%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU723^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 09:36:40 AM UTC 2026
% Result : Theorem 84.44s 13.26s
% Output : Refutation 84.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 48 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 4946 (1371 equ; 0 cnn)
% Maximal formula atoms : 245 ( 103 avg)
% Number of connectives : 2570 ( 73 ~; 44 |; 777 &; 432 @)
% ( 7 <=>;1237 =>; 0 <=; 0 <~>)
% Maximal formula depth : 253 ( 46 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 440 ( 437 usr; 251 con; 0-4 aty)
% Number of variables : 127 ( 0 ^; 91 !; 36 ?; 127 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_213,type,
breln: $i > $i > $i > $o ).
thf(func_def_214,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_222,type,
func: $i > $i > $i > $o ).
thf(func_def_223,type,
funcSet: $i > $i > $i ).
thf(func_def_226,type,
ap: $i > $i > $i > $i > $i ).
thf(func_def_232,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(func_def_259,type,
if: $i > $o > $i > $i > $i ).
thf(func_def_291,type,
sP0: $i > $i > $o ).
thf(func_def_292,type,
sP1: $i > $o ).
thf(func_def_293,type,
sP2: $i > $i > $o ).
thf(func_def_294,type,
sP3: $i > $i > $o ).
thf(func_def_295,type,
sP4: $i > $i > $i > $i > $o ).
thf(func_def_299,type,
sP8: $i > $i > $i > $o ).
thf(func_def_301,type,
sP10: $o > $i > $i > $i > $o ).
thf(func_def_342,type,
sK51: $i > $i > $i ).
thf(func_def_343,type,
sK52: $i > $i > $i ).
thf(func_def_344,type,
sK53: $i > $i > $i ).
thf(func_def_345,type,
sK54: $i > $i > $i ).
thf(func_def_346,type,
sK55: $i > $i > $i ).
thf(func_def_347,type,
sK56: $i > $i > $i > $i ).
thf(func_def_348,type,
sK57: $i > $i ).
thf(func_def_349,type,
sK58: $i > $i ).
thf(func_def_350,type,
sK59: $i > $i ).
thf(func_def_351,type,
sK60: $i > $i ).
thf(func_def_352,type,
sK61: $i > $i > $i > $i ).
thf(func_def_353,type,
sK62: $i > $i > $i > $i ).
thf(func_def_354,type,
sK63: $i > $i > $i ).
thf(func_def_355,type,
sK64: $i > $i > $i ).
thf(func_def_356,type,
sK65: $i > $i > $i ).
thf(func_def_358,type,
sK67: $i > $i ).
thf(func_def_359,type,
sK68: $i > $i ).
thf(func_def_360,type,
sK69: $i > $i ).
thf(func_def_376,type,
sK85: $i > $i > $i > $i ).
thf(func_def_377,type,
sK86: $i > $i > $i > $i ).
thf(func_def_380,type,
sK89: $i > $o ).
thf(func_def_392,type,
sK101: $i > $i > $i ).
thf(func_def_399,type,
sK108: $i > $i > $i > $i > $i ).
thf(func_def_400,type,
sK109: $i > $i > $i > $i > $i ).
thf(func_def_401,type,
sK110: $i > $i > $i > $i > $i ).
thf(func_def_402,type,
sK111: $i > $i > $i > $i > $i ).
thf(func_def_410,type,
sK119: ( $i > $o ) > $i > $i ).
thf(func_def_412,type,
sK121: $i > $o ).
thf(func_def_418,type,
sK127: ( $i > $i ) > $i > $i > $i ).
thf(func_def_421,type,
sK130: $i > $i ).
thf(func_def_430,type,
sK139: $i > $i > $i > $i > $i ).
thf(func_def_431,type,
sK140: $i > $i > $i > $i > $i ).
thf(func_def_434,type,
sK143: $i > $o ).
thf(func_def_437,type,
sK146: $i > $i > $o ).
thf(func_def_439,type,
sK148: $i > $i ).
thf(func_def_440,type,
sK149: $i > $i ).
thf(func_def_441,type,
sK150: $i > ( $i > $i > $o ) > $i ).
thf(func_def_442,type,
sK151: $i > ( $i > $i > $o ) > $i ).
thf(func_def_443,type,
sK152: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_447,type,
sK156: $i > $o ).
thf(func_def_449,type,
sK158: ( $i > $o ) > $i > $i ).
thf(func_def_450,type,
sK159: ( $i > $o ) > $i > $i ).
thf(func_def_456,type,
sK165: $i > $i > $i > $i > $i ).
thf(func_def_480,type,
sK189: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_481,type,
sK190: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_484,type,
sK193: $i > $o ).
thf(func_def_485,type,
sK194: $i > $o ).
thf(func_def_487,type,
sK196: $i > $i > $o ).
thf(func_def_491,type,
sK200: $i > $o ).
thf(func_def_492,type,
sK201: ( $i > $o ) > $i > $i > $i ).
thf(func_def_498,type,
sK207: $i > $i > $i ).
thf(func_def_519,type,
sK228: $i > $i > $i > $i ).
thf(func_def_523,type,
sK232: $i > $i > $i > $i ).
thf(func_def_530,type,
sK239: $i > $o ).
thf(func_def_546,type,
sK255: $i > $o ).
thf(func_def_552,type,
sK261: ( $i > $o ) > $i ).
thf(func_def_553,type,
sK262: ( $i > $o ) > $i ).
thf(func_def_554,type,
sK263: $i > $o ).
thf(func_def_569,type,
sK278: $i > $i ).
thf(func_def_573,type,
sK282: $i > $i > ( $i > $i ) > $i ).
thf(func_def_578,type,
sK287: $i > $o ).
thf(func_def_591,type,
sK300: $i > $i > $o ).
thf(func_def_594,type,
sK303: $i > $i > $o ).
thf(func_def_602,type,
sK311: $i > ( $i > $o ) > $i ).
thf(func_def_603,type,
sK312: $i > $o ).
thf(func_def_608,type,
sK317: $i > $i > $i ).
thf(func_def_619,type,
sK328: $i > $i > $o ).
thf(func_def_625,type,
sK334: $i > $o ).
thf(func_def_639,type,
sK348: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_640,type,
sK349: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_644,type,
sK353: $i > $o ).
thf(func_def_647,type,
sK356: $i > $o ).
thf(func_def_649,type,
sK358: ( $i > $o ) > $i > $i ).
thf(func_def_650,type,
sK359: ( $i > $o ) > $i > $i ).
thf(func_def_656,type,
sK365: ( $i > $i ) > $i > $i > $i ).
thf(func_def_659,type,
sK368: $i > $i ).
thf(func_def_661,type,
sK370: $i > $i > $i ).
thf(func_def_666,type,
sK375: $i > $o ).
thf(func_def_682,type,
sK391: $i > $i > ( $i > $i ) > $i ).
thf(func_def_683,type,
sK392: $i > $i ).
thf(func_def_695,type,
sK404: $i > $o ).
thf(func_def_698,type,
sK407: $i > $o ).
thf(func_def_709,type,
sK418: ( $i > $o ) > $i ).
thf(func_def_710,type,
sK419: $i > $o ).
thf(func_def_711,type,
sK420: $i > $i ).
thf(func_def_718,type,
sK427: $i > $i > $i > $i > $i ).
thf(func_def_726,type,
sK435: $i > $i ).
thf(func_def_732,type,
sK441: ( $i > $i ) > $i > $i > $i ).
thf(func_def_735,type,
sK444: $i > $i ).
thf(func_def_744,type,
sK453: $i > $i ).
thf(func_def_745,type,
sK454: $i > $i > $i > $i ).
thf(func_def_751,type,
sK460: $i > $i > $i ).
thf(func_def_755,type,
sK464: $i > $o ).
thf(func_def_761,type,
sK470: $i > $o ).
thf(func_def_763,type,
sK472: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_764,type,
sK473: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_767,type,
sK476: $i > $i > $o ).
thf(func_def_776,type,
sK485: ( $i > $o ) > $i > $i ).
thf(func_def_778,type,
sK487: $i > $o ).
thf(func_def_780,type,
sK489: $o > $i > $i > $i ).
thf(func_def_787,type,
sK496: ( $i > $o ) > $i > $i ).
thf(func_def_789,type,
sK498: $i > $o ).
thf(func_def_790,type,
sK499: $i > $o ).
thf(func_def_792,type,
sK501: $i > ( $i > $o ) > $i ).
thf(func_def_797,type,
sK506: $i > $i > $i ).
thf(func_def_804,type,
sK513: ( $i > $o ) > $i ).
thf(func_def_805,type,
sK514: $i > $o ).
thf(func_def_806,type,
sK515: $i > $i ).
thf(func_def_818,type,
sK527: $i > $i ).
thf(func_def_821,type,
sK530: $i > $i ).
thf(func_def_823,type,
sK532: $i > $o ).
thf(func_def_839,type,
sK548: $i > $o ).
thf(func_def_840,type,
sK549: ( $i > $o ) > $i ).
thf(func_def_841,type,
sK550: ( $i > $o ) > $i > $i ).
thf(func_def_843,type,
sK552: $i > $o ).
thf(func_def_860,type,
sK569: $i > $i ).
thf(func_def_865,type,
sK574: $i > $o ).
thf(func_def_867,type,
sK576: $i > $i > $o ).
thf(func_def_886,type,
sK595: ( $i > $i ) > $i > $i > $i ).
thf(func_def_889,type,
sK598: $i > $i ).
thf(func_def_898,type,
sK607: $i > $i > $i > $i > $i ).
thf(func_def_915,type,
sK624: $i > $i ).
thf(func_def_925,type,
sK634: ( $i > $o ) > $i > $i ).
thf(func_def_927,type,
sK636: $i > $o ).
thf(func_def_935,type,
sK644: $i > $o ).
thf(func_def_936,type,
sK645: $i > $o ).
thf(func_def_937,type,
sK646: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_938,type,
sK647: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_950,type,
sK659: $i > $i > $o ).
thf(func_def_959,type,
sK668: $i > $o ).
thf(func_def_961,type,
sK670: $i > ( $i > $o ) > $i ).
thf(func_def_968,type,
sK677: $i > $i > $i ).
thf(func_def_983,type,
sK692: $i > $i > $i ).
thf(func_def_991,type,
sK700: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_992,type,
sK701: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_993,type,
sK702: $i > $o ).
thf(func_def_994,type,
sK703: $i > $o ).
thf(func_def_999,type,
sK708: $i > $i > $i ).
thf(func_def_1000,type,
sK709: $i > $i > $i ).
thf(func_def_1004,type,
sK713: $i > $i ).
thf(func_def_1007,type,
sK716: $i > $i > $i > $i ).
thf(func_def_1025,type,
sK734: $i > ( $i > $o ) > $i ).
thf(func_def_1026,type,
sK735: $i > $o ).
thf(func_def_1035,type,
sK744: $i > $o ).
thf(func_def_1050,type,
ph759:
!>[X0: $tType] : X0 ).
thf(f20131,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f20098,f3299]) ).
thf(f3299,plain,
( $true
= ( in @ sK741 @ sK740 ) ),
inference(cnf_transformation,[status(thm)],[f2186]) ).
thf(f2186,plain,
( ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( emptysetimpfalse = $true )
& ( disjointsetsI1 = $true )
& ( symdiffE = $true )
& ( setminusI = $true )
& ( binintersectSubset2 = $true )
& ( eta2 = $true )
& ( subsetE = $true )
& ( powersetT_lem = $true )
& ( subset2powerset = $true )
& ( exuE3u = $true )
& ( setadjoinIR = $true )
& ( ifSingleton = $true )
& ( setukpairinjL = $true )
& ( ksndsingleton = $true )
& ( setOfPairsIsBReln = $true )
& ( eqimpsubset1 = $true )
& ( uniqinunit = $true )
& ( notdexE = $true )
& ( ex1I2 = $true )
& ( emptyI = $true )
& ( in__Cong = $true )
& ( eqimpsubset2 = $true )
& ( ifp = $true )
& ( iffalseProp1 = $true )
& ( emptyinunitempty = $true )
& ( prop2set2propI = $true )
& ( ap2p = $true )
& ( cartprodsndin = $true )
& ( binintersectEL = $true )
& ( dpsetconstrER = $true )
& ( brelnall1 = $true )
& ( ubforcartprodlem3 = $true )
& ( prop2setI = $true )
& ( setminusER = $true )
& ( subbreln = $true )
& ( binunionLsub = $true )
& ( singletonsuniq = $true )
& ( binintersectT_lem = $true )
& ( setminusERneg = $true )
& ( notequalI2 = $true )
& ( funcGraphProp3 = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrER = $true )
& ( emptysetE = $true )
& ( upairset2IR = $true )
& ( quantDeMorgan4 = $true )
& ( iftrueProp2 = $true )
& ( exuI3 = $true )
& ( powerset__Cong = $true )
& ( powersetE1 = $true )
& ( vacuousDall = $true )
& ( emptysetsubset = $true )
& ( dsetconstr__Cong = $true )
& ( nonemptyE1 = $true )
& ( setminusSubset1 = $true )
& ( funcGraphProp2 = $true )
& ( funcext2 = $true )
& ( funcGraphProp4 = $true )
& ( omegaSAx = $true )
& ( setunionsingleton2 = $true )
& ( binintersectTELcontra = $true )
& ( setukpairinjL1 = $true )
& ( eta1 = $true )
& ( kpairsurjEq = $true )
& ( dsetconstrI = $true )
& ( ex1I = $true )
& ( brelnall2 = $true )
& ( cartprodpairmemEL = $true )
& ( subsetTI = $true )
& ( singletonsswitch = $true )
& ( funcext = $true )
& ( ubforcartprodlem2 = $true )
& ( setadjoinAx = $true )
& ( dpsetconstrSub = $true )
& ( sepInPowerset = $true )
& ( beta1 = $true )
& ( lam2lamEq = $true )
& ( setunionAx = $true )
& ( symdiffIneg2 = $true )
& ( binintersectI = $true )
& ( emptyE1 = $true )
& ( dpsetconstrERa = $true )
& ( cartprodpairin = $true )
& ( binunionEcases = $true )
& ( quantDeMorgan2 = $true )
& ( setext = $true )
& ( ex1E2 = $true )
& ( subsetRefl = $true )
& ( binunionE = $true )
& ( dsetconstrEL = $true )
& ( theeq = $true )
& ( setadjoinE = $true )
& ( binintersectSubset5 = $true )
& ( app = $true )
& ( powersetsubset = $true )
& ( iftrueorfalse = $true )
& ( exuI1 = $true )
& ( binintersectSubset3 = $true )
& ( nonemptyImpWitness = $true )
& ( sepSubset = $true )
& ( upairsetIR = $true )
& ( setextAx = $true )
& ( powersetI = $true )
& ( binintersectSubset4 = $true )
& ( powersetTI1 = $true )
& ( cartprodfstin = $true )
& ( iffalse = $true )
& ( quantDeMorgan3 = $true )
& ( setukpairinjR = $true )
& ( wellorderingAx = $true )
& ( kfstsingleton = $true )
& ( exuI2 = $true )
& ( ap2apEq1 = $true )
& ( replAx = $true )
& ( prop2setE = $true )
& ( secondinupair = $true )
& ( emptyinPowerset = $true )
& ( ( subset @ sK739 @ ( setminus @ sK738 @ sK740 ) )
= $true )
& ( ( in @ sK741 @ sK738 )
= $true )
& ( ( in @ sK741 @ sK739 )
= $true )
& ( $true
= ( in @ sK741 @ sK740 ) )
& ( ( in @ sK740 @ ( powerset @ sK738 ) )
= $true )
& ( ( in @ sK739 @ ( powerset @ sK738 ) )
= $true )
& ( setukpairinjR11 = $true )
& ( kfstpairEq = $true )
& ( noeltsimpempty = $true )
& ( lamp = $true )
& ( omegaIndAx = $true )
& ( setunionI = $true )
& ( kpairp = $true )
& ( ex1E1 = $true )
& ( upairequniteq = $true )
& ( setunion__Cong = $true )
& ( setukpairIR = $true )
& ( binunionT_lem = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( setadjoinSub2 = $true )
& ( nonemptyI = $true )
& ( exuE2 = $true )
& ( binunionIR = $true )
& ( funcinfuncset = $true )
& ( notinsingleton = $true )
& ( apProp = $true )
& ( powersetI1 = $true )
& ( ksndpairEq = $true )
& ( inPowerset = $true )
& ( subsetE2 = $true )
& ( binintersectRsub = $true )
& ( upairset2E = $true )
& ( subsetI2 = $true )
& ( setadjoinSub = $true )
& ( setminusLsub = $true )
& ( eqinunit = $true )
& ( powersetAx = $true )
& ( cartprodmempair1 = $true )
& ( iffalseProp2 = $true )
& ( setunionE = $true )
& ( upairinpowunion = $true )
& ( complementTI1 = $true )
& ( exuE1 = $true )
& ( setadjoinIL = $true )
& ( cartprodfstpairEq = $true )
& ( notinemptyset = $true )
& ( kpairiskpair = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjL2 = $true )
& ( cartprodpairsurjEq = $true )
& ( descr__Cong = $true )
& ( setadjoinOr = $true )
& ( setminusELneg = $true )
& ( setukpairinjR1 = $true )
& ( beta2 = $true )
& ( setunionsingleton = $true )
& ( singletoninpowerset = $true )
& ( binunionRsub = $true )
& ( omega0Ax = $true )
& ( dpsetconstrEL1 = $true )
& ( setextT = $true )
& ( setukpairIL = $true )
& ( cartprodmempaircEq = $true )
& ( binintersectTERcontra = $true )
& ( exuEu = $true )
& ( subsetI1 = $true )
& ( bs114d = $true )
& ( setminusT_lem = $true )
& ( binintersectLsub = $true )
& ( subsetTrans = $true )
& ( singletonsubset = $true )
& ( lamProp = $true )
& ( iftrue = $true )
& ( nonemptyI1 = $true )
& ( setminusSubset2 = $true )
& ( ap2apEq2 = $true )
& ( funcextLem = $true )
& ( subPowSU = $true )
& ( symdiffI1 = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodsndpairEq = $true )
& ( descrp = $true )
& ( binintersectSubset1 = $true )
& ( setukpairinjR2 = $true )
& ( dpsetconstrI = $true )
& ( notequalI1 = $true )
& ( complementT_lem = $true )
& ( ubforcartprodlem1 = $true )
& ( omega__Cong = $true )
& ( symdiffIneg1 = $true )
& ( singletoninpowunion = $true )
& ( exu__Cong = $true )
& ( powersetTE1 = $true )
& ( upairsetE = $true )
& ( emptyset__Cong = $true )
& ( upairsubunion = $true )
& ( cartprodpairmemER = $true )
& ( setminusILneg = $true )
& ( theprop = $true )
& ( inCongP = $true )
& ( iftrueProp1 = $true )
& ( dpsetconstrEL2 = $true )
& ( complementTE1 = $true )
& ( funcImageSingleton = $true )
& ( exuE3e = $true )
& ( setextsub = $true )
& ( notsubsetI = $true )
& ( singletonprop = $true )
& ( setukpairinjR12 = $true )
& ( binunionIL = $true )
& ( infuncsetfunc = $true )
& ( setminusEL = $true )
& ( setbeta = $true )
& ( funcGraphProp1 = $true )
& ( symdiffI2 = $true )
& ( setminusIRneg = $true )
& ( lam2p = $true )
& ( foundationAx = $true )
& ( powersetE = $true )
& ( upairsetIL = $true )
& ( setoftrueEq = $true )
& ( emptysetAx = $true )
& ( eqbreln = $true )
& ( binintersectER = $true )
& ( setadjoin__Cong = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK738,sK739,sK740,sK741])],[f997,f2185,f2184,f2183]) ).
thf(f2183,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
=> ( ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ sK739 @ ( setminus @ sK738 @ X2 ) )
= $true )
& ( $true
= ( in @ X3 @ sK738 ) )
& ( $true
= ( in @ X3 @ sK739 ) )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK738 ) )
= $true ) )
& ( ( in @ sK739 @ ( powerset @ sK738 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2184,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ sK739 @ ( setminus @ sK738 @ X2 ) )
= $true )
& ( $true
= ( in @ X3 @ sK738 ) )
& ( $true
= ( in @ X3 @ sK739 ) )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK738 ) )
= $true ) )
=> ( ? [X3: $i] :
( ( ( subset @ sK739 @ ( setminus @ sK738 @ sK740 ) )
= $true )
& ( $true
= ( in @ X3 @ sK738 ) )
& ( $true
= ( in @ X3 @ sK739 ) )
& ( ( in @ X3 @ sK740 )
= $true ) )
& ( ( in @ sK740 @ ( powerset @ sK738 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2185,plain,
( ? [X3: $i] :
( ( ( subset @ sK739 @ ( setminus @ sK738 @ sK740 ) )
= $true )
& ( $true
= ( in @ X3 @ sK738 ) )
& ( $true
= ( in @ X3 @ sK739 ) )
& ( ( in @ X3 @ sK740 )
= $true ) )
=> ( ( ( subset @ sK739 @ ( setminus @ sK738 @ sK740 ) )
= $true )
& ( ( in @ sK741 @ sK738 )
= $true )
& ( ( in @ sK741 @ sK739 )
= $true )
& ( $true
= ( in @ sK741 @ sK740 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f997,plain,
( ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( emptysetimpfalse = $true )
& ( disjointsetsI1 = $true )
& ( symdiffE = $true )
& ( setminusI = $true )
& ( binintersectSubset2 = $true )
& ( eta2 = $true )
& ( subsetE = $true )
& ( powersetT_lem = $true )
& ( subset2powerset = $true )
& ( exuE3u = $true )
& ( setadjoinIR = $true )
& ( ifSingleton = $true )
& ( setukpairinjL = $true )
& ( ksndsingleton = $true )
& ( setOfPairsIsBReln = $true )
& ( eqimpsubset1 = $true )
& ( uniqinunit = $true )
& ( notdexE = $true )
& ( ex1I2 = $true )
& ( emptyI = $true )
& ( in__Cong = $true )
& ( eqimpsubset2 = $true )
& ( ifp = $true )
& ( iffalseProp1 = $true )
& ( emptyinunitempty = $true )
& ( prop2set2propI = $true )
& ( ap2p = $true )
& ( cartprodsndin = $true )
& ( binintersectEL = $true )
& ( dpsetconstrER = $true )
& ( brelnall1 = $true )
& ( ubforcartprodlem3 = $true )
& ( prop2setI = $true )
& ( setminusER = $true )
& ( subbreln = $true )
& ( binunionLsub = $true )
& ( singletonsuniq = $true )
& ( binintersectT_lem = $true )
& ( setminusERneg = $true )
& ( notequalI2 = $true )
& ( funcGraphProp3 = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrER = $true )
& ( emptysetE = $true )
& ( upairset2IR = $true )
& ( quantDeMorgan4 = $true )
& ( iftrueProp2 = $true )
& ( exuI3 = $true )
& ( powerset__Cong = $true )
& ( powersetE1 = $true )
& ( vacuousDall = $true )
& ( emptysetsubset = $true )
& ( dsetconstr__Cong = $true )
& ( nonemptyE1 = $true )
& ( setminusSubset1 = $true )
& ( funcGraphProp2 = $true )
& ( funcext2 = $true )
& ( funcGraphProp4 = $true )
& ( omegaSAx = $true )
& ( setunionsingleton2 = $true )
& ( binintersectTELcontra = $true )
& ( setukpairinjL1 = $true )
& ( eta1 = $true )
& ( kpairsurjEq = $true )
& ( dsetconstrI = $true )
& ( ex1I = $true )
& ( brelnall2 = $true )
& ( cartprodpairmemEL = $true )
& ( subsetTI = $true )
& ( singletonsswitch = $true )
& ( funcext = $true )
& ( ubforcartprodlem2 = $true )
& ( setadjoinAx = $true )
& ( dpsetconstrSub = $true )
& ( sepInPowerset = $true )
& ( beta1 = $true )
& ( lam2lamEq = $true )
& ( setunionAx = $true )
& ( symdiffIneg2 = $true )
& ( binintersectI = $true )
& ( emptyE1 = $true )
& ( dpsetconstrERa = $true )
& ( cartprodpairin = $true )
& ( binunionEcases = $true )
& ( quantDeMorgan2 = $true )
& ( setext = $true )
& ( ex1E2 = $true )
& ( subsetRefl = $true )
& ( binunionE = $true )
& ( dsetconstrEL = $true )
& ( theeq = $true )
& ( setadjoinE = $true )
& ( binintersectSubset5 = $true )
& ( app = $true )
& ( powersetsubset = $true )
& ( iftrueorfalse = $true )
& ( exuI1 = $true )
& ( binintersectSubset3 = $true )
& ( nonemptyImpWitness = $true )
& ( sepSubset = $true )
& ( upairsetIR = $true )
& ( setextAx = $true )
& ( powersetI = $true )
& ( binintersectSubset4 = $true )
& ( powersetTI1 = $true )
& ( cartprodfstin = $true )
& ( iffalse = $true )
& ( quantDeMorgan3 = $true )
& ( setukpairinjR = $true )
& ( wellorderingAx = $true )
& ( kfstsingleton = $true )
& ( exuI2 = $true )
& ( ap2apEq1 = $true )
& ( replAx = $true )
& ( prop2setE = $true )
& ( secondinupair = $true )
& ( emptyinPowerset = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true )
& ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( setukpairinjR11 = $true )
& ( kfstpairEq = $true )
& ( noeltsimpempty = $true )
& ( lamp = $true )
& ( omegaIndAx = $true )
& ( setunionI = $true )
& ( kpairp = $true )
& ( ex1E1 = $true )
& ( upairequniteq = $true )
& ( setunion__Cong = $true )
& ( setukpairIR = $true )
& ( binunionT_lem = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( setadjoinSub2 = $true )
& ( nonemptyI = $true )
& ( exuE2 = $true )
& ( binunionIR = $true )
& ( funcinfuncset = $true )
& ( notinsingleton = $true )
& ( apProp = $true )
& ( powersetI1 = $true )
& ( ksndpairEq = $true )
& ( inPowerset = $true )
& ( subsetE2 = $true )
& ( binintersectRsub = $true )
& ( upairset2E = $true )
& ( subsetI2 = $true )
& ( setadjoinSub = $true )
& ( setminusLsub = $true )
& ( eqinunit = $true )
& ( powersetAx = $true )
& ( cartprodmempair1 = $true )
& ( iffalseProp2 = $true )
& ( setunionE = $true )
& ( upairinpowunion = $true )
& ( complementTI1 = $true )
& ( exuE1 = $true )
& ( setadjoinIL = $true )
& ( cartprodfstpairEq = $true )
& ( notinemptyset = $true )
& ( kpairiskpair = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjL2 = $true )
& ( cartprodpairsurjEq = $true )
& ( descr__Cong = $true )
& ( setadjoinOr = $true )
& ( setminusELneg = $true )
& ( setukpairinjR1 = $true )
& ( beta2 = $true )
& ( setunionsingleton = $true )
& ( singletoninpowerset = $true )
& ( binunionRsub = $true )
& ( omega0Ax = $true )
& ( dpsetconstrEL1 = $true )
& ( setextT = $true )
& ( setukpairIL = $true )
& ( cartprodmempaircEq = $true )
& ( binintersectTERcontra = $true )
& ( exuEu = $true )
& ( subsetI1 = $true )
& ( bs114d = $true )
& ( setminusT_lem = $true )
& ( binintersectLsub = $true )
& ( subsetTrans = $true )
& ( singletonsubset = $true )
& ( lamProp = $true )
& ( iftrue = $true )
& ( nonemptyI1 = $true )
& ( setminusSubset2 = $true )
& ( ap2apEq2 = $true )
& ( funcextLem = $true )
& ( subPowSU = $true )
& ( symdiffI1 = $true )
& ( quantDeMorgan1 = $true )
& ( cartprodsndpairEq = $true )
& ( descrp = $true )
& ( binintersectSubset1 = $true )
& ( setukpairinjR2 = $true )
& ( dpsetconstrI = $true )
& ( notequalI1 = $true )
& ( complementT_lem = $true )
& ( ubforcartprodlem1 = $true )
& ( omega__Cong = $true )
& ( symdiffIneg1 = $true )
& ( singletoninpowunion = $true )
& ( exu__Cong = $true )
& ( powersetTE1 = $true )
& ( upairsetE = $true )
& ( emptyset__Cong = $true )
& ( upairsubunion = $true )
& ( cartprodpairmemER = $true )
& ( setminusILneg = $true )
& ( theprop = $true )
& ( inCongP = $true )
& ( iftrueProp1 = $true )
& ( dpsetconstrEL2 = $true )
& ( complementTE1 = $true )
& ( funcImageSingleton = $true )
& ( exuE3e = $true )
& ( setextsub = $true )
& ( notsubsetI = $true )
& ( singletonprop = $true )
& ( setukpairinjR12 = $true )
& ( binunionIL = $true )
& ( infuncsetfunc = $true )
& ( setminusEL = $true )
& ( setbeta = $true )
& ( funcGraphProp1 = $true )
& ( symdiffI2 = $true )
& ( setminusIRneg = $true )
& ( lam2p = $true )
& ( foundationAx = $true )
& ( powersetE = $true )
& ( upairsetIL = $true )
& ( setoftrueEq = $true )
& ( emptysetAx = $true )
& ( eqbreln = $true )
& ( binintersectER = $true )
& ( setadjoin__Cong = $true ) ),
inference(flattening,[status(thm)],[f996]) ).
thf(f996,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ( ( in @ X3 @ X1 )
= $true )
& ( ( in @ X3 @ X2 )
= $true )
& ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
& ( ( in @ X3 @ X0 )
= $true ) )
& ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) ) )
& ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
& ( binintersectTERcontra = $true )
& ( binintersectTELcontra = $true )
& ( complementTE1 = $true )
& ( complementTI1 = $true )
& ( powersetTE1 = $true )
& ( powersetTI1 = $true )
& ( subsetTI = $true )
& ( setextT = $true )
& ( complementT_lem = $true )
& ( setminusT_lem = $true )
& ( powersetT_lem = $true )
& ( binunionT_lem = $true )
& ( binintersectT_lem = $true )
& ( iftrueorfalse = $true )
& ( iffalse = $true )
& ( iftrue = $true )
& ( theeq = $true )
& ( ifp = $true )
& ( ifSingleton = $true )
& ( iftrueProp2 = $true )
& ( iftrueProp1 = $true )
& ( iffalseProp2 = $true )
& ( iffalseProp1 = $true )
& ( eta2 = $true )
& ( beta2 = $true )
& ( lam2lamEq = $true )
& ( eta1 = $true )
& ( beta1 = $true )
& ( ap2apEq2 = $true )
& ( ap2apEq1 = $true )
& ( funcext2 = $true )
& ( funcext = $true )
& ( eqbreln = $true )
& ( subbreln = $true )
& ( funcGraphProp4 = $true )
& ( funcextLem = $true )
& ( funcGraphProp2 = $true )
& ( funcGraphProp3 = $true )
& ( funcGraphProp1 = $true )
& ( ex1E2 = $true )
& ( brelnall2 = $true )
& ( brelnall1 = $true )
& ( lam2p = $true )
& ( lamp = $true )
& ( lamProp = $true )
& ( funcinfuncset = $true )
& ( ap2p = $true )
& ( infuncsetfunc = $true )
& ( app = $true )
& ( apProp = $true )
& ( funcImageSingleton = $true )
& ( dpsetconstrER = $true )
& ( dpsetconstrEL2 = $true )
& ( dpsetconstrEL1 = $true )
& ( dpsetconstrERa = $true )
& ( setOfPairsIsBReln = $true )
& ( dpsetconstrSub = $true )
& ( dpsetconstrI = $true )
& ( cartprodpairsurjEq = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodfstpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( cartprodpairmemER = $true )
& ( cartprodpairmemEL = $true )
& ( cartprodsndin = $true )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f731]) ).
thf(f731,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f449]) ).
thf(f449,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ( ( cartprodsndin = $true )
=> ( ( cartprodpairmemEL = $true )
=> ( ( cartprodpairmemER = $true )
=> ( ( cartprodmempaircEq = $true )
=> ( ( cartprodfstpairEq = $true )
=> ( ( cartprodsndpairEq = $true )
=> ( ( cartprodpairsurjEq = $true )
=> ( ( dpsetconstrI = $true )
=> ( ( dpsetconstrSub = $true )
=> ( ( setOfPairsIsBReln = $true )
=> ( ( dpsetconstrERa = $true )
=> ( ( dpsetconstrEL1 = $true )
=> ( ( dpsetconstrEL2 = $true )
=> ( ( dpsetconstrER = $true )
=> ( ( funcImageSingleton = $true )
=> ( ( apProp = $true )
=> ( ( app = $true )
=> ( ( infuncsetfunc = $true )
=> ( ( ap2p = $true )
=> ( ( funcinfuncset = $true )
=> ( ( lamProp = $true )
=> ( ( lamp = $true )
=> ( ( lam2p = $true )
=> ( ( brelnall1 = $true )
=> ( ( brelnall2 = $true )
=> ( ( ex1E2 = $true )
=> ( ( funcGraphProp1 = $true )
=> ( ( funcGraphProp3 = $true )
=> ( ( funcGraphProp2 = $true )
=> ( ( funcextLem = $true )
=> ( ( funcGraphProp4 = $true )
=> ( ( subbreln = $true )
=> ( ( eqbreln = $true )
=> ( ( funcext = $true )
=> ( ( funcext2 = $true )
=> ( ( ap2apEq1 = $true )
=> ( ( ap2apEq2 = $true )
=> ( ( beta1 = $true )
=> ( ( eta1 = $true )
=> ( ( lam2lamEq = $true )
=> ( ( beta2 = $true )
=> ( ( eta2 = $true )
=> ( ( iffalseProp1 = $true )
=> ( ( iffalseProp2 = $true )
=> ( ( iftrueProp1 = $true )
=> ( ( iftrueProp2 = $true )
=> ( ( ifSingleton = $true )
=> ( ( ifp = $true )
=> ( ( theeq = $true )
=> ( ( iftrue = $true )
=> ( ( iffalse = $true )
=> ( ( iftrueorfalse = $true )
=> ( ( binintersectT_lem = $true )
=> ( ( binunionT_lem = $true )
=> ( ( powersetT_lem = $true )
=> ( ( setminusT_lem = $true )
=> ( ( complementT_lem = $true )
=> ( ( setextT = $true )
=> ( ( subsetTI = $true )
=> ( ( powersetTI1 = $true )
=> ( ( powersetTE1 = $true )
=> ( ( complementTI1 = $true )
=> ( ( complementTE1 = $true )
=> ( ( binintersectTELcontra = $true )
=> ( ( binintersectTERcontra = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
=> ! [X2: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X0 ) ) )
=> ! [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
=> ( ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
= $true )
=> ( ( ( in @ X3 @ X2 )
= $true )
=> ( ( in @ X3 @ X1 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f448]) ).
thf(f448,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X0 ) )
=> ! [X3: $i] :
( ( in @ X3 @ X0 )
=> ( ( subset @ X1 @ ( setminus @ X0 @ X2 ) )
=> ( ( in @ X3 @ X2 )
=> ~ ( in @ X3 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f245]) ).
thf(f245,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X3: $i,X11: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( subset @ X11 @ ( setminus @ X3 @ X16 ) )
=> ( ( in @ X1 @ X16 )
=> ~ ( in @ X1 @ X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f244]) ).
thf(f244,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ( ap2apEq1
=> ( ap2apEq2
=> ( beta1
=> ( eta1
=> ( lam2lamEq
=> ( beta2
=> ( eta2
=> ( iffalseProp1
=> ( iffalseProp2
=> ( iftrueProp1
=> ( iftrueProp2
=> ( ifSingleton
=> ( ifp
=> ( theeq
=> ( iftrue
=> ( iffalse
=> ( iftrueorfalse
=> ( binintersectT_lem
=> ( binunionT_lem
=> ( powersetT_lem
=> ( setminusT_lem
=> ( complementT_lem
=> ( setextT
=> ( subsetTI
=> ( powersetTI1
=> ( powersetTE1
=> ( complementTI1
=> ( complementTE1
=> ( binintersectTELcontra
=> ( binintersectTERcontra
=> ! [X3: $i,X11: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( subset @ X11 @ ( setminus @ X3 @ X16 ) )
=> ( ( in @ X1 @ X16 )
=> ~ ( in @ X1 @ X11 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BaQAZpWnWT/DTF2THF_13872.p',contrasubsetT) ).
thf(f20098,plain,
( $true
!= ( in @ sK741 @ sK740 ) ),
inference(trivial_inequality_removal,[status(thm)],[f20048]) ).
thf(f20048,plain,
( ( $true != $true )
| ( $true
!= ( in @ sK741 @ sK740 ) ) ),
inference(superposition,[status(thm)],[f4569,f18938]) ).
thf(f18938,plain,
( $true
= ( in @ sK741 @ ( setminus @ sK738 @ sK740 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f18919]) ).
thf(f18919,plain,
( ( $true != $true )
| ( $true
= ( in @ sK741 @ ( setminus @ sK738 @ sK740 ) ) ) ),
inference(superposition,[status(thm)],[f8537,f3302]) ).
thf(f3302,plain,
( ( subset @ sK739 @ ( setminus @ sK738 @ sK740 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f2186]) ).
thf(f8537,plain,
! [X0: $i] :
( ( $true
!= ( subset @ sK739 @ X0 ) )
| ( ( in @ sK741 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f8520]) ).
thf(f8520,plain,
! [X0: $i] :
( ( $true
!= ( subset @ sK739 @ X0 ) )
| ( $true != $true )
| ( ( in @ sK741 @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f4732,f3300]) ).
thf(f3300,plain,
( ( in @ sK741 @ sK739 )
= $true ),
inference(cnf_transformation,[status(thm)],[f2186]) ).
thf(f4732,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3723]) ).
thf(f3723,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( subset @ X2 @ X1 )
!= $true )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( $true != $true )
| ( ( in @ X0 @ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f2565,f3272]) ).
thf(f3272,plain,
subsetE2 = $true,
inference(cnf_transformation,[status(thm)],[f2186]) ).
thf(f2565,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true )
| ( subsetE2 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1454]) ).
thf(f1454,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) )
| ( subsetE2 != $true ) )
& ( ( subsetE2 = $true )
| ( ( $true
= ( in @ sK265 @ sK267 ) )
& ( ( in @ sK265 @ sK266 )
!= $true )
& ( ( subset @ sK267 @ sK266 )
= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK265,sK266,sK267])],[f1452,f1453]) ).
thf(f1453,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
& ( $true
!= ( in @ X3 @ X4 ) )
& ( ( subset @ X5 @ X4 )
= $true ) )
=> ( ( $true
= ( in @ sK265 @ sK267 ) )
& ( ( in @ sK265 @ sK266 )
!= $true )
& ( ( subset @ sK267 @ sK266 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1452,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) )
| ( subsetE2 != $true ) )
& ( ( subsetE2 = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
& ( $true
!= ( in @ X3 @ X4 ) )
& ( ( subset @ X5 @ X4 )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f1451]) ).
thf(f1451,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) )
| ( subsetE2 != $true ) )
& ( ( subsetE2 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ X2 ) )
& ( ( in @ X0 @ X1 )
!= $true )
& ( ( subset @ X2 @ X1 )
= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f781]) ).
thf(f781,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) )
<=> ( subsetE2 = $true ) ),
inference(flattening,[status(thm)],[f780]) ).
thf(f780,plain,
( ( subsetE2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
| ( ( in @ X0 @ X1 )
= $true )
| ( ( subset @ X2 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f754]) ).
thf(f754,plain,
( ( subsetE2 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( $true
!= ( in @ X0 @ X2 ) ) ) ) ),
inference(flattening,[status(thm)],[f419]) ).
thf(f419,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
= $true )
=> ( ( ( in @ X0 @ X1 )
!= $true )
=> ( $true
!= ( in @ X0 @ X2 ) ) ) )
<=> ( subsetE2 = $true ) ),
inference(fool_elimination,[status(thm)],[f418]) ).
thf(f418,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X1 )
=> ( ~ ( in @ X0 @ X1 )
=> ~ ( in @ X0 @ X2 ) ) )
= subsetE2 ),
inference(rectify,[status(thm)],[f84]) ).
thf(f84,axiom,
! [X1: $i,X4: $i,X3: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ~ ( in @ X1 @ X4 )
=> ~ ( in @ X1 @ X3 ) ) )
= subsetE2 ),
file('/export/starexec/sandbox2/tmp/tmp.BaQAZpWnWT/DTF2THF_13872.p',subsetE2) ).
thf(f4569,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X3 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f3949]) ).
thf(f3949,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X3 )
!= $true )
| ( $true != $true )
| ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f2794,f3386]) ).
thf(f3386,plain,
setminusER = $true,
inference(cnf_transformation,[status(thm)],[f2186]) ).
thf(f2794,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X3 )
!= $true )
| ( setminusER != $true ) ),
inference(cnf_transformation,[status(thm)],[f1721]) ).
thf(f1721,plain,
( ( ( setminusER = $true )
| ( ( ( in @ sK439 @ ( setminus @ sK440 @ sK438 ) )
= $true )
& ( ( in @ sK439 @ sK438 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X3 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK438,sK439,sK440])],[f1719,f1720]) ).
thf(f1720,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
& ( ( in @ X1 @ X0 )
= $true ) )
=> ( ( ( in @ sK439 @ ( setminus @ sK440 @ sK438 ) )
= $true )
& ( ( in @ sK439 @ sK438 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1719,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ ( setminus @ X5 @ X3 ) )
!= $true )
| ( ( in @ X4 @ X3 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(rectify,[status(thm)],[f1718]) ).
thf(f1718,plain,
( ( ( setminusER = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
& ( ( in @ X1 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
!= $true ) )
| ( setminusER != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1009]) ).
thf(f1009,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
| ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f759]) ).
thf(f759,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f710]) ).
thf(f710,plain,
( ( setminusER = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setminus @ X2 @ X0 ) ) )
=> ( ( in @ X1 @ X0 )
!= $true ) ) ),
inference(fool_elimination,[status(thm)],[f709]) ).
thf(f709,plain,
( setminusER
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setminus @ X2 @ X0 ) )
=> ~ ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f122]) ).
thf(f122,axiom,
( setminusER
= ( ! [X4: $i,X1: $i,X3: $i] :
( ( in @ X1 @ ( setminus @ X3 @ X4 ) )
=> ~ ( in @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.BaQAZpWnWT/DTF2THF_13872.p',setminusER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU723^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.32 % Computer : n015.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue Feb 24 12:32:16 EST 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.44 ---- Original DTF file ---
% 0.19/0.44 thf(spec,logic,$$dhol).
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 % File : SEU723^1 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.44 % Domain : Set Theory
% 0.19/0.44 % Problem : Typed Set Theory - Laws for Typed Sets
% 0.19/0.44 % Version : Especial.
% 0.19/0.44 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.19/0.44 % (! x:i.in x A -> subset X (setminus A Y) -> in x Y -> ~(in x X))))
% 0.19/0.44
% 0.19/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.44 % Source : [Bro08]
% 0.19/0.44 % Names : ZFC225g [Bro08]
% 0.19/0.44
% 0.19/0.44 % Status : Theorem
% 0.19/0.44 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v6.0.0, 0.43 v5.5.0, 0.67 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.19/0.44 % Syntax : Number of formulae : 521 ( 243 unt; 277 typ; 243 def)
% 0.19/0.44 % Number of atoms : 1387 ( 368 equ; 0 cnn)
% 0.19/0.44 % Maximal formula atoms : 245 ( 5 avg)
% 0.19/0.44 % Number of connectives : 2727 ( 62 ~; 12 |; 44 &;1928 @)
% 0.19/0.44 % ( 14 <=>; 667 =>; 0 <=; 0 <~>)
% 0.19/0.44 % Maximal formula depth : 252 ( 2 avg)
% 0.19/0.44 % Number of types : 2 ( 0 usr)
% 0.19/0.44 % Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% 0.19/0.44 % Number of symbols : 280 ( 277 usr; 243 con; 0-4 aty)
% 0.19/0.44 % Number of variables : 820 ( 74 ^; 711 !; 35 ?; 820 :)
% 0.19/0.44 % SPC : TH0_THM_EQU_NAR
% 0.19/0.44
% 0.19/0.44 % Comments : http://mathgate.info/detsetitem.php?id=283
% 0.19/0.44 %------------------------------------------------------------------------------
% 0.19/0.44 thf(in_type,type,
% 0.19/0.44 in: $i > $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(exu_type,type,
% 0.19/0.44 exu: ( $i > $o ) > $o ).
% 0.19/0.44
% 0.19/0.44 thf(exu,definition,
% 0.19/0.44 ( exu
% 0.19/0.44 = ( ^ [Xphi: $i > $o] :
% 0.19/0.44 ? [Xx: $i] :
% 0.19/0.44 ( ( Xphi @ Xx )
% 0.19/0.44 & ! [Xy: $i] :
% 0.19/0.44 ( ( Xphi @ Xy )
% 0.19/0.44 => ( Xx = Xy ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setextAx_type,type,
% 0.19/0.44 setextAx: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setextAx,definition,
% 0.19/0.44 ( setextAx
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 <=> ( in @ Xx @ B ) )
% 0.19/0.44 => ( A = B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(emptyset_type,type,
% 0.19/0.44 emptyset: $i ).
% 0.19/0.44
% 0.19/0.44 thf(emptysetAx_type,type,
% 0.19/0.44 emptysetAx: $o ).
% 0.19/0.44
% 0.19/0.44 thf(emptysetAx,definition,
% 0.19/0.44 ( emptysetAx
% 0.19/0.44 = ( ! [Xx: $i] :
% 0.19/0.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoin_type,type,
% 0.19/0.44 setadjoin: $i > $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinAx_type,type,
% 0.19/0.44 setadjoinAx: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinAx,definition,
% 0.19/0.44 ( setadjoinAx
% 0.19/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.44 <=> ( ( Xy = Xx )
% 0.19/0.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(powerset_type,type,
% 0.19/0.44 powerset: $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(powersetAx_type,type,
% 0.19/0.44 powersetAx: $o ).
% 0.19/0.44
% 0.19/0.44 thf(powersetAx,definition,
% 0.19/0.44 ( powersetAx
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.44 <=> ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ B )
% 0.19/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setunion_type,type,
% 0.19/0.44 setunion: $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(setunionAx_type,type,
% 0.19/0.44 setunionAx: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setunionAx,definition,
% 0.19/0.44 ( setunionAx
% 0.19/0.44 = ( ! [A: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.44 <=> ? [B: $i] :
% 0.19/0.44 ( ( in @ Xx @ B )
% 0.19/0.44 & ( in @ B @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(omega_type,type,
% 0.19/0.44 omega: $i ).
% 0.19/0.44
% 0.19/0.44 thf(omega0Ax_type,type,
% 0.19/0.44 omega0Ax: $o ).
% 0.19/0.44
% 0.19/0.44 thf(omega0Ax,definition,
% 0.19/0.44 ( omega0Ax
% 0.19/0.44 = ( in @ emptyset @ omega ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(omegaSAx_type,type,
% 0.19/0.44 omegaSAx: $o ).
% 0.19/0.44
% 0.19/0.44 thf(omegaSAx,definition,
% 0.19/0.44 ( omegaSAx
% 0.19/0.44 = ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ omega )
% 0.19/0.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(omegaIndAx_type,type,
% 0.19/0.44 omegaIndAx: $o ).
% 0.19/0.44
% 0.19/0.44 thf(omegaIndAx,definition,
% 0.19/0.44 ( omegaIndAx
% 0.19/0.44 = ( ! [A: $i] :
% 0.19/0.44 ( ( ( in @ emptyset @ A )
% 0.19/0.44 & ! [Xx: $i] :
% 0.19/0.44 ( ( ( in @ Xx @ omega )
% 0.19/0.44 & ( in @ Xx @ A ) )
% 0.19/0.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.19/0.44 => ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ omega )
% 0.19/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(replAx_type,type,
% 0.19/0.44 replAx: $o ).
% 0.19/0.44
% 0.19/0.44 thf(replAx,definition,
% 0.19/0.44 ( replAx
% 0.19/0.44 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( exu
% 0.19/0.44 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.19/0.44 => ? [B: $i] :
% 0.19/0.44 ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ B )
% 0.19/0.44 <=> ? [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ A )
% 0.19/0.44 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(foundationAx_type,type,
% 0.19/0.44 foundationAx: $o ).
% 0.19/0.44
% 0.19/0.44 thf(foundationAx,definition,
% 0.19/0.44 ( foundationAx
% 0.19/0.44 = ( ! [A: $i] :
% 0.19/0.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.19/0.44 => ? [B: $i] :
% 0.19/0.44 ( ( in @ B @ A )
% 0.19/0.44 & ~ ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ B )
% 0.19/0.44 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(wellorderingAx_type,type,
% 0.19/0.44 wellorderingAx: $o ).
% 0.19/0.44
% 0.19/0.44 thf(wellorderingAx,definition,
% 0.19/0.44 ( wellorderingAx
% 0.19/0.44 = ( ! [A: $i] :
% 0.19/0.44 ? [B: $i] :
% 0.19/0.44 ( ! [C: $i] :
% 0.19/0.44 ( ( in @ C @ B )
% 0.19/0.44 => ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ C )
% 0.19/0.44 => ( in @ Xx @ A ) ) )
% 0.19/0.44 & ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( ( in @ Xx @ A )
% 0.19/0.44 & ( in @ Xy @ A ) )
% 0.19/0.44 => ( ! [C: $i] :
% 0.19/0.44 ( ( in @ C @ B )
% 0.19/0.44 => ( ( in @ Xx @ C )
% 0.19/0.44 <=> ( in @ Xy @ C ) ) )
% 0.19/0.44 => ( Xx = Xy ) ) )
% 0.19/0.44 & ! [C: $i,D: $i] :
% 0.19/0.44 ( ( ( in @ C @ B )
% 0.19/0.44 & ( in @ D @ B ) )
% 0.19/0.44 => ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ C )
% 0.19/0.44 => ( in @ Xx @ D ) )
% 0.19/0.44 | ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ D )
% 0.19/0.44 => ( in @ Xx @ C ) ) ) )
% 0.19/0.44 & ! [C: $i] :
% 0.19/0.44 ( ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ C )
% 0.19/0.44 => ( in @ Xx @ A ) )
% 0.19/0.44 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.19/0.44 => ? [D: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ D @ B )
% 0.19/0.44 & ( in @ Xx @ C )
% 0.19/0.44 & ~ ? [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ D )
% 0.19/0.44 & ( in @ Xy @ C ) )
% 0.19/0.44 & ! [E: $i] :
% 0.19/0.44 ( ( in @ E @ B )
% 0.19/0.44 => ( ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ E )
% 0.19/0.44 => ( in @ Xy @ D ) )
% 0.19/0.44 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(descr_type,type,
% 0.19/0.44 descr: ( $i > $o ) > $i ).
% 0.19/0.44
% 0.19/0.44 thf(descrp_type,type,
% 0.19/0.44 descrp: $o ).
% 0.19/0.44
% 0.19/0.44 thf(descrp,definition,
% 0.19/0.44 ( descrp
% 0.19/0.44 = ( ! [Xphi: $i > $o] :
% 0.19/0.44 ( ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 => ( Xphi
% 0.19/0.44 @ ( descr
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(dsetconstr_type,type,
% 0.19/0.44 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.19/0.44
% 0.19/0.44 thf(dsetconstrI_type,type,
% 0.19/0.44 dsetconstrI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(dsetconstrI,definition,
% 0.19/0.44 ( dsetconstrI
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ( Xphi @ Xx )
% 0.19/0.44 => ( in @ Xx
% 0.19/0.44 @ ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(dsetconstrEL_type,type,
% 0.19/0.44 dsetconstrEL: $o ).
