54 @ ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 @ ( powerset @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(sepSubset_type,type,
% 0.30/1.54 sepSubset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(sepSubset,definition,
% 0.30/1.54 ( sepSubset
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( subset
% 0.30/1.54 @ ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 @ A ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binunion_type,type,
% 0.30/1.54 binunion: $i > $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(binunionIL_type,type,
% 0.30/1.54 binunionIL: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binunionIL,definition,
% 0.30/1.54 ( binunionIL
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(upairset2IR_type,type,
% 0.30/1.54 upairset2IR: $o ).
% 0.30/1.54
% 0.30/1.54 thf(upairset2IR,definition,
% 0.30/1.54 ( upairset2IR
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binunionIR_type,type,
% 0.30/1.54 binunionIR: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binunionIR,definition,
% 0.30/1.54 ( binunionIR
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ B )
% 0.30/1.54 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binunionEcases_type,type,
% 0.30/1.54 binunionEcases: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binunionEcases,definition,
% 0.30/1.54 ( binunionEcases
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.30/1.54 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/1.54 => ( ( ( in @ Xx @ A )
% 0.30/1.54 => Xphi )
% 0.30/1.54 => ( ( ( in @ Xx @ B )
% 0.30/1.54 => Xphi )
% 0.30/1.54 => Xphi ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binunionE_type,type,
% 0.30/1.54 binunionE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binunionE,definition,
% 0.30/1.54 ( binunionE
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/1.54 => ( ( in @ Xx @ A )
% 0.30/1.54 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binunionLsub_type,type,
% 0.30/1.54 binunionLsub: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binunionLsub,definition,
% 0.30/1.54 ( binunionLsub
% 0.30/1.54 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binunionRsub_type,type,
% 0.30/1.54 binunionRsub: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binunionRsub,definition,
% 0.30/1.54 ( binunionRsub
% 0.30/1.54 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binintersect_type,type,
% 0.30/1.54 binintersect: $i > $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectI_type,type,
% 0.30/1.54 binintersectI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectI,definition,
% 0.30/1.54 ( binintersectI
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ( in @ Xx @ B )
% 0.30/1.54 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectSubset5_type,type,
% 0.30/1.54 binintersectSubset5: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectSubset5,definition,
% 0.30/1.54 ( binintersectSubset5
% 0.30/1.54 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/1.54 ( ( subset @ C @ A )
% 0.30/1.54 => ( ( subset @ C @ B )
% 0.30/1.54 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectEL_type,type,
% 0.30/1.54 binintersectEL: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectEL,definition,
% 0.30/1.54 ( binintersectEL
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectLsub_type,type,
% 0.30/1.54 binintersectLsub: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectLsub,definition,
% 0.30/1.54 ( binintersectLsub
% 0.30/1.54 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectSubset2_type,type,
% 0.30/1.54 binintersectSubset2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectSubset2,definition,
% 0.30/1.54 ( binintersectSubset2
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( subset @ A @ B )
% 0.30/1.54 => ( ( binintersect @ A @ B )
% 0.30/1.54 = A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectSubset3_type,type,
% 0.30/1.54 binintersectSubset3: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectSubset3,definition,
% 0.30/1.54 ( binintersectSubset3
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( ( binintersect @ A @ B )
% 0.30/1.54 = B )
% 0.30/1.54 => ( subset @ B @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectER_type,type,
% 0.30/1.54 binintersectER: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectER,definition,
% 0.30/1.54 ( binintersectER
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/1.54 => ( in @ Xx @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(disjointsetsI1_type,type,
% 0.30/1.54 disjointsetsI1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(disjointsetsI1,definition,
% 0.30/1.54 ( disjointsetsI1
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ~ ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ( in @ Xx @ B ) )
% 0.30/1.54 => ( ( binintersect @ A @ B )
% 0.30/1.54 = emptyset ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectRsub_type,type,
% 0.30/1.54 binintersectRsub: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectRsub,definition,
% 0.30/1.54 ( binintersectRsub
% 0.30/1.54 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectSubset4_type,type,
% 0.30/1.54 binintersectSubset4: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectSubset4,definition,
% 0.30/1.54 ( binintersectSubset4
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( subset @ B @ A )
% 0.30/1.54 => ( ( binintersect @ A @ B )
% 0.30/1.54 = B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectSubset1_type,type,
% 0.30/1.54 binintersectSubset1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(binintersectSubset1,definition,
% 0.30/1.54 ( binintersectSubset1
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( ( binintersect @ A @ B )
% 0.30/1.54 = A )
% 0.30/1.54 => ( subset @ A @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(bs114d_type,type,
% 0.30/1.54 bs114d: $o ).
% 0.30/1.54
% 0.30/1.54 thf(bs114d,definition,
% 0.30/1.54 ( bs114d
% 0.30/1.54 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/1.54 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.30/1.54 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(regular_type,type,
% 0.30/1.54 regular: $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminus_type,type,
% 0.30/1.54 setminus: $i > $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(setminusI_type,type,
% 0.30/1.54 setminusI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminusI,definition,
% 0.30/1.54 ( setminusI
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ~ ( in @ Xx @ B )
% 0.30/1.54 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setminusEL_type,type,
% 0.30/1.54 setminusEL: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminusEL,definition,
% 0.30/1.54 ( setminusEL
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setminusER_type,type,
% 0.30/1.54 setminusER: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminusER,definition,
% 0.30/1.54 ( setminusER
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/1.54 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setminusSubset2_type,type,
% 0.30/1.54 setminusSubset2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminusSubset2,definition,
% 0.30/1.54 ( setminusSubset2
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( subset @ A @ B )
% 0.30/1.54 => ( ( setminus @ A @ B )
% 0.30/1.54 = emptyset ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setminusERneg_type,type,
% 0.30/1.54 setminusERneg: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminusERneg,definition,
% 0.30/1.54 ( setminusERneg
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/1.54 => ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setminusELneg_type,type,
% 0.30/1.54 setminusELneg: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminusELneg,definition,
% 0.30/1.54 ( setminusELneg
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/1.54 => ( ~ ( in @ Xx @ B )
% 0.30/1.54 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setminusILneg_type,type,
% 0.30/1.54 setminusILneg: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminusILneg,definition,
% 0.30/1.54 ( setminusILneg
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ~ ( in @ Xx @ A )
% 0.30/1.54 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setminusIRneg_type,type,
% 0.30/1.54 setminusIRneg: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminusIRneg,definition,
% 0.30/1.54 ( setminusIRneg
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ B )
% 0.30/1.54 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setminusLsub_type,type,
% 0.30/1.54 setminusLsub: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminusLsub,definition,
% 0.30/1.54 ( setminusLsub
% 0.30/1.54 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setminusSubset1_type,type,
% 0.30/1.54 setminusSubset1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setminusSubset1,definition,
% 0.30/1.54 ( setminusSubset1
% 0.30/1.54 = ( ! [A: $i,B: $i] :
% 0.30/1.54 ( ( ( setminus @ A @ B )
% 0.30/1.54 = emptyset )
% 0.30/1.54 => ( subset @ A @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(symdiff_type,type,
% 0.30/1.54 symdiff: $i > $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(symdiffE_type,type,
% 0.30/1.54 symdiffE: $o ).
% 0.30/1.54
% 0.30/1.54 thf(symdiffE,definition,
% 0.30/1.54 ( symdiffE
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.30/1.54 => ! [Xphi: $o] :
% 0.30/1.54 ( ( ( in @ Xx @ A )
% 0.30/1.54 => ( ~ ( in @ Xx @ B )
% 0.30/1.54 => Xphi ) )
% 0.30/1.54 => ( ( ~ ( in @ Xx @ A )
% 0.30/1.54 => ( ( in @ Xx @ B )
% 0.30/1.54 => Xphi ) )
% 0.30/1.54 => Xphi ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(symdiffI1_type,type,
% 0.30/1.54 symdiffI1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(symdiffI1,definition,
% 0.30/1.54 ( symdiffI1
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ~ ( in @ Xx @ B )
% 0.30/1.54 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(symdiffI2_type,type,
% 0.30/1.54 symdiffI2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(symdiffI2,definition,
% 0.30/1.54 ( symdiffI2
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ~ ( in @ Xx @ A )
% 0.30/1.54 => ( ( in @ Xx @ B )
% 0.30/1.54 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(symdiffIneg1_type,type,
% 0.30/1.54 symdiffIneg1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(symdiffIneg1,definition,
% 0.30/1.54 ( symdiffIneg1
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ( in @ Xx @ B )
% 0.30/1.54 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(symdiffIneg2_type,type,
% 0.30/1.54 symdiffIneg2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(symdiffIneg2,definition,
% 0.30/1.54 ( symdiffIneg2
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ~ ( in @ Xx @ A )
% 0.30/1.54 => ( ~ ( in @ Xx @ B )
% 0.30/1.54 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(iskpair_type,type,
% 0.30/1.54 iskpair: $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(secondinupair_type,type,
% 0.30/1.54 secondinupair: $o ).
% 0.30/1.54
% 0.30/1.54 thf(secondinupair,definition,
% 0.30/1.54 ( secondinupair
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairIL_type,type,
% 0.30/1.54 setukpairIL: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairIL,definition,
% 0.30/1.54 ( setukpairIL
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairIR_type,type,
% 0.30/1.54 setukpairIR: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairIR,definition,
% 0.30/1.54 ( setukpairIR
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(kpairiskpair_type,type,
% 0.30/1.54 kpairiskpair: $o ).
% 0.30/1.54
% 0.30/1.54 thf(kpairiskpair,definition,
% 0.30/1.54 ( kpairiskpair
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(kpair_type,type,
% 0.30/1.54 kpair: $i > $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(kpairp_type,type,
% 0.30/1.54 kpairp: $o ).
% 0.30/1.54
% 0.30/1.54 thf(kpairp,definition,
% 0.30/1.54 ( kpairp
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprod_type,type,
% 0.30/1.54 cartprod: $i > $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(singletonsubset_type,type,
% 0.30/1.54 singletonsubset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(singletonsubset,definition,
% 0.30/1.54 ( singletonsubset
% 0.30/1.54 = ( ! [A: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(singletoninpowerset_type,type,
% 0.30/1.54 singletoninpowerset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(singletoninpowerset,definition,
% 0.30/1.54 ( singletoninpowerset
% 0.30/1.54 = ( ! [A: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(singletoninpowunion_type,type,
% 0.30/1.54 singletoninpowunion: $o ).
% 0.30/1.54
% 0.30/1.54 thf(singletoninpowunion,definition,
% 0.30/1.54 ( singletoninpowunion
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(upairset2E_type,type,
% 0.30/1.54 upairset2E: $o ).
% 0.30/1.54
% 0.30/1.54 thf(upairset2E,definition,
% 0.30/1.54 ( upairset2E
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/1.54 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/1.54 => ( ( Xz = Xx )
% 0.30/1.54 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(upairsubunion_type,type,
% 0.30/1.54 upairsubunion: $o ).
% 0.30/1.54
% 0.30/1.54 thf(upairsubunion,definition,
% 0.30/1.54 ( upairsubunion
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(upairinpowunion_type,type,
% 0.30/1.54 upairinpowunion: $o ).
% 0.30/1.54
% 0.30/1.54 thf(upairinpowunion,definition,
% 0.30/1.54 ( upairinpowunion
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ubforcartprodlem1_type,type,
% 0.30/1.54 ubforcartprodlem1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(ubforcartprodlem1,definition,
% 0.30/1.54 ( ubforcartprodlem1
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ubforcartprodlem2_type,type,
% 0.30/1.54 ubforcartprodlem2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(ubforcartprodlem2,definition,
% 0.30/1.54 ( ubforcartprodlem2
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ubforcartprodlem3_type,type,
% 0.30/1.54 ubforcartprodlem3: $o ).
% 0.30/1.54
% 0.30/1.54 thf(ubforcartprodlem3,definition,
% 0.30/1.54 ( ubforcartprodlem3
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodpairin_type,type,
% 0.30/1.54 cartprodpairin: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodpairin,definition,
% 0.30/1.54 ( cartprodpairin
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodmempair1_type,type,
% 0.30/1.54 cartprodmempair1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodmempair1,definition,
% 0.30/1.54 ( cartprodmempair1
% 0.30/1.54 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/1.54 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/1.54 => ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ? [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 & ( Xu
% 0.30/1.54 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodmempair_type,type,
% 0.30/1.54 cartprodmempair: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodmempair,definition,
% 0.30/1.54 ( cartprodmempair
% 0.30/1.54 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/1.54 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/1.54 => ( iskpair @ Xu ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setunionE2_type,type,
% 0.30/1.54 setunionE2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setunionE2,definition,
% 0.30/1.54 ( setunionE2
% 0.30/1.54 = ( ! [A: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/1.54 => ? [X: $i] :
% 0.30/1.54 ( ( in @ X @ A )
% 0.30/1.54 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setunionsingleton1_type,type,
% 0.30/1.54 setunionsingleton1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setunionsingleton1,definition,
% 0.30/1.54 ( setunionsingleton1
% 0.30/1.54 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setunionsingleton2_type,type,
% 0.30/1.54 setunionsingleton2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setunionsingleton2,definition,
% 0.30/1.54 ( setunionsingleton2
% 0.30/1.54 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setunionsingleton_type,type,
% 0.30/1.54 setunionsingleton: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setunionsingleton,definition,
% 0.30/1.54 ( setunionsingleton
% 0.30/1.54 = ( ! [Xx: $i] :
% 0.30/1.54 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.30/1.54 = Xx ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(singleton_type,type,
% 0.30/1.54 singleton: $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(singleton,definition,
% 0.30/1.54 ( singleton
% 0.30/1.54 = ( ^ [A: $i] :
% 0.30/1.54 ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ( A
% 0.30/1.54 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(singletonprop_type,type,
% 0.30/1.54 singletonprop: $o ).
% 0.30/1.54
% 0.30/1.54 thf(singletonprop,definition,
% 0.30/1.54 ( singletonprop
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ A )
% 0.30/1.54 => ( ( Xphi @ Xx )
% 0.30/1.54 => ( ( Xphi @ Xy )
% 0.30/1.54 => ( Xx = Xy ) ) ) ) )
% 0.30/1.54 => ( ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ( Xphi @ Xx ) )
% 0.30/1.54 => ( singleton
% 0.30/1.54 @ ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ex1_type,type,
% 0.30/1.54 ex1: $i > ( $i > $o ) > $o ).
% 0.30/1.54
% 0.30/1.54 thf(ex1,definition,
% 0.30/1.54 ( ex1
% 0.30/1.54 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( singleton
% 0.30/1.54 @ ( dsetconstr @ A
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ex1E1_type,type,
% 0.30/1.54 ex1E1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(ex1E1,definition,
% 0.30/1.54 ( ex1E1
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ( ex1 @ A
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 => ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ex1I_type,type,
% 0.30/1.54 ex1I: $o ).
% 0.30/1.54
% 0.30/1.54 thf(ex1I,definition,
% 0.30/1.54 ( ex1I
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ( Xphi @ Xx )
% 0.30/1.54 => ( ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ A )
% 0.30/1.54 => ( ( Xphi @ Xy )
% 0.30/1.54 => ( Xy = Xx ) ) )
% 0.30/1.54 => ( ex1 @ A
% 0.30/1.54 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ex1I2_type,type,
% 0.30/1.54 ex1I2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(ex1I2,definition,
% 0.30/1.54 ( ex1I2
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ A )
% 0.30/1.54 => ( ( Xphi @ Xx )
% 0.30/1.54 => ( ( Xphi @ Xy )
% 0.30/1.54 => ( Xx = Xy ) ) ) ) )
% 0.30/1.54 => ( ? [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 & ( Xphi @ Xx ) )
% 0.30/1.54 => ( ex1 @ A
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(singletonsuniq_type,type,
% 0.30/1.54 singletonsuniq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(singletonsuniq,definition,
% 0.30/1.54 ( singletonsuniq
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( ( setadjoin @ Xx @ emptyset )
% 0.30/1.54 = ( setadjoin @ Xy @ emptyset ) )
% 0.30/1.54 => ( Xx = Xy ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(atmost1p_type,type,
% 0.30/1.54 atmost1p: $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(atleast2p_type,type,
% 0.30/1.54 atleast2p: $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(atmost2p_type,type,
% 0.30/1.54 atmost2p: $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(upairsetp_type,type,
% 0.30/1.54 upairsetp: $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjL1_type,type,
% 0.30/1.54 setukpairinjL1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjL1,definition,
% 0.30/1.54 ( setukpairinjL1
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/1.54 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.30/1.54 => ( Xx = Xz ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(kfstsingleton_type,type,
% 0.30/1.54 kfstsingleton: $o ).
% 0.30/1.54
% 0.30/1.54 thf(kfstsingleton,definition,
% 0.30/1.54 ( kfstsingleton
% 0.30/1.54 = ( ! [Xu: $i] :
% 0.30/1.54 ( ( iskpair @ Xu )
% 0.30/1.54 => ( singleton
% 0.30/1.54 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/1.54 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(theprop_type,type,
% 0.30/1.54 theprop: $o ).
% 0.30/1.54
% 0.30/1.54 thf(theprop,definition,
% 0.30/1.54 ( theprop
% 0.30/1.54 = ( ! [X: $i] :
% 0.30/1.54 ( ( singleton @ X )
% 0.30/1.54 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(kfst_type,type,
% 0.30/1.54 kfst: $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(kfstpairEq_type,type,
% 0.30/1.54 kfstpairEq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(kfstpairEq,definition,
% 0.30/1.54 ( kfstpairEq
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.30/1.54 = Xx ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodfstin_type,type,
% 0.30/1.54 cartprodfstin: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodfstin,definition,
% 0.30/1.54 ( cartprodfstin
% 0.30/1.54 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/1.54 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/1.54 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjL2_type,type,
% 0.30/1.54 setukpairinjL2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjL2,definition,
% 0.30/1.54 ( setukpairinjL2
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/1.54 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/1.54 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/1.54 => ( Xx = Xz ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjL_type,type,
% 0.30/1.54 setukpairinjL: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjL,definition,
% 0.30/1.54 ( setukpairinjL
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/1.54 ( ( ( kpair @ Xx @ Xy )
% 0.30/1.54 = ( kpair @ Xz @ Xu ) )
% 0.30/1.54 => ( Xx = Xz ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjR11_type,type,
% 0.30/1.54 setukpairinjR11: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjR11,definition,
% 0.30/1.54 ( setukpairinjR11
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xx = Xy )
% 0.30/1.54 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/1.54 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjR12_type,type,
% 0.30/1.54 setukpairinjR12: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjR12,definition,
% 0.30/1.54 ( setukpairinjR12
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xx = Xy )
% 0.30/1.54 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/1.54 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjR1_type,type,
% 0.30/1.54 setukpairinjR1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjR1,definition,
% 0.30/1.54 ( setukpairinjR1
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/1.54 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/1.54 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/1.54 => ( ( Xz = Xu )
% 0.30/1.54 => ( Xy = Xu ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(upairequniteq_type,type,
% 0.30/1.54 upairequniteq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(upairequniteq,definition,
% 0.30/1.54 ( upairequniteq
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/1.54 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/1.54 = ( setadjoin @ Xz @ emptyset ) )
% 0.30/1.54 => ( Xx = Xy ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjR2_type,type,
% 0.30/1.54 setukpairinjR2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjR2,definition,
% 0.30/1.54 ( setukpairinjR2
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/1.54 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.30/1.54 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.30/1.54 => ( Xy = Xu ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjR_type,type,
% 0.30/1.54 setukpairinjR: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setukpairinjR,definition,
% 0.30/1.54 ( setukpairinjR
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.30/1.54 ( ( ( kpair @ Xx @ Xy )
% 0.30/1.54 = ( kpair @ Xz @ Xu ) )
% 0.30/1.54 => ( Xy = Xu ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ksndsingleton_type,type,
% 0.30/1.54 ksndsingleton: $o ).
% 0.30/1.54
% 0.30/1.54 thf(ksndsingleton,definition,
% 0.30/1.54 ( ksndsingleton
% 0.30/1.54 = ( ! [Xu: $i] :
% 0.30/1.54 ( ( iskpair @ Xu )
% 0.30/1.54 => ( singleton
% 0.30/1.54 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/1.54 @ ^ [Xx: $i] :
% 0.30/1.54 ( Xu
% 0.30/1.54 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ksnd_type,type,
% 0.30/1.54 ksnd: $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(ksndpairEq_type,type,
% 0.30/1.54 ksndpairEq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(ksndpairEq,definition,
% 0.30/1.54 ( ksndpairEq
% 0.30/1.54 = ( ! [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.30/1.54 = Xy ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(kpairsurjEq_type,type,
% 0.30/1.54 kpairsurjEq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(kpairsurjEq,definition,
% 0.30/1.54 ( kpairsurjEq
% 0.30/1.54 = ( ! [Xu: $i] :
% 0.30/1.54 ( ( iskpair @ Xu )
% 0.30/1.54 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.30/1.54 = Xu ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodsndin_type,type,
% 0.30/1.54 cartprodsndin: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodsndin,definition,
% 0.30/1.54 ( cartprodsndin
% 0.30/1.54 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/1.54 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/1.54 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodpairmemEL_type,type,
% 0.30/1.54 cartprodpairmemEL: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodpairmemEL,definition,
% 0.30/1.54 ( cartprodpairmemEL
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.30/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodpairmemER_type,type,
% 0.30/1.54 cartprodpairmemER: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodpairmemER,definition,
% 0.30/1.54 ( cartprodpairmemER
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.30/1.54 => ( in @ Xy @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodmempaircEq_type,type,
% 0.30/1.54 cartprodmempaircEq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodmempaircEq,definition,
% 0.30/1.54 ( cartprodmempaircEq
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( kpair @ Xx @ Xy )
% 0.30/1.54 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodfstpairEq_type,type,
% 0.30/1.54 cartprodfstpairEq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodfstpairEq,definition,
% 0.30/1.54 ( cartprodfstpairEq
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.30/1.54 = Xx ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodsndpairEq_type,type,
% 0.30/1.54 cartprodsndpairEq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodsndpairEq,definition,
% 0.30/1.54 ( cartprodsndpairEq
% 0.30/1.54 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.30/1.54 = Xy ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodpairsurjEq_type,type,
% 0.30/1.54 cartprodpairsurjEq: $o ).
% 0.30/1.54
% 0.30/1.54 thf(cartprodpairsurjEq,definition,
% 0.30/1.54 ( cartprodpairsurjEq
% 0.30/1.54 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/1.54 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/1.54 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.30/1.54 = Xu ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(breln_type,type,
% 0.30/1.54 breln: $i > $i > $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(breln,definition,
% 0.30/1.54 ( breln
% 0.30/1.54 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstr_type,type,
% 0.30/1.54 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrI_type,type,
% 0.30/1.54 dpsetconstrI: $o ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrI,definition,
% 0.30/1.54 ( dpsetconstrI
% 0.30/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( Xphi @ Xx @ Xy )
% 0.30/1.54 => ( in @ ( kpair @ Xx @ Xy )
% 0.30/1.54 @ ( dpsetconstr @ A @ B
% 0.30/1.54 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrSub_type,type,
% 0.30/1.54 dpsetconstrSub: $o ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrSub,definition,
% 0.30/1.54 ( dpsetconstrSub
% 0.30/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/1.54 ( subset
% 0.30/1.54 @ ( dpsetconstr @ A @ B
% 0.30/1.54 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.30/1.54 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(setOfPairsIsBReln_type,type,
% 0.30/1.54 setOfPairsIsBReln: $o ).
% 0.30/1.54
% 0.30/1.54 thf(setOfPairsIsBReln,definition,
% 0.30/1.54 ( setOfPairsIsBReln
% 0.30/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.30/1.54 ( breln @ A @ B
% 0.30/1.54 @ ( dpsetconstr @ A @ B
% 0.30/1.54 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrERa_type,type,
% 0.30/1.54 dpsetconstrERa: $o ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrERa,definition,
% 0.30/1.54 ( dpsetconstrERa
% 0.30/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/1.54 @ ( dpsetconstr @ A @ B
% 0.30/1.54 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/1.54 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrEL1_type,type,
% 0.30/1.54 dpsetconstrEL1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrEL1,definition,
% 0.30/1.54 ( dpsetconstrEL1
% 0.30/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/1.54 @ ( dpsetconstr @ A @ B
% 0.30/1.54 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/1.54 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrEL2_type,type,
% 0.30/1.54 dpsetconstrEL2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrEL2,definition,
% 0.30/1.54 ( dpsetconstrEL2
% 0.30/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/1.54 @ ( dpsetconstr @ A @ B
% 0.30/1.54 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/1.54 => ( in @ Xy @ B ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrER_type,type,
% 0.30/1.54 dpsetconstrER: $o ).
% 0.30/1.54
% 0.30/1.54 thf(dpsetconstrER,definition,
% 0.30/1.54 ( dpsetconstrER
% 0.30/1.54 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( in @ ( kpair @ Xx @ Xy )
% 0.30/1.54 @ ( dpsetconstr @ A @ B
% 0.30/1.54 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.30/1.54 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(func_type,type,
% 0.30/1.54 func: $i > $i > $i > $o ).
% 0.30/1.54
% 0.30/1.54 thf(func,definition,
% 0.30/1.54 ( func
% 0.30/1.54 = ( ^ [A: $i,B: $i,R: $i] :
% 0.30/1.54 ( ( breln @ A @ B @ R )
% 0.30/1.54 & ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ex1 @ B
% 0.30/1.54 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(funcSet_type,type,
% 0.30/1.54 funcSet: $i > $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(funcImageSingleton_type,type,
% 0.30/1.54 funcImageSingleton: $o ).
% 0.30/1.54
% 0.30/1.54 thf(funcImageSingleton,definition,
% 0.30/1.54 ( funcImageSingleton
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( func @ A @ B @ Xf )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( singleton
% 0.30/1.54 @ ( dsetconstr @ B
% 0.30/1.54 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(apProp_type,type,
% 0.30/1.54 apProp: $o ).
% 0.30/1.54
% 0.30/1.54 thf(apProp,definition,
% 0.30/1.54 ( apProp
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( func @ A @ B @ Xf )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in
% 0.30/1.54 @ ( setunion
% 0.30/1.54 @ ( dsetconstr @ B
% 0.30/1.54 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.30/1.54 @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ap_type,type,
% 0.30/1.54 ap: $i > $i > $i > $i > $i ).
% 0.30/1.54
% 0.30/1.54 thf(app_type,type,
% 0.30/1.54 app: $o ).
% 0.30/1.54
% 0.30/1.54 thf(app,definition,
% 0.30/1.54 ( app
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( func @ A @ B @ Xf )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(infuncsetfunc_type,type,
% 0.30/1.54 infuncsetfunc: $o ).
% 0.30/1.54
% 0.30/1.54 thf(infuncsetfunc,definition,
% 0.30/1.54 ( infuncsetfunc
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/1.54 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ap2p_type,type,
% 0.30/1.54 ap2p: $o ).
% 0.30/1.54
% 0.30/1.54 thf(ap2p,definition,
% 0.30/1.54 ( ap2p
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(funcinfuncset_type,type,
% 0.30/1.54 funcinfuncset: $o ).
% 0.30/1.54
% 0.30/1.54 thf(funcinfuncset,definition,
% 0.30/1.54 ( funcinfuncset
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( func @ A @ B @ Xf )
% 0.30/1.54 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(lamProp_type,type,
% 0.30/1.54 lamProp: $o ).
% 0.30/1.54
% 0.30/1.54 thf(lamProp,definition,
% 0.30/1.54 ( lamProp
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/1.54 => ( func @ A @ B
% 0.30/1.54 @ ( dpsetconstr @ A @ B
% 0.30/1.54 @ ^ [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xf @ Xx )
% 0.30/1.54 = Xy ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(lam_type,type,
% 0.30/1.54 lam: $i > $i > ( $i > $i ) > $i ).
% 0.30/1.54
% 0.30/1.54 thf(lam,definition,
% 0.30/1.54 ( lam
% 0.30/1.54 = ( ^ [A: $i,B: $i,Xf: $i > $i] :
% 0.30/1.54 ( dpsetconstr @ A @ B
% 0.30/1.54 @ ^ [Xx: $i,Xy: $i] :
% 0.30/1.54 ( ( Xf @ Xx )
% 0.30/1.54 = Xy ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(lamp_type,type,
% 0.30/1.54 lamp: $o ).
% 0.30/1.54
% 0.30/1.54 thf(lamp,definition,
% 0.30/1.54 ( lamp
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/1.54 => ( func @ A @ B
% 0.30/1.54 @ ( lam @ A @ B
% 0.30/1.54 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(lam2p_type,type,
% 0.30/1.54 lam2p: $o ).
% 0.30/1.54
% 0.30/1.54 thf(lam2p,definition,
% 0.30/1.54 ( lam2p
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.30/1.54 => ( in
% 0.30/1.54 @ ( lam @ A @ B
% 0.30/1.54 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.30/1.54 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(brelnall1_type,type,
% 0.30/1.54 brelnall1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(brelnall1,definition,
% 0.30/1.54 ( brelnall1
% 0.30/1.54 = ( ! [A: $i,B: $i,R: $i] :
% 0.30/1.54 ( ( breln @ A @ B @ R )
% 0.30/1.54 => ! [Xphi: $i > $o] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/1.54 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ R )
% 0.30/1.54 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(brelnall2_type,type,
% 0.30/1.54 brelnall2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(brelnall2,definition,
% 0.30/1.54 ( brelnall2
% 0.30/1.54 = ( ! [A: $i,B: $i,R: $i] :
% 0.30/1.54 ( ( breln @ A @ B @ R )
% 0.30/1.54 => ! [Xphi: $i > $o] :
% 0.30/1.54 ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/1.54 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ R )
% 0.30/1.54 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(ex1E2_type,type,
% 0.30/1.54 ex1E2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(ex1E2,definition,
% 0.30/1.54 ( ex1E2
% 0.30/1.54 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/1.54 ( ( ex1 @ A
% 0.30/1.54 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ A )
% 0.30/1.54 => ( ( Xphi @ Xx )
% 0.30/1.54 => ( ( Xphi @ Xy )
% 0.30/1.54 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(funcGraphProp1_type,type,
% 0.30/1.54 funcGraphProp1: $o ).
% 0.30/1.54
% 0.30/1.54 thf(funcGraphProp1,definition,
% 0.30/1.54 ( funcGraphProp1
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( func @ A @ B @ Xf )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(funcGraphProp3_type,type,
% 0.30/1.54 funcGraphProp3: $o ).
% 0.30/1.54
% 0.30/1.54 thf(funcGraphProp3,definition,
% 0.30/1.54 ( funcGraphProp3
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(funcGraphProp2_type,type,
% 0.30/1.54 funcGraphProp2: $o ).
% 0.30/1.54
% 0.30/1.54 thf(funcGraphProp2,definition,
% 0.30/1.54 ( funcGraphProp2
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( func @ A @ B @ Xf )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.30/1.54 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/1.54 = Xy ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(funcextLem_type,type,
% 0.30/1.54 funcextLem: $o ).
% 0.30/1.54
% 0.30/1.54 thf(funcextLem,definition,
% 0.30/1.54 ( funcextLem
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( func @ A @ B @ Xf )
% 0.30/1.54 => ! [Xg: $i] :
% 0.30/1.54 ( ( func @ A @ B @ Xg )
% 0.30/1.54 => ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/1.54 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.30/1.54 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(funcGraphProp4_type,type,
% 0.30/1.54 funcGraphProp4: $o ).
% 0.30/1.54
% 0.30/1.54 thf(funcGraphProp4,definition,
% 0.30/1.54 ( funcGraphProp4
% 0.30/1.54 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.30/1.54 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.30/1.54 => ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.30/1.54 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.30/1.54 = Xy ) ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(subbreln_type,type,
% 0.30/1.54 subbreln: $o ).