% 0.19/0.44
% 0.19/0.44 thf(dsetconstrEL,definition,
% 0.19/0.44 ( dsetconstrEL
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx
% 0.19/0.44 @ ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(dsetconstrER_type,type,
% 0.19/0.44 dsetconstrER: $o ).
% 0.19/0.44
% 0.19/0.44 thf(dsetconstrER,definition,
% 0.19/0.44 ( dsetconstrER
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx
% 0.19/0.44 @ ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(exuE1_type,type,
% 0.19/0.44 exuE1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(exuE1,definition,
% 0.19/0.44 ( exuE1
% 0.19/0.44 = ( ! [Xphi: $i > $o] :
% 0.19/0.44 ( ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 => ? [Xx: $i] :
% 0.19/0.44 ( ( Xphi @ Xx )
% 0.19/0.44 & ! [Xy: $i] :
% 0.19/0.44 ( ( Xphi @ Xy )
% 0.19/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(prop2set_type,type,
% 0.19/0.44 prop2set: $o > $i ).
% 0.19/0.44
% 0.19/0.44 thf(prop2setE_type,type,
% 0.19/0.44 prop2setE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(prop2setE,definition,
% 0.19/0.44 ( prop2setE
% 0.19/0.44 = ( ! [Xphi: $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.19/0.44 => Xphi ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(emptysetE_type,type,
% 0.19/0.44 emptysetE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(emptysetE,definition,
% 0.19/0.44 ( emptysetE
% 0.19/0.44 = ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ emptyset )
% 0.19/0.44 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(emptysetimpfalse_type,type,
% 0.19/0.44 emptysetimpfalse: $o ).
% 0.19/0.44
% 0.19/0.44 thf(emptysetimpfalse,definition,
% 0.19/0.44 ( emptysetimpfalse
% 0.19/0.44 = ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ emptyset )
% 0.19/0.44 => $false ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(notinemptyset_type,type,
% 0.19/0.44 notinemptyset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(notinemptyset,definition,
% 0.19/0.44 ( notinemptyset
% 0.19/0.44 = ( ! [Xx: $i] :
% 0.19/0.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(exuE3e_type,type,
% 0.19/0.44 exuE3e: $o ).
% 0.19/0.44
% 0.19/0.44 thf(exuE3e,definition,
% 0.19/0.44 ( exuE3e
% 0.19/0.44 = ( ! [Xphi: $i > $o] :
% 0.19/0.44 ( ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setext_type,type,
% 0.19/0.44 setext: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setext,definition,
% 0.19/0.44 ( setext
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ Xx @ B ) )
% 0.19/0.44 => ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ B )
% 0.19/0.44 => ( in @ Xx @ A ) )
% 0.19/0.44 => ( A = B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(emptyI_type,type,
% 0.19/0.44 emptyI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(emptyI,definition,
% 0.19/0.44 ( emptyI
% 0.19/0.44 = ( ! [A: $i] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ~ ( in @ Xx @ A )
% 0.19/0.44 => ( A = emptyset ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(noeltsimpempty_type,type,
% 0.19/0.44 noeltsimpempty: $o ).
% 0.19/0.44
% 0.19/0.44 thf(noeltsimpempty,definition,
% 0.19/0.44 ( noeltsimpempty
% 0.19/0.44 = ( ! [A: $i] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ~ ( in @ Xx @ A )
% 0.19/0.44 => ( A = emptyset ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setbeta_type,type,
% 0.19/0.44 setbeta: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setbeta,definition,
% 0.19/0.44 ( setbeta
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ( in @ Xx
% 0.19/0.44 @ ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.19/0.44 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(nonempty_type,type,
% 0.19/0.44 nonempty: $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(nonempty,definition,
% 0.19/0.44 ( nonempty
% 0.19/0.44 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(nonemptyE1_type,type,
% 0.19/0.44 nonemptyE1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(nonemptyE1,definition,
% 0.19/0.44 ( nonemptyE1
% 0.19/0.44 = ( ! [A: $i] :
% 0.19/0.44 ( ( nonempty @ A )
% 0.19/0.44 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(nonemptyI_type,type,
% 0.19/0.44 nonemptyI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(nonemptyI,definition,
% 0.19/0.44 ( nonemptyI
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ( Xphi @ Xx )
% 0.19/0.44 => ( nonempty
% 0.19/0.44 @ ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(nonemptyI1_type,type,
% 0.19/0.44 nonemptyI1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(nonemptyI1,definition,
% 0.19/0.44 ( nonemptyI1
% 0.19/0.44 = ( ! [A: $i] :
% 0.19/0.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.19/0.44 => ( nonempty @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinIL_type,type,
% 0.19/0.44 setadjoinIL: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinIL,definition,
% 0.19/0.44 ( setadjoinIL
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(emptyinunitempty_type,type,
% 0.19/0.44 emptyinunitempty: $o ).
% 0.19/0.44
% 0.19/0.44 thf(emptyinunitempty,definition,
% 0.19/0.44 ( emptyinunitempty
% 0.19/0.44 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinIR_type,type,
% 0.19/0.44 setadjoinIR: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinIR,definition,
% 0.19/0.44 ( setadjoinIR
% 0.19/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ A )
% 0.19/0.44 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinE_type,type,
% 0.19/0.44 setadjoinE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinE,definition,
% 0.19/0.44 ( setadjoinE
% 0.19/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.44 => ! [Xphi: $o] :
% 0.19/0.44 ( ( ( Xy = Xx )
% 0.19/0.44 => Xphi )
% 0.19/0.44 => ( ( ( in @ Xy @ A )
% 0.19/0.44 => Xphi )
% 0.19/0.44 => Xphi ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinOr_type,type,
% 0.19/0.44 setadjoinOr: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinOr,definition,
% 0.19/0.44 ( setadjoinOr
% 0.19/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.19/0.44 => ( ( Xy = Xx )
% 0.19/0.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setoftrueEq_type,type,
% 0.19/0.44 setoftrueEq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setoftrueEq,definition,
% 0.19/0.44 ( setoftrueEq
% 0.19/0.44 = ( ! [A: $i] :
% 0.19/0.44 ( ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xx: $i] : $true )
% 0.19/0.44 = A ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(powersetI_type,type,
% 0.19/0.44 powersetI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(powersetI,definition,
% 0.19/0.44 ( powersetI
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ B )
% 0.19/0.44 => ( in @ Xx @ A ) )
% 0.19/0.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(emptyinPowerset_type,type,
% 0.19/0.44 emptyinPowerset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(emptyinPowerset,definition,
% 0.19/0.44 ( emptyinPowerset
% 0.19/0.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(emptyInPowerset_type,type,
% 0.19/0.44 emptyInPowerset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(emptyInPowerset,definition,
% 0.19/0.44 ( emptyInPowerset
% 0.19/0.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(powersetE_type,type,
% 0.19/0.44 powersetE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(powersetE,definition,
% 0.19/0.44 ( powersetE
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.44 => ( ( in @ Xx @ B )
% 0.19/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setunionI_type,type,
% 0.19/0.44 setunionI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setunionI,definition,
% 0.19/0.44 ( setunionI
% 0.19/0.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.44 ( ( in @ Xx @ B )
% 0.19/0.44 => ( ( in @ B @ A )
% 0.19/0.44 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setunionE_type,type,
% 0.19/0.44 setunionE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setunionE,definition,
% 0.19/0.44 ( setunionE
% 0.19/0.44 = ( ! [A: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.44 => ! [Xphi: $o] :
% 0.19/0.44 ( ! [B: $i] :
% 0.19/0.44 ( ( in @ Xx @ B )
% 0.19/0.44 => ( ( in @ B @ A )
% 0.19/0.44 => Xphi ) )
% 0.19/0.44 => Xphi ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(subPowSU_type,type,
% 0.19/0.44 subPowSU: $o ).
% 0.19/0.44
% 0.19/0.44 thf(subPowSU,definition,
% 0.19/0.44 ( subPowSU
% 0.19/0.44 = ( ! [A: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(exuE2_type,type,
% 0.19/0.44 exuE2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(exuE2,definition,
% 0.19/0.44 ( exuE2
% 0.19/0.44 = ( ! [Xphi: $i > $o] :
% 0.19/0.44 ( ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 => ? [Xx: $i] :
% 0.19/0.44 ! [Xy: $i] :
% 0.19/0.44 ( ( Xphi @ Xy )
% 0.19/0.44 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(nonemptyImpWitness_type,type,
% 0.19/0.44 nonemptyImpWitness: $o ).
% 0.19/0.44
% 0.19/0.44 thf(nonemptyImpWitness,definition,
% 0.19/0.44 ( nonemptyImpWitness
% 0.19/0.44 = ( ! [A: $i] :
% 0.19/0.44 ( ( nonempty @ A )
% 0.19/0.44 => ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & $true ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(uniqinunit_type,type,
% 0.19/0.44 uniqinunit: $o ).
% 0.19/0.44
% 0.19/0.44 thf(uniqinunit,definition,
% 0.19/0.44 ( uniqinunit
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.44 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(notinsingleton_type,type,
% 0.19/0.44 notinsingleton: $o ).
% 0.19/0.44
% 0.19/0.44 thf(notinsingleton,definition,
% 0.19/0.44 ( notinsingleton
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xx != Xy )
% 0.19/0.44 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(eqinunit_type,type,
% 0.19/0.44 eqinunit: $o ).
% 0.19/0.44
% 0.19/0.44 thf(eqinunit,definition,
% 0.19/0.44 ( eqinunit
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xx = Xy )
% 0.19/0.44 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(singletonsswitch_type,type,
% 0.19/0.44 singletonsswitch: $o ).
% 0.19/0.44
% 0.19/0.44 thf(singletonsswitch,definition,
% 0.19/0.44 ( singletonsswitch
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.44 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(upairsetE_type,type,
% 0.19/0.44 upairsetE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(upairsetE,definition,
% 0.19/0.44 ( upairsetE
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.44 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.19/0.44 => ( ( Xz = Xx )
% 0.19/0.44 | ( Xz = Xy ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(upairsetIL_type,type,
% 0.19/0.44 upairsetIL: $o ).
% 0.19/0.44
% 0.19/0.44 thf(upairsetIL,definition,
% 0.19/0.44 ( upairsetIL
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(upairsetIR_type,type,
% 0.19/0.44 upairsetIR: $o ).
% 0.19/0.44
% 0.19/0.44 thf(upairsetIR,definition,
% 0.19/0.44 ( upairsetIR
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(emptyE1_type,type,
% 0.19/0.44 emptyE1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(emptyE1,definition,
% 0.19/0.44 ( emptyE1
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ( Xphi @ Xx ) )
% 0.19/0.44 => ( ( ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 = emptyset )
% 0.19/0.44 => $false ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(vacuousDall_type,type,
% 0.19/0.44 vacuousDall: $o ).
% 0.19/0.44
% 0.19/0.44 thf(vacuousDall,definition,
% 0.19/0.44 ( vacuousDall
% 0.19/0.44 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ emptyset )
% 0.19/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(quantDeMorgan1_type,type,
% 0.19/0.44 quantDeMorgan1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(quantDeMorgan1,definition,
% 0.19/0.44 ( quantDeMorgan1
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( ~ ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( Xphi @ Xx ) )
% 0.19/0.44 => ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(quantDeMorgan2_type,type,
% 0.19/0.44 quantDeMorgan2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(quantDeMorgan2,definition,
% 0.19/0.44 ( quantDeMorgan2
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ~ ( Xphi @ Xx ) )
% 0.19/0.44 => ~ ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(quantDeMorgan3_type,type,
% 0.19/0.44 quantDeMorgan3: $o ).
% 0.19/0.44
% 0.19/0.44 thf(quantDeMorgan3,definition,
% 0.19/0.44 ( quantDeMorgan3
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( ~ ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ( Xphi @ Xx ) )
% 0.19/0.44 => ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(quantDeMorgan4_type,type,
% 0.19/0.44 quantDeMorgan4: $o ).
% 0.19/0.44
% 0.19/0.44 thf(quantDeMorgan4,definition,
% 0.19/0.44 ( quantDeMorgan4
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ~ ( Xphi @ Xx ) )
% 0.19/0.44 => ~ ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(prop2setI_type,type,
% 0.19/0.44 prop2setI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(prop2setI,definition,
% 0.19/0.44 ( prop2setI
% 0.19/0.44 = ( ! [Xphi: $o] :
% 0.19/0.44 ( Xphi
% 0.19/0.44 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(set2prop_type,type,
% 0.19/0.44 set2prop: $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(prop2set2propI_type,type,
% 0.19/0.44 prop2set2propI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(prop2set2propI,definition,
% 0.19/0.44 ( prop2set2propI
% 0.19/0.44 = ( ! [Xphi: $o] :
% 0.19/0.44 ( Xphi
% 0.19/0.44 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(notdexE_type,type,
% 0.19/0.44 notdexE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(notdexE,definition,
% 0.19/0.44 ( notdexE
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( ~ ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ( Xphi @ Xx ) )
% 0.19/0.44 => ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(notdallE_type,type,
% 0.19/0.44 notdallE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(notdallE,definition,
% 0.19/0.44 ( notdallE
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( ~ ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( Xphi @ Xx ) )
% 0.19/0.44 => ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(exuI1_type,type,
% 0.19/0.44 exuI1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(exuI1,definition,
% 0.19/0.44 ( exuI1
% 0.19/0.44 = ( ! [Xphi: $i > $o] :
% 0.19/0.44 ( ? [Xx: $i] :
% 0.19/0.44 ( ( Xphi @ Xx )
% 0.19/0.44 & ! [Xy: $i] :
% 0.19/0.44 ( ( Xphi @ Xy )
% 0.19/0.44 => ( Xx = Xy ) ) )
% 0.19/0.44 => ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(exuI3_type,type,
% 0.19/0.44 exuI3: $o ).
% 0.19/0.44
% 0.19/0.44 thf(exuI3,definition,
% 0.19/0.44 ( exuI3
% 0.19/0.44 = ( ! [Xphi: $i > $o] :
% 0.19/0.44 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.19/0.44 => ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xphi @ Xx )
% 0.19/0.44 => ( ( Xphi @ Xy )
% 0.19/0.44 => ( Xx = Xy ) ) )
% 0.19/0.44 => ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(exuI2_type,type,
% 0.19/0.44 exuI2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(exuI2,definition,
% 0.19/0.44 ( exuI2
% 0.19/0.44 = ( ! [Xphi: $i > $o] :
% 0.19/0.44 ( ? [Xx: $i] :
% 0.19/0.44 ! [Xy: $i] :
% 0.19/0.44 ( ( Xphi @ Xy )
% 0.19/0.44 <=> ( Xy = Xx ) )
% 0.19/0.44 => ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(inCongP_type,type,
% 0.19/0.44 inCongP: $o ).
% 0.19/0.44
% 0.19/0.44 thf(inCongP,definition,
% 0.19/0.44 ( inCongP
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xx = Xy )
% 0.19/0.44 => ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(in__Cong_type,type,
% 0.19/0.44 in__Cong: $o ).
% 0.19/0.44
% 0.19/0.44 thf(in__Cong,definition,
% 0.19/0.44 ( in__Cong
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xx = Xy )
% 0.19/0.44 => ( ( in @ Xx @ A )
% 0.19/0.44 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(exuE3u_type,type,
% 0.19/0.44 exuE3u: $o ).
% 0.19/0.44
% 0.19/0.44 thf(exuE3u,definition,
% 0.19/0.44 ( exuE3u
% 0.19/0.44 = ( ! [Xphi: $i > $o] :
% 0.19/0.44 ( ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 => ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xphi @ Xx )
% 0.19/0.44 => ( ( Xphi @ Xy )
% 0.19/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(exu__Cong_type,type,
% 0.19/0.44 exu__Cong: $o ).
% 0.19/0.44
% 0.19/0.44 thf(exu__Cong,definition,
% 0.19/0.44 ( exu__Cong
% 0.19/0.44 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.44 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xx = Xy )
% 0.19/0.44 => ( ( Xphi @ Xx )
% 0.19/0.44 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.44 => ( ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 <=> ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(emptyset__Cong_type,type,
% 0.19/0.44 emptyset__Cong: $o ).
% 0.19/0.44
% 0.19/0.44 thf(emptyset__Cong,definition,
% 0.19/0.44 ( emptyset__Cong
% 0.19/0.44 = ( emptyset = emptyset ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoin__Cong_type,type,
% 0.19/0.44 setadjoin__Cong: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoin__Cong,definition,
% 0.19/0.44 ( setadjoin__Cong
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xx = Xy )
% 0.19/0.44 => ! [Xz: $i,Xu: $i] :
% 0.19/0.44 ( ( Xz = Xu )
% 0.19/0.44 => ( ( setadjoin @ Xx @ Xz )
% 0.19/0.44 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(powerset__Cong_type,type,
% 0.19/0.44 powerset__Cong: $o ).
% 0.19/0.44
% 0.19/0.44 thf(powerset__Cong,definition,
% 0.19/0.44 ( powerset__Cong
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( ( powerset @ A )
% 0.19/0.44 = ( powerset @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setunion__Cong_type,type,
% 0.19/0.44 setunion__Cong: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setunion__Cong,definition,
% 0.19/0.44 ( setunion__Cong
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( ( setunion @ A )
% 0.19/0.44 = ( setunion @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(omega__Cong_type,type,
% 0.19/0.44 omega__Cong: $o ).
% 0.19/0.44
% 0.19/0.44 thf(omega__Cong,definition,
% 0.19/0.44 ( omega__Cong
% 0.19/0.44 = ( omega = omega ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(exuEu_type,type,
% 0.19/0.44 exuEu: $o ).
% 0.19/0.44
% 0.19/0.44 thf(exuEu,definition,
% 0.19/0.44 ( exuEu
% 0.19/0.44 = ( ! [Xphi: $i > $o] :
% 0.19/0.44 ( ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 => ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xphi @ Xx )
% 0.19/0.44 => ( ( Xphi @ Xy )
% 0.19/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(descr__Cong_type,type,
% 0.19/0.44 descr__Cong: $o ).
% 0.19/0.44
% 0.19/0.44 thf(descr__Cong,definition,
% 0.19/0.44 ( descr__Cong
% 0.19/0.44 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.44 ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xx = Xy )
% 0.19/0.44 => ( ( Xphi @ Xx )
% 0.19/0.44 <=> ( Xpsi @ Xy ) ) )
% 0.19/0.44 => ( ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 => ( ( exu
% 0.19/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.19/0.44 => ( ( descr
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 = ( descr
% 0.19/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(dsetconstr__Cong_type,type,
% 0.19/0.44 dsetconstr__Cong: $o ).
% 0.19/0.44
% 0.19/0.44 thf(dsetconstr__Cong,definition,
% 0.19/0.44 ( dsetconstr__Cong
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( ( Xx = Xy )
% 0.19/0.44 => ( ( Xphi @ Xx )
% 0.19/0.44 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.19/0.44 => ( ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 = ( dsetconstr @ B
% 0.19/0.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(subset_type,type,
% 0.19/0.44 subset: $i > $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(disjoint_type,type,
% 0.19/0.44 disjoint: $i > $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(setsmeet_type,type,
% 0.19/0.44 setsmeet: $i > $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(subsetI1_type,type,
% 0.19/0.44 subsetI1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(subsetI1,definition,
% 0.19/0.44 ( subsetI1
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ Xx @ B ) )
% 0.19/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(eqimpsubset2_type,type,
% 0.19/0.44 eqimpsubset2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(eqimpsubset2,definition,
% 0.19/0.44 ( eqimpsubset2
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(eqimpsubset1_type,type,
% 0.19/0.44 eqimpsubset1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(eqimpsubset1,definition,
% 0.19/0.44 ( eqimpsubset1
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( A = B )
% 0.19/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(subsetI2_type,type,
% 0.19/0.44 subsetI2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(subsetI2,definition,
% 0.19/0.44 ( subsetI2
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ Xx @ B ) )
% 0.19/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(emptysetsubset_type,type,
% 0.19/0.44 emptysetsubset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(emptysetsubset,definition,
% 0.19/0.44 ( emptysetsubset
% 0.19/0.44 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(subsetE_type,type,
% 0.19/0.44 subsetE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(subsetE,definition,
% 0.19/0.44 ( subsetE
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( subset @ A @ B )
% 0.19/0.44 => ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(subsetE2_type,type,
% 0.19/0.44 subsetE2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(subsetE2,definition,
% 0.19/0.44 ( subsetE2
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( subset @ A @ B )
% 0.19/0.44 => ( ~ ( in @ Xx @ B )
% 0.19/0.44 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(notsubsetI_type,type,
% 0.19/0.44 notsubsetI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(notsubsetI,definition,
% 0.19/0.44 ( notsubsetI
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ~ ( in @ Xx @ B )
% 0.19/0.44 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(notequalI1_type,type,
% 0.19/0.44 notequalI1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(notequalI1,definition,
% 0.19/0.44 ( notequalI1
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ~ ( subset @ A @ B )
% 0.19/0.44 => ( A != B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(notequalI2_type,type,
% 0.19/0.44 notequalI2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(notequalI2,definition,
% 0.19/0.44 ( notequalI2
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ~ ( in @ Xx @ B )
% 0.19/0.44 => ( A != B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(subsetRefl_type,type,
% 0.19/0.44 subsetRefl: $o ).
% 0.19/0.44
% 0.19/0.44 thf(subsetRefl,definition,
% 0.19/0.44 ( subsetRefl
% 0.19/0.44 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(subsetTrans_type,type,
% 0.19/0.44 subsetTrans: $o ).
% 0.19/0.44
% 0.19/0.44 thf(subsetTrans,definition,
% 0.19/0.44 ( subsetTrans
% 0.19/0.44 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.44 ( ( subset @ A @ B )
% 0.19/0.44 => ( ( subset @ B @ C )
% 0.19/0.44 => ( subset @ A @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinSub_type,type,
% 0.19/0.44 setadjoinSub: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinSub,definition,
% 0.19/0.44 ( setadjoinSub
% 0.19/0.44 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinSub2_type,type,
% 0.19/0.44 setadjoinSub2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setadjoinSub2,definition,
% 0.19/0.44 ( setadjoinSub2
% 0.19/0.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.19/0.44 ( ( subset @ A @ B )
% 0.19/0.44 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(subset2powerset_type,type,
% 0.19/0.44 subset2powerset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(subset2powerset,definition,
% 0.19/0.44 ( subset2powerset
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( subset @ A @ B )
% 0.19/0.44 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setextsub_type,type,
% 0.19/0.44 setextsub: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setextsub,definition,
% 0.19/0.44 ( setextsub
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( subset @ A @ B )
% 0.19/0.44 => ( ( subset @ B @ A )
% 0.19/0.44 => ( A = B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(subsetemptysetimpeq_type,type,
% 0.19/0.44 subsetemptysetimpeq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(subsetemptysetimpeq,definition,
% 0.19/0.44 ( subsetemptysetimpeq
% 0.19/0.44 = ( ! [A: $i] :
% 0.19/0.44 ( ( subset @ A @ emptyset )
% 0.19/0.44 => ( A = emptyset ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(powersetI1_type,type,
% 0.19/0.44 powersetI1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(powersetI1,definition,
% 0.19/0.44 ( powersetI1
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( subset @ B @ A )
% 0.19/0.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(powersetE1_type,type,
% 0.19/0.44 powersetE1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(powersetE1,definition,
% 0.19/0.44 ( powersetE1
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.19/0.44 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(inPowerset_type,type,
% 0.19/0.44 inPowerset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(inPowerset,definition,
% 0.19/0.44 ( inPowerset
% 0.19/0.44 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(powersetsubset_type,type,
% 0.19/0.44 powersetsubset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(powersetsubset,definition,
% 0.19/0.44 ( powersetsubset
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( subset @ A @ B )
% 0.19/0.44 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sepInPowerset_type,type,
% 0.19/0.44 sepInPowerset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(sepInPowerset,definition,
% 0.19/0.44 ( sepInPowerset
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( in
% 0.19/0.44 @ ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 @ ( powerset @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(sepSubset_type,type,
% 0.19/0.44 sepSubset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(sepSubset,definition,
% 0.19/0.44 ( sepSubset
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( subset
% 0.19/0.44 @ ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 @ A ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binunion_type,type,
% 0.19/0.44 binunion: $i > $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(binunionIL_type,type,
% 0.19/0.44 binunionIL: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binunionIL,definition,
% 0.19/0.44 ( binunionIL
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(upairset2IR_type,type,
% 0.19/0.44 upairset2IR: $o ).
% 0.19/0.44
% 0.19/0.44 thf(upairset2IR,definition,
% 0.19/0.44 ( upairset2IR
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binunionIR_type,type,
% 0.19/0.44 binunionIR: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binunionIR,definition,
% 0.19/0.44 ( binunionIR
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ B )
% 0.19/0.44 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binunionEcases_type,type,
% 0.19/0.44 binunionEcases: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binunionEcases,definition,
% 0.19/0.44 ( binunionEcases
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.19/0.44 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.44 => ( ( ( in @ Xx @ A )
% 0.19/0.44 => Xphi )
% 0.19/0.44 => ( ( ( in @ Xx @ B )
% 0.19/0.44 => Xphi )
% 0.19/0.44 => Xphi ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binunionE_type,type,
% 0.19/0.44 binunionE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binunionE,definition,
% 0.19/0.44 ( binunionE
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.19/0.44 => ( ( in @ Xx @ A )
% 0.19/0.44 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binunionLsub_type,type,
% 0.19/0.44 binunionLsub: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binunionLsub,definition,
% 0.19/0.44 ( binunionLsub
% 0.19/0.44 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binunionRsub_type,type,
% 0.19/0.44 binunionRsub: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binunionRsub,definition,
% 0.19/0.44 ( binunionRsub
% 0.19/0.44 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binintersect_type,type,
% 0.19/0.44 binintersect: $i > $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectI_type,type,
% 0.19/0.44 binintersectI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectI,definition,
% 0.19/0.44 ( binintersectI
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ( in @ Xx @ B )
% 0.19/0.44 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectSubset5_type,type,
% 0.19/0.44 binintersectSubset5: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectSubset5,definition,
% 0.19/0.44 ( binintersectSubset5
% 0.19/0.44 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.44 ( ( subset @ C @ A )
% 0.19/0.44 => ( ( subset @ C @ B )
% 0.19/0.44 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectEL_type,type,
% 0.19/0.44 binintersectEL: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectEL,definition,
% 0.19/0.44 ( binintersectEL
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectLsub_type,type,
% 0.19/0.44 binintersectLsub: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectLsub,definition,
% 0.19/0.44 ( binintersectLsub
% 0.19/0.44 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectSubset2_type,type,
% 0.19/0.44 binintersectSubset2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectSubset2,definition,
% 0.19/0.44 ( binintersectSubset2
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( subset @ A @ B )
% 0.19/0.44 => ( ( binintersect @ A @ B )
% 0.19/0.44 = A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectSubset3_type,type,
% 0.19/0.44 binintersectSubset3: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectSubset3,definition,
% 0.19/0.44 ( binintersectSubset3
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( ( binintersect @ A @ B )
% 0.19/0.44 = B )
% 0.19/0.44 => ( subset @ B @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectER_type,type,
% 0.19/0.44 binintersectER: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectER,definition,
% 0.19/0.44 ( binintersectER
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.19/0.44 => ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(disjointsetsI1_type,type,
% 0.19/0.44 disjointsetsI1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(disjointsetsI1,definition,
% 0.19/0.44 ( disjointsetsI1
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ~ ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ( in @ Xx @ B ) )
% 0.19/0.44 => ( ( binintersect @ A @ B )
% 0.19/0.44 = emptyset ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectRsub_type,type,
% 0.19/0.44 binintersectRsub: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectRsub,definition,
% 0.19/0.44 ( binintersectRsub
% 0.19/0.44 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectSubset4_type,type,
% 0.19/0.44 binintersectSubset4: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectSubset4,definition,
% 0.19/0.44 ( binintersectSubset4
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( subset @ B @ A )
% 0.19/0.44 => ( ( binintersect @ A @ B )
% 0.19/0.44 = B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectSubset1_type,type,
% 0.19/0.44 binintersectSubset1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(binintersectSubset1,definition,
% 0.19/0.44 ( binintersectSubset1
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( ( binintersect @ A @ B )
% 0.19/0.44 = A )
% 0.19/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(bs114d_type,type,
% 0.19/0.44 bs114d: $o ).
% 0.19/0.44
% 0.19/0.44 thf(bs114d,definition,
% 0.19/0.44 ( bs114d
% 0.19/0.44 = ( ! [A: $i,B: $i,C: $i] :
% 0.19/0.44 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.19/0.44 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(regular_type,type,
% 0.19/0.44 regular: $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminus_type,type,
% 0.19/0.44 setminus: $i > $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(setminusI_type,type,
% 0.19/0.44 setminusI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminusI,definition,
% 0.19/0.44 ( setminusI
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ~ ( in @ Xx @ B )
% 0.19/0.44 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setminusEL_type,type,
% 0.19/0.44 setminusEL: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminusEL,definition,
% 0.19/0.44 ( setminusEL
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setminusER_type,type,
% 0.19/0.44 setminusER: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminusER,definition,
% 0.19/0.44 ( setminusER
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.44 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setminusSubset2_type,type,
% 0.19/0.44 setminusSubset2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminusSubset2,definition,
% 0.19/0.44 ( setminusSubset2
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( subset @ A @ B )
% 0.19/0.44 => ( ( setminus @ A @ B )
% 0.19/0.44 = emptyset ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setminusERneg_type,type,
% 0.19/0.44 setminusERneg: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminusERneg,definition,
% 0.19/0.44 ( setminusERneg
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.44 => ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setminusELneg_type,type,
% 0.19/0.44 setminusELneg: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminusELneg,definition,
% 0.19/0.44 ( setminusELneg
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.19/0.44 => ( ~ ( in @ Xx @ B )
% 0.19/0.44 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setminusILneg_type,type,
% 0.19/0.44 setminusILneg: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminusILneg,definition,
% 0.19/0.44 ( setminusILneg
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ~ ( in @ Xx @ A )
% 0.19/0.44 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setminusIRneg_type,type,
% 0.19/0.44 setminusIRneg: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminusIRneg,definition,
% 0.19/0.44 ( setminusIRneg
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ B )
% 0.19/0.44 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setminusLsub_type,type,
% 0.19/0.44 setminusLsub: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminusLsub,definition,
% 0.19/0.44 ( setminusLsub
% 0.19/0.44 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setminusSubset1_type,type,
% 0.19/0.44 setminusSubset1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setminusSubset1,definition,
% 0.19/0.44 ( setminusSubset1
% 0.19/0.44 = ( ! [A: $i,B: $i] :
% 0.19/0.44 ( ( ( setminus @ A @ B )
% 0.19/0.44 = emptyset )
% 0.19/0.44 => ( subset @ A @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(symdiff_type,type,
% 0.19/0.44 symdiff: $i > $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(symdiffE_type,type,
% 0.19/0.44 symdiffE: $o ).
% 0.19/0.44
% 0.19/0.44 thf(symdiffE,definition,
% 0.19/0.44 ( symdiffE
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.19/0.44 => ! [Xphi: $o] :
% 0.19/0.44 ( ( ( in @ Xx @ A )
% 0.19/0.44 => ( ~ ( in @ Xx @ B )
% 0.19/0.44 => Xphi ) )
% 0.19/0.44 => ( ( ~ ( in @ Xx @ A )
% 0.19/0.44 => ( ( in @ Xx @ B )
% 0.19/0.44 => Xphi ) )
% 0.19/0.44 => Xphi ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(symdiffI1_type,type,
% 0.19/0.44 symdiffI1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(symdiffI1,definition,
% 0.19/0.44 ( symdiffI1
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ~ ( in @ Xx @ B )
% 0.19/0.44 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(symdiffI2_type,type,
% 0.19/0.44 symdiffI2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(symdiffI2,definition,
% 0.19/0.44 ( symdiffI2
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ~ ( in @ Xx @ A )
% 0.19/0.44 => ( ( in @ Xx @ B )
% 0.19/0.44 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(symdiffIneg1_type,type,
% 0.19/0.44 symdiffIneg1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(symdiffIneg1,definition,
% 0.19/0.44 ( symdiffIneg1
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ( in @ Xx @ B )
% 0.19/0.44 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(symdiffIneg2_type,type,
% 0.19/0.44 symdiffIneg2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(symdiffIneg2,definition,
% 0.19/0.44 ( symdiffIneg2
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ~ ( in @ Xx @ A )
% 0.19/0.44 => ( ~ ( in @ Xx @ B )
% 0.19/0.44 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(iskpair_type,type,
% 0.19/0.44 iskpair: $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(secondinupair_type,type,
% 0.19/0.44 secondinupair: $o ).
% 0.19/0.44
% 0.19/0.44 thf(secondinupair,definition,
% 0.19/0.44 ( secondinupair
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairIL_type,type,
% 0.19/0.44 setukpairIL: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairIL,definition,
% 0.19/0.44 ( setukpairIL
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairIR_type,type,
% 0.19/0.44 setukpairIR: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairIR,definition,
% 0.19/0.44 ( setukpairIR
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(kpairiskpair_type,type,
% 0.19/0.44 kpairiskpair: $o ).
% 0.19/0.44
% 0.19/0.44 thf(kpairiskpair,definition,
% 0.19/0.44 ( kpairiskpair
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(kpair_type,type,
% 0.19/0.44 kpair: $i > $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(kpairp_type,type,
% 0.19/0.44 kpairp: $o ).
% 0.19/0.44
% 0.19/0.44 thf(kpairp,definition,
% 0.19/0.44 ( kpairp
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprod_type,type,
% 0.19/0.44 cartprod: $i > $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(singletonsubset_type,type,
% 0.19/0.44 singletonsubset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(singletonsubset,definition,
% 0.19/0.44 ( singletonsubset
% 0.19/0.44 = ( ! [A: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(singletoninpowerset_type,type,
% 0.19/0.44 singletoninpowerset: $o ).
% 0.19/0.44
% 0.19/0.44 thf(singletoninpowerset,definition,
% 0.19/0.44 ( singletoninpowerset
% 0.19/0.44 = ( ! [A: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(singletoninpowunion_type,type,
% 0.19/0.44 singletoninpowunion: $o ).
% 0.19/0.44
% 0.19/0.44 thf(singletoninpowunion,definition,
% 0.19/0.44 ( singletoninpowunion
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(upairset2E_type,type,
% 0.19/0.44 upairset2E: $o ).
% 0.19/0.44
% 0.19/0.44 thf(upairset2E,definition,
% 0.19/0.44 ( upairset2E
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.44 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.19/0.44 => ( ( Xz = Xx )
% 0.19/0.44 | ( Xz = Xy ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(upairsubunion_type,type,
% 0.19/0.44 upairsubunion: $o ).
% 0.19/0.44
% 0.19/0.44 thf(upairsubunion,definition,
% 0.19/0.44 ( upairsubunion
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(upairinpowunion_type,type,
% 0.19/0.44 upairinpowunion: $o ).
% 0.19/0.44
% 0.19/0.44 thf(upairinpowunion,definition,
% 0.19/0.44 ( upairinpowunion
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(ubforcartprodlem1_type,type,
% 0.19/0.44 ubforcartprodlem1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(ubforcartprodlem1,definition,
% 0.19/0.44 ( ubforcartprodlem1
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(ubforcartprodlem2_type,type,
% 0.19/0.44 ubforcartprodlem2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(ubforcartprodlem2,definition,
% 0.19/0.44 ( ubforcartprodlem2
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(ubforcartprodlem3_type,type,
% 0.19/0.44 ubforcartprodlem3: $o ).
% 0.19/0.44
% 0.19/0.44 thf(ubforcartprodlem3,definition,
% 0.19/0.44 ( ubforcartprodlem3
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodpairin_type,type,
% 0.19/0.44 cartprodpairin: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodpairin,definition,
% 0.19/0.44 ( cartprodpairin
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodmempair1_type,type,
% 0.19/0.44 cartprodmempair1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodmempair1,definition,
% 0.19/0.44 ( cartprodmempair1
% 0.19/0.44 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.19/0.44 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.19/0.44 => ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ? [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 & ( Xu
% 0.19/0.44 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodmempair_type,type,
% 0.19/0.44 cartprodmempair: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodmempair,definition,
% 0.19/0.44 ( cartprodmempair
% 0.19/0.44 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.19/0.44 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.19/0.44 => ( iskpair @ Xu ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setunionE2_type,type,
% 0.19/0.44 setunionE2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setunionE2,definition,
% 0.19/0.44 ( setunionE2
% 0.19/0.44 = ( ! [A: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.19/0.44 => ? [X: $i] :
% 0.19/0.44 ( ( in @ X @ A )
% 0.19/0.44 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setunionsingleton1_type,type,
% 0.19/0.44 setunionsingleton1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setunionsingleton1,definition,
% 0.19/0.44 ( setunionsingleton1
% 0.19/0.44 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setunionsingleton2_type,type,
% 0.19/0.44 setunionsingleton2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setunionsingleton2,definition,
% 0.19/0.44 ( setunionsingleton2
% 0.19/0.44 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setunionsingleton_type,type,
% 0.19/0.44 setunionsingleton: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setunionsingleton,definition,
% 0.19/0.44 ( setunionsingleton
% 0.19/0.44 = ( ! [Xx: $i] :
% 0.19/0.44 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.19/0.44 = Xx ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(singleton_type,type,
% 0.19/0.44 singleton: $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(singletonprop_type,type,
% 0.19/0.44 singletonprop: $o ).
% 0.19/0.44
% 0.19/0.44 thf(singletonprop,definition,
% 0.19/0.44 ( singletonprop
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ A )
% 0.19/0.44 => ( ( Xphi @ Xx )
% 0.19/0.44 => ( ( Xphi @ Xy )
% 0.19/0.44 => ( Xx = Xy ) ) ) ) )
% 0.19/0.44 => ( ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ( Xphi @ Xx ) )
% 0.19/0.44 => ( singleton
% 0.19/0.44 @ ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(ex1_type,type,
% 0.19/0.44 ex1: $i > ( $i > $o ) > $o ).
% 0.19/0.44
% 0.19/0.44 thf(ex1,definition,
% 0.19/0.44 ( ex1
% 0.19/0.44 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( singleton
% 0.19/0.44 @ ( dsetconstr @ A
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(ex1E1_type,type,
% 0.19/0.44 ex1E1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(ex1E1,definition,
% 0.19/0.44 ( ex1E1
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( ( ex1 @ A
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.44 => ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(ex1I_type,type,
% 0.19/0.44 ex1I: $o ).
% 0.19/0.44
% 0.19/0.44 thf(ex1I,definition,
% 0.19/0.44 ( ex1I
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ( ( Xphi @ Xx )
% 0.19/0.44 => ( ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ A )
% 0.19/0.44 => ( ( Xphi @ Xy )
% 0.19/0.44 => ( Xy = Xx ) ) )
% 0.19/0.44 => ( ex1 @ A
% 0.19/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(ex1I2_type,type,
% 0.19/0.44 ex1I2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(ex1I2,definition,
% 0.19/0.44 ( ex1I2
% 0.19/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.44 ( ! [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ A )
% 0.19/0.44 => ( ( Xphi @ Xx )
% 0.19/0.44 => ( ( Xphi @ Xy )
% 0.19/0.44 => ( Xx = Xy ) ) ) ) )
% 0.19/0.44 => ( ? [Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 & ( Xphi @ Xx ) )
% 0.19/0.44 => ( ex1 @ A
% 0.19/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(singletonsuniq_type,type,
% 0.19/0.44 singletonsuniq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(singletonsuniq,definition,
% 0.19/0.44 ( singletonsuniq
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( ( setadjoin @ Xx @ emptyset )
% 0.19/0.44 = ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.44 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(atmost1p_type,type,
% 0.19/0.44 atmost1p: $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(atleast2p_type,type,
% 0.19/0.44 atleast2p: $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(atmost2p_type,type,
% 0.19/0.44 atmost2p: $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(upairsetp_type,type,
% 0.19/0.44 upairsetp: $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjL1_type,type,
% 0.19/0.44 setukpairinjL1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjL1,definition,
% 0.19/0.44 ( setukpairinjL1
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.44 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.19/0.44 => ( Xx = Xz ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(kfstsingleton_type,type,
% 0.19/0.44 kfstsingleton: $o ).
% 0.19/0.44
% 0.19/0.44 thf(kfstsingleton,definition,
% 0.19/0.44 ( kfstsingleton
% 0.19/0.44 = ( ! [Xu: $i] :
% 0.19/0.44 ( ( iskpair @ Xu )
% 0.19/0.44 => ( singleton
% 0.19/0.44 @ ( dsetconstr @ ( setunion @ Xu )
% 0.19/0.44 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(theprop_type,type,
% 0.19/0.44 theprop: $o ).
% 0.19/0.44
% 0.19/0.44 thf(theprop,definition,
% 0.19/0.44 ( theprop
% 0.19/0.44 = ( ! [X: $i] :
% 0.19/0.44 ( ( singleton @ X )
% 0.19/0.44 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(kfst_type,type,
% 0.19/0.44 kfst: $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(kfstpairEq_type,type,
% 0.19/0.44 kfstpairEq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(kfstpairEq,definition,
% 0.19/0.44 ( kfstpairEq
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.19/0.44 = Xx ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodfstin_type,type,
% 0.19/0.44 cartprodfstin: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodfstin,definition,
% 0.19/0.44 ( cartprodfstin
% 0.19/0.44 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.19/0.44 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.19/0.44 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjL2_type,type,
% 0.19/0.44 setukpairinjL2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjL2,definition,
% 0.19/0.44 ( setukpairinjL2
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.19/0.44 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.19/0.44 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.19/0.44 => ( Xx = Xz ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjL_type,type,
% 0.19/0.44 setukpairinjL: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjL,definition,
% 0.19/0.44 ( setukpairinjL
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.19/0.44 ( ( ( kpair @ Xx @ Xy )
% 0.19/0.44 = ( kpair @ Xz @ Xu ) )
% 0.19/0.44 => ( Xx = Xz ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjR11_type,type,
% 0.19/0.44 setukpairinjR11: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjR11,definition,
% 0.19/0.44 ( setukpairinjR11
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xx = Xy )
% 0.19/0.44 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.44 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjR12_type,type,
% 0.19/0.44 setukpairinjR12: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjR12,definition,
% 0.19/0.44 ( setukpairinjR12
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( Xx = Xy )
% 0.19/0.44 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.19/0.44 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjR1_type,type,
% 0.19/0.44 setukpairinjR1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjR1,definition,
% 0.19/0.44 ( setukpairinjR1
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.19/0.44 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.19/0.44 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.19/0.44 => ( ( Xz = Xu )
% 0.19/0.44 => ( Xy = Xu ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(upairequniteq_type,type,
% 0.19/0.44 upairequniteq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(upairequniteq,definition,
% 0.19/0.44 ( upairequniteq
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.19/0.44 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.19/0.44 = ( setadjoin @ Xz @ emptyset ) )
% 0.19/0.44 => ( Xx = Xy ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjR2_type,type,
% 0.19/0.44 setukpairinjR2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjR2,definition,
% 0.19/0.44 ( setukpairinjR2
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.19/0.44 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.19/0.44 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.19/0.44 => ( Xy = Xu ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjR_type,type,
% 0.19/0.44 setukpairinjR: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setukpairinjR,definition,
% 0.19/0.44 ( setukpairinjR
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.19/0.44 ( ( ( kpair @ Xx @ Xy )
% 0.19/0.44 = ( kpair @ Xz @ Xu ) )
% 0.19/0.44 => ( Xy = Xu ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(ksndsingleton_type,type,
% 0.19/0.44 ksndsingleton: $o ).
% 0.19/0.44
% 0.19/0.44 thf(ksndsingleton,definition,
% 0.19/0.44 ( ksndsingleton
% 0.19/0.44 = ( ! [Xu: $i] :
% 0.19/0.44 ( ( iskpair @ Xu )
% 0.19/0.44 => ( singleton
% 0.19/0.44 @ ( dsetconstr @ ( setunion @ Xu )
% 0.19/0.44 @ ^ [Xx: $i] :
% 0.19/0.44 ( Xu
% 0.19/0.44 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(ksnd_type,type,
% 0.19/0.44 ksnd: $i > $i ).
% 0.19/0.44
% 0.19/0.44 thf(ksndpairEq_type,type,
% 0.19/0.44 ksndpairEq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(ksndpairEq,definition,
% 0.19/0.44 ( ksndpairEq
% 0.19/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.19/0.44 = Xy ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(kpairsurjEq_type,type,
% 0.19/0.44 kpairsurjEq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(kpairsurjEq,definition,
% 0.19/0.44 ( kpairsurjEq
% 0.19/0.44 = ( ! [Xu: $i] :
% 0.19/0.44 ( ( iskpair @ Xu )
% 0.19/0.44 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.19/0.44 = Xu ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodsndin_type,type,
% 0.19/0.44 cartprodsndin: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodsndin,definition,
% 0.19/0.44 ( cartprodsndin
% 0.19/0.44 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.19/0.44 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.19/0.44 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodpairmemEL_type,type,
% 0.19/0.44 cartprodpairmemEL: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodpairmemEL,definition,
% 0.19/0.44 ( cartprodpairmemEL
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.19/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodpairmemER_type,type,
% 0.19/0.44 cartprodpairmemER: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodpairmemER,definition,
% 0.19/0.44 ( cartprodpairmemER
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.19/0.44 => ( in @ Xy @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodmempaircEq_type,type,
% 0.19/0.44 cartprodmempaircEq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodmempaircEq,definition,
% 0.19/0.44 ( cartprodmempaircEq
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( ( kpair @ Xx @ Xy )
% 0.19/0.44 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodfstpairEq_type,type,
% 0.19/0.44 cartprodfstpairEq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodfstpairEq,definition,
% 0.19/0.44 ( cartprodfstpairEq
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.19/0.44 = Xx ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodsndpairEq_type,type,
% 0.19/0.44 cartprodsndpairEq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodsndpairEq,definition,
% 0.19/0.44 ( cartprodsndpairEq
% 0.19/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.19/0.44 = Xy ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodpairsurjEq_type,type,
% 0.19/0.44 cartprodpairsurjEq: $o ).
% 0.19/0.44
% 0.19/0.44 thf(cartprodpairsurjEq,definition,
% 0.19/0.44 ( cartprodpairsurjEq
% 0.19/0.44 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.19/0.44 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.19/0.44 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.19/0.44 = Xu ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(breln_type,type,
% 0.19/0.44 breln: $i > $i > $i > $o ).
% 0.19/0.44
% 0.19/0.44 thf(breln,definition,
% 0.19/0.44 ( breln
% 0.19/0.44 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstr_type,type,
% 0.19/0.44 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrI_type,type,
% 0.19/0.44 dpsetconstrI: $o ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrI,definition,
% 0.19/0.44 ( dpsetconstrI
% 0.19/0.44 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( ( Xphi @ Xx @ Xy )
% 0.19/0.44 => ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.44 @ ( dpsetconstr @ A @ B
% 0.19/0.44 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrSub_type,type,
% 0.19/0.44 dpsetconstrSub: $o ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrSub,definition,
% 0.19/0.44 ( dpsetconstrSub
% 0.19/0.44 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.19/0.44 ( subset
% 0.19/0.44 @ ( dpsetconstr @ A @ B
% 0.19/0.44 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.19/0.44 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(setOfPairsIsBReln_type,type,
% 0.19/0.44 setOfPairsIsBReln: $o ).
% 0.19/0.44
% 0.19/0.44 thf(setOfPairsIsBReln,definition,
% 0.19/0.44 ( setOfPairsIsBReln
% 0.19/0.44 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.19/0.44 ( breln @ A @ B
% 0.19/0.44 @ ( dpsetconstr @ A @ B
% 0.19/0.44 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrERa_type,type,
% 0.19/0.44 dpsetconstrERa: $o ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrERa,definition,
% 0.19/0.44 ( dpsetconstrERa
% 0.19/0.44 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.19/0.44 ( ( in @ Xx @ A )
% 0.19/0.44 => ! [Xy: $i] :
% 0.19/0.44 ( ( in @ Xy @ B )
% 0.19/0.44 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.44 @ ( dpsetconstr @ A @ B
% 0.19/0.44 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.19/0.44 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrEL1_type,type,
% 0.19/0.44 dpsetconstrEL1: $o ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrEL1,definition,
% 0.19/0.44 ( dpsetconstrEL1
% 0.19/0.44 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.19/0.44 ( ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.44 @ ( dpsetconstr @ A @ B
% 0.19/0.44 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.19/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrEL2_type,type,
% 0.19/0.44 dpsetconstrEL2: $o ).
% 0.19/0.44
% 0.19/0.44 thf(dpsetconstrEL2,definition,
% 0.19/0.45 ( dpsetconstrEL2
% 0.19/0.45 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.19/0.45 ( ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.45 @ ( dpsetconstr @ A @ B
% 0.19/0.45 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.19/0.45 => ( in @ Xy @ B ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(dpsetconstrER_type,type,
% 0.19/0.45 dpsetconstrER: $o ).
% 0.19/0.45
% 0.19/0.45 thf(dpsetconstrER,definition,
% 0.19/0.45 ( dpsetconstrER
% 0.19/0.45 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.19/0.45 ( ( in @ ( kpair @ Xx @ Xy )
% 0.19/0.45 @ ( dpsetconstr @ A @ B
% 0.19/0.45 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.19/0.45 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(func_type,type,
% 0.19/0.45 func: $i > $i > $i > $o ).
% 0.19/0.45
% 0.19/0.45 thf(funcSet_type,type,
% 0.19/0.45 funcSet: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(funcImageSingleton_type,type,
% 0.19/0.45 funcImageSingleton: $o ).
% 0.19/0.45
% 0.19/0.45 thf(funcImageSingleton,definition,
% 0.19/0.45 ( funcImageSingleton
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xf )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( singleton
% 0.19/0.45 @ ( dsetconstr @ B
% 0.19/0.45 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(apProp_type,type,
% 0.19/0.45 apProp: $o ).
% 0.19/0.45
% 0.19/0.45 thf(apProp,definition,
% 0.19/0.45 ( apProp
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xf )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in
% 0.19/0.45 @ ( setunion
% 0.19/0.45 @ ( dsetconstr @ B
% 0.19/0.45 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.19/0.45 @ B ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(ap_type,type,
% 0.19/0.45 ap: $i > $i > $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(app_type,type,
% 0.19/0.45 app: $o ).
% 0.19/0.45
% 0.19/0.45 thf(app,definition,
% 0.19/0.45 ( app
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xf )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(infuncsetfunc_type,type,
% 0.19/0.45 infuncsetfunc: $o ).
% 0.19/0.45
% 0.19/0.45 thf(infuncsetfunc,definition,
% 0.19/0.45 ( infuncsetfunc
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.45 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(ap2p_type,type,
% 0.19/0.45 ap2p: $o ).
% 0.19/0.45
% 0.19/0.45 thf(ap2p,definition,
% 0.19/0.45 ( ap2p
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(funcinfuncset_type,type,
% 0.19/0.45 funcinfuncset: $o ).
% 0.19/0.45
% 0.19/0.45 thf(funcinfuncset,definition,
% 0.19/0.45 ( funcinfuncset
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xf )
% 0.19/0.45 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(lamProp_type,type,
% 0.19/0.45 lamProp: $o ).