% 0.30/1.54
% 0.30/1.54 thf(subbreln,definition,
% 0.30/1.54 ( subbreln
% 0.30/1.54 = ( ! [A: $i,B: $i,R: $i] :
% 0.30/1.54 ( ( breln @ A @ B @ R )
% 0.30/1.54 => ! [S: $i] :
% 0.30/1.54 ( ( breln @ A @ B @ S )
% 0.30/1.54 => ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/1.54 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.30/1.54 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.30/1.54
% 0.30/1.54 thf(eqbreln,conjecture,
% 0.30/1.54 ( setextAx
% 0.30/1.54 => ( emptysetAx
% 0.30/1.54 => ( setadjoinAx
% 0.30/1.54 => ( powersetAx
% 0.30/1.54 => ( setunionAx
% 0.30/1.54 => ( omega0Ax
% 0.30/1.54 => ( omegaSAx
% 0.30/1.54 => ( omegaIndAx
% 0.30/1.54 => ( replAx
% 0.30/1.54 => ( foundationAx
% 0.30/1.54 => ( wellorderingAx
% 0.30/1.54 => ( descrp
% 0.30/1.54 => ( dsetconstrI
% 0.30/1.54 => ( dsetconstrEL
% 0.30/1.54 => ( dsetconstrER
% 0.30/1.54 => ( exuE1
% 0.30/1.54 => ( prop2setE
% 0.30/1.54 => ( emptysetE
% 0.30/1.54 => ( emptysetimpfalse
% 0.30/1.54 => ( notinemptyset
% 0.30/1.54 => ( exuE3e
% 0.30/1.54 => ( setext
% 0.30/1.54 => ( emptyI
% 0.30/1.54 => ( noeltsimpempty
% 0.30/1.54 => ( setbeta
% 0.30/1.54 => ( nonemptyE1
% 0.30/1.54 => ( nonemptyI
% 0.30/1.54 => ( nonemptyI1
% 0.30/1.54 => ( setadjoinIL
% 0.30/1.54 => ( emptyinunitempty
% 0.30/1.54 => ( setadjoinIR
% 0.30/1.54 => ( setadjoinE
% 0.30/1.54 => ( setadjoinOr
% 0.30/1.54 => ( setoftrueEq
% 0.30/1.54 => ( powersetI
% 0.30/1.54 => ( emptyinPowerset
% 0.30/1.54 => ( emptyInPowerset
% 0.30/1.54 => ( powersetE
% 0.30/1.54 => ( setunionI
% 0.30/1.54 => ( setunionE
% 0.30/1.54 => ( subPowSU
% 0.30/1.54 => ( exuE2
% 0.30/1.54 => ( nonemptyImpWitness
% 0.30/1.54 => ( uniqinunit
% 0.30/1.54 => ( notinsingleton
% 0.30/1.54 => ( eqinunit
% 0.30/1.54 => ( singletonsswitch
% 0.30/1.54 => ( upairsetE
% 0.30/1.54 => ( upairsetIL
% 0.30/1.54 => ( upairsetIR
% 0.30/1.54 => ( emptyE1
% 0.30/1.54 => ( vacuousDall
% 0.30/1.54 => ( quantDeMorgan1
% 0.30/1.54 => ( quantDeMorgan2
% 0.30/1.54 => ( quantDeMorgan3
% 0.30/1.54 => ( quantDeMorgan4
% 0.30/1.54 => ( prop2setI
% 0.30/1.54 => ( prop2set2propI
% 0.30/1.54 => ( notdexE
% 0.30/1.54 => ( notdallE
% 0.30/1.54 => ( exuI1
% 0.30/1.54 => ( exuI3
% 0.30/1.54 => ( exuI2
% 0.30/1.54 => ( inCongP
% 0.30/1.54 => ( in__Cong
% 0.30/1.54 => ( exuE3u
% 0.30/1.54 => ( exu__Cong
% 0.30/1.54 => ( emptyset__Cong
% 0.30/1.54 => ( setadjoin__Cong
% 0.30/1.54 => ( powerset__Cong
% 0.30/1.54 => ( setunion__Cong
% 0.30/1.54 => ( omega__Cong
% 0.30/1.54 => ( exuEu
% 0.30/1.54 => ( descr__Cong
% 0.30/1.54 => ( dsetconstr__Cong
% 0.30/1.54 => ( subsetI1
% 0.30/1.54 => ( eqimpsubset2
% 0.30/1.54 => ( eqimpsubset1
% 0.30/1.54 => ( subsetI2
% 0.30/1.54 => ( emptysetsubset
% 0.30/1.54 => ( subsetE
% 0.30/1.54 => ( subsetE2
% 0.30/1.54 => ( notsubsetI
% 0.30/1.54 => ( notequalI1
% 0.30/1.54 => ( notequalI2
% 0.30/1.54 => ( subsetRefl
% 0.30/1.54 => ( subsetTrans
% 0.30/1.54 => ( setadjoinSub
% 0.30/1.54 => ( setadjoinSub2
% 0.30/1.54 => ( subset2powerset
% 0.30/1.54 => ( setextsub
% 0.30/1.54 => ( subsetemptysetimpeq
% 0.30/1.54 => ( powersetI1
% 0.30/1.54 => ( powersetE1
% 0.30/1.54 => ( inPowerset
% 0.30/1.54 => ( powersetsubset
% 0.30/1.54 => ( sepInPowerset
% 0.30/1.54 => ( sepSubset
% 0.30/1.54 => ( binunionIL
% 0.30/1.54 => ( upairset2IR
% 0.30/1.54 => ( binunionIR
% 0.30/1.54 => ( binunionEcases
% 0.30/1.54 => ( binunionE
% 0.30/1.54 => ( binunionLsub
% 0.30/1.54 => ( binunionRsub
% 0.30/1.54 => ( binintersectI
% 0.30/1.54 => ( binintersectSubset5
% 0.30/1.54 => ( binintersectEL
% 0.30/1.54 => ( binintersectLsub
% 0.30/1.54 => ( binintersectSubset2
% 0.30/1.54 => ( binintersectSubset3
% 0.30/1.54 => ( binintersectER
% 0.30/1.54 => ( disjointsetsI1
% 0.30/1.54 => ( binintersectRsub
% 0.30/1.54 => ( binintersectSubset4
% 0.30/1.54 => ( binintersectSubset1
% 0.30/1.54 => ( bs114d
% 0.30/1.54 => ( setminusI
% 0.30/1.54 => ( setminusEL
% 0.30/1.54 => ( setminusER
% 0.30/1.54 => ( setminusSubset2
% 0.30/1.54 => ( setminusERneg
% 0.30/1.54 => ( setminusELneg
% 0.30/1.54 => ( setminusILneg
% 0.30/1.54 => ( setminusIRneg
% 0.30/1.54 => ( setminusLsub
% 0.30/1.54 => ( setminusSubset1
% 0.30/1.54 => ( symdiffE
% 0.30/1.54 => ( symdiffI1
% 0.30/1.54 => ( symdiffI2
% 0.30/1.54 => ( symdiffIneg1
% 0.30/1.54 => ( symdiffIneg2
% 0.30/1.54 => ( secondinupair
% 0.30/1.54 => ( setukpairIL
% 0.30/1.54 => ( setukpairIR
% 0.30/1.54 => ( kpairiskpair
% 0.30/1.54 => ( kpairp
% 0.30/1.54 => ( singletonsubset
% 0.30/1.54 => ( singletoninpowerset
% 0.30/1.54 => ( singletoninpowunion
% 0.30/1.54 => ( upairset2E
% 0.30/1.54 => ( upairsubunion
% 0.30/1.54 => ( upairinpowunion
% 0.30/1.54 => ( ubforcartprodlem1
% 0.30/1.54 => ( ubforcartprodlem2
% 0.30/1.54 => ( ubforcartprodlem3
% 0.30/1.54 => ( cartprodpairin
% 0.30/1.54 => ( cartprodmempair1
% 0.30/1.54 => ( cartprodmempair
% 0.30/1.54 => ( setunionE2
% 0.30/1.54 => ( setunionsingleton1
% 0.30/1.54 => ( setunionsingleton2
% 0.30/1.54 => ( setunionsingleton
% 0.30/1.54 => ( singletonprop
% 0.30/1.54 => ( ex1E1
% 0.30/1.54 => ( ex1I
% 0.30/1.54 => ( ex1I2
% 0.30/1.54 => ( singletonsuniq
% 0.30/1.54 => ( setukpairinjL1
% 0.30/1.54 => ( kfstsingleton
% 0.30/1.54 => ( theprop
% 0.30/1.54 => ( kfstpairEq
% 0.30/1.54 => ( cartprodfstin
% 0.30/1.54 => ( setukpairinjL2
% 0.30/1.54 => ( setukpairinjL
% 0.30/1.54 => ( setukpairinjR11
% 0.30/1.54 => ( setukpairinjR12
% 0.30/1.54 => ( setukpairinjR1
% 0.30/1.54 => ( upairequniteq
% 0.30/1.54 => ( setukpairinjR2
% 0.30/1.54 => ( setukpairinjR
% 0.30/1.54 => ( ksndsingleton
% 0.30/1.54 => ( ksndpairEq
% 0.30/1.54 => ( kpairsurjEq
% 0.30/1.54 => ( cartprodsndin
% 0.30/1.54 => ( cartprodpairmemEL
% 0.30/1.54 => ( cartprodpairmemER
% 0.30/1.54 => ( cartprodmempaircEq
% 0.30/1.54 => ( cartprodfstpairEq
% 0.30/1.54 => ( cartprodsndpairEq
% 0.30/1.54 => ( cartprodpairsurjEq
% 0.30/1.54 => ( dpsetconstrI
% 0.30/1.54 => ( dpsetconstrSub
% 0.30/1.54 => ( setOfPairsIsBReln
% 0.30/1.54 => ( dpsetconstrERa
% 0.30/1.54 => ( dpsetconstrEL1
% 0.30/1.54 => ( dpsetconstrEL2
% 0.30/1.54 => ( dpsetconstrER
% 0.30/1.54 => ( funcImageSingleton
% 0.30/1.54 => ( apProp
% 0.30/1.54 => ( app
% 0.30/1.54 => ( infuncsetfunc
% 0.30/1.54 => ( ap2p
% 0.30/1.54 => ( funcinfuncset
% 0.30/1.54 => ( lamProp
% 0.30/1.54 => ( lamp
% 0.30/1.54 => ( lam2p
% 0.30/1.54 => ( brelnall1
% 0.30/1.54 => ( brelnall2
% 0.30/1.54 => ( ex1E2
% 0.30/1.54 => ( funcGraphProp1
% 0.30/1.54 => ( funcGraphProp3
% 0.30/1.54 => ( funcGraphProp2
% 0.30/1.54 => ( funcextLem
% 0.30/1.54 => ( funcGraphProp4
% 0.30/1.54 => ( subbreln
% 0.30/1.54 => ! [A: $i,B: $i,R: $i] :
% 0.30/1.54 ( ( breln @ A @ B @ R )
% 0.30/1.54 => ! [S: $i] :
% 0.30/1.54 ( ( breln @ A @ B @ S )
% 0.30/1.54 => ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.30/1.54 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.30/1.54 => ( ! [Xx: $i] :
% 0.30/1.54 ( ( in @ Xx @ A )
% 0.30/1.54 => ! [Xy: $i] :
% 0.30/1.54 ( ( in @ Xy @ B )
% 0.30/1.54 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.30/1.54 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.30/1.54 => ( R = S ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/1.54 ------------------------
% 0.30/1.57 % (5314)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_5039 for (2999ds/4Mi)
% 0.30/1.57 % (5313)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/183Mi)
% 0.30/1.57 % (5314)Instruction limit reached!
% 0.30/1.57 % (5314)------------------------------
% 0.30/1.57 % (5314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.57 % (5314)Termination reason: Unknown
% 0.30/1.57 % (5314)Termination phase: shuffling
% 0.30/1.57
% 0.30/1.57 % (5314)Memory used [KB]: 1407
% 0.30/1.57 % (5314)Time elapsed: 0.003 s
% 0.30/1.57 % (5314)Instructions burned: 4 (million)
% 0.30/1.57 % (5314)------------------------------
% 0.30/1.57 % (5314)------------------------------
% 0.30/1.58 % (5315)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_5039 for (2999ds/27Mi)
% 0.30/1.58 % (5316)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/2Mi)
% 0.30/1.58 % (5317)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_5039 for (2999ds/2Mi)
% 0.30/1.58 % (5318)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_5039 for (2999ds/275Mi)
% 0.30/1.58 % (5319)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/18Mi)
% 0.30/1.58 % (5316)Instruction limit reached!
% 0.30/1.58 % (5316)------------------------------
% 0.30/1.58 % (5316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.58 % (5316)Termination reason: Unknown
% 0.30/1.58 % (5316)Termination phase: shuffling
% 0.30/1.58
% 0.30/1.58 % (5316)Memory used [KB]: 1407
% 0.30/1.58 % (5316)Time elapsed: 0.004 s
% 0.30/1.58 % (5316)Instructions burned: 3 (million)
% 0.30/1.58 % (5316)------------------------------
% 0.30/1.58 % (5316)------------------------------
% 0.30/1.58 % (5317)Instruction limit reached!
% 0.30/1.58 % (5317)------------------------------
% 0.30/1.58 % (5317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.58 % (5317)Termination reason: Unknown
% 0.30/1.58 % (5317)Termination phase: shuffling
% 0.30/1.58
% 0.30/1.58 % (5317)Memory used [KB]: 1407
% 0.30/1.58 % (5317)Time elapsed: 0.004 s
% 0.30/1.58 % (5317)Instructions burned: 3 (million)
% 0.30/1.58 % (5317)------------------------------
% 0.30/1.58 % (5317)------------------------------
% 0.30/1.58 % (5320)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/3Mi)
% 0.30/1.58 % (5320)Instruction limit reached!
% 0.30/1.58 % (5320)------------------------------
% 0.30/1.58 % (5320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.58 % (5320)Termination reason: Unknown
% 0.30/1.58 % (5320)Termination phase: shuffling
% 0.30/1.58
% 0.30/1.58 % (5320)Memory used [KB]: 1407
% 0.30/1.58 % (5320)Time elapsed: 0.002 s
% 0.30/1.58 % (5320)Instructions burned: 3 (million)
% 0.30/1.58 % (5320)------------------------------
% 0.30/1.58 % (5320)------------------------------
% 0.30/1.59 % (5319)Instruction limit reached!
% 0.30/1.59 % (5319)------------------------------
% 0.30/1.59 % (5319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (5319)Termination reason: Unknown
% 0.30/1.59 % (5319)Termination phase: shuffling
% 0.30/1.59
% 0.30/1.59 % (5319)Memory used [KB]: 1791
% 0.30/1.59 % (5319)Time elapsed: 0.014 s
% 0.30/1.59 % (5319)Instructions burned: 19 (million)
% 0.30/1.59 % (5319)------------------------------
% 0.30/1.59 % (5319)------------------------------
% 0.30/1.59 % (5323)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_5039 for (2999ds/3Mi)
% 0.30/1.59 % (5323)Instruction limit reached!
% 0.30/1.59 % (5323)------------------------------
% 0.30/1.59 % (5323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (5323)Termination reason: Unknown
% 0.30/1.59 % (5323)Termination phase: shuffling
% 0.30/1.59
% 0.30/1.59 % (5323)Memory used [KB]: 1407
% 0.30/1.59 % (5323)Time elapsed: 0.002 s
% 0.30/1.59 % (5323)Instructions burned: 3 (million)
% 0.30/1.59 % (5323)------------------------------
% 0.30/1.59 % (5323)------------------------------
% 0.30/1.59 % (5315)Instruction limit reached!
% 0.30/1.59 % (5315)------------------------------
% 0.30/1.59 % (5315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.30/1.59 % (5315)Termination reason: Unknown
% 0.30/1.59 % (5315)Termination phase: shuffling
% 0.30/1.59
% 0.30/1.59 % (5315)Memory used [KB]: 1918
% 0.30/1.59 % (5315)Time elapsed: 0.017 s
% 0.30/1.59 % (5315)Instructions burned: 28 (million)
% 0.30/1.59 % (5315)------------------------------
% 0.30/1.59 % (5315)------------------------------
% 2.74/1.60 % (5321)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_5039 for (2999ds/37Mi)
% 2.74/1.60 % (5322)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_5039 for (2999ds/15Mi)
% 2.74/1.60 % (5325)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/7Mi)
% 2.74/1.60 % (5324)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_5039 for (2999ds/1041Mi)
% 2.74/1.60 % (5325)Instruction limit reached!
% 2.74/1.60 % (5325)------------------------------
% 2.74/1.60 % (5325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.60 % (5325)Termination reason: Unknown
% 2.74/1.60 % (5325)Termination phase: shuffling
% 2.74/1.60
% 2.74/1.60 % (5325)Memory used [KB]: 1407
% 2.74/1.60 % (5325)Time elapsed: 0.003 s
% 2.74/1.60 % (5325)Instructions burned: 7 (million)
% 2.74/1.60 % (5325)------------------------------
% 2.74/1.60 % (5325)------------------------------
% 2.74/1.61 % (5322)Instruction limit reached!
% 2.74/1.61 % (5322)------------------------------
% 2.74/1.61 % (5322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (5322)Termination reason: Unknown
% 2.74/1.61 % (5322)Termination phase: shuffling
% 2.74/1.61
% 2.74/1.61 % (5322)Memory used [KB]: 1663
% 2.74/1.61 % (5322)Time elapsed: 0.011 s
% 2.74/1.61 % (5322)Instructions burned: 15 (million)
% 2.74/1.61 % (5322)------------------------------
% 2.74/1.61 % (5322)------------------------------
% 2.74/1.61 % (5326)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/16Mi)
% 2.74/1.61 % (5327)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_5039 for (2999ds/3Mi)
% 2.74/1.61 % (5327)Instruction limit reached!
% 2.74/1.61 % (5327)------------------------------
% 2.74/1.61 % (5327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.61 % (5327)Termination reason: Unknown
% 2.74/1.61 % (5327)Termination phase: shuffling
% 2.74/1.61
% 2.74/1.61 % (5327)Memory used [KB]: 1407
% 2.74/1.61 % (5327)Time elapsed: 0.002 s
% 2.74/1.61 % (5327)Instructions burned: 3 (million)
% 2.74/1.61 % (5327)------------------------------
% 2.74/1.61 % (5327)------------------------------
% 2.74/1.62 % (5321)Instruction limit reached!
% 2.74/1.62 % (5321)------------------------------
% 2.74/1.62 % (5321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (5321)Termination reason: Unknown
% 2.74/1.62 % (5321)Termination phase: Property scanning
% 2.74/1.62
% 2.74/1.62 % (5321)Memory used [KB]: 2174
% 2.74/1.62 % (5321)Time elapsed: 0.021 s
% 2.74/1.62 % (5321)Instructions burned: 38 (million)
% 2.74/1.62 % (5321)------------------------------
% 2.74/1.62 % (5321)------------------------------
% 2.74/1.62 % (5328)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_5039 for (2999ds/3Mi)
% 2.74/1.62 % (5328)Instruction limit reached!
% 2.74/1.62 % (5328)------------------------------
% 2.74/1.62 % (5328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (5328)Termination reason: Unknown
% 2.74/1.62 % (5328)Termination phase: shuffling
% 2.74/1.62
% 2.74/1.62 % (5328)Memory used [KB]: 1407
% 2.74/1.62 % (5328)Time elapsed: 0.002 s
% 2.74/1.62 % (5328)Instructions burned: 3 (million)
% 2.74/1.62 % (5328)------------------------------
% 2.74/1.62 % (5328)------------------------------
% 2.74/1.62 % (5326)Instruction limit reached!
% 2.74/1.62 % (5326)------------------------------
% 2.74/1.62 % (5326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (5326)Termination reason: Unknown
% 2.74/1.62 % (5326)Termination phase: shuffling
% 2.74/1.62
% 2.74/1.62 % (5326)Memory used [KB]: 1663
% 2.74/1.62 % (5326)Time elapsed: 0.010 s
% 2.74/1.62 % (5326)Instructions burned: 17 (million)
% 2.74/1.62 % (5326)------------------------------
% 2.74/1.62 % (5326)------------------------------
% 2.74/1.62 % (5313)Instruction limit reached!
% 2.74/1.62 % (5313)------------------------------
% 2.74/1.62 % (5313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.62 % (5313)Termination reason: Unknown
% 2.74/1.62 % (5313)Termination phase: Saturation
% 2.74/1.62
% 2.74/1.62 % (5313)Memory used [KB]: 7547
% 2.74/1.62 % (5313)Time elapsed: 0.053 s
% 2.74/1.62 % (5313)Instructions burned: 184 (million)
% 2.74/1.62 % (5313)------------------------------
% 2.74/1.62 % (5313)------------------------------
% 2.74/1.62 % (5329)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/7Mi)
% 2.74/1.63 % (5329)Instruction limit reached!
% 2.74/1.63 % (5329)------------------------------
% 2.74/1.63 % (5329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.63 % (5329)Termination reason: Unknown
% 2.74/1.63 % (5329)Termination phase: shuffling
% 2.74/1.63
% 2.74/1.63 % (5329)Memory used [KB]: 1535
% 2.74/1.63 % (5329)Time elapsed: 0.004 s
% 2.74/1.63 % (5329)Instructions burned: 10 (million)
% 2.74/1.63 % (5329)------------------------------
% 2.74/1.63 % (5329)------------------------------
% 2.74/1.63 % (5332)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/18Mi)
% 2.74/1.63 % (5333)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/710Mi)
% 2.74/1.63 % (5330)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/3Mi)
% 2.74/1.64 % (5330)Instruction limit reached!
% 2.74/1.64 % (5330)------------------------------
% 2.74/1.64 % (5330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.64 % (5330)Termination reason: Unknown
% 2.74/1.64 % (5330)Termination phase: shuffling
% 2.74/1.64
% 2.74/1.64 % (5330)Memory used [KB]: 1407
% 2.74/1.64 % (5330)Time elapsed: 0.003 s
% 2.74/1.64 % (5330)Instructions burned: 4 (million)
% 2.74/1.64 % (5330)------------------------------
% 2.74/1.64 % (5330)------------------------------
% 2.74/1.64 % (5331)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/4Mi)
% 2.74/1.64 % (5334)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/6Mi)
% 2.74/1.64 % (5334)Instruction limit reached!
% 2.74/1.64 % (5334)------------------------------
% 2.74/1.64 % (5334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.64 % (5334)Termination reason: Unknown
% 2.74/1.64 % (5334)Termination phase: shuffling
% 2.74/1.64
% 2.74/1.64 % (5334)Memory used [KB]: 1407
% 2.74/1.64 % (5334)Time elapsed: 0.003 s
% 2.74/1.64 % (5334)Instructions burned: 6 (million)
% 2.74/1.64 % (5334)------------------------------
% 2.74/1.64 % (5334)------------------------------
% 2.74/1.64 % (5332)Instruction limit reached!
% 2.74/1.64 % (5332)------------------------------
% 2.74/1.64 % (5332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.64 % (5332)Termination reason: Unknown
% 2.74/1.64 % (5332)Termination phase: shuffling
% 2.74/1.64
% 2.74/1.64 % (5332)Memory used [KB]: 1791
% 2.74/1.64 % (5332)Time elapsed: 0.007 s
% 2.74/1.64 % (5332)Instructions burned: 19 (million)
% 2.74/1.64 % (5332)------------------------------
% 2.74/1.64 % (5332)------------------------------
% 2.74/1.64 % (5331)Instruction limit reached!
% 2.74/1.64 % (5331)------------------------------
% 2.74/1.64 % (5331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.64 % (5331)Termination reason: Unknown
% 2.74/1.64 % (5331)Termination phase: shuffling
% 2.74/1.64
% 2.74/1.64 % (5331)Memory used [KB]: 1407
% 2.74/1.64 % (5331)Time elapsed: 0.005 s
% 2.74/1.64 % (5331)Instructions burned: 5 (million)
% 2.74/1.64 % (5331)------------------------------
% 2.74/1.64 % (5331)------------------------------
% 2.74/1.65 % (5335)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_5039 for (2999ds/902Mi)
% 2.74/1.65 % (5336)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_5039 for (2999ds/21Mi)
% 2.74/1.65 % (5337)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/5Mi)
% 2.74/1.65 % (5337)Instruction limit reached!
% 2.74/1.65 % (5337)------------------------------
% 2.74/1.65 % (5337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.65 % (5337)Termination reason: Unknown
% 2.74/1.65 % (5337)Termination phase: shuffling
% 2.74/1.65
% 2.74/1.65 % (5337)Memory used [KB]: 1535
% 2.74/1.65 % (5337)Time elapsed: 0.004 s
% 2.74/1.65 % (5337)Instructions burned: 7 (million)
% 2.74/1.65 % (5337)------------------------------
% 2.74/1.65 % (5337)------------------------------
% 2.74/1.65 % (5336)Instruction limit reached!
% 2.74/1.65 % (5336)------------------------------
% 2.74/1.65 % (5336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.65 % (5336)Termination reason: Unknown
% 2.74/1.65 % (5336)Termination phase: shuffling
% 2.74/1.65
% 2.74/1.65 % (5336)Memory used [KB]: 1791
% 2.74/1.65 % (5336)Time elapsed: 0.007 s
% 2.74/1.65 % (5336)Instructions burned: 21 (million)
% 2.74/1.65 % (5336)------------------------------
% 2.74/1.65 % (5336)------------------------------
% 2.74/1.66 % (5338)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_5039 for (2999ds/6Mi)
% 2.74/1.66 % (5338)Instruction limit reached!
% 2.74/1.66 % (5338)------------------------------
% 2.74/1.66 % (5338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.66 % (5338)Termination reason: Unknown
% 2.74/1.66 % (5338)Termination phase: shuffling
% 2.74/1.66
% 2.74/1.66 % (5338)Memory used [KB]: 1407
% 2.74/1.66 % (5338)Time elapsed: 0.005 s
% 2.74/1.66 % (5338)Instructions burned: 6 (million)
% 2.74/1.66 % (5338)------------------------------
% 2.74/1.66 % (5338)------------------------------
% 2.74/1.66 % (5339)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5039 for (2999ds/377Mi)
% 2.74/1.66 % (5340)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_5039 for (2999ds/779Mi)
% 2.74/1.68 % (5341)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_5039 for (2998ds/19Mi)
% 2.74/1.69 % (5341)Instruction limit reached!
% 2.74/1.69 % (5341)------------------------------
% 2.74/1.69 % (5341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.69 % (5341)Termination reason: Unknown
% 2.74/1.69 % (5341)Termination phase: shuffling
% 2.74/1.69
% 2.74/1.69 % (5341)Memory used [KB]: 1791
% 2.74/1.69 % (5341)Time elapsed: 0.012 s
% 2.74/1.69 % (5341)Instructions burned: 20 (million)
% 2.74/1.69 % (5341)------------------------------
% 2.74/1.69 % (5341)------------------------------
% 2.74/1.70 % (5342)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5039 for (2998ds/879Mi)
% 2.74/1.71 % (5318)Instruction limit reached!
% 2.74/1.71 % (5318)------------------------------
% 2.74/1.71 % (5318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.71 % (5318)Termination reason: Unknown
% 2.74/1.71 % (5318)Termination phase: Saturation
% 2.74/1.71
% 2.74/1.71 % (5318)Memory used [KB]: 8827
% 2.74/1.71 % (5318)Time elapsed: 0.129 s
% 2.74/1.71 % (5318)Instructions burned: 276 (million)
% 2.74/1.71 % (5318)------------------------------
% 2.74/1.71 % (5318)------------------------------
% 2.74/1.72 % (5343)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5039 for (2998ds/17Mi)
% 2.74/1.72 % (5343)Instruction limit reached!
% 2.74/1.72 % (5343)------------------------------
% 2.74/1.72 % (5343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.72 % (5343)Termination reason: Unknown
% 2.74/1.72 % (5343)Termination phase: shuffling
% 2.74/1.72
% 2.74/1.72 % (5343)Memory used [KB]: 1663
% 2.74/1.72 % (5343)Time elapsed: 0.006 s
% 2.74/1.72 % (5343)Instructions burned: 17 (million)
% 2.74/1.72 % (5343)------------------------------
% 2.74/1.72 % (5343)------------------------------
% 2.74/1.73 % (5344)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5039 for (2998ds/3Mi)
% 2.74/1.73 % (5344)Instruction limit reached!
% 2.74/1.73 % (5344)------------------------------
% 2.74/1.73 % (5344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.73 % (5344)Termination reason: Unknown
% 2.74/1.73 % (5344)Termination phase: shuffling
% 2.74/1.73
% 2.74/1.73 % (5344)Memory used [KB]: 1407
% 2.74/1.73 % (5344)Time elapsed: 0.003 s
% 2.74/1.73 % (5344)Instructions burned: 4 (million)
% 2.74/1.73 % (5344)------------------------------
% 2.74/1.73 % (5344)------------------------------
% 2.74/1.74 % (5345)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_5039 for (2998ds/30Mi)
% 2.74/1.75 % (5345)Instruction limit reached!
% 2.74/1.75 % (5345)------------------------------
% 2.74/1.75 % (5345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.75 % (5345)Termination reason: Unknown
% 2.74/1.75 % (5345)Termination phase: shuffling
% 2.74/1.75
% 2.74/1.75 % (5345)Memory used [KB]: 1918
% 2.74/1.75 % (5345)Time elapsed: 0.010 s
% 2.74/1.75 % (5345)Instructions burned: 30 (million)
% 2.74/1.75 % (5345)------------------------------
% 2.74/1.75 % (5345)------------------------------
% 2.74/1.76 % (5346)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_5039 for (2998ds/127Mi)
% 2.74/1.78 % (5339)Instruction limit reached!
% 2.74/1.78 % (5339)------------------------------
% 2.74/1.78 % (5339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.78 % (5339)Termination reason: Unknown
% 2.74/1.78 % (5339)Termination phase: Saturation
% 2.74/1.78
% 2.74/1.78 % (5339)Memory used [KB]: 8571
% 2.74/1.78 % (5339)Time elapsed: 0.115 s
% 2.74/1.78 % (5339)Instructions burned: 378 (million)
% 2.74/1.78 % (5339)------------------------------
% 2.74/1.78 % (5339)------------------------------
% 2.74/1.79 % (5347)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_5039 for (2997ds/100Mi)
% 2.74/1.80 % (5346)Instruction limit reached!
% 2.74/1.80 % (5346)------------------------------
% 2.74/1.80 % (5346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.80 % (5346)Termination reason: Unknown
% 2.74/1.80 % (5346)Termination phase: Saturation
% 2.74/1.80
% 2.74/1.80 % (5346)Memory used [KB]: 6908
% 2.74/1.80 % (5346)Time elapsed: 0.037 s
% 2.74/1.80 % (5346)Instructions burned: 128 (million)
% 2.74/1.80 % (5346)------------------------------
% 2.74/1.80 % (5346)------------------------------
% 2.74/1.81 % (5348)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_5039 for (2997ds/3Mi)
% 2.74/1.81 % (5348)Instruction limit reached!
% 2.74/1.81 % (5348)------------------------------
% 2.74/1.81 % (5348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.81 % (5348)Termination reason: Unknown
% 2.74/1.81 % (5348)Termination phase: shuffling
% 2.74/1.81
% 2.74/1.81 % (5348)Memory used [KB]: 1407
% 2.74/1.81 % (5348)Time elapsed: 0.002 s
% 2.74/1.81 % (5348)Instructions burned: 4 (million)
% 2.74/1.81 % (5348)------------------------------
% 2.74/1.81 % (5348)------------------------------
% 2.74/1.81 % (5347)Instruction limit reached!
% 2.74/1.81 % (5347)------------------------------
% 2.74/1.81 % (5347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.81 % (5347)Termination reason: Unknown
% 2.74/1.81 % (5347)Termination phase: Property scanning
% 2.74/1.81
% 2.74/1.81 % (5347)Memory used [KB]: 2430
% 2.74/1.81 % (5347)Time elapsed: 0.029 s
% 2.74/1.81 % (5347)Instructions burned: 103 (million)
% 2.74/1.81 % (5347)------------------------------
% 2.74/1.81 % (5347)------------------------------
% 2.74/1.82 % (5349)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_5039 for (2997ds/20Mi)
% 2.74/1.82 % (5350)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_5039 for (2997ds/86Mi)
% 2.74/1.83 % (5349)Instruction limit reached!
% 2.74/1.83 % (5349)------------------------------
% 2.74/1.83 % (5349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.83 % (5349)Termination reason: Unknown
% 2.74/1.83 % (5349)Termination phase: shuffling
% 2.74/1.83
% 2.74/1.83 % (5349)Memory used [KB]: 1791
% 2.74/1.83 % (5349)Time elapsed: 0.009 s
% 2.74/1.83 % (5349)Instructions burned: 21 (million)
% 2.74/1.83 % (5349)------------------------------
% 2.74/1.83 % (5349)------------------------------
% 2.74/1.84 % (5351)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_5039 for (2997ds/107Mi)
% 2.74/1.85 % (5350)Instruction limit reached!
% 2.74/1.85 % (5350)------------------------------
% 2.74/1.85 % (5350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.85 % (5350)Termination reason: Unknown
% 2.74/1.85 % (5350)Termination phase: Function definition elimination
% 2.74/1.85
% 2.74/1.85 % (5350)Memory used [KB]: 2430
% 2.74/1.85 % (5350)Time elapsed: 0.025 s
% 2.74/1.85 % (5350)Instructions burned: 88 (million)
% 2.74/1.85 % (5350)------------------------------
% 2.74/1.85 % (5350)------------------------------
% 2.74/1.85 % (5340)Instruction limit reached!
% 2.74/1.85 % (5340)------------------------------
% 2.74/1.85 % (5340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.85 % (5340)Termination reason: Unknown
% 2.74/1.85 % (5340)Termination phase: Saturation
% 2.74/1.85
% 2.74/1.85 % (5340)Memory used [KB]: 7291
% 2.74/1.85 % (5340)Time elapsed: 0.190 s
% 2.74/1.85 % (5340)Instructions burned: 779 (million)
% 2.74/1.85 % (5340)------------------------------
% 2.74/1.85 % (5340)------------------------------
% 2.74/1.85 % (5333)Instruction limit reached!
% 2.74/1.85 % (5333)------------------------------
% 2.74/1.85 % (5333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.85 % (5333)Termination reason: Unknown
% 2.74/1.85 % (5333)Termination phase: Saturation
% 2.74/1.85
% 2.74/1.85 % (5333)Memory used [KB]: 9978
% 2.74/1.85 % (5333)Time elapsed: 0.221 s
% 2.74/1.85 % (5333)Instructions burned: 712 (million)
% 2.74/1.85 % (5333)------------------------------
% 2.74/1.85 % (5333)------------------------------
% 2.74/1.86 % (5352)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_5039 for (2996ds/39Mi)
% 2.74/1.86 % (5353)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_5039 for (2996ds/448Mi)
% 2.74/1.86 % (5354)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_5039 for (2996ds/46Mi)
% 2.74/1.87 % (5351)Instruction limit reached!