% 0.19/0.45
% 0.19/0.45 thf(lamProp,definition,
% 0.19/0.45 ( lamProp
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.45 => ( func @ A @ B
% 0.19/0.45 @ ( dpsetconstr @ A @ B
% 0.19/0.45 @ ^ [Xx: $i,Xy: $i] :
% 0.19/0.45 ( ( Xf @ Xx )
% 0.19/0.45 = Xy ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(lam_type,type,
% 0.19/0.45 lam: $i > $i > ( $i > $i ) > $i ).
% 0.19/0.45
% 0.19/0.45 thf(lamp_type,type,
% 0.19/0.45 lamp: $o ).
% 0.19/0.45
% 0.19/0.45 thf(lamp,definition,
% 0.19/0.45 ( lamp
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.45 => ( func @ A @ B
% 0.19/0.45 @ ( lam @ A @ B
% 0.19/0.45 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(lam2p_type,type,
% 0.19/0.45 lam2p: $o ).
% 0.19/0.45
% 0.19/0.45 thf(lam2p,definition,
% 0.19/0.45 ( lam2p
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.45 => ( in
% 0.19/0.45 @ ( lam @ A @ B
% 0.19/0.45 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.19/0.45 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(brelnall1_type,type,
% 0.19/0.45 brelnall1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(brelnall1,definition,
% 0.19/0.45 ( brelnall1
% 0.19/0.45 = ( ! [A: $i,B: $i,R: $i] :
% 0.19/0.45 ( ( breln @ A @ B @ R )
% 0.19/0.45 => ! [Xphi: $i > $o] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ B )
% 0.19/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.19/0.45 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ R )
% 0.19/0.45 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(brelnall2_type,type,
% 0.19/0.45 brelnall2: $o ).
% 0.19/0.45
% 0.19/0.45 thf(brelnall2,definition,
% 0.19/0.45 ( brelnall2
% 0.19/0.45 = ( ! [A: $i,B: $i,R: $i] :
% 0.19/0.45 ( ( breln @ A @ B @ R )
% 0.19/0.45 => ! [Xphi: $i > $o] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ B )
% 0.19/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.19/0.45 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ R )
% 0.19/0.45 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(ex1E2_type,type,
% 0.19/0.45 ex1E2: $o ).
% 0.19/0.45
% 0.19/0.45 thf(ex1E2,definition,
% 0.19/0.45 ( ex1E2
% 0.19/0.45 = ( ! [A: $i,Xphi: $i > $o] :
% 0.19/0.45 ( ( ex1 @ A
% 0.19/0.45 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( ( Xphi @ Xx )
% 0.19/0.45 => ( ( Xphi @ Xy )
% 0.19/0.45 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(funcGraphProp1_type,type,
% 0.19/0.45 funcGraphProp1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(funcGraphProp1,definition,
% 0.19/0.45 ( funcGraphProp1
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xf )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(funcGraphProp3_type,type,
% 0.19/0.45 funcGraphProp3: $o ).
% 0.19/0.45
% 0.19/0.45 thf(funcGraphProp3,definition,
% 0.19/0.45 ( funcGraphProp3
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(funcGraphProp2_type,type,
% 0.19/0.45 funcGraphProp2: $o ).
% 0.19/0.45
% 0.19/0.45 thf(funcGraphProp2,definition,
% 0.19/0.45 ( funcGraphProp2
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xf )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ B )
% 0.19/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.19/0.45 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.45 = Xy ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(funcextLem_type,type,
% 0.19/0.45 funcextLem: $o ).
% 0.19/0.45
% 0.19/0.45 thf(funcextLem,definition,
% 0.19/0.45 ( funcextLem
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xf )
% 0.19/0.45 => ! [Xg: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xg )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.45 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ B )
% 0.19/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.19/0.45 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(funcGraphProp4_type,type,
% 0.19/0.45 funcGraphProp4: $o ).
% 0.19/0.45
% 0.19/0.45 thf(funcGraphProp4,definition,
% 0.19/0.45 ( funcGraphProp4
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ B )
% 0.19/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.19/0.45 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.45 = Xy ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(subbreln_type,type,
% 0.19/0.45 subbreln: $o ).
% 0.19/0.45
% 0.19/0.45 thf(subbreln,definition,
% 0.19/0.45 ( subbreln
% 0.19/0.45 = ( ! [A: $i,B: $i,R: $i] :
% 0.19/0.45 ( ( breln @ A @ B @ R )
% 0.19/0.45 => ! [S: $i] :
% 0.19/0.45 ( ( breln @ A @ B @ S )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ B )
% 0.19/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.19/0.45 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.19/0.45 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(eqbreln_type,type,
% 0.19/0.45 eqbreln: $o ).
% 0.19/0.45
% 0.19/0.45 thf(eqbreln,definition,
% 0.19/0.45 ( eqbreln
% 0.19/0.45 = ( ! [A: $i,B: $i,R: $i] :
% 0.19/0.45 ( ( breln @ A @ B @ R )
% 0.19/0.45 => ! [S: $i] :
% 0.19/0.45 ( ( breln @ A @ B @ S )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ B )
% 0.19/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.19/0.45 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ B )
% 0.19/0.45 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.19/0.45 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.19/0.45 => ( R = S ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(funcext_type,type,
% 0.19/0.45 funcext: $o ).
% 0.19/0.45
% 0.19/0.45 thf(funcext,definition,
% 0.19/0.45 ( funcext
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xf )
% 0.19/0.45 => ! [Xg: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xg )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.45 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.19/0.45 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(funcext2_type,type,
% 0.19/0.45 funcext2: $o ).
% 0.19/0.45
% 0.19/0.45 thf(funcext2,definition,
% 0.19/0.45 ( funcext2
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.45 => ! [Xg: $i] :
% 0.19/0.45 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.45 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.19/0.45 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(ap2apEq1_type,type,
% 0.19/0.45 ap2apEq1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(ap2apEq1,definition,
% 0.19/0.45 ( ap2apEq1
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.45 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(ap2apEq2_type,type,
% 0.19/0.45 ap2apEq2: $o ).
% 0.19/0.45
% 0.19/0.45 thf(ap2apEq2,definition,
% 0.19/0.45 ( ap2apEq2
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xf )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.19/0.45 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(beta1_type,type,
% 0.19/0.45 beta1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(beta1,definition,
% 0.19/0.45 ( beta1
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( ap @ A @ B
% 0.19/0.45 @ ( lam @ A @ B
% 0.19/0.45 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.19/0.45 @ Xx )
% 0.19/0.45 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(eta1_type,type,
% 0.19/0.45 eta1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(eta1,definition,
% 0.19/0.45 ( eta1
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( func @ A @ B @ Xf )
% 0.19/0.45 => ( ( lam @ A @ B
% 0.19/0.45 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.19/0.45 = Xf ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(lam2lamEq_type,type,
% 0.19/0.45 lam2lamEq: $o ).
% 0.19/0.45
% 0.19/0.45 thf(lam2lamEq,definition,
% 0.19/0.45 ( lam2lamEq
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.45 => ( ( lam @ A @ B
% 0.19/0.45 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.19/0.45 = ( lam @ A @ B
% 0.19/0.45 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(beta2_type,type,
% 0.19/0.45 beta2: $o ).
% 0.19/0.45
% 0.19/0.45 thf(beta2,definition,
% 0.19/0.45 ( beta2
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.19/0.45 ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( ap @ A @ B
% 0.19/0.45 @ ( lam @ A @ B
% 0.19/0.45 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.19/0.45 @ Xx )
% 0.19/0.45 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(eta2_type,type,
% 0.19/0.45 eta2: $o ).
% 0.19/0.45
% 0.19/0.45 thf(eta2,definition,
% 0.19/0.45 ( eta2
% 0.19/0.45 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.19/0.45 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.19/0.45 => ( ( lam @ A @ B
% 0.19/0.45 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.19/0.45 = Xf ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(iffalseProp1_type,type,
% 0.19/0.45 iffalseProp1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(iffalseProp1,definition,
% 0.19/0.45 ( iffalseProp1
% 0.19/0.45 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( ~ Xphi
% 0.19/0.45 => ( in @ Xy
% 0.19/0.45 @ ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xz: $i] :
% 0.19/0.45 ( ( Xphi
% 0.19/0.45 & ( Xz = Xx ) )
% 0.19/0.45 | ( ~ Xphi
% 0.19/0.45 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(iffalseProp2_type,type,
% 0.19/0.45 iffalseProp2: $o ).
% 0.19/0.45
% 0.19/0.45 thf(iffalseProp2,definition,
% 0.19/0.45 ( iffalseProp2
% 0.19/0.45 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( ~ Xphi
% 0.19/0.45 => ( ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xz: $i] :
% 0.19/0.45 ( ( Xphi
% 0.19/0.45 & ( Xz = Xx ) )
% 0.19/0.45 | ( ~ Xphi
% 0.19/0.45 & ( Xz = Xy ) ) ) )
% 0.19/0.45 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(iftrueProp1_type,type,
% 0.19/0.45 iftrueProp1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(iftrueProp1,definition,
% 0.19/0.45 ( iftrueProp1
% 0.19/0.45 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( Xphi
% 0.19/0.45 => ( in @ Xx
% 0.19/0.45 @ ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xz: $i] :
% 0.19/0.45 ( ( Xphi
% 0.19/0.45 & ( Xz = Xx ) )
% 0.19/0.45 | ( ~ Xphi
% 0.19/0.45 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(iftrueProp2_type,type,
% 0.19/0.45 iftrueProp2: $o ).
% 0.19/0.45
% 0.19/0.45 thf(iftrueProp2,definition,
% 0.19/0.45 ( iftrueProp2
% 0.19/0.45 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( Xphi
% 0.19/0.45 => ( ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xz: $i] :
% 0.19/0.45 ( ( Xphi
% 0.19/0.45 & ( Xz = Xx ) )
% 0.19/0.45 | ( ~ Xphi
% 0.19/0.45 & ( Xz = Xy ) ) ) )
% 0.19/0.45 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(ifSingleton_type,type,
% 0.19/0.45 ifSingleton: $o ).
% 0.19/0.45
% 0.19/0.45 thf(ifSingleton,definition,
% 0.19/0.45 ( ifSingleton
% 0.19/0.45 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( singleton
% 0.19/0.45 @ ( dsetconstr @ A
% 0.19/0.45 @ ^ [Xz: $i] :
% 0.19/0.45 ( ( Xphi
% 0.19/0.45 & ( Xz = Xx ) )
% 0.19/0.45 | ( ~ Xphi
% 0.19/0.45 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(if_type,type,
% 0.19/0.45 if: $i > $o > $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(ifp_type,type,
% 0.19/0.45 ifp: $o ).
% 0.19/0.45
% 0.19/0.45 thf(ifp,definition,
% 0.19/0.45 ( ifp
% 0.19/0.45 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(theeq_type,type,
% 0.19/0.45 theeq: $o ).
% 0.19/0.45
% 0.19/0.45 thf(theeq,definition,
% 0.19/0.45 ( theeq
% 0.19/0.45 = ( ! [X: $i] :
% 0.19/0.45 ( ( singleton @ X )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ X )
% 0.19/0.45 => ( ( setunion @ X )
% 0.19/0.45 = Xx ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(iftrue_type,type,
% 0.19/0.45 iftrue: $o ).
% 0.19/0.45
% 0.19/0.45 thf(iftrue,definition,
% 0.19/0.45 ( iftrue
% 0.19/0.45 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( Xphi
% 0.19/0.45 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.19/0.45 = Xx ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(iffalse_type,type,
% 0.19/0.45 iffalse: $o ).
% 0.19/0.45
% 0.19/0.45 thf(iffalse,definition,
% 0.19/0.45 ( iffalse
% 0.19/0.45 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( ~ Xphi
% 0.19/0.45 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.19/0.45 = Xy ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(iftrueorfalse_type,type,
% 0.19/0.45 iftrueorfalse: $o ).
% 0.19/0.45
% 0.19/0.45 thf(iftrueorfalse,definition,
% 0.19/0.45 ( iftrueorfalse
% 0.19/0.45 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ! [Xy: $i] :
% 0.19/0.45 ( ( in @ Xy @ A )
% 0.19/0.45 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(binintersectT_lem_type,type,
% 0.19/0.45 binintersectT_lem: $o ).
% 0.19/0.45
% 0.19/0.45 thf(binintersectT_lem,definition,
% 0.19/0.45 ( binintersectT_lem
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(binunionT_lem_type,type,
% 0.19/0.45 binunionT_lem: $o ).
% 0.19/0.45
% 0.19/0.45 thf(binunionT_lem,definition,
% 0.19/0.45 ( binunionT_lem
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(powersetT_lem_type,type,
% 0.19/0.45 powersetT_lem: $o ).
% 0.19/0.45
% 0.19/0.45 thf(powersetT_lem,definition,
% 0.19/0.45 ( powersetT_lem
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setminusT_lem_type,type,
% 0.19/0.45 setminusT_lem: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setminusT_lem,definition,
% 0.19/0.45 ( setminusT_lem
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(complementT_lem_type,type,
% 0.19/0.45 complementT_lem: $o ).
% 0.19/0.45
% 0.19/0.45 thf(complementT_lem,definition,
% 0.19/0.45 ( complementT_lem
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(setextT_type,type,
% 0.19/0.45 setextT: $o ).
% 0.19/0.45
% 0.19/0.45 thf(setextT,definition,
% 0.19/0.45 ( setextT
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( in @ Xx @ X )
% 0.19/0.45 => ( in @ Xx @ Y ) ) )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( in @ Xx @ Y )
% 0.19/0.45 => ( in @ Xx @ X ) ) )
% 0.19/0.45 => ( X = Y ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(subsetTI_type,type,
% 0.19/0.45 subsetTI: $o ).
% 0.19/0.45
% 0.19/0.45 thf(subsetTI,definition,
% 0.19/0.45 ( subsetTI
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( in @ Xx @ X )
% 0.19/0.45 => ( in @ Xx @ Y ) ) )
% 0.19/0.45 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(powersetTI1_type,type,
% 0.19/0.45 powersetTI1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(powersetTI1,definition,
% 0.19/0.45 ( powersetTI1
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ( ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( in @ Xx @ X )
% 0.19/0.45 => ( in @ Xx @ Y ) ) )
% 0.19/0.45 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(powersetTE1_type,type,
% 0.19/0.45 powersetTE1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(powersetTE1,definition,
% 0.19/0.45 ( powersetTE1
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( in @ X @ ( powerset @ Y ) )
% 0.19/0.45 => ( ( in @ Xx @ X )
% 0.19/0.45 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(complementTI1_type,type,
% 0.19/0.45 complementTI1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(complementTI1,definition,
% 0.19/0.45 ( complementTI1
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( in @ Xx @ X )
% 0.19/0.45 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(complementTE1_type,type,
% 0.19/0.45 complementTE1: $o ).
% 0.19/0.45
% 0.19/0.45 thf(complementTE1,definition,
% 0.19/0.45 ( complementTE1
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.19/0.45 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(binintersectTELcontra_type,type,
% 0.19/0.45 binintersectTELcontra: $o ).
% 0.19/0.45
% 0.19/0.45 thf(binintersectTELcontra,definition,
% 0.19/0.45 ( binintersectTELcontra
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ~ ( in @ Xx @ X )
% 0.19/0.45 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(binintersectTERcontra_type,type,
% 0.19/0.45 binintersectTERcontra: $o ).
% 0.19/0.45
% 0.19/0.45 thf(binintersectTERcontra,definition,
% 0.19/0.45 ( binintersectTERcontra
% 0.19/0.45 = ( ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ~ ( in @ Xx @ Y )
% 0.19/0.45 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(contrasubsetT,conjecture,
% 0.19/0.45 ( setextAx
% 0.19/0.45 => ( emptysetAx
% 0.19/0.45 => ( setadjoinAx
% 0.19/0.45 => ( powersetAx
% 0.19/0.45 => ( setunionAx
% 0.19/0.45 => ( omega0Ax
% 0.19/0.45 => ( omegaSAx
% 0.19/0.45 => ( omegaIndAx
% 0.19/0.45 => ( replAx
% 0.19/0.45 => ( foundationAx
% 0.19/0.45 => ( wellorderingAx
% 0.19/0.45 => ( descrp
% 0.19/0.45 => ( dsetconstrI
% 0.19/0.45 => ( dsetconstrEL
% 0.19/0.45 => ( dsetconstrER
% 0.19/0.45 => ( exuE1
% 0.19/0.45 => ( prop2setE
% 0.19/0.45 => ( emptysetE
% 0.19/0.45 => ( emptysetimpfalse
% 0.19/0.45 => ( notinemptyset
% 0.19/0.45 => ( exuE3e
% 0.19/0.45 => ( setext
% 0.19/0.45 => ( emptyI
% 0.19/0.45 => ( noeltsimpempty
% 0.19/0.45 => ( setbeta
% 0.19/0.45 => ( nonemptyE1
% 0.19/0.45 => ( nonemptyI
% 0.19/0.45 => ( nonemptyI1
% 0.19/0.45 => ( setadjoinIL
% 0.19/0.45 => ( emptyinunitempty
% 0.19/0.45 => ( setadjoinIR
% 0.19/0.45 => ( setadjoinE
% 0.19/0.45 => ( setadjoinOr
% 0.19/0.45 => ( setoftrueEq
% 0.19/0.45 => ( powersetI
% 0.19/0.45 => ( emptyinPowerset
% 0.19/0.45 => ( emptyInPowerset
% 0.19/0.45 => ( powersetE
% 0.19/0.45 => ( setunionI
% 0.19/0.45 => ( setunionE
% 0.19/0.45 => ( subPowSU
% 0.19/0.45 => ( exuE2
% 0.19/0.45 => ( nonemptyImpWitness
% 0.19/0.45 => ( uniqinunit
% 0.19/0.45 => ( notinsingleton
% 0.19/0.45 => ( eqinunit
% 0.19/0.45 => ( singletonsswitch
% 0.19/0.45 => ( upairsetE
% 0.19/0.45 => ( upairsetIL
% 0.19/0.45 => ( upairsetIR
% 0.19/0.45 => ( emptyE1
% 0.19/0.45 => ( vacuousDall
% 0.19/0.45 => ( quantDeMorgan1
% 0.19/0.45 => ( quantDeMorgan2
% 0.19/0.45 => ( quantDeMorgan3
% 0.19/0.45 => ( quantDeMorgan4
% 0.19/0.45 => ( prop2setI
% 0.19/0.45 => ( prop2set2propI
% 0.19/0.45 => ( notdexE
% 0.19/0.45 => ( notdallE
% 0.19/0.45 => ( exuI1
% 0.19/0.45 => ( exuI3
% 0.19/0.45 => ( exuI2
% 0.19/0.45 => ( inCongP
% 0.19/0.45 => ( in__Cong
% 0.19/0.45 => ( exuE3u
% 0.19/0.45 => ( exu__Cong
% 0.19/0.45 => ( emptyset__Cong
% 0.19/0.45 => ( setadjoin__Cong
% 0.19/0.45 => ( powerset__Cong
% 0.19/0.45 => ( setunion__Cong
% 0.19/0.45 => ( omega__Cong
% 0.19/0.45 => ( exuEu
% 0.19/0.45 => ( descr__Cong
% 0.19/0.45 => ( dsetconstr__Cong
% 0.19/0.45 => ( subsetI1
% 0.19/0.45 => ( eqimpsubset2
% 0.19/0.45 => ( eqimpsubset1
% 0.19/0.45 => ( subsetI2
% 0.19/0.45 => ( emptysetsubset
% 0.19/0.45 => ( subsetE
% 0.19/0.45 => ( subsetE2
% 0.19/0.45 => ( notsubsetI
% 0.19/0.45 => ( notequalI1
% 0.19/0.45 => ( notequalI2
% 0.19/0.45 => ( subsetRefl
% 0.19/0.45 => ( subsetTrans
% 0.19/0.45 => ( setadjoinSub
% 0.19/0.45 => ( setadjoinSub2
% 0.19/0.45 => ( subset2powerset
% 0.19/0.45 => ( setextsub
% 0.19/0.45 => ( subsetemptysetimpeq
% 0.19/0.45 => ( powersetI1
% 0.19/0.45 => ( powersetE1
% 0.19/0.45 => ( inPowerset
% 0.19/0.45 => ( powersetsubset
% 0.19/0.45 => ( sepInPowerset
% 0.19/0.45 => ( sepSubset
% 0.19/0.45 => ( binunionIL
% 0.19/0.45 => ( upairset2IR
% 0.19/0.45 => ( binunionIR
% 0.19/0.45 => ( binunionEcases
% 0.19/0.45 => ( binunionE
% 0.19/0.45 => ( binunionLsub
% 0.19/0.45 => ( binunionRsub
% 0.19/0.45 => ( binintersectI
% 0.19/0.45 => ( binintersectSubset5
% 0.19/0.45 => ( binintersectEL
% 0.19/0.45 => ( binintersectLsub
% 0.19/0.45 => ( binintersectSubset2
% 0.19/0.45 => ( binintersectSubset3
% 0.19/0.45 => ( binintersectER
% 0.19/0.45 => ( disjointsetsI1
% 0.19/0.45 => ( binintersectRsub
% 0.19/0.45 => ( binintersectSubset4
% 0.19/0.45 => ( binintersectSubset1
% 0.19/0.45 => ( bs114d
% 0.19/0.45 => ( setminusI
% 0.19/0.45 => ( setminusEL
% 0.19/0.45 => ( setminusER
% 0.19/0.45 => ( setminusSubset2
% 0.19/0.45 => ( setminusERneg
% 0.19/0.45 => ( setminusELneg
% 0.19/0.45 => ( setminusILneg
% 0.19/0.45 => ( setminusIRneg
% 0.19/0.45 => ( setminusLsub
% 0.19/0.45 => ( setminusSubset1
% 0.19/0.45 => ( symdiffE
% 0.19/0.45 => ( symdiffI1
% 0.19/0.45 => ( symdiffI2
% 0.19/0.45 => ( symdiffIneg1
% 0.19/0.45 => ( symdiffIneg2
% 0.19/0.45 => ( secondinupair
% 0.19/0.45 => ( setukpairIL
% 0.19/0.45 => ( setukpairIR
% 0.19/0.45 => ( kpairiskpair
% 0.19/0.45 => ( kpairp
% 0.19/0.45 => ( singletonsubset
% 0.19/0.45 => ( singletoninpowerset
% 0.19/0.45 => ( singletoninpowunion
% 0.19/0.45 => ( upairset2E
% 0.19/0.45 => ( upairsubunion
% 0.19/0.45 => ( upairinpowunion
% 0.19/0.45 => ( ubforcartprodlem1
% 0.19/0.45 => ( ubforcartprodlem2
% 0.19/0.45 => ( ubforcartprodlem3
% 0.19/0.45 => ( cartprodpairin
% 0.19/0.45 => ( cartprodmempair1
% 0.19/0.45 => ( cartprodmempair
% 0.19/0.45 => ( setunionE2
% 0.19/0.45 => ( setunionsingleton1
% 0.19/0.45 => ( setunionsingleton2
% 0.19/0.45 => ( setunionsingleton
% 0.19/0.45 => ( singletonprop
% 0.19/0.45 => ( ex1E1
% 0.19/0.45 => ( ex1I
% 0.19/0.45 => ( ex1I2
% 0.19/0.45 => ( singletonsuniq
% 0.19/0.45 => ( setukpairinjL1
% 0.19/0.45 => ( kfstsingleton
% 0.19/0.45 => ( theprop
% 0.19/0.45 => ( kfstpairEq
% 0.19/0.45 => ( cartprodfstin
% 0.19/0.45 => ( setukpairinjL2
% 0.19/0.45 => ( setukpairinjL
% 0.19/0.45 => ( setukpairinjR11
% 0.19/0.45 => ( setukpairinjR12
% 0.19/0.45 => ( setukpairinjR1
% 0.19/0.45 => ( upairequniteq
% 0.19/0.45 => ( setukpairinjR2
% 0.19/0.45 => ( setukpairinjR
% 0.19/0.45 => ( ksndsingleton
% 0.19/0.45 => ( ksndpairEq
% 0.19/0.45 => ( kpairsurjEq
% 0.19/0.45 => ( cartprodsndin
% 0.19/0.45 => ( cartprodpairmemEL
% 0.19/0.45 => ( cartprodpairmemER
% 0.19/0.45 => ( cartprodmempaircEq
% 0.19/0.45 => ( cartprodfstpairEq
% 0.19/0.45 => ( cartprodsndpairEq
% 0.19/0.45 => ( cartprodpairsurjEq
% 0.19/0.45 => ( dpsetconstrI
% 0.19/0.45 => ( dpsetconstrSub
% 0.19/0.45 => ( setOfPairsIsBReln
% 0.19/0.45 => ( dpsetconstrERa
% 0.19/0.45 => ( dpsetconstrEL1
% 0.19/0.45 => ( dpsetconstrEL2
% 0.19/0.45 => ( dpsetconstrER
% 0.19/0.45 => ( funcImageSingleton
% 0.19/0.45 => ( apProp
% 0.19/0.45 => ( app
% 0.19/0.45 => ( infuncsetfunc
% 0.19/0.45 => ( ap2p
% 0.19/0.45 => ( funcinfuncset
% 0.19/0.45 => ( lamProp
% 0.19/0.45 => ( lamp
% 0.19/0.45 => ( lam2p
% 0.19/0.45 => ( brelnall1
% 0.19/0.45 => ( brelnall2
% 0.19/0.45 => ( ex1E2
% 0.19/0.45 => ( funcGraphProp1
% 0.19/0.45 => ( funcGraphProp3
% 0.19/0.45 => ( funcGraphProp2
% 0.19/0.45 => ( funcextLem
% 0.19/0.45 => ( funcGraphProp4
% 0.19/0.45 => ( subbreln
% 0.19/0.45 => ( eqbreln
% 0.19/0.45 => ( funcext
% 0.19/0.45 => ( funcext2
% 0.19/0.45 => ( ap2apEq1
% 0.19/0.45 => ( ap2apEq2
% 0.19/0.45 => ( beta1
% 0.19/0.45 => ( eta1
% 0.19/0.45 => ( lam2lamEq
% 0.19/0.45 => ( beta2
% 0.19/0.45 => ( eta2
% 0.19/0.45 => ( iffalseProp1
% 0.19/0.45 => ( iffalseProp2
% 0.19/0.45 => ( iftrueProp1
% 0.19/0.45 => ( iftrueProp2
% 0.19/0.45 => ( ifSingleton
% 0.19/0.45 => ( ifp
% 0.19/0.45 => ( theeq
% 0.19/0.45 => ( iftrue
% 0.19/0.45 => ( iffalse
% 0.19/0.45 => ( iftrueorfalse
% 0.19/0.45 => ( binintersectT_lem
% 0.19/0.45 => ( binunionT_lem
% 0.19/0.45 => ( powersetT_lem
% 0.19/0.45 => ( setminusT_lem
% 0.19/0.45 => ( complementT_lem
% 0.19/0.45 => ( setextT
% 0.19/0.45 => ( subsetTI
% 0.19/0.45 => ( powersetTI1
% 0.19/0.45 => ( powersetTE1
% 0.19/0.45 => ( complementTI1
% 0.19/0.45 => ( complementTE1
% 0.19/0.45 => ( binintersectTELcontra
% 0.19/0.45 => ( binintersectTERcontra
% 0.19/0.45 => ! [A: $i,X: $i] :
% 0.19/0.45 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.45 => ! [Y: $i] :
% 0.19/0.45 ( ( in @ Y @ ( powerset @ A ) )
% 0.19/0.45 => ! [Xx: $i] :
% 0.19/0.45 ( ( in @ Xx @ A )
% 0.19/0.45 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.19/0.45 => ( ( in @ Xx @ Y )
% 0.19/0.45 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 2.46/1.47 ---- Embedded in THF ---
% 2.46/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.46/1.48 %%% Generated on Tue Feb 24 12:32:17 EST 2026
% 2.46/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.46/1.48 %%% Logic specification used:
% 2.46/1.48 %%% thf(spec, logic, $$dhol).
% 2.46/1.48
% 2.46/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.BaQAZpWnWT/DTF2DTF13872.p
% See solution above
% 2.46/1.48 ------------------------
% 2.74/1.53 ---- Cleaned THF ---
% 2.74/1.53 thf(in_type,type,
% 2.74/1.53 in: $i > $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(exu_type,type,
% 2.74/1.53 exu: ( $i > $o ) > $o ).
% 2.74/1.53
% 2.74/1.53 thf(exu,definition,
% 2.74/1.53 ( exu
% 2.74/1.53 = ( ^ [Xphi: $i > $o] :
% 2.74/1.53 ? [Xx: $i] :
% 2.74/1.53 ( ( Xphi @ Xx )
% 2.74/1.53 & ! [Xy: $i] :
% 2.74/1.53 ( ( Xphi @ Xy )
% 2.74/1.53 => ( Xx = Xy ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setextAx_type,type,
% 2.74/1.53 setextAx: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setextAx,definition,
% 2.74/1.53 ( setextAx
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 <=> ( in @ Xx @ B ) )
% 2.74/1.53 => ( A = B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(emptyset_type,type,
% 2.74/1.53 emptyset: $i ).
% 2.74/1.53
% 2.74/1.53 thf(emptysetAx_type,type,
% 2.74/1.53 emptysetAx: $o ).
% 2.74/1.53
% 2.74/1.53 thf(emptysetAx,definition,
% 2.74/1.53 ( emptysetAx
% 2.74/1.53 = ( ! [Xx: $i] :
% 2.74/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoin_type,type,
% 2.74/1.53 setadjoin: $i > $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinAx_type,type,
% 2.74/1.53 setadjoinAx: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinAx,definition,
% 2.74/1.53 ( setadjoinAx
% 2.74/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.74/1.53 <=> ( ( Xy = Xx )
% 2.74/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(powerset_type,type,
% 2.74/1.53 powerset: $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(powersetAx_type,type,
% 2.74/1.53 powersetAx: $o ).
% 2.74/1.53
% 2.74/1.53 thf(powersetAx,definition,
% 2.74/1.53 ( powersetAx
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.74/1.53 <=> ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ B )
% 2.74/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setunion_type,type,
% 2.74/1.53 setunion: $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(setunionAx_type,type,
% 2.74/1.53 setunionAx: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setunionAx,definition,
% 2.74/1.53 ( setunionAx
% 2.74/1.53 = ( ! [A: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.74/1.53 <=> ? [B: $i] :
% 2.74/1.53 ( ( in @ Xx @ B )
% 2.74/1.53 & ( in @ B @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(omega_type,type,
% 2.74/1.53 omega: $i ).
% 2.74/1.53
% 2.74/1.53 thf(omega0Ax_type,type,
% 2.74/1.53 omega0Ax: $o ).
% 2.74/1.53
% 2.74/1.53 thf(omega0Ax,definition,
% 2.74/1.53 ( omega0Ax
% 2.74/1.53 = ( in @ emptyset @ omega ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(omegaSAx_type,type,
% 2.74/1.53 omegaSAx: $o ).
% 2.74/1.53
% 2.74/1.53 thf(omegaSAx,definition,
% 2.74/1.53 ( omegaSAx
% 2.74/1.53 = ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ omega )
% 2.74/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(omegaIndAx_type,type,
% 2.74/1.53 omegaIndAx: $o ).
% 2.74/1.53
% 2.74/1.53 thf(omegaIndAx,definition,
% 2.74/1.53 ( omegaIndAx
% 2.74/1.53 = ( ! [A: $i] :
% 2.74/1.53 ( ( ( in @ emptyset @ A )
% 2.74/1.53 & ! [Xx: $i] :
% 2.74/1.53 ( ( ( in @ Xx @ omega )
% 2.74/1.53 & ( in @ Xx @ A ) )
% 2.74/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ omega )
% 2.74/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(replAx_type,type,
% 2.74/1.53 replAx: $o ).
% 2.74/1.53
% 2.74/1.53 thf(replAx,definition,
% 2.74/1.53 ( replAx
% 2.74/1.53 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( exu
% 2.74/1.53 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.74/1.53 => ? [B: $i] :
% 2.74/1.53 ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ B )
% 2.74/1.53 <=> ? [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(foundationAx_type,type,
% 2.74/1.53 foundationAx: $o ).
% 2.74/1.53
% 2.74/1.53 thf(foundationAx,definition,
% 2.74/1.53 ( foundationAx
% 2.74/1.53 = ( ! [A: $i] :
% 2.74/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.74/1.53 => ? [B: $i] :
% 2.74/1.53 ( ( in @ B @ A )
% 2.74/1.53 & ~ ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ B )
% 2.74/1.53 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(wellorderingAx_type,type,
% 2.74/1.53 wellorderingAx: $o ).
% 2.74/1.53
% 2.74/1.53 thf(wellorderingAx,definition,
% 2.74/1.53 ( wellorderingAx
% 2.74/1.53 = ( ! [A: $i] :
% 2.74/1.53 ? [B: $i] :
% 2.74/1.53 ( ! [C: $i] :
% 2.74/1.53 ( ( in @ C @ B )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ C )
% 2.74/1.53 => ( in @ Xx @ A ) ) )
% 2.74/1.53 & ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( ( in @ Xx @ A )
% 2.74/1.53 & ( in @ Xy @ A ) )
% 2.74/1.53 => ( ! [C: $i] :
% 2.74/1.53 ( ( in @ C @ B )
% 2.74/1.53 => ( ( in @ Xx @ C )
% 2.74/1.53 <=> ( in @ Xy @ C ) ) )
% 2.74/1.53 => ( Xx = Xy ) ) )
% 2.74/1.53 & ! [C: $i,D: $i] :
% 2.74/1.53 ( ( ( in @ C @ B )
% 2.74/1.53 & ( in @ D @ B ) )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ C )
% 2.74/1.53 => ( in @ Xx @ D ) )
% 2.74/1.53 | ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ D )
% 2.74/1.53 => ( in @ Xx @ C ) ) ) )
% 2.74/1.53 & ! [C: $i] :
% 2.74/1.53 ( ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ C )
% 2.74/1.53 => ( in @ Xx @ A ) )
% 2.74/1.53 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.74/1.53 => ? [D: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ D @ B )
% 2.74/1.53 & ( in @ Xx @ C )
% 2.74/1.53 & ~ ? [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ D )
% 2.74/1.53 & ( in @ Xy @ C ) )
% 2.74/1.53 & ! [E: $i] :
% 2.74/1.53 ( ( in @ E @ B )
% 2.74/1.53 => ( ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ E )
% 2.74/1.53 => ( in @ Xy @ D ) )
% 2.74/1.53 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(descr_type,type,
% 2.74/1.53 descr: ( $i > $o ) > $i ).
% 2.74/1.53
% 2.74/1.53 thf(descrp_type,type,
% 2.74/1.53 descrp: $o ).
% 2.74/1.53
% 2.74/1.53 thf(descrp,definition,
% 2.74/1.53 ( descrp
% 2.74/1.53 = ( ! [Xphi: $i > $o] :
% 2.74/1.53 ( ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 => ( Xphi
% 2.74/1.53 @ ( descr
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(dsetconstr_type,type,
% 2.74/1.53 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.74/1.53
% 2.74/1.53 thf(dsetconstrI_type,type,
% 2.74/1.53 dsetconstrI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(dsetconstrI,definition,
% 2.74/1.53 ( dsetconstrI
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( Xphi @ Xx )
% 2.74/1.53 => ( in @ Xx
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(dsetconstrEL_type,type,
% 2.74/1.53 dsetconstrEL: $o ).
% 2.74/1.53
% 2.74/1.53 thf(dsetconstrEL,definition,
% 2.74/1.53 ( dsetconstrEL
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.74/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(dsetconstrER_type,type,
% 2.74/1.53 dsetconstrER: $o ).
% 2.74/1.53
% 2.74/1.53 thf(dsetconstrER,definition,
% 2.74/1.53 ( dsetconstrER
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.74/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(exuE1_type,type,
% 2.74/1.53 exuE1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(exuE1,definition,
% 2.74/1.53 ( exuE1
% 2.74/1.53 = ( ! [Xphi: $i > $o] :
% 2.74/1.53 ( ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 => ? [Xx: $i] :
% 2.74/1.53 ( ( Xphi @ Xx )
% 2.74/1.53 & ! [Xy: $i] :
% 2.74/1.53 ( ( Xphi @ Xy )
% 2.74/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(prop2set_type,type,
% 2.74/1.53 prop2set: $o > $i ).
% 2.74/1.53
% 2.74/1.53 thf(prop2setE_type,type,
% 2.74/1.53 prop2setE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(prop2setE,definition,
% 2.74/1.53 ( prop2setE
% 2.74/1.53 = ( ! [Xphi: $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.74/1.53 => Xphi ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(emptysetE_type,type,
% 2.74/1.53 emptysetE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(emptysetE,definition,
% 2.74/1.53 ( emptysetE
% 2.74/1.53 = ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ emptyset )
% 2.74/1.53 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(emptysetimpfalse_type,type,
% 2.74/1.53 emptysetimpfalse: $o ).
% 2.74/1.53
% 2.74/1.53 thf(emptysetimpfalse,definition,
% 2.74/1.53 ( emptysetimpfalse
% 2.74/1.53 = ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ emptyset )
% 2.74/1.53 => $false ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(notinemptyset_type,type,
% 2.74/1.53 notinemptyset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(notinemptyset,definition,
% 2.74/1.53 ( notinemptyset
% 2.74/1.53 = ( ! [Xx: $i] :
% 2.74/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(exuE3e_type,type,
% 2.74/1.53 exuE3e: $o ).
% 2.74/1.53
% 2.74/1.53 thf(exuE3e,definition,
% 2.74/1.53 ( exuE3e
% 2.74/1.53 = ( ! [Xphi: $i > $o] :
% 2.74/1.53 ( ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setext_type,type,
% 2.74/1.53 setext: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setext,definition,
% 2.74/1.53 ( setext
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ Xx @ B ) )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ B )
% 2.74/1.53 => ( in @ Xx @ A ) )
% 2.74/1.53 => ( A = B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(emptyI_type,type,
% 2.74/1.53 emptyI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(emptyI,definition,
% 2.74/1.53 ( emptyI
% 2.74/1.53 = ( ! [A: $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ~ ( in @ Xx @ A )
% 2.74/1.53 => ( A = emptyset ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(noeltsimpempty_type,type,
% 2.74/1.53 noeltsimpempty: $o ).
% 2.74/1.53
% 2.74/1.53 thf(noeltsimpempty,definition,
% 2.74/1.53 ( noeltsimpempty
% 2.74/1.53 = ( ! [A: $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ~ ( in @ Xx @ A )
% 2.74/1.53 => ( A = emptyset ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setbeta_type,type,
% 2.74/1.53 setbeta: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setbeta,definition,
% 2.74/1.53 ( setbeta
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ Xx
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.74/1.53 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(nonempty_type,type,
% 2.74/1.53 nonempty: $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(nonempty,definition,
% 2.74/1.53 ( nonempty
% 2.74/1.53 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(nonemptyE1_type,type,
% 2.74/1.53 nonemptyE1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(nonemptyE1,definition,
% 2.74/1.53 ( nonemptyE1
% 2.74/1.53 = ( ! [A: $i] :
% 2.74/1.53 ( ( nonempty @ A )
% 2.74/1.53 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(nonemptyI_type,type,
% 2.74/1.53 nonemptyI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(nonemptyI,definition,
% 2.74/1.53 ( nonemptyI
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( Xphi @ Xx )
% 2.74/1.53 => ( nonempty
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(nonemptyI1_type,type,
% 2.74/1.53 nonemptyI1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(nonemptyI1,definition,
% 2.74/1.53 ( nonemptyI1
% 2.74/1.53 = ( ! [A: $i] :
% 2.74/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.74/1.53 => ( nonempty @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinIL_type,type,
% 2.74/1.53 setadjoinIL: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinIL,definition,
% 2.74/1.53 ( setadjoinIL
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(emptyinunitempty_type,type,
% 2.74/1.53 emptyinunitempty: $o ).
% 2.74/1.53
% 2.74/1.53 thf(emptyinunitempty,definition,
% 2.74/1.53 ( emptyinunitempty
% 2.74/1.53 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinIR_type,type,
% 2.74/1.53 setadjoinIR: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinIR,definition,
% 2.74/1.53 ( setadjoinIR
% 2.74/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinE_type,type,
% 2.74/1.53 setadjoinE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinE,definition,
% 2.74/1.53 ( setadjoinE
% 2.74/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.74/1.53 => ! [Xphi: $o] :
% 2.74/1.53 ( ( ( Xy = Xx )
% 2.74/1.53 => Xphi )
% 2.74/1.53 => ( ( ( in @ Xy @ A )
% 2.74/1.53 => Xphi )
% 2.74/1.53 => Xphi ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinOr_type,type,
% 2.74/1.53 setadjoinOr: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinOr,definition,
% 2.74/1.53 ( setadjoinOr
% 2.74/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.74/1.53 => ( ( Xy = Xx )
% 2.74/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setoftrueEq_type,type,
% 2.74/1.53 setoftrueEq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setoftrueEq,definition,
% 2.74/1.53 ( setoftrueEq
% 2.74/1.53 = ( ! [A: $i] :
% 2.74/1.53 ( ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xx: $i] : $true )
% 2.74/1.53 = A ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(powersetI_type,type,
% 2.74/1.53 powersetI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(powersetI,definition,
% 2.74/1.53 ( powersetI
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ B )
% 2.74/1.53 => ( in @ Xx @ A ) )
% 2.74/1.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(emptyinPowerset_type,type,
% 2.74/1.53 emptyinPowerset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(emptyinPowerset,definition,
% 2.74/1.53 ( emptyinPowerset
% 2.74/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(emptyInPowerset_type,type,
% 2.74/1.53 emptyInPowerset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(emptyInPowerset,definition,
% 2.74/1.53 ( emptyInPowerset
% 2.74/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(powersetE_type,type,
% 2.74/1.53 powersetE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(powersetE,definition,
% 2.74/1.53 ( powersetE
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.74/1.53 => ( ( in @ Xx @ B )
% 2.74/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setunionI_type,type,
% 2.74/1.53 setunionI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setunionI,definition,
% 2.74/1.53 ( setunionI
% 2.74/1.53 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.74/1.53 ( ( in @ Xx @ B )
% 2.74/1.53 => ( ( in @ B @ A )
% 2.74/1.53 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setunionE_type,type,
% 2.74/1.53 setunionE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setunionE,definition,
% 2.74/1.53 ( setunionE
% 2.74/1.53 = ( ! [A: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.74/1.53 => ! [Xphi: $o] :
% 2.74/1.53 ( ! [B: $i] :
% 2.74/1.53 ( ( in @ Xx @ B )
% 2.74/1.53 => ( ( in @ B @ A )
% 2.74/1.53 => Xphi ) )
% 2.74/1.53 => Xphi ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subPowSU_type,type,
% 2.74/1.53 subPowSU: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subPowSU,definition,
% 2.74/1.53 ( subPowSU
% 2.74/1.53 = ( ! [A: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(exuE2_type,type,
% 2.74/1.53 exuE2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(exuE2,definition,
% 2.74/1.53 ( exuE2
% 2.74/1.53 = ( ! [Xphi: $i > $o] :
% 2.74/1.53 ( ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 => ? [Xx: $i] :
% 2.74/1.53 ! [Xy: $i] :
% 2.74/1.53 ( ( Xphi @ Xy )
% 2.74/1.53 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(nonemptyImpWitness_type,type,
% 2.74/1.53 nonemptyImpWitness: $o ).
% 2.74/1.53
% 2.74/1.53 thf(nonemptyImpWitness,definition,
% 2.74/1.53 ( nonemptyImpWitness
% 2.74/1.53 = ( ! [A: $i] :
% 2.74/1.53 ( ( nonempty @ A )
% 2.74/1.53 => ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & $true ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(uniqinunit_type,type,
% 2.74/1.53 uniqinunit: $o ).
% 2.74/1.53
% 2.74/1.53 thf(uniqinunit,definition,
% 2.74/1.53 ( uniqinunit
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.74/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(notinsingleton_type,type,
% 2.74/1.53 notinsingleton: $o ).
% 2.74/1.53
% 2.74/1.53 thf(notinsingleton,definition,
% 2.74/1.53 ( notinsingleton
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xx != Xy )
% 2.74/1.53 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(eqinunit_type,type,
% 2.74/1.53 eqinunit: $o ).
% 2.74/1.53
% 2.74/1.53 thf(eqinunit,definition,
% 2.74/1.53 ( eqinunit
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xx = Xy )
% 2.74/1.53 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(singletonsswitch_type,type,
% 2.74/1.53 singletonsswitch: $o ).
% 2.74/1.53
% 2.74/1.53 thf(singletonsswitch,definition,
% 2.74/1.53 ( singletonsswitch
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.74/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(upairsetE_type,type,
% 2.74/1.53 upairsetE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(upairsetE,definition,
% 2.74/1.53 ( upairsetE
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.74/1.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.74/1.53 => ( ( Xz = Xx )
% 2.74/1.53 | ( Xz = Xy ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(upairsetIL_type,type,
% 2.74/1.53 upairsetIL: $o ).
% 2.74/1.53
% 2.74/1.53 thf(upairsetIL,definition,
% 2.74/1.53 ( upairsetIL
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(upairsetIR_type,type,
% 2.74/1.53 upairsetIR: $o ).
% 2.74/1.53
% 2.74/1.53 thf(upairsetIR,definition,
% 2.74/1.53 ( upairsetIR
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(emptyE1_type,type,
% 2.74/1.53 emptyE1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(emptyE1,definition,
% 2.74/1.53 ( emptyE1
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ( Xphi @ Xx ) )
% 2.74/1.53 => ( ( ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 = emptyset )
% 2.74/1.53 => $false ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(vacuousDall_type,type,
% 2.74/1.53 vacuousDall: $o ).
% 2.74/1.53
% 2.74/1.53 thf(vacuousDall,definition,
% 2.74/1.53 ( vacuousDall
% 2.74/1.53 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ emptyset )
% 2.74/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(quantDeMorgan1_type,type,
% 2.74/1.53 quantDeMorgan1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(quantDeMorgan1,definition,
% 2.74/1.53 ( quantDeMorgan1
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ~ ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( Xphi @ Xx ) )
% 2.74/1.53 => ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(quantDeMorgan2_type,type,
% 2.74/1.53 quantDeMorgan2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(quantDeMorgan2,definition,
% 2.74/1.53 ( quantDeMorgan2
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ~ ( Xphi @ Xx ) )
% 2.74/1.53 => ~ ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(quantDeMorgan3_type,type,
% 2.74/1.53 quantDeMorgan3: $o ).
% 2.74/1.53
% 2.74/1.53 thf(quantDeMorgan3,definition,
% 2.74/1.53 ( quantDeMorgan3
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ~ ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ( Xphi @ Xx ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(quantDeMorgan4_type,type,
% 2.74/1.53 quantDeMorgan4: $o ).
% 2.74/1.53
% 2.74/1.53 thf(quantDeMorgan4,definition,
% 2.74/1.53 ( quantDeMorgan4
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ~ ( Xphi @ Xx ) )
% 2.74/1.53 => ~ ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(prop2setI_type,type,
% 2.74/1.53 prop2setI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(prop2setI,definition,
% 2.74/1.53 ( prop2setI
% 2.74/1.53 = ( ! [Xphi: $o] :
% 2.74/1.53 ( Xphi
% 2.74/1.53 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(set2prop_type,type,
% 2.74/1.53 set2prop: $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(prop2set2propI_type,type,
% 2.74/1.53 prop2set2propI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(prop2set2propI,definition,
% 2.74/1.53 ( prop2set2propI
% 2.74/1.53 = ( ! [Xphi: $o] :
% 2.74/1.53 ( Xphi
% 2.74/1.53 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(notdexE_type,type,
% 2.74/1.53 notdexE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(notdexE,definition,
% 2.74/1.53 ( notdexE
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ~ ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ( Xphi @ Xx ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(notdallE_type,type,
% 2.74/1.53 notdallE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(notdallE,definition,
% 2.74/1.53 ( notdallE
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ~ ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( Xphi @ Xx ) )
% 2.74/1.53 => ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(exuI1_type,type,
% 2.74/1.53 exuI1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(exuI1,definition,
% 2.74/1.53 ( exuI1
% 2.74/1.53 = ( ! [Xphi: $i > $o] :
% 2.74/1.53 ( ? [Xx: $i] :
% 2.74/1.53 ( ( Xphi @ Xx )
% 2.74/1.53 & ! [Xy: $i] :
% 2.74/1.53 ( ( Xphi @ Xy )
% 2.74/1.53 => ( Xx = Xy ) ) )
% 2.74/1.53 => ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(exuI3_type,type,
% 2.74/1.53 exuI3: $o ).
% 2.74/1.53
% 2.74/1.53 thf(exuI3,definition,
% 2.74/1.53 ( exuI3
% 2.74/1.53 = ( ! [Xphi: $i > $o] :
% 2.74/1.53 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.74/1.53 => ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xphi @ Xx )
% 2.74/1.53 => ( ( Xphi @ Xy )
% 2.74/1.53 => ( Xx = Xy ) ) )
% 2.74/1.53 => ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(exuI2_type,type,
% 2.74/1.53 exuI2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(exuI2,definition,
% 2.74/1.53 ( exuI2
% 2.74/1.53 = ( ! [Xphi: $i > $o] :
% 2.74/1.53 ( ? [Xx: $i] :
% 2.74/1.53 ! [Xy: $i] :
% 2.74/1.53 ( ( Xphi @ Xy )
% 2.74/1.53 <=> ( Xy = Xx ) )
% 2.74/1.53 => ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(inCongP_type,type,
% 2.74/1.53 inCongP: $o ).
% 2.74/1.53
% 2.74/1.53 thf(inCongP,definition,
% 2.74/1.53 ( inCongP
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( A = B )
% 2.74/1.53 => ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xx = Xy )
% 2.74/1.53 => ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(in__Cong_type,type,
% 2.74/1.53 in__Cong: $o ).
% 2.74/1.53
% 2.74/1.53 thf(in__Cong,definition,
% 2.74/1.53 ( in__Cong
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( A = B )
% 2.74/1.53 => ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xx = Xy )
% 2.74/1.53 => ( ( in @ Xx @ A )
% 2.74/1.53 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(exuE3u_type,type,
% 2.74/1.53 exuE3u: $o ).
% 2.74/1.53
% 2.74/1.53 thf(exuE3u,definition,
% 2.74/1.53 ( exuE3u
% 2.74/1.53 = ( ! [Xphi: $i > $o] :
% 2.74/1.53 ( ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 => ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xphi @ Xx )
% 2.74/1.53 => ( ( Xphi @ Xy )
% 2.74/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(exu__Cong_type,type,
% 2.74/1.53 exu__Cong: $o ).
% 2.74/1.53
% 2.74/1.53 thf(exu__Cong,definition,
% 2.74/1.53 ( exu__Cong
% 2.74/1.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.74/1.53 ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xx = Xy )
% 2.74/1.53 => ( ( Xphi @ Xx )
% 2.74/1.53 <=> ( Xpsi @ Xy ) ) )
% 2.74/1.53 => ( ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 <=> ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(emptyset__Cong_type,type,
% 2.74/1.53 emptyset__Cong: $o ).
% 2.74/1.53
% 2.74/1.53 thf(emptyset__Cong,definition,
% 2.74/1.53 ( emptyset__Cong
% 2.74/1.53 = ( emptyset = emptyset ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoin__Cong_type,type,
% 2.74/1.53 setadjoin__Cong: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoin__Cong,definition,
% 2.74/1.53 ( setadjoin__Cong
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xx = Xy )
% 2.74/1.53 => ! [Xz: $i,Xu: $i] :
% 2.74/1.53 ( ( Xz = Xu )
% 2.74/1.53 => ( ( setadjoin @ Xx @ Xz )
% 2.74/1.53 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(powerset__Cong_type,type,
% 2.74/1.53 powerset__Cong: $o ).