% 2.74/1.87 % (5351)------------------------------
% 2.74/1.87 % (5351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.87 % (5351)Termination reason: Unknown
% 2.74/1.87 % (5351)Termination phase: Property scanning
% 2.74/1.87
% 2.74/1.87 % (5351)Memory used [KB]: 2430
% 2.74/1.87 % (5351)Time elapsed: 0.031 s
% 2.74/1.87 % (5351)Instructions burned: 107 (million)
% 2.74/1.87 % (5351)------------------------------
% 2.74/1.87 % (5351)------------------------------
% 2.74/1.87 % (5352)Instruction limit reached!
% 2.74/1.87 % (5352)------------------------------
% 2.74/1.87 % (5352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.87 % (5352)Termination reason: Unknown
% 2.74/1.87 % (5352)Termination phase: Property scanning
% 2.74/1.87
% 2.74/1.87 % (5352)Memory used [KB]: 2174
% 2.74/1.87 % (5352)Time elapsed: 0.013 s
% 2.74/1.87 % (5352)Instructions burned: 39 (million)
% 2.74/1.87 % (5352)------------------------------
% 2.74/1.87 % (5352)------------------------------
% 2.74/1.88 % (5354)Instruction limit reached!
% 2.74/1.88 % (5354)------------------------------
% 2.74/1.88 % (5354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.88 % (5354)Termination reason: Unknown
% 2.74/1.88 % (5354)Termination phase: Property scanning
% 2.74/1.88
% 2.74/1.88 % (5354)Memory used [KB]: 2174
% 2.74/1.88 % (5354)Time elapsed: 0.014 s
% 2.74/1.88 % (5354)Instructions burned: 48 (million)
% 2.74/1.88 % (5354)------------------------------
% 2.74/1.88 % (5354)------------------------------
% 2.74/1.88 % (5355)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_5039 for (2996ds/98Mi)
% 2.74/1.88 % (5356)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_5039 for (2996ds/507Mi)
% 2.74/1.89 % (5357)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_5039 for (2996ds/149Mi)
% 2.74/1.89 % (5324)Instruction limit reached!
% 2.74/1.89 % (5324)------------------------------
% 2.74/1.89 % (5324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.89 % (5324)Termination reason: Unknown
% 2.74/1.89 % (5324)Termination phase: Saturation
% 2.74/1.89
% 2.74/1.89 % (5324)Memory used [KB]: 12153
% 2.74/1.89 % (5324)Time elapsed: 0.283 s
% 2.74/1.89 % (5324)Instructions burned: 1043 (million)
% 2.74/1.89 % (5324)------------------------------
% 2.74/1.89 % (5324)------------------------------
% 2.74/1.90 % (5358)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_5039 for (2996ds/39Mi)
% 2.74/1.90 % (5355)Instruction limit reached!
% 2.74/1.90 % (5355)------------------------------
% 2.74/1.90 % (5355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.90 % (5355)Termination reason: Unknown
% 2.74/1.90 % (5355)Termination phase: Property scanning
% 2.74/1.90
% 2.74/1.90 % (5355)Memory used [KB]: 2302
% 2.74/1.90 % (5355)Time elapsed: 0.027 s
% 2.74/1.90 % (5355)Instructions burned: 98 (million)
% 2.74/1.90 % (5355)------------------------------
% 2.74/1.90 % (5355)------------------------------
% 2.74/1.91 % (5358)Instruction limit reached!
% 2.74/1.91 % (5358)------------------------------
% 2.74/1.91 % (5358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.91 % (5358)Termination reason: Unknown
% 2.74/1.91 % (5358)Termination phase: Property scanning
% 2.74/1.91
% 2.74/1.91 % (5358)Memory used [KB]: 2046
% 2.74/1.91 % (5358)Time elapsed: 0.013 s
% 2.74/1.91 % (5358)Instructions burned: 41 (million)
% 2.74/1.91 % (5358)------------------------------
% 2.74/1.91 % (5358)------------------------------
% 2.74/1.91 % (5359)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_5039 for (2996ds/6Mi)
% 2.74/1.91 % (5359)Instruction limit reached!
% 2.74/1.91 % (5359)------------------------------
% 2.74/1.91 % (5359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.91 % (5359)Termination reason: Unknown
% 2.74/1.91 % (5359)Termination phase: shuffling
% 2.74/1.91
% 2.74/1.91 % (5359)Memory used [KB]: 1535
% 2.74/1.91 % (5359)Time elapsed: 0.004 s
% 2.74/1.91 % (5359)Instructions burned: 7 (million)
% 2.74/1.91 % (5359)------------------------------
% 2.74/1.91 % (5359)------------------------------
% 2.74/1.92 % (5360)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_5039 for (2996ds/1087Mi)
% 2.74/1.92 % (5357)Instruction limit reached!
% 2.74/1.92 % (5357)------------------------------
% 2.74/1.92 % (5357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.92 % (5357)Termination reason: Unknown
% 2.74/1.92 % (5357)Termination phase: Saturation
% 2.74/1.92 % (5361)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_5039 for (2996ds/47Mi)
% 2.74/1.92
% 2.74/1.92 % (5357)Memory used [KB]: 7419
% 2.74/1.92 % (5357)Time elapsed: 0.041 s
% 2.74/1.93 % (5357)Instructions burned: 152 (million)
% 2.74/1.93 % (5357)------------------------------
% 2.74/1.93 % (5357)------------------------------
% 2.74/1.93 % (5362)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_5039 for (2996ds/44Mi)
% 2.74/1.94 % (5335)Instruction limit reached!
% 2.74/1.94 % (5335)------------------------------
% 2.74/1.94 % (5335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.94 % (5361)Instruction limit reached!
% 2.74/1.94 % (5361)------------------------------
% 2.74/1.94 % (5361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.94 % (5361)Termination reason: Unknown
% 2.74/1.94 % (5335)Termination reason: Unknown
% 2.74/1.94 % (5335)Termination phase: Saturation
% 2.74/1.94
% 2.74/1.94 % (5361)Termination phase: Property scanning
% 2.74/1.94
% 2.74/1.94 % (5335)Memory used [KB]: 10490
% 2.74/1.94 % (5361)Memory used [KB]: 2174
% 2.74/1.94 % (5335)Time elapsed: 0.293 s
% 2.74/1.94 % (5361)Time elapsed: 0.016 s
% 2.74/1.94 % (5335)Instructions burned: 904 (million)
% 2.74/1.94 % (5361)Instructions burned: 50 (million)
% 2.74/1.94 % (5335)------------------------------
% 2.74/1.94 % (5335)------------------------------
% 2.74/1.94 % (5361)------------------------------
% 2.74/1.94 % (5361)------------------------------
% 2.74/1.95 % (5362)Instruction limit reached!
% 2.74/1.95 % (5362)------------------------------
% 2.74/1.95 % (5362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.95 % (5362)Termination reason: Unknown
% 2.74/1.95 % (5362)Termination phase: Property scanning
% 2.74/1.95
% 2.74/1.95 % (5362)Memory used [KB]: 2174
% 2.74/1.95 % (5362)Time elapsed: 0.013 s
% 2.74/1.95 % (5362)Instructions burned: 45 (million)
% 2.74/1.95 % (5362)------------------------------
% 2.74/1.95 % (5362)------------------------------
% 2.74/1.95 % (5363)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_5039 for (2996ds/432Mi)
% 2.74/1.95 % (5364)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_5039 for (2996ds/62Mi)
% 2.74/1.96 % (5365)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_5039 for (2996ds/31Mi)
% 2.74/1.96 % (5365)Instruction limit reached!
% 2.74/1.96 % (5365)------------------------------
% 2.74/1.96 % (5365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.96 % (5365)Termination reason: Unknown
% 2.74/1.96 % (5365)Termination phase: shuffling
% 2.74/1.96
% 2.74/1.96 % (5365)Memory used [KB]: 1918
% 2.74/1.96 % (5365)Time elapsed: 0.010 s
% 2.74/1.96 % (5365)Instructions burned: 33 (million)
% 2.74/1.96 % (5365)------------------------------
% 2.74/1.96 % (5365)------------------------------
% 2.74/1.97 % (5364)Instruction limit reached!
% 2.74/1.97 % (5364)------------------------------
% 2.74/1.97 % (5364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.97 % (5364)Termination reason: Unknown
% 2.74/1.97 % (5364)Termination phase: Property scanning
% 2.74/1.97
% 2.74/1.97 % (5364)Memory used [KB]: 2302
% 2.74/1.97 % (5364)Time elapsed: 0.018 s
% 2.74/1.97 % (5364)Instructions burned: 62 (million)
% 2.74/1.97 % (5364)------------------------------
% 2.74/1.97 % (5364)------------------------------
% 2.74/1.97 % (5353)Instruction limit reached!
% 2.74/1.97 % (5353)------------------------------
% 2.74/1.97 % (5353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.97 % (5353)Termination reason: Unknown
% 2.74/1.97 % (5353)Termination phase: Saturation
% 2.74/1.97
% 2.74/1.97 % (5353)Memory used [KB]: 7291
% 2.74/1.97 % (5353)Time elapsed: 0.112 s
% 2.74/1.97 % (5353)Instructions burned: 449 (million)
% 2.74/1.97 % (5353)------------------------------
% 2.74/1.97 % (5353)------------------------------
% 2.74/1.97 % (5366)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_5039 for (2995ds/96Mi)
% 2.74/1.98 % (5367)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_5039 for (2995ds/453Mi)
% 2.74/1.98 % (5368)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_5039 for (2995ds/71Mi)
% 2.74/1.99 % (5342)Instruction limit reached!
% 2.74/1.99 % (5342)------------------------------
% 2.74/1.99 % (5342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.99 % (5342)Termination reason: Unknown
% 2.74/1.99 % (5342)Termination phase: Saturation
% 2.74/1.99
% 2.74/1.99 % (5342)Memory used [KB]: 9466
% 2.74/1.99 % (5342)Time elapsed: 0.314 s
% 2.74/1.99 % (5342)Instructions burned: 879 (million)
% 2.74/1.99 % (5342)------------------------------
% 2.74/1.99 % (5342)------------------------------
% 2.74/2.00 % (5366)Instruction limit reached!
% 2.74/2.00 % (5366)------------------------------
% 2.74/2.00 % (5366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/2.00 % (5366)Termination reason: Unknown
% 2.74/2.00 % (5366)Termination phase: Property scanning
% 2.74/2.00
% 2.74/2.00 % (5366)Memory used [KB]: 2430
% 2.74/2.00 % (5366)Time elapsed: 0.026 s
% 2.74/2.00 % (5366)Instructions burned: 96 (million)
% 2.74/2.00 % (5366)------------------------------
% 2.74/2.00 % (5366)------------------------------
% 2.74/2.00 % (5368)Instruction limit reached!
% 2.74/2.00 % (5368)------------------------------
% 2.74/2.00 % (5368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/2.00 % (5368)Termination reason: Unknown
% 2.74/2.00 % (5368)Termination phase: Property scanning
% 2.74/2.00
% 2.74/2.00 % (5368)Memory used [KB]: 2302
% 2.74/2.00 % (5368)Time elapsed: 0.020 s
% 2.74/2.00 % (5368)Instructions burned: 72 (million)
% 2.74/2.00 % (5368)------------------------------
% 2.74/2.00 % (5368)------------------------------
% 2.74/2.01 % (5369)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_5039 for (2995ds/83Mi)
% 2.74/2.01 % (5370)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_5039 for (2995ds/11Mi)
% 2.74/2.01 % (5371)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_5039 for (2995ds/41Mi)
% 5.82/2.01 % (5370)Instruction limit reached!
% 5.82/2.01 % (5370)------------------------------
% 5.82/2.01 % (5370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.01 % (5370)Termination reason: Unknown
% 5.82/2.01 % (5370)Termination phase: shuffling
% 5.82/2.01
% 5.82/2.01 % (5370)Memory used [KB]: 1663
% 5.82/2.01 % (5370)Time elapsed: 0.004 s
% 5.82/2.01 % (5370)Instructions burned: 11 (million)
% 5.82/2.01 % (5370)------------------------------
% 5.82/2.01 % (5370)------------------------------
% 5.82/2.02 % (5372)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5039 for (2995ds/6Mi)
% 5.82/2.02 % (5371)Instruction limit reached!
% 5.82/2.02 % (5371)------------------------------
% 5.82/2.02 % (5371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.02 % (5371)Termination reason: Unknown
% 5.82/2.02 % (5371)Termination phase: Property scanning
% 5.82/2.02
% 5.82/2.02 % (5371)Memory used [KB]: 2174
% 5.82/2.02 % (5371)Time elapsed: 0.013 s
% 5.82/2.02 % (5371)Instructions burned: 45 (million)
% 5.82/2.02 % (5371)------------------------------
% 5.82/2.02 % (5371)------------------------------
% 5.82/2.02 % (5372)Instruction limit reached!
% 5.82/2.02 % (5372)------------------------------
% 5.82/2.02 % (5372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.02 % (5372)Termination reason: Unknown
% 5.82/2.02 % (5372)Termination phase: shuffling
% 5.82/2.02
% 5.82/2.02 % (5372)Memory used [KB]: 1407
% 5.82/2.02 % (5372)Time elapsed: 0.003 s
% 5.82/2.02 % (5372)Instructions burned: 6 (million)
% 5.82/2.02 % (5372)------------------------------
% 5.82/2.02 % (5372)------------------------------
% 5.82/2.03 % (5369)Instruction limit reached!
% 5.82/2.03 % (5369)------------------------------
% 5.82/2.03 % (5369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.03 % (5369)Termination reason: Unknown
% 5.82/2.03 % (5369)Termination phase: Property scanning
% 5.82/2.03
% 5.82/2.03 % (5369)Memory used [KB]: 2302
% 5.82/2.03 % (5369)Time elapsed: 0.024 s
% 5.82/2.03 % (5369)Instructions burned: 83 (million)
% 5.82/2.03 % (5369)------------------------------
% 5.82/2.03 % (5369)------------------------------
% 5.82/2.03 % (5373)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_5039 for (2995ds/150Mi)
% 5.82/2.03 % (5374)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_5039 for (2995ds/343Mi)
% 5.82/2.04 % (5356)Instruction limit reached!
% 5.82/2.04 % (5356)------------------------------
% 5.82/2.04 % (5356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.04 % (5356)Termination reason: Unknown
% 5.82/2.04 % (5356)Termination phase: Saturation
% 5.82/2.04
% 5.82/2.04 % (5356)Memory used [KB]: 7931
% 5.82/2.04 % (5356)Time elapsed: 0.160 s
% 5.82/2.04 % (5356)Instructions burned: 507 (million)
% 5.82/2.04 % (5356)------------------------------
% 5.82/2.04 % (5356)------------------------------
% 5.82/2.04 % (5375)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_5039 for (2995ds/109Mi)
% 5.82/2.05 % (5376)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_5039 for (2995ds/253Mi)
% 5.82/2.06 % (5363)Instruction limit reached!
% 5.82/2.06 % (5363)------------------------------
% 5.82/2.06 % (5363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.06 % (5363)Termination reason: Unknown
% 5.82/2.06 % (5363)Termination phase: Saturation
% 5.82/2.06
% 5.82/2.06 % (5363)Memory used [KB]: 2942
% 5.82/2.06 % (5363)Time elapsed: 0.113 s
% 5.82/2.06 % (5363)Instructions burned: 433 (million)
% 5.82/2.06 % (5363)------------------------------
% 5.82/2.06 % (5363)------------------------------
% 5.82/2.07 % (5375)Instruction limit reached!
% 5.82/2.07 % (5375)------------------------------
% 5.82/2.07 % (5375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.07 % (5375)Termination reason: Unknown
% 5.82/2.07 % (5375)Termination phase: Property scanning
% 5.82/2.07
% 5.82/2.07 % (5375)Memory used [KB]: 2430
% 5.82/2.07 % (5375)Time elapsed: 0.032 s
% 5.82/2.07 % (5375)Instructions burned: 110 (million)
% 5.82/2.07 % (5375)------------------------------
% 5.82/2.07 % (5375)------------------------------
% 5.82/2.07 % (5377)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_5039 for (2994ds/140Mi)
% 5.82/2.07 % (5373)Instruction limit reached!
% 5.82/2.07 % (5373)------------------------------
% 5.82/2.07 % (5373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.07 % (5373)Termination reason: Unknown
% 5.82/2.07 % (5373)Termination phase: Saturation
% 5.82/2.07
% 5.82/2.07 % (5373)Memory used [KB]: 3837
% 5.82/2.07 % (5373)Time elapsed: 0.042 s
% 5.82/2.07 % (5373)Instructions burned: 150 (million)
% 5.82/2.07 % (5373)------------------------------
% 5.82/2.07 % (5373)------------------------------
% 5.82/2.08 % (5378)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_5039 for (2994ds/614Mi)
% 5.82/2.08 % (5379)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_5039 for (2994ds/202Mi)
% 5.82/2.09 % (5367)Instruction limit reached!
% 5.82/2.09 % (5367)------------------------------
% 5.82/2.09 % (5367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.09 % (5367)Termination reason: Unknown
% 5.82/2.09 % (5367)Termination phase: Saturation
% 5.82/2.09
% 5.82/2.09 % (5367)Memory used [KB]: 7291
% 5.82/2.09 % (5367)Time elapsed: 0.115 s
% 5.82/2.09 % (5367)Instructions burned: 456 (million)
% 5.82/2.09 % (5367)------------------------------
% 5.82/2.09 % (5367)------------------------------
% 5.82/2.10 % (5380)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_5039 for (2994ds/339Mi)
% 5.82/2.11 % (5377)Instruction limit reached!
% 5.82/2.11 % (5377)------------------------------
% 5.82/2.11 % (5377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.82/2.11 % (5377)Termination reason: Unknown
% 5.82/2.11 % (5377)Termination phase: Saturation
% 5.82/2.11
% 5.82/2.11 % (5377)Memory used [KB]: 7036
% 5.82/2.11 % (5377)Time elapsed: 0.037 s
% 5.82/2.11 % (5377)Instructions burned: 140 (million)
% 5.82/2.11 % (5377)------------------------------
% 5.82/2.11 % (5377)------------------------------
% 6.33/2.12 % (5381)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_5039 for (2994ds/283Mi)
% 6.33/2.12 % (5376)Instruction limit reached!
% 6.33/2.12 % (5376)------------------------------
% 6.33/2.12 % (5376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.12 % (5376)Termination reason: Unknown
% 6.33/2.12 % (5376)Termination phase: Saturation
% 6.33/2.12
% 6.33/2.12 % (5376)Memory used [KB]: 9210
% 6.33/2.12 % (5376)Time elapsed: 0.076 s
% 6.33/2.12 % (5376)Instructions burned: 255 (million)
% 6.33/2.12 % (5376)------------------------------
% 6.33/2.12 % (5376)------------------------------
% 6.33/2.12 % (5374)Instruction limit reached!
% 6.33/2.12 % (5374)------------------------------
% 6.33/2.12 % (5374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.12 % (5374)Termination reason: Unknown
% 6.33/2.12 % (5374)Termination phase: Saturation
% 6.33/2.12
% 6.33/2.12 % (5374)Memory used [KB]: 8315
% 6.33/2.12 % (5374)Time elapsed: 0.093 s
% 6.33/2.12 % (5374)Instructions burned: 344 (million)
% 6.33/2.12 % (5374)------------------------------
% 6.33/2.12 % (5374)------------------------------
% 6.33/2.13 % (5382)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_5039 for (2994ds/134Mi)
% 6.33/2.13 % (5383)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_5039 for (2994ds/298Mi)
% 6.33/2.14 % (5379)Instruction limit reached!
% 6.33/2.14 % (5379)------------------------------
% 6.33/2.14 % (5379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.14 % (5379)Termination reason: Unknown
% 6.33/2.14 % (5379)Termination phase: Saturation
% 6.33/2.14
% 6.33/2.14 % (5379)Memory used [KB]: 4733
% 6.33/2.14 % (5379)Time elapsed: 0.059 s
% 6.33/2.14 % (5379)Instructions burned: 204 (million)
% 6.33/2.14 % (5379)------------------------------
% 6.33/2.14 % (5379)------------------------------
% 6.33/2.15 % (5384)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_5039 for (2994ds/192Mi)
% 6.33/2.17 % (5382)Instruction limit reached!
% 6.33/2.17 % (5382)------------------------------
% 6.33/2.17 % (5382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.17 % (5382)Termination reason: Unknown
% 6.33/2.17 % (5382)Termination phase: Saturation
% 6.33/2.17
% 6.33/2.17 % (5382)Memory used [KB]: 7036
% 6.33/2.17 % (5382)Time elapsed: 0.037 s
% 6.33/2.17 % (5382)Instructions burned: 136 (million)
% 6.33/2.17 % (5382)------------------------------
% 6.33/2.17 % (5382)------------------------------
% 6.33/2.18 % (5385)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_5039 for (2993ds/258Mi)
% 6.33/2.19 % (5381)Instruction limit reached!
% 6.33/2.19 % (5381)------------------------------
% 6.33/2.19 % (5381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.19 % (5381)Termination reason: Unknown
% 6.33/2.19 % (5381)Termination phase: Saturation
% 6.33/2.19
% 6.33/2.19 % (5381)Memory used [KB]: 7291
% 6.33/2.19 % (5381)Time elapsed: 0.073 s
% 6.33/2.19 % (5381)Instructions burned: 285 (million)
% 6.33/2.19 % (5381)------------------------------
% 6.33/2.19 % (5381)------------------------------
% 6.33/2.19 % (5380)Instruction limit reached!
% 6.33/2.19 % (5380)------------------------------
% 6.33/2.19 % (5380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.33/2.19 % (5380)Termination reason: Unknown
% 6.33/2.19 % (5380)Termination phase: Saturation
% 6.33/2.19
% 6.33/2.19 % (5380)Memory used [KB]: 7547
% 6.33/2.19 % (5380)Time elapsed: 0.092 s
% 6.33/2.19 % (5380)Instructions burned: 341 (million)
% 6.33/2.19 % (5380)------------------------------
% 6.33/2.19 % (5380)------------------------------
% 6.89/2.20 % (5386)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_5039 for (2993ds/90Mi)
% 6.89/2.20 % (5387)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_5039 for (2993ds/231Mi)
% 6.89/2.20 % (5384)Instruction limit reached!
% 6.89/2.20 % (5384)------------------------------
% 6.89/2.20 % (5384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.20 % (5384)Termination reason: Unknown
% 6.89/2.20 % (5384)Termination phase: Saturation
% 6.89/2.20
% 6.89/2.20 % (5384)Memory used [KB]: 7547
% 6.89/2.20 % (5384)Time elapsed: 0.053 s
% 6.89/2.20 % (5384)Instructions burned: 193 (million)
% 6.89/2.20 % (5384)------------------------------
% 6.89/2.20 % (5384)------------------------------
% 6.89/2.21 % (5383)Instruction limit reached!
% 6.89/2.21 % (5383)------------------------------
% 6.89/2.21 % (5383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.21 % (5383)Termination reason: Unknown
% 6.89/2.21 % (5383)Termination phase: Saturation
% 6.89/2.21
% 6.89/2.21 % (5383)Memory used [KB]: 7291
% 6.89/2.21 % (5383)Time elapsed: 0.077 s
% 6.89/2.21 % (5383)Instructions burned: 301 (million)
% 6.89/2.21 % (5383)------------------------------
% 6.89/2.21 % (5383)------------------------------
% 6.89/2.21 % (5388)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_5039 for (2993ds/458Mi)
% 6.89/2.22 % (5389)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_5039 for (2993ds/31Mi)
% 6.89/2.22 % (5386)Instruction limit reached!
% 6.89/2.22 % (5386)------------------------------
% 6.89/2.22 % (5386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.22 % (5386)Termination reason: Unknown
% 6.89/2.22 % (5386)Termination phase: Twee Goal Transformation
% 6.89/2.22
% 6.89/2.22 % (5386)Memory used [KB]: 2430
% 6.89/2.22 % (5386)Time elapsed: 0.025 s
% 6.89/2.22 % (5386)Instructions burned: 92 (million)
% 6.89/2.22 % (5386)------------------------------
% 6.89/2.22 % (5386)------------------------------
% 6.89/2.23 % (5389)Instruction limit reached!
% 6.89/2.23 % (5389)------------------------------
% 6.89/2.23 % (5389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.23 % (5389)Termination reason: Unknown
% 6.89/2.23 % (5389)Termination phase: shuffling
% 6.89/2.23
% 6.89/2.23 % (5389)Memory used [KB]: 2046
% 6.89/2.23 % (5389)Time elapsed: 0.010 s
% 6.89/2.23 % (5389)Instructions burned: 33 (million)
% 6.89/2.23 % (5389)------------------------------
% 6.89/2.23 % (5389)------------------------------
% 6.89/2.23 % (5390)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_5039 for (2993ds/297Mi)
% 6.89/2.24 % (5391)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_5039 for (2993ds/987Mi)
% 6.89/2.25 % (5385)Instruction limit reached!
% 6.89/2.25 % (5385)------------------------------
% 6.89/2.25 % (5385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.25 % (5385)Termination reason: Unknown
% 6.89/2.25 % (5385)Termination phase: Saturation
% 6.89/2.25
% 6.89/2.25 % (5385)Memory used [KB]: 7803
% 6.89/2.25 % (5385)Time elapsed: 0.070 s
% 6.89/2.25 % (5385)Instructions burned: 261 (million)
% 6.89/2.25 % (5385)------------------------------
% 6.89/2.25 % (5385)------------------------------
% 6.89/2.26 % (5392)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_5039 for (2992ds/182Mi)
% 6.89/2.26 % (5378)Instruction limit reached!
% 6.89/2.26 % (5378)------------------------------
% 6.89/2.26 % (5378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.26 % (5378)Termination reason: Unknown
% 6.89/2.26 % (5378)Termination phase: Saturation
% 6.89/2.26
% 6.89/2.26 % (5378)Memory used [KB]: 9466
% 6.89/2.26 % (5378)Time elapsed: 0.183 s
% 6.89/2.26 % (5378)Instructions burned: 616 (million)
% 6.89/2.26 % (5378)------------------------------
% 6.89/2.26 % (5378)------------------------------
% 6.89/2.27 % (5387)Instruction limit reached!
% 6.89/2.27 % (5387)------------------------------
% 6.89/2.27 % (5387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.27 % (5387)Termination reason: Unknown
% 6.89/2.27 % (5387)Termination phase: Saturation
% 6.89/2.27
% 6.89/2.27 % (5387)Memory used [KB]: 12792
% 6.89/2.27 % (5387)Time elapsed: 0.065 s
% 6.89/2.27 % (5387)Instructions burned: 231 (million)
% 6.89/2.27 % (5387)------------------------------
% 6.89/2.27 % (5387)------------------------------
% 6.89/2.27 % (5393)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_5039 for (2992ds/182Mi)
% 6.89/2.28 % (5394)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_5039 for (2992ds/154Mi)
% 7.54/2.31 % (5392)Instruction limit reached!
% 7.54/2.31 % (5392)------------------------------
% 7.54/2.31 % (5392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.31 % (5392)Termination reason: Unknown
% 7.54/2.31 % (5392)Termination phase: Saturation
% 7.54/2.31
% 7.54/2.31 % (5392)Memory used [KB]: 7419
% 7.54/2.31 % (5392)Time elapsed: 0.050 s
% 7.54/2.31 % (5392)Instructions burned: 182 (million)
% 7.54/2.31 % (5392)------------------------------
% 7.54/2.31 % (5392)------------------------------
% 7.54/2.31 % (5390)Instruction limit reached!
% 7.54/2.31 % (5390)------------------------------
% 7.54/2.31 % (5390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.31 % (5390)Termination reason: Unknown
% 7.54/2.31 % (5390)Termination phase: Saturation
% 7.54/2.31
% 7.54/2.31 % (5390)Memory used [KB]: 7291
% 7.54/2.31 % (5390)Time elapsed: 0.076 s
% 7.54/2.31 % (5390)Instructions burned: 298 (million)
% 7.54/2.31 % (5390)------------------------------
% 7.54/2.31 % (5390)------------------------------
% 7.54/2.32 % (5394)Instruction limit reached!
% 7.54/2.32 % (5394)------------------------------
% 7.54/2.32 % (5394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.32 % (5394)Termination reason: Unknown
% 7.54/2.32 % (5394)Termination phase: Saturation
% 7.54/2.32
% 7.54/2.32 % (5394)Memory used [KB]: 6908
% 7.54/2.32 % (5394)Time elapsed: 0.041 s
% 7.54/2.32 % (5394)Instructions burned: 156 (million)
% 7.54/2.32 % (5394)------------------------------
% 7.54/2.32 % (5394)------------------------------
% 7.54/2.32 % (5395)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_5039 for (2992ds/79Mi)
% 7.54/2.32 % (5396)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_5039 for (2992ds/216Mi)
% 7.54/2.32 % (5393)Instruction limit reached!
% 7.54/2.32 % (5393)------------------------------
% 7.54/2.32 % (5393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.32 % (5393)Termination reason: Unknown
% 7.54/2.32 % (5393)Termination phase: Saturation
% 7.54/2.32
% 7.54/2.32 % (5393)Memory used [KB]: 9722
% 7.54/2.32 % (5393)Time elapsed: 0.054 s
% 7.54/2.32 % (5393)Instructions burned: 183 (million)
% 7.54/2.32 % (5393)------------------------------
% 7.54/2.32 % (5393)------------------------------
% 7.54/2.33 % (5397)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_5039 for (2992ds/114Mi)
% 7.54/2.33 % (5398)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_5039 for (2992ds/922Mi)
% 7.54/2.34 % (5395)Instruction limit reached!
% 7.54/2.34 % (5395)------------------------------
% 7.54/2.34 % (5395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.34 % (5395)Termination reason: Unknown
% 7.54/2.34 % (5395)Termination phase: Function definition elimination
% 7.54/2.34
% 7.54/2.34 % (5395)Memory used [KB]: 2302
% 7.54/2.34 % (5395)Time elapsed: 0.022 s
% 7.54/2.34 % (5395)Instructions burned: 80 (million)
% 7.54/2.34 % (5395)------------------------------
% 7.54/2.34 % (5395)------------------------------
% 7.54/2.34 % (5360)Instruction limit reached!
% 7.54/2.34 % (5360)------------------------------
% 7.54/2.34 % (5360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.34 % (5360)Termination reason: Unknown
% 7.54/2.34 % (5360)Termination phase: Saturation
% 7.54/2.34
% 7.54/2.34 % (5360)Memory used [KB]: 10746
% 7.54/2.34 % (5360)Time elapsed: 0.423 s
% 7.54/2.34 % (5360)Instructions burned: 1087 (million)
% 7.54/2.34 % (5360)------------------------------
% 7.54/2.34 % (5360)------------------------------
% 7.54/2.34 % (5388)Instruction limit reached!
% 7.54/2.34 % (5388)------------------------------
% 7.54/2.34 % (5388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.34 % (5388)Termination reason: Unknown
% 7.54/2.34 % (5388)Termination phase: Saturation
% 7.54/2.34
% 7.54/2.34 % (5388)Memory used [KB]: 9338
% 7.54/2.34 % (5388)Time elapsed: 0.131 s
% 7.54/2.34 % (5388)Instructions burned: 458 (million)
% 7.54/2.34 % (5388)------------------------------
% 7.54/2.34 % (5388)------------------------------
% 7.54/2.35 % (5399)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_5039 for (2992ds/182Mi)
% 7.54/2.35 % (5401)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_5039 for (2992ds/50Mi)
% 7.54/2.35 % (5400)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_5039 for (2992ds/164Mi)
% 7.54/2.35 % (5397)Instruction limit reached!
% 7.54/2.35 % (5397)------------------------------
% 7.54/2.35 % (5397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.35 % (5397)Termination reason: Unknown
% 7.54/2.35 % (5397)Termination phase: Saturation
% 7.54/2.35
% 7.54/2.35 % (5397)Memory used [KB]: 6908
% 7.54/2.35 % (5397)Time elapsed: 0.030 s
% 7.54/2.35 % (5397)Instructions burned: 114 (million)
% 7.54/2.35 % (5397)------------------------------
% 7.54/2.35 % (5397)------------------------------
% 7.54/2.36 % (5402)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_5039 for (2991ds/368Mi)
% 7.54/2.37 % (5401)Instruction limit reached!
% 7.54/2.37 % (5401)------------------------------
% 7.54/2.37 % (5401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.37 % (5401)Termination reason: Unknown
% 7.54/2.37 % (5401)Termination phase: Property scanning
% 7.54/2.37
% 7.54/2.37 % (5401)Memory used [KB]: 2174
% 7.54/2.37 % (5401)Time elapsed: 0.015 s
% 7.54/2.37 % (5401)Instructions burned: 53 (million)
% 7.54/2.37 % (5401)------------------------------
% 7.54/2.37 % (5401)------------------------------
% 7.54/2.37 % (5396)Instruction limit reached!