% 2.74/1.53
% 2.74/1.53 thf(powerset__Cong,definition,
% 2.74/1.53 ( powerset__Cong
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( A = B )
% 2.74/1.53 => ( ( powerset @ A )
% 2.74/1.53 = ( powerset @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setunion__Cong_type,type,
% 2.74/1.53 setunion__Cong: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setunion__Cong,definition,
% 2.74/1.53 ( setunion__Cong
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( A = B )
% 2.74/1.53 => ( ( setunion @ A )
% 2.74/1.53 = ( setunion @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(omega__Cong_type,type,
% 2.74/1.53 omega__Cong: $o ).
% 2.74/1.53
% 2.74/1.53 thf(omega__Cong,definition,
% 2.74/1.53 ( omega__Cong
% 2.74/1.53 = ( omega = omega ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(exuEu_type,type,
% 2.74/1.53 exuEu: $o ).
% 2.74/1.53
% 2.74/1.53 thf(exuEu,definition,
% 2.74/1.53 ( exuEu
% 2.74/1.53 = ( ! [Xphi: $i > $o] :
% 2.74/1.53 ( ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 => ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xphi @ Xx )
% 2.74/1.53 => ( ( Xphi @ Xy )
% 2.74/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(descr__Cong_type,type,
% 2.74/1.53 descr__Cong: $o ).
% 2.74/1.53
% 2.74/1.53 thf(descr__Cong,definition,
% 2.74/1.53 ( descr__Cong
% 2.74/1.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.74/1.53 ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xx = Xy )
% 2.74/1.53 => ( ( Xphi @ Xx )
% 2.74/1.53 <=> ( Xpsi @ Xy ) ) )
% 2.74/1.53 => ( ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 => ( ( exu
% 2.74/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.74/1.53 => ( ( descr
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 = ( descr
% 2.74/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(dsetconstr__Cong_type,type,
% 2.74/1.53 dsetconstr__Cong: $o ).
% 2.74/1.53
% 2.74/1.53 thf(dsetconstr__Cong,definition,
% 2.74/1.53 ( dsetconstr__Cong
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( A = B )
% 2.74/1.53 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( Xx = Xy )
% 2.74/1.53 => ( ( Xphi @ Xx )
% 2.74/1.53 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.74/1.53 => ( ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 = ( dsetconstr @ B
% 2.74/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subset_type,type,
% 2.74/1.53 subset: $i > $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(disjoint_type,type,
% 2.74/1.53 disjoint: $i > $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(setsmeet_type,type,
% 2.74/1.53 setsmeet: $i > $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(subsetI1_type,type,
% 2.74/1.53 subsetI1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subsetI1,definition,
% 2.74/1.53 ( subsetI1
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ Xx @ B ) )
% 2.74/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(eqimpsubset2_type,type,
% 2.74/1.53 eqimpsubset2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(eqimpsubset2,definition,
% 2.74/1.53 ( eqimpsubset2
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( A = B )
% 2.74/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(eqimpsubset1_type,type,
% 2.74/1.53 eqimpsubset1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(eqimpsubset1,definition,
% 2.74/1.53 ( eqimpsubset1
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( A = B )
% 2.74/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subsetI2_type,type,
% 2.74/1.53 subsetI2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subsetI2,definition,
% 2.74/1.53 ( subsetI2
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ Xx @ B ) )
% 2.74/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(emptysetsubset_type,type,
% 2.74/1.53 emptysetsubset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(emptysetsubset,definition,
% 2.74/1.53 ( emptysetsubset
% 2.74/1.53 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subsetE_type,type,
% 2.74/1.53 subsetE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subsetE,definition,
% 2.74/1.53 ( subsetE
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( subset @ A @ B )
% 2.74/1.53 => ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subsetE2_type,type,
% 2.74/1.53 subsetE2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subsetE2,definition,
% 2.74/1.53 ( subsetE2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( subset @ A @ B )
% 2.74/1.53 => ( ~ ( in @ Xx @ B )
% 2.74/1.53 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(notsubsetI_type,type,
% 2.74/1.53 notsubsetI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(notsubsetI,definition,
% 2.74/1.53 ( notsubsetI
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ~ ( in @ Xx @ B )
% 2.74/1.53 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(notequalI1_type,type,
% 2.74/1.53 notequalI1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(notequalI1,definition,
% 2.74/1.53 ( notequalI1
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ~ ( subset @ A @ B )
% 2.74/1.53 => ( A != B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(notequalI2_type,type,
% 2.74/1.53 notequalI2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(notequalI2,definition,
% 2.74/1.53 ( notequalI2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ~ ( in @ Xx @ B )
% 2.74/1.53 => ( A != B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subsetRefl_type,type,
% 2.74/1.53 subsetRefl: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subsetRefl,definition,
% 2.74/1.53 ( subsetRefl
% 2.74/1.53 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subsetTrans_type,type,
% 2.74/1.53 subsetTrans: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subsetTrans,definition,
% 2.74/1.53 ( subsetTrans
% 2.74/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.74/1.53 ( ( subset @ A @ B )
% 2.74/1.53 => ( ( subset @ B @ C )
% 2.74/1.53 => ( subset @ A @ C ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinSub_type,type,
% 2.74/1.53 setadjoinSub: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinSub,definition,
% 2.74/1.53 ( setadjoinSub
% 2.74/1.53 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinSub2_type,type,
% 2.74/1.53 setadjoinSub2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setadjoinSub2,definition,
% 2.74/1.53 ( setadjoinSub2
% 2.74/1.53 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.74/1.53 ( ( subset @ A @ B )
% 2.74/1.53 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subset2powerset_type,type,
% 2.74/1.53 subset2powerset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subset2powerset,definition,
% 2.74/1.53 ( subset2powerset
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( subset @ A @ B )
% 2.74/1.53 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setextsub_type,type,
% 2.74/1.53 setextsub: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setextsub,definition,
% 2.74/1.53 ( setextsub
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( subset @ A @ B )
% 2.74/1.53 => ( ( subset @ B @ A )
% 2.74/1.53 => ( A = B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subsetemptysetimpeq_type,type,
% 2.74/1.53 subsetemptysetimpeq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subsetemptysetimpeq,definition,
% 2.74/1.53 ( subsetemptysetimpeq
% 2.74/1.53 = ( ! [A: $i] :
% 2.74/1.53 ( ( subset @ A @ emptyset )
% 2.74/1.53 => ( A = emptyset ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(powersetI1_type,type,
% 2.74/1.53 powersetI1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(powersetI1,definition,
% 2.74/1.53 ( powersetI1
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( subset @ B @ A )
% 2.74/1.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(powersetE1_type,type,
% 2.74/1.53 powersetE1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(powersetE1,definition,
% 2.74/1.53 ( powersetE1
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.74/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(inPowerset_type,type,
% 2.74/1.53 inPowerset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(inPowerset,definition,
% 2.74/1.53 ( inPowerset
% 2.74/1.53 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(powersetsubset_type,type,
% 2.74/1.53 powersetsubset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(powersetsubset,definition,
% 2.74/1.53 ( powersetsubset
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( subset @ A @ B )
% 2.74/1.53 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(sepInPowerset_type,type,
% 2.74/1.53 sepInPowerset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(sepInPowerset,definition,
% 2.74/1.53 ( sepInPowerset
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( in
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 @ ( powerset @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(sepSubset_type,type,
% 2.74/1.53 sepSubset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(sepSubset,definition,
% 2.74/1.53 ( sepSubset
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( subset
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 @ A ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binunion_type,type,
% 2.74/1.53 binunion: $i > $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(binunionIL_type,type,
% 2.74/1.53 binunionIL: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binunionIL,definition,
% 2.74/1.53 ( binunionIL
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(upairset2IR_type,type,
% 2.74/1.53 upairset2IR: $o ).
% 2.74/1.53
% 2.74/1.53 thf(upairset2IR,definition,
% 2.74/1.53 ( upairset2IR
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binunionIR_type,type,
% 2.74/1.53 binunionIR: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binunionIR,definition,
% 2.74/1.53 ( binunionIR
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ B )
% 2.74/1.53 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binunionEcases_type,type,
% 2.74/1.53 binunionEcases: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binunionEcases,definition,
% 2.74/1.53 ( binunionEcases
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.74/1.53 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.74/1.53 => ( ( ( in @ Xx @ A )
% 2.74/1.53 => Xphi )
% 2.74/1.53 => ( ( ( in @ Xx @ B )
% 2.74/1.53 => Xphi )
% 2.74/1.53 => Xphi ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binunionE_type,type,
% 2.74/1.53 binunionE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binunionE,definition,
% 2.74/1.53 ( binunionE
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.74/1.53 => ( ( in @ Xx @ A )
% 2.74/1.53 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binunionLsub_type,type,
% 2.74/1.53 binunionLsub: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binunionLsub,definition,
% 2.74/1.53 ( binunionLsub
% 2.74/1.53 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binunionRsub_type,type,
% 2.74/1.53 binunionRsub: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binunionRsub,definition,
% 2.74/1.53 ( binunionRsub
% 2.74/1.53 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersect_type,type,
% 2.74/1.53 binintersect: $i > $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectI_type,type,
% 2.74/1.53 binintersectI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectI,definition,
% 2.74/1.53 ( binintersectI
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ Xx @ B )
% 2.74/1.53 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectSubset5_type,type,
% 2.74/1.53 binintersectSubset5: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectSubset5,definition,
% 2.74/1.53 ( binintersectSubset5
% 2.74/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.74/1.53 ( ( subset @ C @ A )
% 2.74/1.53 => ( ( subset @ C @ B )
% 2.74/1.53 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectEL_type,type,
% 2.74/1.53 binintersectEL: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectEL,definition,
% 2.74/1.53 ( binintersectEL
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.74/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectLsub_type,type,
% 2.74/1.53 binintersectLsub: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectLsub,definition,
% 2.74/1.53 ( binintersectLsub
% 2.74/1.53 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectSubset2_type,type,
% 2.74/1.53 binintersectSubset2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectSubset2,definition,
% 2.74/1.53 ( binintersectSubset2
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( subset @ A @ B )
% 2.74/1.53 => ( ( binintersect @ A @ B )
% 2.74/1.53 = A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectSubset3_type,type,
% 2.74/1.53 binintersectSubset3: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectSubset3,definition,
% 2.74/1.53 ( binintersectSubset3
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( ( binintersect @ A @ B )
% 2.74/1.53 = B )
% 2.74/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectER_type,type,
% 2.74/1.53 binintersectER: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectER,definition,
% 2.74/1.53 ( binintersectER
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.74/1.53 => ( in @ Xx @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(disjointsetsI1_type,type,
% 2.74/1.53 disjointsetsI1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(disjointsetsI1,definition,
% 2.74/1.53 ( disjointsetsI1
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ~ ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ( in @ Xx @ B ) )
% 2.74/1.53 => ( ( binintersect @ A @ B )
% 2.74/1.53 = emptyset ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectRsub_type,type,
% 2.74/1.53 binintersectRsub: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectRsub,definition,
% 2.74/1.53 ( binintersectRsub
% 2.74/1.53 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectSubset4_type,type,
% 2.74/1.53 binintersectSubset4: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectSubset4,definition,
% 2.74/1.53 ( binintersectSubset4
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( subset @ B @ A )
% 2.74/1.53 => ( ( binintersect @ A @ B )
% 2.74/1.53 = B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectSubset1_type,type,
% 2.74/1.53 binintersectSubset1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectSubset1,definition,
% 2.74/1.53 ( binintersectSubset1
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( ( binintersect @ A @ B )
% 2.74/1.53 = A )
% 2.74/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(bs114d_type,type,
% 2.74/1.53 bs114d: $o ).
% 2.74/1.53
% 2.74/1.53 thf(bs114d,definition,
% 2.74/1.53 ( bs114d
% 2.74/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.74/1.53 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.74/1.53 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(regular_type,type,
% 2.74/1.53 regular: $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminus_type,type,
% 2.74/1.53 setminus: $i > $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(setminusI_type,type,
% 2.74/1.53 setminusI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusI,definition,
% 2.74/1.53 ( setminusI
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ~ ( in @ Xx @ B )
% 2.74/1.53 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setminusEL_type,type,
% 2.74/1.53 setminusEL: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusEL,definition,
% 2.74/1.53 ( setminusEL
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.74/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setminusER_type,type,
% 2.74/1.53 setminusER: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusER,definition,
% 2.74/1.53 ( setminusER
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.74/1.53 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setminusSubset2_type,type,
% 2.74/1.53 setminusSubset2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusSubset2,definition,
% 2.74/1.53 ( setminusSubset2
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( subset @ A @ B )
% 2.74/1.53 => ( ( setminus @ A @ B )
% 2.74/1.53 = emptyset ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setminusERneg_type,type,
% 2.74/1.53 setminusERneg: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusERneg,definition,
% 2.74/1.53 ( setminusERneg
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.74/1.53 => ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setminusELneg_type,type,
% 2.74/1.53 setminusELneg: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusELneg,definition,
% 2.74/1.53 ( setminusELneg
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.74/1.53 => ( ~ ( in @ Xx @ B )
% 2.74/1.53 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setminusILneg_type,type,
% 2.74/1.53 setminusILneg: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusILneg,definition,
% 2.74/1.53 ( setminusILneg
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ~ ( in @ Xx @ A )
% 2.74/1.53 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setminusIRneg_type,type,
% 2.74/1.53 setminusIRneg: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusIRneg,definition,
% 2.74/1.53 ( setminusIRneg
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ B )
% 2.74/1.53 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setminusLsub_type,type,
% 2.74/1.53 setminusLsub: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusLsub,definition,
% 2.74/1.53 ( setminusLsub
% 2.74/1.53 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setminusSubset1_type,type,
% 2.74/1.53 setminusSubset1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusSubset1,definition,
% 2.74/1.53 ( setminusSubset1
% 2.74/1.53 = ( ! [A: $i,B: $i] :
% 2.74/1.53 ( ( ( setminus @ A @ B )
% 2.74/1.53 = emptyset )
% 2.74/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(symdiff_type,type,
% 2.74/1.53 symdiff: $i > $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(symdiffE_type,type,
% 2.74/1.53 symdiffE: $o ).
% 2.74/1.53
% 2.74/1.53 thf(symdiffE,definition,
% 2.74/1.53 ( symdiffE
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.74/1.53 => ! [Xphi: $o] :
% 2.74/1.53 ( ( ( in @ Xx @ A )
% 2.74/1.53 => ( ~ ( in @ Xx @ B )
% 2.74/1.53 => Xphi ) )
% 2.74/1.53 => ( ( ~ ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ Xx @ B )
% 2.74/1.53 => Xphi ) )
% 2.74/1.53 => Xphi ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(symdiffI1_type,type,
% 2.74/1.53 symdiffI1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(symdiffI1,definition,
% 2.74/1.53 ( symdiffI1
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ~ ( in @ Xx @ B )
% 2.74/1.53 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(symdiffI2_type,type,
% 2.74/1.53 symdiffI2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(symdiffI2,definition,
% 2.74/1.53 ( symdiffI2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ~ ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ Xx @ B )
% 2.74/1.53 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(symdiffIneg1_type,type,
% 2.74/1.53 symdiffIneg1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(symdiffIneg1,definition,
% 2.74/1.53 ( symdiffIneg1
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ Xx @ B )
% 2.74/1.53 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(symdiffIneg2_type,type,
% 2.74/1.53 symdiffIneg2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(symdiffIneg2,definition,
% 2.74/1.53 ( symdiffIneg2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ~ ( in @ Xx @ A )
% 2.74/1.53 => ( ~ ( in @ Xx @ B )
% 2.74/1.53 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(iskpair_type,type,
% 2.74/1.53 iskpair: $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(secondinupair_type,type,
% 2.74/1.53 secondinupair: $o ).
% 2.74/1.53
% 2.74/1.53 thf(secondinupair,definition,
% 2.74/1.53 ( secondinupair
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairIL_type,type,
% 2.74/1.53 setukpairIL: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairIL,definition,
% 2.74/1.53 ( setukpairIL
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairIR_type,type,
% 2.74/1.53 setukpairIR: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairIR,definition,
% 2.74/1.53 ( setukpairIR
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(kpairiskpair_type,type,
% 2.74/1.53 kpairiskpair: $o ).
% 2.74/1.53
% 2.74/1.53 thf(kpairiskpair,definition,
% 2.74/1.53 ( kpairiskpair
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(kpair_type,type,
% 2.74/1.53 kpair: $i > $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(kpairp_type,type,
% 2.74/1.53 kpairp: $o ).
% 2.74/1.53
% 2.74/1.53 thf(kpairp,definition,
% 2.74/1.53 ( kpairp
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprod_type,type,
% 2.74/1.53 cartprod: $i > $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(singletonsubset_type,type,
% 2.74/1.53 singletonsubset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(singletonsubset,definition,
% 2.74/1.53 ( singletonsubset
% 2.74/1.53 = ( ! [A: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(singletoninpowerset_type,type,
% 2.74/1.53 singletoninpowerset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(singletoninpowerset,definition,
% 2.74/1.53 ( singletoninpowerset
% 2.74/1.53 = ( ! [A: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(singletoninpowunion_type,type,
% 2.74/1.53 singletoninpowunion: $o ).
% 2.74/1.53
% 2.74/1.53 thf(singletoninpowunion,definition,
% 2.74/1.53 ( singletoninpowunion
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(upairset2E_type,type,
% 2.74/1.53 upairset2E: $o ).
% 2.74/1.53
% 2.74/1.53 thf(upairset2E,definition,
% 2.74/1.53 ( upairset2E
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.74/1.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.74/1.53 => ( ( Xz = Xx )
% 2.74/1.53 | ( Xz = Xy ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(upairsubunion_type,type,
% 2.74/1.53 upairsubunion: $o ).
% 2.74/1.53
% 2.74/1.53 thf(upairsubunion,definition,
% 2.74/1.53 ( upairsubunion
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(upairinpowunion_type,type,
% 2.74/1.53 upairinpowunion: $o ).
% 2.74/1.53
% 2.74/1.53 thf(upairinpowunion,definition,
% 2.74/1.53 ( upairinpowunion
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ubforcartprodlem1_type,type,
% 2.74/1.53 ubforcartprodlem1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ubforcartprodlem1,definition,
% 2.74/1.53 ( ubforcartprodlem1
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ubforcartprodlem2_type,type,
% 2.74/1.53 ubforcartprodlem2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ubforcartprodlem2,definition,
% 2.74/1.53 ( ubforcartprodlem2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ubforcartprodlem3_type,type,
% 2.74/1.53 ubforcartprodlem3: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ubforcartprodlem3,definition,
% 2.74/1.53 ( ubforcartprodlem3
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodpairin_type,type,
% 2.74/1.53 cartprodpairin: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodpairin,definition,
% 2.74/1.53 ( cartprodpairin
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodmempair1_type,type,
% 2.74/1.53 cartprodmempair1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodmempair1,definition,
% 2.74/1.53 ( cartprodmempair1
% 2.74/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.74/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.74/1.53 => ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ? [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 & ( Xu
% 2.74/1.53 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodmempair_type,type,
% 2.74/1.53 cartprodmempair: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodmempair,definition,
% 2.74/1.53 ( cartprodmempair
% 2.74/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.74/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.74/1.53 => ( iskpair @ Xu ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setunionE2_type,type,
% 2.74/1.53 setunionE2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setunionE2,definition,
% 2.74/1.53 ( setunionE2
% 2.74/1.53 = ( ! [A: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.74/1.53 => ? [X: $i] :
% 2.74/1.53 ( ( in @ X @ A )
% 2.74/1.53 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setunionsingleton1_type,type,
% 2.74/1.53 setunionsingleton1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setunionsingleton1,definition,
% 2.74/1.53 ( setunionsingleton1
% 2.74/1.53 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setunionsingleton2_type,type,
% 2.74/1.53 setunionsingleton2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setunionsingleton2,definition,
% 2.74/1.53 ( setunionsingleton2
% 2.74/1.53 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setunionsingleton_type,type,
% 2.74/1.53 setunionsingleton: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setunionsingleton,definition,
% 2.74/1.53 ( setunionsingleton
% 2.74/1.53 = ( ! [Xx: $i] :
% 2.74/1.53 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.74/1.53 = Xx ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(singleton_type,type,
% 2.74/1.53 singleton: $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(singletonprop_type,type,
% 2.74/1.53 singletonprop: $o ).
% 2.74/1.53
% 2.74/1.53 thf(singletonprop,definition,
% 2.74/1.53 ( singletonprop
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( ( Xphi @ Xx )
% 2.74/1.53 => ( ( Xphi @ Xy )
% 2.74/1.53 => ( Xx = Xy ) ) ) ) )
% 2.74/1.53 => ( ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ( Xphi @ Xx ) )
% 2.74/1.53 => ( singleton
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ex1_type,type,
% 2.74/1.53 ex1: $i > ( $i > $o ) > $o ).
% 2.74/1.53
% 2.74/1.53 thf(ex1,definition,
% 2.74/1.53 ( ex1
% 2.74/1.53 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( singleton
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ex1E1_type,type,
% 2.74/1.53 ex1E1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ex1E1,definition,
% 2.74/1.53 ( ex1E1
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ( ex1 @ A
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 => ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ex1I_type,type,
% 2.74/1.53 ex1I: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ex1I,definition,
% 2.74/1.53 ( ex1I
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( Xphi @ Xx )
% 2.74/1.53 => ( ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( ( Xphi @ Xy )
% 2.74/1.53 => ( Xy = Xx ) ) )
% 2.74/1.53 => ( ex1 @ A
% 2.74/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ex1I2_type,type,
% 2.74/1.53 ex1I2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ex1I2,definition,
% 2.74/1.53 ( ex1I2
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( ( Xphi @ Xx )
% 2.74/1.53 => ( ( Xphi @ Xy )
% 2.74/1.53 => ( Xx = Xy ) ) ) ) )
% 2.74/1.53 => ( ? [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 & ( Xphi @ Xx ) )
% 2.74/1.53 => ( ex1 @ A
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(singletonsuniq_type,type,
% 2.74/1.53 singletonsuniq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(singletonsuniq,definition,
% 2.74/1.53 ( singletonsuniq
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( ( setadjoin @ Xx @ emptyset )
% 2.74/1.53 = ( setadjoin @ Xy @ emptyset ) )
% 2.74/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(atmost1p_type,type,
% 2.74/1.53 atmost1p: $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(atleast2p_type,type,
% 2.74/1.53 atleast2p: $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(atmost2p_type,type,
% 2.74/1.53 atmost2p: $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(upairsetp_type,type,
% 2.74/1.53 upairsetp: $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjL1_type,type,
% 2.74/1.53 setukpairinjL1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjL1,definition,
% 2.74/1.53 ( setukpairinjL1
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.74/1.53 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.74/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(kfstsingleton_type,type,
% 2.74/1.53 kfstsingleton: $o ).
% 2.74/1.53
% 2.74/1.53 thf(kfstsingleton,definition,
% 2.74/1.53 ( kfstsingleton
% 2.74/1.53 = ( ! [Xu: $i] :
% 2.74/1.53 ( ( iskpair @ Xu )
% 2.74/1.53 => ( singleton
% 2.74/1.53 @ ( dsetconstr @ ( setunion @ Xu )
% 2.74/1.53 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(theprop_type,type,
% 2.74/1.53 theprop: $o ).
% 2.74/1.53
% 2.74/1.53 thf(theprop,definition,
% 2.74/1.53 ( theprop
% 2.74/1.53 = ( ! [X: $i] :
% 2.74/1.53 ( ( singleton @ X )
% 2.74/1.53 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(kfst_type,type,
% 2.74/1.53 kfst: $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(kfstpairEq_type,type,
% 2.74/1.53 kfstpairEq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(kfstpairEq,definition,
% 2.74/1.53 ( kfstpairEq
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.74/1.53 = Xx ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodfstin_type,type,
% 2.74/1.53 cartprodfstin: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodfstin,definition,
% 2.74/1.53 ( cartprodfstin
% 2.74/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.74/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.74/1.53 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjL2_type,type,
% 2.74/1.53 setukpairinjL2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjL2,definition,
% 2.74/1.53 ( setukpairinjL2
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.74/1.53 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.74/1.53 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.74/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjL_type,type,
% 2.74/1.53 setukpairinjL: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjL,definition,
% 2.74/1.53 ( setukpairinjL
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.74/1.53 ( ( ( kpair @ Xx @ Xy )
% 2.74/1.53 = ( kpair @ Xz @ Xu ) )
% 2.74/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjR11_type,type,
% 2.74/1.53 setukpairinjR11: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjR11,definition,
% 2.74/1.53 ( setukpairinjR11
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xx = Xy )
% 2.74/1.53 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.74/1.53 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjR12_type,type,
% 2.74/1.53 setukpairinjR12: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjR12,definition,
% 2.74/1.53 ( setukpairinjR12
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xx = Xy )
% 2.74/1.53 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.74/1.53 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjR1_type,type,
% 2.74/1.53 setukpairinjR1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjR1,definition,
% 2.74/1.53 ( setukpairinjR1
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.74/1.53 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.74/1.53 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.74/1.53 => ( ( Xz = Xu )
% 2.74/1.53 => ( Xy = Xu ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(upairequniteq_type,type,
% 2.74/1.53 upairequniteq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(upairequniteq,definition,
% 2.74/1.53 ( upairequniteq
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.74/1.53 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.74/1.53 = ( setadjoin @ Xz @ emptyset ) )
% 2.74/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjR2_type,type,
% 2.74/1.53 setukpairinjR2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjR2,definition,
% 2.74/1.53 ( setukpairinjR2
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.74/1.53 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.74/1.53 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.74/1.53 => ( Xy = Xu ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjR_type,type,
% 2.74/1.53 setukpairinjR: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setukpairinjR,definition,
% 2.74/1.53 ( setukpairinjR
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.74/1.53 ( ( ( kpair @ Xx @ Xy )
% 2.74/1.53 = ( kpair @ Xz @ Xu ) )
% 2.74/1.53 => ( Xy = Xu ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ksndsingleton_type,type,
% 2.74/1.53 ksndsingleton: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ksndsingleton,definition,
% 2.74/1.53 ( ksndsingleton
% 2.74/1.53 = ( ! [Xu: $i] :
% 2.74/1.53 ( ( iskpair @ Xu )
% 2.74/1.53 => ( singleton
% 2.74/1.53 @ ( dsetconstr @ ( setunion @ Xu )
% 2.74/1.53 @ ^ [Xx: $i] :
% 2.74/1.53 ( Xu
% 2.74/1.53 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ksnd_type,type,
% 2.74/1.53 ksnd: $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(ksndpairEq_type,type,
% 2.74/1.53 ksndpairEq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ksndpairEq,definition,
% 2.74/1.53 ( ksndpairEq
% 2.74/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.74/1.53 = Xy ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(kpairsurjEq_type,type,
% 2.74/1.53 kpairsurjEq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(kpairsurjEq,definition,
% 2.74/1.53 ( kpairsurjEq
% 2.74/1.53 = ( ! [Xu: $i] :
% 2.74/1.53 ( ( iskpair @ Xu )
% 2.74/1.53 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.74/1.53 = Xu ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodsndin_type,type,
% 2.74/1.53 cartprodsndin: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodsndin,definition,
% 2.74/1.53 ( cartprodsndin
% 2.74/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.74/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.74/1.53 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodpairmemEL_type,type,
% 2.74/1.53 cartprodpairmemEL: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodpairmemEL,definition,
% 2.74/1.53 ( cartprodpairmemEL
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.74/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodpairmemER_type,type,
% 2.74/1.53 cartprodpairmemER: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodpairmemER,definition,
% 2.74/1.53 ( cartprodpairmemER
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 2.74/1.53 => ( in @ Xy @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodmempaircEq_type,type,
% 2.74/1.53 cartprodmempaircEq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodmempaircEq,definition,
% 2.74/1.53 ( cartprodmempaircEq
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( kpair @ Xx @ Xy )
% 2.74/1.53 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodfstpairEq_type,type,
% 2.74/1.53 cartprodfstpairEq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodfstpairEq,definition,
% 2.74/1.53 ( cartprodfstpairEq
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.74/1.53 = Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodsndpairEq_type,type,
% 2.74/1.53 cartprodsndpairEq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodsndpairEq,definition,
% 2.74/1.53 ( cartprodsndpairEq
% 2.74/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.74/1.53 = Xy ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodpairsurjEq_type,type,
% 2.74/1.53 cartprodpairsurjEq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(cartprodpairsurjEq,definition,
% 2.74/1.53 ( cartprodpairsurjEq
% 2.74/1.53 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.74/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.74/1.53 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.74/1.53 = Xu ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(breln_type,type,
% 2.74/1.53 breln: $i > $i > $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(breln,definition,
% 2.74/1.53 ( breln
% 2.74/1.53 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstr_type,type,
% 2.74/1.53 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrI_type,type,
% 2.74/1.53 dpsetconstrI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrI,definition,
% 2.74/1.53 ( dpsetconstrI
% 2.74/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( Xphi @ Xx @ Xy )
% 2.74/1.53 => ( in @ ( kpair @ Xx @ Xy )
% 2.74/1.53 @ ( dpsetconstr @ A @ B
% 2.74/1.53 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrSub_type,type,
% 2.74/1.53 dpsetconstrSub: $o ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrSub,definition,
% 2.74/1.53 ( dpsetconstrSub
% 2.74/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.74/1.53 ( subset
% 2.74/1.53 @ ( dpsetconstr @ A @ B
% 2.74/1.53 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 2.74/1.53 @ ( cartprod @ A @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setOfPairsIsBReln_type,type,
% 2.74/1.53 setOfPairsIsBReln: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setOfPairsIsBReln,definition,
% 2.74/1.53 ( setOfPairsIsBReln
% 2.74/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 2.74/1.53 ( breln @ A @ B
% 2.74/1.53 @ ( dpsetconstr @ A @ B
% 2.74/1.53 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrERa_type,type,
% 2.74/1.53 dpsetconstrERa: $o ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrERa,definition,
% 2.74/1.53 ( dpsetconstrERa
% 2.74/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( in @ ( kpair @ Xx @ Xy )
% 2.74/1.53 @ ( dpsetconstr @ A @ B
% 2.74/1.53 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.74/1.53 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrEL1_type,type,
% 2.74/1.53 dpsetconstrEL1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrEL1,definition,
% 2.74/1.53 ( dpsetconstrEL1
% 2.74/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ ( kpair @ Xx @ Xy )
% 2.74/1.53 @ ( dpsetconstr @ A @ B
% 2.74/1.53 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.74/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrEL2_type,type,
% 2.74/1.53 dpsetconstrEL2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrEL2,definition,
% 2.74/1.53 ( dpsetconstrEL2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ ( kpair @ Xx @ Xy )
% 2.74/1.53 @ ( dpsetconstr @ A @ B
% 2.74/1.53 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.74/1.53 => ( in @ Xy @ B ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrER_type,type,
% 2.74/1.53 dpsetconstrER: $o ).
% 2.74/1.53
% 2.74/1.53 thf(dpsetconstrER,definition,
% 2.74/1.53 ( dpsetconstrER
% 2.74/1.53 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( in @ ( kpair @ Xx @ Xy )
% 2.74/1.53 @ ( dpsetconstr @ A @ B
% 2.74/1.53 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 2.74/1.53 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(func_type,type,
% 2.74/1.53 func: $i > $i > $i > $o ).
% 2.74/1.53
% 2.74/1.53 thf(funcSet_type,type,
% 2.74/1.53 funcSet: $i > $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(funcImageSingleton_type,type,
% 2.74/1.53 funcImageSingleton: $o ).
% 2.74/1.53
% 2.74/1.53 thf(funcImageSingleton,definition,
% 2.74/1.53 ( funcImageSingleton
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xf )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( singleton
% 2.74/1.53 @ ( dsetconstr @ B
% 2.74/1.53 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(apProp_type,type,
% 2.74/1.53 apProp: $o ).
% 2.74/1.53
% 2.74/1.53 thf(apProp,definition,
% 2.74/1.53 ( apProp
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xf )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in
% 2.74/1.53 @ ( setunion
% 2.74/1.53 @ ( dsetconstr @ B
% 2.74/1.53 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 2.74/1.53 @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ap_type,type,
% 2.74/1.53 ap: $i > $i > $i > $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(app_type,type,
% 2.74/1.53 app: $o ).
% 2.74/1.53
% 2.74/1.53 thf(app,definition,
% 2.74/1.53 ( app
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xf )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(infuncsetfunc_type,type,
% 2.74/1.53 infuncsetfunc: $o ).
% 2.74/1.53
% 2.74/1.53 thf(infuncsetfunc,definition,
% 2.74/1.53 ( infuncsetfunc
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.74/1.53 => ( func @ A @ B @ Xf ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ap2p_type,type,
% 2.74/1.53 ap2p: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ap2p,definition,
% 2.74/1.53 ( ap2p
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(funcinfuncset_type,type,
% 2.74/1.53 funcinfuncset: $o ).
% 2.74/1.53
% 2.74/1.53 thf(funcinfuncset,definition,
% 2.74/1.53 ( funcinfuncset
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xf )
% 2.74/1.53 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(lamProp_type,type,
% 2.74/1.53 lamProp: $o ).
% 2.74/1.53
% 2.74/1.53 thf(lamProp,definition,
% 2.74/1.53 ( lamProp
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.74/1.53 => ( func @ A @ B
% 2.74/1.53 @ ( dpsetconstr @ A @ B
% 2.74/1.53 @ ^ [Xx: $i,Xy: $i] :
% 2.74/1.53 ( ( Xf @ Xx )
% 2.74/1.53 = Xy ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(lam_type,type,
% 2.74/1.53 lam: $i > $i > ( $i > $i ) > $i ).
% 2.74/1.53
% 2.74/1.53 thf(lamp_type,type,
% 2.74/1.53 lamp: $o ).
% 2.74/1.53
% 2.74/1.53 thf(lamp,definition,
% 2.74/1.53 ( lamp
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.74/1.53 => ( func @ A @ B
% 2.74/1.53 @ ( lam @ A @ B
% 2.74/1.53 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(lam2p_type,type,
% 2.74/1.53 lam2p: $o ).
% 2.74/1.53
% 2.74/1.53 thf(lam2p,definition,
% 2.74/1.53 ( lam2p
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.74/1.53 => ( in
% 2.74/1.53 @ ( lam @ A @ B
% 2.74/1.53 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.74/1.53 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(brelnall1_type,type,
% 2.74/1.53 brelnall1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(brelnall1,definition,
% 2.74/1.53 ( brelnall1
% 2.74/1.53 = ( ! [A: $i,B: $i,R: $i] :
% 2.74/1.53 ( ( breln @ A @ B @ R )
% 2.74/1.53 => ! [Xphi: $i > $o] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.74/1.53 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ R )
% 2.74/1.53 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(brelnall2_type,type,
% 2.74/1.53 brelnall2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(brelnall2,definition,
% 2.74/1.53 ( brelnall2
% 2.74/1.53 = ( ! [A: $i,B: $i,R: $i] :
% 2.74/1.53 ( ( breln @ A @ B @ R )
% 2.74/1.53 => ! [Xphi: $i > $o] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.74/1.53 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ R )
% 2.74/1.53 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ex1E2_type,type,
% 2.74/1.53 ex1E2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ex1E2,definition,
% 2.74/1.53 ( ex1E2
% 2.74/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.74/1.53 ( ( ex1 @ A
% 2.74/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( ( Xphi @ Xx )
% 2.74/1.53 => ( ( Xphi @ Xy )
% 2.74/1.53 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(funcGraphProp1_type,type,
% 2.74/1.53 funcGraphProp1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(funcGraphProp1,definition,
% 2.74/1.53 ( funcGraphProp1
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xf )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(funcGraphProp3_type,type,
% 2.74/1.53 funcGraphProp3: $o ).
% 2.74/1.53
% 2.74/1.53 thf(funcGraphProp3,definition,
% 2.74/1.53 ( funcGraphProp3
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(funcGraphProp2_type,type,
% 2.74/1.53 funcGraphProp2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(funcGraphProp2,definition,
% 2.74/1.53 ( funcGraphProp2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xf )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.74/1.53 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.74/1.53 = Xy ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(funcextLem_type,type,
% 2.74/1.53 funcextLem: $o ).
% 2.74/1.53
% 2.74/1.53 thf(funcextLem,definition,
% 2.74/1.53 ( funcextLem
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xf )
% 2.74/1.53 => ! [Xg: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xg )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.74/1.53 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 2.74/1.53 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(funcGraphProp4_type,type,
% 2.74/1.53 funcGraphProp4: $o ).
% 2.74/1.53
% 2.74/1.53 thf(funcGraphProp4,definition,
% 2.74/1.53 ( funcGraphProp4
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 2.74/1.53 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.74/1.53 = Xy ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subbreln_type,type,
% 2.74/1.53 subbreln: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subbreln,definition,
% 2.74/1.53 ( subbreln
% 2.74/1.53 = ( ! [A: $i,B: $i,R: $i] :
% 2.74/1.53 ( ( breln @ A @ B @ R )
% 2.74/1.53 => ! [S: $i] :
% 2.74/1.53 ( ( breln @ A @ B @ S )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.74/1.53 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.74/1.53 => ( subset @ R @ S ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(eqbreln_type,type,
% 2.74/1.53 eqbreln: $o ).
% 2.74/1.53
% 2.74/1.53 thf(eqbreln,definition,
% 2.74/1.53 ( eqbreln
% 2.74/1.53 = ( ! [A: $i,B: $i,R: $i] :
% 2.74/1.53 ( ( breln @ A @ B @ R )
% 2.74/1.53 => ! [S: $i] :
% 2.74/1.53 ( ( breln @ A @ B @ S )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 2.74/1.53 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ B )
% 2.74/1.53 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 2.74/1.53 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 2.74/1.53 => ( R = S ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(funcext_type,type,
% 2.74/1.53 funcext: $o ).
% 2.74/1.53
% 2.74/1.53 thf(funcext,definition,
% 2.74/1.53 ( funcext
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xf )
% 2.74/1.53 => ! [Xg: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xg )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.74/1.53 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.74/1.53 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(funcext2_type,type,
% 2.74/1.53 funcext2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(funcext2,definition,
% 2.74/1.53 ( funcext2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.74/1.53 => ! [Xg: $i] :
% 2.74/1.53 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.74/1.53 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 2.74/1.53 => ( Xf = Xg ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ap2apEq1_type,type,
% 2.74/1.53 ap2apEq1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ap2apEq1,definition,
% 2.74/1.53 ( ap2apEq1
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.74/1.53 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ap2apEq2_type,type,
% 2.74/1.53 ap2apEq2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ap2apEq2,definition,
% 2.74/1.53 ( ap2apEq2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xf )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( ap @ A @ B @ Xf @ Xx )
% 2.74/1.53 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(beta1_type,type,
% 2.74/1.53 beta1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(beta1,definition,
% 2.74/1.53 ( beta1
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( ap @ A @ B
% 2.74/1.53 @ ( lam @ A @ B
% 2.74/1.53 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.74/1.53 @ Xx )
% 2.74/1.53 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(eta1_type,type,
% 2.74/1.53 eta1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(eta1,definition,
% 2.74/1.53 ( eta1
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( func @ A @ B @ Xf )
% 2.74/1.53 => ( ( lam @ A @ B
% 2.74/1.53 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.74/1.53 = Xf ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(lam2lamEq_type,type,
% 2.74/1.53 lam2lamEq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(lam2lamEq,definition,
% 2.74/1.53 ( lam2lamEq
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.74/1.53 => ( ( lam @ A @ B
% 2.74/1.53 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 2.74/1.53 = ( lam @ A @ B
% 2.74/1.53 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(beta2_type,type,
% 2.74/1.53 beta2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(beta2,definition,
% 2.74/1.53 ( beta2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 2.74/1.53 ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( in @ ( Xf @ Xx ) @ B ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( ap @ A @ B
% 2.74/1.53 @ ( lam @ A @ B
% 2.74/1.53 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 2.74/1.53 @ Xx )
% 2.74/1.53 = ( Xf @ Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(eta2_type,type,
% 2.74/1.53 eta2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(eta2,definition,
% 2.74/1.53 ( eta2
% 2.74/1.53 = ( ! [A: $i,B: $i,Xf: $i] :
% 2.74/1.53 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 2.74/1.53 => ( ( lam @ A @ B
% 2.74/1.53 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 2.74/1.53 = Xf ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(iffalseProp1_type,type,
% 2.74/1.53 iffalseProp1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(iffalseProp1,definition,
% 2.74/1.53 ( iffalseProp1
% 2.74/1.53 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( ~ Xphi
% 2.74/1.53 => ( in @ Xy
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xz: $i] :
% 2.74/1.53 ( ( Xphi
% 2.74/1.53 & ( Xz = Xx ) )
% 2.74/1.53 | ( ~ Xphi
% 2.74/1.53 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(iffalseProp2_type,type,
% 2.74/1.53 iffalseProp2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(iffalseProp2,definition,
% 2.74/1.53 ( iffalseProp2
% 2.74/1.53 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( ~ Xphi
% 2.74/1.53 => ( ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xz: $i] :
% 2.74/1.53 ( ( Xphi
% 2.74/1.53 & ( Xz = Xx ) )
% 2.74/1.53 | ( ~ Xphi
% 2.74/1.53 & ( Xz = Xy ) ) ) )
% 2.74/1.53 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(iftrueProp1_type,type,
% 2.74/1.53 iftrueProp1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(iftrueProp1,definition,
% 2.74/1.53 ( iftrueProp1
% 2.74/1.53 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( Xphi
% 2.74/1.53 => ( in @ Xx
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xz: $i] :
% 2.74/1.53 ( ( Xphi
% 2.74/1.53 & ( Xz = Xx ) )
% 2.74/1.53 | ( ~ Xphi
% 2.74/1.53 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(iftrueProp2_type,type,
% 2.74/1.53 iftrueProp2: $o ).
% 2.74/1.53
% 2.74/1.53 thf(iftrueProp2,definition,
% 2.74/1.53 ( iftrueProp2
% 2.74/1.53 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( Xphi
% 2.74/1.53 => ( ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xz: $i] :
% 2.74/1.53 ( ( Xphi
% 2.74/1.53 & ( Xz = Xx ) )
% 2.74/1.53 | ( ~ Xphi
% 2.74/1.53 & ( Xz = Xy ) ) ) )
% 2.74/1.53 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(ifSingleton_type,type,
% 2.74/1.53 ifSingleton: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ifSingleton,definition,
% 2.74/1.53 ( ifSingleton
% 2.74/1.53 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( singleton
% 2.74/1.53 @ ( dsetconstr @ A
% 2.74/1.53 @ ^ [Xz: $i] :
% 2.74/1.53 ( ( Xphi
% 2.74/1.53 & ( Xz = Xx ) )
% 2.74/1.53 | ( ~ Xphi
% 2.74/1.53 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(if_type,type,
% 2.74/1.53 if: $i > $o > $i > $i > $i ).
% 2.74/1.53
% 2.74/1.53 thf(ifp_type,type,
% 2.74/1.53 ifp: $o ).
% 2.74/1.53
% 2.74/1.53 thf(ifp,definition,
% 2.74/1.53 ( ifp
% 2.74/1.53 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(theeq_type,type,
% 2.74/1.53 theeq: $o ).
% 2.74/1.53
% 2.74/1.53 thf(theeq,definition,
% 2.74/1.53 ( theeq
% 2.74/1.53 = ( ! [X: $i] :
% 2.74/1.53 ( ( singleton @ X )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ X )
% 2.74/1.53 => ( ( setunion @ X )
% 2.74/1.53 = Xx ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(iftrue_type,type,
% 2.74/1.53 iftrue: $o ).
% 2.74/1.53
% 2.74/1.53 thf(iftrue,definition,
% 2.74/1.53 ( iftrue
% 2.74/1.53 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( Xphi
% 2.74/1.53 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.74/1.53 = Xx ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(iffalse_type,type,
% 2.74/1.53 iffalse: $o ).
% 2.74/1.53
% 2.74/1.53 thf(iffalse,definition,
% 2.74/1.53 ( iffalse
% 2.74/1.53 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( ~ Xphi
% 2.74/1.53 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 2.74/1.53 = Xy ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(iftrueorfalse_type,type,
% 2.74/1.53 iftrueorfalse: $o ).
% 2.74/1.53
% 2.74/1.53 thf(iftrueorfalse,definition,
% 2.74/1.53 ( iftrueorfalse
% 2.74/1.53 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ! [Xy: $i] :
% 2.74/1.53 ( ( in @ Xy @ A )
% 2.74/1.53 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectT_lem_type,type,
% 2.74/1.53 binintersectT_lem: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectT_lem,definition,
% 2.74/1.53 ( binintersectT_lem
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Y: $i] :
% 2.74/1.53 ( ( in @ Y @ ( powerset @ A ) )
% 2.74/1.53 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binunionT_lem_type,type,
% 2.74/1.53 binunionT_lem: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binunionT_lem,definition,
% 2.74/1.53 ( binunionT_lem
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Y: $i] :
% 2.74/1.53 ( ( in @ Y @ ( powerset @ A ) )
% 2.74/1.53 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(powersetT_lem_type,type,
% 2.74/1.53 powersetT_lem: $o ).
% 2.74/1.53
% 2.74/1.53 thf(powersetT_lem,definition,
% 2.74/1.53 ( powersetT_lem
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setminusT_lem_type,type,
% 2.74/1.53 setminusT_lem: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setminusT_lem,definition,
% 2.74/1.53 ( setminusT_lem
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Y: $i] :
% 2.74/1.53 ( ( in @ Y @ ( powerset @ A ) )
% 2.74/1.53 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(complementT_lem_type,type,
% 2.74/1.53 complementT_lem: $o ).
% 2.74/1.53
% 2.74/1.53 thf(complementT_lem,definition,
% 2.74/1.53 ( complementT_lem
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(setextT_type,type,
% 2.74/1.53 setextT: $o ).
% 2.74/1.53
% 2.74/1.53 thf(setextT,definition,
% 2.74/1.53 ( setextT
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Y: $i] :
% 2.74/1.53 ( ( in @ Y @ ( powerset @ A ) )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ Xx @ X )
% 2.74/1.53 => ( in @ Xx @ Y ) ) )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ Xx @ Y )
% 2.74/1.53 => ( in @ Xx @ X ) ) )
% 2.74/1.53 => ( X = Y ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(subsetTI_type,type,
% 2.74/1.53 subsetTI: $o ).
% 2.74/1.53
% 2.74/1.53 thf(subsetTI,definition,
% 2.74/1.53 ( subsetTI
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Y: $i] :
% 2.74/1.53 ( ( in @ Y @ ( powerset @ A ) )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ Xx @ X )
% 2.74/1.53 => ( in @ Xx @ Y ) ) )
% 2.74/1.53 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(powersetTI1_type,type,
% 2.74/1.53 powersetTI1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(powersetTI1,definition,
% 2.74/1.53 ( powersetTI1
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Y: $i] :
% 2.74/1.53 ( ( in @ Y @ ( powerset @ A ) )
% 2.74/1.53 => ( ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ Xx @ X )
% 2.74/1.53 => ( in @ Xx @ Y ) ) )
% 2.74/1.53 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(powersetTE1_type,type,
% 2.74/1.53 powersetTE1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(powersetTE1,definition,
% 2.74/1.53 ( powersetTE1
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Y: $i] :
% 2.74/1.53 ( ( in @ Y @ ( powerset @ A ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ X @ ( powerset @ Y ) )
% 2.74/1.53 => ( ( in @ Xx @ X )
% 2.74/1.53 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(complementTI1_type,type,
% 2.74/1.53 complementTI1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(complementTI1,definition,
% 2.74/1.53 ( complementTI1
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ( in @ Xx @ X )
% 2.74/1.53 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(complementTE1_type,type,
% 2.74/1.53 complementTE1: $o ).
% 2.74/1.53
% 2.74/1.53 thf(complementTE1,definition,
% 2.74/1.53 ( complementTE1
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 2.74/1.53 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectTELcontra_type,type,
% 2.74/1.53 binintersectTELcontra: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectTELcontra,definition,
% 2.74/1.53 ( binintersectTELcontra
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Y: $i] :
% 2.74/1.53 ( ( in @ Y @ ( powerset @ A ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ~ ( in @ Xx @ X )
% 2.74/1.53 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectTERcontra_type,type,
% 2.74/1.53 binintersectTERcontra: $o ).
% 2.74/1.53
% 2.74/1.53 thf(binintersectTERcontra,definition,
% 2.74/1.53 ( binintersectTERcontra
% 2.74/1.53 = ( ! [A: $i,X: $i] :
% 2.74/1.53 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.53 => ! [Y: $i] :
% 2.74/1.53 ( ( in @ Y @ ( powerset @ A ) )
% 2.74/1.53 => ! [Xx: $i] :
% 2.74/1.53 ( ( in @ Xx @ A )
% 2.74/1.53 => ( ~ ( in @ Xx @ Y )
% 2.74/1.53 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.74/1.53
% 2.74/1.53 thf(contrasubsetT,conjecture,
% 2.74/1.53 ( setextAx
% 2.74/1.53 => ( emptysetAx
% 2.74/1.53 => ( setadjoinAx
% 2.74/1.53 => ( powersetAx
% 2.74/1.53 => ( setunionAx
% 2.74/1.53 => ( omega0Ax
% 2.74/1.53 => ( omegaSAx
% 2.74/1.53 => ( omegaIndAx
% 2.74/1.53 => ( replAx
% 2.74/1.53 => ( foundationAx
% 2.74/1.53 => ( wellorderingAx
% 2.74/1.53 => ( descrp
% 2.74/1.53 => ( dsetconstrI
% 2.74/1.53 => ( dsetconstrEL
% 2.74/1.53 => ( dsetconstrER
% 2.74/1.53 => ( exuE1
% 2.74/1.53 => ( prop2setE
% 2.74/1.53 => ( emptysetE
% 2.74/1.53 => ( emptysetimpfalse
% 2.74/1.53 => ( notinemptyset
% 2.74/1.53 => ( exuE3e
% 2.74/1.53 => ( setext
% 2.74/1.53 => ( emptyI
% 2.74/1.53 => ( noeltsimpempty
% 2.74/1.53 => ( setbeta
% 2.74/1.53 => ( nonemptyE1
% 2.74/1.53 => ( nonemptyI
% 2.74/1.53 => ( nonemptyI1
% 2.74/1.53 => ( setadjoinIL
% 2.74/1.53 => ( emptyinunitempty
% 2.74/1.53 => ( setadjoinIR
% 2.74/1.53 => ( setadjoinE
% 2.74/1.53 => ( setadjoinOr
% 2.74/1.53 => ( setoftrueEq
% 2.74/1.53 => ( powersetI
% 2.74/1.53 => ( emptyinPowerset
% 2.74/1.53 => ( emptyInPowerset
% 2.74/1.53 => ( powersetE
% 2.74/1.53 => ( setunionI
% 2.74/1.53 => ( setunionE
% 2.74/1.53 => ( subPowSU
% 2.74/1.53 => ( exuE2
% 2.74/1.53 => ( nonemptyImpWitness
% 2.74/1.53 => ( uniqinunit
% 2.74/1.53 => ( notinsingleton
% 2.74/1.53 => ( eqinunit
% 2.74/1.53 => ( singletonsswitch
% 2.74/1.53 => ( upairsetE
% 2.74/1.53 => ( upairsetIL
% 2.74/1.53 => ( upairsetIR
% 2.74/1.53 => ( emptyE1
% 2.74/1.53 => ( vacuousDall
% 2.74/1.53 => ( quantDeMorgan1
% 2.74/1.53 => ( quantDeMorgan2
% 2.74/1.53 => ( quantDeMorgan3
% 2.74/1.53 => ( quantDeMorgan4
% 2.74/1.53 => ( prop2setI
% 2.74/1.53 => ( prop2set2propI
% 2.74/1.53 => ( notdexE
% 2.74/1.53 => ( notdallE
% 2.74/1.53 => ( exuI1
% 2.74/1.53 => ( exuI3
% 2.74/1.53 => ( exuI2
% 2.74/1.53 => ( inCongP
% 2.74/1.53 => ( in__Cong
% 2.74/1.53 => ( exuE3u
% 2.74/1.53 => ( exu__Cong
% 2.74/1.53 => ( emptyset__Cong
% 2.74/1.53 => ( setadjoin__Cong
% 2.74/1.53 => ( powerset__Cong
% 2.74/1.53 => ( setunion__Cong
% 2.74/1.53 => ( omega__Cong
% 2.74/1.53 => ( exuEu
% 2.74/1.53 => ( descr__Cong
% 2.74/1.53 => ( dsetconstr__Cong
% 2.74/1.53 => ( subsetI1
% 2.74/1.53 => ( eqimpsubset2
% 2.74/1.53 => ( eqimpsubset1
% 2.74/1.53 => ( subsetI2
% 2.74/1.53 => ( emptysetsubset
% 2.74/1.53 => ( subsetE
% 2.74/1.53 => ( subsetE2
% 2.74/1.53 => ( notsubsetI
% 2.74/1.53 => ( notequalI1
% 2.74/1.53 => ( notequalI2
% 2.74/1.53 => ( subsetRefl
% 2.74/1.53 => ( subsetTrans
% 2.74/1.53 => ( setadjoinSub
% 2.74/1.53 => ( setadjoinSub2
% 2.74/1.53 => ( subset2powerset
% 2.74/1.53 => ( setextsub
% 2.74/1.53 => ( subsetemptysetimpeq
% 2.74/1.53 => ( powersetI1
% 2.74/1.53 => ( powersetE1
% 2.74/1.53 => ( inPowerset
% 2.74/1.53 => ( powersetsubset
% 2.74/1.53 => ( sepInPowerset
% 2.74/1.53 => ( sepSubset
% 2.74/1.53 => ( binunionIL
% 2.74/1.53 => ( upairset2IR
% 2.74/1.53 => ( binunionIR
% 2.74/1.53 => ( binunionEcases
% 2.74/1.53 => ( binunionE
% 2.74/1.53 => ( binunionLsub
% 2.74/1.53 => ( binunionRsub
% 2.74/1.53 => ( binintersectI
% 2.74/1.53 => ( binintersectSubset5
% 2.74/1.53 => ( binintersectEL
% 2.74/1.53 => ( binintersectLsub
% 2.74/1.53 => ( binintersectSubset2
% 2.74/1.53 => ( binintersectSubset3
% 2.74/1.53 => ( binintersectER
% 2.74/1.53 => ( disjointsetsI1
% 2.74/1.53 => ( binintersectRsub
% 2.74/1.53 => ( binintersectSubset4
% 2.74/1.53 => ( binintersectSubset1
% 2.74/1.53 => ( bs114d
% 2.74/1.53 => ( setminusI
% 2.74/1.53 => ( setminusEL
% 2.74/1.53 => ( setminusER
% 2.74/1.53 => ( setminusSubset2
% 2.74/1.53 => ( setminusERneg
% 2.74/1.53 => ( setminusELneg
% 2.74/1.53 => ( setminusILneg
% 2.74/1.53 => ( setminusIRneg
% 2.74/1.53 => ( setminusLsub
% 2.74/1.53 => ( setminusSubset1
% 2.74/1.53 => ( symdiffE
% 2.74/1.53 => ( symdiffI1
% 2.74/1.53 => ( symdiffI2
% 2.74/1.53 => ( symdiffIneg1
% 2.74/1.53 => ( symdiffIneg2
% 2.74/1.53 => ( secondinupair
% 2.74/1.53 => ( setukpairIL
% 2.74/1.53 => ( setukpairIR
% 2.74/1.53 => ( kpairiskpair
% 2.74/1.53 => ( kpairp
% 2.74/1.53 => ( singletonsubset
% 2.74/1.53 => ( singletoninpowerset
% 2.74/1.53 => ( singletoninpowunion
% 2.74/1.53 => ( upairset2E
% 2.74/1.53 => ( upairsubunion
% 2.74/1.53 => ( upairinpowunion
% 2.74/1.53 => ( ubforcartprodlem1
% 2.74/1.53 => ( ubforcartprodlem2
% 2.74/1.53 => ( ubforcartprodlem3
% 2.74/1.53 => ( cartprodpairin
% 2.74/1.53 => ( cartprodmempair1
% 2.74/1.53 => ( cartprodmempair
% 2.74/1.53 => ( setunionE2
% 2.74/1.53 => ( setunionsingleton1
% 2.74/1.53 => ( setunionsingleton2
% 2.74/1.53 => ( setunionsingleton
% 2.74/1.53 => ( singletonprop
% 2.74/1.53 => ( ex1E1
% 2.74/1.54 => ( ex1I
% 2.74/1.54 => ( ex1I2
% 2.74/1.54 => ( singletonsuniq
% 2.74/1.54 => ( setukpairinjL1
% 2.74/1.54 => ( kfstsingleton
% 2.74/1.54 => ( theprop
% 2.74/1.54 => ( kfstpairEq
% 2.74/1.54 => ( cartprodfstin
% 2.74/1.54 => ( setukpairinjL2
% 2.74/1.54 => ( setukpairinjL
% 2.74/1.54 => ( setukpairinjR11
% 2.74/1.54 => ( setukpairinjR12
% 2.74/1.54 => ( setukpairinjR1
% 2.74/1.54 => ( upairequniteq
% 2.74/1.54 => ( setukpairinjR2
% 2.74/1.54 => ( setukpairinjR
% 2.74/1.54 => ( ksndsingleton
% 2.74/1.54 => ( ksndpairEq
% 2.74/1.54 => ( kpairsurjEq
% 2.74/1.54 => ( cartprodsndin
% 2.74/1.54 => ( cartprodpairmemEL
% 2.74/1.54 => ( cartprodpairmemER
% 2.74/1.54 => ( cartprodmempaircEq
% 2.74/1.54 => ( cartprodfstpairEq
% 2.74/1.54 => ( cartprodsndpairEq
% 2.74/1.54 => ( cartprodpairsurjEq
% 2.74/1.54 => ( dpsetconstrI
% 2.74/1.54 => ( dpsetconstrSub
% 2.74/1.54 => ( setOfPairsIsBReln
% 2.74/1.54 => ( dpsetconstrERa
% 2.74/1.54 => ( dpsetconstrEL1
% 2.74/1.54 => ( dpsetconstrEL2
% 2.74/1.54 => ( dpsetconstrER
% 2.74/1.54 => ( funcImageSingleton
% 2.74/1.54 => ( apProp
% 2.74/1.54 => ( app
% 2.74/1.54 => ( infuncsetfunc
% 2.74/1.54 => ( ap2p
% 2.74/1.54 => ( funcinfuncset
% 2.74/1.54 => ( lamProp
% 2.74/1.54 => ( lamp
% 2.74/1.54 => ( lam2p
% 2.74/1.54 => ( brelnall1
% 2.74/1.54 => ( brelnall2
% 2.74/1.54 => ( ex1E2
% 2.74/1.54 => ( funcGraphProp1
% 2.74/1.54 => ( funcGraphProp3
% 2.74/1.54 => ( funcGraphProp2
% 2.74/1.54 => ( funcextLem
% 2.74/1.54 => ( funcGraphProp4
% 2.74/1.54 => ( subbreln
% 2.74/1.54 => ( eqbreln
% 2.74/1.54 => ( funcext
% 2.74/1.54 => ( funcext2
% 2.74/1.54 => ( ap2apEq1
% 2.74/1.54 => ( ap2apEq2
% 2.74/1.54 => ( beta1
% 2.74/1.54 => ( eta1
% 2.74/1.54 => ( lam2lamEq
% 2.74/1.54 => ( beta2
% 2.74/1.54 => ( eta2
% 2.74/1.54 => ( iffalseProp1
% 2.74/1.54 => ( iffalseProp2
% 2.74/1.54 => ( iftrueProp1
% 2.74/1.54 => ( iftrueProp2
% 2.74/1.54 => ( ifSingleton
% 2.74/1.54 => ( ifp
% 2.74/1.54 => ( theeq
% 2.74/1.54 => ( iftrue
% 2.74/1.54 => ( iffalse
% 2.74/1.54 => ( iftrueorfalse
% 2.74/1.54 => ( binintersectT_lem
% 2.74/1.54 => ( binunionT_lem
% 2.74/1.54 => ( powersetT_lem
% 2.74/1.54 => ( setminusT_lem
% 2.74/1.54 => ( complementT_lem
% 2.74/1.54 => ( setextT
% 2.74/1.54 => ( subsetTI
% 2.74/1.54 => ( powersetTI1
% 2.74/1.54 => ( powersetTE1
% 2.74/1.54 => ( complementTI1
% 2.74/1.54 => ( complementTE1
% 2.74/1.54 => ( binintersectTELcontra
% 2.74/1.54 => ( binintersectTERcontra
% 2.74/1.54 => ! [A: $i,X: $i] :
% 2.74/1.54 ( ( in @ X @ ( powerset @ A ) )
% 2.74/1.54 => ! [Y: $i] :
% 2.74/1.54 ( ( in @ Y @ ( powerset @ A ) )
% 2.74/1.54 => ! [Xx: $i] :
% 2.74/1.54 ( ( in @ Xx @ A )
% 2.74/1.54 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 2.74/1.54 => ( ( in @ Xx @ Y )
% 2.74/1.54 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.74/1.54 ------------------------
% 2.74/1.57 % (14094)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_13872 for (2999ds/27Mi)
% 2.74/1.57 % (14095)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/2Mi)
% 2.74/1.57 % (14097)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_13872 for (2999ds/275Mi)
% 2.74/1.57 % (14095)Instruction limit reached!
% 2.74/1.57 % (14095)------------------------------
% 2.74/1.57 % (14095)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.57 % (14095)Termination reason: Unknown
% 2.74/1.57 % (14095)Termination phase: shuffling
% 2.74/1.57
% 2.74/1.57 % (14095)Memory used [KB]: 1407
% 2.74/1.57 % (14095)Time elapsed: 0.003 s
% 2.74/1.57 % (14095)Instructions burned: 4 (million)
% 2.74/1.57 % (14095)------------------------------
% 2.74/1.57 % (14095)------------------------------
% 2.74/1.58 % (14092)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/183Mi)
% 2.74/1.58 % (14093)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_13872 for (2999ds/4Mi)
% 2.74/1.58 % (14096)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_13872 for (2999ds/2Mi)
% 2.74/1.58 % (14094)Instruction limit reached!
% 2.74/1.58 % (14094)------------------------------
% 2.74/1.58 % (14094)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.58 % (14094)Termination reason: Unknown
% 2.74/1.58 % (14094)Termination phase: shuffling
% 2.74/1.58
% 2.74/1.58 % (14094)Memory used [KB]: 1918
% 2.74/1.58 % (14094)Time elapsed: 0.010 s
% 2.74/1.58 % (14094)Instructions burned: 29 (million)
% 2.74/1.58 % (14094)------------------------------
% 2.74/1.58 % (14094)------------------------------
% 2.74/1.58 % (14098)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/18Mi)
% 2.74/1.58 % (14096)Instruction limit reached!
% 2.74/1.58 % (14096)------------------------------
% 2.74/1.58 % (14096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.58 % (14096)Termination reason: Unknown
% 2.74/1.58 % (14096)Termination phase: shuffling
% 2.74/1.58
% 2.74/1.58 % (14096)Memory used [KB]: 1407
% 2.74/1.58 % (14096)Time elapsed: 0.003 s
% 2.74/1.58 % (14096)Instructions burned: 3 (million)
% 2.74/1.58 % (14096)------------------------------
% 2.74/1.58 % (14096)------------------------------
% 2.74/1.58 % (14093)Instruction limit reached!
% 2.74/1.58 % (14093)------------------------------
% 2.74/1.58 % (14093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.58 % (14093)Termination reason: Unknown
% 2.74/1.58 % (14093)Termination phase: shuffling
% 2.74/1.58
% 2.74/1.58 % (14093)Memory used [KB]: 1407
% 2.74/1.58 % (14093)Time elapsed: 0.004 s
% 2.74/1.58 % (14093)Instructions burned: 4 (million)
% 2.74/1.58 % (14093)------------------------------
% 2.74/1.58 % (14093)------------------------------
% 2.74/1.58 % (14099)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/3Mi)
% 2.74/1.58 % (14099)Instruction limit reached!
% 2.74/1.58 % (14099)------------------------------
% 2.74/1.58 % (14099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.58 % (14099)Termination reason: Unknown
% 2.74/1.58 % (14099)Termination phase: shuffling
% 2.74/1.58
% 2.74/1.58 % (14099)Memory used [KB]: 1535
% 2.74/1.58 % (14099)Time elapsed: 0.003 s
% 2.74/1.58 % (14099)Instructions burned: 6 (million)
% 2.74/1.58 % (14099)------------------------------
% 2.74/1.58 % (14099)------------------------------
% 2.74/1.59 % (14100)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_13872 for (2999ds/37Mi)
% 2.74/1.59 % (14098)Instruction limit reached!
% 2.74/1.59 % (14098)------------------------------
% 2.74/1.59 % (14098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.74/1.59 % (14098)Termination reason: Unknown
% 2.74/1.59 % (14098)Termination phase: shuffling
% 2.74/1.59
% 2.74/1.59 % (14098)Memory used [KB]: 1791
% 2.74/1.59 % (14098)Time elapsed: 0.013 s
% 2.74/1.59 % (14098)Instructions burned: 19 (million)
% 2.74/1.59 % (14098)------------------------------
% 2.74/1.59 % (14098)------------------------------
% 2.74/1.59 % (14103)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_13872 for (2999ds/1041Mi)
% 2.78/1.60 % (14101)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_13872 for (2999ds/15Mi)
% 2.78/1.60 % (14102)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_13872 for (2999ds/3Mi)
% 2.78/1.60 % (14100)Instruction limit reached!
% 2.78/1.60 % (14100)------------------------------
% 2.78/1.60 % (14100)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.60 % (14100)Termination reason: Unknown
% 2.78/1.60 % (14100)Termination phase: shuffling
% 2.78/1.60
% 2.78/1.60 % (14100)Memory used [KB]: 2302
% 2.78/1.60 % (14100)Time elapsed: 0.012 s
% 2.78/1.60 % (14100)Instructions burned: 40 (million)
% 2.78/1.60 % (14100)------------------------------
% 2.78/1.60 % (14100)------------------------------
% 2.78/1.60 % (14102)Instruction limit reached!
% 2.78/1.60 % (14102)------------------------------
% 2.78/1.60 % (14102)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.60 % (14102)Termination reason: Unknown
% 2.78/1.60 % (14102)Termination phase: shuffling
% 2.78/1.60
% 2.78/1.60 % (14102)Memory used [KB]: 1407
% 2.78/1.60 % (14102)Time elapsed: 0.004 s
% 2.78/1.60 % (14102)Instructions burned: 3 (million)
% 2.78/1.60 % (14102)------------------------------
% 2.78/1.60 % (14102)------------------------------
% 2.78/1.61 % (14101)Instruction limit reached!
% 2.78/1.61 % (14101)------------------------------
% 2.78/1.61 % (14101)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.61 % (14101)Termination reason: Unknown
% 2.78/1.61 % (14101)Termination phase: shuffling
% 2.78/1.61
% 2.78/1.61 % (14101)Memory used [KB]: 1663
% 2.78/1.61 % (14101)Time elapsed: 0.011 s
% 2.78/1.61 % (14101)Instructions burned: 16 (million)
% 2.78/1.61 % (14101)------------------------------
% 2.78/1.61 % (14101)------------------------------
% 2.78/1.61 % (14104)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/7Mi)
% 2.78/1.61 % (14105)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/16Mi)
% 2.78/1.61 % (14104)Instruction limit reached!
% 2.78/1.61 % (14104)------------------------------
% 2.78/1.61 % (14104)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.61 % (14104)Termination reason: Unknown
% 2.78/1.61 % (14104)Termination phase: shuffling
% 2.78/1.61
% 2.78/1.61 % (14104)Memory used [KB]: 1535
% 2.78/1.61 % (14104)Time elapsed: 0.006 s
% 2.78/1.61 % (14104)Instructions burned: 7 (million)
% 2.78/1.61 % (14104)------------------------------
% 2.78/1.61 % (14104)------------------------------
% 2.78/1.61 % (14105)Instruction limit reached!
% 2.78/1.61 % (14105)------------------------------
% 2.78/1.61 % (14105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.61 % (14105)Termination reason: Unknown
% 2.78/1.61 % (14105)Termination phase: shuffling
% 2.78/1.61
% 2.78/1.61 % (14105)Memory used [KB]: 1791
% 2.78/1.61 % (14105)Time elapsed: 0.006 s
% 2.78/1.61 % (14105)Instructions burned: 18 (million)
% 2.78/1.61 % (14105)------------------------------
% 2.78/1.61 % (14105)------------------------------
% 2.78/1.62 % (14106)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_13872 for (2999ds/3Mi)
% 2.78/1.62 % (14106)Instruction limit reached!
% 2.78/1.62 % (14106)------------------------------
% 2.78/1.62 % (14106)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.62 % (14106)Termination reason: Unknown
% 2.78/1.62 % (14106)Termination phase: shuffling
% 2.78/1.62
% 2.78/1.62 % (14106)Memory used [KB]: 1407
% 2.78/1.62 % (14106)Time elapsed: 0.004 s
% 2.78/1.62 % (14106)Instructions burned: 3 (million)
% 2.78/1.62 % (14106)------------------------------
% 2.78/1.62 % (14106)------------------------------
% 2.78/1.62 % (14109)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/3Mi)
% 2.78/1.62 % (14109)Instruction limit reached!
% 2.78/1.62 % (14109)------------------------------
% 2.78/1.62 % (14109)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.62 % (14109)Termination reason: Unknown
% 2.78/1.62 % (14109)Termination phase: shuffling
% 2.78/1.62
% 2.78/1.62 % (14109)Memory used [KB]: 1407
% 2.78/1.62 % (14109)Time elapsed: 0.002 s
% 2.78/1.62 % (14109)Instructions burned: 3 (million)
% 2.78/1.62 % (14109)------------------------------
% 2.78/1.62 % (14109)------------------------------
% 2.78/1.62 % (14107)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_13872 for (2999ds/3Mi)
% 2.78/1.62 % (14107)Instruction limit reached!
% 2.78/1.62 % (14107)------------------------------
% 2.78/1.62 % (14107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.62 % (14107)Termination reason: Unknown
% 2.78/1.62 % (14107)Termination phase: shuffling
% 2.78/1.62
% 2.78/1.62 % (14107)Memory used [KB]: 1407
% 2.78/1.62 % (14107)Time elapsed: 0.004 s
% 2.78/1.62 % (14107)Instructions burned: 4 (million)
% 2.78/1.62 % (14107)------------------------------
% 2.78/1.62 % (14107)------------------------------
% 2.78/1.63 % (14108)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/7Mi)
% 2.78/1.63 % (14108)Instruction limit reached!
% 2.78/1.63 % (14108)------------------------------
% 2.78/1.63 % (14108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.63 % (14108)Termination reason: Unknown
% 2.78/1.63 % (14108)Termination phase: shuffling
% 2.78/1.63
% 2.78/1.63 % (14108)Memory used [KB]: 1535
% 2.78/1.63 % (14108)Time elapsed: 0.005 s
% 2.78/1.63 % (14108)Instructions burned: 7 (million)
% 2.78/1.63 % (14108)------------------------------
% 2.78/1.63 % (14108)------------------------------
% 2.78/1.63 % (14111)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/18Mi)
% 2.78/1.64 % (14110)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/4Mi)
% 2.78/1.64 % (14112)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/710Mi)
% 2.78/1.64 % (14111)Instruction limit reached!
% 2.78/1.64 % (14111)------------------------------
% 2.78/1.64 % (14111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.64 % (14111)Termination reason: Unknown
% 2.78/1.64 % (14111)Termination phase: shuffling
% 2.78/1.64
% 2.78/1.64 % (14111)Memory used [KB]: 1791
% 2.78/1.64 % (14111)Time elapsed: 0.006 s
% 2.78/1.64 % (14111)Instructions burned: 18 (million)
% 2.78/1.64 % (14111)------------------------------
% 2.78/1.64 % (14111)------------------------------
% 2.78/1.64 % (14110)Instruction limit reached!
% 2.78/1.64 % (14110)------------------------------
% 2.78/1.64 % (14110)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.64 % (14110)Termination reason: Unknown
% 2.78/1.64 % (14110)Termination phase: shuffling
% 2.78/1.64
% 2.78/1.64 % (14110)Memory used [KB]: 1535
% 2.78/1.64 % (14110)Time elapsed: 0.005 s
% 2.78/1.64 % (14110)Instructions burned: 5 (million)
% 2.78/1.64 % (14110)------------------------------
% 2.78/1.64 % (14110)------------------------------
% 2.78/1.64 % (14113)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/6Mi)
% 2.78/1.64 % (14113)Instruction limit reached!
% 2.78/1.64 % (14113)------------------------------
% 2.78/1.64 % (14113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.64 % (14113)Termination reason: Unknown
% 2.78/1.64 % (14113)Termination phase: shuffling
% 2.78/1.64
% 2.78/1.64 % (14113)Memory used [KB]: 1535
% 2.78/1.64 % (14113)Time elapsed: 0.004 s
% 2.78/1.64 % (14113)Instructions burned: 9 (million)
% 2.78/1.64 % (14113)------------------------------
% 2.78/1.64 % (14113)------------------------------
% 2.78/1.65 % (14114)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_13872 for (2999ds/902Mi)
% 2.78/1.65 % (14116)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13872 for (2999ds/5Mi)
% 2.78/1.66 % (14116)Instruction limit reached!
% 2.78/1.66 % (14116)------------------------------
% 2.78/1.66 % (14116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.66 % (14116)Termination reason: Unknown
% 2.78/1.66 % (14116)Termination phase: shuffling
% 2.78/1.66
% 2.78/1.66 % (14116)Memory used [KB]: 1535
% 2.78/1.66 % (14116)Time elapsed: 0.004 s
% 2.78/1.66 % (14116)Instructions burned: 7 (million)
% 2.78/1.66 % (14116)------------------------------
% 2.78/1.66 % (14116)------------------------------
% 2.78/1.66 % (14115)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_13872 for (2999ds/21Mi)
% 2.78/1.66 % (14097)Instruction limit reached!
% 2.78/1.66 % (14097)------------------------------
% 2.78/1.66 % (14097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.66 % (14097)Termination reason: Unknown
% 2.78/1.66 % (14097)Termination phase: Saturation
% 2.78/1.66
% 2.78/1.66 % (14097)Memory used [KB]: 9466
% 2.78/1.66 % (14097)Time elapsed: 0.089 s
% 2.78/1.66 % (14097)Instructions burned: 277 (million)
% 2.78/1.66 % (14097)------------------------------
% 2.78/1.66 % (14097)------------------------------
% 2.78/1.67 % (14115)Instruction limit reached!
% 2.78/1.67 % (14115)------------------------------
% 2.78/1.67 % (14115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.67 % (14115)Termination reason: Unknown
% 2.78/1.67 % (14115)Termination phase: shuffling
% 2.78/1.67
% 2.78/1.67 % (14115)Memory used [KB]: 1791
% 2.78/1.67 % (14115)Time elapsed: 0.012 s
% 2.78/1.67 % (14115)Instructions burned: 22 (million)
% 2.78/1.67 % (14115)------------------------------
% 2.78/1.67 % (14115)------------------------------
% 2.78/1.67 % (14117)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_13872 for (2998ds/6Mi)
% 2.78/1.67 % (14118)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13872 for (2998ds/377Mi)
% 2.78/1.67 % (14117)Instruction limit reached!
% 2.78/1.67 % (14117)------------------------------
% 2.78/1.67 % (14117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.67 % (14117)Termination reason: Unknown
% 2.78/1.67 % (14117)Termination phase: shuffling
% 2.78/1.67
% 2.78/1.67 % (14117)Memory used [KB]: 1535
% 2.78/1.67 % (14117)Time elapsed: 0.003 s
% 2.78/1.67 % (14117)Instructions burned: 7 (million)
% 2.78/1.67 % (14117)------------------------------
% 2.78/1.67 % (14117)------------------------------
% 2.78/1.67 % (14092)Instruction limit reached!
% 2.78/1.67 % (14092)------------------------------
% 2.78/1.67 % (14092)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.67 % (14092)Termination reason: Unknown
% 2.78/1.67 % (14092)Termination phase: Saturation
% 2.78/1.67
% 2.78/1.67 % (14092)Memory used [KB]: 7547
% 2.78/1.67 % (14092)Time elapsed: 0.094 s
% 2.78/1.67 % (14092)Instructions burned: 185 (million)
% 2.78/1.67 % (14092)------------------------------
% 2.78/1.67 % (14092)------------------------------
% 2.78/1.68 % (14119)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_13872 for (2998ds/779Mi)
% 2.78/1.68 % (14120)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_13872 for (2998ds/19Mi)
% 2.78/1.68 % (14121)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13872 for (2998ds/879Mi)
% 2.78/1.68 % (14120)Instruction limit reached!
% 2.78/1.68 % (14120)------------------------------
% 2.78/1.68 % (14120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.68 % (14120)Termination reason: Unknown
% 2.78/1.68 % (14120)Termination phase: shuffling
% 2.78/1.68
% 2.78/1.68 % (14120)Memory used [KB]: 1791
% 2.78/1.68 % (14120)Time elapsed: 0.008 s
% 2.78/1.68 % (14120)Instructions burned: 21 (million)
% 2.78/1.68 % (14120)------------------------------
% 2.78/1.68 % (14120)------------------------------
% 2.78/1.70 % (14122)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13872 for (2998ds/17Mi)
% 2.78/1.70 % (14122)Instruction limit reached!
% 2.78/1.70 % (14122)------------------------------
% 2.78/1.70 % (14122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.70 % (14122)Termination reason: Unknown
% 2.78/1.70 % (14122)Termination phase: shuffling
% 2.78/1.70
% 2.78/1.70 % (14122)Memory used [KB]: 1791
% 2.78/1.70 % (14122)Time elapsed: 0.006 s
% 2.78/1.70 % (14122)Instructions burned: 17 (million)
% 2.78/1.70 % (14122)------------------------------
% 2.78/1.70 % (14122)------------------------------
% 2.78/1.71 % (14123)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13872 for (2998ds/3Mi)
% 2.78/1.71 % (14123)Instruction limit reached!
% 2.78/1.71 % (14123)------------------------------
% 2.78/1.71 % (14123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.71 % (14123)Termination reason: Unknown
% 2.78/1.71 % (14123)Termination phase: shuffling
% 2.78/1.71
% 2.78/1.71 % (14123)Memory used [KB]: 1407
% 2.78/1.71 % (14123)Time elapsed: 0.002 s
% 2.78/1.71 % (14123)Instructions burned: 4 (million)
% 2.78/1.71 % (14123)------------------------------
% 2.78/1.71 % (14123)------------------------------
% 2.78/1.72 % (14124)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13872 for (2998ds/30Mi)
% 2.78/1.73 % (14124)Instruction limit reached!
% 2.78/1.73 % (14124)------------------------------
% 2.78/1.73 % (14124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.73 % (14124)Termination reason: Unknown
% 2.78/1.73 % (14124)Termination phase: shuffling
% 2.78/1.73
% 2.78/1.73 % (14124)Memory used [KB]: 2046
% 2.78/1.73 % (14124)Time elapsed: 0.011 s
% 2.78/1.73 % (14124)Instructions burned: 31 (million)
% 2.78/1.73 % (14124)------------------------------
% 2.78/1.73 % (14124)------------------------------
% 2.78/1.74 % (14125)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13872 for (2998ds/127Mi)
% 2.78/1.78 % (14125)Instruction limit reached!
% 2.78/1.78 % (14125)------------------------------
% 2.78/1.78 % (14125)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.78 % (14125)Termination reason: Unknown
% 2.78/1.78 % (14125)Termination phase: Property scanning
% 2.78/1.78
% 2.78/1.78 % (14125)Memory used [KB]: 2558
% 2.78/1.78 % (14125)Time elapsed: 0.036 s
% 2.78/1.78 % (14125)Instructions burned: 127 (million)
% 2.78/1.78 % (14125)------------------------------
% 2.78/1.78 % (14125)------------------------------
% 2.78/1.78 % (14118)Instruction limit reached!
% 2.78/1.78 % (14118)------------------------------
% 2.78/1.78 % (14118)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.78 % (14118)Termination reason: Unknown
% 2.78/1.78 % (14118)Termination phase: Saturation
% 2.78/1.78
% 2.78/1.78 % (14118)Memory used [KB]: 8827
% 2.78/1.78 % (14118)Time elapsed: 0.111 s
% 2.78/1.78 % (14118)Instructions burned: 378 (million)
% 2.78/1.78 % (14118)------------------------------
% 2.78/1.78 % (14118)------------------------------
% 2.78/1.79 % (14126)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13872 for (2997ds/100Mi)
% 2.78/1.79 % (14127)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_13872 for (2997ds/3Mi)
% 2.78/1.79 % (14127)Instruction limit reached!
% 2.78/1.79 % (14127)------------------------------
% 2.78/1.79 % (14127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.79 % (14127)Termination reason: Unknown
% 2.78/1.79 % (14127)Termination phase: shuffling
% 2.78/1.79
% 2.78/1.79 % (14127)Memory used [KB]: 1407
% 2.78/1.79 % (14127)Time elapsed: 0.002 s
% 2.78/1.79 % (14127)Instructions burned: 3 (million)
% 2.78/1.79 % (14127)------------------------------
% 2.78/1.79 % (14127)------------------------------
% 2.78/1.80 % (14128)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_13872 for (2997ds/20Mi)
% 2.78/1.80 % (14128)Instruction limit reached!
% 2.78/1.80 % (14128)------------------------------
% 2.78/1.80 % (14128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.80 % (14128)Termination reason: Unknown
% 2.78/1.80 % (14128)Termination phase: shuffling
% 2.78/1.80
% 2.78/1.80 % (14128)Memory used [KB]: 1918
% 2.78/1.81 % (14128)Time elapsed: 0.008 s
% 2.78/1.81 % (14128)Instructions burned: 22 (million)
% 2.78/1.81 % (14128)------------------------------
% 2.78/1.81 % (14128)------------------------------
% 2.78/1.81 % (14129)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_13872 for (2997ds/86Mi)
% 2.78/1.81 % (14126)Instruction limit reached!
% 2.78/1.81 % (14126)------------------------------
% 2.78/1.81 % (14126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.81 % (14126)Termination reason: Unknown
% 2.78/1.81 % (14126)Termination phase: Function definition elimination
% 2.78/1.81
% 2.78/1.81 % (14126)Memory used [KB]: 2558
% 2.78/1.81 % (14126)Time elapsed: 0.029 s
% 2.78/1.81 % (14126)Instructions burned: 102 (million)
% 2.78/1.81 % (14126)------------------------------
% 2.78/1.81 % (14126)------------------------------
% 2.78/1.83 % (14130)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_13872 for (2997ds/107Mi)
% 2.78/1.84 % (14129)Instruction limit reached!
% 2.78/1.84 % (14129)------------------------------
% 2.78/1.84 % (14129)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.84 % (14129)Termination reason: Unknown
% 2.78/1.84 % (14129)Termination phase: Property scanning
% 2.78/1.84
% 2.78/1.84 % (14129)Memory used [KB]: 2430
% 2.78/1.84 % (14129)Time elapsed: 0.024 s
% 2.78/1.84 % (14129)Instructions burned: 86 (million)
% 2.78/1.84 % (14129)------------------------------
% 2.78/1.84 % (14129)------------------------------
% 2.78/1.85 % (14131)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_13872 for (2997ds/39Mi)
% 2.78/1.86 % (14130)Instruction limit reached!
% 2.78/1.86 % (14130)------------------------------
% 2.78/1.86 % (14130)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.86 % (14130)Termination reason: Unknown
% 2.78/1.86 % (14130)Termination phase: Property scanning
% 2.78/1.86
% 2.78/1.86 % (14130)Memory used [KB]: 2430
% 2.78/1.86 % (14130)Time elapsed: 0.031 s
% 2.78/1.86 % (14130)Instructions burned: 108 (million)
% 2.78/1.86 % (14130)------------------------------
% 2.78/1.86 % (14130)------------------------------
% 2.78/1.86 % (14103)Instruction limit reached!
% 2.78/1.86 % (14103)------------------------------
% 2.78/1.86 % (14103)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.86 % (14131)Instruction limit reached!
% 2.78/1.86 % (14131)------------------------------
% 2.78/1.86 % (14131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.86 % (14103)Termination reason: Unknown
% 2.78/1.86 % (14131)Termination reason: Unknown
% 2.78/1.86 % (14103)Termination phase: Saturation
% 2.78/1.86
% 2.78/1.86 % (14131)Termination phase: shuffling
% 2.78/1.86
% 2.78/1.86 % (14131)Memory used [KB]: 2302
% 2.78/1.86 % (14103)Memory used [KB]: 14072
% 2.78/1.86 % (14131)Time elapsed: 0.012 s
% 2.78/1.86 % (14103)Time elapsed: 0.268 s
% 2.78/1.86 % (14131)Instructions burned: 42 (million)
% 2.78/1.86 % (14103)Instructions burned: 1043 (million)
% 2.78/1.86 % (14131)------------------------------
% 2.78/1.86 % (14131)------------------------------
% 2.78/1.86 % (14103)------------------------------
% 2.78/1.86 % (14103)------------------------------
% 2.78/1.87 % (14132)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_13872 for (2997ds/448Mi)
% 2.78/1.87 % (14133)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_13872 for (2996ds/46Mi)
% 2.78/1.87 % (14134)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_13872 for (2996ds/98Mi)
% 2.78/1.87 % (14112)Refutation not found, non-redundant clauses discarded% (14112)------------------------------
% 2.78/1.87 % (14112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.87 % (14112)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.78/1.87
% 2.78/1.87 % (14112)Memory used [KB]: 10234
% 2.78/1.87 % (14112)Time elapsed: 0.237 s
% 2.78/1.87 % (14112)Instructions burned: 691 (million)
% 2.78/1.87 % (14112)------------------------------
% 2.78/1.87 % (14112)------------------------------
% 2.78/1.88 % (14133)Instruction limit reached!
% 2.78/1.88 % (14133)------------------------------
% 2.78/1.88 % (14133)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.88 % (14133)Termination reason: Unknown
% 2.78/1.88 % (14133)Termination phase: Property scanning
% 2.78/1.88
% 2.78/1.88 % (14133)Memory used [KB]: 2302
% 2.78/1.88 % (14133)Time elapsed: 0.014 s
% 2.78/1.88 % (14133)Instructions burned: 48 (million)
% 2.78/1.88 % (14133)------------------------------
% 2.78/1.88 % (14133)------------------------------
% 2.78/1.88 % (14135)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_13872 for (2996ds/507Mi)
% 2.78/1.89 % (14119)Instruction limit reached!
% 2.78/1.89 % (14119)------------------------------
% 2.78/1.89 % (14119)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.89 % (14119)Termination reason: Unknown
% 2.78/1.89 % (14119)Termination phase: Saturation
% 2.78/1.89
% 2.78/1.89 % (14119)Memory used [KB]: 7419
% 2.78/1.89 % (14119)Time elapsed: 0.212 s
% 2.78/1.89 % (14119)Instructions burned: 781 (million)
% 2.78/1.89 % (14119)------------------------------
% 2.78/1.89 % (14119)------------------------------
% 2.78/1.89 % (14136)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_13872 for (2996ds/149Mi)
% 2.78/1.89 % (14134)Instruction limit reached!
% 2.78/1.89 % (14134)------------------------------
% 2.78/1.89 % (14134)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.89 % (14134)Termination reason: Unknown
% 2.78/1.89 % (14134)Termination phase: Function definition elimination
% 2.78/1.89
% 2.78/1.89 % (14134)Memory used [KB]: 2430
% 2.78/1.89 % (14134)Time elapsed: 0.026 s
% 2.78/1.89 % (14134)Instructions burned: 99 (million)
% 2.78/1.89 % (14134)------------------------------
% 2.78/1.89 % (14134)------------------------------
% 2.78/1.90 % (14137)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_13872 for (2996ds/39Mi)
% 2.78/1.90 % (14138)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_13872 for (2996ds/6Mi)
% 2.78/1.90 % (14138)Instruction limit reached!
% 2.78/1.90 % (14138)------------------------------
% 2.78/1.90 % (14138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.90 % (14138)Termination reason: Unknown
% 2.78/1.90 % (14138)Termination phase: shuffling
% 2.78/1.90
% 2.78/1.90 % (14138)Memory used [KB]: 1535
% 2.78/1.90 % (14138)Time elapsed: 0.003 s
% 2.78/1.90 % (14138)Instructions burned: 6 (million)
% 2.78/1.90 % (14138)------------------------------
% 2.78/1.90 % (14138)------------------------------
% 2.78/1.91 % (14137)Instruction limit reached!
% 2.78/1.91 % (14137)------------------------------
% 2.78/1.91 % (14137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.91 % (14137)Termination reason: Unknown
% 2.78/1.91 % (14137)Termination phase: shuffling
% 2.78/1.91
% 2.78/1.91 % (14137)Memory used [KB]: 2302
% 2.78/1.91 % (14137)Time elapsed: 0.013 s
% 2.78/1.91 % (14137)Instructions burned: 41 (million)
% 2.78/1.91 % (14137)------------------------------
% 2.78/1.91 % (14137)------------------------------
% 2.78/1.91 % (14139)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_13872 for (2996ds/1087Mi)
% 2.78/1.92 % (14114)Instruction limit reached!
% 2.78/1.92 % (14114)------------------------------
% 2.78/1.92 % (14114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.92 % (14114)Termination reason: Unknown
% 2.78/1.92 % (14114)Termination phase: Saturation
% 2.78/1.92
% 2.78/1.92 % (14114)Memory used [KB]: 12281
% 2.78/1.92 % (14114)Time elapsed: 0.274 s
% 2.78/1.92 % (14114)Instructions burned: 903 (million)
% 2.78/1.92 % (14114)------------------------------
% 2.78/1.92 % (14114)------------------------------
% 2.78/1.92 % (14140)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_13872 for (2996ds/47Mi)
% 2.78/1.93 % (14136)Instruction limit reached!
% 2.78/1.93 % (14136)------------------------------
% 2.78/1.93 % (14136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.93 % (14136)Termination reason: Unknown
% 2.78/1.93 % (14136)Termination phase: Property scanning
% 2.78/1.93
% 2.78/1.93 % (14136)Memory used [KB]: 3070
% 2.78/1.93 % (14136)Time elapsed: 0.040 s
% 2.78/1.93 % (14136)Instructions burned: 150 (million)
% 2.78/1.93 % (14136)------------------------------
% 2.78/1.93 % (14136)------------------------------
% 2.78/1.93 % (14141)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_13872 for (2996ds/44Mi)
% 2.78/1.94 % (14140)Instruction limit reached!
% 2.78/1.94 % (14140)------------------------------
% 2.78/1.94 % (14140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.94 % (14140)Termination reason: Unknown
% 2.78/1.94 % (14140)Termination phase: Property scanning
% 2.78/1.94
% 2.78/1.94 % (14140)Memory used [KB]: 2302
% 2.78/1.94 % (14140)Time elapsed: 0.015 s
% 2.78/1.94 % (14140)Instructions burned: 48 (million)
% 2.78/1.94 % (14140)------------------------------
% 2.78/1.94 % (14140)------------------------------
% 2.78/1.94 % (14142)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_13872 for (2996ds/432Mi)
% 2.78/1.94 % (14141)Instruction limit reached!
% 2.78/1.94 % (14141)------------------------------
% 2.78/1.94 % (14141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.94 % (14141)Termination reason: Unknown
% 2.78/1.94 % (14141)Termination phase: Property scanning
% 2.78/1.94
% 2.78/1.94 % (14141)Memory used [KB]: 2302
% 2.78/1.94 % (14141)Time elapsed: 0.013 s
% 2.78/1.94 % (14141)Instructions burned: 46 (million)
% 2.78/1.94 % (14141)------------------------------
% 2.78/1.94 % (14141)------------------------------
% 2.78/1.95 % (14143)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_13872 for (2996ds/62Mi)
% 2.78/1.95 % (14144)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_13872 for (2996ds/31Mi)
% 2.78/1.96 % (14144)Instruction limit reached!
% 2.78/1.96 % (14144)------------------------------
% 2.78/1.96 % (14144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.96 % (14144)Termination reason: Unknown
% 2.78/1.96 % (14144)Termination phase: shuffling
% 2.78/1.96
% 2.78/1.96 % (14144)Memory used [KB]: 2046
% 2.78/1.96 % (14144)Time elapsed: 0.010 s
% 2.78/1.96 % (14144)Instructions burned: 33 (million)
% 2.78/1.96 % (14144)------------------------------
% 2.78/1.96 % (14144)------------------------------
% 2.78/1.96 % (14143)Instruction limit reached!
% 2.78/1.96 % (14143)------------------------------
% 2.78/1.96 % (14143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.96 % (14143)Termination reason: Unknown
% 2.78/1.96 % (14143)Termination phase: Property scanning
% 2.78/1.96
% 2.78/1.96 % (14143)Memory used [KB]: 2302
% 2.78/1.96 % (14143)Time elapsed: 0.019 s
% 2.78/1.96 % (14143)Instructions burned: 65 (million)
% 2.78/1.96 % (14143)------------------------------
% 2.78/1.96 % (14143)------------------------------
% 2.78/1.97 % (14145)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_13872 for (2995ds/96Mi)
% 2.78/1.97 % (14121)Instruction limit reached!
% 2.78/1.97 % (14121)------------------------------
% 2.78/1.97 % (14121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.97 % (14121)Termination reason: Unknown
% 2.78/1.97 % (14121)Termination phase: Saturation
% 2.78/1.97
% 2.78/1.97 % (14121)Memory used [KB]: 9594
% 2.78/1.97 % (14121)Time elapsed: 0.291 s
% 2.78/1.97 % (14121)Instructions burned: 880 (million)
% 2.78/1.97 % (14121)------------------------------
% 2.78/1.97 % (14121)------------------------------
% 2.78/1.97 % (14146)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_13872 for (2995ds/453Mi)
% 2.78/1.99 % (14132)Instruction limit reached!
% 2.78/1.99 % (14132)------------------------------
% 2.78/1.99 % (14132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.99 % (14132)Termination reason: Unknown
% 2.78/1.99 % (14132)Termination phase: Saturation
% 2.78/1.99
% 2.78/1.99 % (14132)Memory used [KB]: 7291
% 2.78/1.99 % (14132)Time elapsed: 0.122 s
% 2.78/1.99 % (14132)Instructions burned: 451 (million)
% 2.78/1.99 % (14132)------------------------------
% 2.78/1.99 % (14132)------------------------------
% 2.78/1.99 % (14147)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_13872 for (2995ds/71Mi)
% 2.78/1.99 % (14145)Instruction limit reached!
% 2.78/1.99 % (14145)------------------------------
% 2.78/1.99 % (14145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/1.99 % (14145)Termination reason: Unknown
% 2.78/1.99 % (14145)Termination phase: Function definition elimination
% 2.78/1.99
% 2.78/1.99 % (14145)Memory used [KB]: 2558
% 2.78/1.99 % (14145)Time elapsed: 0.027 s
% 2.78/1.99 % (14145)Instructions burned: 98 (million)
% 2.78/1.99 % (14145)------------------------------
% 2.78/1.99 % (14145)------------------------------
% 2.78/2.00 % (14148)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_13872 for (2995ds/83Mi)
% 2.78/2.00 % (14149)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_13872 for (2995ds/11Mi)
% 2.78/2.01 % (14149)Instruction limit reached!
% 2.78/2.01 % (14149)------------------------------
% 2.78/2.01 % (14149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.78/2.01 % (14149)Termination reason: Unknown
% 2.78/2.01 % (14149)Termination phase: shuffling
% 2.78/2.01
% 2.78/2.01 % (14149)Memory used [KB]: 1535
% 2.78/2.01 % (14149)Time elapsed: 0.004 s
% 2.78/2.01 % (14149)Instructions burned: 12 (million)
% 2.78/2.01 % (14149)------------------------------
% 2.78/2.01 % (14149)------------------------------
% 5.93/2.02 % (14150)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_13872 for (2995ds/41Mi)
% 5.93/2.02 % (14148)Instruction limit reached!
% 5.93/2.02 % (14148)------------------------------
% 5.93/2.02 % (14148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.02 % (14148)Termination reason: Unknown
% 5.93/2.02 % (14148)Termination phase: SInE selection
% 5.93/2.02
% 5.93/2.02 % (14148)Memory used [KB]: 2302
% 5.93/2.02 % (14148)Time elapsed: 0.023 s
% 5.93/2.02 % (14148)Instructions burned: 84 (million)
% 5.93/2.02 % (14148)------------------------------
% 5.93/2.02 % (14148)------------------------------
% 5.93/2.03 % (14150)Instruction limit reached!
% 5.93/2.03 % (14150)------------------------------
% 5.93/2.03 % (14150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.03 % (14150)Termination reason: Unknown
% 5.93/2.03 % (14150)Termination phase: shuffling
% 5.93/2.03
% 5.93/2.03 % (14150)Memory used [KB]: 2302
% 5.93/2.03 % (14150)Time elapsed: 0.012 s
% 5.93/2.03 % (14150)Instructions burned: 41 (million)
% 5.93/2.03 % (14150)------------------------------
% 5.93/2.03 % (14150)------------------------------
% 5.93/2.03 % (14147)Instruction limit reached!
% 5.93/2.03 % (14147)------------------------------
% 5.93/2.03 % (14147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.03 % (14147)Termination reason: Unknown
% 5.93/2.03 % (14147)Termination phase: Property scanning
% 5.93/2.03
% 5.93/2.03 % (14147)Memory used [KB]: 2430
% 5.93/2.03 % (14147)Time elapsed: 0.038 s
% 5.93/2.03 % (14147)Instructions burned: 71 (million)
% 5.93/2.03 % (14147)------------------------------
% 5.93/2.03 % (14147)------------------------------
% 5.93/2.03 % (14151)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13872 for (2995ds/6Mi)
% 5.93/2.03 % (14151)Instruction limit reached!
% 5.93/2.03 % (14151)------------------------------
% 5.93/2.03 % (14151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.03 % (14151)Termination reason: Unknown
% 5.93/2.03 % (14151)Termination phase: shuffling
% 5.93/2.03
% 5.93/2.03 % (14151)Memory used [KB]: 1535
% 5.93/2.03 % (14151)Time elapsed: 0.003 s
% 5.93/2.03 % (14151)Instructions burned: 7 (million)
% 5.93/2.03 % (14151)------------------------------
% 5.93/2.03 % (14151)------------------------------
% 5.93/2.04 % (14135)Instruction limit reached!
% 5.93/2.04 % (14135)------------------------------
% 5.93/2.04 % (14135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.04 % (14135)Termination reason: Unknown
% 5.93/2.04 % (14135)Termination phase: Saturation
% 5.93/2.04
% 5.93/2.04 % (14135)Memory used [KB]: 7931
% 5.93/2.04 % (14135)Time elapsed: 0.177 s
% 5.93/2.04 % (14135)Instructions burned: 507 (million)
% 5.93/2.04 % (14135)------------------------------
% 5.93/2.04 % (14135)------------------------------
% 5.93/2.04 % (14152)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_13872 for (2995ds/150Mi)
% 5.93/2.04 % (14154)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_13872 for (2995ds/109Mi)
% 5.93/2.05 % (14153)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_13872 for (2995ds/343Mi)
% 5.93/2.05 % (14155)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_13872 for (2995ds/253Mi)
% 5.93/2.05 % (14142)Instruction limit reached!
% 5.93/2.05 % (14142)------------------------------
% 5.93/2.05 % (14142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.05 % (14142)Termination reason: Unknown
% 5.93/2.05 % (14142)Termination phase: Saturation
% 5.93/2.05
% 5.93/2.05 % (14142)Memory used [KB]: 2942
% 5.93/2.05 % (14142)Time elapsed: 0.109 s
% 5.93/2.05 % (14142)Instructions burned: 432 (million)
% 5.93/2.05 % (14142)------------------------------
% 5.93/2.05 % (14142)------------------------------
% 5.93/2.06 % (14156)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_13872 for (2995ds/140Mi)
% 5.93/2.07 % (14154)Instruction limit reached!
% 5.93/2.07 % (14154)------------------------------
% 5.93/2.07 % (14154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.07 % (14154)Termination reason: Unknown
% 5.93/2.07 % (14154)Termination phase: Property scanning
% 5.93/2.07
% 5.93/2.07 % (14154)Memory used [KB]: 2430
% 5.93/2.07 % (14154)Time elapsed: 0.029 s
% 5.93/2.07 % (14154)Instructions burned: 111 (million)
% 5.93/2.07 % (14154)------------------------------
% 5.93/2.07 % (14154)------------------------------
% 5.93/2.08 % (14157)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_13872 for (2994ds/614Mi)
% 5.93/2.08 % (14152)Instruction limit reached!
% 5.93/2.08 % (14152)------------------------------
% 5.93/2.08 % (14152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.08 % (14152)Termination reason: Unknown
% 5.93/2.08 % (14152)Termination phase: Property scanning
% 5.93/2.08
% 5.93/2.08 % (14152)Memory used [KB]: 4349
% 5.93/2.08 % (14152)Time elapsed: 0.044 s
% 5.93/2.08 % (14152)Instructions burned: 153 (million)
% 5.93/2.08 % (14152)------------------------------
% 5.93/2.08 % (14152)------------------------------
% 5.93/2.09 % (14158)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_13872 for (2994ds/202Mi)
% 5.93/2.09 % (14146)Instruction limit reached!
% 5.93/2.09 % (14146)------------------------------
% 5.93/2.09 % (14146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.09 % (14146)Termination reason: Unknown
% 5.93/2.09 % (14146)Termination phase: Saturation
% 5.93/2.09
% 5.93/2.09 % (14146)Memory used [KB]: 7419
% 5.93/2.09 % (14146)Time elapsed: 0.118 s
% 5.93/2.09 % (14146)Instructions burned: 455 (million)
% 5.93/2.09 % (14146)------------------------------
% 5.93/2.09 % (14146)------------------------------
% 5.93/2.09 % (14156)Instruction limit reached!
% 5.93/2.09 % (14156)------------------------------
% 5.93/2.09 % (14156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.93/2.09 % (14156)Termination reason: Unknown
% 5.93/2.09 % (14156)Termination phase: Saturation
% 5.93/2.09
% 5.93/2.09 % (14156)Memory used [KB]: 7036
% 5.93/2.09 % (14156)Time elapsed: 0.038 s
% 5.93/2.09 % (14156)Instructions burned: 142 (million)
% 5.93/2.09 % (14156)------------------------------
% 5.93/2.09 % (14156)------------------------------
% 5.93/2.10 % (14159)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_13872 for (2994ds/339Mi)
% 5.93/2.10 % (14160)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_13872 for (2994ds/283Mi)
% 6.38/2.12 % (14155)Instruction limit reached!