% 7.54/2.37 % (5396)------------------------------
% 7.54/2.37 % (5396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.37 % (5396)Termination reason: Unknown
% 7.54/2.37 % (5396)Termination phase: Saturation
% 7.54/2.37
% 7.54/2.37 % (5396)Memory used [KB]: 7291
% 7.54/2.37 % (5396)Time elapsed: 0.055 s
% 7.54/2.37 % (5396)Instructions burned: 216 (million)
% 7.54/2.37 % (5396)------------------------------
% 7.54/2.37 % (5396)------------------------------
% 7.54/2.37 % (5403)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_5039 for (2991ds/1021Mi)
% 7.54/2.38 % (5404)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_5039 for (2991ds/267Mi)
% 7.54/2.39 % (5399)Instruction limit reached!
% 7.54/2.39 % (5399)------------------------------
% 7.54/2.39 % (5399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.39 % (5399)Termination reason: Unknown
% 7.54/2.39 % (5399)Termination phase: Saturation
% 7.54/2.39
% 7.54/2.39 % (5399)Memory used [KB]: 7291
% 7.54/2.39 % (5399)Time elapsed: 0.047 s
% 7.54/2.39 % (5399)Instructions burned: 183 (million)
% 7.54/2.39 % (5399)------------------------------
% 7.54/2.39 % (5399)------------------------------
% 7.54/2.39 % (5400)Instruction limit reached!
% 7.54/2.39 % (5400)------------------------------
% 7.54/2.39 % (5400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.39 % (5400)Termination reason: Unknown
% 7.54/2.39 % (5400)Termination phase: Saturation
% 7.54/2.39
% 7.54/2.39 % (5400)Memory used [KB]: 2558
% 7.54/2.39 % (5400)Time elapsed: 0.044 s
% 7.54/2.39 % (5400)Instructions burned: 165 (million)
% 7.54/2.39 % (5400)------------------------------
% 7.54/2.39 % (5400)------------------------------
% 8.25/2.40 % (5405)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_5039 for (2991ds/204Mi)
% 8.25/2.40 % (5406)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_5039 for (2991ds/26Mi)
% 8.25/2.41 % (5406)Instruction limit reached!
% 8.25/2.41 % (5406)------------------------------
% 8.25/2.41 % (5406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.25/2.41 % (5406)Termination reason: Unknown
% 8.25/2.41 % (5406)Termination phase: shuffling
% 8.25/2.41
% 8.25/2.41 % (5406)Memory used [KB]: 1918
% 8.25/2.41 % (5406)Time elapsed: 0.009 s
% 8.25/2.41 % (5406)Instructions burned: 28 (million)
% 8.25/2.41 % (5406)------------------------------
% 8.25/2.41 % (5406)------------------------------
% 8.25/2.42 % (5407)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_5039 for (2991ds/53Mi)
% 8.25/2.44 % (5407)Instruction limit reached!
% 8.25/2.44 % (5407)------------------------------
% 8.25/2.44 % (5407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.25/2.44 % (5407)Termination reason: Unknown
% 8.25/2.44 % (5407)Termination phase: Property scanning
% 8.25/2.44
% 8.25/2.44 % (5407)Memory used [KB]: 2174
% 8.25/2.44 % (5407)Time elapsed: 0.015 s
% 8.25/2.44 % (5407)Instructions burned: 54 (million)
% 8.25/2.44 % (5407)------------------------------
% 8.25/2.44 % (5407)------------------------------
% 8.25/2.45 % (5408)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_5039 for (2991ds/4436Mi)
% 8.25/2.45 % (5404)Instruction limit reached!
% 8.25/2.45 % (5404)------------------------------
% 8.25/2.45 % (5404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.25/2.45 % (5404)Termination reason: Unknown
% 8.25/2.45 % (5404)Termination phase: Saturation
% 8.25/2.45
% 8.25/2.45 % (5404)Memory used [KB]: 7291
% 8.25/2.45 % (5404)Time elapsed: 0.069 s
% 8.25/2.45 % (5404)Instructions burned: 270 (million)
% 8.25/2.45 % (5404)------------------------------
% 8.25/2.45 % (5404)------------------------------
% 8.25/2.46 % (5405)Instruction limit reached!
% 8.25/2.46 % (5405)------------------------------
% 8.25/2.46 % (5405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.25/2.46 % (5405)Termination reason: Unknown
% 8.25/2.46 % (5405)Termination phase: Saturation
% 8.25/2.46
% 8.25/2.46 % (5405)Memory used [KB]: 7547
% 8.25/2.46 % (5405)Time elapsed: 0.055 s
% 8.25/2.46 % (5405)Instructions burned: 207 (million)
% 8.25/2.46 % (5405)------------------------------
% 8.25/2.46 % (5405)------------------------------
% 8.25/2.46 % (5409)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_5039 for (2991ds/1539Mi)
% 8.25/2.47 % (5410)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_5039 for (2991ds/408Mi)
% 8.25/2.47 % (5402)Instruction limit reached!
% 8.25/2.47 % (5402)------------------------------
% 8.25/2.47 % (5402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.25/2.47 % (5402)Termination reason: Unknown
% 8.25/2.47 % (5402)Termination phase: Saturation
% 8.25/2.47
% 8.25/2.47 % (5402)Memory used [KB]: 8571
% 8.25/2.47 % (5402)Time elapsed: 0.105 s
% 8.25/2.47 % (5402)Instructions burned: 368 (million)
% 8.25/2.47 % (5402)------------------------------
% 8.25/2.47 % (5402)------------------------------
% 8.25/2.48 % (5411)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_5039 for (2990ds/5205Mi)
% 8.25/2.48 % (5391)Instruction limit reached!
% 8.25/2.48 % (5391)------------------------------
% 8.25/2.48 % (5391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.25/2.48 % (5391)Termination reason: Unknown
% 8.25/2.48 % (5391)Termination phase: Saturation
% 8.25/2.48
% 8.25/2.48 % (5391)Memory used [KB]: 12025
% 8.25/2.48 % (5391)Time elapsed: 0.247 s
% 8.25/2.48 % (5391)Instructions burned: 987 (million)
% 8.25/2.48 % (5391)------------------------------
% 8.25/2.48 % (5391)------------------------------
% 8.25/2.49 % (5412)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_5039 for (2990ds/1913Mi)
% 8.81/2.59 % (5410)Instruction limit reached!
% 8.81/2.59 % (5410)------------------------------
% 8.81/2.59 % (5410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.81/2.59 % (5410)Termination reason: Unknown
% 8.81/2.59 % (5410)Termination phase: Saturation
% 8.81/2.59
% 8.81/2.59 % (5410)Memory used [KB]: 10106
% 8.81/2.59 % (5410)Time elapsed: 0.127 s
% 8.81/2.59 % (5410)Instructions burned: 409 (million)
% 8.81/2.59 % (5410)------------------------------
% 8.81/2.59 % (5410)------------------------------
% 8.96/2.60 % (5413)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_5039 for (2989ds/4350Mi)
% 8.96/2.62 % (5398)Instruction limit reached!
% 8.96/2.62 % (5398)------------------------------
% 8.96/2.62 % (5398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.62 % (5398)Termination reason: Unknown
% 8.96/2.62 % (5398)Termination phase: Saturation
% 8.96/2.62
% 8.96/2.62 % (5398)Memory used [KB]: 10490
% 8.96/2.62 % (5398)Time elapsed: 0.287 s
% 8.96/2.62 % (5398)Instructions burned: 924 (million)
% 8.96/2.62 % (5398)------------------------------
% 8.96/2.62 % (5398)------------------------------
% 8.96/2.63 % (5414)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_5039 for (2989ds/68Mi)
% 8.96/2.65 % (5414)Instruction limit reached!
% 8.96/2.65 % (5414)------------------------------
% 8.96/2.65 % (5414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.65 % (5414)Termination reason: Unknown
% 8.96/2.65 % (5414)Termination phase: SInE selection
% 8.96/2.65
% 8.96/2.65 % (5414)Memory used [KB]: 2174
% 8.96/2.65 % (5414)Time elapsed: 0.019 s
% 8.96/2.65 % (5414)Instructions burned: 70 (million)
% 8.96/2.65 % (5414)------------------------------
% 8.96/2.65 % (5414)------------------------------
% 8.96/2.66 % (5415)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_5039 for (2988ds/358Mi)
% 8.96/2.69 % (5403)Instruction limit reached!
% 8.96/2.69 % (5403)------------------------------
% 8.96/2.69 % (5403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.96/2.69 % (5403)Termination reason: Unknown
% 8.96/2.69 % (5403)Termination phase: Saturation
% 8.96/2.69
% 8.96/2.69 % (5403)Memory used [KB]: 11513
% 8.96/2.69 % (5403)Time elapsed: 0.320 s
% 8.96/2.69 % (5403)Instructions burned: 1022 (million)
% 8.96/2.69 % (5403)------------------------------
% 8.96/2.69 % (5403)------------------------------
% 9.61/2.70 % (5416)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_5039 for (2988ds/31Mi)
% 9.61/2.71 % (5416)Instruction limit reached!
% 9.61/2.71 % (5416)------------------------------
% 9.61/2.71 % (5416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.71 % (5416)Termination reason: Unknown
% 9.61/2.71 % (5416)Termination phase: shuffling
% 9.61/2.71
% 9.61/2.71 % (5416)Memory used [KB]: 1918
% 9.61/2.71 % (5416)Time elapsed: 0.010 s
% 9.61/2.71 % (5416)Instructions burned: 32 (million)
% 9.61/2.71 % (5416)------------------------------
% 9.61/2.71 % (5416)------------------------------
% 9.61/2.72 % (5417)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_5039 for (2988ds/279Mi)
% 9.61/2.76 % (5415)Instruction limit reached!
% 9.61/2.76 % (5415)------------------------------
% 9.61/2.76 % (5415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.76 % (5415)Termination reason: Unknown
% 9.61/2.76 % (5415)Termination phase: Saturation
% 9.61/2.76
% 9.61/2.76 % (5415)Memory used [KB]: 8315
% 9.61/2.76 % (5415)Time elapsed: 0.101 s
% 9.61/2.76 % (5415)Instructions burned: 358 (million)
% 9.61/2.76 % (5415)------------------------------
% 9.61/2.76 % (5415)------------------------------
% 9.61/2.77 % (5418)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_5039 for (2987ds/258Mi)
% 9.61/2.79 % (5417)Instruction limit reached!
% 9.61/2.79 % (5417)------------------------------
% 9.61/2.79 % (5417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.61/2.79 % (5417)Termination reason: Unknown
% 9.61/2.79 % (5417)Termination phase: Saturation
% 9.61/2.79
% 9.61/2.79 % (5417)Memory used [KB]: 7291
% 9.61/2.79 % (5417)Time elapsed: 0.072 s
% 9.61/2.79 % (5417)Instructions burned: 280 (million)
% 9.61/2.79 % (5417)------------------------------
% 9.61/2.79 % (5417)------------------------------
% 9.82/2.80 % (5419)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_5039 for (2987ds/26Mi)
% 9.82/2.81 % (5419)Instruction limit reached!
% 9.82/2.81 % (5419)------------------------------
% 9.82/2.81 % (5419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.81 % (5419)Termination reason: Unknown
% 9.82/2.81 % (5419)Termination phase: shuffling
% 9.82/2.81
% 9.82/2.81 % (5419)Memory used [KB]: 1918
% 9.82/2.81 % (5419)Time elapsed: 0.008 s
% 9.82/2.81 % (5419)Instructions burned: 26 (million)
% 9.82/2.81 % (5419)------------------------------
% 9.82/2.81 % (5419)------------------------------
% 9.82/2.82 % (5420)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_5039 for (2987ds/995Mi)
% 9.82/2.84 % (5418)Instruction limit reached!
% 9.82/2.84 % (5418)------------------------------
% 9.82/2.84 % (5418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.82/2.84 % (5418)Termination reason: Unknown
% 9.82/2.84 % (5418)Termination phase: Saturation
% 9.82/2.84
% 9.82/2.84 % (5418)Memory used [KB]: 8443
% 9.82/2.84 % (5418)Time elapsed: 0.071 s
% 9.82/2.84 % (5418)Instructions burned: 260 (million)
% 9.82/2.84 % (5418)------------------------------
% 9.82/2.84 % (5418)------------------------------
% 9.82/2.85 % (5421)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_5039 for (2987ds/373Mi)
% 9.92/2.94 % (5409)Instruction limit reached!
% 9.92/2.94 % (5409)------------------------------
% 9.92/2.94 % (5409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.92/2.94 % (5409)Termination reason: Unknown
% 9.92/2.94 % (5409)Termination phase: Saturation
% 9.92/2.94
% 9.92/2.94 % (5409)Memory used [KB]: 10106
% 9.92/2.94 % (5409)Time elapsed: 0.480 s
% 9.92/2.94 % (5409)Instructions burned: 1541 (million)
% 9.92/2.94 % (5409)------------------------------
% 9.92/2.94 % (5409)------------------------------
% 9.92/2.95 % (5422)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_5039 for (2986ds/253Mi)
% 9.92/2.95 % (5421)Instruction limit reached!
% 9.92/2.95 % (5421)------------------------------
% 9.92/2.95 % (5421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.92/2.95 % (5421)Termination reason: Unknown
% 9.92/2.95 % (5421)Termination phase: Saturation
% 9.92/2.95
% 9.92/2.95 % (5421)Memory used [KB]: 8443
% 9.92/2.95 % (5421)Time elapsed: 0.107 s
% 9.92/2.95 % (5421)Instructions burned: 375 (million)
% 9.92/2.95 % (5421)------------------------------
% 9.92/2.95 % (5421)------------------------------
% 9.92/2.96 % (5423)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_5039 for (2985ds/832Mi)
% 9.92/3.01 % (5422)Instruction limit reached!
% 9.92/3.01 % (5422)------------------------------
% 9.92/3.01 % (5422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.92/3.01 % (5422)Termination reason: Unknown
% 9.92/3.01 % (5422)Termination phase: Saturation
% 9.92/3.01
% 9.92/3.01 % (5422)Memory used [KB]: 7291
% 9.92/3.01 % (5422)Time elapsed: 0.066 s
% 9.92/3.01 % (5422)Instructions burned: 255 (million)
% 9.92/3.01 % (5422)------------------------------
% 9.92/3.01 % (5422)------------------------------
% 9.92/3.02 % (5424)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_5039 for (2985ds/668Mi)
% 12.90/3.07 % (5420)Instruction limit reached!
% 12.90/3.07 % (5420)------------------------------
% 12.90/3.07 % (5420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.90/3.07 % (5420)Termination reason: Unknown
% 12.90/3.07 % (5420)Termination phase: Saturation
% 12.90/3.07
% 12.90/3.07 % (5420)Memory used [KB]: 11769
% 12.90/3.07 % (5420)Time elapsed: 0.248 s
% 12.90/3.07 % (5420)Instructions burned: 995 (million)
% 12.90/3.07 % (5420)------------------------------
% 12.90/3.07 % (5420)------------------------------
% 12.90/3.08 % (5425)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_5039 for (2984ds/40Mi)
% 12.90/3.08 % (5412)Instruction limit reached!
% 12.90/3.08 % (5412)------------------------------
% 12.90/3.08 % (5412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.90/3.08 % (5412)Termination reason: Unknown
% 12.90/3.08 % (5412)Termination phase: Saturation
% 12.90/3.08
% 12.90/3.08 % (5412)Memory used [KB]: 4989
% 12.90/3.08 % (5412)Time elapsed: 0.610 s
% 12.90/3.08 % (5412)Instructions burned: 1913 (million)
% 12.90/3.08 % (5412)------------------------------
% 12.90/3.08 % (5412)------------------------------
% 12.90/3.09 % (5425)Instruction limit reached!
% 12.90/3.09 % (5425)------------------------------
% 12.90/3.09 % (5425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.90/3.09 % (5425)Termination reason: Unknown
% 12.90/3.09 % (5425)Termination phase: Property scanning
% 12.90/3.09
% 12.90/3.09 % (5425)Memory used [KB]: 2174
% 12.90/3.09 % (5425)Time elapsed: 0.013 s
% 12.90/3.09 % (5425)Instructions burned: 42 (million)
% 12.90/3.09 % (5425)------------------------------
% 12.90/3.09 % (5425)------------------------------
% 12.90/3.09 % (5426)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_5039 for (2984ds/294Mi)
% 12.90/3.10 % (5427)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_5039 for (2984ds/187Mi)
% 13.48/3.15 % (5427)Instruction limit reached!
% 13.48/3.15 % (5427)------------------------------
% 13.48/3.15 % (5427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.15 % (5427)Termination reason: Unknown
% 13.48/3.15 % (5427)Termination phase: Saturation
% 13.48/3.15
% 13.48/3.15 % (5427)Memory used [KB]: 7547
% 13.48/3.15 % (5427)Time elapsed: 0.050 s
% 13.48/3.15 % (5427)Instructions burned: 188 (million)
% 13.48/3.15 % (5427)------------------------------
% 13.48/3.15 % (5427)------------------------------
% 13.48/3.16 % (5428)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_5039 for (2983ds/371Mi)
% 13.48/3.16 % (5426)Instruction limit reached!
% 13.48/3.16 % (5426)------------------------------
% 13.48/3.16 % (5426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.16 % (5426)Termination reason: Unknown
% 13.48/3.16 % (5426)Termination phase: Saturation
% 13.48/3.16
% 13.48/3.16 % (5426)Memory used [KB]: 6908
% 13.48/3.16 % (5426)Time elapsed: 0.074 s
% 13.48/3.16 % (5426)Instructions burned: 297 (million)
% 13.48/3.16 % (5426)------------------------------
% 13.48/3.16 % (5426)------------------------------
% 13.48/3.17 % (5429)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_5039 for (2983ds/1827Mi)
% 13.48/3.19 % (5424)Instruction limit reached!
% 13.48/3.19 % (5424)------------------------------
% 13.48/3.19 % (5424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.48/3.19 % (5424)Termination reason: Unknown
% 13.48/3.19 % (5424)Termination phase: Saturation
% 13.48/3.19
% 13.48/3.19 % (5424)Memory used [KB]: 16375
% 13.48/3.19 % (5424)Time elapsed: 0.170 s
% 13.48/3.19 % (5424)Instructions burned: 670 (million)
% 13.48/3.19 % (5424)------------------------------
% 13.48/3.19 % (5424)------------------------------
% 14.10/3.20 % (5430)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_5039 for (2983ds/70Mi)
% 14.10/3.21 % (5423)Instruction limit reached!
% 14.10/3.21 % (5423)------------------------------
% 14.10/3.21 % (5423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.10/3.21 % (5423)Termination reason: Unknown
% 14.10/3.21 % (5423)Termination phase: Saturation
% 14.10/3.21
% 14.10/3.21 % (5423)Memory used [KB]: 9850
% 14.10/3.21 % (5423)Time elapsed: 0.252 s
% 14.10/3.21 % (5423)Instructions burned: 832 (million)
% 14.10/3.21 % (5423)------------------------------
% 14.10/3.21 % (5423)------------------------------
% 14.10/3.22 % (5430)Instruction limit reached!
% 14.10/3.22 % (5430)------------------------------
% 14.10/3.22 % (5430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.10/3.22 % (5430)Termination reason: Unknown
% 14.10/3.22 % (5430)Termination phase: Property scanning
% 14.10/3.22
% 14.10/3.22 % (5430)Memory used [KB]: 2302
% 14.10/3.22 % (5430)Time elapsed: 0.019 s
% 14.10/3.22 % (5430)Instructions burned: 71 (million)
% 14.10/3.22 % (5430)------------------------------
% 14.10/3.22 % (5430)------------------------------
% 14.10/3.22 % (5431)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_5039 for (2983ds/316Mi)
% 14.10/3.23 % (5432)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_5039 for (2983ds/932Mi)
% 14.10/3.26 % (5428)Instruction limit reached!
% 14.10/3.26 % (5428)------------------------------
% 14.10/3.26 % (5428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.10/3.26 % (5428)Termination reason: Unknown
% 14.10/3.26 % (5428)Termination phase: Saturation
% 14.10/3.26
% 14.10/3.26 % (5428)Memory used [KB]: 8571
% 14.10/3.26 % (5428)Time elapsed: 0.105 s
% 14.10/3.26 % (5428)Instructions burned: 373 (million)
% 14.10/3.26 % (5428)------------------------------
% 14.10/3.26 % (5428)------------------------------
% 14.10/3.27 % (5433)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_5039 for (2982ds/4714Mi)
% 14.56/3.30 % (5431)Instruction limit reached!
% 14.56/3.30 % (5431)------------------------------
% 14.56/3.30 % (5431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.56/3.30 % (5431)Termination reason: Unknown
% 14.56/3.30 % (5431)Termination phase: Saturation
% 14.56/3.30
% 14.56/3.30 % (5431)Memory used [KB]: 7291
% 14.56/3.30 % (5431)Time elapsed: 0.082 s
% 14.56/3.30 % (5431)Instructions burned: 317 (million)
% 14.56/3.30 % (5431)------------------------------
% 14.56/3.30 % (5431)------------------------------
% 14.56/3.31 % (5434)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_5039 for (2982ds/8250Mi)
% 14.95/3.46 % (5432)Instruction limit reached!
% 14.95/3.46 % (5432)------------------------------
% 14.95/3.46 % (5432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.95/3.46 % (5432)Termination reason: Unknown
% 14.95/3.46 % (5432)Termination phase: Saturation
% 14.95/3.46
% 14.95/3.46 % (5432)Memory used [KB]: 13176
% 14.95/3.46 % (5432)Time elapsed: 0.238 s
% 14.95/3.46 % (5432)Instructions burned: 933 (million)
% 14.95/3.46 % (5432)------------------------------
% 14.95/3.46 % (5432)------------------------------
% 14.95/3.48 % (5435)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_5039 for (2980ds/770Mi)
% 15.81/3.69 % (5435)Instruction limit reached!
% 15.81/3.69 % (5435)------------------------------
% 15.81/3.69 % (5435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.81/3.69 % (5435)Termination reason: Unknown
% 15.81/3.69 % (5435)Termination phase: Saturation
% 15.81/3.69
% 15.81/3.69 % (5435)Memory used [KB]: 7164
% 15.81/3.69 % (5435)Time elapsed: 0.221 s
% 15.81/3.69 % (5435)Instructions burned: 772 (million)
% 15.81/3.69 % (5435)------------------------------
% 15.81/3.69 % (5435)------------------------------
% 16.33/3.70 % (5436)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_5039 for (2978ds/794Mi)
% 16.33/3.72 % (5429)Instruction limit reached!
% 16.33/3.72 % (5429)------------------------------
% 16.33/3.72 % (5429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.33/3.72 % (5429)Termination reason: Unknown
% 16.33/3.72 % (5429)Termination phase: Saturation
% 16.33/3.72
% 16.33/3.72 % (5429)Memory used [KB]: 17910
% 16.33/3.72 % (5429)Time elapsed: 0.545 s
% 16.33/3.72 % (5429)Instructions burned: 1829 (million)
% 16.33/3.72 % (5429)------------------------------
% 16.33/3.72 % (5429)------------------------------
% 16.33/3.73 % (5437)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_5039 for (2978ds/464Mi)
% 16.33/3.76 % (5411)Instruction limit reached!
% 16.33/3.76 % (5411)------------------------------
% 16.33/3.76 % (5411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.33/3.76 % (5411)Termination reason: Unknown
% 16.33/3.76 % (5411)Termination phase: Saturation
% 16.33/3.76
% 16.33/3.76 % (5411)Memory used [KB]: 12281
% 16.33/3.76 % (5411)Time elapsed: 1.282 s
% 16.33/3.76 % (5411)Instructions burned: 5207 (million)
% 16.33/3.76 % (5411)------------------------------
% 16.33/3.76 % (5411)------------------------------
% 16.33/3.77 % (5438)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_5039 for (2977ds/1376Mi)
% 17.17/3.86 % (5437)Instruction limit reached!
% 17.17/3.86 % (5437)------------------------------
% 17.17/3.86 % (5437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.17/3.86 % (5437)Termination reason: Unknown
% 17.17/3.86 % (5437)Termination phase: Saturation
% 17.17/3.86
% 17.17/3.86 % (5437)Memory used [KB]: 8571
% 17.17/3.86 % (5437)Time elapsed: 0.135 s
% 17.17/3.86 % (5437)Instructions burned: 466 (million)
% 17.17/3.86 % (5437)------------------------------
% 17.17/3.86 % (5437)------------------------------
% 17.17/3.87 % (5408)Instruction limit reached!
% 17.17/3.87 % (5408)------------------------------
% 17.17/3.87 % (5408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.17/3.87 % (5408)Termination reason: Unknown
% 17.17/3.87 % (5408)Termination phase: Saturation
% 17.17/3.87
% 17.17/3.87 % (5408)Memory used [KB]: 16119
% 17.17/3.87 % (5408)Time elapsed: 1.426 s
% 17.17/3.87 % (5408)Instructions burned: 4437 (million)
% 17.17/3.87 % (5408)------------------------------
% 17.17/3.87 % (5408)------------------------------
% 17.17/3.87 % (5439)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_5039 for (2976ds/906Mi)
% 17.17/3.88 % (5440)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_5039 for (2976ds/434Mi)
% 17.49/3.95 % (5436)Instruction limit reached!
% 17.49/3.95 % (5436)------------------------------
% 17.49/3.95 % (5436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.49/3.95 % (5436)Termination reason: Unknown
% 17.49/3.95 % (5436)Termination phase: Saturation
% 17.49/3.95
% 17.49/3.95 % (5436)Memory used [KB]: 5245
% 17.49/3.95 % (5436)Time elapsed: 0.242 s
% 17.49/3.95 % (5436)Instructions burned: 796 (million)
% 17.49/3.95 % (5436)------------------------------
% 17.49/3.95 % (5436)------------------------------
% 17.49/3.96 % (5441)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_5039 for (2975ds/865Mi)
% 17.49/3.96 % (5413)Instruction limit reached!
% 17.49/3.96 % (5413)------------------------------
% 17.49/3.96 % (5413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.49/3.96 % (5413)Termination reason: Unknown
% 17.49/3.96 % (5413)Termination phase: Saturation
% 17.49/3.96
% 17.49/3.96 % (5413)Memory used [KB]: 13176
% 17.49/3.96 % (5413)Time elapsed: 1.378 s
% 17.49/3.96 % (5413)Instructions burned: 4351 (million)
% 17.49/3.96 % (5413)------------------------------
% 17.49/3.96 % (5413)------------------------------
% 17.49/3.97 % (5442)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_5039 for (2975ds/593Mi)
% 17.49/4.01 % (5440)Instruction limit reached!
% 17.49/4.01 % (5440)------------------------------
% 17.49/4.01 % (5440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.49/4.01 % (5440)Termination reason: Unknown
% 17.49/4.01 % (5440)Termination phase: Saturation
% 17.49/4.01
% 17.49/4.01 % (5440)Memory used [KB]: 9850
% 17.49/4.01 % (5440)Time elapsed: 0.128 s
% 17.49/4.01 % (5440)Instructions burned: 436 (million)
% 17.49/4.01 % (5440)------------------------------
% 17.49/4.01 % (5440)------------------------------
% 17.49/4.02 % (5443)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_5039 for (2975ds/443Mi)
% 19.94/4.11 % (5442)Instruction limit reached!
% 19.94/4.11 % (5442)------------------------------
% 19.94/4.11 % (5442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.94/4.11 % (5442)Termination reason: Unknown
% 19.94/4.11 % (5442)Termination phase: Saturation
% 19.94/4.11
% 19.94/4.11 % (5442)Memory used [KB]: 7291
% 19.94/4.11 % (5442)Time elapsed: 0.146 s
% 19.94/4.11 % (5442)Instructions burned: 594 (million)
% 19.94/4.11 % (5442)------------------------------
% 19.94/4.11 % (5442)------------------------------
% 19.94/4.11 % (5438)Instruction limit reached!
% 19.94/4.11 % (5438)------------------------------
% 19.94/4.11 % (5438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.94/4.11 % (5438)Termination reason: Unknown
% 19.94/4.11 % (5438)Termination phase: Saturation
% 19.94/4.11
% 19.94/4.11 % (5438)Memory used [KB]: 8827
% 19.94/4.11 % (5438)Time elapsed: 0.347 s
% 19.94/4.11 % (5438)Instructions burned: 1376 (million)
% 19.94/4.11 % (5438)------------------------------
% 19.94/4.11 % (5438)------------------------------
% 19.94/4.12 % (5444)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_5039 for (2974ds/594Mi)
% 20.55/4.12 % (5445)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_5039 for (2974ds/327Mi)
% 20.55/4.14 % (5443)Instruction limit reached!
% 20.55/4.14 % (5443)------------------------------
% 20.55/4.14 % (5443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.55/4.14 % (5443)Termination reason: Unknown
% 20.55/4.14 % (5443)Termination phase: Saturation
% 20.55/4.14
% 20.55/4.14 % (5443)Memory used [KB]: 8571
% 20.55/4.14 % (5443)Time elapsed: 0.127 s
% 20.55/4.14 % (5443)Instructions burned: 443 (million)
% 20.55/4.14 % (5443)------------------------------
% 20.55/4.14 % (5443)------------------------------
% 20.55/4.15 % (5439)Instruction limit reached!
% 20.55/4.15 % (5439)------------------------------
% 20.55/4.15 % (5439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.55/4.15 % (5439)Termination reason: Unknown
% 20.55/4.15 % (5439)Termination phase: Saturation
% 20.55/4.15
% 20.55/4.15 % (5439)Memory used [KB]: 10618
% 20.55/4.15 % (5439)Time elapsed: 0.282 s
% 20.55/4.15 % (5439)Instructions burned: 907 (million)
% 20.55/4.15 % (5439)------------------------------
% 20.55/4.15 % (5439)------------------------------
% 20.55/4.15 % (5446)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_5039 for (2974ds/5411Mi)
% 20.55/4.16 % (5447)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_5039 for (2974ds/1762Mi)
% 20.95/4.21 % (5441)Instruction limit reached!
% 20.95/4.21 % (5441)------------------------------
% 20.95/4.21 % (5441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.95/4.21 % (5441)Termination reason: Unknown
% 20.95/4.21 % (5441)Termination phase: Saturation
% 20.95/4.21
% 20.95/4.21 % (5441)Memory used [KB]: 9466
% 20.95/4.21 % (5441)Time elapsed: 0.259 s
% 20.95/4.21 % (5441)Instructions burned: 865 (million)
% 20.95/4.21 % (5441)------------------------------
% 20.95/4.21 % (5441)------------------------------
% 20.95/4.22 % (5448)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_5039 for (2973ds/96Mi)
% 20.95/4.23 % (5445)Instruction limit reached!
% 20.95/4.23 % (5445)------------------------------
% 20.95/4.23 % (5445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.95/4.23 % (5445)Termination reason: Unknown
% 20.95/4.23 % (5445)Termination phase: Saturation
% 20.95/4.23
% 20.95/4.23 % (5445)Memory used [KB]: 10490
% 20.95/4.23 % (5445)Time elapsed: 0.104 s
% 20.95/4.23 % (5445)Instructions burned: 328 (million)
% 20.95/4.23 % (5445)------------------------------
% 20.95/4.23 % (5445)------------------------------
% 20.95/4.24 % (5449)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_5039 for (2973ds/503Mi)
% 20.95/4.25 % (5448)Instruction limit reached!
% 20.95/4.25 % (5448)------------------------------
% 20.95/4.25 % (5448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.95/4.25 % (5448)Termination reason: Unknown
% 20.95/4.25 % (5448)Termination phase: Property scanning
% 20.95/4.25
% 20.95/4.25 % (5448)Memory used [KB]: 2302
% 20.95/4.25 % (5448)Time elapsed: 0.025 s
% 20.95/4.25 % (5448)Instructions burned: 96 (million)
% 20.95/4.25 % (5448)------------------------------
% 20.95/4.25 % (5448)------------------------------
% 20.95/4.26 % (5450)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_5039 for (2972ds/90Mi)
% 20.95/4.28 % (5450)Instruction limit reached!
% 20.95/4.28 % (5450)------------------------------
% 20.95/4.28 % (5450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.95/4.28 % (5450)Termination reason: Unknown
% 20.95/4.28 % (5450)Termination phase: Twee Goal Transformation
% 20.95/4.28
% 20.95/4.28 % (5450)Memory used [KB]: 2430
% 20.95/4.28 % (5450)Time elapsed: 0.026 s
% 20.95/4.28 % (5450)Instructions burned: 93 (million)
% 20.95/4.28 % (5450)------------------------------
% 20.95/4.28 % (5450)------------------------------
% 20.95/4.29 % (5451)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_5039 for (2972ds/593Mi)
% 21.36/4.30 % (5444)Instruction limit reached!
% 21.36/4.30 % (5444)------------------------------
% 21.36/4.30 % (5444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.36/4.30 % (5444)Termination reason: Unknown
% 21.36/4.30 % (5444)Termination phase: Saturation
% 21.36/4.30
% 21.36/4.30 % (5444)Memory used [KB]: 8699
% 21.36/4.30 % (5444)Time elapsed: 0.178 s
% 21.36/4.30 % (5444)Instructions burned: 594 (million)
% 21.36/4.30 % (5444)------------------------------
% 21.36/4.30 % (5444)------------------------------
% 21.36/4.31 % (5452)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_5039 for (2972ds/1512Mi)
% 21.36/4.38 % (5449)Instruction limit reached!
% 21.36/4.38 % (5449)------------------------------
% 21.36/4.38 % (5449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.36/4.38 % (5449)Termination reason: Unknown
% 21.36/4.38 % (5449)Termination phase: Saturation
% 21.36/4.38
% 21.36/4.38 % (5449)Memory used [KB]: 9338
% 21.36/4.38 % (5449)Time elapsed: 0.148 s
% 21.36/4.38 % (5449)Instructions burned: 504 (million)
% 21.36/4.38 % (5449)------------------------------
% 21.36/4.38 % (5449)------------------------------
% 21.36/4.39 % (5453)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_5039 for (2971ds/569Mi)
% 21.91/4.42 % (5433)Instruction limit reached!
% 21.91/4.42 % (5433)------------------------------
% 21.91/4.42 % (5433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.91/4.42 % (5433)Termination reason: Unknown
% 21.91/4.42 % (5433)Termination phase: Saturation
% 21.91/4.42
% 21.91/4.42 % (5433)Memory used [KB]: 7291
% 21.91/4.42 % (5433)Time elapsed: 1.146 s
% 21.91/4.42 % (5433)Instructions burned: 4715 (million)
% 21.91/4.42 % (5433)------------------------------
% 21.91/4.42 % (5433)------------------------------
% 21.91/4.42 % (5454)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_5039 for (2971ds/501Mi)
% 21.91/4.47 % (5451)Instruction limit reached!
% 21.91/4.47 % (5451)------------------------------
% 21.91/4.47 % (5451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.91/4.47 % (5451)Termination reason: Unknown
% 21.91/4.47 % (5451)Termination phase: Saturation
% 21.91/4.47
% 21.91/4.47 % (5451)Memory used [KB]: 9594
% 21.91/4.47 % (5451)Time elapsed: 0.177 s
% 21.91/4.47 % (5451)Instructions burned: 593 (million)
% 21.91/4.47 % (5451)------------------------------
% 21.91/4.47 % (5451)------------------------------
% 21.91/4.48 % (5455)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_5039 for (2970ds/562Mi)
% 22.23/4.54 % (5453)Instruction limit reached!
% 22.23/4.54 % (5453)------------------------------
% 22.23/4.54 % (5453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.23/4.54 % (5453)Termination reason: Unknown
% 22.23/4.54 % (5453)Termination phase: Saturation
% 22.23/4.54
% 22.23/4.54 % (5453)Memory used [KB]: 11641
% 22.23/4.54 % (5453)Time elapsed: 0.144 s
% 22.23/4.54 % (5453)Instructions burned: 572 (million)
% 22.23/4.54 % (5453)------------------------------
% 22.23/4.54 % (5453)------------------------------
% 22.23/4.55 % (5456)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_5039 for (2970ds/406Mi)
% 22.23/4.57 % (5454)Instruction limit reached!
% 22.23/4.57 % (5454)------------------------------
% 22.23/4.57 % (5454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.23/4.57 % (5454)Termination reason: Unknown
% 22.23/4.57 % (5454)Termination phase: Saturation
% 22.23/4.57
% 22.23/4.57 % (5454)Memory used [KB]: 9466
% 22.23/4.57 % (5454)Time elapsed: 0.149 s
% 22.23/4.57 % (5454)Instructions burned: 501 (million)
% 22.23/4.57 % (5454)------------------------------
% 22.23/4.57 % (5454)------------------------------
% 22.23/4.58 % (5457)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_5039 for (2969ds/582Mi)
% 22.64/4.60 % (5447)Instruction limit reached!
% 22.64/4.60 % (5447)------------------------------
% 22.64/4.60 % (5447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.64/4.60 % (5447)Termination reason: Unknown
% 22.64/4.60 % (5447)Termination phase: Saturation
% 22.64/4.60
% 22.64/4.60 % (5447)Memory used [KB]: 15735
% 22.64/4.60 % (5447)Time elapsed: 0.436 s
% 22.64/4.60 % (5447)Instructions burned: 1762 (million)
% 22.64/4.60 % (5447)------------------------------
% 22.64/4.60 % (5447)------------------------------
% 22.64/4.61 % (5458)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_5039 for (2969ds/456Mi)
% 22.64/4.64 % (5455)Instruction limit reached!
% 22.64/4.64 % (5455)------------------------------
% 22.64/4.64 % (5455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.64/4.64 % (5455)Termination reason: Unknown
% 22.64/4.64 % (5455)Termination phase: Saturation
% 22.64/4.64
% 22.64/4.64 % (5455)Memory used [KB]: 8187
% 22.64/4.64 % (5455)Time elapsed: 0.164 s
% 22.64/4.64 % (5455)Instructions burned: 563 (million)
% 22.64/4.64 % (5455)------------------------------
% 22.64/4.64 % (5455)------------------------------
% 22.64/4.65 % (5459)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_5039 for (2969ds/393Mi)
% 22.64/4.66 % (5456)Instruction limit reached!
% 22.64/4.66 % (5456)------------------------------
% 22.64/4.66 % (5456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.64/4.66 % (5456)Termination reason: Unknown
% 22.64/4.66 % (5456)Termination phase: Saturation
% 22.64/4.66
% 22.64/4.66 % (5456)Memory used [KB]: 7419
% 22.64/4.66 % (5456)Time elapsed: 0.112 s
% 22.64/4.66 % (5456)Instructions burned: 406 (million)
% 22.64/4.66 % (5456)------------------------------
% 22.64/4.66 % (5456)------------------------------
% 22.64/4.67 % (5460)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_5039 for (2968ds/1335Mi)
% 23.48/4.74 % (5458)Instruction limit reached!
% 23.48/4.74 % (5458)------------------------------
% 23.48/4.74 % (5458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.48/4.74 % (5458)Termination reason: Unknown
% 23.48/4.74 % (5458)Termination phase: Saturation
% 23.48/4.74
% 23.48/4.74 % (5458)Memory used [KB]: 9210
% 23.48/4.74 % (5458)Time elapsed: 0.133 s
% 23.48/4.74 % (5458)Instructions burned: 456 (million)
% 23.48/4.74 % (5458)------------------------------
% 23.48/4.74 % (5458)------------------------------
% 23.48/4.75 % (5461)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_5039 for (2968ds/3373Mi)
% 23.48/4.76 % (5457)Instruction limit reached!
% 23.48/4.76 % (5457)------------------------------
% 23.48/4.76 % (5457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.48/4.76 % (5457)Termination reason: Unknown
% 23.48/4.76 % (5457)Termination phase: Saturation
% 23.48/4.76
% 23.48/4.76 % (5457)Memory used [KB]: 9722
% 23.48/4.76 % (5457)Time elapsed: 0.182 s
% 23.48/4.76 % (5457)Instructions burned: 584 (million)
% 23.48/4.76 % (5457)------------------------------
% 23.48/4.76 % (5457)------------------------------
% 23.48/4.77 % (5459)Instruction limit reached!
% 23.48/4.77 % (5459)------------------------------
% 23.48/4.77 % (5459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.48/4.77 % (5459)Termination reason: Unknown
% 23.48/4.77 % (5459)Termination phase: Saturation
% 23.48/4.77
% 23.48/4.77 % (5459)Memory used [KB]: 9083
% 23.48/4.77 % (5459)Time elapsed: 0.120 s
% 23.48/4.77 % (5459)Instructions burned: 393 (million)
% 23.48/4.77 % (5459)------------------------------
% 23.48/4.77 % (5459)------------------------------
% 23.48/4.77 % (5462)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_5039 for (2967ds/474Mi)
% 23.48/4.78 % (5452)Instruction limit reached!
% 23.48/4.78 % (5452)------------------------------
% 23.48/4.78 % (5452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.48/4.78 % (5452)Termination reason: Unknown
% 23.48/4.78 % (5452)Termination phase: Saturation
% 23.48/4.78
% 23.48/4.78 % (5452)Memory used [KB]: 10362
% 23.48/4.78 % (5452)Time elapsed: 0.469 s
% 23.48/4.78 % (5452)Instructions burned: 1514 (million)
% 23.48/4.78 % (5452)------------------------------
% 23.48/4.78 % (5452)------------------------------
% 23.48/4.78 % (5463)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_5039 for (2967ds/157Mi)
% 23.48/4.79 % (5464)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_5039 for (2967ds/590Mi)
% 24.52/4.82 % (5463)Instruction limit reached!
% 24.52/4.82 % (5463)------------------------------
% 24.52/4.82 % (5463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.52/4.82 % (5463)Termination reason: Unknown
% 24.52/4.82 % (5463)Termination phase: Saturation
% 24.52/4.82
% 24.52/4.82 % (5463)Memory used [KB]: 6908
% 24.52/4.82 % (5463)Time elapsed: 0.041 s
% 24.52/4.82 % (5463)Instructions burned: 157 (million)
% 24.52/4.82 % (5463)------------------------------
% 24.52/4.82 % (5463)------------------------------
% 24.52/4.83 % (5465)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_5039 for (2967ds/104Mi)
% 24.52/4.85 % (5465)Instruction limit reached!
% 24.52/4.85 % (5465)------------------------------
% 24.52/4.85 % (5465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.52/4.85 % (5465)Termination reason: Unknown
% 24.52/4.85 % (5465)Termination phase: Property scanning
% 24.52/4.85
% 24.52/4.85 % (5465)Memory used [KB]: 2430
% 24.52/4.85 % (5465)Time elapsed: 0.028 s
% 24.52/4.85 % (5465)Instructions burned: 105 (million)
% 24.52/4.85 % (5465)------------------------------
% 24.52/4.85 % (5465)------------------------------
% 24.52/4.86 % (5466)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_5039 for (2966ds/414Mi)
% 24.52/4.89 % (5462)Instruction limit reached!
% 24.52/4.89 % (5462)------------------------------
% 24.52/4.89 % (5462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.52/4.89 % (5462)Termination reason: Unknown
% 24.52/4.89 % (5462)Termination phase: Saturation
% 24.52/4.89
% 24.52/4.89 % (5462)Memory used [KB]: 11385
% 24.52/4.89 % (5462)Time elapsed: 0.121 s
% 24.52/4.89 % (5462)Instructions burned: 476 (million)
% 24.52/4.89 % (5462)------------------------------
% 24.52/4.89 % (5462)------------------------------
% 24.84/4.90 % (5467)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_5039 for (2966ds/715Mi)
% 24.84/4.95 % (5464)Instruction limit reached!
% 24.84/4.95 % (5464)------------------------------
% 24.84/4.95 % (5464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.84/4.95 % (5464)Termination reason: Unknown
% 24.84/4.95 % (5464)Termination phase: Saturation
% 24.84/4.95
% 24.84/4.95 % (5464)Memory used [KB]: 8443
% 24.84/4.95 % (5464)Time elapsed: 0.168 s
% 24.84/4.95 % (5464)Instructions burned: 592 (million)
% 24.84/4.95 % (5464)------------------------------
% 24.84/4.95 % (5464)------------------------------
% 24.84/4.96 % (5468)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_5039 for (2965ds/961Mi)
% 24.84/4.97 % (5466)Instruction limit reached!
% 24.84/4.97 % (5466)------------------------------
% 24.84/4.97 % (5466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.84/4.97 % (5466)Termination reason: Unknown
% 24.84/4.97 % (5466)Termination phase: Saturation
% 24.84/4.97
% 24.84/4.97 % (5466)Memory used [KB]: 7164
% 24.84/4.97 % (5466)Time elapsed: 0.105 s
% 24.84/4.97 % (5466)Instructions burned: 416 (million)
% 24.84/4.97 % (5466)------------------------------
% 24.84/4.97 % (5466)------------------------------
% 24.84/4.98 % (5469)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_5039 for (2965ds/1213Mi)
% 26.95/5.04 % (5460)Instruction limit reached!
% 26.95/5.04 % (5460)------------------------------
% 26.95/5.04 % (5460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.95/5.04 % (5460)Termination reason: Unknown
% 26.95/5.04 % (5460)Termination phase: Saturation
% 26.95/5.04
% 26.95/5.04 % (5460)Memory used [KB]: 9083
% 26.95/5.04 % (5460)Time elapsed: 0.374 s
% 26.95/5.04 % (5460)Instructions burned: 1336 (million)
% 26.95/5.04 % (5460)------------------------------
% 26.95/5.04 % (5460)------------------------------
% 26.95/5.05 % (5470)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_5039 for (2965ds/1979Mi)
% 26.95/5.12 % (5467)Instruction limit reached!
% 26.95/5.12 % (5467)------------------------------
% 26.95/5.12 % (5467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.95/5.12 % (5467)Termination reason: Unknown
% 26.95/5.12 % (5467)Termination phase: Saturation
% 26.95/5.12
% 26.95/5.12 % (5467)Memory used [KB]: 4861
% 26.95/5.12 % (5467)Time elapsed: 0.216 s
% 26.95/5.12 % (5467)Instructions burned: 715 (million)
% 26.95/5.12 % (5467)------------------------------
% 26.95/5.12 % (5467)------------------------------
% 27.63/5.13 % (5471)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_5039 for (2964ds/481Mi)
% 28.00/5.25 % (5471)Instruction limit reached!
% 28.00/5.25 % (5471)------------------------------
% 28.00/5.25 % (5471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.00/5.25 % (5471)Termination reason: Unknown
% 28.00/5.25 % (5471)Termination phase: Saturation
% 28.00/5.25
% 28.00/5.25 % (5471)Memory used [KB]: 11641
% 28.00/5.25 % (5471)Time elapsed: 0.123 s
% 28.00/5.25 % (5471)Instructions burned: 484 (million)
% 28.00/5.25 % (5471)------------------------------
% 28.00/5.25 % (5471)------------------------------
% 28.00/5.25 % (5468)Instruction limit reached!
% 28.00/5.25 % (5468)------------------------------
% 28.00/5.25 % (5468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.00/5.25 % (5468)Termination reason: Unknown
% 28.00/5.25 % (5468)Termination phase: Saturation
% 28.00/5.25
% 28.00/5.25 % (5468)Memory used [KB]: 8955
% 28.00/5.25 % (5468)Time elapsed: 0.291 s
% 28.00/5.25 % (5468)Instructions burned: 962 (million)
% 28.00/5.25 % (5468)------------------------------
% 28.00/5.25 % (5468)------------------------------
% 28.00/5.26 % (5472)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_5039 for (2962ds/783Mi)
% 28.00/5.26 % (5473)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_5039 for (2962ds/432Mi)
% 28.58/5.35 % (5469)Instruction limit reached!
% 28.58/5.35 % (5469)------------------------------
% 28.58/5.35 % (5469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.58/5.35 % (5469)Termination reason: Unknown
% 28.58/5.35 % (5469)Termination phase: Saturation
% 28.58/5.35
% 28.58/5.35 % (5469)Memory used [KB]: 13048
% 28.58/5.35 % (5469)Time elapsed: 0.374 s
% 28.58/5.35 % (5469)Instructions burned: 1214 (million)
% 28.58/5.35 % (5469)------------------------------
% 28.58/5.35 % (5469)------------------------------
% 28.58/5.36 % (5474)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_5039 for (2961ds/1670Mi)
% 28.58/5.39 % (5473)Instruction limit reached!
% 28.58/5.39 % (5473)------------------------------
% 28.58/5.39 % (5473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.58/5.39 % (5473)Termination reason: Unknown
% 28.58/5.39 % (5473)Termination phase: Saturation
% 28.58/5.39
% 28.58/5.39 % (5473)Memory used [KB]: 8443
% 28.58/5.39 % (5473)Time elapsed: 0.126 s
% 28.58/5.39 % (5473)Instructions burned: 433 (million)
% 28.58/5.39 % (5473)------------------------------
% 28.58/5.39 % (5473)------------------------------
% 29.08/5.40 % (5475)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_5039 for (2961ds/90Mi)
% 29.08/5.42 % (5475)Instruction limit reached!
% 29.08/5.42 % (5475)------------------------------
% 29.08/5.42 % (5475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.08/5.42 % (5475)Termination reason: Unknown
% 29.08/5.42 % (5475)Termination phase: Property scanning
% 29.08/5.42
% 29.08/5.42 % (5475)Memory used [KB]: 2430
% 29.08/5.42 % (5475)Time elapsed: 0.026 s
% 29.08/5.42 % (5475)Instructions burned: 93 (million)
% 29.08/5.42 % (5475)------------------------------
% 29.08/5.42 % (5475)------------------------------
% 29.08/5.43 % (5476)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_5039 for (2961ds/346Mi)
% 29.42/5.50 % (5472)Instruction limit reached!
% 29.42/5.50 % (5472)------------------------------
% 29.42/5.50 % (5472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.50 % (5472)Termination reason: Unknown
% 29.42/5.50 % (5472)Termination phase: Saturation
% 29.42/5.50
% 29.42/5.50 % (5472)Memory used [KB]: 10746
% 29.42/5.50 % (5472)Time elapsed: 0.244 s
% 29.42/5.50 % (5472)Instructions burned: 784 (million)
% 29.42/5.50 % (5472)------------------------------
% 29.42/5.50 % (5472)------------------------------
% 29.42/5.51 % (5477)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_5039 for (2960ds/401Mi)
% 29.42/5.52 % (5476)Instruction limit reached!
% 29.42/5.52 % (5476)------------------------------
% 29.42/5.52 % (5476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.42/5.52 % (5476)Termination reason: Unknown
% 29.42/5.52 % (5476)Termination phase: Saturation
% 29.42/5.52
% 29.42/5.52 % (5476)Memory used [KB]: 7291
% 29.42/5.52 % (5476)Time elapsed: 0.087 s
% 29.42/5.52 % (5476)Instructions burned: 348 (million)
% 29.42/5.52 % (5476)------------------------------
% 29.42/5.52 % (5476)------------------------------
% 29.42/5.53 % (5478)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_5039 for (2960ds/6454Mi)
% 30.08/5.62 % (5477)Instruction limit reached!
% 30.08/5.62 % (5477)------------------------------
% 30.08/5.62 % (5477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.08/5.62 % (5477)Termination reason: Unknown
% 30.08/5.62 % (5477)Termination phase: Saturation
% 30.08/5.62
% 30.08/5.62 % (5477)Memory used [KB]: 7291
% 30.08/5.62 % (5477)Time elapsed: 0.104 s
% 30.08/5.62 % (5477)Instructions burned: 403 (million)
% 30.08/5.62 % (5477)------------------------------
% 30.08/5.62 % (5477)------------------------------
% 30.08/5.63 % (5479)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_5039 for (2959ds/283Mi)
% 30.08/5.65 % (5470)Refutation not found, non-redundant clauses discarded% (5470)------------------------------
% 30.08/5.65 % (5470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.08/5.65 % (5470)Termination reason: Refutation not found, non-redundant clauses discarded
% 30.08/5.65
% 30.08/5.65 % (5470)Memory used [KB]: 10234
% 30.08/5.65 % (5470)Time elapsed: 0.603 s
% 30.08/5.65 % (5470)Instructions burned: 1976 (million)
% 30.08/5.65 % (5470)------------------------------
% 30.08/5.65 % (5470)------------------------------
% 30.08/5.66 % (5480)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_5039 for (2958ds/865Mi)
% 31.10/5.70 % (5479)Instruction limit reached!
% 31.10/5.70 % (5479)------------------------------
% 31.10/5.70 % (5479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.10/5.70 % (5479)Termination reason: Unknown
% 31.10/5.70 % (5479)Termination phase: Saturation
% 31.10/5.70
% 31.10/5.70 % (5479)Memory used [KB]: 7931
% 31.10/5.70 % (5479)Time elapsed: 0.078 s
% 31.10/5.70 % (5479)Instructions burned: 284 (million)
% 31.10/5.70 % (5479)------------------------------
% 31.10/5.70 % (5479)------------------------------
% 31.10/5.71 % (5481)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_5039 for (2958ds/4528Mi)
% 31.10/5.78 % (5474)Instruction limit reached!
% 31.10/5.78 % (5474)------------------------------
% 31.10/5.78 % (5474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.10/5.78 % (5474)Termination reason: Unknown
% 31.10/5.78 % (5474)Termination phase: Saturation
% 31.10/5.78
% 31.10/5.78 % (5474)Memory used [KB]: 12665
% 31.10/5.78 % (5474)Time elapsed: 0.425 s
% 31.10/5.78 % (5474)Instructions burned: 1673 (million)
% 31.10/5.78 % (5474)------------------------------
% 31.10/5.78 % (5474)------------------------------
% 31.10/5.80 % (5482)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_5039 for (2957ds/1001Mi)
% 31.91/5.81 % (5461)Instruction limit reached!
% 31.91/5.81 % (5461)------------------------------
% 31.91/5.81 % (5461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.91/5.81 % (5461)Termination reason: Unknown
% 31.91/5.81 % (5461)Termination phase: Saturation
% 31.91/5.81
% 31.91/5.81 % (5461)Memory used [KB]: 12409
% 31.91/5.81 % (5461)Time elapsed: 1.058 s
% 31.91/5.81 % (5461)Instructions burned: 3373 (million)
% 31.91/5.81 % (5461)------------------------------
% 31.91/5.81 % (5461)------------------------------
% 31.91/5.82 % (5446)Refutation not found, non-redundant clauses discarded% (5446)------------------------------
% 31.91/5.82 % (5446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.91/5.82 % (5446)Termination reason: Refutation not found, non-redundant clauses discarded
% 31.91/5.82
% 31.91/5.82 % (5446)Memory used [KB]: 15991
% 31.91/5.82 % (5446)Time elapsed: 1.664 s
% 31.91/5.82 % (5446)Instructions burned: 5267 (million)
% 31.91/5.82 % (5446)------------------------------
% 31.91/5.82 % (5446)------------------------------
% 31.91/5.82 % (5483)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_5039 for (2957ds/102Mi)
% 31.91/5.82 % (5481)Refutation not found, incomplete strategy
% 31.91/5.82 % (5481)------------------------------
% 31.91/5.82 % (5481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.91/5.82 % (5481)Termination reason: Refutation not found, incomplete strategy
% 31.91/5.82
% 31.91/5.82
% 31.91/5.82 % (5481)Memory used [KB]: 2558
% 31.91/5.82 % (5481)Time elapsed: 0.111 s
% 31.91/5.82 % (5481)Instructions burned: 416 (million)
% 31.91/5.82 % (5481)------------------------------
% 31.91/5.82 % (5481)------------------------------
% 31.91/5.83 % (5484)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_5039 for (2957ds/952Mi)
% 31.91/5.83 % (5485)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_5039 for (2957ds/578Mi)
% 31.91/5.84 % (5483)Instruction limit reached!
% 31.91/5.84 % (5483)------------------------------
% 31.91/5.84 % (5483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.91/5.84 % (5483)Termination reason: Unknown
% 31.91/5.84 % (5483)Termination phase: Property scanning
% 31.91/5.84
% 31.91/5.84 % (5483)Memory used [KB]: 2430
% 31.91/5.84 % (5483)Time elapsed: 0.028 s
% 31.91/5.84 % (5483)Instructions burned: 106 (million)
% 31.91/5.84 % (5483)------------------------------
% 31.91/5.84 % (5483)------------------------------
% 31.91/5.85 % (5486)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_5039 for (2957ds/643Mi)
% 32.24/5.91 % (5480)Instruction limit reached!
% 32.24/5.91 % (5480)------------------------------
% 32.24/5.91 % (5480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.24/5.91 % (5480)Termination reason: Unknown
% 32.24/5.91 % (5480)Termination phase: Saturation
% 32.24/5.91
% 32.24/5.91 % (5480)Memory used [KB]: 8315
% 32.24/5.91 % (5480)Time elapsed: 0.244 s
% 32.24/5.91 % (5480)Instructions burned: 866 (million)
% 32.24/5.91 % (5480)------------------------------
% 32.24/5.91 % (5480)------------------------------
% 32.24/5.92 % (5487)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_5039 for (2956ds/865Mi)
% 32.24/5.97 % (5485)Instruction limit reached!
% 32.24/5.97 % (5485)------------------------------
% 32.24/5.97 % (5485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.24/5.97 % (5485)Termination reason: Unknown
% 32.24/5.97 % (5485)Termination phase: Saturation
% 32.24/5.97
% 32.24/5.97 % (5485)Memory used [KB]: 8827
% 32.24/5.97 % (5485)Time elapsed: 0.135 s
% 32.24/5.97 % (5485)Instructions burned: 581 (million)
% 32.24/5.97 % (5485)------------------------------
% 32.24/5.97 % (5485)------------------------------
% 32.24/5.98 % (5488)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_5039 for (2955ds/1174Mi)
% 32.24/5.98 % (5434)Instruction limit reached!
% 32.24/5.98 % (5434)------------------------------
% 32.24/5.98 % (5434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.24/5.98 % (5434)Termination reason: Unknown
% 32.24/5.98 % (5434)Termination phase: Saturation
% 32.24/5.98
% 32.24/5.98 % (5434)Memory used [KB]: 24306
% 32.24/5.98 % (5434)Time elapsed: 2.669 s
% 32.24/5.98 % (5434)Instructions burned: 8252 (million)
% 32.24/5.98 % (5434)------------------------------
% 32.24/5.98 % (5434)------------------------------
% 32.24/5.99 % (5489)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_5039 for (2955ds/644Mi)
% 32.24/6.02 % (5486)Instruction limit reached!
% 32.24/6.02 % (5486)------------------------------
% 32.24/6.02 % (5486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.24/6.02 % (5486)Termination reason: Unknown
% 32.24/6.02 % (5486)Termination phase: Saturation
% 32.24/6.02
% 32.24/6.02 % (5486)Memory used [KB]: 11641
% 32.24/6.02 % (5486)Time elapsed: 0.163 s
% 32.24/6.02 % (5486)Instructions burned: 643 (million)
% 32.24/6.02 % (5486)------------------------------
% 32.24/6.02 % (5486)------------------------------
% 33.99/6.03 % (5490)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_5039 for (2955ds/1201Mi)
% 33.99/6.09 % (5482)Instruction limit reached!
% 33.99/6.09 % (5482)------------------------------
% 33.99/6.09 % (5482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.99/6.09 % (5482)Termination reason: Unknown
% 33.99/6.09 % (5482)Termination phase: Saturation
% 33.99/6.09
% 33.99/6.09 % (5482)Memory used [KB]: 9850
% 33.99/6.09 % (5482)Time elapsed: 0.296 s
% 33.99/6.09 % (5482)Instructions burned: 1004 (million)
% 33.99/6.09 % (5482)------------------------------
% 33.99/6.09 % (5482)------------------------------
% 33.99/6.10 % (5491)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_5039 for (2954ds/1046Mi)
% 33.99/6.12 % (5484)Instruction limit reached!
% 33.99/6.12 % (5484)------------------------------
% 33.99/6.12 % (5484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.99/6.12 % (5484)Termination reason: Unknown
% 33.99/6.12 % (5484)Termination phase: Saturation
% 33.99/6.12
% 33.99/6.12 % (5484)Memory used [KB]: 9850
% 33.99/6.12 % (5484)Time elapsed: 0.291 s
% 33.99/6.12 % (5484)Instructions burned: 954 (million)
% 33.99/6.12 % (5484)------------------------------
% 33.99/6.12 % (5484)------------------------------
% 34.59/6.13 % (5492)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_5039 for (2954ds/222Mi)
% 34.59/6.15 % (5487)Instruction limit reached!
% 34.59/6.15 % (5487)------------------------------
% 34.59/6.15 % (5487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.59/6.15 % (5487)Termination reason: Unknown
% 34.59/6.15 % (5487)Termination phase: Saturation
% 34.59/6.15
% 34.59/6.15 % (5487)Memory used [KB]: 7419
% 34.59/6.15 % (5487)Time elapsed: 0.239 s
% 34.59/6.15 % (5487)Instructions burned: 866 (million)
% 34.59/6.15 % (5487)------------------------------
% 34.59/6.15 % (5487)------------------------------
% 34.59/6.16 % (5493)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_5039 for (2953ds/68Mi)
% 34.59/6.18 % (5493)Instruction limit reached!
% 34.59/6.18 % (5493)------------------------------
% 34.59/6.18 % (5493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.59/6.18 % (5493)Termination reason: Unknown
% 34.59/6.18 % (5493)Termination phase: SInE selection
% 34.59/6.18
% 34.59/6.18 % (5493)Memory used [KB]: 2174
% 34.59/6.18 % (5493)Time elapsed: 0.019 s
% 34.59/6.18 % (5493)Instructions burned: 71 (million)
% 34.59/6.18 % (5493)------------------------------
% 34.59/6.18 % (5493)------------------------------
% 34.59/6.18 % (5489)Instruction limit reached!
% 34.59/6.18 % (5489)------------------------------
% 34.59/6.18 % (5489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.59/6.18 % (5489)Termination reason: Unknown
% 34.59/6.18 % (5489)Termination phase: Saturation
% 34.59/6.18
% 34.59/6.18 % (5489)Memory used [KB]: 7803
% 34.59/6.18 % (5489)Time elapsed: 0.190 s
% 34.59/6.18 % (5489)Instructions burned: 644 (million)
% 34.59/6.18 % (5489)------------------------------
% 34.59/6.18 % (5489)------------------------------
% 34.59/6.18 % (5492)Instruction limit reached!
% 34.59/6.18 % (5492)------------------------------
% 34.59/6.18 % (5492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.59/6.18 % (5492)Termination reason: Unknown
% 34.59/6.18 % (5492)Termination phase: Saturation
% 34.59/6.18
% 34.59/6.18 % (5492)Memory used [KB]: 7291
% 34.59/6.18 % (5492)Time elapsed: 0.057 s
% 34.59/6.18 % (5492)Instructions burned: 222 (million)
% 34.59/6.18 % (5492)------------------------------
% 34.59/6.18 % (5492)------------------------------
% 34.59/6.19 % (5494)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_5039 for (2953ds/454Mi)
% 34.59/6.19 % (5495)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_5039 for (2953ds/360Mi)
% 34.59/6.19 % (5496)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_5039 for (2953ds/157Mi)
% 34.94/6.23 % (5496)Instruction limit reached!
% 34.94/6.23 % (5496)------------------------------
% 34.94/6.23 % (5496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.94/6.23 % (5496)Termination reason: Unknown
% 34.94/6.23 % (5496)Termination phase: Saturation
% 34.94/6.23
% 34.94/6.23 % (5496)Memory used [KB]: 7036
% 34.94/6.23 % (5496)Time elapsed: 0.040 s
% 34.94/6.23 % (5496)Instructions burned: 157 (million)
% 34.94/6.23 % (5496)------------------------------
% 34.94/6.23 % (5496)------------------------------
% 34.94/6.24 % (5497)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_5039 for (2953ds/5061Mi)
% 34.94/6.28 % (5495)Instruction limit reached!
% 34.94/6.28 % (5495)------------------------------
% 34.94/6.28 % (5495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.94/6.28 % (5495)Termination reason: Unknown
% 34.94/6.28 % (5495)Termination phase: Saturation
% 34.94/6.28
% 34.94/6.28 % (5495)Memory used [KB]: 7291
% 34.94/6.28 % (5495)Time elapsed: 0.091 s
% 34.94/6.28 % (5495)Instructions burned: 362 (million)
% 34.94/6.28 % (5495)------------------------------
% 34.94/6.28 % (5495)------------------------------
% 34.94/6.29 % (5498)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_5039 for (2952ds/2401Mi)
% 35.29/6.30 % (5494)Instruction limit reached!
% 35.29/6.30 % (5494)------------------------------
% 35.29/6.30 % (5494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.29/6.30 % (5494)Termination reason: Unknown
% 35.29/6.30 % (5494)Termination phase: Saturation
% 35.29/6.30
% 35.29/6.30 % (5494)Memory used [KB]: 15991
% 35.29/6.30 % (5494)Time elapsed: 0.115 s
% 35.29/6.30 % (5494)Instructions burned: 456 (million)
% 35.29/6.30 % (5494)------------------------------
% 35.29/6.30 % (5494)------------------------------
% 35.29/6.31 % (5499)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_5039 for (2952ds/5798Mi)
% 35.29/6.33 % (5488)Instruction limit reached!
% 35.29/6.33 % (5488)------------------------------
% 35.29/6.33 % (5488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.29/6.33 % (5488)Termination reason: Unknown
% 35.29/6.33 % (5488)Termination phase: Saturation
% 35.29/6.33
% 35.29/6.33 % (5488)Memory used [KB]: 9594
% 35.29/6.33 % (5488)Time elapsed: 0.358 s
% 35.29/6.33 % (5488)Instructions burned: 1176 (million)
% 35.29/6.33 % (5488)------------------------------
% 35.29/6.33 % (5488)------------------------------
% 35.29/6.34 % (5500)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_5039 for (2952ds/346Mi)
% 35.29/6.35 % (5490)Instruction limit reached!
% 35.29/6.35 % (5490)------------------------------
% 35.29/6.35 % (5490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.29/6.35 % (5490)Termination reason: Unknown
% 35.29/6.35 % (5490)Termination phase: Saturation
% 35.29/6.35
% 35.29/6.35 % (5490)Memory used [KB]: 9850
% 35.29/6.35 % (5490)Time elapsed: 0.329 s
% 35.29/6.35 % (5490)Instructions burned: 1202 (million)
% 35.29/6.35 % (5490)------------------------------
% 35.29/6.35 % (5490)------------------------------
% 35.29/6.36 % (5491)Instruction limit reached!