% 6.38/2.12 % (14155)------------------------------
% 6.38/2.12 % (14155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.12 % (14155)Termination reason: Unknown
% 6.38/2.12 % (14155)Termination phase: Saturation
% 6.38/2.12
% 6.38/2.12 % (14155)Memory used [KB]: 9466
% 6.38/2.12 % (14155)Time elapsed: 0.074 s
% 6.38/2.12 % (14155)Instructions burned: 253 (million)
% 6.38/2.12 % (14155)------------------------------
% 6.38/2.12 % (14155)------------------------------
% 6.38/2.13 % (14161)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_13872 for (2994ds/134Mi)
% 6.38/2.15 % (14158)Instruction limit reached!
% 6.38/2.15 % (14158)------------------------------
% 6.38/2.15 % (14158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.15 % (14158)Termination reason: Unknown
% 6.38/2.15 % (14158)Termination phase: Saturation
% 6.38/2.15
% 6.38/2.15 % (14158)Memory used [KB]: 4733
% 6.38/2.15 % (14158)Time elapsed: 0.058 s
% 6.38/2.15 % (14158)Instructions burned: 203 (million)
% 6.38/2.15 % (14158)------------------------------
% 6.38/2.15 % (14158)------------------------------
% 6.38/2.16 % (14163)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_13872 for (2993ds/298Mi)
% 6.38/2.16 % (14161)Instruction limit reached!
% 6.38/2.16 % (14161)------------------------------
% 6.38/2.16 % (14161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.16 % (14161)Termination reason: Unknown
% 6.38/2.16 % (14161)Termination phase: Saturation
% 6.38/2.16
% 6.38/2.16 % (14161)Memory used [KB]: 7036
% 6.38/2.16 % (14161)Time elapsed: 0.035 s
% 6.38/2.16 % (14161)Instructions burned: 134 (million)
% 6.38/2.16 % (14161)------------------------------
% 6.38/2.16 % (14161)------------------------------
% 6.38/2.16 % (14153)Instruction limit reached!
% 6.38/2.16 % (14153)------------------------------
% 6.38/2.16 % (14153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.16 % (14153)Termination reason: Unknown
% 6.38/2.16 % (14153)Termination phase: Saturation
% 6.38/2.16
% 6.38/2.16 % (14153)Memory used [KB]: 8571
% 6.38/2.16 % (14153)Time elapsed: 0.120 s
% 6.38/2.16 % (14153)Instructions burned: 344 (million)
% 6.38/2.16 % (14153)------------------------------
% 6.38/2.16 % (14153)------------------------------
% 6.38/2.17 % (14164)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_13872 for (2993ds/192Mi)
% 6.38/2.17 % (14160)Instruction limit reached!
% 6.38/2.17 % (14160)------------------------------
% 6.38/2.17 % (14160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.38/2.17 % (14160)Termination reason: Unknown
% 6.38/2.17 % (14160)Termination phase: Saturation
% 6.38/2.17
% 6.38/2.17 % (14160)Memory used [KB]: 7291
% 6.38/2.17 % (14160)Time elapsed: 0.072 s
% 6.38/2.17 % (14160)Instructions burned: 284 (million)
% 6.38/2.17 % (14160)------------------------------
% 6.38/2.17 % (14160)------------------------------
% 6.38/2.17 % (14165)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_13872 for (2993ds/258Mi)
% 6.38/2.18 % (14166)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_13872 for (2993ds/90Mi)
% 6.88/2.20 % (14159)Instruction limit reached!
% 6.88/2.20 % (14159)------------------------------
% 6.88/2.20 % (14159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.20 % (14159)Termination reason: Unknown
% 6.88/2.20 % (14159)Termination phase: Saturation
% 6.88/2.20
% 6.88/2.20 % (14159)Memory used [KB]: 7675
% 6.88/2.20 % (14159)Time elapsed: 0.097 s
% 6.88/2.20 % (14159)Instructions burned: 342 (million)
% 6.88/2.20 % (14159)------------------------------
% 6.88/2.20 % (14159)------------------------------
% 6.88/2.21 % (14166)Instruction limit reached!
% 6.88/2.21 % (14166)------------------------------
% 6.88/2.21 % (14166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.21 % (14166)Termination reason: Unknown
% 6.88/2.21 % (14166)Termination phase: Property scanning
% 6.88/2.21
% 6.88/2.21 % (14166)Memory used [KB]: 2430
% 6.88/2.21 % (14166)Time elapsed: 0.025 s
% 6.88/2.21 % (14166)Instructions burned: 92 (million)
% 6.88/2.21 % (14166)------------------------------
% 6.88/2.21 % (14166)------------------------------
% 6.88/2.21 % (14167)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_13872 for (2993ds/231Mi)
% 6.88/2.22 % (14168)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_13872 for (2993ds/458Mi)
% 6.88/2.22 % (14164)Instruction limit reached!
% 6.88/2.22 % (14164)------------------------------
% 6.88/2.22 % (14164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.22 % (14164)Termination reason: Unknown
% 6.88/2.22 % (14164)Termination phase: Saturation
% 6.88/2.22
% 6.88/2.22 % (14164)Memory used [KB]: 7547
% 6.88/2.22 % (14164)Time elapsed: 0.052 s
% 6.88/2.22 % (14164)Instructions burned: 194 (million)
% 6.88/2.22 % (14164)------------------------------
% 6.88/2.22 % (14164)------------------------------
% 6.88/2.23 % (14163)Instruction limit reached!
% 6.88/2.23 % (14163)------------------------------
% 6.88/2.23 % (14163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.23 % (14163)Termination reason: Unknown
% 6.88/2.23 % (14163)Termination phase: Saturation
% 6.88/2.23
% 6.88/2.23 % (14163)Memory used [KB]: 7291
% 6.88/2.23 % (14163)Time elapsed: 0.076 s
% 6.88/2.23 % (14163)Instructions burned: 300 (million)
% 6.88/2.23 % (14163)------------------------------
% 6.88/2.23 % (14163)------------------------------
% 6.88/2.23 % (14169)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_13872 for (2993ds/31Mi)
% 6.88/2.24 % (14170)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_13872 for (2993ds/297Mi)
% 6.88/2.24 % (14169)Instruction limit reached!
% 6.88/2.24 % (14169)------------------------------
% 6.88/2.24 % (14169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.24 % (14169)Termination reason: Unknown
% 6.88/2.24 % (14169)Termination phase: shuffling
% 6.88/2.24
% 6.88/2.24 % (14169)Memory used [KB]: 2046
% 6.88/2.24 % (14169)Time elapsed: 0.010 s
% 6.88/2.24 % (14169)Instructions burned: 33 (million)
% 6.88/2.24 % (14169)------------------------------
% 6.88/2.24 % (14169)------------------------------
% 6.88/2.25 % (14165)Instruction limit reached!
% 6.88/2.25 % (14165)------------------------------
% 6.88/2.25 % (14165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.25 % (14165)Termination reason: Unknown
% 6.88/2.25 % (14165)Termination phase: Saturation
% 6.88/2.25
% 6.88/2.25 % (14165)Memory used [KB]: 7931
% 6.88/2.25 % (14165)Time elapsed: 0.074 s
% 6.88/2.25 % (14165)Instructions burned: 259 (million)
% 6.88/2.25 % (14165)------------------------------
% 6.88/2.25 % (14165)------------------------------
% 6.88/2.25 % (14171)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_13872 for (2993ds/987Mi)
% 6.88/2.25 % (14139)Instruction limit reached!
% 6.88/2.25 % (14139)------------------------------
% 6.88/2.25 % (14139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.25 % (14139)Termination reason: Unknown
% 6.88/2.25 % (14139)Termination phase: Saturation
% 6.88/2.25
% 6.88/2.25 % (14139)Memory used [KB]: 11897
% 6.88/2.25 % (14139)Time elapsed: 0.364 s
% 6.88/2.25 % (14139)Instructions burned: 1087 (million)
% 6.88/2.25 % (14139)------------------------------
% 6.88/2.25 % (14139)------------------------------
% 6.88/2.26 % (14157)Instruction limit reached!
% 6.88/2.26 % (14157)------------------------------
% 6.88/2.26 % (14157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.26 % (14157)Termination reason: Unknown
% 6.88/2.26 % (14157)Termination phase: Saturation
% 6.88/2.26
% 6.88/2.26 % (14157)Memory used [KB]: 9722
% 6.88/2.26 % (14157)Time elapsed: 0.181 s
% 6.88/2.26 % (14157)Instructions burned: 615 (million)
% 6.88/2.26 % (14157)------------------------------
% 6.88/2.26 % (14157)------------------------------
% 6.88/2.26 % (14172)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_13872 for (2992ds/182Mi)
% 6.88/2.26 % (14173)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_13872 for (2992ds/182Mi)
% 6.88/2.27 % (14167)Instruction limit reached!
% 6.88/2.27 % (14167)------------------------------
% 6.88/2.27 % (14167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.88/2.27 % (14167)Termination reason: Unknown
% 6.88/2.27 % (14167)Termination phase: Saturation
% 6.88/2.27
% 6.88/2.27 % (14167)Memory used [KB]: 9466
% 6.88/2.27 % (14167)Time elapsed: 0.063 s
% 6.88/2.27 % (14167)Instructions burned: 231 (million)
% 6.88/2.27 % (14167)------------------------------
% 6.88/2.27 % (14167)------------------------------
% 6.88/2.27 % (14174)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_13872 for (2992ds/154Mi)
% 6.88/2.28 % (14175)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_13872 for (2992ds/79Mi)
% 7.60/2.30 % (14175)Instruction limit reached!
% 7.60/2.30 % (14175)------------------------------
% 7.60/2.30 % (14175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.30 % (14175)Termination reason: Unknown
% 7.60/2.30 % (14175)Termination phase: Property scanning
% 7.60/2.30
% 7.60/2.30 % (14175)Memory used [KB]: 2430
% 7.60/2.30 % (14175)Time elapsed: 0.022 s
% 7.60/2.30 % (14175)Instructions burned: 80 (million)
% 7.60/2.30 % (14175)------------------------------
% 7.60/2.30 % (14175)------------------------------
% 7.60/2.31 % (14176)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_13872 for (2992ds/216Mi)
% 7.60/2.31 % (14172)Instruction limit reached!
% 7.60/2.31 % (14172)------------------------------
% 7.60/2.31 % (14172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.31 % (14172)Termination reason: Unknown
% 7.60/2.31 % (14172)Termination phase: Saturation
% 7.60/2.31
% 7.60/2.31 % (14172)Memory used [KB]: 7547
% 7.60/2.31 % (14172)Time elapsed: 0.053 s
% 7.60/2.31 % (14172)Instructions burned: 184 (million)
% 7.60/2.31 % (14172)------------------------------
% 7.60/2.31 % (14172)------------------------------
% 7.60/2.31 % (14170)Instruction limit reached!
% 7.60/2.31 % (14170)------------------------------
% 7.60/2.31 % (14170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.31 % (14170)Termination reason: Unknown
% 7.60/2.31 % (14170)Termination phase: Saturation
% 7.60/2.31
% 7.60/2.31 % (14170)Memory used [KB]: 7291
% 7.60/2.31 % (14170)Time elapsed: 0.075 s
% 7.60/2.31 % (14170)Instructions burned: 298 (million)
% 7.60/2.31 % (14170)------------------------------
% 7.60/2.31 % (14170)------------------------------
% 7.60/2.31 % (14173)Instruction limit reached!
% 7.60/2.31 % (14173)------------------------------
% 7.60/2.31 % (14173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.31 % (14173)Termination reason: Unknown
% 7.60/2.31 % (14173)Termination phase: Saturation
% 7.60/2.31
% 7.60/2.31 % (14173)Memory used [KB]: 8699
% 7.60/2.31 % (14173)Time elapsed: 0.052 s
% 7.60/2.31 % (14173)Instructions burned: 184 (million)
% 7.60/2.31 % (14173)------------------------------
% 7.60/2.31 % (14173)------------------------------
% 7.60/2.32 % (14177)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_13872 for (2992ds/114Mi)
% 7.60/2.32 % (14178)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_13872 for (2992ds/922Mi)
% 7.60/2.32 % (14179)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_13872 for (2992ds/182Mi)
% 7.60/2.34 % (14174)Instruction limit reached!
% 7.60/2.34 % (14174)------------------------------
% 7.60/2.34 % (14174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.34 % (14174)Termination reason: Unknown
% 7.60/2.34 % (14174)Termination phase: Saturation
% 7.60/2.34
% 7.60/2.34 % (14174)Memory used [KB]: 7036
% 7.60/2.34 % (14174)Time elapsed: 0.063 s
% 7.60/2.34 % (14174)Instructions burned: 156 (million)
% 7.60/2.34 % (14174)------------------------------
% 7.60/2.34 % (14174)------------------------------
% 7.60/2.35 % (14168)Instruction limit reached!
% 7.60/2.35 % (14168)------------------------------
% 7.60/2.35 % (14168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.35 % (14168)Termination reason: Unknown
% 7.60/2.35 % (14168)Termination phase: Saturation
% 7.60/2.35
% 7.60/2.35 % (14168)Memory used [KB]: 9466
% 7.60/2.35 % (14168)Time elapsed: 0.130 s
% 7.60/2.35 % (14168)Instructions burned: 459 (million)
% 7.60/2.35 % (14168)------------------------------
% 7.60/2.35 % (14168)------------------------------
% 7.60/2.35 % (14180)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_13872 for (2992ds/164Mi)
% 7.60/2.35 % (14177)Instruction limit reached!
% 7.60/2.35 % (14177)------------------------------
% 7.60/2.35 % (14177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.35 % (14177)Termination reason: Unknown
% 7.60/2.35 % (14177)Termination phase: Property scanning
% 7.60/2.35
% 7.60/2.35 % (14177)Memory used [KB]: 2558
% 7.60/2.35 % (14177)Time elapsed: 0.033 s
% 7.60/2.35 % (14177)Instructions burned: 116 (million)
% 7.60/2.35 % (14177)------------------------------
% 7.60/2.35 % (14177)------------------------------
% 7.60/2.35 % (14181)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_13872 for (2992ds/50Mi)
% 7.60/2.36 % (14182)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_13872 for (2991ds/368Mi)
% 7.60/2.36 % (14176)Instruction limit reached!
% 7.60/2.36 % (14176)------------------------------
% 7.60/2.36 % (14176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.36 % (14176)Termination reason: Unknown
% 7.60/2.36 % (14176)Termination phase: Saturation
% 7.60/2.36
% 7.60/2.36 % (14176)Memory used [KB]: 7291
% 7.60/2.36 % (14176)Time elapsed: 0.056 s
% 7.60/2.36 % (14176)Instructions burned: 218 (million)
% 7.60/2.36 % (14176)------------------------------
% 7.60/2.36 % (14176)------------------------------
% 7.60/2.37 % (14181)Instruction limit reached!
% 7.60/2.37 % (14181)------------------------------
% 7.60/2.37 % (14181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.37 % (14181)Termination reason: Unknown
% 7.60/2.37 % (14181)Termination phase: Property scanning
% 7.60/2.37
% 7.60/2.37 % (14181)Memory used [KB]: 2302
% 7.60/2.37 % (14181)Time elapsed: 0.015 s
% 7.60/2.37 % (14181)Instructions burned: 52 (million)
% 7.60/2.37 % (14181)------------------------------
% 7.60/2.37 % (14181)------------------------------
% 7.60/2.37 % (14179)Instruction limit reached!
% 7.60/2.37 % (14179)------------------------------
% 7.60/2.37 % (14179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.37 % (14179)Termination reason: Unknown
% 7.60/2.37 % (14179)Termination phase: Saturation
% 7.60/2.37
% 7.60/2.37 % (14179)Memory used [KB]: 7291
% 7.60/2.37 % (14179)Time elapsed: 0.048 s
% 7.60/2.37 % (14179)Instructions burned: 185 (million)
% 7.60/2.37 % (14179)------------------------------
% 7.60/2.37 % (14179)------------------------------
% 7.60/2.37 % (14183)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_13872 for (2991ds/1021Mi)
% 7.60/2.38 % (14184)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_13872 for (2991ds/267Mi)
% 7.60/2.38 % (14185)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_13872 for (2991ds/204Mi)
% 7.60/2.39 % (14180)Instruction limit reached!
% 7.60/2.39 % (14180)------------------------------
% 7.60/2.39 % (14180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.60/2.39 % (14180)Termination reason: Unknown
% 7.60/2.39 % (14180)Termination phase: Saturation
% 7.60/2.39
% 7.60/2.39 % (14180)Memory used [KB]: 2558
% 7.60/2.39 % (14180)Time elapsed: 0.043 s
% 7.60/2.39 % (14180)Instructions burned: 164 (million)
% 7.60/2.39 % (14180)------------------------------
% 7.60/2.39 % (14180)------------------------------
% 8.29/2.40 % (14186)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_13872 for (2991ds/26Mi)
% 8.29/2.41 % (14186)Instruction limit reached!
% 8.29/2.41 % (14186)------------------------------
% 8.29/2.41 % (14186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.41 % (14186)Termination reason: Unknown
% 8.29/2.41 % (14186)Termination phase: shuffling
% 8.29/2.41
% 8.29/2.41 % (14186)Memory used [KB]: 1918
% 8.29/2.41 % (14186)Time elapsed: 0.009 s
% 8.29/2.41 % (14186)Instructions burned: 26 (million)
% 8.29/2.41 % (14186)------------------------------
% 8.29/2.41 % (14186)------------------------------
% 8.29/2.41 % (14187)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_13872 for (2991ds/53Mi)
% 8.29/2.43 % (14187)Instruction limit reached!
% 8.29/2.43 % (14187)------------------------------
% 8.29/2.43 % (14187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.43 % (14187)Termination reason: Unknown
% 8.29/2.43 % (14187)Termination phase: Property scanning
% 8.29/2.43
% 8.29/2.43 % (14187)Memory used [KB]: 2302
% 8.29/2.43 % (14187)Time elapsed: 0.015 s
% 8.29/2.43 % (14187)Instructions burned: 54 (million)
% 8.29/2.43 % (14187)------------------------------
% 8.29/2.43 % (14187)------------------------------
% 8.29/2.43 % (14185)Instruction limit reached!
% 8.29/2.43 % (14185)------------------------------
% 8.29/2.43 % (14185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.43 % (14185)Termination reason: Unknown
% 8.29/2.43 % (14185)Termination phase: Saturation
% 8.29/2.43
% 8.29/2.43 % (14185)Memory used [KB]: 7291
% 8.29/2.43 % (14185)Time elapsed: 0.053 s
% 8.29/2.43 % (14185)Instructions burned: 204 (million)
% 8.29/2.43 % (14185)------------------------------
% 8.29/2.43 % (14185)------------------------------
% 8.29/2.44 % (14188)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_13872 for (2991ds/4436Mi)
% 8.29/2.44 % (14189)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_13872 for (2991ds/1539Mi)
% 8.29/2.45 % (14184)Instruction limit reached!
% 8.29/2.45 % (14184)------------------------------
% 8.29/2.45 % (14184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.45 % (14184)Termination reason: Unknown
% 8.29/2.45 % (14184)Termination phase: Saturation
% 8.29/2.45
% 8.29/2.45 % (14184)Memory used [KB]: 7291
% 8.29/2.45 % (14184)Time elapsed: 0.069 s
% 8.29/2.45 % (14184)Instructions burned: 270 (million)
% 8.29/2.45 % (14184)------------------------------
% 8.29/2.45 % (14184)------------------------------
% 8.29/2.46 % (14190)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_13872 for (2991ds/408Mi)
% 8.29/2.47 % (14182)Instruction limit reached!
% 8.29/2.47 % (14182)------------------------------
% 8.29/2.47 % (14182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.29/2.47 % (14182)Termination reason: Unknown
% 8.29/2.47 % (14182)Termination phase: Saturation
% 8.29/2.47
% 8.29/2.47 % (14182)Memory used [KB]: 8699
% 8.29/2.47 % (14182)Time elapsed: 0.109 s
% 8.29/2.47 % (14182)Instructions burned: 368 (million)
% 8.29/2.47 % (14182)------------------------------
% 8.29/2.47 % (14182)------------------------------
% 8.29/2.48 % (14191)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_13872 for (2990ds/5205Mi)
% 8.59/2.51 % (14171)Instruction limit reached!
% 8.59/2.51 % (14171)------------------------------
% 8.59/2.51 % (14171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.51 % (14171)Termination reason: Unknown
% 8.59/2.51 % (14171)Termination phase: Saturation
% 8.59/2.51
% 8.59/2.51 % (14171)Memory used [KB]: 13944
% 8.59/2.51 % (14171)Time elapsed: 0.256 s
% 8.59/2.51 % (14171)Instructions burned: 989 (million)
% 8.59/2.51 % (14171)------------------------------
% 8.59/2.51 % (14171)------------------------------
% 8.59/2.52 % (14192)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_13872 for (2990ds/1913Mi)
% 8.59/2.58 % (14190)Instruction limit reached!
% 8.59/2.58 % (14190)------------------------------
% 8.59/2.58 % (14190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.58 % (14190)Termination reason: Unknown
% 8.59/2.58 % (14190)Termination phase: Saturation
% 8.59/2.58
% 8.59/2.58 % (14190)Memory used [KB]: 10618
% 8.59/2.58 % (14190)Time elapsed: 0.127 s
% 8.59/2.58 % (14190)Instructions burned: 409 (million)
% 8.59/2.58 % (14190)------------------------------
% 8.59/2.58 % (14190)------------------------------
% 8.59/2.59 % (14193)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_13872 for (2989ds/4350Mi)
% 8.99/2.61 % (14178)Instruction limit reached!
% 8.99/2.61 % (14178)------------------------------
% 8.99/2.61 % (14178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.61 % (14178)Termination reason: Unknown
% 8.99/2.61 % (14178)Termination phase: Saturation
% 8.99/2.61
% 8.99/2.61 % (14178)Memory used [KB]: 11001
% 8.99/2.61 % (14178)Time elapsed: 0.291 s
% 8.99/2.61 % (14178)Instructions burned: 924 (million)
% 8.99/2.61 % (14178)------------------------------
% 8.99/2.61 % (14178)------------------------------
% 8.99/2.62 % (14194)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_13872 for (2989ds/68Mi)
% 8.99/2.64 % (14194)Instruction limit reached!
% 8.99/2.64 % (14194)------------------------------
% 8.99/2.64 % (14194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.64 % (14194)Termination reason: Unknown
% 8.99/2.64 % (14194)Termination phase: SInE selection
% 8.99/2.64
% 8.99/2.64 % (14194)Memory used [KB]: 2302
% 8.99/2.64 % (14194)Time elapsed: 0.019 s
% 8.99/2.64 % (14194)Instructions burned: 69 (million)
% 8.99/2.64 % (14194)------------------------------
% 8.99/2.64 % (14194)------------------------------
% 8.99/2.65 % (14195)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_13872 for (2989ds/358Mi)
% 8.99/2.70 % (14183)Instruction limit reached!
% 8.99/2.70 % (14183)------------------------------
% 8.99/2.70 % (14183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.70 % (14183)Termination reason: Unknown
% 8.99/2.70 % (14183)Termination phase: Saturation
% 8.99/2.70
% 8.99/2.70 % (14183)Memory used [KB]: 12025
% 8.99/2.70 % (14183)Time elapsed: 0.323 s
% 8.99/2.70 % (14183)Instructions burned: 1021 (million)
% 8.99/2.70 % (14183)------------------------------
% 8.99/2.70 % (14183)------------------------------
% 9.65/2.71 % (14196)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_13872 for (2988ds/31Mi)
% 9.65/2.71 % (14196)Instruction limit reached!
% 9.65/2.71 % (14196)------------------------------
% 9.65/2.71 % (14196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.65/2.71 % (14196)Termination reason: Unknown
% 9.65/2.71 % (14196)Termination phase: shuffling
% 9.65/2.71
% 9.65/2.71 % (14196)Memory used [KB]: 2046
% 9.65/2.71 % (14196)Time elapsed: 0.010 s
% 9.65/2.71 % (14196)Instructions burned: 32 (million)
% 9.65/2.71 % (14196)------------------------------
% 9.65/2.71 % (14196)------------------------------
% 9.65/2.72 % (14197)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_13872 for (2988ds/279Mi)
% 9.65/2.75 % (14195)Instruction limit reached!
% 9.65/2.75 % (14195)------------------------------
% 9.65/2.75 % (14195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.65/2.75 % (14195)Termination reason: Unknown
% 9.65/2.75 % (14195)Termination phase: Saturation
% 9.65/2.75
% 9.65/2.75 % (14195)Memory used [KB]: 8571
% 9.65/2.75 % (14195)Time elapsed: 0.100 s
% 9.65/2.75 % (14195)Instructions burned: 359 (million)
% 9.65/2.75 % (14195)------------------------------
% 9.65/2.75 % (14195)------------------------------
% 9.65/2.76 % (14198)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_13872 for (2988ds/258Mi)
% 9.65/2.79 % (14197)Instruction limit reached!
% 9.65/2.79 % (14197)------------------------------
% 9.65/2.79 % (14197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.65/2.79 % (14197)Termination reason: Unknown
% 9.65/2.79 % (14197)Termination phase: Saturation
% 9.65/2.79
% 9.65/2.79 % (14197)Memory used [KB]: 7291
% 9.65/2.79 % (14197)Time elapsed: 0.072 s
% 9.65/2.79 % (14197)Instructions burned: 281 (million)
% 9.65/2.79 % (14197)------------------------------
% 9.65/2.79 % (14197)------------------------------
% 9.87/2.80 % (14199)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_13872 for (2987ds/26Mi)
% 9.87/2.81 % (14199)Instruction limit reached!
% 9.87/2.81 % (14199)------------------------------
% 9.87/2.81 % (14199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.81 % (14199)Termination reason: Unknown
% 9.87/2.81 % (14199)Termination phase: shuffling
% 9.87/2.81
% 9.87/2.81 % (14199)Memory used [KB]: 1918
% 9.87/2.81 % (14199)Time elapsed: 0.008 s
% 9.87/2.81 % (14199)Instructions burned: 26 (million)
% 9.87/2.81 % (14199)------------------------------
% 9.87/2.81 % (14199)------------------------------
% 9.87/2.82 % (14200)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_13872 for (2987ds/995Mi)
% 9.87/2.83 % (14198)Instruction limit reached!
% 9.87/2.83 % (14198)------------------------------
% 9.87/2.83 % (14198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.83 % (14198)Termination reason: Unknown
% 9.87/2.83 % (14198)Termination phase: Saturation
% 9.87/2.83
% 9.87/2.83 % (14198)Memory used [KB]: 8443
% 9.87/2.83 % (14198)Time elapsed: 0.070 s
% 9.87/2.83 % (14198)Instructions burned: 259 (million)
% 9.87/2.83 % (14198)------------------------------
% 9.87/2.83 % (14198)------------------------------
% 9.87/2.84 % (14201)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_13872 for (2987ds/373Mi)
% 9.96/2.92 % (14189)Instruction limit reached!
% 9.96/2.92 % (14189)------------------------------
% 9.96/2.92 % (14189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.92 % (14189)Termination reason: Unknown
% 9.96/2.92 % (14189)Termination phase: Saturation
% 9.96/2.92
% 9.96/2.92 % (14189)Memory used [KB]: 10490
% 9.96/2.92 % (14189)Time elapsed: 0.478 s
% 9.96/2.92 % (14189)Instructions burned: 1541 (million)
% 9.96/2.92 % (14189)------------------------------
% 9.96/2.92 % (14189)------------------------------
% 9.96/2.93 % (14202)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_13872 for (2986ds/253Mi)
% 9.96/2.94 % (14201)Instruction limit reached!
% 9.96/2.94 % (14201)------------------------------
% 9.96/2.94 % (14201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/2.94 % (14201)Termination reason: Unknown
% 9.96/2.94 % (14201)Termination phase: Saturation
% 9.96/2.94
% 9.96/2.94 % (14201)Memory used [KB]: 8699
% 9.96/2.94 % (14201)Time elapsed: 0.128 s
% 9.96/2.94 % (14201)Instructions burned: 375 (million)
% 9.96/2.94 % (14201)------------------------------
% 9.96/2.94 % (14201)------------------------------
% 9.96/2.95 % (14203)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_13872 for (2986ds/832Mi)
% 9.96/3.00 % (14202)Instruction limit reached!
% 9.96/3.00 % (14202)------------------------------
% 9.96/3.00 % (14202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.96/3.00 % (14202)Termination reason: Unknown
% 9.96/3.00 % (14202)Termination phase: Saturation
% 9.96/3.00
% 9.96/3.00 % (14202)Memory used [KB]: 7291
% 9.96/3.00 % (14202)Time elapsed: 0.067 s
% 9.96/3.00 % (14202)Instructions burned: 254 (million)
% 9.96/3.00 % (14202)------------------------------
% 9.96/3.00 % (14202)------------------------------
% 9.96/3.01 % (14204)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_13872 for (2985ds/668Mi)
% 12.91/3.08 % (14200)Instruction limit reached!
% 12.91/3.08 % (14200)------------------------------
% 12.91/3.08 % (14200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.91/3.08 % (14200)Termination reason: Unknown
% 12.91/3.08 % (14200)Termination phase: Saturation
% 12.91/3.08
% 12.91/3.08 % (14200)Memory used [KB]: 13432
% 12.91/3.08 % (14200)Time elapsed: 0.257 s
% 12.91/3.08 % (14200)Instructions burned: 999 (million)
% 12.91/3.08 % (14200)------------------------------
% 12.91/3.08 % (14200)------------------------------
% 12.91/3.09 % (14205)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_13872 for (2984ds/40Mi)
% 12.91/3.10 % (14205)Instruction limit reached!
% 12.91/3.10 % (14205)------------------------------
% 12.91/3.10 % (14205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.91/3.10 % (14205)Termination reason: Unknown
% 12.91/3.10 % (14205)Termination phase: shuffling
% 12.91/3.10
% 12.91/3.10 % (14205)Memory used [KB]: 2302
% 12.91/3.10 % (14205)Time elapsed: 0.013 s
% 12.91/3.10 % (14205)Instructions burned: 41 (million)
% 12.91/3.10 % (14205)------------------------------
% 12.91/3.10 % (14205)------------------------------
% 12.91/3.10 % (14192)Instruction limit reached!
% 12.91/3.10 % (14192)------------------------------
% 12.91/3.10 % (14192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.91/3.10 % (14192)Termination reason: Unknown
% 12.91/3.10 % (14192)Termination phase: Saturation
% 12.91/3.10
% 12.91/3.10 % (14192)Memory used [KB]: 5884
% 12.91/3.10 % (14192)Time elapsed: 0.587 s
% 12.91/3.10 % (14192)Instructions burned: 1914 (million)
% 12.91/3.10 % (14192)------------------------------
% 12.91/3.10 % (14192)------------------------------
% 12.91/3.11 % (14206)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_13872 for (2984ds/294Mi)
% 13.61/3.11 % (14207)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_13872 for (2984ds/187Mi)
% 13.61/3.16 % (14207)Instruction limit reached!
% 13.61/3.16 % (14207)------------------------------
% 13.61/3.16 % (14207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.61/3.16 % (14207)Termination reason: Unknown
% 13.61/3.16 % (14207)Termination phase: Saturation
% 13.61/3.16
% 13.61/3.16 % (14207)Memory used [KB]: 7675
% 13.61/3.16 % (14207)Time elapsed: 0.050 s
% 13.61/3.16 % (14207)Instructions burned: 188 (million)
% 13.61/3.16 % (14207)------------------------------
% 13.61/3.16 % (14207)------------------------------
% 13.61/3.17 % (14208)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_13872 for (2983ds/371Mi)
% 13.61/3.17 % (14204)Instruction limit reached!
% 13.61/3.17 % (14204)------------------------------
% 13.61/3.17 % (14204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.61/3.17 % (14204)Termination reason: Unknown
% 13.61/3.17 % (14204)Termination phase: Saturation
% 13.61/3.17
% 13.61/3.17 % (14204)Memory used [KB]: 18166
% 13.61/3.17 % (14204)Time elapsed: 0.192 s
% 13.61/3.17 % (14204)Instructions burned: 668 (million)
% 13.61/3.17 % (14204)------------------------------
% 13.61/3.17 % (14204)------------------------------
% 13.61/3.18 % (14206)Instruction limit reached!
% 13.61/3.18 % (14206)------------------------------
% 13.61/3.18 % (14206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.61/3.18 % (14206)Termination reason: Unknown
% 13.61/3.18 % (14206)Termination phase: Saturation
% 13.61/3.18
% 13.61/3.18 % (14206)Memory used [KB]: 7291
% 13.61/3.18 % (14206)Time elapsed: 0.075 s
% 13.61/3.18 % (14206)Instructions burned: 297 (million)
% 13.61/3.18 % (14206)------------------------------
% 13.61/3.18 % (14206)------------------------------
% 13.61/3.19 % (14209)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_13872 for (2983ds/1827Mi)
% 13.61/3.19 % (14210)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_13872 for (2983ds/70Mi)
% 14.14/3.21 % (14203)Instruction limit reached!
% 14.14/3.21 % (14203)------------------------------
% 14.14/3.21 % (14203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.14/3.21 % (14203)Termination reason: Unknown
% 14.14/3.21 % (14203)Termination phase: Saturation
% 14.14/3.21
% 14.14/3.21 % (14203)Memory used [KB]: 10746
% 14.14/3.21 % (14203)Time elapsed: 0.279 s
% 14.14/3.21 % (14203)Instructions burned: 834 (million)
% 14.14/3.21 % (14203)------------------------------
% 14.14/3.21 % (14203)------------------------------
% 14.14/3.21 % (14210)Instruction limit reached!
% 14.14/3.21 % (14210)------------------------------
% 14.14/3.21 % (14210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.14/3.21 % (14210)Termination reason: Unknown
% 14.14/3.21 % (14210)Termination phase: Property scanning
% 14.14/3.21
% 14.14/3.21 % (14210)Memory used [KB]: 2302
% 14.14/3.21 % (14210)Time elapsed: 0.020 s
% 14.14/3.21 % (14210)Instructions burned: 70 (million)
% 14.14/3.21 % (14210)------------------------------
% 14.14/3.21 % (14210)------------------------------
% 14.14/3.22 % (14211)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_13872 for (2983ds/316Mi)
% 14.14/3.22 % (14212)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_13872 for (2983ds/932Mi)
% 14.14/3.27 % (14208)Instruction limit reached!
% 14.14/3.27 % (14208)------------------------------
% 14.14/3.27 % (14208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.14/3.27 % (14208)Termination reason: Unknown
% 14.14/3.27 % (14208)Termination phase: Saturation
% 14.14/3.27
% 14.14/3.27 % (14208)Memory used [KB]: 8699
% 14.14/3.27 % (14208)Time elapsed: 0.103 s
% 14.14/3.27 % (14208)Instructions burned: 372 (million)
% 14.14/3.27 % (14208)------------------------------
% 14.14/3.27 % (14208)------------------------------
% 14.14/3.28 % (14213)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_13872 for (2982ds/4714Mi)
% 14.62/3.30 % (14211)Instruction limit reached!
% 14.62/3.30 % (14211)------------------------------
% 14.62/3.30 % (14211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.62/3.30 % (14211)Termination reason: Unknown
% 14.62/3.30 % (14211)Termination phase: Saturation
% 14.62/3.30
% 14.62/3.30 % (14211)Memory used [KB]: 7291
% 14.62/3.30 % (14211)Time elapsed: 0.080 s
% 14.62/3.30 % (14211)Instructions burned: 316 (million)
% 14.62/3.30 % (14211)------------------------------
% 14.62/3.30 % (14211)------------------------------
% 14.62/3.31 % (14214)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_13872 for (2982ds/8250Mi)
% 15.01/3.46 % (14212)Instruction limit reached!
% 15.01/3.46 % (14212)------------------------------
% 15.01/3.46 % (14212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.01/3.46 % (14212)Termination reason: Unknown
% 15.01/3.46 % (14212)Termination phase: Saturation
% 15.01/3.46
% 15.01/3.46 % (14212)Memory used [KB]: 14839
% 15.01/3.46 % (14212)Time elapsed: 0.239 s
% 15.01/3.46 % (14212)Instructions burned: 934 (million)
% 15.01/3.46 % (14212)------------------------------
% 15.01/3.46 % (14212)------------------------------
% 15.01/3.47 % (14215)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_13872 for (2980ds/770Mi)
% 15.85/3.68 % (14215)Instruction limit reached!
% 15.85/3.68 % (14215)------------------------------
% 15.85/3.68 % (14215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.85/3.68 % (14215)Termination reason: Unknown
% 15.85/3.68 % (14215)Termination phase: Saturation
% 15.85/3.68
% 15.85/3.68 % (14215)Memory used [KB]: 7419
% 15.85/3.68 % (14215)Time elapsed: 0.213 s
% 15.85/3.68 % (14215)Instructions burned: 773 (million)
% 15.85/3.68 % (14215)------------------------------
% 15.85/3.68 % (14215)------------------------------
% 15.85/3.69 % (14216)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_13872 for (2978ds/794Mi)
% 16.38/3.72 % (14209)Instruction limit reached!
% 16.38/3.72 % (14209)------------------------------
% 16.38/3.72 % (14209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.38/3.72 % (14209)Termination reason: Unknown
% 16.38/3.72 % (14209)Termination phase: Saturation
% 16.38/3.72
% 16.38/3.72 % (14209)Memory used [KB]: 19701
% 16.38/3.72 % (14209)Time elapsed: 0.533 s
% 16.38/3.72 % (14209)Instructions burned: 1829 (million)
% 16.38/3.72 % (14209)------------------------------
% 16.38/3.72 % (14209)------------------------------
% 16.38/3.73 % (14217)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_13872 for (2978ds/464Mi)
% 16.38/3.77 % (14191)Instruction limit reached!
% 16.38/3.77 % (14191)------------------------------
% 16.38/3.77 % (14191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.38/3.77 % (14191)Termination reason: Unknown
% 16.38/3.77 % (14191)Termination phase: Saturation
% 16.38/3.77
% 16.38/3.77 % (14191)Memory used [KB]: 14328
% 16.38/3.77 % (14191)Time elapsed: 1.294 s
% 16.38/3.77 % (14191)Instructions burned: 5205 (million)
% 16.38/3.77 % (14191)------------------------------
% 16.38/3.77 % (14191)------------------------------
% 16.38/3.78 % (14218)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_13872 for (2977ds/1376Mi)
% 17.23/3.86 % (14217)Instruction limit reached!
% 17.23/3.86 % (14217)------------------------------
% 17.23/3.86 % (14217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.23/3.86 % (14217)Termination reason: Unknown
% 17.23/3.86 % (14217)Termination phase: Saturation
% 17.23/3.86
% 17.23/3.86 % (14217)Memory used [KB]: 9466
% 17.23/3.86 % (14217)Time elapsed: 0.134 s
% 17.23/3.86 % (14217)Instructions burned: 464 (million)
% 17.23/3.86 % (14217)------------------------------
% 17.23/3.86 % (14217)------------------------------
% 17.23/3.87 % (14219)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_13872 for (2976ds/906Mi)
% 17.57/3.93 % (14216)Instruction limit reached!
% 17.57/3.93 % (14216)------------------------------
% 17.57/3.93 % (14216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.57/3.93 % (14216)Termination reason: Unknown
% 17.57/3.93 % (14216)Termination phase: Saturation
% 17.57/3.93
% 17.57/3.93 % (14216)Memory used [KB]: 5628
% 17.57/3.93 % (14216)Time elapsed: 0.243 s
% 17.57/3.93 % (14216)Instructions burned: 795 (million)
% 17.57/3.93 % (14216)------------------------------
% 17.57/3.93 % (14216)------------------------------
% 17.57/3.93 % (14188)Instruction limit reached!
% 17.57/3.93 % (14188)------------------------------
% 17.57/3.93 % (14188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.57/3.93 % (14188)Termination reason: Unknown
% 17.57/3.93 % (14188)Termination phase: Saturation
% 17.57/3.93
% 17.57/3.93 % (14188)Memory used [KB]: 17270
% 17.57/3.93 % (14188)Time elapsed: 1.496 s
% 17.57/3.93 % (14188)Instructions burned: 4438 (million)
% 17.57/3.93 % (14188)------------------------------
% 17.57/3.93 % (14188)------------------------------
% 17.57/3.94 % (14193)Instruction limit reached!
% 17.57/3.94 % (14193)------------------------------
% 17.57/3.94 % (14193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.57/3.94 % (14193)Termination reason: Unknown
% 17.57/3.94 % (14193)Termination phase: Saturation
% 17.57/3.94
% 17.57/3.94 % (14193)Memory used [KB]: 13176
% 17.57/3.94 % (14193)Time elapsed: 1.346 s
% 17.57/3.94 % (14193)Instructions burned: 4351 (million)
% 17.57/3.94 % (14193)------------------------------
% 17.57/3.94 % (14193)------------------------------
% 17.57/3.94 % (14220)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_13872 for (2976ds/434Mi)
% 17.57/3.94 % (14221)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_13872 for (2976ds/865Mi)
% 17.57/3.95 % (14222)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_13872 for (2976ds/593Mi)
% 20.01/4.07 % (14220)Refutation not found, non-redundant clauses discarded% (14220)------------------------------
% 20.01/4.07 % (14220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.01/4.07 % (14220)Termination reason: Refutation not found, non-redundant clauses discarded
% 20.01/4.07
% 20.01/4.07 % (14220)Memory used [KB]: 10234
% 20.01/4.07 % (14220)Time elapsed: 0.126 s
% 20.01/4.07 % (14220)Instructions burned: 425 (million)
% 20.01/4.07 % (14220)------------------------------
% 20.01/4.07 % (14220)------------------------------
% 20.01/4.08 % (14223)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_13872 for (2974ds/443Mi)
% 20.01/4.09 % (14222)Instruction limit reached!
% 20.01/4.09 % (14222)------------------------------
% 20.01/4.09 % (14222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.01/4.09 % (14222)Termination reason: Unknown
% 20.01/4.09 % (14222)Termination phase: Saturation
% 20.01/4.09
% 20.01/4.09 % (14222)Memory used [KB]: 7419
% 20.01/4.09 % (14222)Time elapsed: 0.149 s
% 20.01/4.09 % (14222)Instructions burned: 595 (million)
% 20.01/4.09 % (14222)------------------------------
% 20.01/4.09 % (14222)------------------------------
% 20.01/4.10 % (14224)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_13872 for (2974ds/594Mi)
% 20.65/4.14 % (14218)Instruction limit reached!
% 20.65/4.14 % (14218)------------------------------
% 20.65/4.14 % (14218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.65/4.14 % (14218)Termination reason: Unknown
% 20.65/4.14 % (14218)Termination phase: Saturation
% 20.65/4.14
% 20.65/4.14 % (14218)Memory used [KB]: 9210
% 20.65/4.14 % (14218)Time elapsed: 0.354 s
% 20.65/4.14 % (14218)Instructions burned: 1379 (million)
% 20.65/4.14 % (14218)------------------------------
% 20.65/4.14 % (14218)------------------------------
% 20.65/4.15 % (14225)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_13872 for (2974ds/327Mi)
% 20.65/4.15 % (14219)Instruction limit reached!
% 20.65/4.15 % (14219)------------------------------
% 20.65/4.15 % (14219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.65/4.15 % (14219)Termination reason: Unknown
% 20.65/4.15 % (14219)Termination phase: Saturation
% 20.65/4.15
% 20.65/4.15 % (14219)Memory used [KB]: 10874
% 20.65/4.15 % (14219)Time elapsed: 0.280 s
% 20.65/4.15 % (14219)Instructions burned: 909 (million)
% 20.65/4.15 % (14219)------------------------------
% 20.65/4.15 % (14219)------------------------------
% 20.65/4.16 % (14226)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_13872 for (2973ds/5411Mi)
% 20.94/4.20 % (14221)Instruction limit reached!
% 20.94/4.20 % (14221)------------------------------
% 20.94/4.20 % (14221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.20 % (14221)Termination reason: Unknown
% 20.94/4.20 % (14221)Termination phase: Saturation
% 20.94/4.20
% 20.94/4.20 % (14221)Memory used [KB]: 10362
% 20.94/4.20 % (14221)Time elapsed: 0.258 s
% 20.94/4.20 % (14221)Instructions burned: 867 (million)
% 20.94/4.20 % (14221)------------------------------
% 20.94/4.20 % (14221)------------------------------
% 20.94/4.20 % (14223)Instruction limit reached!
% 20.94/4.20 % (14223)------------------------------
% 20.94/4.20 % (14223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.20 % (14223)Termination reason: Unknown
% 20.94/4.20 % (14223)Termination phase: Saturation
% 20.94/4.20
% 20.94/4.20 % (14223)Memory used [KB]: 8827
% 20.94/4.20 % (14223)Time elapsed: 0.128 s
% 20.94/4.20 % (14223)Instructions burned: 443 (million)
% 20.94/4.20 % (14223)------------------------------
% 20.94/4.20 % (14223)------------------------------
% 20.94/4.21 % (14227)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_13872 for (2973ds/1762Mi)
% 20.94/4.21 % (14228)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_13872 for (2973ds/96Mi)
% 20.94/4.24 % (14228)Instruction limit reached!
% 20.94/4.24 % (14228)------------------------------
% 20.94/4.24 % (14228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.24 % (14228)Termination reason: Unknown
% 20.94/4.24 % (14228)Termination phase: Function definition elimination
% 20.94/4.24
% 20.94/4.24 % (14228)Memory used [KB]: 2430
% 20.94/4.24 % (14228)Time elapsed: 0.026 s
% 20.94/4.24 % (14228)Instructions burned: 98 (million)
% 20.94/4.24 % (14228)------------------------------
% 20.94/4.24 % (14228)------------------------------
% 20.94/4.24 % (14225)Instruction limit reached!
% 20.94/4.24 % (14225)------------------------------
% 20.94/4.24 % (14225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.24 % (14225)Termination reason: Unknown
% 20.94/4.24 % (14225)Termination phase: Saturation
% 20.94/4.24
% 20.94/4.24 % (14225)Memory used [KB]: 10874
% 20.94/4.24 % (14225)Time elapsed: 0.100 s
% 20.94/4.24 % (14225)Instructions burned: 327 (million)
% 20.94/4.25 % (14225)------------------------------
% 20.94/4.25 % (14225)------------------------------
% 20.94/4.25 % (14229)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_13872 for (2973ds/503Mi)
% 20.94/4.25 % (14230)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_13872 for (2972ds/90Mi)
% 20.94/4.28 % (14224)Instruction limit reached!
% 20.94/4.28 % (14224)------------------------------
% 20.94/4.28 % (14224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.28 % (14224)Termination reason: Unknown
% 20.94/4.28 % (14224)Termination phase: Saturation
% 20.94/4.28
% 20.94/4.28 % (14224)Memory used [KB]: 8827
% 20.94/4.28 % (14224)Time elapsed: 0.174 s
% 20.94/4.28 % (14224)Instructions burned: 596 (million)
% 20.94/4.28 % (14224)------------------------------
% 20.94/4.28 % (14224)------------------------------
% 20.94/4.28 % (14230)Instruction limit reached!
% 20.94/4.28 % (14230)------------------------------
% 20.94/4.28 % (14230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.28 % (14230)Termination reason: Unknown
% 20.94/4.28 % (14230)Termination phase: Property scanning
% 20.94/4.28
% 20.94/4.28 % (14230)Memory used [KB]: 2430
% 20.94/4.28 % (14230)Time elapsed: 0.024 s
% 20.94/4.28 % (14230)Instructions burned: 90 (million)
% 20.94/4.28 % (14230)------------------------------
% 20.94/4.28 % (14230)------------------------------
% 20.94/4.29 % (14231)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_13872 for (2972ds/593Mi)
% 20.94/4.29 % (14232)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_13872 for (2972ds/1512Mi)
% 21.84/4.40 % (14229)Instruction limit reached!
% 21.84/4.40 % (14229)------------------------------
% 21.84/4.40 % (14229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.84/4.40 % (14229)Termination reason: Unknown
% 21.84/4.40 % (14229)Termination phase: Saturation
% 21.84/4.40
% 21.84/4.40 % (14229)Memory used [KB]: 9594
% 21.84/4.40 % (14229)Time elapsed: 0.149 s
% 21.84/4.40 % (14229)Instructions burned: 505 (million)
% 21.84/4.40 % (14229)------------------------------
% 21.84/4.40 % (14229)------------------------------
% 21.84/4.41 % (14233)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_13872 for (2971ds/569Mi)
% 21.84/4.46 % (14231)Instruction limit reached!
% 21.84/4.46 % (14231)------------------------------
% 21.84/4.46 % (14231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.84/4.46 % (14231)Termination reason: Unknown
% 21.84/4.46 % (14231)Termination phase: Saturation
% 21.84/4.46
% 21.84/4.46 % (14231)Memory used [KB]: 9594
% 21.84/4.46 % (14231)Time elapsed: 0.176 s
% 21.84/4.46 % (14231)Instructions burned: 593 (million)
% 21.84/4.46 % (14231)------------------------------
% 21.84/4.46 % (14231)------------------------------
% 21.84/4.47 % (14234)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_13872 for (2970ds/501Mi)
% 21.84/4.47 % (14213)Instruction limit reached!
% 21.84/4.47 % (14213)------------------------------
% 21.84/4.47 % (14213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.84/4.47 % (14213)Termination reason: Unknown
% 21.84/4.47 % (14213)Termination phase: Saturation
% 21.84/4.47
% 21.84/4.47 % (14213)Memory used [KB]: 7419
% 21.84/4.47 % (14213)Time elapsed: 1.191 s
% 21.84/4.47 % (14213)Instructions burned: 4718 (million)
% 21.84/4.47 % (14213)------------------------------
% 21.84/4.47 % (14213)------------------------------
% 21.84/4.48 % (14235)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_13872 for (2970ds/562Mi)
% 22.37/4.55 % (14233)Instruction limit reached!
% 22.37/4.55 % (14233)------------------------------
% 22.37/4.55 % (14233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.37/4.55 % (14233)Termination reason: Unknown
% 22.37/4.55 % (14233)Termination phase: Saturation
% 22.37/4.55
% 22.37/4.55 % (14233)Memory used [KB]: 12792
% 22.37/4.55 % (14233)Time elapsed: 0.146 s
% 22.37/4.55 % (14233)Instructions burned: 570 (million)
% 22.37/4.55 % (14233)------------------------------
% 22.37/4.55 % (14233)------------------------------
% 22.37/4.56 % (14236)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_13872 for (2969ds/406Mi)
% 22.64/4.62 % (14234)Instruction limit reached!
% 22.64/4.62 % (14234)------------------------------
% 22.64/4.62 % (14234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.64/4.62 % (14234)Termination reason: Unknown
% 22.64/4.62 % (14234)Termination phase: Saturation
% 22.64/4.62
% 22.64/4.62 % (14234)Memory used [KB]: 9978
% 22.64/4.62 % (14234)Time elapsed: 0.149 s
% 22.64/4.62 % (14234)Instructions burned: 501 (million)
% 22.64/4.62 % (14234)------------------------------
% 22.64/4.62 % (14234)------------------------------
% 22.64/4.63 % (14237)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_13872 for (2969ds/582Mi)
% 22.64/4.64 % (14235)Instruction limit reached!
% 22.64/4.64 % (14235)------------------------------
% 22.64/4.64 % (14235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.64/4.64 % (14235)Termination reason: Unknown
% 22.64/4.64 % (14235)Termination phase: Saturation
% 22.64/4.64
% 22.64/4.64 % (14235)Memory used [KB]: 8443
% 22.64/4.64 % (14235)Time elapsed: 0.161 s
% 22.64/4.64 % (14235)Instructions burned: 565 (million)
% 22.64/4.64 % (14235)------------------------------
% 22.64/4.64 % (14235)------------------------------
% 22.64/4.65 % (14227)Instruction limit reached!