% 35.29/6.36 % (5491)------------------------------
% 35.29/6.36 % (5491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.29/6.36 % (5491)Termination reason: Unknown
% 35.29/6.36 % (5491)Termination phase: Saturation
% 35.29/6.36
% 35.29/6.36 % (5491)Memory used [KB]: 7164
% 35.29/6.36 % (5491)Time elapsed: 0.257 s
% 35.29/6.36 % (5491)Instructions burned: 1048 (million)
% 35.29/6.36 % (5491)------------------------------
% 35.29/6.36 % (5491)------------------------------
% 35.29/6.36 % (5501)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_5039 for (2951ds/1321Mi)
% 35.29/6.37 % (5502)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_5039 for (2951ds/1312Mi)
% 36.17/6.43 % (5500)Instruction limit reached!
% 36.17/6.43 % (5500)------------------------------
% 36.17/6.43 % (5500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.17/6.43 % (5500)Termination reason: Unknown
% 36.17/6.43 % (5500)Termination phase: Saturation
% 36.17/6.43
% 36.17/6.43 % (5500)Memory used [KB]: 7291
% 36.17/6.43 % (5500)Time elapsed: 0.090 s
% 36.17/6.43 % (5500)Instructions burned: 348 (million)
% 36.17/6.43 % (5500)------------------------------
% 36.17/6.43 % (5500)------------------------------
% 36.17/6.44 % (5503)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_5039 for (2951ds/672Mi)
% 36.46/6.64 % (5503)Instruction limit reached!
% 36.46/6.64 % (5503)------------------------------
% 36.46/6.64 % (5503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.46/6.64 % (5503)Termination reason: Unknown
% 36.46/6.64 % (5503)Termination phase: Saturation
% 36.46/6.64
% 36.46/6.64 % (5503)Memory used [KB]: 10106
% 36.46/6.64 % (5503)Time elapsed: 0.204 s
% 36.46/6.64 % (5503)Instructions burned: 674 (million)
% 36.46/6.64 % (5503)------------------------------
% 36.46/6.64 % (5503)------------------------------
% 36.46/6.66 % (5504)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_5039 for (2948ds/1897Mi)
% 36.80/6.70 % (5502)Instruction limit reached!
% 36.80/6.70 % (5502)------------------------------
% 36.80/6.70 % (5502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.80/6.70 % (5502)Termination reason: Unknown
% 36.80/6.70 % (5502)Termination phase: Saturation
% 36.80/6.70
% 36.80/6.70 % (5502)Memory used [KB]: 12281
% 36.80/6.70 % (5502)Time elapsed: 0.335 s
% 36.80/6.70 % (5502)Instructions burned: 1312 (million)
% 36.80/6.70 % (5502)------------------------------
% 36.80/6.70 % (5502)------------------------------
% 36.80/6.71 % (5505)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_5039 for (2948ds/1202Mi)
% 36.80/6.76 % (5501)Instruction limit reached!
% 36.80/6.76 % (5501)------------------------------
% 36.80/6.76 % (5501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.80/6.76 % (5501)Termination reason: Unknown
% 36.80/6.76 % (5501)Termination phase: Saturation
% 36.80/6.76
% 36.80/6.76 % (5501)Memory used [KB]: 7164
% 36.80/6.76 % (5501)Time elapsed: 0.397 s
% 36.80/6.76 % (5501)Instructions burned: 1322 (million)
% 36.80/6.76 % (5501)------------------------------
% 36.80/6.76 % (5501)------------------------------
% 36.80/6.77 % (5506)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_5039 for (2947ds/1493Mi)
% 37.74/7.01 % (5498)Instruction limit reached!
% 37.74/7.01 % (5498)------------------------------
% 37.74/7.01 % (5498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.74/7.01 % (5498)Termination reason: Unknown
% 37.74/7.01 % (5498)Termination phase: Saturation
% 37.74/7.01
% 37.74/7.01 % (5498)Memory used [KB]: 9594
% 37.74/7.01 % (5498)Time elapsed: 0.721 s
% 37.74/7.01 % (5498)Instructions burned: 2401 (million)
% 37.74/7.01 % (5498)------------------------------
% 37.74/7.01 % (5498)------------------------------
% 37.74/7.02 % (5507)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_5039 for (2945ds/7679Mi)
% 41.00/7.06 % (5505)Instruction limit reached!
% 41.00/7.06 % (5505)------------------------------
% 41.00/7.06 % (5505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.00/7.06 % (5505)Termination reason: Unknown
% 41.00/7.06 % (5505)Termination phase: Saturation
% 41.00/7.06
% 41.00/7.06 % (5505)Memory used [KB]: 6908
% 41.00/7.06 % (5505)Time elapsed: 0.349 s
% 41.00/7.06 % (5505)Instructions burned: 1205 (million)
% 41.00/7.06 % (5505)------------------------------
% 41.00/7.06 % (5505)------------------------------
% 41.00/7.07 % (5508)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_5039 for (2945ds/340Mi)
% 41.57/7.13 % (5506)Instruction limit reached!
% 41.57/7.13 % (5506)------------------------------
% 41.57/7.13 % (5506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.57/7.13 % (5506)Termination reason: Unknown
% 41.57/7.13 % (5506)Termination phase: Saturation
% 41.57/7.13
% 41.57/7.13 % (5506)Memory used [KB]: 7291
% 41.57/7.13 % (5506)Time elapsed: 0.357 s
% 41.57/7.13 % (5506)Instructions burned: 1496 (million)
% 41.57/7.13 % (5506)------------------------------
% 41.57/7.13 % (5506)------------------------------
% 41.57/7.14 % (5509)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_5039 for (2944ds/3672Mi)
% 41.57/7.17 % (5508)Instruction limit reached!
% 41.57/7.17 % (5508)------------------------------
% 41.57/7.17 % (5508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.57/7.17 % (5508)Termination reason: Unknown
% 41.57/7.17 % (5508)Termination phase: Saturation
% 41.57/7.17
% 41.57/7.17 % (5508)Memory used [KB]: 9850
% 41.57/7.17 % (5508)Time elapsed: 0.100 s
% 41.57/7.17 % (5508)Instructions burned: 341 (million)
% 41.57/7.17 % (5508)------------------------------
% 41.57/7.17 % (5508)------------------------------
% 41.57/7.18 % (5510)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_5039 for (2943ds/1535Mi)
% 42.01/7.25 % (5504)Instruction limit reached!
% 42.01/7.25 % (5504)------------------------------
% 42.01/7.25 % (5504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.01/7.25 % (5504)Termination reason: Unknown
% 42.01/7.25 % (5504)Termination phase: Saturation
% 42.01/7.25
% 42.01/7.25 % (5504)Memory used [KB]: 12537
% 42.01/7.25 % (5504)Time elapsed: 0.601 s
% 42.01/7.25 % (5504)Instructions burned: 1897 (million)
% 42.01/7.25 % (5504)------------------------------
% 42.01/7.25 % (5504)------------------------------
% 42.01/7.27 % (5511)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_5039 for (2942ds/4637Mi)
% 42.67/7.45 % (5497)Instruction limit reached!
% 42.67/7.45 % (5497)------------------------------
% 42.67/7.45 % (5497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.67/7.45 % (5497)Termination reason: Unknown
% 42.67/7.45 % (5497)Termination phase: Saturation
% 42.67/7.45
% 42.67/7.45 % (5497)Memory used [KB]: 7675
% 42.67/7.45 % (5497)Time elapsed: 1.208 s
% 42.67/7.45 % (5497)Instructions burned: 5063 (million)
% 42.67/7.45 % (5497)------------------------------
% 42.67/7.45 % (5497)------------------------------
% 42.67/7.46 % (5512)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_5039 for (2940ds/3174Mi)
% 42.94/7.55 % (5510)Instruction limit reached!
% 42.94/7.55 % (5510)------------------------------
% 42.94/7.55 % (5510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.94/7.55 % (5510)Termination reason: Unknown
% 42.94/7.55 % (5510)Termination phase: Saturation
% 42.94/7.55
% 42.94/7.55 % (5510)Memory used [KB]: 11769
% 42.94/7.55 % (5510)Time elapsed: 0.379 s
% 42.94/7.55 % (5510)Instructions burned: 1537 (million)
% 42.94/7.55 % (5510)------------------------------
% 42.94/7.55 % (5510)------------------------------
% 42.94/7.56 % (5513)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_5039 for (2939ds/307Mi)
% 42.94/7.58 % (5478)Instruction limit reached!
% 42.94/7.58 % (5478)------------------------------
% 42.94/7.58 % (5478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.94/7.58 % (5478)Termination reason: Unknown
% 42.94/7.58 % (5478)Termination phase: Saturation
% 42.94/7.58
% 42.94/7.58 % (5478)Memory used [KB]: 13176
% 42.94/7.58 % (5478)Time elapsed: 2.054 s
% 42.94/7.58 % (5478)Instructions burned: 6455 (million)
% 42.94/7.58 % (5478)------------------------------
% 42.94/7.58 % (5478)------------------------------
% 42.94/7.59 % (5514)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_5039 for (2939ds/3619Mi)
% 43.51/7.64 % (5513)Instruction limit reached!
% 43.51/7.64 % (5513)------------------------------
% 43.51/7.64 % (5513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.51/7.64 % (5513)Termination reason: Unknown
% 43.51/7.64 % (5513)Termination phase: Saturation
% 43.51/7.64
% 43.51/7.64 % (5513)Memory used [KB]: 7164
% 43.51/7.64 % (5513)Time elapsed: 0.078 s
% 43.51/7.64 % (5513)Instructions burned: 307 (million)
% 43.51/7.64 % (5513)------------------------------
% 43.51/7.64 % (5513)------------------------------
% 43.51/7.65 % (5515)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_5039 for (2938ds/2325Mi)
% 48.01/8.12 % (5499)Instruction limit reached!
% 48.01/8.12 % (5499)------------------------------
% 48.01/8.12 % (5499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.01/8.12 % (5499)Termination reason: Unknown
% 48.01/8.12 % (5499)Termination phase: Saturation
% 48.01/8.12
% 48.01/8.12 % (5499)Memory used [KB]: 13048
% 48.01/8.12 % (5499)Time elapsed: 1.809 s
% 48.01/8.12 % (5499)Instructions burned: 5800 (million)
% 48.01/8.12 % (5499)------------------------------
% 48.01/8.12 % (5499)------------------------------
% 48.77/8.13 % (5516)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_5039 for (2934ds/2341Mi)
% 49.20/8.28 % (5509)Instruction limit reached!
% 49.20/8.28 % (5509)------------------------------
% 49.20/8.28 % (5509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.20/8.28 % (5509)Termination reason: Unknown
% 49.20/8.28 % (5509)Termination phase: Saturation
% 49.20/8.28
% 49.20/8.28 % (5509)Memory used [KB]: 12281
% 49.20/8.28 % (5509)Time elapsed: 1.169 s
% 49.20/8.28 % (5509)Instructions burned: 3673 (million)
% 49.20/8.28 % (5509)------------------------------
% 49.20/8.28 % (5509)------------------------------
% 49.20/8.29 % (5517)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_5039 for (2932ds/7257Mi)
% 49.80/8.31 % (5512)Refutation not found, non-redundant clauses discarded% (5512)------------------------------
% 49.80/8.31 % (5512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.80/8.31 % (5512)Termination reason: Refutation not found, non-redundant clauses discarded
% 49.80/8.31
% 49.80/8.31 % (5512)Memory used [KB]: 18549
% 49.80/8.31 % (5512)Time elapsed: 0.851 s
% 49.80/8.31 % (5512)Instructions burned: 2788 (million)
% 49.80/8.31 % (5512)------------------------------
% 49.80/8.31 % (5512)------------------------------
% 49.80/8.32 % (5518)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_5039 for (2932ds/3710Mi)
% 49.80/8.35 % (5515)Instruction limit reached!
% 49.80/8.35 % (5515)------------------------------
% 49.80/8.35 % (5515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.80/8.35 % (5515)Termination reason: Unknown
% 49.80/8.35 % (5515)Termination phase: Saturation
% 49.80/8.35
% 49.80/8.35 % (5515)Memory used [KB]: 15223
% 49.80/8.35 % (5515)Time elapsed: 0.702 s
% 49.80/8.35 % (5515)Instructions burned: 2326 (million)
% 49.80/8.35 % (5515)------------------------------
% 49.80/8.35 % (5515)------------------------------
% 49.80/8.36 % (5519)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_5039 for (2932ds/326Mi)
% 50.18/8.40 % (5514)First to succeed.
% 50.18/8.41 % (5514)Refutation found. Thanks to Tanya!
% 50.18/8.41 % SZS status Theorem for DTF2THF_5039
% 50.18/8.41 % SZS output start Proof for DTF2THF_5039
% 50.18/8.41 thf(func_def_0, type, in: $i > $i > $o).
% 50.18/8.41 thf(func_def_1, type, exu: ($i > $o) > $o).
% 50.18/8.41 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 50.18/8.41 thf(func_def_8, type, powerset: $i > $i).
% 50.18/8.41 thf(func_def_10, type, setunion: $i > $i).
% 50.18/8.41 thf(func_def_19, type, descr: ($i > $o) > $i).
% 50.18/8.41 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_26, type, prop2set: $o > $i).
% 50.18/8.41 thf(func_def_36, type, nonempty: $i > $o).
% 50.18/8.41 thf(func_def_69, type, set2prop: $i > $o).
% 50.18/8.41 thf(func_def_88, type, subset: $i > $i > $o).
% 50.18/8.41 thf(func_def_89, type, disjoint: $i > $i > $o).
% 50.18/8.41 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 50.18/8.41 thf(func_def_114, type, binunion: $i > $i > $i).
% 50.18/8.41 thf(func_def_122, type, binintersect: $i > $i > $i).
% 50.18/8.41 thf(func_def_135, type, regular: $i > $o).
% 50.18/8.41 thf(func_def_136, type, setminus: $i > $i > $i).
% 50.18/8.41 thf(func_def_147, type, symdiff: $i > $i > $i).
% 50.18/8.41 thf(func_def_153, type, iskpair: $i > $o).
% 50.18/8.41 thf(func_def_158, type, kpair: $i > $i > $i).
% 50.18/8.41 thf(func_def_160, type, cartprod: $i > $i > $i).
% 50.18/8.41 thf(func_def_177, type, singleton: $i > $o).
% 50.18/8.41 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 50.18/8.41 thf(func_def_184, type, atmost1p: $i > $o).
% 50.18/8.41 thf(func_def_185, type, atleast2p: $i > $o).
% 50.18/8.41 thf(func_def_186, type, atmost2p: $i > $o).
% 50.18/8.41 thf(func_def_187, type, upairsetp: $i > $o).
% 50.18/8.41 thf(func_def_191, type, kfst: $i > $i).
% 50.18/8.41 thf(func_def_203, type, ksnd: $i > $i).
% 50.18/8.41 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 50.18/8.41 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 50.18/8.41 thf(func_def_222, type, func: $i > $i > $i > $o).
% 50.18/8.41 thf(func_def_223, type, funcSet: $i > $i > $i).
% 50.18/8.41 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 50.18/8.41 thf(func_def_260, type, sP3: $o > $i > $i > $i > $o).
% 50.18/8.41 thf(func_def_262, type, sP5: $i > $i > $o).
% 50.18/8.41 thf(func_def_263, type, sP6: $i > $o).
% 50.18/8.41 thf(func_def_264, type, sP7: $i > $i > $o).
% 50.18/8.41 thf(func_def_265, type, sP8: $i > $i > $o).
% 50.18/8.41 thf(func_def_281, type, sK24: $i > $o).
% 50.18/8.41 thf(func_def_282, type, sK25: $i > $o).
% 50.18/8.41 thf(func_def_283, type, sK26: ($i > $o) > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_284, type, sK27: ($i > $o) > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_294, type, sK37: $i > $o).
% 50.18/8.41 thf(func_def_295, type, sK38: $i > $i).
% 50.18/8.41 thf(func_def_296, type, sK39: ($i > $o) > $i).
% 50.18/8.41 thf(func_def_298, type, sK41: $i > $o).
% 50.18/8.41 thf(func_def_302, type, sK45: ($i > $o) > $i).
% 50.18/8.41 thf(func_def_303, type, sK46: ($i > $o) > $i).
% 50.18/8.41 thf(func_def_304, type, sK47: $i > $o).
% 50.18/8.41 thf(func_def_311, type, sK54: $i > $o).
% 50.18/8.41 thf(func_def_313, type, sK56: ($i > $o) > $i > $i).
% 50.18/8.41 thf(func_def_321, type, sK64: ($i > $o) > $i).
% 50.18/8.41 thf(func_def_322, type, sK65: $i > $o).
% 50.18/8.41 thf(func_def_325, type, sK68: $i > $o).
% 50.18/8.41 thf(func_def_335, type, sK78: $i > $o).
% 50.18/8.41 thf(func_def_337, type, sK80: ($i > $o) > $i > $i).
% 50.18/8.41 thf(func_def_338, type, sK81: ($i > $o) > $i > $i).
% 50.18/8.41 thf(func_def_344, type, sK87: $i > $i).
% 50.18/8.41 thf(func_def_347, type, sK90: $i > $i > $i).
% 50.18/8.41 thf(func_def_349, type, sK92: $i > $o).
% 50.18/8.41 thf(func_def_351, type, sK94: ($i > $o) > $i > $i).
% 50.18/8.41 thf(func_def_352, type, sK95: ($i > $o) > $i > $i).
% 50.18/8.41 thf(func_def_355, type, sK98: $i > $o).
% 50.18/8.41 thf(func_def_387, type, sK130: $i > $i).
% 50.18/8.41 thf(func_def_391, type, sK134: $i > $i > $o).
% 50.18/8.41 thf(func_def_407, type, sK150: ($i > $o) > $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_408, type, sK151: ($i > $o) > $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_412, type, sK155: $i > $o).
% 50.18/8.41 thf(func_def_420, type, sK163: $i > $i > $o).
% 50.18/8.41 thf(func_def_429, type, sK172: $i > $o).
% 50.18/8.41 thf(func_def_434, type, sK177: $i > $o).
% 50.18/8.41 thf(func_def_437, type, sK180: $i > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_438, type, sK181: $i > $o).
% 50.18/8.41 thf(func_def_450, type, sK193: $i > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_451, type, sK194: $i > $o).
% 50.18/8.41 thf(func_def_454, type, sK197: $i > $i > $o).
% 50.18/8.41 thf(func_def_466, type, sK209: $i > $o).
% 50.18/8.41 thf(func_def_471, type, sK214: $i > $i).
% 50.18/8.41 thf(func_def_478, type, sK221: $i > $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_482, type, sK225: $i > $o).
% 50.18/8.41 thf(func_def_484, type, sK227: ($i > $o) > $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_485, type, sK228: ($i > $o) > $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_492, type, sK235: $i > $i > $i).
% 50.18/8.41 thf(func_def_497, type, sK240: $i > $o).
% 50.18/8.41 thf(func_def_500, type, sK243: $i > $i > $o).
% 50.18/8.41 thf(func_def_515, type, sK258: $i > $o).
% 50.18/8.41 thf(func_def_519, type, sK262: $i > $i > $i).
% 50.18/8.41 thf(func_def_520, type, sK263: $i > $i > $i).
% 50.18/8.41 thf(func_def_534, type, sK277: $i > $o).
% 50.18/8.41 thf(func_def_535, type, sK278: $i > $i).
% 50.18/8.41 thf(func_def_536, type, sK279: ($i > $o) > $i).
% 50.18/8.41 thf(func_def_540, type, sK283: $i > $i > $i).
% 50.18/8.41 thf(func_def_548, type, sK291: $i > $o).
% 50.18/8.41 thf(func_def_555, type, sK298: $i > $i > $o).
% 50.18/8.41 thf(func_def_585, type, sK328: $i > $i).
% 50.18/8.41 thf(func_def_587, type, sK330: $i > $i).
% 50.18/8.41 thf(func_def_593, type, sK336: $i > $i > $i).
% 50.18/8.41 thf(func_def_605, type, sK348: $i > $i > $o).
% 50.18/8.41 thf(func_def_618, type, sK361: $i > ($i > $i) > $i > $i).
% 50.18/8.41 thf(func_def_620, type, sK363: $i > $i).
% 50.18/8.41 thf(func_def_630, type, sK373: ($i > $i) > $i > $i > $i).
% 50.18/8.41 thf(func_def_633, type, sK376: $i > $i).
% 50.18/8.41 thf(func_def_641, type, sK384: $i > $o).
% 50.18/8.41 thf(func_def_646, type, sK389: ($i > $o) > ($i > $o) > $i > $i > $i).
% 50.18/8.41 thf(func_def_647, type, sK390: ($i > $o) > ($i > $o) > $i > $i > $i).
% 50.18/8.41 thf(func_def_650, type, sK393: $i > $o).
% 50.18/8.41 thf(func_def_651, type, sK394: $i > $o).
% 50.18/8.41 thf(func_def_652, type, sK395: ($i > $o) > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_653, type, sK396: ($i > $o) > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_654, type, sK397: $i > $o).
% 50.18/8.41 thf(func_def_655, type, sK398: $i > $o).
% 50.18/8.41 thf(func_def_665, type, sK408: $i > $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_666, type, sK409: $i > $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_672, type, sK415: $i > $o).
% 50.18/8.41 thf(func_def_674, type, sK417: $i > ($i > $o) > $i > $i).
% 50.18/8.41 thf(func_def_676, type, sK419: $i > $i > $o).
% 50.18/8.41 thf(func_def_677, type, sK420: $i > $i).
% 50.18/8.41 thf(func_def_678, type, sK421: $i > $i).
% 50.18/8.41 thf(func_def_679, type, sK422: ($i > $i > $o) > $i > $i).
% 50.18/8.41 thf(func_def_680, type, sK423: ($i > $i > $o) > $i > $i).
% 50.18/8.41 thf(func_def_681, type, sK424: $i > ($i > $i > $o) > $i > $i).
% 50.18/8.41 thf(func_def_684, type, sK427: $i > $i > $i).
% 50.18/8.41 thf(func_def_685, type, sK428: $i > $i > $i).
% 50.18/8.41 thf(func_def_686, type, sK429: $i > $i > $i).
% 50.18/8.41 thf(func_def_687, type, sK430: $i > $i > $i).
% 50.18/8.41 thf(func_def_688, type, sK431: $i > $i > $i).
% 50.18/8.41 thf(func_def_689, type, sK432: $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_690, type, sK433: $i > $i).
% 50.18/8.41 thf(func_def_691, type, sK434: $i > $i).
% 50.18/8.41 thf(func_def_692, type, sK435: $i > $i).
% 50.18/8.41 thf(func_def_693, type, sK436: $i > $i).
% 50.18/8.41 thf(func_def_694, type, sK437: $i > $i > $i).
% 50.18/8.41 thf(func_def_695, type, sK438: $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_696, type, sK439: $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_697, type, sK440: $i > $i > $i).
% 50.18/8.41 thf(func_def_698, type, sK441: $i > $i > $i).
% 50.18/8.41 thf(func_def_699, type, sK442: $i > $i).
% 50.18/8.41 thf(func_def_701, type, sK444: $i > $i).
% 50.18/8.41 thf(func_def_702, type, sK445: $i > $i).
% 50.18/8.41 thf(func_def_712, type, sK455: $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_713, type, sK456: $i > $i > $i > $i).
% 50.18/8.41 thf(func_def_726, type, sK469: $i > $o).
% 50.18/8.41 thf(func_def_734, type, sK477: $i > $i > $i).
% 50.18/8.41 thf(func_def_738, type, sK481: $i > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_739, type, sK482: $i > $o).
% 50.18/8.41 thf(func_def_760, type, sK503: $i > $o).
% 50.18/8.41 thf(func_def_778, type, sK521: $o > $i > $i > $i).
% 50.18/8.41 thf(func_def_783, type, sK526: $i > $i).
% 50.18/8.41 thf(func_def_794, type, sK537: ($i > $o) > $i > $i).
% 50.18/8.41 thf(func_def_796, type, sK539: $i > $o).
% 50.18/8.41 thf(func_def_797, type, sK540: $i > $o).
% 50.18/8.41 thf(func_def_800, type, sK543: $i > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_802, type, sK545: $i > $o).
% 50.18/8.41 thf(func_def_809, type, sK552: $i > $i).
% 50.18/8.41 thf(func_def_812, type, sK555: $i > $i > $i).
% 50.18/8.41 thf(func_def_813, type, sK556: $i > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_814, type, sK557: $i > $o).
% 50.18/8.41 thf(func_def_822, type, sK565: $i > $i).
% 50.18/8.41 thf(func_def_823, type, sK566: ($i > $i) > $i > $i > $i).
% 50.18/8.41 thf(func_def_853, type, sK596: $i > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_854, type, sK597: $i > $o).
% 50.18/8.41 thf(func_def_864, type, sK607: $i > $i > $i).
% 50.18/8.41 thf(func_def_869, type, sK612: $i > $i > $o).
% 50.18/8.41 thf(func_def_875, type, sK618: $i > $i > $i).
% 50.18/8.41 thf(func_def_882, type, sK625: $i > $o).
% 50.18/8.41 thf(func_def_884, type, sK627: $i > ($i > $o) > $i).
% 50.18/8.41 thf(func_def_886, type, ph629: !>[X0: $tType]:(X0)).
% 50.18/8.41 thf(f19683,plain,(
% 50.18/8.41 $false),
% 50.18/8.41 inference(avatar_sat_refutation,[status(thm)],[f3475,f3505,f6076,f6567,f6602,f11308,f19450,f19477,f19678])).
% 50.18/8.41 thf(f19678,plain,(
% 50.18/8.41 ~spl628_122 | spl628_8 | ~spl628_18),
% 50.18/8.41 inference(avatar_split_clause,[status(thm)],[f19677,f6600,f3469,f11305])).
% 50.18/8.41 thf(f11305,definition,(
% 50.18/8.41 spl628_122 <=> ($true = (breln @ sK204 @ sK205 @ sK207))),
% 50.18/8.41 introduced(definition,[new_symbols(naming,[spl628_122])],[avatar_definition])).
% 50.18/8.41 thf(f3469,definition,(
% 50.18/8.41 spl628_8 <=> ((subset @ sK206 @ sK207) = $true)),
% 50.18/8.41 introduced(definition,[new_symbols(naming,[spl628_8])],[avatar_definition])).
% 50.18/8.41 thf(f6600,definition,(
% 50.18/8.41 spl628_18 <=> ! [X0 : $i] : (((in @ (sK408 @ sK207 @ X0 @ sK205 @ sK206) @ sK204) != $true) | ($true != (breln @ X0 @ sK205 @ sK207)) | ((breln @ X0 @ sK205 @ sK206) != $true))),
% 50.18/8.41 introduced(definition,[new_symbols(naming,[spl628_18])],[avatar_definition])).
% 50.18/8.41 thf(f19677,plain,(
% 50.18/8.41 ((subset @ sK206 @ sK207) = $true) | ($true != (breln @ sK204 @ sK205 @ sK207)) | ~spl628_18),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f19676])).
% 50.18/8.41 thf(f19676,plain,(
% 50.18/8.41 ($true != (breln @ sK204 @ sK205 @ sK207)) | ((subset @ sK206 @ sK207) = $true) | ($true != $true) | ~spl628_18),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f19675,f2269])).
% 50.18/8.41 thf(f2269,plain,(
% 50.18/8.41 ($true = (breln @ sK204 @ sK205 @ sK206))),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1213])).
% 50.18/8.41 thf(f1213,plain,(
% 50.18/8.41 (subsetemptysetimpeq = $true) & (nonemptyI1 = $true) & (setminusSubset1 = $true) & (binintersectLsub = $true) & (notequalI1 = $true) & (exu__Cong = $true) & (setukpairinjL2 = $true) & (emptyinunitempty = $true) & (exuE2 = $true) & (upairset2IR = $true) & (subset2powerset = $true) & (omegaIndAx = $true) & (subsetTrans = $true) & (powerset__Cong = $true) & (setminusIRneg = $true) & (powersetI = $true) & (symdiffIneg2 = $true) & (setminusELneg = $true) & (lam2p = $true) & (binunionE = $true) & (cartprodpairsurjEq = $true) & (bs114d = $true) & (subsetE = $true) & (lamp = $true) & (dpsetconstrI = $true) & (exuE3e = $true) & (emptysetAx = $true) & (prop2set2propI = $true) & (quantDeMorgan4 = $true) & (funcextLem = $true) & (kpairiskpair = $true) & (setminusLsub = $true) & (symdiffIneg1 = $true) & (singletonsuniq = $true) & (infuncsetfunc = $true) & (subPowSU = $true) & (setextAx = $true) & (cartprodsndin = $true) & (setadjoinIL = $true) & (inPowerset = $true) & (replAx = $true) & (upairsubunion = $true) & (powersetAx = $true) & (exuE1 = $true) & (cartprodmempair1 = $true) & (symdiffI2 = $true) & (dsetconstrEL = $true) & (exuI2 = $true) & (quantDeMorgan3 = $true) & (setextsub = $true) & (descr__Cong = $true) & (descrp = $true) & (cartprodpairmemEL = $true) & (setunionsingleton2 = $true) & (setadjoinE = $true) & (eqimpsubset2 = $true) & (in__Cong = $true) & (setukpairinjL1 = $true) & (wellorderingAx = $true) & (prop2setE = $true) & (lamProp = $true) & (cartprodpairin = $true) & (dpsetconstrEL2 = $true) & (setukpairIR = $true) & (binintersectRsub = $true) & (setext = $true) & (setminusILneg = $true) & (cartprodfstpairEq = $true) & (omega0Ax = $true) & (disjointsetsI1 = $true) & (kpairp = $true) & (binintersectSubset2 = $true) & (($true = (breln @ sK204 @ sK205 @ sK206)) & (($true = (breln @ sK204 @ sK205 @ sK207)) & ! [X4 : $i] : (! [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ sK206)) | ((in @ X5 @ sK205) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK207))) | ($true != (in @ X4 @ sK204))) & ! [X6 : $i] : (((in @ X6 @ sK204) != $true) | ! [X7 : $i] : (($true = (in @ (kpair @ X6 @ X7) @ sK207)) | ($true != (in @ (kpair @ X6 @ X7) @ sK206)) | ($true != (in @ X7 @ sK205)))) & (sK206 != sK207))) & (dsetconstrER = $true) & (cartprodfstin = $true) & (notequalI2 = $true) & (binunionRsub = $true) & (quantDeMorgan2 = $true) & (setunionI = $true) & (emptysetE = $true) & (brelnall2 = $true) & (setunionsingleton = $true) & (binintersectER = $true) & (funcGraphProp4 = $true) & (singletoninpowerset = $true) & (exuE3u = $true) & (setOfPairsIsBReln = $true) & (kfstsingleton = $true) & (ubforcartprodlem1 = $true) & (setoftrueEq = $true) & (setadjoinSub = $true) & (setadjoinIR = $true) & (binunionIL = $true) & (setunionAx = $true) & (cartprodpairmemER = $true) & (binintersectEL = $true) & (funcGraphProp1 = $true) & (ex1E1 = $true) & (ksndsingleton = $true) & (upairsetIL = $true) & (setukpairinjL = $true) & (theprop = $true) & (sepSubset = $true) & (setukpairIL = $true) & (emptyset__Cong = $true) & (binintersectSubset1 = $true) & (ap2p = $true) & (setminusEL = $true) & (subsetI1 = $true) & (upairset2E = $true) & (funcinfuncset = $true) & (nonemptyE1 = $true) & (inCongP = $true) & (subbreln = $true) & (prop2setI = $true) & (cartprodsndpairEq = $true) & (upairinpowunion = $true) & (singletonprop = $true) & (notsubsetI = $true) & (notinsingleton = $true) & (setbeta = $true) & (setadjoinOr = $true) & (noeltsimpempty = $true) & (omegaSAx = $true) & (setukpairinjR11 = $true) & (dpsetconstrERa = $true) & (setunionE = $true) & (dpsetconstrEL1 = $true) & (setminusER = $true) & (apProp = $true) & (singletoninpowunion = $true) & (sepInPowerset = $true) & (foundationAx = $true) & (setminusI = $true) & (upairsetIR = $true) & (upairequniteq = $true) & (emptyInPowerset = $true) & (setminusERneg = $true) & (notdexE = $true) & (emptyI = $true) & (binintersectSubset3 = $true) & (setunion__Cong = $true) & (ubforcartprodlem3 = $true) & (notdallE = $true) & (emptysetimpfalse = $true) & (setadjoin__Cong = $true) & (ex1I2 = $true) & (exuI1 = $true) & (emptysetsubset = $true) & (setukpairinjR2 = $true) & (omega__Cong = $true) & (setukpairinjR1 = $true) & (vacuousDall = $true) & (binintersectSubset5 = $true) & (eqinunit = $true) & (singletonsubset = $true) & (powersetsubset = $true) & (symdiffE = $true) & (dpsetconstrER = $true) & (secondinupair = $true) & (setunionsingleton1 = $true) & (funcImageSingleton = $true) & (exuI3 = $true) & (setukpairinjR12 = $true) & (funcGraphProp2 = $true) & (dsetconstr__Cong = $true) & (powersetE = $true) & (binunionEcases = $true) & (binintersectSubset4 = $true) & (powersetI1 = $true) & (ex1E2 = $true) & (cartprodmempair = $true) & (ubforcartprodlem2 = $true) & (dpsetconstrSub = $true) & (cartprodmempaircEq = $true) & (subsetRefl = $true) & (eqimpsubset1 = $true) & (dsetconstrI = $true) & (quantDeMorgan1 = $true) & (subsetE2 = $true) & (setadjoinSub2 = $true) & (nonemptyImpWitness = $true) & (nonemptyI = $true) & (ksndpairEq = $true) & (upairsetE = $true) & (setadjoinAx = $true) & (kfstpairEq = $true) & (ex1I = $true) & (setunionE2 = $true) & (subsetI2 = $true) & (notinemptyset = $true) & (setminusSubset2 = $true) & (kpairsurjEq = $true) & (singletonsswitch = $true) & (binunionIR = $true) & (funcGraphProp3 = $true) & (exuEu = $true) & (binunionLsub = $true) & (setukpairinjR = $true) & (symdiffI1 = $true) & (uniqinunit = $true) & (emptyE1 = $true) & (app = $true) & (powersetE1 = $true) & (emptyinPowerset = $true) & (brelnall1 = $true) & (binintersectI = $true)),
% 50.18/8.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK204,sK205,sK206,sK207])],[f1210,f1212,f1211])).