% 22.64/4.65 % (14227)------------------------------
% 22.64/4.65 % (14227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.64/4.65 % (14227)Termination reason: Unknown
% 22.64/4.65 % (14227)Termination phase: Saturation
% 22.64/4.65
% 22.64/4.65 % (14227)Memory used [KB]: 21108
% 22.64/4.65 % (14227)Time elapsed: 0.436 s
% 22.64/4.65 % (14227)Instructions burned: 1763 (million)
% 22.64/4.65 % (14227)------------------------------
% 22.64/4.65 % (14227)------------------------------
% 22.64/4.65 % (14238)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_13872 for (2969ds/456Mi)
% 22.64/4.66 % (14239)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_13872 for (2969ds/393Mi)
% 22.64/4.67 % (14236)Instruction limit reached!
% 22.64/4.67 % (14236)------------------------------
% 22.64/4.67 % (14236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.64/4.67 % (14236)Termination reason: Unknown
% 22.64/4.67 % (14236)Termination phase: Saturation
% 22.64/4.67
% 22.64/4.67 % (14236)Memory used [KB]: 7547
% 22.64/4.67 % (14236)Time elapsed: 0.112 s
% 22.64/4.67 % (14236)Instructions burned: 407 (million)
% 22.64/4.67 % (14236)------------------------------
% 22.64/4.67 % (14236)------------------------------
% 22.64/4.68 % (14240)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_13872 for (2968ds/1335Mi)
% 23.63/4.77 % (14239)Instruction limit reached!
% 23.63/4.77 % (14239)------------------------------
% 23.63/4.77 % (14239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.77 % (14232)Instruction limit reached!
% 23.63/4.77 % (14232)------------------------------
% 23.63/4.77 % (14232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.77 % (14232)Termination reason: Unknown
% 23.63/4.77 % (14239)Termination reason: Unknown
% 23.63/4.77 % (14232)Termination phase: Saturation
% 23.63/4.77 % (14239)Termination phase: Saturation
% 23.63/4.77
% 23.63/4.77
% 23.63/4.77 % (14239)Memory used [KB]: 9594
% 23.63/4.77 % (14232)Memory used [KB]: 12025
% 23.63/4.77 % (14239)Time elapsed: 0.115 s
% 23.63/4.77 % (14232)Time elapsed: 0.484 s
% 23.63/4.77 % (14239)Instructions burned: 394 (million)
% 23.63/4.77 % (14232)Instructions burned: 1513 (million)
% 23.63/4.77 % (14239)------------------------------
% 23.63/4.77 % (14239)------------------------------
% 23.63/4.77 % (14232)------------------------------
% 23.63/4.77 % (14232)------------------------------
% 23.63/4.78 % (14241)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_13872 for (2967ds/3373Mi)
% 23.63/4.78 % (14242)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_13872 for (2967ds/474Mi)
% 23.63/4.78 % (14238)Instruction limit reached!
% 23.63/4.78 % (14238)------------------------------
% 23.63/4.78 % (14238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.63/4.78 % (14238)Termination reason: Unknown
% 23.63/4.78 % (14238)Termination phase: Saturation
% 23.63/4.78
% 23.63/4.78 % (14238)Memory used [KB]: 9338
% 23.63/4.78 % (14238)Time elapsed: 0.134 s
% 23.63/4.78 % (14238)Instructions burned: 458 (million)
% 23.63/4.78 % (14238)------------------------------
% 23.63/4.78 % (14238)------------------------------
% 23.63/4.79 % (14243)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_13872 for (2967ds/157Mi)
% 24.49/4.81 % (14237)Instruction limit reached!
% 24.49/4.81 % (14237)------------------------------
% 24.49/4.81 % (14237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.49/4.81 % (14237)Termination reason: Unknown
% 24.49/4.81 % (14237)Termination phase: Saturation
% 24.49/4.81
% 24.49/4.81 % (14237)Memory used [KB]: 10106
% 24.49/4.81 % (14237)Time elapsed: 0.184 s
% 24.49/4.81 % (14237)Instructions burned: 584 (million)
% 24.49/4.81 % (14237)------------------------------
% 24.49/4.81 % (14237)------------------------------
% 24.49/4.82 % (14244)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_13872 for (2967ds/590Mi)
% 24.49/4.83 % (14243)Instruction limit reached!
% 24.49/4.83 % (14243)------------------------------
% 24.49/4.83 % (14243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.49/4.83 % (14243)Termination reason: Unknown
% 24.49/4.83 % (14243)Termination phase: Saturation
% 24.49/4.83
% 24.49/4.83 % (14243)Memory used [KB]: 7036
% 24.49/4.83 % (14243)Time elapsed: 0.041 s
% 24.49/4.83 % (14243)Instructions burned: 157 (million)
% 24.49/4.83 % (14243)------------------------------
% 24.49/4.83 % (14243)------------------------------
% 24.49/4.84 % (14245)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_13872 for (2967ds/104Mi)
% 24.49/4.87 % (14245)Instruction limit reached!
% 24.49/4.87 % (14245)------------------------------
% 24.49/4.87 % (14245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.49/4.87 % (14245)Termination reason: Unknown
% 24.49/4.87 % (14245)Termination phase: Property scanning
% 24.49/4.87
% 24.49/4.87 % (14245)Memory used [KB]: 2558
% 24.49/4.87 % (14245)Time elapsed: 0.028 s
% 24.49/4.87 % (14245)Instructions burned: 107 (million)
% 24.49/4.87 % (14245)------------------------------
% 24.49/4.87 % (14245)------------------------------
% 24.49/4.88 % (14246)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_13872 for (2966ds/414Mi)
% 24.88/4.90 % (14242)Instruction limit reached!
% 24.88/4.90 % (14242)------------------------------
% 24.88/4.90 % (14242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.88/4.90 % (14242)Termination reason: Unknown
% 24.88/4.90 % (14242)Termination phase: Saturation
% 24.88/4.90
% 24.88/4.90 % (14242)Memory used [KB]: 7675
% 24.88/4.90 % (14242)Time elapsed: 0.121 s
% 24.88/4.90 % (14242)Instructions burned: 474 (million)
% 24.88/4.90 % (14242)------------------------------
% 24.88/4.90 % (14242)------------------------------
% 24.88/4.91 % (14247)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_13872 for (2966ds/715Mi)
% 24.88/4.98 % (14246)Instruction limit reached!
% 24.88/4.98 % (14246)------------------------------
% 24.88/4.98 % (14246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.88/4.98 % (14246)Termination reason: Unknown
% 24.88/4.98 % (14246)Termination phase: Saturation
% 24.88/4.98
% 24.88/4.98 % (14246)Memory used [KB]: 7291
% 24.88/4.98 % (14246)Time elapsed: 0.104 s
% 24.88/4.98 % (14246)Instructions burned: 414 (million)
% 24.88/4.98 % (14246)------------------------------
% 24.88/4.98 % (14246)------------------------------
% 24.88/4.99 % (14248)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_13872 for (2965ds/961Mi)
% 24.88/5.00 % (14244)Instruction limit reached!
% 24.88/5.00 % (14244)------------------------------
% 24.88/5.00 % (14244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.88/5.00 % (14244)Termination reason: Unknown
% 24.88/5.00 % (14244)Termination phase: Saturation
% 24.88/5.00
% 24.88/5.00 % (14244)Memory used [KB]: 8443
% 24.88/5.00 % (14244)Time elapsed: 0.174 s
% 24.88/5.00 % (14244)Instructions burned: 592 (million)
% 24.88/5.00 % (14244)------------------------------
% 24.88/5.00 % (14244)------------------------------
% 24.88/5.01 % (14249)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_13872 for (2965ds/1213Mi)
% 27.02/5.09 % (14240)Instruction limit reached!
% 27.02/5.09 % (14240)------------------------------
% 27.02/5.09 % (14240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.02/5.09 % (14240)Termination reason: Unknown
% 27.02/5.09 % (14240)Termination phase: Saturation
% 27.02/5.09
% 27.02/5.09 % (14240)Memory used [KB]: 9850
% 27.02/5.09 % (14240)Time elapsed: 0.410 s
% 27.02/5.09 % (14240)Instructions burned: 1336 (million)
% 27.02/5.09 % (14240)------------------------------
% 27.02/5.09 % (14240)------------------------------
% 27.02/5.10 % (14250)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_13872 for (2964ds/1979Mi)
% 27.02/5.12 % (14247)Instruction limit reached!
% 27.02/5.12 % (14247)------------------------------
% 27.02/5.12 % (14247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.02/5.12 % (14247)Termination reason: Unknown
% 27.02/5.12 % (14247)Termination phase: Saturation
% 27.02/5.12
% 27.02/5.12 % (14247)Memory used [KB]: 5117
% 27.02/5.12 % (14247)Time elapsed: 0.213 s
% 27.02/5.12 % (14247)Instructions burned: 716 (million)
% 27.02/5.12 % (14247)------------------------------
% 27.02/5.12 % (14247)------------------------------
% 27.72/5.13 % (14251)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_13872 for (2964ds/481Mi)
% 28.07/5.25 % (14251)Instruction limit reached!
% 28.07/5.25 % (14251)------------------------------
% 28.07/5.25 % (14251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.07/5.25 % (14251)Termination reason: Unknown
% 28.07/5.25 % (14251)Termination phase: Saturation
% 28.07/5.25
% 28.07/5.25 % (14251)Memory used [KB]: 7675
% 28.07/5.25 % (14251)Time elapsed: 0.120 s
% 28.07/5.25 % (14251)Instructions burned: 481 (million)
% 28.07/5.25 % (14251)------------------------------
% 28.07/5.25 % (14251)------------------------------
% 28.07/5.26 % (14252)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_13872 for (2963ds/783Mi)
% 28.07/5.28 % (14248)Instruction limit reached!
% 28.07/5.28 % (14248)------------------------------
% 28.07/5.28 % (14248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.07/5.28 % (14248)Termination reason: Unknown
% 28.07/5.28 % (14248)Termination phase: Saturation
% 28.07/5.28
% 28.07/5.28 % (14248)Memory used [KB]: 9850
% 28.07/5.28 % (14248)Time elapsed: 0.292 s
% 28.07/5.28 % (14248)Instructions burned: 961 (million)
% 28.07/5.28 % (14248)------------------------------
% 28.07/5.28 % (14248)------------------------------
% 28.07/5.29 % (14253)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_13872 for (2962ds/432Mi)
% 28.71/5.38 % (14249)Instruction limit reached!
% 28.71/5.38 % (14249)------------------------------
% 28.71/5.38 % (14249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.71/5.38 % (14249)Termination reason: Unknown
% 28.71/5.38 % (14249)Termination phase: Saturation
% 28.71/5.38
% 28.71/5.38 % (14249)Memory used [KB]: 13816
% 28.71/5.38 % (14249)Time elapsed: 0.377 s
% 28.71/5.38 % (14249)Instructions burned: 1213 (million)
% 28.71/5.38 % (14249)------------------------------
% 28.71/5.38 % (14249)------------------------------
% 28.71/5.39 % (14254)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_13872 for (2961ds/1670Mi)
% 29.11/5.42 % (14253)Instruction limit reached!
% 29.11/5.42 % (14253)------------------------------
% 29.11/5.42 % (14253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.11/5.42 % (14253)Termination reason: Unknown
% 29.11/5.42 % (14253)Termination phase: Saturation
% 29.11/5.42
% 29.11/5.42 % (14253)Memory used [KB]: 8955
% 29.11/5.42 % (14253)Time elapsed: 0.124 s
% 29.11/5.42 % (14253)Instructions burned: 432 (million)
% 29.11/5.42 % (14253)------------------------------
% 29.11/5.42 % (14253)------------------------------
% 29.11/5.43 % (14255)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_13872 for (2961ds/90Mi)
% 29.11/5.45 % (14255)Instruction limit reached!
% 29.11/5.45 % (14255)------------------------------
% 29.11/5.45 % (14255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.11/5.45 % (14255)Termination reason: Unknown
% 29.11/5.45 % (14255)Termination phase: Property scanning
% 29.11/5.45
% 29.11/5.45 % (14255)Memory used [KB]: 2430
% 29.11/5.45 % (14255)Time elapsed: 0.025 s
% 29.11/5.45 % (14255)Instructions burned: 92 (million)
% 29.11/5.45 % (14255)------------------------------
% 29.11/5.45 % (14255)------------------------------
% 29.11/5.46 % (14256)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_13872 for (2961ds/346Mi)
% 29.58/5.50 % (14252)Instruction limit reached!
% 29.58/5.50 % (14252)------------------------------
% 29.58/5.50 % (14252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.58/5.50 % (14252)Termination reason: Unknown
% 29.58/5.50 % (14252)Termination phase: Saturation
% 29.58/5.50
% 29.58/5.50 % (14252)Memory used [KB]: 11129
% 29.58/5.50 % (14252)Time elapsed: 0.245 s
% 29.58/5.50 % (14252)Instructions burned: 783 (million)
% 29.58/5.50 % (14252)------------------------------
% 29.58/5.50 % (14252)------------------------------
% 29.58/5.51 % (14257)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_13872 for (2960ds/401Mi)
% 29.58/5.55 % (14256)Instruction limit reached!
% 29.58/5.55 % (14256)------------------------------
% 29.58/5.55 % (14256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.58/5.55 % (14256)Termination reason: Unknown
% 29.58/5.55 % (14256)Termination phase: Saturation
% 29.58/5.55
% 29.58/5.55 % (14256)Memory used [KB]: 7291
% 29.58/5.55 % (14256)Time elapsed: 0.088 s
% 29.58/5.55 % (14256)Instructions burned: 346 (million)
% 29.58/5.55 % (14256)------------------------------
% 29.58/5.55 % (14256)------------------------------
% 29.58/5.56 % (14258)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_13872 for (2960ds/6454Mi)
% 30.23/5.62 % (14257)Instruction limit reached!
% 30.23/5.62 % (14257)------------------------------
% 30.23/5.62 % (14257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.23/5.62 % (14257)Termination reason: Unknown
% 30.23/5.62 % (14257)Termination phase: Saturation
% 30.23/5.62
% 30.23/5.62 % (14257)Memory used [KB]: 7291
% 30.23/5.62 % (14257)Time elapsed: 0.103 s
% 30.23/5.62 % (14257)Instructions burned: 403 (million)
% 30.23/5.62 % (14257)------------------------------
% 30.23/5.62 % (14257)------------------------------
% 30.23/5.63 % (14259)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_13872 for (2959ds/283Mi)
% 30.65/5.70 % (14259)Instruction limit reached!
% 30.65/5.70 % (14259)------------------------------
% 30.65/5.70 % (14259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.65/5.70 % (14259)Termination reason: Unknown
% 30.65/5.70 % (14259)Termination phase: Saturation
% 30.65/5.70
% 30.65/5.70 % (14259)Memory used [KB]: 8315
% 30.65/5.70 % (14259)Time elapsed: 0.076 s
% 30.65/5.70 % (14259)Instructions burned: 286 (million)
% 30.65/5.70 % (14259)------------------------------
% 30.65/5.70 % (14259)------------------------------
% 30.65/5.71 % (14260)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_13872 for (2958ds/865Mi)
% 30.65/5.71 % (14250)Refutation not found, non-redundant clauses discarded% (14250)------------------------------
% 30.65/5.71 % (14250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.65/5.71 % (14250)Termination reason: Refutation not found, non-redundant clauses discarded
% 30.65/5.71
% 30.65/5.71 % (14250)Memory used [KB]: 10234
% 30.65/5.71 % (14250)Time elapsed: 0.612 s
% 30.65/5.71 % (14250)Instructions burned: 1975 (million)
% 30.65/5.71 % (14250)------------------------------
% 30.65/5.71 % (14250)------------------------------
% 30.65/5.72 % (14261)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_13872 for (2958ds/4528Mi)
% 31.66/5.81 % (14241)Instruction limit reached!
% 31.66/5.81 % (14241)------------------------------
% 31.66/5.81 % (14241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.66/5.81 % (14241)Termination reason: Unknown
% 31.66/5.81 % (14241)Termination phase: Saturation
% 31.66/5.81
% 31.66/5.81 % (14241)Memory used [KB]: 12537
% 31.66/5.81 % (14241)Time elapsed: 1.034 s
% 31.66/5.81 % (14241)Instructions burned: 3375 (million)
% 31.66/5.81 % (14241)------------------------------
% 31.66/5.81 % (14241)------------------------------
% 31.66/5.82 % (14254)Instruction limit reached!
% 31.66/5.82 % (14254)------------------------------
% 31.66/5.82 % (14254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.66/5.82 % (14254)Termination reason: Unknown
% 31.66/5.82 % (14254)Termination phase: Saturation
% 31.66/5.82
% 31.66/5.82 % (14254)Memory used [KB]: 14711
% 31.66/5.82 % (14254)Time elapsed: 0.427 s
% 31.66/5.82 % (14254)Instructions burned: 1670 (million)
% 31.66/5.82 % (14254)------------------------------
% 31.66/5.82 % (14254)------------------------------
% 31.66/5.82 % (14262)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_13872 for (2957ds/1001Mi)
% 31.66/5.83 % (14263)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_13872 for (2957ds/102Mi)
% 31.66/5.85 % (14263)Instruction limit reached!
% 31.66/5.85 % (14263)------------------------------
% 31.66/5.85 % (14263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.66/5.85 % (14263)Termination reason: Unknown
% 31.66/5.85 % (14263)Termination phase: Function definition elimination
% 31.66/5.85
% 31.66/5.85 % (14263)Memory used [KB]: 2558
% 31.66/5.85 % (14263)Time elapsed: 0.027 s
% 31.66/5.85 % (14263)Instructions burned: 102 (million)
% 31.66/5.85 % (14263)------------------------------
% 31.66/5.85 % (14263)------------------------------
% 31.66/5.86 % (14264)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_13872 for (2956ds/952Mi)
% 31.66/5.86 % (14226)Instruction limit reached!
% 31.66/5.86 % (14226)------------------------------
% 31.66/5.86 % (14226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.66/5.86 % (14226)Termination reason: Unknown
% 31.66/5.86 % (14226)Termination phase: Saturation
% 31.66/5.86
% 31.66/5.86 % (14226)Memory used [KB]: 15991
% 31.66/5.86 % (14226)Time elapsed: 1.706 s
% 31.66/5.86 % (14226)Instructions burned: 5414 (million)
% 31.66/5.86 % (14226)------------------------------
% 31.66/5.86 % (14226)------------------------------
% 31.66/5.87 % (14261)Refutation not found, incomplete strategy
% 31.66/5.87 % (14261)------------------------------
% 31.66/5.87 % (14261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.66/5.87 % (14261)Termination reason: Refutation not found, incomplete strategy
% 31.66/5.87
% 31.66/5.87
% 31.66/5.87 % (14261)Memory used [KB]: 2814
% 31.66/5.87 % (14261)Time elapsed: 0.143 s
% 31.66/5.87 % (14261)Instructions burned: 549 (million)
% 31.66/5.87 % (14261)------------------------------
% 31.66/5.87 % (14261)------------------------------
% 31.66/5.87 % (14265)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_13872 for (2956ds/578Mi)
% 31.66/5.88 % (14266)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_13872 for (2956ds/643Mi)
% 32.49/5.95 % (14214)Instruction limit reached!
% 32.49/5.95 % (14214)------------------------------
% 32.49/5.95 % (14214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.49/5.95 % (14214)Termination reason: Unknown
% 32.49/5.95 % (14214)Termination phase: Saturation
% 32.49/5.95
% 32.49/5.95 % (14214)Memory used [KB]: 28912
% 32.49/5.95 % (14214)Time elapsed: 2.643 s
% 32.49/5.95 % (14214)Instructions burned: 8251 (million)
% 32.49/5.95 % (14214)------------------------------
% 32.49/5.95 % (14214)------------------------------
% 32.49/5.96 % (14260)Instruction limit reached!
% 32.49/5.96 % (14260)------------------------------
% 32.49/5.96 % (14260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.49/5.96 % (14260)Termination reason: Unknown
% 32.49/5.96 % (14260)Termination phase: Saturation
% 32.49/5.96
% 32.49/5.96 % (14260)Memory used [KB]: 8315
% 32.49/5.96 % (14260)Time elapsed: 0.250 s
% 32.49/5.96 % (14260)Instructions burned: 865 (million)
% 32.49/5.96 % (14260)------------------------------
% 32.49/5.96 % (14260)------------------------------
% 32.49/5.96 % (14267)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_13872 for (2955ds/865Mi)
% 32.49/5.97 % (14268)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_13872 for (2955ds/1174Mi)
% 32.49/6.01 % (14265)Instruction limit reached!
% 32.49/6.01 % (14265)------------------------------
% 32.49/6.01 % (14265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.49/6.01 % (14265)Termination reason: Unknown
% 32.49/6.01 % (14265)Termination phase: Saturation
% 32.49/6.01
% 32.49/6.01 % (14265)Memory used [KB]: 9850
% 32.49/6.01 % (14265)Time elapsed: 0.138 s
% 32.49/6.01 % (14265)Instructions burned: 578 (million)
% 32.49/6.01 % (14265)------------------------------
% 32.49/6.01 % (14265)------------------------------
% 32.49/6.02 % (14269)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_13872 for (2955ds/644Mi)
% 34.04/6.04 % (14266)Instruction limit reached!
% 34.04/6.04 % (14266)------------------------------
% 34.04/6.04 % (14266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.04/6.04 % (14266)Termination reason: Unknown
% 34.04/6.04 % (14266)Termination phase: Saturation
% 34.04/6.04
% 34.04/6.04 % (14266)Memory used [KB]: 13304
% 34.04/6.04 % (14266)Time elapsed: 0.164 s
% 34.04/6.04 % (14266)Instructions burned: 645 (million)
% 34.04/6.04 % (14266)------------------------------
% 34.04/6.04 % (14266)------------------------------
% 34.04/6.05 % (14270)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_13872 for (2955ds/1201Mi)
% 34.59/6.13 % (14262)Instruction limit reached!
% 34.59/6.13 % (14262)------------------------------
% 34.59/6.13 % (14262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.59/6.13 % (14262)Termination reason: Unknown
% 34.59/6.13 % (14262)Termination phase: Saturation
% 34.59/6.13
% 34.59/6.13 % (14262)Memory used [KB]: 11257
% 34.59/6.13 % (14262)Time elapsed: 0.307 s
% 34.59/6.13 % (14262)Instructions burned: 1002 (million)
% 34.59/6.13 % (14262)------------------------------
% 34.59/6.13 % (14262)------------------------------
% 34.59/6.14 % (14271)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_13872 for (2954ds/1046Mi)
% 34.59/6.15 % (14264)Instruction limit reached!
% 34.59/6.15 % (14264)------------------------------
% 34.59/6.15 % (14264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.59/6.15 % (14264)Termination reason: Unknown
% 34.59/6.15 % (14264)Termination phase: Saturation
% 34.59/6.15
% 34.59/6.15 % (14264)Memory used [KB]: 10106
% 34.59/6.15 % (14264)Time elapsed: 0.287 s
% 34.59/6.15 % (14264)Instructions burned: 953 (million)
% 34.59/6.15 % (14264)------------------------------
% 34.59/6.15 % (14264)------------------------------
% 34.59/6.16 % (14272)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_13872 for (2954ds/222Mi)
% 34.59/6.20 % (14267)Instruction limit reached!
% 34.59/6.20 % (14267)------------------------------
% 34.59/6.20 % (14267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.59/6.20 % (14267)Termination reason: Unknown
% 34.59/6.20 % (14267)Termination phase: Saturation
% 34.59/6.20
% 34.59/6.20 % (14267)Memory used [KB]: 7547
% 34.59/6.20 % (14267)Time elapsed: 0.236 s
% 34.59/6.20 % (14267)Instructions burned: 866 (million)
% 34.59/6.20 % (14267)------------------------------
% 34.59/6.20 % (14267)------------------------------
% 34.87/6.21 % (14273)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_13872 for (2953ds/68Mi)
% 34.87/6.21 % (14269)Instruction limit reached!
% 34.87/6.21 % (14269)------------------------------
% 34.87/6.21 % (14269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.87/6.21 % (14269)Termination reason: Unknown
% 34.87/6.21 % (14269)Termination phase: Saturation
% 34.87/6.21
% 34.87/6.21 % (14269)Memory used [KB]: 7931
% 34.87/6.21 % (14269)Time elapsed: 0.189 s
% 34.87/6.21 % (14269)Instructions burned: 646 (million)
% 34.87/6.21 % (14269)------------------------------
% 34.87/6.21 % (14269)------------------------------
% 34.87/6.21 % (14272)Instruction limit reached!
% 34.87/6.21 % (14272)------------------------------
% 34.87/6.21 % (14272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.87/6.21 % (14272)Termination reason: Unknown
% 34.87/6.21 % (14272)Termination phase: Saturation
% 34.87/6.21
% 34.87/6.21 % (14272)Memory used [KB]: 7291
% 34.87/6.21 % (14272)Time elapsed: 0.056 s
% 34.87/6.21 % (14272)Instructions burned: 222 (million)
% 34.87/6.21 % (14272)------------------------------
% 34.87/6.21 % (14272)------------------------------
% 34.87/6.22 % (14274)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_13872 for (2953ds/454Mi)
% 34.87/6.22 % (14275)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_13872 for (2953ds/360Mi)
% 34.87/6.22 % (14273)Instruction limit reached!
% 34.87/6.22 % (14273)------------------------------
% 34.87/6.22 % (14273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.87/6.22 % (14273)Termination reason: Unknown
% 34.87/6.22 % (14273)Termination phase: SInE selection
% 34.87/6.22
% 34.87/6.22 % (14273)Memory used [KB]: 2302
% 34.87/6.22 % (14273)Time elapsed: 0.020 s
% 34.87/6.22 % (14273)Instructions burned: 71 (million)
% 34.87/6.22 % (14273)------------------------------
% 34.87/6.22 % (14273)------------------------------
% 34.87/6.23 % (14276)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_13872 for (2953ds/157Mi)
% 34.87/6.27 % (14276)Instruction limit reached!
% 34.87/6.27 % (14276)------------------------------
% 34.87/6.27 % (14276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.87/6.27 % (14276)Termination reason: Unknown
% 34.87/6.27 % (14276)Termination phase: Saturation
% 34.87/6.27
% 34.87/6.27 % (14276)Memory used [KB]: 7036
% 34.87/6.27 % (14276)Time elapsed: 0.040 s
% 34.87/6.27 % (14276)Instructions burned: 158 (million)
% 34.87/6.27 % (14276)------------------------------
% 34.87/6.27 % (14276)------------------------------
% 34.87/6.28 % (14277)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_13872 for (2952ds/5061Mi)
% 35.41/6.31 % (14275)Instruction limit reached!
% 35.41/6.31 % (14275)------------------------------
% 35.41/6.31 % (14275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.41/6.31 % (14275)Termination reason: Unknown
% 35.41/6.31 % (14275)Termination phase: Saturation
% 35.41/6.31
% 35.41/6.31 % (14275)Memory used [KB]: 7291
% 35.41/6.31 % (14275)Time elapsed: 0.091 s
% 35.41/6.31 % (14275)Instructions burned: 362 (million)
% 35.41/6.31 % (14275)------------------------------
% 35.41/6.31 % (14275)------------------------------
% 35.41/6.32 % (14278)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_13872 for (2952ds/2401Mi)
% 35.41/6.33 % (14268)Instruction limit reached!
% 35.41/6.33 % (14268)------------------------------
% 35.41/6.33 % (14268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.41/6.33 % (14268)Termination reason: Unknown
% 35.41/6.33 % (14268)Termination phase: Saturation
% 35.41/6.33
% 35.41/6.33 % (14268)Memory used [KB]: 9850
% 35.41/6.33 % (14268)Time elapsed: 0.358 s
% 35.41/6.33 % (14268)Instructions burned: 1174 (million)
% 35.41/6.33 % (14268)------------------------------
% 35.41/6.33 % (14268)------------------------------
% 35.41/6.33 % (14274)Instruction limit reached!
% 35.41/6.33 % (14274)------------------------------
% 35.41/6.33 % (14274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.41/6.33 % (14274)Termination reason: Unknown
% 35.41/6.33 % (14274)Termination phase: Saturation
% 35.41/6.33
% 35.41/6.33 % (14274)Memory used [KB]: 13432
% 35.41/6.33 % (14274)Time elapsed: 0.115 s
% 35.41/6.33 % (14274)Instructions burned: 455 (million)
% 35.41/6.33 % (14274)------------------------------
% 35.41/6.33 % (14274)------------------------------
% 35.41/6.34 % (14279)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_13872 for (2952ds/5798Mi)
% 35.41/6.34 % (14280)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_13872 for (2952ds/346Mi)
% 35.41/6.38 % (14270)Instruction limit reached!
% 35.41/6.38 % (14270)------------------------------
% 35.41/6.38 % (14270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.41/6.38 % (14270)Termination reason: Unknown
% 35.41/6.38 % (14270)Termination phase: Saturation
% 35.41/6.38
% 35.41/6.38 % (14270)Memory used [KB]: 10490
% 35.41/6.38 % (14270)Time elapsed: 0.334 s
% 35.41/6.38 % (14270)Instructions burned: 1202 (million)
% 35.41/6.38 % (14270)------------------------------
% 35.41/6.38 % (14270)------------------------------
% 35.41/6.39 % (14281)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_13872 for (2951ds/1321Mi)
% 36.11/6.40 % (14271)Instruction limit reached!
% 36.11/6.40 % (14271)------------------------------
% 36.11/6.40 % (14271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.11/6.40 % (14271)Termination reason: Unknown
% 36.11/6.40 % (14271)Termination phase: Saturation
% 36.11/6.40
% 36.11/6.40 % (14271)Memory used [KB]: 7419
% 36.11/6.40 % (14271)Time elapsed: 0.260 s
% 36.11/6.40 % (14271)Instructions burned: 1046 (million)
% 36.11/6.40 % (14271)------------------------------
% 36.11/6.40 % (14271)------------------------------
% 36.11/6.41 % (14282)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_13872 for (2951ds/1312Mi)
% 36.11/6.43 % (14280)Instruction limit reached!
% 36.11/6.43 % (14280)------------------------------
% 36.11/6.43 % (14280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.11/6.43 % (14280)Termination reason: Unknown
% 36.11/6.43 % (14280)Termination phase: Saturation
% 36.11/6.43
% 36.11/6.43 % (14280)Memory used [KB]: 7291
% 36.11/6.43 % (14280)Time elapsed: 0.087 s
% 36.11/6.43 % (14280)Instructions burned: 349 (million)
% 36.11/6.43 % (14280)------------------------------
% 36.11/6.43 % (14280)------------------------------
% 36.11/6.44 % (14283)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_13872 for (2951ds/672Mi)
% 36.68/6.64 % (14283)Instruction limit reached!
% 36.68/6.64 % (14283)------------------------------
% 36.68/6.64 % (14283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.68/6.64 % (14283)Termination reason: Unknown
% 36.68/6.64 % (14283)Termination phase: Saturation
% 36.68/6.64
% 36.68/6.64 % (14283)Memory used [KB]: 10490
% 36.68/6.64 % (14283)Time elapsed: 0.207 s
% 36.68/6.64 % (14283)Instructions burned: 673 (million)
% 36.68/6.64 % (14283)------------------------------
% 36.68/6.64 % (14283)------------------------------
% 36.68/6.65 % (14284)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_13872 for (2948ds/1897Mi)
% 37.00/6.74 % (14282)Instruction limit reached!
% 37.00/6.74 % (14282)------------------------------
% 37.00/6.74 % (14282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.74 % (14282)Termination reason: Unknown
% 37.00/6.74 % (14282)Termination phase: Saturation
% 37.00/6.74
% 37.00/6.74 % (14282)Memory used [KB]: 14200
% 37.00/6.74 % (14282)Time elapsed: 0.336 s
% 37.00/6.74 % (14282)Instructions burned: 1315 (million)
% 37.00/6.74 % (14282)------------------------------
% 37.00/6.74 % (14282)------------------------------
% 37.00/6.75 % (14285)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_13872 for (2947ds/1202Mi)
% 37.00/6.79 % (14281)Instruction limit reached!
% 37.00/6.79 % (14281)------------------------------
% 37.00/6.79 % (14281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.00/6.79 % (14281)Termination reason: Unknown
% 37.00/6.79 % (14281)Termination phase: Saturation
% 37.00/6.79
% 37.00/6.79 % (14281)Memory used [KB]: 8955
% 37.00/6.79 % (14281)Time elapsed: 0.399 s
% 37.00/6.79 % (14281)Instructions burned: 1323 (million)
% 37.00/6.79 % (14281)------------------------------
% 37.00/6.79 % (14281)------------------------------
% 37.86/6.80 % (14286)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_13872 for (2947ds/1493Mi)
% 41.07/7.05 % (14278)Instruction limit reached!
% 41.07/7.05 % (14278)------------------------------
% 41.07/7.05 % (14278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.07/7.05 % (14278)Termination reason: Unknown
% 41.07/7.05 % (14278)Termination phase: Saturation
% 41.07/7.05
% 41.07/7.05 % (14278)Memory used [KB]: 10106
% 41.07/7.05 % (14278)Time elapsed: 0.754 s
% 41.07/7.05 % (14278)Instructions burned: 2403 (million)
% 41.07/7.05 % (14278)------------------------------
% 41.07/7.05 % (14278)------------------------------
% 41.07/7.06 % (14287)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_13872 for (2945ds/7679Mi)
% 41.07/7.10 % (14285)Instruction limit reached!
% 41.07/7.10 % (14285)------------------------------
% 41.07/7.10 % (14285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.07/7.10 % (14285)Termination reason: Unknown
% 41.07/7.10 % (14285)Termination phase: Saturation
% 41.07/7.10
% 41.07/7.10 % (14285)Memory used [KB]: 8571
% 41.07/7.10 % (14285)Time elapsed: 0.348 s
% 41.07/7.10 % (14285)Instructions burned: 1204 (million)
% 41.07/7.10 % (14285)------------------------------
% 41.07/7.10 % (14285)------------------------------
% 41.07/7.11 % (14288)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_13872 for (2944ds/340Mi)
% 41.72/7.17 % (14286)Instruction limit reached!
% 41.72/7.17 % (14286)------------------------------
% 41.72/7.17 % (14286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.72/7.17 % (14286)Termination reason: Unknown
% 41.72/7.17 % (14286)Termination phase: Saturation
% 41.72/7.17
% 41.72/7.17 % (14286)Memory used [KB]: 7547
% 41.72/7.17 % (14286)Time elapsed: 0.372 s
% 41.72/7.17 % (14286)Instructions burned: 1495 (million)
% 41.72/7.17 % (14286)------------------------------
% 41.72/7.17 % (14286)------------------------------
% 41.72/7.18 % (14289)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_13872 for (2943ds/3672Mi)
% 42.06/7.21 % (14288)Instruction limit reached!
% 42.06/7.21 % (14288)------------------------------
% 42.06/7.21 % (14288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.06/7.21 % (14288)Termination reason: Unknown
% 42.06/7.21 % (14288)Termination phase: Saturation
% 42.06/7.21
% 42.06/7.21 % (14288)Memory used [KB]: 10490
% 42.06/7.21 % (14288)Time elapsed: 0.099 s
% 42.06/7.21 % (14288)Instructions burned: 341 (million)
% 42.06/7.21 % (14288)------------------------------
% 42.06/7.21 % (14288)------------------------------
% 42.06/7.22 % (14290)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_13872 for (2943ds/1535Mi)
% 42.06/7.24 % (14284)Instruction limit reached!
% 42.06/7.24 % (14284)------------------------------
% 42.06/7.24 % (14284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.06/7.24 % (14284)Termination reason: Unknown
% 42.06/7.24 % (14284)Termination phase: Saturation
% 42.06/7.24
% 42.06/7.24 % (14284)Memory used [KB]: 13176
% 42.06/7.24 % (14284)Time elapsed: 0.586 s
% 42.06/7.24 % (14284)Instructions burned: 1897 (million)
% 42.06/7.24 % (14284)------------------------------
% 42.06/7.24 % (14284)------------------------------
% 42.06/7.25 % (14291)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_13872 for (2943ds/4637Mi)
% 43.12/7.53 % (14277)Instruction limit reached!
% 43.12/7.53 % (14277)------------------------------
% 43.12/7.53 % (14277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.12/7.53 % (14277)Termination reason: Unknown
% 43.12/7.53 % (14277)Termination phase: Saturation
% 43.12/7.53
% 43.12/7.53 % (14277)Memory used [KB]: 7675
% 43.12/7.53 % (14277)Time elapsed: 1.250 s
% 43.12/7.53 % (14277)Instructions burned: 5064 (million)
% 43.12/7.53 % (14277)------------------------------
% 43.12/7.53 % (14277)------------------------------
% 43.12/7.54 % (14292)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_13872 for (2940ds/3174Mi)
% 43.12/7.59 % (14258)Instruction limit reached!
% 43.12/7.59 % (14258)------------------------------
% 43.12/7.59 % (14258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.12/7.59 % (14258)Termination reason: Unknown
% 43.12/7.59 % (14258)Termination phase: Saturation
% 43.12/7.59
% 43.12/7.59 % (14258)Memory used [KB]: 14583
% 43.12/7.59 % (14258)Time elapsed: 2.051 s
% 43.12/7.59 % (14258)Instructions burned: 6455 (million)
% 43.12/7.59 % (14258)------------------------------
% 43.12/7.59 % (14258)------------------------------
% 43.12/7.60 % (14293)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_13872 for (2939ds/307Mi)
% 43.37/7.60 % (14290)Instruction limit reached!
% 43.37/7.60 % (14290)------------------------------
% 43.37/7.60 % (14290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.37/7.60 % (14290)Termination reason: Unknown
% 43.37/7.60 % (14290)Termination phase: Saturation
% 43.37/7.60
% 43.37/7.60 % (14290)Memory used [KB]: 13560
% 43.37/7.60 % (14290)Time elapsed: 0.401 s
% 43.37/7.60 % (14290)Instructions burned: 1536 (million)
% 43.37/7.60 % (14290)------------------------------
% 43.37/7.60 % (14290)------------------------------
% 43.37/7.61 % (14294)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_13872 for (2939ds/3619Mi)
% 43.37/7.67 % (14293)Instruction limit reached!
% 43.37/7.67 % (14293)------------------------------
% 43.37/7.67 % (14293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.37/7.67 % (14293)Termination reason: Unknown
% 43.37/7.67 % (14293)Termination phase: Saturation
% 43.37/7.67
% 43.37/7.67 % (14293)Memory used [KB]: 7291
% 43.37/7.67 % (14293)Time elapsed: 0.077 s
% 43.37/7.67 % (14293)Instructions burned: 307 (million)
% 43.37/7.67 % (14293)------------------------------
% 43.37/7.67 % (14293)------------------------------
% 43.37/7.68 % (14295)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_13872 for (2938ds/2325Mi)
% 48.80/8.17 % (14279)Instruction limit reached!
% 48.80/8.17 % (14279)------------------------------
% 48.80/8.17 % (14279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.80/8.17 % (14279)Termination reason: Unknown
% 48.80/8.17 % (14279)Termination phase: Saturation
% 48.80/8.17
% 48.80/8.17 % (14279)Memory used [KB]: 13432
% 48.80/8.17 % (14279)Time elapsed: 1.838 s
% 48.80/8.17 % (14279)Instructions burned: 5800 (million)
% 48.80/8.17 % (14279)------------------------------
% 48.80/8.17 % (14279)------------------------------
% 48.80/8.18 % (14296)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_13872 for (2933ds/2341Mi)
% 49.31/8.26 % (14295)Refutation not found, non-redundant clauses discarded% (14295)------------------------------
% 49.31/8.26 % (14295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.31/8.26 % (14295)Termination reason: Refutation not found, non-redundant clauses discarded
% 49.31/8.26
% 49.31/8.26 % (14295)Memory used [KB]: 18421
% 49.31/8.26 % (14295)Time elapsed: 0.579 s
% 49.31/8.26 % (14295)Instructions burned: 1882 (million)
% 49.31/8.26 % (14295)------------------------------
% 49.31/8.26 % (14295)------------------------------
% 49.31/8.27 % (14297)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_13872 for (2932ds/7257Mi)
% 49.89/8.34 % (14289)Instruction limit reached!
% 49.89/8.34 % (14289)------------------------------
% 49.89/8.34 % (14289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.89/8.34 % (14289)Termination reason: Unknown
% 49.89/8.34 % (14289)Termination phase: Saturation
% 49.89/8.34
% 49.89/8.34 % (14289)Memory used [KB]: 12792
% 49.89/8.34 % (14289)Time elapsed: 1.188 s
% 49.89/8.34 % (14289)Instructions burned: 3672 (million)
% 49.89/8.34 % (14289)------------------------------
% 49.89/8.34 % (14289)------------------------------
% 49.89/8.36 % (14298)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_13872 for (2932ds/3710Mi)
% 50.75/8.52 % (14292)Instruction limit reached!
% 50.75/8.52 % (14292)------------------------------
% 50.75/8.52 % (14292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.75/8.52 % (14292)Termination reason: Unknown
% 50.75/8.52 % (14292)Termination phase: Saturation
% 50.75/8.52
% 50.75/8.52 % (14292)Memory used [KB]: 19957
% 50.75/8.52 % (14292)Time elapsed: 0.999 s
% 50.75/8.52 % (14292)Instructions burned: 3175 (million)
% 50.75/8.52 % (14292)------------------------------
% 50.75/8.52 % (14292)------------------------------
% 50.75/8.53 % (14299)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_13872 for (2930ds/326Mi)
% 51.09/8.62 % (14299)Instruction limit reached!
% 51.09/8.62 % (14299)------------------------------
% 51.09/8.62 % (14299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.09/8.62 % (14299)Termination reason: Unknown
% 51.09/8.62 % (14299)Termination phase: Saturation
% 51.09/8.62
% 51.09/8.62 % (14299)Memory used [KB]: 8443
% 51.09/8.62 % (14299)Time elapsed: 0.090 s
% 51.09/8.62 % (14299)Instructions burned: 326 (million)
% 51.09/8.62 % (14299)------------------------------
% 51.09/8.62 % (14299)------------------------------
% 51.09/8.63 % (14300)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_13872 for (2929ds/1100Mi)
% 51.47/8.70 % (14291)Instruction limit reached!
% 51.47/8.70 % (14291)------------------------------
% 51.47/8.70 % (14291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.47/8.70 % (14291)Termination reason: Unknown
% 51.47/8.70 % (14291)Termination phase: Saturation
% 51.47/8.70
% 51.47/8.70 % (14291)Memory used [KB]: 11257
% 51.47/8.70 % (14291)Time elapsed: 1.472 s
% 51.47/8.70 % (14291)Instructions burned: 4638 (million)
% 51.47/8.70 % (14291)------------------------------
% 51.47/8.70 % (14291)------------------------------
% 51.47/8.71 % (14301)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_13872 for (2928ds/406Mi)
% 51.47/8.73 % (14294)Instruction limit reached!
% 51.47/8.73 % (14294)------------------------------
% 51.47/8.73 % (14294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.47/8.73 % (14294)Termination reason: Unknown
% 51.47/8.73 % (14294)Termination phase: Saturation
% 51.47/8.73
% 51.47/8.73 % (14294)Memory used [KB]: 19317
% 51.47/8.73 % (14294)Time elapsed: 1.121 s
% 51.47/8.73 % (14294)Instructions burned: 3622 (million)
% 51.47/8.73 % (14294)------------------------------
% 51.47/8.73 % (14294)------------------------------
% 51.47/8.74 % (14302)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_13872 for (2928ds/1871Mi)
% 51.63/8.82 % (14301)Instruction limit reached!
% 51.63/8.82 % (14301)------------------------------
% 51.63/8.82 % (14301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.63/8.82 % (14301)Termination reason: Unknown
% 51.63/8.82 % (14301)Termination phase: Saturation
% 51.63/8.82
% 51.63/8.82 % (14301)Memory used [KB]: 7547
% 51.63/8.82 % (14301)Time elapsed: 0.115 s
% 51.63/8.82 % (14301)Instructions burned: 409 (million)
% 51.63/8.82 % (14301)------------------------------
% 51.63/8.82 % (14301)------------------------------
% 51.63/8.83 % (14303)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_13872 for (2927ds/1194Mi)
% 51.85/8.90 % (14296)Instruction limit reached!
% 51.85/8.90 % (14296)------------------------------
% 51.85/8.90 % (14296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.85/8.90 % (14296)Termination reason: Unknown
% 51.85/8.90 % (14296)Termination phase: Saturation
% 51.85/8.90
% 51.85/8.90 % (14296)Memory used [KB]: 11129
% 51.85/8.90 % (14296)Time elapsed: 0.740 s
% 51.85/8.90 % (14296)Instructions burned: 2343 (million)
% 51.85/8.90 % (14296)------------------------------
% 51.85/8.90 % (14296)------------------------------
% 51.85/8.91 % (14304)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_13872 for (2926ds/474Mi)
% 51.85/8.97 % (14300)Instruction limit reached!
% 51.85/8.97 % (14300)------------------------------
% 51.85/8.97 % (14300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 51.85/8.97 % (14300)Termination reason: Unknown
% 51.85/8.97 % (14300)Termination phase: Saturation
% 51.85/8.97
% 51.85/8.97 % (14300)Memory used [KB]: 14583
% 51.85/8.97 % (14300)Time elapsed: 0.349 s
% 51.85/8.97 % (14300)Instructions burned: 1100 (million)
% 51.85/8.97 % (14300)------------------------------
% 51.85/8.97 % (14300)------------------------------
% 51.85/8.98 % (14305)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_13872 for (2925ds/3115Mi)
% 55.11/9.03 % (14304)Instruction limit reached!
% 55.11/9.03 % (14304)------------------------------
% 55.11/9.03 % (14304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.11/9.03 % (14304)Termination reason: Unknown
% 55.11/9.03 % (14304)Termination phase: Saturation
% 55.11/9.03
% 55.11/9.03 % (14304)Memory used [KB]: 7419
% 55.11/9.03 % (14304)Time elapsed: 0.119 s
% 55.11/9.03 % (14304)Instructions burned: 474 (million)
% 55.11/9.03 % (14304)------------------------------
% 55.11/9.03 % (14304)------------------------------
% 55.11/9.04 % (14306)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_13872 for (2925ds/831Mi)
% 56.19/9.20 % (14303)Instruction limit reached!
% 56.19/9.20 % (14303)------------------------------
% 56.19/9.20 % (14303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.19/9.20 % (14303)Termination reason: Unknown
% 56.19/9.20 % (14303)Termination phase: Saturation
% 56.19/9.20
% 56.19/9.20 % (14303)Memory used [KB]: 12281
% 56.19/9.20 % (14303)Time elapsed: 0.371 s
% 56.19/9.20 % (14303)Instructions burned: 1195 (million)
% 56.19/9.20 % (14303)------------------------------
% 56.19/9.20 % (14303)------------------------------
% 56.19/9.21 % (14307)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_13872 for (2923ds/1188Mi)
% 56.19/9.29 % (14306)Instruction limit reached!
% 56.19/9.29 % (14306)------------------------------
% 56.19/9.29 % (14306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.19/9.29 % (14306)Termination reason: Unknown
% 56.19/9.29 % (14306)Termination phase: Saturation
% 56.19/9.29
% 56.19/9.29 % (14306)Memory used [KB]: 9722
% 56.19/9.29 % (14306)Time elapsed: 0.255 s
% 56.19/9.29 % (14306)Instructions burned: 833 (million)
% 56.19/9.29 % (14306)------------------------------
% 56.19/9.29 % (14306)------------------------------
% 56.96/9.30 % (14308)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_13872 for (2922ds/2868Mi)
% 56.96/9.31 % (14298)Instruction limit reached!
% 56.96/9.31 % (14298)------------------------------
% 56.96/9.31 % (14298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.96/9.31 % (14298)Termination reason: Unknown
% 56.96/9.31 % (14298)Termination phase: Saturation
% 56.96/9.31
% 56.96/9.31 % (14298)Memory used [KB]: 15735
% 56.96/9.31 % (14298)Time elapsed: 0.954 s
% 56.96/9.31 % (14298)Instructions burned: 3711 (million)
% 56.96/9.31 % (14298)------------------------------
% 56.96/9.31 % (14298)------------------------------
% 56.96/9.32 % (14309)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_13872 for (2922ds/1516Mi)
% 56.96/9.32 % (14302)Instruction limit reached!
% 56.96/9.32 % (14302)------------------------------
% 56.96/9.32 % (14302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.96/9.32 % (14302)Termination reason: Unknown
% 56.96/9.32 % (14302)Termination phase: Saturation
% 56.96/9.32
% 56.96/9.32 % (14302)Memory used [KB]: 18038
% 56.96/9.32 % (14302)Time elapsed: 0.583 s
% 56.96/9.32 % (14302)Instructions burned: 1871 (million)
% 56.96/9.32 % (14302)------------------------------
% 56.96/9.32 % (14302)------------------------------
% 56.96/9.33 % (14310)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_13872 for (2922ds/2321Mi)
% 56.96/9.39 % (14287)Instruction limit reached!
% 56.96/9.39 % (14287)------------------------------
% 56.96/9.39 % (14287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.96/9.39 % (14287)Termination reason: Unknown
% 56.96/9.39 % (14287)Termination phase: Saturation
% 56.96/9.39
% 56.96/9.39 % (14287)Memory used [KB]: 18293
% 56.96/9.39 % (14287)Time elapsed: 2.347 s
% 56.96/9.39 % (14287)Instructions burned: 7681 (million)
% 56.96/9.39 % (14287)------------------------------
% 56.96/9.39 % (14287)------------------------------
% 57.33/9.40 % (14311)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_13872 for (2921ds/2812Mi)
% 57.53/9.52 % (14307)Instruction limit reached!
% 57.53/9.52 % (14307)------------------------------
% 57.53/9.52 % (14307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.53/9.52 % (14307)Termination reason: Unknown
% 57.53/9.52 % (14307)Termination phase: Saturation
% 57.53/9.52
% 57.53/9.52 % (14307)Memory used [KB]: 14711
% 57.53/9.52 % (14307)Time elapsed: 0.306 s
% 57.53/9.52 % (14307)Instructions burned: 1190 (million)
% 57.53/9.52 % (14307)------------------------------
% 57.53/9.52 % (14307)------------------------------
% 57.53/9.53 % (14312)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_13872 for (2920ds/4604Mi)
% 58.25/9.76 % (14305)Instruction limit reached!
% 58.25/9.76 % (14305)------------------------------
% 58.25/9.76 % (14305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.25/9.76 % (14305)Termination reason: Unknown
% 58.25/9.76 % (14305)Termination phase: Saturation
% 58.25/9.76
% 58.25/9.76 % (14305)Memory used [KB]: 13944
% 58.25/9.76 % (14305)Time elapsed: 0.776 s
% 58.25/9.76 % (14305)Instructions burned: 3115 (million)
% 58.25/9.76 % (14305)------------------------------
% 58.25/9.76 % (14305)------------------------------
% 58.25/9.77 % (14313)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_13872 for (2917ds/2678Mi)
% 58.25/9.80 % (14309)Instruction limit reached!
% 58.25/9.80 % (14309)------------------------------
% 58.25/9.80 % (14309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 58.25/9.80 % (14309)Termination reason: Unknown
% 58.25/9.80 % (14309)Termination phase: Saturation
% 58.25/9.80
% 58.25/9.80 % (14309)Memory used [KB]: 11769
% 58.25/9.80 % (14309)Time elapsed: 0.479 s
% 58.25/9.80 % (14309)Instructions burned: 1517 (million)
% 58.25/9.80 % (14309)------------------------------
% 58.25/9.80 % (14309)------------------------------
% 58.42/9.81 % (14314)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_13872 for (2917ds/643Mi)
% 59.01/9.92 % (14310)Instruction limit reached!