% 50.18/8.41 thf(f1211,plain,(
% 50.18/8.41 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X0 @ X1 @ X2)) & ? [X3 : $i] : (($true = (breln @ X0 @ X1 @ X3)) & ! [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ X2) = $true) | ($true != (in @ X5 @ X1)) | ($true != (in @ (kpair @ X4 @ X5) @ X3))) | ((in @ X4 @ X0) != $true)) & ! [X6 : $i] : (($true != (in @ X6 @ X0)) | ! [X7 : $i] : (((in @ (kpair @ X6 @ X7) @ X3) = $true) | ((in @ (kpair @ X6 @ X7) @ X2) != $true) | ($true != (in @ X7 @ X1)))) & (X2 != X3))) => (($true = (breln @ sK204 @ sK205 @ sK206)) & ? [X3 : $i] : (($true = (breln @ sK204 @ sK205 @ X3)) & ! [X4 : $i] : (! [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ sK206)) | ((in @ X5 @ sK205) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ X3))) | ($true != (in @ X4 @ sK204))) & ! [X6 : $i] : (((in @ X6 @ sK204) != $true) | ! [X7 : $i] : (((in @ (kpair @ X6 @ X7) @ X3) = $true) | ($true != (in @ (kpair @ X6 @ X7) @ sK206)) | ($true != (in @ X7 @ sK205)))) & (sK206 != X3)))),
% 50.18/8.41 introduced(definition,[],[choice_axiom])).
% 50.18/8.41 thf(f1212,plain,(
% 50.18/8.41 ? [X3 : $i] : (($true = (breln @ sK204 @ sK205 @ X3)) & ! [X4 : $i] : (! [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ sK206)) | ((in @ X5 @ sK205) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ X3))) | ($true != (in @ X4 @ sK204))) & ! [X6 : $i] : (((in @ X6 @ sK204) != $true) | ! [X7 : $i] : (((in @ (kpair @ X6 @ X7) @ X3) = $true) | ($true != (in @ (kpair @ X6 @ X7) @ sK206)) | ($true != (in @ X7 @ sK205)))) & (sK206 != X3)) => (($true = (breln @ sK204 @ sK205 @ sK207)) & ! [X4 : $i] : (! [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ sK206)) | ((in @ X5 @ sK205) != $true) | ($true != (in @ (kpair @ X4 @ X5) @ sK207))) | ($true != (in @ X4 @ sK204))) & ! [X6 : $i] : (((in @ X6 @ sK204) != $true) | ! [X7 : $i] : (($true = (in @ (kpair @ X6 @ X7) @ sK207)) | ($true != (in @ (kpair @ X6 @ X7) @ sK206)) | ($true != (in @ X7 @ sK205)))) & (sK206 != sK207))),
% 50.18/8.41 introduced(definition,[],[choice_axiom])).
% 50.18/8.41 thf(f1210,plain,(
% 50.18/8.41 (subsetemptysetimpeq = $true) & (nonemptyI1 = $true) & (setminusSubset1 = $true) & (binintersectLsub = $true) & (notequalI1 = $true) & (exu__Cong = $true) & (setukpairinjL2 = $true) & (emptyinunitempty = $true) & (exuE2 = $true) & (upairset2IR = $true) & (subset2powerset = $true) & (omegaIndAx = $true) & (subsetTrans = $true) & (powerset__Cong = $true) & (setminusIRneg = $true) & (powersetI = $true) & (symdiffIneg2 = $true) & (setminusELneg = $true) & (lam2p = $true) & (binunionE = $true) & (cartprodpairsurjEq = $true) & (bs114d = $true) & (subsetE = $true) & (lamp = $true) & (dpsetconstrI = $true) & (exuE3e = $true) & (emptysetAx = $true) & (prop2set2propI = $true) & (quantDeMorgan4 = $true) & (funcextLem = $true) & (kpairiskpair = $true) & (setminusLsub = $true) & (symdiffIneg1 = $true) & (singletonsuniq = $true) & (infuncsetfunc = $true) & (subPowSU = $true) & (setextAx = $true) & (cartprodsndin = $true) & (setadjoinIL = $true) & (inPowerset = $true) & (replAx = $true) & (upairsubunion = $true) & (powersetAx = $true) & (exuE1 = $true) & (cartprodmempair1 = $true) & (symdiffI2 = $true) & (dsetconstrEL = $true) & (exuI2 = $true) & (quantDeMorgan3 = $true) & (setextsub = $true) & (descr__Cong = $true) & (descrp = $true) & (cartprodpairmemEL = $true) & (setunionsingleton2 = $true) & (setadjoinE = $true) & (eqimpsubset2 = $true) & (in__Cong = $true) & (setukpairinjL1 = $true) & (wellorderingAx = $true) & (prop2setE = $true) & (lamProp = $true) & (cartprodpairin = $true) & (dpsetconstrEL2 = $true) & (setukpairIR = $true) & (binintersectRsub = $true) & (setext = $true) & (setminusILneg = $true) & (cartprodfstpairEq = $true) & (omega0Ax = $true) & (disjointsetsI1 = $true) & (kpairp = $true) & (binintersectSubset2 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X0 @ X1 @ X2)) & ? [X3 : $i] : (($true = (breln @ X0 @ X1 @ X3)) & ! [X4 : $i] : (! [X5 : $i] : (((in @ (kpair @ X4 @ X5) @ X2) = $true) | ($true != (in @ X5 @ X1)) | ($true != (in @ (kpair @ X4 @ X5) @ X3))) | ((in @ X4 @ X0) != $true)) & ! [X6 : $i] : (($true != (in @ X6 @ X0)) | ! [X7 : $i] : (((in @ (kpair @ X6 @ X7) @ X3) = $true) | ((in @ (kpair @ X6 @ X7) @ X2) != $true) | ($true != (in @ X7 @ X1)))) & (X2 != X3))) & (dsetconstrER = $true) & (cartprodfstin = $true) & (notequalI2 = $true) & (binunionRsub = $true) & (quantDeMorgan2 = $true) & (setunionI = $true) & (emptysetE = $true) & (brelnall2 = $true) & (setunionsingleton = $true) & (binintersectER = $true) & (funcGraphProp4 = $true) & (singletoninpowerset = $true) & (exuE3u = $true) & (setOfPairsIsBReln = $true) & (kfstsingleton = $true) & (ubforcartprodlem1 = $true) & (setoftrueEq = $true) & (setadjoinSub = $true) & (setadjoinIR = $true) & (binunionIL = $true) & (setunionAx = $true) & (cartprodpairmemER = $true) & (binintersectEL = $true) & (funcGraphProp1 = $true) & (ex1E1 = $true) & (ksndsingleton = $true) & (upairsetIL = $true) & (setukpairinjL = $true) & (theprop = $true) & (sepSubset = $true) & (setukpairIL = $true) & (emptyset__Cong = $true) & (binintersectSubset1 = $true) & (ap2p = $true) & (setminusEL = $true) & (subsetI1 = $true) & (upairset2E = $true) & (funcinfuncset = $true) & (nonemptyE1 = $true) & (inCongP = $true) & (subbreln = $true) & (prop2setI = $true) & (cartprodsndpairEq = $true) & (upairinpowunion = $true) & (singletonprop = $true) & (notsubsetI = $true) & (notinsingleton = $true) & (setbeta = $true) & (setadjoinOr = $true) & (noeltsimpempty = $true) & (omegaSAx = $true) & (setukpairinjR11 = $true) & (dpsetconstrERa = $true) & (setunionE = $true) & (dpsetconstrEL1 = $true) & (setminusER = $true) & (apProp = $true) & (singletoninpowunion = $true) & (sepInPowerset = $true) & (foundationAx = $true) & (setminusI = $true) & (upairsetIR = $true) & (upairequniteq = $true) & (emptyInPowerset = $true) & (setminusERneg = $true) & (notdexE = $true) & (emptyI = $true) & (binintersectSubset3 = $true) & (setunion__Cong = $true) & (ubforcartprodlem3 = $true) & (notdallE = $true) & (emptysetimpfalse = $true) & (setadjoin__Cong = $true) & (ex1I2 = $true) & (exuI1 = $true) & (emptysetsubset = $true) & (setukpairinjR2 = $true) & (omega__Cong = $true) & (setukpairinjR1 = $true) & (vacuousDall = $true) & (binintersectSubset5 = $true) & (eqinunit = $true) & (singletonsubset = $true) & (powersetsubset = $true) & (symdiffE = $true) & (dpsetconstrER = $true) & (secondinupair = $true) & (setunionsingleton1 = $true) & (funcImageSingleton = $true) & (exuI3 = $true) & (setukpairinjR12 = $true) & (funcGraphProp2 = $true) & (dsetconstr__Cong = $true) & (powersetE = $true) & (binunionEcases = $true) & (binintersectSubset4 = $true) & (powersetI1 = $true) & (ex1E2 = $true) & (cartprodmempair = $true) & (ubforcartprodlem2 = $true) & (dpsetconstrSub = $true) & (cartprodmempaircEq = $true) & (subsetRefl = $true) & (eqimpsubset1 = $true) & (dsetconstrI = $true) & (quantDeMorgan1 = $true) & (subsetE2 = $true) & (setadjoinSub2 = $true) & (nonemptyImpWitness = $true) & (nonemptyI = $true) & (ksndpairEq = $true) & (upairsetE = $true) & (setadjoinAx = $true) & (kfstpairEq = $true) & (ex1I = $true) & (setunionE2 = $true) & (subsetI2 = $true) & (notinemptyset = $true) & (setminusSubset2 = $true) & (kpairsurjEq = $true) & (singletonsswitch = $true) & (binunionIR = $true) & (funcGraphProp3 = $true) & (exuEu = $true) & (binunionLsub = $true) & (setukpairinjR = $true) & (symdiffI1 = $true) & (uniqinunit = $true) & (emptyE1 = $true) & (app = $true) & (powersetE1 = $true) & (emptyinPowerset = $true) & (brelnall1 = $true) & (binintersectI = $true)),
% 50.18/8.41 inference(rectify,[status(thm)],[f864])).
% 50.18/8.41 thf(f864,plain,(
% 50.18/8.41 (subsetemptysetimpeq = $true) & (nonemptyI1 = $true) & (setminusSubset1 = $true) & (binintersectLsub = $true) & (notequalI1 = $true) & (exu__Cong = $true) & (setukpairinjL2 = $true) & (emptyinunitempty = $true) & (exuE2 = $true) & (upairset2IR = $true) & (subset2powerset = $true) & (omegaIndAx = $true) & (subsetTrans = $true) & (powerset__Cong = $true) & (setminusIRneg = $true) & (powersetI = $true) & (symdiffIneg2 = $true) & (setminusELneg = $true) & (lam2p = $true) & (binunionE = $true) & (cartprodpairsurjEq = $true) & (bs114d = $true) & (subsetE = $true) & (lamp = $true) & (dpsetconstrI = $true) & (exuE3e = $true) & (emptysetAx = $true) & (prop2set2propI = $true) & (quantDeMorgan4 = $true) & (funcextLem = $true) & (kpairiskpair = $true) & (setminusLsub = $true) & (symdiffIneg1 = $true) & (singletonsuniq = $true) & (infuncsetfunc = $true) & (subPowSU = $true) & (setextAx = $true) & (cartprodsndin = $true) & (setadjoinIL = $true) & (inPowerset = $true) & (replAx = $true) & (upairsubunion = $true) & (powersetAx = $true) & (exuE1 = $true) & (cartprodmempair1 = $true) & (symdiffI2 = $true) & (dsetconstrEL = $true) & (exuI2 = $true) & (quantDeMorgan3 = $true) & (setextsub = $true) & (descr__Cong = $true) & (descrp = $true) & (cartprodpairmemEL = $true) & (setunionsingleton2 = $true) & (setadjoinE = $true) & (eqimpsubset2 = $true) & (in__Cong = $true) & (setukpairinjL1 = $true) & (wellorderingAx = $true) & (prop2setE = $true) & (lamProp = $true) & (cartprodpairin = $true) & (dpsetconstrEL2 = $true) & (setukpairIR = $true) & (binintersectRsub = $true) & (setext = $true) & (setminusILneg = $true) & (cartprodfstpairEq = $true) & (omega0Ax = $true) & (disjointsetsI1 = $true) & (kpairp = $true) & (binintersectSubset2 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X0 @ X1 @ X2)) & ? [X3 : $i] : (($true = (breln @ X0 @ X1 @ X3)) & ! [X6 : $i] : (! [X7 : $i] : (((in @ (kpair @ X6 @ X7) @ X2) = $true) | ($true != (in @ X7 @ X1)) | ((in @ (kpair @ X6 @ X7) @ X3) != $true)) | ($true != (in @ X6 @ X0))) & ! [X4 : $i] : (((in @ X4 @ X0) != $true) | ! [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X3)) | ((in @ (kpair @ X4 @ X5) @ X2) != $true) | ($true != (in @ X5 @ X1)))) & (X2 != X3))) & (dsetconstrER = $true) & (cartprodfstin = $true) & (notequalI2 = $true) & (binunionRsub = $true) & (quantDeMorgan2 = $true) & (setunionI = $true) & (emptysetE = $true) & (brelnall2 = $true) & (setunionsingleton = $true) & (binintersectER = $true) & (funcGraphProp4 = $true) & (singletoninpowerset = $true) & (exuE3u = $true) & (setOfPairsIsBReln = $true) & (kfstsingleton = $true) & (ubforcartprodlem1 = $true) & (setoftrueEq = $true) & (setadjoinSub = $true) & (setadjoinIR = $true) & (binunionIL = $true) & (setunionAx = $true) & (cartprodpairmemER = $true) & (binintersectEL = $true) & (funcGraphProp1 = $true) & (ex1E1 = $true) & (ksndsingleton = $true) & (upairsetIL = $true) & (setukpairinjL = $true) & (theprop = $true) & (sepSubset = $true) & (setukpairIL = $true) & (emptyset__Cong = $true) & (binintersectSubset1 = $true) & (ap2p = $true) & (setminusEL = $true) & (subsetI1 = $true) & (upairset2E = $true) & (funcinfuncset = $true) & (nonemptyE1 = $true) & (inCongP = $true) & (subbreln = $true) & (prop2setI = $true) & (cartprodsndpairEq = $true) & (upairinpowunion = $true) & (singletonprop = $true) & (notsubsetI = $true) & (notinsingleton = $true) & (setbeta = $true) & (setadjoinOr = $true) & (noeltsimpempty = $true) & (omegaSAx = $true) & (setukpairinjR11 = $true) & (dpsetconstrERa = $true) & (setunionE = $true) & (dpsetconstrEL1 = $true) & (setminusER = $true) & (apProp = $true) & (singletoninpowunion = $true) & (sepInPowerset = $true) & (foundationAx = $true) & (setminusI = $true) & (upairsetIR = $true) & (upairequniteq = $true) & (emptyInPowerset = $true) & (setminusERneg = $true) & (notdexE = $true) & (emptyI = $true) & (binintersectSubset3 = $true) & (setunion__Cong = $true) & (ubforcartprodlem3 = $true) & (notdallE = $true) & (emptysetimpfalse = $true) & (setadjoin__Cong = $true) & (ex1I2 = $true) & (exuI1 = $true) & (emptysetsubset = $true) & (setukpairinjR2 = $true) & (omega__Cong = $true) & (setukpairinjR1 = $true) & (vacuousDall = $true) & (binintersectSubset5 = $true) & (eqinunit = $true) & (singletonsubset = $true) & (powersetsubset = $true) & (symdiffE = $true) & (dpsetconstrER = $true) & (secondinupair = $true) & (setunionsingleton1 = $true) & (funcImageSingleton = $true) & (exuI3 = $true) & (setukpairinjR12 = $true) & (funcGraphProp2 = $true) & (dsetconstr__Cong = $true) & (powersetE = $true) & (binunionEcases = $true) & (binintersectSubset4 = $true) & (powersetI1 = $true) & (ex1E2 = $true) & (cartprodmempair = $true) & (ubforcartprodlem2 = $true) & (dpsetconstrSub = $true) & (cartprodmempaircEq = $true) & (subsetRefl = $true) & (eqimpsubset1 = $true) & (dsetconstrI = $true) & (quantDeMorgan1 = $true) & (subsetE2 = $true) & (setadjoinSub2 = $true) & (nonemptyImpWitness = $true) & (nonemptyI = $true) & (ksndpairEq = $true) & (upairsetE = $true) & (setadjoinAx = $true) & (kfstpairEq = $true) & (ex1I = $true) & (setunionE2 = $true) & (subsetI2 = $true) & (notinemptyset = $true) & (setminusSubset2 = $true) & (kpairsurjEq = $true) & (singletonsswitch = $true) & (binunionIR = $true) & (funcGraphProp3 = $true) & (exuEu = $true) & (binunionLsub = $true) & (setukpairinjR = $true) & (symdiffI1 = $true) & (uniqinunit = $true) & (emptyE1 = $true) & (app = $true) & (powersetE1 = $true) & (emptyinPowerset = $true) & (brelnall1 = $true) & (binintersectI = $true)),
% 50.18/8.41 inference(flattening,[status(thm)],[f863])).
% 50.18/8.41 thf(f863,plain,(
% 50.18/8.41 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : ((((X2 != X3) & ! [X6 : $i] : (! [X7 : $i] : ((((in @ (kpair @ X6 @ X7) @ X2) = $true) | ((in @ (kpair @ X6 @ X7) @ X3) != $true)) | ($true != (in @ X7 @ X1))) | ($true != (in @ X6 @ X0)))) & ! [X4 : $i] : (! [X5 : $i] : ((($true = (in @ (kpair @ X4 @ X5) @ X3)) | ((in @ (kpair @ X4 @ X5) @ X2) != $true)) | ($true != (in @ X5 @ X1))) | ((in @ X4 @ X0) != $true))) & ($true = (breln @ X0 @ X1 @ X3))) & ($true = (breln @ X0 @ X1 @ X2))) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 50.18/8.41 inference(ennf_transformation,[status(thm)],[f600])).
% 50.18/8.41 thf(f600,plain,(
% 50.18/8.41 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X0 @ X1 @ X2)) => ! [X3 : $i] : (($true = (breln @ X0 @ X1 @ X3)) => (! [X4 : $i] : (((in @ X4 @ X0) = $true) => ! [X5 : $i] : (($true = (in @ X5 @ X1)) => (((in @ (kpair @ X4 @ X5) @ X2) = $true) => ($true = (in @ (kpair @ X4 @ X5) @ X3))))) => (! [X6 : $i] : (($true = (in @ X6 @ X0)) => ! [X7 : $i] : (($true = (in @ X7 @ X1)) => (((in @ (kpair @ X6 @ X7) @ X3) = $true) => ((in @ (kpair @ X6 @ X7) @ X2) = $true)))) => (X2 = X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 50.18/8.41 inference(fool_elimination,[status(thm)],[f599])).
% 50.18/8.41 thf(f599,plain,(
% 50.18/8.41 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X0 @ X1 @ X2) => ! [X3 : $i] : ((breln @ X0 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X0) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X2) => (in @ (kpair @ X4 @ X5) @ X3)))) => (! [X6 : $i] : ((in @ X6 @ X0) => ! [X7 : $i] : ((in @ X7 @ X1) => ((in @ (kpair @ X6 @ X7) @ X3) => (in @ (kpair @ X6 @ X7) @ X2)))) => (X2 = X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 50.18/8.41 inference(rectify,[status(thm)],[f215])).
% 50.18/8.41 thf(f215,negated_conjecture,(
% 50.18/8.41 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => ! [X3 : $i,X4 : $i,X12 : $i] : ((breln @ X3 @ X4 @ X12) => ! [X15 : $i] : ((breln @ X3 @ X4 @ X15) => (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X12) => (in @ (kpair @ X1 @ X2) @ X15)))) => (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X15) => (in @ (kpair @ X1 @ X2) @ X12)))) => (X12 = X15)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 50.18/8.41 inference(negated_conjecture,[status(cth)],[f214])).
% 50.18/8.41 thf(f214,conjecture,(
% 50.18/8.41 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => ! [X3 : $i,X4 : $i,X12 : $i] : ((breln @ X3 @ X4 @ X12) => ! [X15 : $i] : ((breln @ X3 @ X4 @ X15) => (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X12) => (in @ (kpair @ X1 @ X2) @ X15)))) => (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X15) => (in @ (kpair @ X1 @ X2) @ X12)))) => (X12 = X15))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 50.18/8.41 file('/export/starexec/sandbox/tmp/tmp.rJod2NOsaw/DTF2THF_5039.p',eqbreln)).
% 50.18/8.41 thf(f19675,plain,(
% 50.18/8.41 ($true != (breln @ sK204 @ sK205 @ sK206)) | ((subset @ sK206 @ sK207) = $true) | ($true != (breln @ sK204 @ sK205 @ sK207)) | ~spl628_18),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f19674])).
% 50.18/8.41 thf(f19674,plain,(
% 50.18/8.41 ($true != $true) | ($true != (breln @ sK204 @ sK205 @ sK206)) | ($true != (breln @ sK204 @ sK205 @ sK207)) | ((subset @ sK206 @ sK207) = $true) | ~spl628_18),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f19669,f2224])).
% 50.18/8.41 thf(f2224,plain,(
% 50.18/8.41 (subbreln = $true)),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1213])).
% 50.18/8.41 thf(f19669,plain,(
% 50.18/8.41 ((subset @ sK206 @ sK207) = $true) | ($true != (breln @ sK204 @ sK205 @ sK207)) | (subbreln != $true) | ($true != (breln @ sK204 @ sK205 @ sK206)) | ~spl628_18),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f19668])).
% 50.18/8.41 thf(f19668,plain,(
% 50.18/8.41 (subbreln != $true) | ($true != $true) | ((subset @ sK206 @ sK207) = $true) | ($true != (breln @ sK204 @ sK205 @ sK206)) | ($true != (breln @ sK204 @ sK205 @ sK207)) | ~spl628_18),
% 50.18/8.41 inference(duplicate_literal_removal,[status(thm)],[f19661])).
% 50.18/8.41 thf(f19661,plain,(
% 50.18/8.41 ($true != (breln @ sK204 @ sK205 @ sK206)) | ($true != (breln @ sK204 @ sK205 @ sK207)) | (subbreln != $true) | ($true != $true) | ($true != (breln @ sK204 @ sK205 @ sK207)) | ((subset @ sK206 @ sK207) = $true) | ($true != (breln @ sK204 @ sK205 @ sK206)) | ~spl628_18),
% 50.18/8.41 inference(superposition,[status(thm)],[f6601,f2600])).
% 50.18/8.41 thf(f2600,plain,(
% 50.18/8.41 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK408 @ X3 @ X2 @ X1 @ X0) @ X2) = $true) | ($true = (subset @ X0 @ X3)) | ((breln @ X2 @ X1 @ X3) != $true) | ($true != (breln @ X2 @ X1 @ X0)) | (subbreln != $true)) )),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1524])).
% 50.18/8.41 thf(f1524,plain,(
% 50.18/8.41 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (breln @ X2 @ X1 @ X0)) | ! [X3 : $i] : ((((in @ (sK408 @ X3 @ X2 @ X1 @ X0) @ X2) = $true) & (($true = (in @ (kpair @ (sK408 @ X3 @ X2 @ X1 @ X0) @ (sK409 @ X3 @ X2 @ X1 @ X0)) @ X0)) & ($true != (in @ (kpair @ (sK408 @ X3 @ X2 @ X1 @ X0) @ (sK409 @ X3 @ X2 @ X1 @ X0)) @ X3)) & ((in @ (sK409 @ X3 @ X2 @ X1 @ X0) @ X1) = $true))) | ((breln @ X2 @ X1 @ X3) != $true) | ($true = (subset @ X0 @ X3)))) | (subbreln != $true)) & ((subbreln = $true) | (($true = (breln @ sK412 @ sK411 @ sK410)) & (! [X10 : $i] : (($true != (in @ X10 @ sK412)) | ! [X11 : $i] : (((in @ (kpair @ X10 @ X11) @ sK410) != $true) | ((in @ (kpair @ X10 @ X11) @ sK413) = $true) | ((in @ X11 @ sK411) != $true))) & ($true = (breln @ sK412 @ sK411 @ sK413)) & ($true != (subset @ sK410 @ sK413)))))),
% 50.18/8.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK408,sK409,sK410,sK411,sK412,sK413])],[f1519,f1523,f1522,f1521,f1520])).
% 50.18/8.41 thf(f1520,plain,(
% 50.18/8.41 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X2)) & ? [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X0)) & ($true != (in @ (kpair @ X4 @ X5) @ X3)) & ($true = (in @ X5 @ X1)))) => (((in @ (sK408 @ X3 @ X2 @ X1 @ X0) @ X2) = $true) & ? [X5 : $i] : (($true = (in @ (kpair @ (sK408 @ X3 @ X2 @ X1 @ X0) @ X5) @ X0)) & ((in @ (kpair @ (sK408 @ X3 @ X2 @ X1 @ X0) @ X5) @ X3) != $true) & ($true = (in @ X5 @ X1)))))),
% 50.18/8.41 introduced(definition,[],[choice_axiom])).
% 50.18/8.41 thf(f1521,plain,(
% 50.18/8.41 ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (? [X5 : $i] : (($true = (in @ (kpair @ (sK408 @ X3 @ X2 @ X1 @ X0) @ X5) @ X0)) & ((in @ (kpair @ (sK408 @ X3 @ X2 @ X1 @ X0) @ X5) @ X3) != $true) & ($true = (in @ X5 @ X1))) => (($true = (in @ (kpair @ (sK408 @ X3 @ X2 @ X1 @ X0) @ (sK409 @ X3 @ X2 @ X1 @ X0)) @ X0)) & ($true != (in @ (kpair @ (sK408 @ X3 @ X2 @ X1 @ X0) @ (sK409 @ X3 @ X2 @ X1 @ X0)) @ X3)) & ((in @ (sK409 @ X3 @ X2 @ X1 @ X0) @ X1) = $true)))),
% 50.18/8.41 introduced(definition,[],[choice_axiom])).
% 50.18/8.41 thf(f1522,plain,(
% 50.18/8.41 ? [X6 : $i,X7 : $i,X8 : $i] : (($true = (breln @ X8 @ X7 @ X6)) & ? [X9 : $i] : (! [X10 : $i] : (((in @ X10 @ X8) != $true) | ! [X11 : $i] : (((in @ (kpair @ X10 @ X11) @ X6) != $true) | ((in @ (kpair @ X10 @ X11) @ X9) = $true) | ($true != (in @ X11 @ X7)))) & ((breln @ X8 @ X7 @ X9) = $true) & ((subset @ X6 @ X9) != $true))) => (($true = (breln @ sK412 @ sK411 @ sK410)) & ? [X9 : $i] : (! [X10 : $i] : (($true != (in @ X10 @ sK412)) | ! [X11 : $i] : (((in @ (kpair @ X10 @ X11) @ sK410) != $true) | ((in @ (kpair @ X10 @ X11) @ X9) = $true) | ((in @ X11 @ sK411) != $true))) & ((breln @ sK412 @ sK411 @ X9) = $true) & ((subset @ sK410 @ X9) != $true)))),
% 50.18/8.41 introduced(definition,[],[choice_axiom])).
% 50.18/8.41 thf(f1523,plain,(
% 50.18/8.41 ? [X9 : $i] : (! [X10 : $i] : (($true != (in @ X10 @ sK412)) | ! [X11 : $i] : (((in @ (kpair @ X10 @ X11) @ sK410) != $true) | ((in @ (kpair @ X10 @ X11) @ X9) = $true) | ((in @ X11 @ sK411) != $true))) & ((breln @ sK412 @ sK411 @ X9) = $true) & ((subset @ sK410 @ X9) != $true)) => (! [X10 : $i] : (($true != (in @ X10 @ sK412)) | ! [X11 : $i] : (((in @ (kpair @ X10 @ X11) @ sK410) != $true) | ((in @ (kpair @ X10 @ X11) @ sK413) = $true) | ((in @ X11 @ sK411) != $true))) & ($true = (breln @ sK412 @ sK411 @ sK413)) & ($true != (subset @ sK410 @ sK413)))),
% 50.18/8.41 introduced(definition,[],[choice_axiom])).
% 50.18/8.41 thf(f1519,plain,(
% 50.18/8.41 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (breln @ X2 @ X1 @ X0)) | ! [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X2)) & ? [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X0)) & ($true != (in @ (kpair @ X4 @ X5) @ X3)) & ($true = (in @ X5 @ X1)))) | ((breln @ X2 @ X1 @ X3) != $true) | ($true = (subset @ X0 @ X3)))) | (subbreln != $true)) & ((subbreln = $true) | ? [X6 : $i,X7 : $i,X8 : $i] : (($true = (breln @ X8 @ X7 @ X6)) & ? [X9 : $i] : (! [X10 : $i] : (((in @ X10 @ X8) != $true) | ! [X11 : $i] : (((in @ (kpair @ X10 @ X11) @ X6) != $true) | ((in @ (kpair @ X10 @ X11) @ X9) = $true) | ($true != (in @ X11 @ X7)))) & ((breln @ X8 @ X7 @ X9) = $true) & ((subset @ X6 @ X9) != $true))))),
% 50.18/8.41 inference(rectify,[status(thm)],[f1518])).
% 50.18/8.41 thf(f1518,plain,(
% 50.18/8.41 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (breln @ X2 @ X1 @ X0)) | ! [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X2)) & ? [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X0)) & ($true != (in @ (kpair @ X4 @ X5) @ X3)) & ($true = (in @ X5 @ X1)))) | ((breln @ X2 @ X1 @ X3) != $true) | ($true = (subset @ X0 @ X3)))) | (subbreln != $true)) & ((subbreln = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X2 @ X1 @ X0)) & ? [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ X2)) | ! [X5 : $i] : (($true != (in @ (kpair @ X4 @ X5) @ X0)) | ($true = (in @ (kpair @ X4 @ X5) @ X3)) | ($true != (in @ X5 @ X1)))) & ((breln @ X2 @ X1 @ X3) = $true) & ($true != (subset @ X0 @ X3)))))),
% 50.18/8.41 inference(nnf_transformation,[status(thm)],[f804])).
% 50.18/8.41 thf(f804,plain,(
% 50.18/8.41 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (breln @ X2 @ X1 @ X0)) | ! [X3 : $i] : (? [X4 : $i] : (($true = (in @ X4 @ X2)) & ? [X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ X0)) & ($true != (in @ (kpair @ X4 @ X5) @ X3)) & ($true = (in @ X5 @ X1)))) | ((breln @ X2 @ X1 @ X3) != $true) | ($true = (subset @ X0 @ X3)))) <=> (subbreln = $true)),
% 50.18/8.41 inference(flattening,[status(thm)],[f803])).
% 50.18/8.41 thf(f803,plain,(
% 50.18/8.41 ! [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : ((($true = (subset @ X0 @ X3)) | ? [X4 : $i] : (? [X5 : $i] : ((($true != (in @ (kpair @ X4 @ X5) @ X3)) & ($true = (in @ (kpair @ X4 @ X5) @ X0))) & ($true = (in @ X5 @ X1))) & ($true = (in @ X4 @ X2)))) | ((breln @ X2 @ X1 @ X3) != $true)) | ($true != (breln @ X2 @ X1 @ X0))) <=> (subbreln = $true)),
% 50.18/8.41 inference(ennf_transformation,[status(thm)],[f622])).
% 50.18/8.41 thf(f622,plain,(
% 50.18/8.41 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (breln @ X2 @ X1 @ X0)) => ! [X3 : $i] : (((breln @ X2 @ X1 @ X3) = $true) => (! [X4 : $i] : (($true = (in @ X4 @ X2)) => ! [X5 : $i] : (($true = (in @ X5 @ X1)) => (($true = (in @ (kpair @ X4 @ X5) @ X0)) => ($true = (in @ (kpair @ X4 @ X5) @ X3))))) => ($true = (subset @ X0 @ X3))))) <=> (subbreln = $true)),
% 50.18/8.41 inference(fool_elimination,[status(thm)],[f621])).
% 50.18/8.41 thf(f621,plain,(
% 50.18/8.41 (subbreln = ! [X0 : $i,X1 : $i,X2 : $i] : ((breln @ X2 @ X1 @ X0) => ! [X3 : $i] : ((breln @ X2 @ X1 @ X3) => (! [X4 : $i] : ((in @ X4 @ X2) => ! [X5 : $i] : ((in @ X5 @ X1) => ((in @ (kpair @ X4 @ X5) @ X0) => (in @ (kpair @ X4 @ X5) @ X3)))) => (subset @ X0 @ X3)))))),
% 50.18/8.41 inference(rectify,[status(thm)],[f213])).
% 50.18/8.41 thf(f213,axiom,(
% 50.18/8.41 (subbreln = ! [X12 : $i,X4 : $i,X3 : $i] : ((breln @ X3 @ X4 @ X12) => ! [X15 : $i] : ((breln @ X3 @ X4 @ X15) => (! [X1 : $i] : ((in @ X1 @ X3) => ! [X2 : $i] : ((in @ X2 @ X4) => ((in @ (kpair @ X1 @ X2) @ X12) => (in @ (kpair @ X1 @ X2) @ X15)))) => (subset @ X12 @ X15)))))),
% 50.18/8.41 file('/export/starexec/sandbox/tmp/tmp.rJod2NOsaw/DTF2THF_5039.p',subbreln)).
% 50.18/8.41 thf(f6601,plain,(
% 50.18/8.41 ( ! [X0 : $i] : (((in @ (sK408 @ sK207 @ X0 @ sK205 @ sK206) @ sK204) != $true) | ($true != (breln @ X0 @ sK205 @ sK207)) | ((breln @ X0 @ sK205 @ sK206) != $true)) ) | ~spl628_18),
% 50.18/8.41 inference(avatar_component_clause,[status(thm)],[f6600])).
% 50.18/8.41 thf(f19477,plain,(
% 50.18/8.41 spl628_12 | ~spl628_8 | ~spl628_11),
% 50.18/8.41 inference(avatar_split_clause,[status(thm)],[f19476,f3502,f3469,f3511])).
% 50.18/8.41 thf(f3511,definition,(
% 50.18/8.41 spl628_12 <=> (sK206 = sK207)),
% 50.18/8.41 introduced(definition,[new_symbols(naming,[spl628_12])],[avatar_definition])).
% 50.18/8.41 thf(f3502,definition,(
% 50.18/8.41 spl628_11 <=> ($true = (subset @ sK207 @ sK206))),
% 50.18/8.41 introduced(definition,[new_symbols(naming,[spl628_11])],[avatar_definition])).
% 50.18/8.41 thf(f19476,plain,(
% 50.18/8.41 ((subset @ sK206 @ sK207) != $true) | (sK206 = sK207) | ~spl628_11),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f19475])).
% 50.18/8.41 thf(f19475,plain,(
% 50.18/8.41 ((subset @ sK206 @ sK207) != $true) | ($true != $true) | (sK206 = sK207) | ~spl628_11),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f19474,f2292])).
% 50.18/8.41 thf(f2292,plain,(
% 50.18/8.41 (setextsub = $true)),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1213])).
% 50.18/8.41 thf(f19474,plain,(
% 50.18/8.41 (setextsub != $true) | ((subset @ sK206 @ sK207) != $true) | (sK206 = sK207) | ~spl628_11),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f19473])).
% 50.18/8.41 thf(f19473,plain,(
% 50.18/8.41 (setextsub != $true) | ($true != $true) | ((subset @ sK206 @ sK207) != $true) | (sK206 = sK207) | ~spl628_11),
% 50.18/8.41 inference(superposition,[status(thm)],[f1945,f3504])).
% 50.18/8.41 thf(f3504,plain,(
% 50.18/8.41 ($true = (subset @ sK207 @ sK206)) | ~spl628_11),
% 50.18/8.41 inference(avatar_component_clause,[status(thm)],[f3502])).
% 50.18/8.41 thf(f1945,plain,(
% 50.18/8.41 ( ! [X2 : $i,X3 : $i] : (($true != (subset @ X3 @ X2)) | (X2 = X3) | ($true != (subset @ X2 @ X3)) | (setextsub != $true)) )),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f988])).
% 50.18/8.41 thf(f988,plain,(
% 50.18/8.41 ((setextsub = $true) | (($true = (subset @ sK62 @ sK63)) & (sK63 != sK62) & ($true = (subset @ sK63 @ sK62)))) & (! [X2 : $i,X3 : $i] : (($true != (subset @ X2 @ X3)) | (X2 = X3) | ($true != (subset @ X3 @ X2))) | (setextsub != $true))),
% 50.18/8.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63])],[f986,f987])).
% 50.18/8.41 thf(f987,plain,(
% 50.18/8.41 ? [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) & (X0 != X1) & ((subset @ X1 @ X0) = $true)) => (($true = (subset @ sK62 @ sK63)) & (sK63 != sK62) & ($true = (subset @ sK63 @ sK62)))),
% 50.18/8.41 introduced(definition,[],[choice_axiom])).
% 50.18/8.41 thf(f986,plain,(
% 50.18/8.41 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) & (X0 != X1) & ((subset @ X1 @ X0) = $true))) & (! [X2 : $i,X3 : $i] : (($true != (subset @ X2 @ X3)) | (X2 = X3) | ($true != (subset @ X3 @ X2))) | (setextsub != $true))),
% 50.18/8.41 inference(rectify,[status(thm)],[f985])).
% 50.18/8.41 thf(f985,plain,(
% 50.18/8.41 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : (($true = (subset @ X0 @ X1)) & (X0 != X1) & ((subset @ X1 @ X0) = $true))) & (! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | (X0 = X1) | ((subset @ X1 @ X0) != $true)) | (setextsub != $true))),
% 50.18/8.41 inference(nnf_transformation,[status(thm)],[f826])).
% 50.18/8.41 thf(f826,plain,(
% 50.18/8.41 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (($true != (subset @ X0 @ X1)) | (X0 = X1) | ((subset @ X1 @ X0) != $true))),
% 50.18/8.41 inference(flattening,[status(thm)],[f825])).
% 50.18/8.41 thf(f825,plain,(
% 50.18/8.41 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((X0 = X1) | ($true != (subset @ X0 @ X1))) | ((subset @ X1 @ X0) != $true))),
% 50.18/8.41 inference(ennf_transformation,[status(thm)],[f473])).
% 50.18/8.41 thf(f473,plain,(
% 50.18/8.41 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X1 @ X0) = $true) => (($true = (subset @ X0 @ X1)) => (X0 = X1)))),
% 50.18/8.41 inference(fool_elimination,[status(thm)],[f472])).
% 50.18/8.41 thf(f472,plain,(
% 50.18/8.41 (! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((subset @ X0 @ X1) => (X0 = X1))) = setextsub)),
% 50.18/8.41 inference(rectify,[status(thm)],[f93])).
% 50.18/8.41 thf(f93,axiom,(
% 50.18/8.41 (! [X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))) = setextsub)),
% 50.18/8.41 file('/export/starexec/sandbox/tmp/tmp.rJod2NOsaw/DTF2THF_5039.p',setextsub)).
% 50.18/8.41 thf(f19450,plain,(
% 50.18/8.41 spl628_122),
% 50.18/8.41 inference(avatar_contradiction_clause,[status(thm)],[f19449])).
% 50.18/8.41 thf(f19449,plain,(
% 50.18/8.41 $false | spl628_122),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f19448])).
% 50.18/8.41 thf(f19448,plain,(
% 50.18/8.41 ($true != $true) | spl628_122),
% 50.18/8.41 inference(superposition,[status(thm)],[f11307,f2268])).
% 50.18/8.41 thf(f2268,plain,(
% 50.18/8.41 ($true = (breln @ sK204 @ sK205 @ sK207))),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1213])).
% 50.18/8.41 thf(f11307,plain,(
% 50.18/8.41 ($true != (breln @ sK204 @ sK205 @ sK207)) | spl628_122),
% 50.18/8.41 inference(avatar_component_clause,[status(thm)],[f11305])).
% 50.18/8.41 thf(f11308,plain,(
% 50.18/8.41 ~spl628_122 | spl628_11 | ~spl628_17),
% 50.18/8.41 inference(avatar_split_clause,[status(thm)],[f11303,f6074,f3502,f11305])).
% 50.18/8.41 thf(f6074,definition,(
% 50.18/8.41 spl628_17 <=> ! [X0 : $i] : (($true != (in @ (sK409 @ sK206 @ sK204 @ X0 @ sK207) @ sK205)) | ((breln @ sK204 @ X0 @ sK206) != $true) | ($true != (breln @ sK204 @ X0 @ sK207)))),
% 50.18/8.41 introduced(definition,[new_symbols(naming,[spl628_17])],[avatar_definition])).
% 50.18/8.41 thf(f11303,plain,(
% 50.18/8.41 ($true != (breln @ sK204 @ sK205 @ sK207)) | ($true = (subset @ sK207 @ sK206)) | ~spl628_17),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f11302])).
% 50.18/8.41 thf(f11302,plain,(
% 50.18/8.41 ($true != (breln @ sK204 @ sK205 @ sK207)) | ($true != $true) | ($true = (subset @ sK207 @ sK206)) | ~spl628_17),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f11301,f2269])).
% 50.18/8.41 thf(f11301,plain,(
% 50.18/8.41 ($true != (breln @ sK204 @ sK205 @ sK207)) | ($true = (subset @ sK207 @ sK206)) | ($true != (breln @ sK204 @ sK205 @ sK206)) | ~spl628_17),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f11300])).
% 50.18/8.41 thf(f11300,plain,(
% 50.18/8.41 ($true != (breln @ sK204 @ sK205 @ sK206)) | ($true = (subset @ sK207 @ sK206)) | ($true != (breln @ sK204 @ sK205 @ sK207)) | ($true != $true) | ~spl628_17),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f11298,f2224])).
% 50.18/8.41 thf(f11298,plain,(
% 50.18/8.41 (subbreln != $true) | ($true != (breln @ sK204 @ sK205 @ sK207)) | ($true = (subset @ sK207 @ sK206)) | ($true != (breln @ sK204 @ sK205 @ sK206)) | ~spl628_17),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f11297])).
% 50.18/8.41 thf(f11297,plain,(
% 50.18/8.41 ($true = (subset @ sK207 @ sK206)) | (subbreln != $true) | ($true != (breln @ sK204 @ sK205 @ sK206)) | ($true != $true) | ($true != (breln @ sK204 @ sK205 @ sK207)) | ~spl628_17),
% 50.18/8.41 inference(duplicate_literal_removal,[status(thm)],[f11293])).
% 50.18/8.41 thf(f11293,plain,(
% 50.18/8.41 ($true != (breln @ sK204 @ sK205 @ sK207)) | ($true != (breln @ sK204 @ sK205 @ sK207)) | (subbreln != $true) | ($true != (breln @ sK204 @ sK205 @ sK206)) | ($true != $true) | ($true != (breln @ sK204 @ sK205 @ sK206)) | ($true = (subset @ sK207 @ sK206)) | ~spl628_17),
% 50.18/8.41 inference(superposition,[status(thm)],[f6075,f2597])).
% 50.18/8.41 thf(f2597,plain,(
% 50.18/8.41 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (((in @ (sK409 @ X3 @ X2 @ X1 @ X0) @ X1) = $true) | (subbreln != $true) | ($true = (subset @ X0 @ X3)) | ((breln @ X2 @ X1 @ X3) != $true) | ($true != (breln @ X2 @ X1 @ X0))) )),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1524])).
% 50.18/8.41 thf(f6075,plain,(
% 50.18/8.41 ( ! [X0 : $i] : (($true != (in @ (sK409 @ sK206 @ sK204 @ X0 @ sK207) @ sK205)) | ((breln @ sK204 @ X0 @ sK206) != $true) | ($true != (breln @ sK204 @ X0 @ sK207))) ) | ~spl628_17),
% 50.18/8.41 inference(avatar_component_clause,[status(thm)],[f6074])).
% 50.18/8.41 thf(f6602,plain,(
% 50.18/8.41 spl628_8 | spl628_18 | ~spl628_9),
% 50.18/8.41 inference(avatar_split_clause,[status(thm)],[f6598,f3473,f6600,f3469])).
% 50.18/8.41 thf(f3473,definition,(
% 50.18/8.41 spl628_9 <=> ! [X0 : $i,X1 : $i] : (((breln @ X0 @ X1 @ sK207) != $true) | ((in @ (sK408 @ sK207 @ X0 @ X1 @ sK206) @ sK204) != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | ((in @ (sK409 @ sK207 @ X0 @ X1 @ sK206) @ sK205) != $true))),
% 50.18/8.41 introduced(definition,[new_symbols(naming,[spl628_9])],[avatar_definition])).
% 50.18/8.41 thf(f6598,plain,(
% 50.18/8.41 ( ! [X0 : $i] : (((subset @ sK206 @ sK207) = $true) | ((in @ (sK408 @ sK207 @ X0 @ sK205 @ sK206) @ sK204) != $true) | ((breln @ X0 @ sK205 @ sK206) != $true) | ($true != (breln @ X0 @ sK205 @ sK207))) ) | ~spl628_9),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f6597])).
% 50.18/8.41 thf(f6597,plain,(
% 50.18/8.41 ( ! [X0 : $i] : (((in @ (sK408 @ sK207 @ X0 @ sK205 @ sK206) @ sK204) != $true) | ((subset @ sK206 @ sK207) = $true) | ((breln @ X0 @ sK205 @ sK206) != $true) | ($true != (breln @ X0 @ sK205 @ sK207)) | ($true != $true)) ) | ~spl628_9),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f6596,f2224])).
% 50.18/8.41 thf(f6596,plain,(
% 50.18/8.41 ( ! [X0 : $i] : ((subbreln != $true) | ((breln @ X0 @ sK205 @ sK206) != $true) | ((subset @ sK206 @ sK207) = $true) | ($true != (breln @ X0 @ sK205 @ sK207)) | ((in @ (sK408 @ sK207 @ X0 @ sK205 @ sK206) @ sK204) != $true)) ) | ~spl628_9),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f6595])).
% 50.18/8.41 thf(f6595,plain,(
% 50.18/8.41 ( ! [X0 : $i] : (((breln @ X0 @ sK205 @ sK206) != $true) | (subbreln != $true) | ($true != (breln @ X0 @ sK205 @ sK207)) | ((subset @ sK206 @ sK207) = $true) | ((in @ (sK408 @ sK207 @ X0 @ sK205 @ sK206) @ sK204) != $true) | ($true != $true)) ) | ~spl628_9),
% 50.18/8.41 inference(duplicate_literal_removal,[status(thm)],[f6590])).
% 50.18/8.41 thf(f6590,plain,(
% 50.18/8.41 ( ! [X0 : $i] : (($true != $true) | ($true != (breln @ X0 @ sK205 @ sK207)) | ((breln @ X0 @ sK205 @ sK206) != $true) | (subbreln != $true) | ($true != (breln @ X0 @ sK205 @ sK207)) | ((subset @ sK206 @ sK207) = $true) | ((breln @ X0 @ sK205 @ sK206) != $true) | ((in @ (sK408 @ sK207 @ X0 @ sK205 @ sK206) @ sK204) != $true)) ) | ~spl628_9),
% 50.18/8.41 inference(superposition,[status(thm)],[f3474,f2597])).
% 50.18/8.41 thf(f3474,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (((in @ (sK409 @ sK207 @ X0 @ X1 @ sK206) @ sK205) != $true) | ((in @ (sK408 @ sK207 @ X0 @ X1 @ sK206) @ sK204) != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | ((breln @ X0 @ X1 @ sK207) != $true)) ) | ~spl628_9),
% 50.18/8.41 inference(avatar_component_clause,[status(thm)],[f3473])).
% 50.18/8.41 thf(f6567,plain,(
% 50.18/8.41 ~spl628_12),
% 50.18/8.41 inference(avatar_contradiction_clause,[status(thm)],[f6566])).
% 50.18/8.41 thf(f6566,plain,(
% 50.18/8.41 $false | ~spl628_12),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f6557])).
% 50.18/8.41 thf(f6557,plain,(
% 50.18/8.41 (sK206 != sK206) | ~spl628_12),
% 50.18/8.41 inference(superposition,[status(thm)],[f2265,f3513])).
% 50.18/8.41 thf(f3513,plain,(
% 50.18/8.41 (sK206 = sK207) | ~spl628_12),
% 50.18/8.41 inference(avatar_component_clause,[status(thm)],[f3511])).
% 50.18/8.41 thf(f2265,plain,(
% 50.18/8.41 (sK206 != sK207)),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1213])).
% 50.18/8.41 thf(f6076,plain,(
% 50.18/8.41 spl628_17 | spl628_11 | ~spl628_10),
% 50.18/8.41 inference(avatar_split_clause,[status(thm)],[f6072,f3499,f3502,f6074])).
% 50.18/8.41 thf(f3499,definition,(
% 50.18/8.41 spl628_10 <=> ! [X0 : $i,X1 : $i] : (((breln @ X0 @ X1 @ sK206) != $true) | ($true != (in @ (sK408 @ sK206 @ X0 @ X1 @ sK207) @ sK204)) | ((breln @ X0 @ X1 @ sK207) != $true) | ((in @ (sK409 @ sK206 @ X0 @ X1 @ sK207) @ sK205) != $true))),
% 50.18/8.41 introduced(definition,[new_symbols(naming,[spl628_10])],[avatar_definition])).
% 50.18/8.41 thf(f6072,plain,(
% 50.18/8.41 ( ! [X0 : $i] : (($true != (in @ (sK409 @ sK206 @ sK204 @ X0 @ sK207) @ sK205)) | ($true != (breln @ sK204 @ X0 @ sK207)) | ($true = (subset @ sK207 @ sK206)) | ((breln @ sK204 @ X0 @ sK206) != $true)) ) | ~spl628_10),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f6071])).
% 50.18/8.41 thf(f6071,plain,(
% 50.18/8.41 ( ! [X0 : $i] : (($true != (in @ (sK409 @ sK206 @ sK204 @ X0 @ sK207) @ sK205)) | ($true != (breln @ sK204 @ X0 @ sK207)) | ((breln @ sK204 @ X0 @ sK206) != $true) | ($true != $true) | ($true = (subset @ sK207 @ sK206))) ) | ~spl628_10),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f6069,f2224])).
% 50.18/8.41 thf(f6069,plain,(
% 50.18/8.41 ( ! [X0 : $i] : ((subbreln != $true) | ((breln @ sK204 @ X0 @ sK206) != $true) | ($true != (in @ (sK409 @ sK206 @ sK204 @ X0 @ sK207) @ sK205)) | ($true = (subset @ sK207 @ sK206)) | ($true != (breln @ sK204 @ X0 @ sK207))) ) | ~spl628_10),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f6068])).
% 50.18/8.41 thf(f6068,plain,(
% 50.18/8.41 ( ! [X0 : $i] : (($true != (breln @ sK204 @ X0 @ sK207)) | (subbreln != $true) | ($true = (subset @ sK207 @ sK206)) | ($true != (in @ (sK409 @ sK206 @ sK204 @ X0 @ sK207) @ sK205)) | ((breln @ sK204 @ X0 @ sK206) != $true) | ($true != $true)) ) | ~spl628_10),
% 50.18/8.41 inference(duplicate_literal_removal,[status(thm)],[f6060])).
% 50.18/8.41 thf(f6060,plain,(
% 50.18/8.41 ( ! [X0 : $i] : (($true = (subset @ sK207 @ sK206)) | ($true != (breln @ sK204 @ X0 @ sK207)) | ($true != (in @ (sK409 @ sK206 @ sK204 @ X0 @ sK207) @ sK205)) | ($true != (breln @ sK204 @ X0 @ sK207)) | (subbreln != $true) | ($true != $true) | ((breln @ sK204 @ X0 @ sK206) != $true) | ((breln @ sK204 @ X0 @ sK206) != $true)) ) | ~spl628_10),
% 50.18/8.41 inference(superposition,[status(thm)],[f3500,f2600])).
% 50.18/8.41 thf(f3500,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK408 @ sK206 @ X0 @ X1 @ sK207) @ sK204)) | ((breln @ X0 @ X1 @ sK207) != $true) | ((in @ (sK409 @ sK206 @ X0 @ X1 @ sK207) @ sK205) != $true) | ((breln @ X0 @ X1 @ sK206) != $true)) ) | ~spl628_10),
% 50.18/8.41 inference(avatar_component_clause,[status(thm)],[f3499])).
% 50.18/8.41 thf(f3505,plain,(
% 50.18/8.41 spl628_10 | spl628_11),
% 50.18/8.41 inference(avatar_split_clause,[status(thm)],[f3497,f3502,f3499])).
% 50.18/8.41 thf(f3497,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (((breln @ X0 @ X1 @ sK206) != $true) | ((in @ (sK409 @ sK206 @ X0 @ X1 @ sK207) @ sK205) != $true) | ((breln @ X0 @ X1 @ sK207) != $true) | ($true = (subset @ sK207 @ sK206)) | ($true != (in @ (sK408 @ sK206 @ X0 @ X1 @ sK207) @ sK204))) )),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f3496])).
% 50.18/8.41 thf(f3496,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (($true != (in @ (sK408 @ sK206 @ X0 @ X1 @ sK207) @ sK204)) | ($true = (subset @ sK207 @ sK206)) | ((breln @ X0 @ X1 @ sK207) != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | ($true != $true) | ((in @ (sK409 @ sK206 @ X0 @ X1 @ sK207) @ sK205) != $true)) )),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f3483,f2224])).
% 50.18/8.41 thf(f3483,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (($true = (subset @ sK207 @ sK206)) | ((breln @ X0 @ X1 @ sK207) != $true) | ((in @ (sK409 @ sK206 @ X0 @ X1 @ sK207) @ sK205) != $true) | ($true != (in @ (sK408 @ sK206 @ X0 @ X1 @ sK207) @ sK204)) | (subbreln != $true) | ((breln @ X0 @ X1 @ sK206) != $true)) )),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f3482])).
% 50.18/8.41 thf(f3482,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : ((subbreln != $true) | ((in @ (sK409 @ sK206 @ X0 @ X1 @ sK207) @ sK205) != $true) | ($true != $true) | ($true = (subset @ sK207 @ sK206)) | ((breln @ X0 @ X1 @ sK207) != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | ($true != (in @ (sK408 @ sK206 @ X0 @ X1 @ sK207) @ sK204))) )),
% 50.18/8.41 inference(duplicate_literal_removal,[status(thm)],[f3481])).
% 50.18/8.41 thf(f3481,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (((in @ (sK409 @ sK206 @ X0 @ X1 @ sK207) @ sK205) != $true) | (subbreln != $true) | ($true != $true) | ($true != (in @ (sK408 @ sK206 @ X0 @ X1 @ sK207) @ sK204)) | ($true = (subset @ sK207 @ sK206)) | ((breln @ X0 @ X1 @ sK206) != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | ($true = (subset @ sK207 @ sK206)) | ((breln @ X0 @ X1 @ sK207) != $true) | ((breln @ X0 @ X1 @ sK207) != $true)) )),
% 50.18/8.41 inference(superposition,[status(thm)],[f3079,f2599])).
% 50.18/8.41 thf(f2599,plain,(
% 50.18/8.41 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true = (in @ (kpair @ (sK408 @ X3 @ X2 @ X1 @ X0) @ (sK409 @ X3 @ X2 @ X1 @ X0)) @ X0)) | ((breln @ X2 @ X1 @ X3) != $true) | ($true = (subset @ X0 @ X3)) | ($true != (breln @ X2 @ X1 @ X0)) | (subbreln != $true)) )),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1524])).
% 50.18/8.41 thf(f3079,plain,(
% 50.18/8.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK408 @ sK206 @ X0 @ X1 @ X2) @ (sK409 @ sK206 @ X0 @ X1 @ X2)) @ sK207) != $true) | ($true != (breln @ X0 @ X1 @ X2)) | ((in @ (sK409 @ sK206 @ X0 @ X1 @ X2) @ sK205) != $true) | ($true = (subset @ X2 @ sK206)) | ((breln @ X0 @ X1 @ sK206) != $true) | ((in @ (sK408 @ sK206 @ X0 @ X1 @ X2) @ sK204) != $true)) )),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f3078])).
% 50.18/8.41 thf(f3078,plain,(
% 50.18/8.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK408 @ sK206 @ X0 @ X1 @ X2) @ (sK409 @ sK206 @ X0 @ X1 @ X2)) @ sK207) != $true) | ($true != $true) | ((in @ (sK409 @ sK206 @ X0 @ X1 @ X2) @ sK205) != $true) | ($true != (breln @ X0 @ X1 @ X2)) | ((breln @ X0 @ X1 @ sK206) != $true) | ((in @ (sK408 @ sK206 @ X0 @ X1 @ X2) @ sK204) != $true) | ($true = (subset @ X2 @ sK206))) )),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f3077,f2224])).
% 50.18/8.41 thf(f3077,plain,(
% 50.18/8.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ (kpair @ (sK408 @ sK206 @ X0 @ X1 @ X2) @ (sK409 @ sK206 @ X0 @ X1 @ X2)) @ sK207) != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | ($true = (subset @ X2 @ sK206)) | ((in @ (sK409 @ sK206 @ X0 @ X1 @ X2) @ sK205) != $true) | (subbreln != $true) | ($true != (breln @ X0 @ X1 @ X2)) | ((in @ (sK408 @ sK206 @ X0 @ X1 @ X2) @ sK204) != $true)) )),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f3074])).
% 50.18/8.41 thf(f3074,plain,(
% 50.18/8.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((breln @ X0 @ X1 @ sK206) != $true) | ((in @ (kpair @ (sK408 @ sK206 @ X0 @ X1 @ X2) @ (sK409 @ sK206 @ X0 @ X1 @ X2)) @ sK207) != $true) | ($true != $true) | ($true = (subset @ X2 @ sK206)) | ((in @ (sK408 @ sK206 @ X0 @ X1 @ X2) @ sK204) != $true) | (subbreln != $true) | ((in @ (sK409 @ sK206 @ X0 @ X1 @ X2) @ sK205) != $true) | ($true != (breln @ X0 @ X1 @ X2))) )),
% 50.18/8.41 inference(superposition,[status(thm)],[f2598,f2267])).
% 50.18/8.41 thf(f2267,plain,(
% 50.18/8.41 ( ! [X4 : $i,X5 : $i] : (($true = (in @ (kpair @ X4 @ X5) @ sK206)) | ($true != (in @ (kpair @ X4 @ X5) @ sK207)) | ($true != (in @ X4 @ sK204)) | ((in @ X5 @ sK205) != $true)) )),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1213])).
% 50.18/8.41 thf(f2598,plain,(
% 50.18/8.41 ( ! [X2 : $i,X3 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ (sK408 @ X3 @ X2 @ X1 @ X0) @ (sK409 @ X3 @ X2 @ X1 @ X0)) @ X3)) | ($true != (breln @ X2 @ X1 @ X0)) | ((breln @ X2 @ X1 @ X3) != $true) | ($true = (subset @ X0 @ X3)) | (subbreln != $true)) )),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1524])).
% 50.18/8.41 thf(f3475,plain,(
% 50.18/8.41 spl628_8 | spl628_9),
% 50.18/8.41 inference(avatar_split_clause,[status(thm)],[f3467,f3473,f3469])).
% 50.18/8.41 thf(f3467,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (((breln @ X0 @ X1 @ sK207) != $true) | ((subset @ sK206 @ sK207) = $true) | ((in @ (sK409 @ sK207 @ X0 @ X1 @ sK206) @ sK205) != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | ((in @ (sK408 @ sK207 @ X0 @ X1 @ sK206) @ sK204) != $true)) )),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f3466])).
% 50.18/8.41 thf(f3466,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (((subset @ sK206 @ sK207) = $true) | ((in @ (sK408 @ sK207 @ X0 @ X1 @ sK206) @ sK204) != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | ($true != $true) | ((in @ (sK409 @ sK207 @ X0 @ X1 @ sK206) @ sK205) != $true) | ((breln @ X0 @ X1 @ sK207) != $true)) )),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f3453,f2224])).
% 50.18/8.41 thf(f3453,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (((in @ (sK408 @ sK207 @ X0 @ X1 @ sK206) @ sK204) != $true) | (subbreln != $true) | ((breln @ X0 @ X1 @ sK207) != $true) | ((in @ (sK409 @ sK207 @ X0 @ X1 @ sK206) @ sK205) != $true) | ((subset @ sK206 @ sK207) = $true) | ((breln @ X0 @ X1 @ sK206) != $true)) )),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f3452])).
% 50.18/8.41 thf(f3452,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (($true != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | ((subset @ sK206 @ sK207) = $true) | ((breln @ X0 @ X1 @ sK207) != $true) | (subbreln != $true) | ((in @ (sK408 @ sK207 @ X0 @ X1 @ sK206) @ sK204) != $true) | ((in @ (sK409 @ sK207 @ X0 @ X1 @ sK206) @ sK205) != $true)) )),
% 50.18/8.41 inference(duplicate_literal_removal,[status(thm)],[f3451])).
% 50.18/8.41 thf(f3451,plain,(
% 50.18/8.41 ( ! [X0 : $i,X1 : $i] : (((breln @ X0 @ X1 @ sK207) != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | ((subset @ sK206 @ sK207) = $true) | ((in @ (sK408 @ sK207 @ X0 @ X1 @ sK206) @ sK204) != $true) | ((in @ (sK409 @ sK207 @ X0 @ X1 @ sK206) @ sK205) != $true) | ((breln @ X0 @ X1 @ sK207) != $true) | ((breln @ X0 @ X1 @ sK206) != $true) | (subbreln != $true) | ($true != $true) | ((subset @ sK206 @ sK207) = $true)) )),
% 50.18/8.41 inference(superposition,[status(thm)],[f3055,f2599])).
% 50.18/8.41 thf(f3055,plain,(
% 50.18/8.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ (sK408 @ sK207 @ X0 @ X1 @ X2) @ (sK409 @ sK207 @ X0 @ X1 @ X2)) @ sK206)) | ($true != (in @ (sK408 @ sK207 @ X0 @ X1 @ X2) @ sK204)) | ((breln @ X0 @ X1 @ sK207) != $true) | ($true != (breln @ X0 @ X1 @ X2)) | ((subset @ X2 @ sK207) = $true) | ($true != (in @ (sK409 @ sK207 @ X0 @ X1 @ X2) @ sK205))) )),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f3054])).
% 50.18/8.41 thf(f3054,plain,(
% 50.18/8.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ (sK408 @ sK207 @ X0 @ X1 @ X2) @ (sK409 @ sK207 @ X0 @ X1 @ X2)) @ sK206)) | ((breln @ X0 @ X1 @ sK207) != $true) | ($true != $true) | ($true != (in @ (sK408 @ sK207 @ X0 @ X1 @ X2) @ sK204)) | ($true != (in @ (sK409 @ sK207 @ X0 @ X1 @ X2) @ sK205)) | ($true != (breln @ X0 @ X1 @ X2)) | ((subset @ X2 @ sK207) = $true)) )),
% 50.18/8.41 inference(forward_demodulation,[status(thm)],[f3053,f2224])).
% 50.18/8.41 thf(f3053,plain,(
% 50.18/8.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (kpair @ (sK408 @ sK207 @ X0 @ X1 @ X2) @ (sK409 @ sK207 @ X0 @ X1 @ X2)) @ sK206)) | ((subset @ X2 @ sK207) = $true) | ($true != (breln @ X0 @ X1 @ X2)) | ((breln @ X0 @ X1 @ sK207) != $true) | ($true != (in @ (sK408 @ sK207 @ X0 @ X1 @ X2) @ sK204)) | (subbreln != $true) | ($true != (in @ (sK409 @ sK207 @ X0 @ X1 @ X2) @ sK205))) )),
% 50.18/8.41 inference(trivial_inequality_removal,[status(thm)],[f3050])).
% 50.18/8.41 thf(f3050,plain,(
% 50.18/8.41 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ (sK409 @ sK207 @ X0 @ X1 @ X2) @ sK205)) | ($true != (in @ (sK408 @ sK207 @ X0 @ X1 @ X2) @ sK204)) | ($true != (breln @ X0 @ X1 @ X2)) | ($true != (in @ (kpair @ (sK408 @ sK207 @ X0 @ X1 @ X2) @ (sK409 @ sK207 @ X0 @ X1 @ X2)) @ sK206)) | ((subset @ X2 @ sK207) = $true) | ((breln @ X0 @ X1 @ sK207) != $true) | ($true != $true) | (subbreln != $true)) )),
% 50.18/8.41 inference(superposition,[status(thm)],[f2598,f2266])).
% 50.18/8.41 thf(f2266,plain,(
% 50.18/8.41 ( ! [X6 : $i,X7 : $i] : (($true = (in @ (kpair @ X6 @ X7) @ sK207)) | ((in @ X6 @ sK204) != $true) | ($true != (in @ (kpair @ X6 @ X7) @ sK206)) | ($true != (in @ X7 @ sK205))) )),
% 50.18/8.41 inference(cnf_transformation,[status(thm)],[f1213])).
% 50.18/8.41 % SZS output end Proof for DTF2THF_5039
% 50.18/8.41 % (5514)------------------------------
% 50.18/8.41 % (5514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.18/8.41 % (5514)Termination reason: Refutation
% 50.18/8.41
% 50.18/8.41 % (5514)Memory used [KB]: 13816
% 50.18/8.41 % (5514)Time elapsed: 0.814 s
% 50.18/8.41 % (5514)Instructions burned: 2787 (million)
% 50.18/8.41 % (5514)------------------------------
% 50.18/8.41 % (5514)------------------------------
% 50.18/8.41 % (5312)Success in time 6.852 s
%------------------------------------------------------------------------------