% 59.01/9.92 % (14310)------------------------------
% 59.01/9.92 % (14310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.01/9.92 % (14310)Termination reason: Unknown
% 59.01/9.92 % (14310)Termination phase: Saturation
% 59.01/9.92
% 59.01/9.92 % (14310)Memory used [KB]: 13304
% 59.01/9.92 % (14310)Time elapsed: 0.592 s
% 59.01/9.92 % (14310)Instructions burned: 2323 (million)
% 59.01/9.92 % (14310)------------------------------
% 59.01/9.92 % (14310)------------------------------
% 59.01/9.93 % (14315)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_13872 for (2916ds/458Mi)
% 59.01/9.97 % (14314)Instruction limit reached!
% 59.01/9.97 % (14314)------------------------------
% 59.01/9.97 % (14314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.01/9.97 % (14314)Termination reason: Unknown
% 59.01/9.97 % (14314)Termination phase: Saturation
% 59.01/9.97
% 59.01/9.97 % (14314)Memory used [KB]: 13304
% 59.01/9.97 % (14314)Time elapsed: 0.165 s
% 59.01/9.97 % (14314)Instructions burned: 646 (million)
% 59.01/9.97 % (14314)------------------------------
% 59.01/9.97 % (14314)------------------------------
% 59.01/9.98 % (14316)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_13872 for (2915ds/2546Mi)
% 62.13/10.03 % (14308)Instruction limit reached!
% 62.13/10.03 % (14308)------------------------------
% 62.13/10.03 % (14308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.13/10.03 % (14308)Termination reason: Unknown
% 62.13/10.03 % (14308)Termination phase: Saturation
% 62.13/10.03
% 62.13/10.03 % (14308)Memory used [KB]: 7419
% 62.13/10.03 % (14308)Time elapsed: 0.728 s
% 62.13/10.03 % (14308)Instructions burned: 2869 (million)
% 62.13/10.03 % (14308)------------------------------
% 62.13/10.03 % (14308)------------------------------
% 62.13/10.04 % (14317)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_13872 for (2915ds/1432Mi)
% 62.13/10.05 % (14315)Instruction limit reached!
% 62.13/10.05 % (14315)------------------------------
% 62.13/10.05 % (14315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.13/10.05 % (14315)Termination reason: Unknown
% 62.13/10.05 % (14315)Termination phase: Saturation
% 62.13/10.05
% 62.13/10.05 % (14315)Memory used [KB]: 8187
% 62.13/10.05 % (14315)Time elapsed: 0.116 s
% 62.13/10.05 % (14315)Instructions burned: 459 (million)
% 62.13/10.05 % (14315)------------------------------
% 62.13/10.05 % (14315)------------------------------
% 62.13/10.06 % (14318)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_13872 for (2915ds/386Mi)
% 62.71/10.15 % (14318)Instruction limit reached!
% 62.71/10.15 % (14318)------------------------------
% 62.71/10.15 % (14318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.71/10.15 % (14318)Termination reason: Unknown
% 62.71/10.15 % (14318)Termination phase: Saturation
% 62.71/10.15
% 62.71/10.15 % (14318)Memory used [KB]: 7291
% 62.71/10.15 % (14318)Time elapsed: 0.097 s
% 62.71/10.15 % (14318)Instructions burned: 387 (million)
% 62.71/10.15 % (14318)------------------------------
% 62.71/10.15 % (14318)------------------------------
% 62.71/10.16 % (14319)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_13872 for (2914ds/360Mi)
% 63.16/10.26 % (14319)Instruction limit reached!
% 63.16/10.26 % (14319)------------------------------
% 63.16/10.26 % (14319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.16/10.26 % (14319)Termination reason: Unknown
% 63.16/10.26 % (14319)Termination phase: Saturation
% 63.16/10.26
% 63.16/10.26 % (14319)Memory used [KB]: 7291
% 63.16/10.26 % (14319)Time elapsed: 0.095 s
% 63.16/10.26 % (14319)Instructions burned: 363 (million)
% 63.16/10.26 % (14319)------------------------------
% 63.16/10.26 % (14319)------------------------------
% 63.16/10.26 % (14320)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_13872 for (2912ds/5446Mi)
% 63.16/10.28 % (14311)Instruction limit reached!
% 63.16/10.28 % (14311)------------------------------
% 63.16/10.28 % (14311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.16/10.28 % (14311)Termination reason: Unknown
% 63.16/10.28 % (14311)Termination phase: Saturation
% 63.16/10.28
% 63.16/10.28 % (14311)Memory used [KB]: 11513
% 63.16/10.28 % (14311)Time elapsed: 0.903 s
% 63.16/10.28 % (14311)Instructions burned: 2814 (million)
% 63.16/10.28 % (14311)------------------------------
% 63.16/10.28 % (14311)------------------------------
% 63.16/10.29 % (14321)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_13872 for (2912ds/2573Mi)
% 63.77/10.39 % (14317)Instruction limit reached!
% 63.77/10.39 % (14317)------------------------------
% 63.77/10.39 % (14317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.77/10.39 % (14317)Termination reason: Unknown
% 63.77/10.39 % (14317)Termination phase: Saturation
% 63.77/10.39
% 63.77/10.39 % (14317)Memory used [KB]: 17398
% 63.77/10.39 % (14317)Time elapsed: 0.353 s
% 63.77/10.39 % (14317)Instructions burned: 1434 (million)
% 63.77/10.39 % (14317)------------------------------
% 63.77/10.39 % (14317)------------------------------
% 64.53/10.40 % (14322)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_13872 for (2911ds/2655Mi)
% 64.53/10.44 % (14313)Instruction limit reached!
% 64.53/10.44 % (14313)------------------------------
% 64.53/10.44 % (14313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.53/10.44 % (14313)Termination reason: Unknown
% 64.53/10.44 % (14313)Termination phase: Saturation
% 64.53/10.44
% 64.53/10.44 % (14313)Memory used [KB]: 21236
% 64.53/10.44 % (14313)Time elapsed: 0.694 s
% 64.53/10.44 % (14313)Instructions burned: 2680 (million)
% 64.53/10.44 % (14313)------------------------------
% 64.53/10.44 % (14313)------------------------------
% 64.53/10.45 % (14323)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_13872 for (2911ds/2781Mi)
% 64.89/10.52 % (14297)Instruction limit reached!
% 64.89/10.52 % (14297)------------------------------
% 64.89/10.52 % (14297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 64.89/10.52 % (14297)Termination reason: Unknown
% 64.89/10.52 % (14297)Termination phase: Saturation
% 64.89/10.52
% 64.89/10.52 % (14297)Memory used [KB]: 10874
% 64.89/10.52 % (14297)Time elapsed: 2.266 s
% 64.89/10.52 % (14297)Instructions burned: 7258 (million)
% 64.89/10.52 % (14297)------------------------------
% 64.89/10.52 % (14297)------------------------------
% 64.89/10.53 % (14324)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_13872 for (2910ds/307Mi)
% 65.13/10.60 % (14324)Instruction limit reached!
% 65.13/10.60 % (14324)------------------------------
% 65.13/10.60 % (14324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.13/10.60 % (14324)Termination reason: Unknown
% 65.13/10.60 % (14324)Termination phase: Saturation
% 65.13/10.60
% 65.13/10.60 % (14324)Memory used [KB]: 7291
% 65.13/10.60 % (14324)Time elapsed: 0.077 s
% 65.13/10.60 % (14324)Instructions burned: 307 (million)
% 65.13/10.60 % (14324)------------------------------
% 65.13/10.60 % (14324)------------------------------
% 65.13/10.61 % (14325)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_13872 for (2909ds/1548Mi)
% 65.42/10.73 % (14316)Instruction limit reached!
% 65.42/10.73 % (14316)------------------------------
% 65.42/10.73 % (14316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.42/10.73 % (14316)Termination reason: Unknown
% 65.42/10.73 % (14316)Termination phase: Saturation
% 65.42/10.73
% 65.42/10.73 % (14316)Memory used [KB]: 10362
% 65.42/10.73 % (14316)Time elapsed: 0.755 s
% 65.42/10.73 % (14316)Instructions burned: 2548 (million)
% 65.42/10.73 % (14316)------------------------------
% 65.42/10.73 % (14316)------------------------------
% 65.42/10.74 % (14326)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_13872 for (2908ds/5214Mi)
% 65.66/10.95 % (14321)Instruction limit reached!
% 65.66/10.95 % (14321)------------------------------
% 65.66/10.95 % (14321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.66/10.95 % (14321)Termination reason: Unknown
% 65.66/10.95 % (14321)Termination phase: Saturation
% 65.66/10.95
% 65.66/10.95 % (14321)Memory used [KB]: 15479
% 65.66/10.95 % (14321)Time elapsed: 0.664 s
% 65.66/10.95 % (14321)Instructions burned: 2576 (million)
% 65.66/10.95 % (14321)------------------------------
% 65.66/10.95 % (14321)------------------------------
% 65.66/10.96 % (14312)Instruction limit reached!
% 65.66/10.96 % (14312)------------------------------
% 65.66/10.96 % (14312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 65.66/10.96 % (14312)Termination reason: Unknown
% 65.66/10.96 % (14312)Termination phase: Saturation
% 65.66/10.96
% 65.66/10.96 % (14312)Memory used [KB]: 14711
% 65.66/10.96 % (14312)Time elapsed: 1.454 s
% 65.66/10.96 % (14312)Instructions burned: 4606 (million)
% 65.66/10.96 % (14312)------------------------------
% 65.66/10.96 % (14312)------------------------------
% 65.66/10.97 % (14327)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_13872 for (2906ds/3201Mi)
% 65.66/10.97 % (14328)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_13872 for (2906ds/454Mi)
% 69.15/11.08 % (14325)Instruction limit reached!
% 69.15/11.08 % (14325)------------------------------
% 69.15/11.08 % (14325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.15/11.08 % (14325)Termination reason: Unknown
% 69.15/11.08 % (14325)Termination phase: Saturation
% 69.15/11.08
% 69.15/11.08 % (14325)Memory used [KB]: 10490
% 69.15/11.08 % (14325)Time elapsed: 0.488 s
% 69.15/11.08 % (14325)Instructions burned: 1551 (million)
% 69.15/11.08 % (14325)------------------------------
% 69.15/11.08 % (14325)------------------------------
% 69.15/11.08 % (14322)Instruction limit reached!
% 69.15/11.08 % (14322)------------------------------
% 69.15/11.08 % (14322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.15/11.08 % (14322)Termination reason: Unknown
% 69.15/11.08 % (14322)Termination phase: Saturation
% 69.15/11.08
% 69.15/11.08 % (14322)Memory used [KB]: 5373
% 69.15/11.08 % (14322)Time elapsed: 0.676 s
% 69.15/11.08 % (14322)Instructions burned: 2655 (million)
% 69.15/11.08 % (14322)------------------------------
% 69.15/11.08 % (14322)------------------------------
% 69.15/11.08 % (14328)Instruction limit reached!
% 69.15/11.08 % (14328)------------------------------
% 69.15/11.08 % (14328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.15/11.08 % (14328)Termination reason: Unknown
% 69.15/11.08 % (14328)Termination phase: Saturation
% 69.15/11.08
% 69.15/11.08 % (14328)Memory used [KB]: 12665
% 69.15/11.08 % (14328)Time elapsed: 0.118 s
% 69.15/11.08 % (14328)Instructions burned: 457 (million)
% 69.15/11.08 % (14328)------------------------------
% 69.15/11.08 % (14328)------------------------------
% 69.15/11.09 % (14330)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_13872 for (2904ds/7311Mi)
% 69.15/11.09 % (14331)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_13872 for (2904ds/6804Mi)
% 69.15/11.09 % (14329)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_13872 for (2904ds/3049Mi)
% 70.07/11.29 % (14323)Instruction limit reached!
% 70.07/11.29 % (14323)------------------------------
% 70.07/11.29 % (14323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 70.07/11.29 % (14323)Termination reason: Unknown
% 70.07/11.29 % (14323)Termination phase: Saturation
% 70.07/11.29
% 70.07/11.29 % (14323)Memory used [KB]: 8571
% 70.07/11.29 % (14323)Time elapsed: 0.842 s
% 70.07/11.29 % (14323)Instructions burned: 2783 (million)
% 70.07/11.29 % (14323)------------------------------
% 70.07/11.29 % (14323)------------------------------
% 70.47/11.30 % (14332)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_13872 for (2902ds/1683Mi)
% 71.68/11.79 % (14332)Instruction limit reached!
% 71.68/11.79 % (14332)------------------------------
% 71.68/11.79 % (14332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 71.68/11.79 % (14332)Termination reason: Unknown
% 71.68/11.79 % (14332)Termination phase: Saturation
% 71.68/11.79
% 71.68/11.79 % (14332)Memory used [KB]: 19445
% 71.68/11.79 % (14332)Time elapsed: 0.487 s
% 71.68/11.79 % (14332)Instructions burned: 1685 (million)
% 71.68/11.79 % (14332)------------------------------
% 71.68/11.79 % (14332)------------------------------
% 72.49/11.80 % (14333)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_13872 for (2897ds/4688Mi)
% 72.79/11.96 % (14327)Instruction limit reached!
% 72.79/11.96 % (14327)------------------------------
% 72.79/11.96 % (14327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.79/11.96 % (14327)Termination reason: Unknown
% 72.79/11.96 % (14327)Termination phase: Saturation
% 72.79/11.96
% 72.79/11.96 % (14327)Memory used [KB]: 12025
% 72.79/11.96 % (14327)Time elapsed: 1.014 s
% 72.79/11.96 % (14327)Instructions burned: 3203 (million)
% 72.79/11.96 % (14327)------------------------------
% 72.79/11.96 % (14327)------------------------------
% 72.79/11.97 % (14334)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_13872 for (2895ds/2207Mi)
% 72.79/12.01 % (14320)Instruction limit reached!
% 72.79/12.01 % (14320)------------------------------
% 72.79/12.01 % (14320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 72.79/12.01 % (14320)Termination reason: Unknown
% 72.79/12.01 % (14320)Termination phase: Saturation
% 72.79/12.01
% 72.79/12.01 % (14320)Memory used [KB]: 15479
% 72.79/12.01 % (14320)Time elapsed: 1.750 s
% 72.79/12.01 % (14320)Instructions burned: 5446 (million)
% 72.79/12.01 % (14320)------------------------------
% 72.79/12.01 % (14320)------------------------------
% 76.16/12.02 % (14335)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_13872 for (2895ds/8216Mi)
% 76.16/12.05 % (14329)Instruction limit reached!
% 76.16/12.05 % (14329)------------------------------
% 76.16/12.05 % (14329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.16/12.05 % (14329)Termination reason: Unknown
% 76.16/12.05 % (14329)Termination phase: Saturation
% 76.16/12.05
% 76.16/12.05 % (14329)Memory used [KB]: 11001
% 76.16/12.05 % (14329)Time elapsed: 0.954 s
% 76.16/12.05 % (14329)Instructions burned: 3050 (million)
% 76.16/12.05 % (14329)------------------------------
% 76.16/12.05 % (14329)------------------------------
% 76.16/12.06 % (14336)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_13872 for (2895ds/430Mi)
% 76.73/12.17 % (14336)Instruction limit reached!
% 76.73/12.17 % (14336)------------------------------
% 76.73/12.17 % (14336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.73/12.17 % (14336)Termination reason: Unknown
% 76.73/12.17 % (14336)Termination phase: Saturation
% 76.73/12.17
% 76.73/12.17 % (14336)Memory used [KB]: 7419
% 76.73/12.17 % (14336)Time elapsed: 0.114 s
% 76.73/12.17 % (14336)Instructions burned: 434 (million)
% 76.73/12.17 % (14336)------------------------------
% 76.73/12.17 % (14336)------------------------------
% 76.73/12.18 % (14337)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_13872 for (2893ds/2012Mi)
% 77.71/12.31 % (14326)Instruction limit reached!
% 77.71/12.31 % (14326)------------------------------
% 77.71/12.31 % (14326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.71/12.31 % (14326)Termination reason: Unknown
% 77.71/12.31 % (14326)Termination phase: Saturation
% 77.71/12.31
% 77.71/12.31 % (14326)Memory used [KB]: 10874
% 77.71/12.31 % (14326)Time elapsed: 1.587 s
% 77.71/12.31 % (14326)Instructions burned: 5214 (million)
% 77.71/12.31 % (14326)------------------------------
% 77.71/12.31 % (14326)------------------------------
% 77.71/12.32 % (14338)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_13872 for (2892ds/631Mi)
% 78.55/12.50 % (14338)Instruction limit reached!
% 78.55/12.50 % (14338)------------------------------
% 78.55/12.50 % (14338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 78.55/12.50 % (14338)Termination reason: Unknown
% 78.55/12.50 % (14338)Termination phase: Saturation
% 78.55/12.50
% 78.55/12.50 % (14338)Memory used [KB]: 7931
% 78.55/12.50 % (14338)Time elapsed: 0.209 s
% 78.55/12.50 % (14338)Instructions burned: 633 (million)
% 78.55/12.50 % (14338)------------------------------
% 78.55/12.50 % (14338)------------------------------
% 78.55/12.51 % (14339)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_13872 for (2890ds/8785Mi)
% 79.14/12.64 % (14334)Instruction limit reached!
% 79.14/12.64 % (14334)------------------------------
% 79.14/12.64 % (14334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.14/12.64 % (14334)Termination reason: Unknown
% 79.14/12.64 % (14334)Termination phase: Saturation
% 79.14/12.64
% 79.14/12.64 % (14334)Memory used [KB]: 11001
% 79.14/12.64 % (14334)Time elapsed: 0.676 s
% 79.14/12.64 % (14334)Instructions burned: 2209 (million)
% 79.14/12.64 % (14334)------------------------------
% 79.14/12.64 % (14334)------------------------------
% 79.14/12.65 % (14340)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_13872 for (2889ds/739Mi)
% 79.14/12.68 % (14337)Instruction limit reached!
% 79.14/12.68 % (14337)------------------------------
% 79.14/12.68 % (14337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 79.14/12.68 % (14337)Termination reason: Unknown
% 79.14/12.68 % (14337)Termination phase: Saturation
% 79.14/12.68
% 79.14/12.68 % (14337)Memory used [KB]: 11897
% 79.14/12.68 % (14337)Time elapsed: 0.506 s
% 79.14/12.68 % (14337)Instructions burned: 2013 (million)
% 79.14/12.68 % (14337)------------------------------
% 79.14/12.68 % (14337)------------------------------
% 79.14/12.69 % (14341)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_13872 for (2888ds/5473Mi)
% 80.32/12.88 % (14340)Instruction limit reached!
% 80.32/12.88 % (14340)------------------------------
% 80.32/12.88 % (14340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.32/12.88 % (14340)Termination reason: Unknown
% 80.32/12.88 % (14340)Termination phase: Saturation
% 80.32/12.88
% 80.32/12.88 % (14340)Memory used [KB]: 12537
% 80.32/12.88 % (14340)Time elapsed: 0.254 s
% 80.32/12.88 % (14340)Instructions burned: 740 (million)
% 80.32/12.88 % (14340)------------------------------
% 80.32/12.88 % (14340)------------------------------
% 80.32/12.89 % (14342)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_13872 for (2886ds/43570Mi)
% 84.44/13.24 % (14331)Instruction limit reached!
% 84.44/13.24 % (14331)------------------------------
% 84.44/13.24 % (14331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.44/13.24 % (14331)Termination reason: Unknown
% 84.44/13.24 % (14331)Termination phase: Saturation
% 84.44/13.24
% 84.44/13.24 % (14331)Memory used [KB]: 18038
% 84.44/13.24 % (14331)Time elapsed: 2.142 s
% 84.44/13.24 % (14331)Instructions burned: 6806 (million)
% 84.44/13.24 % (14331)------------------------------
% 84.44/13.24 % (14331)------------------------------
% 84.44/13.24 % (14333)Instruction limit reached!
% 84.44/13.24 % (14333)------------------------------
% 84.44/13.24 % (14333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.44/13.24 % (14333)Termination reason: Unknown
% 84.44/13.24 % (14333)Termination phase: Saturation
% 84.44/13.24
% 84.44/13.24 % (14333)Memory used [KB]: 13432
% 84.44/13.24 % (14333)Time elapsed: 1.438 s
% 84.44/13.24 % (14333)Instructions burned: 4688 (million)
% 84.44/13.24 % (14333)------------------------------
% 84.44/13.24 % (14333)------------------------------
% 84.44/13.25 % (14343)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_13872 for (2883ds/8382Mi)
% 84.44/13.25 % (14344)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_13872 for (2883ds/407Mi)
% 84.44/13.25 % (14330)First to succeed.
% 84.44/13.26 % (14330)Refutation found. Thanks to Tanya!
% 84.44/13.26 % SZS status Theorem for DTF2THF_13872
% 84.44/13.26 % SZS output start Proof for DTF2THF_13872
% 84.44/13.26 thf(func_def_0, type, in: $i > $i > $o).
% 84.44/13.26 thf(func_def_1, type, exu: ($i > $o) > $o).
% 84.44/13.26 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 84.44/13.26 thf(func_def_8, type, powerset: $i > $i).
% 84.44/13.26 thf(func_def_10, type, setunion: $i > $i).
% 84.44/13.26 thf(func_def_19, type, descr: ($i > $o) > $i).
% 84.44/13.26 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 84.44/13.26 thf(func_def_26, type, prop2set: $o > $i).
% 84.44/13.26 thf(func_def_36, type, nonempty: $i > $o).
% 84.44/13.26 thf(func_def_69, type, set2prop: $i > $o).
% 84.44/13.26 thf(func_def_88, type, subset: $i > $i > $o).
% 84.44/13.26 thf(func_def_89, type, disjoint: $i > $i > $o).
% 84.44/13.26 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 84.44/13.26 thf(func_def_114, type, binunion: $i > $i > $i).
% 84.44/13.26 thf(func_def_122, type, binintersect: $i > $i > $i).
% 84.44/13.26 thf(func_def_135, type, regular: $i > $o).
% 84.44/13.26 thf(func_def_136, type, setminus: $i > $i > $i).
% 84.44/13.26 thf(func_def_147, type, symdiff: $i > $i > $i).
% 84.44/13.26 thf(func_def_153, type, iskpair: $i > $o).
% 84.44/13.26 thf(func_def_158, type, kpair: $i > $i > $i).
% 84.44/13.26 thf(func_def_160, type, cartprod: $i > $i > $i).
% 84.44/13.26 thf(func_def_177, type, singleton: $i > $o).
% 84.44/13.26 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 84.44/13.26 thf(func_def_184, type, atmost1p: $i > $o).
% 84.44/13.26 thf(func_def_185, type, atleast2p: $i > $o).
% 84.44/13.26 thf(func_def_186, type, atmost2p: $i > $o).
% 84.44/13.26 thf(func_def_187, type, upairsetp: $i > $o).
% 84.44/13.26 thf(func_def_191, type, kfst: $i > $i).
% 84.44/13.26 thf(func_def_203, type, ksnd: $i > $i).
% 84.44/13.26 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 84.44/13.26 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 84.44/13.26 thf(func_def_222, type, func: $i > $i > $i > $o).
% 84.44/13.26 thf(func_def_223, type, funcSet: $i > $i > $i).
% 84.44/13.26 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 84.44/13.26 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 84.44/13.26 thf(func_def_291, type, sP0: $i > $i > $o).
% 84.44/13.26 thf(func_def_292, type, sP1: $i > $o).
% 84.44/13.26 thf(func_def_293, type, sP2: $i > $i > $o).
% 84.44/13.26 thf(func_def_294, type, sP3: $i > $i > $o).
% 84.44/13.26 thf(func_def_295, type, sP4: $i > $i > $i > $i > $o).
% 84.44/13.26 thf(func_def_299, type, sP8: $i > $i > $i > $o).
% 84.44/13.26 thf(func_def_301, type, sP10: $o > $i > $i > $i > $o).
% 84.44/13.26 thf(func_def_342, type, sK51: $i > $i > $i).
% 84.44/13.26 thf(func_def_343, type, sK52: $i > $i > $i).
% 84.44/13.26 thf(func_def_344, type, sK53: $i > $i > $i).
% 84.44/13.26 thf(func_def_345, type, sK54: $i > $i > $i).
% 84.44/13.26 thf(func_def_346, type, sK55: $i > $i > $i).
% 84.44/13.26 thf(func_def_347, type, sK56: $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_348, type, sK57: $i > $i).
% 84.44/13.26 thf(func_def_349, type, sK58: $i > $i).
% 84.44/13.26 thf(func_def_350, type, sK59: $i > $i).
% 84.44/13.26 thf(func_def_351, type, sK60: $i > $i).
% 84.44/13.26 thf(func_def_352, type, sK61: $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_353, type, sK62: $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_354, type, sK63: $i > $i > $i).
% 84.44/13.26 thf(func_def_355, type, sK64: $i > $i > $i).
% 84.44/13.26 thf(func_def_356, type, sK65: $i > $i > $i).
% 84.44/13.26 thf(func_def_358, type, sK67: $i > $i).
% 84.44/13.26 thf(func_def_359, type, sK68: $i > $i).
% 84.44/13.26 thf(func_def_360, type, sK69: $i > $i).
% 84.44/13.26 thf(func_def_376, type, sK85: $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_377, type, sK86: $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_380, type, sK89: $i > $o).
% 84.44/13.26 thf(func_def_392, type, sK101: $i > $i > $i).
% 84.44/13.26 thf(func_def_399, type, sK108: $i > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_400, type, sK109: $i > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_401, type, sK110: $i > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_402, type, sK111: $i > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_410, type, sK119: ($i > $o) > $i > $i).
% 84.44/13.26 thf(func_def_412, type, sK121: $i > $o).
% 84.44/13.26 thf(func_def_418, type, sK127: ($i > $i) > $i > $i > $i).
% 84.44/13.26 thf(func_def_421, type, sK130: $i > $i).
% 84.44/13.26 thf(func_def_430, type, sK139: $i > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_431, type, sK140: $i > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_434, type, sK143: $i > $o).
% 84.44/13.26 thf(func_def_437, type, sK146: $i > $i > $o).
% 84.44/13.26 thf(func_def_439, type, sK148: $i > $i).
% 84.44/13.26 thf(func_def_440, type, sK149: $i > $i).
% 84.44/13.26 thf(func_def_441, type, sK150: $i > ($i > $i > $o) > $i).
% 84.44/13.26 thf(func_def_442, type, sK151: $i > ($i > $i > $o) > $i).
% 84.44/13.26 thf(func_def_443, type, sK152: $i > $i > ($i > $i > $o) > $i).
% 84.44/13.26 thf(func_def_447, type, sK156: $i > $o).
% 84.44/13.26 thf(func_def_449, type, sK158: ($i > $o) > $i > $i).
% 84.44/13.26 thf(func_def_450, type, sK159: ($i > $o) > $i > $i).
% 84.44/13.26 thf(func_def_456, type, sK165: $i > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_480, type, sK189: ($i > $o) > ($i > $o) > $i > $i > $i).
% 84.44/13.26 thf(func_def_481, type, sK190: ($i > $o) > ($i > $o) > $i > $i > $i).
% 84.44/13.26 thf(func_def_484, type, sK193: $i > $o).
% 84.44/13.26 thf(func_def_485, type, sK194: $i > $o).
% 84.44/13.26 thf(func_def_487, type, sK196: $i > $i > $o).
% 84.44/13.26 thf(func_def_491, type, sK200: $i > $o).
% 84.44/13.26 thf(func_def_492, type, sK201: ($i > $o) > $i > $i > $i).
% 84.44/13.26 thf(func_def_498, type, sK207: $i > $i > $i).
% 84.44/13.26 thf(func_def_519, type, sK228: $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_523, type, sK232: $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_530, type, sK239: $i > $o).
% 84.44/13.26 thf(func_def_546, type, sK255: $i > $o).
% 84.44/13.26 thf(func_def_552, type, sK261: ($i > $o) > $i).
% 84.44/13.26 thf(func_def_553, type, sK262: ($i > $o) > $i).
% 84.44/13.26 thf(func_def_554, type, sK263: $i > $o).
% 84.44/13.26 thf(func_def_569, type, sK278: $i > $i).
% 84.44/13.26 thf(func_def_573, type, sK282: $i > $i > ($i > $i) > $i).
% 84.44/13.26 thf(func_def_578, type, sK287: $i > $o).
% 84.44/13.26 thf(func_def_591, type, sK300: $i > $i > $o).
% 84.44/13.26 thf(func_def_594, type, sK303: $i > $i > $o).
% 84.44/13.26 thf(func_def_602, type, sK311: $i > ($i > $o) > $i).
% 84.44/13.26 thf(func_def_603, type, sK312: $i > $o).
% 84.44/13.26 thf(func_def_608, type, sK317: $i > $i > $i).
% 84.44/13.26 thf(func_def_619, type, sK328: $i > $i > $o).
% 84.44/13.26 thf(func_def_625, type, sK334: $i > $o).
% 84.44/13.26 thf(func_def_639, type, sK348: ($i > $o) > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_640, type, sK349: ($i > $o) > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_644, type, sK353: $i > $o).
% 84.44/13.26 thf(func_def_647, type, sK356: $i > $o).
% 84.44/13.26 thf(func_def_649, type, sK358: ($i > $o) > $i > $i).
% 84.44/13.26 thf(func_def_650, type, sK359: ($i > $o) > $i > $i).
% 84.44/13.26 thf(func_def_656, type, sK365: ($i > $i) > $i > $i > $i).
% 84.44/13.26 thf(func_def_659, type, sK368: $i > $i).
% 84.44/13.26 thf(func_def_661, type, sK370: $i > $i > $i).
% 84.44/13.26 thf(func_def_666, type, sK375: $i > $o).
% 84.44/13.26 thf(func_def_682, type, sK391: $i > $i > ($i > $i) > $i).
% 84.44/13.26 thf(func_def_683, type, sK392: $i > $i).
% 84.44/13.26 thf(func_def_695, type, sK404: $i > $o).
% 84.44/13.26 thf(func_def_698, type, sK407: $i > $o).
% 84.44/13.26 thf(func_def_709, type, sK418: ($i > $o) > $i).
% 84.44/13.26 thf(func_def_710, type, sK419: $i > $o).
% 84.44/13.26 thf(func_def_711, type, sK420: $i > $i).
% 84.44/13.26 thf(func_def_718, type, sK427: $i > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_726, type, sK435: $i > $i).
% 84.44/13.26 thf(func_def_732, type, sK441: ($i > $i) > $i > $i > $i).
% 84.44/13.26 thf(func_def_735, type, sK444: $i > $i).
% 84.44/13.26 thf(func_def_744, type, sK453: $i > $i).
% 84.44/13.26 thf(func_def_745, type, sK454: $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_751, type, sK460: $i > $i > $i).
% 84.44/13.26 thf(func_def_755, type, sK464: $i > $o).
% 84.44/13.26 thf(func_def_761, type, sK470: $i > $o).
% 84.44/13.26 thf(func_def_763, type, sK472: ($i > $o) > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_764, type, sK473: ($i > $o) > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_767, type, sK476: $i > $i > $o).
% 84.44/13.26 thf(func_def_776, type, sK485: ($i > $o) > $i > $i).
% 84.44/13.26 thf(func_def_778, type, sK487: $i > $o).
% 84.44/13.26 thf(func_def_780, type, sK489: $o > $i > $i > $i).
% 84.44/13.26 thf(func_def_787, type, sK496: ($i > $o) > $i > $i).
% 84.44/13.26 thf(func_def_789, type, sK498: $i > $o).
% 84.44/13.26 thf(func_def_790, type, sK499: $i > $o).
% 84.44/13.26 thf(func_def_792, type, sK501: $i > ($i > $o) > $i).
% 84.44/13.26 thf(func_def_797, type, sK506: $i > $i > $i).
% 84.44/13.26 thf(func_def_804, type, sK513: ($i > $o) > $i).
% 84.44/13.26 thf(func_def_805, type, sK514: $i > $o).
% 84.44/13.26 thf(func_def_806, type, sK515: $i > $i).
% 84.44/13.26 thf(func_def_818, type, sK527: $i > $i).
% 84.44/13.26 thf(func_def_821, type, sK530: $i > $i).
% 84.44/13.26 thf(func_def_823, type, sK532: $i > $o).
% 84.44/13.26 thf(func_def_839, type, sK548: $i > $o).
% 84.44/13.26 thf(func_def_840, type, sK549: ($i > $o) > $i).
% 84.44/13.26 thf(func_def_841, type, sK550: ($i > $o) > $i > $i).
% 84.44/13.26 thf(func_def_843, type, sK552: $i > $o).
% 84.44/13.26 thf(func_def_860, type, sK569: $i > $i).
% 84.44/13.26 thf(func_def_865, type, sK574: $i > $o).
% 84.44/13.26 thf(func_def_867, type, sK576: $i > $i > $o).
% 84.44/13.26 thf(func_def_886, type, sK595: ($i > $i) > $i > $i > $i).
% 84.44/13.26 thf(func_def_889, type, sK598: $i > $i).
% 84.44/13.26 thf(func_def_898, type, sK607: $i > $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_915, type, sK624: $i > $i).
% 84.44/13.26 thf(func_def_925, type, sK634: ($i > $o) > $i > $i).
% 84.44/13.26 thf(func_def_927, type, sK636: $i > $o).
% 84.44/13.26 thf(func_def_935, type, sK644: $i > $o).
% 84.44/13.26 thf(func_def_936, type, sK645: $i > $o).
% 84.44/13.26 thf(func_def_937, type, sK646: ($i > $o) > ($i > $o) > $i).
% 84.44/13.26 thf(func_def_938, type, sK647: ($i > $o) > ($i > $o) > $i).
% 84.44/13.26 thf(func_def_950, type, sK659: $i > $i > $o).
% 84.44/13.26 thf(func_def_959, type, sK668: $i > $o).
% 84.44/13.26 thf(func_def_961, type, sK670: $i > ($i > $o) > $i).
% 84.44/13.26 thf(func_def_968, type, sK677: $i > $i > $i).
% 84.44/13.26 thf(func_def_983, type, sK692: $i > $i > $i).
% 84.44/13.26 thf(func_def_991, type, sK700: ($i > $o) > ($i > $o) > $i).
% 84.44/13.26 thf(func_def_992, type, sK701: ($i > $o) > ($i > $o) > $i).
% 84.44/13.26 thf(func_def_993, type, sK702: $i > $o).
% 84.44/13.26 thf(func_def_994, type, sK703: $i > $o).
% 84.44/13.26 thf(func_def_999, type, sK708: $i > $i > $i).
% 84.44/13.26 thf(func_def_1000, type, sK709: $i > $i > $i).
% 84.44/13.26 thf(func_def_1004, type, sK713: $i > $i).
% 84.44/13.26 thf(func_def_1007, type, sK716: $i > $i > $i > $i).
% 84.44/13.26 thf(func_def_1025, type, sK734: $i > ($i > $o) > $i).
% 84.44/13.26 thf(func_def_1026, type, sK735: $i > $o).
% 84.44/13.26 thf(func_def_1035, type, sK744: $i > $o).
% 84.44/13.26 thf(func_def_1050, type, ph759: !>[X0: $tType]:(X0)).
% 84.44/13.26 thf(f20131,plain,(
% 84.44/13.26 $false),
% 84.44/13.26 inference(subsumption_resolution,[status(thm)],[f20098,f3299])).
% 84.44/13.26 thf(f3299,plain,(
% 84.44/13.26 ($true = (in @ sK741 @ sK740))),
% 84.44/13.26 inference(cnf_transformation,[status(thm)],[f2186])).
% 84.44/13.26 thf(f2186,plain,(
% 84.44/13.26 (emptyInPowerset = $true) & (notdallE = $true) & (emptysetimpfalse = $true) & (disjointsetsI1 = $true) & (symdiffE = $true) & (setminusI = $true) & (binintersectSubset2 = $true) & (eta2 = $true) & (subsetE = $true) & (powersetT_lem = $true) & (subset2powerset = $true) & (exuE3u = $true) & (setadjoinIR = $true) & (ifSingleton = $true) & (setukpairinjL = $true) & (ksndsingleton = $true) & (setOfPairsIsBReln = $true) & (eqimpsubset1 = $true) & (uniqinunit = $true) & (notdexE = $true) & (ex1I2 = $true) & (emptyI = $true) & (in__Cong = $true) & (eqimpsubset2 = $true) & (ifp = $true) & (iffalseProp1 = $true) & (emptyinunitempty = $true) & (prop2set2propI = $true) & (ap2p = $true) & (cartprodsndin = $true) & (binintersectEL = $true) & (dpsetconstrER = $true) & (brelnall1 = $true) & (ubforcartprodlem3 = $true) & (prop2setI = $true) & (setminusER = $true) & (subbreln = $true) & (binunionLsub = $true) & (singletonsuniq = $true) & (binintersectT_lem = $true) & (setminusERneg = $true) & (notequalI2 = $true) & (funcGraphProp3 = $true) & (subsetemptysetimpeq = $true) & (dsetconstrER = $true) & (emptysetE = $true) & (upairset2IR = $true) & (quantDeMorgan4 = $true) & (iftrueProp2 = $true) & (exuI3 = $true) & (powerset__Cong = $true) & (powersetE1 = $true) & (vacuousDall = $true) & (emptysetsubset = $true) & (dsetconstr__Cong = $true) & (nonemptyE1 = $true) & (setminusSubset1 = $true) & (funcGraphProp2 = $true) & (funcext2 = $true) & (funcGraphProp4 = $true) & (omegaSAx = $true) & (setunionsingleton2 = $true) & (binintersectTELcontra = $true) & (setukpairinjL1 = $true) & (eta1 = $true) & (kpairsurjEq = $true) & (dsetconstrI = $true) & (ex1I = $true) & (brelnall2 = $true) & (cartprodpairmemEL = $true) & (subsetTI = $true) & (singletonsswitch = $true) & (funcext = $true) & (ubforcartprodlem2 = $true) & (setadjoinAx = $true) & (dpsetconstrSub = $true) & (sepInPowerset = $true) & (beta1 = $true) & (lam2lamEq = $true) & (setunionAx = $true) & (symdiffIneg2 = $true) & (binintersectI = $true) & (emptyE1 = $true) & (dpsetconstrERa = $true) & (cartprodpairin = $true) & (binunionEcases = $true) & (quantDeMorgan2 = $true) & (setext = $true) & (ex1E2 = $true) & (subsetRefl = $true) & (binunionE = $true) & (dsetconstrEL = $true) & (theeq = $true) & (setadjoinE = $true) & (binintersectSubset5 = $true) & (app = $true) & (powersetsubset = $true) & (iftrueorfalse = $true) & (exuI1 = $true) & (binintersectSubset3 = $true) & (nonemptyImpWitness = $true) & (sepSubset = $true) & (upairsetIR = $true) & (setextAx = $true) & (powersetI = $true) & (binintersectSubset4 = $true) & (powersetTI1 = $true) & (cartprodfstin = $true) & (iffalse = $true) & (quantDeMorgan3 = $true) & (setukpairinjR = $true) & (wellorderingAx = $true) & (kfstsingleton = $true) & (exuI2 = $true) & (ap2apEq1 = $true) & (replAx = $true) & (prop2setE = $true) & (secondinupair = $true) & (emptyinPowerset = $true) & (((((subset @ sK739 @ (setminus @ sK738 @ sK740)) = $true) & ((in @ sK741 @ sK738) = $true) & ((in @ sK741 @ sK739) = $true) & ($true = (in @ sK741 @ sK740))) & ((in @ sK740 @ (powerset @ sK738)) = $true)) & ((in @ sK739 @ (powerset @ sK738)) = $true)) & (setukpairinjR11 = $true) & (kfstpairEq = $true) & (noeltsimpempty = $true) & (lamp = $true) & (omegaIndAx = $true) & (setunionI = $true) & (kpairp = $true) & (ex1E1 = $true) & (upairequniteq = $true) & (setunion__Cong = $true) & (setukpairIR = $true) & (binunionT_lem = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (setadjoinSub2 = $true) & (nonemptyI = $true) & (exuE2 = $true) & (binunionIR = $true) & (funcinfuncset = $true) & (notinsingleton = $true) & (apProp = $true) & (powersetI1 = $true) & (ksndpairEq = $true) & (inPowerset = $true) & (subsetE2 = $true) & (binintersectRsub = $true) & (upairset2E = $true) & (subsetI2 = $true) & (setadjoinSub = $true) & (setminusLsub = $true) & (eqinunit = $true) & (powersetAx = $true) & (cartprodmempair1 = $true) & (iffalseProp2 = $true) & (setunionE = $true) & (upairinpowunion = $true) & (complementTI1 = $true) & (exuE1 = $true) & (setadjoinIL = $true) & (cartprodfstpairEq = $true) & (notinemptyset = $true) & (kpairiskpair = $true) & (setunionsingleton1 = $true) & (setukpairinjL2 = $true) & (cartprodpairsurjEq = $true) & (descr__Cong = $true) & (setadjoinOr = $true) & (setminusELneg = $true) & (setukpairinjR1 = $true) & (beta2 = $true) & (setunionsingleton = $true) & (singletoninpowerset = $true) & (binunionRsub = $true) & (omega0Ax = $true) & (dpsetconstrEL1 = $true) & (setextT = $true) & (setukpairIL = $true) & (cartprodmempaircEq = $true) & (binintersectTERcontra = $true) & (exuEu = $true) & (subsetI1 = $true) & (bs114d = $true) & (setminusT_lem = $true) & (binintersectLsub = $true) & (subsetTrans = $true) & (singletonsubset = $true) & (lamProp = $true) & (iftrue = $true) & (nonemptyI1 = $true) & (setminusSubset2 = $true) & (ap2apEq2 = $true) & (funcextLem = $true) & (subPowSU = $true) & (symdiffI1 = $true) & (quantDeMorgan1 = $true) & (cartprodsndpairEq = $true) & (descrp = $true) & (binintersectSubset1 = $true) & (setukpairinjR2 = $true) & (dpsetconstrI = $true) & (notequalI1 = $true) & (complementT_lem = $true) & (ubforcartprodlem1 = $true) & (omega__Cong = $true) & (symdiffIneg1 = $true) & (singletoninpowunion = $true) & (exu__Cong = $true) & (powersetTE1 = $true) & (upairsetE = $true) & (emptyset__Cong = $true) & (upairsubunion = $true) & (cartprodpairmemER = $true) & (setminusILneg = $true) & (theprop = $true) & (inCongP = $true) & (iftrueProp1 = $true) & (dpsetconstrEL2 = $true) & (complementTE1 = $true) & (funcImageSingleton = $true) & (exuE3e = $true) & (setextsub = $true) & (notsubsetI = $true) & (singletonprop = $true) & (setukpairinjR12 = $true) & (binunionIL = $true) & (infuncsetfunc = $true) & (setminusEL = $true) & (setbeta = $true) & (funcGraphProp1 = $true) & (symdiffI2 = $true) & (setminusIRneg = $true) & (lam2p = $true) & (foundationAx = $true) & (powersetE = $true) & (upairsetIL = $true) & (setoftrueEq = $true) & (emptysetAx = $true) & (eqbreln = $true) & (binintersectER = $true) & (setadjoin__Cong = $true)),
% 84.44/13.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK738,sK739,sK740,sK741])],[f997,f2185,f2184,f2183])).
% 84.44/13.26 thf(f2183,plain,(
% 84.44/13.26 ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((subset @ X1 @ (setminus @ X0 @ X2)) = $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) = $true)) & ($true = (in @ X2 @ (powerset @ X0)))) & ((in @ X1 @ (powerset @ X0)) = $true)) => (? [X2 : $i] : (? [X3 : $i] : (((subset @ sK739 @ (setminus @ sK738 @ X2)) = $true) & ($true = (in @ X3 @ sK738)) & ($true = (in @ X3 @ sK739)) & ((in @ X3 @ X2) = $true)) & ((in @ X2 @ (powerset @ sK738)) = $true)) & ((in @ sK739 @ (powerset @ sK738)) = $true))),
% 84.44/13.26 introduced(definition,[],[choice_axiom])).
% 84.44/13.26 thf(f2184,plain,(
% 84.44/13.26 ? [X2 : $i] : (? [X3 : $i] : (((subset @ sK739 @ (setminus @ sK738 @ X2)) = $true) & ($true = (in @ X3 @ sK738)) & ($true = (in @ X3 @ sK739)) & ((in @ X3 @ X2) = $true)) & ((in @ X2 @ (powerset @ sK738)) = $true)) => (? [X3 : $i] : (((subset @ sK739 @ (setminus @ sK738 @ sK740)) = $true) & ($true = (in @ X3 @ sK738)) & ($true = (in @ X3 @ sK739)) & ((in @ X3 @ sK740) = $true)) & ((in @ sK740 @ (powerset @ sK738)) = $true))),
% 84.44/13.26 introduced(definition,[],[choice_axiom])).
% 84.44/13.26 thf(f2185,plain,(
% 84.44/13.26 ? [X3 : $i] : (((subset @ sK739 @ (setminus @ sK738 @ sK740)) = $true) & ($true = (in @ X3 @ sK738)) & ($true = (in @ X3 @ sK739)) & ((in @ X3 @ sK740) = $true)) => (((subset @ sK739 @ (setminus @ sK738 @ sK740)) = $true) & ((in @ sK741 @ sK738) = $true) & ((in @ sK741 @ sK739) = $true) & ($true = (in @ sK741 @ sK740)))),
% 84.44/13.26 introduced(definition,[],[choice_axiom])).
% 84.44/13.26 thf(f997,plain,(
% 84.44/13.26 (emptyInPowerset = $true) & (notdallE = $true) & (emptysetimpfalse = $true) & (disjointsetsI1 = $true) & (symdiffE = $true) & (setminusI = $true) & (binintersectSubset2 = $true) & (eta2 = $true) & (subsetE = $true) & (powersetT_lem = $true) & (subset2powerset = $true) & (exuE3u = $true) & (setadjoinIR = $true) & (ifSingleton = $true) & (setukpairinjL = $true) & (ksndsingleton = $true) & (setOfPairsIsBReln = $true) & (eqimpsubset1 = $true) & (uniqinunit = $true) & (notdexE = $true) & (ex1I2 = $true) & (emptyI = $true) & (in__Cong = $true) & (eqimpsubset2 = $true) & (ifp = $true) & (iffalseProp1 = $true) & (emptyinunitempty = $true) & (prop2set2propI = $true) & (ap2p = $true) & (cartprodsndin = $true) & (binintersectEL = $true) & (dpsetconstrER = $true) & (brelnall1 = $true) & (ubforcartprodlem3 = $true) & (prop2setI = $true) & (setminusER = $true) & (subbreln = $true) & (binunionLsub = $true) & (singletonsuniq = $true) & (binintersectT_lem = $true) & (setminusERneg = $true) & (notequalI2 = $true) & (funcGraphProp3 = $true) & (subsetemptysetimpeq = $true) & (dsetconstrER = $true) & (emptysetE = $true) & (upairset2IR = $true) & (quantDeMorgan4 = $true) & (iftrueProp2 = $true) & (exuI3 = $true) & (powerset__Cong = $true) & (powersetE1 = $true) & (vacuousDall = $true) & (emptysetsubset = $true) & (dsetconstr__Cong = $true) & (nonemptyE1 = $true) & (setminusSubset1 = $true) & (funcGraphProp2 = $true) & (funcext2 = $true) & (funcGraphProp4 = $true) & (omegaSAx = $true) & (setunionsingleton2 = $true) & (binintersectTELcontra = $true) & (setukpairinjL1 = $true) & (eta1 = $true) & (kpairsurjEq = $true) & (dsetconstrI = $true) & (ex1I = $true) & (brelnall2 = $true) & (cartprodpairmemEL = $true) & (subsetTI = $true) & (singletonsswitch = $true) & (funcext = $true) & (ubforcartprodlem2 = $true) & (setadjoinAx = $true) & (dpsetconstrSub = $true) & (sepInPowerset = $true) & (beta1 = $true) & (lam2lamEq = $true) & (setunionAx = $true) & (symdiffIneg2 = $true) & (binintersectI = $true) & (emptyE1 = $true) & (dpsetconstrERa = $true) & (cartprodpairin = $true) & (binunionEcases = $true) & (quantDeMorgan2 = $true) & (setext = $true) & (ex1E2 = $true) & (subsetRefl = $true) & (binunionE = $true) & (dsetconstrEL = $true) & (theeq = $true) & (setadjoinE = $true) & (binintersectSubset5 = $true) & (app = $true) & (powersetsubset = $true) & (iftrueorfalse = $true) & (exuI1 = $true) & (binintersectSubset3 = $true) & (nonemptyImpWitness = $true) & (sepSubset = $true) & (upairsetIR = $true) & (setextAx = $true) & (powersetI = $true) & (binintersectSubset4 = $true) & (powersetTI1 = $true) & (cartprodfstin = $true) & (iffalse = $true) & (quantDeMorgan3 = $true) & (setukpairinjR = $true) & (wellorderingAx = $true) & (kfstsingleton = $true) & (exuI2 = $true) & (ap2apEq1 = $true) & (replAx = $true) & (prop2setE = $true) & (secondinupair = $true) & (emptyinPowerset = $true) & ? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((subset @ X1 @ (setminus @ X0 @ X2)) = $true) & ((in @ X3 @ X0) = $true) & ((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) = $true)) & ($true = (in @ X2 @ (powerset @ X0)))) & ((in @ X1 @ (powerset @ X0)) = $true)) & (setukpairinjR11 = $true) & (kfstpairEq = $true) & (noeltsimpempty = $true) & (lamp = $true) & (omegaIndAx = $true) & (setunionI = $true) & (kpairp = $true) & (ex1E1 = $true) & (upairequniteq = $true) & (setunion__Cong = $true) & (setukpairIR = $true) & (binunionT_lem = $true) & (setunionE2 = $true) & (cartprodmempair = $true) & (setadjoinSub2 = $true) & (nonemptyI = $true) & (exuE2 = $true) & (binunionIR = $true) & (funcinfuncset = $true) & (notinsingleton = $true) & (apProp = $true) & (powersetI1 = $true) & (ksndpairEq = $true) & (inPowerset = $true) & (subsetE2 = $true) & (binintersectRsub = $true) & (upairset2E = $true) & (subsetI2 = $true) & (setadjoinSub = $true) & (setminusLsub = $true) & (eqinunit = $true) & (powersetAx = $true) & (cartprodmempair1 = $true) & (iffalseProp2 = $true) & (setunionE = $true) & (upairinpowunion = $true) & (complementTI1 = $true) & (exuE1 = $true) & (setadjoinIL = $true) & (cartprodfstpairEq = $true) & (notinemptyset = $true) & (kpairiskpair = $true) & (setunionsingleton1 = $true) & (setukpairinjL2 = $true) & (cartprodpairsurjEq = $true) & (descr__Cong = $true) & (setadjoinOr = $true) & (setminusELneg = $true) & (setukpairinjR1 = $true) & (beta2 = $true) & (setunionsingleton = $true) & (singletoninpowerset = $true) & (binunionRsub = $true) & (omega0Ax = $true) & (dpsetconstrEL1 = $true) & (setextT = $true) & (setukpairIL = $true) & (cartprodmempaircEq = $true) & (binintersectTERcontra = $true) & (exuEu = $true) & (subsetI1 = $true) & (bs114d = $true) & (setminusT_lem = $true) & (binintersectLsub = $true) & (subsetTrans = $true) & (singletonsubset = $true) & (lamProp = $true) & (iftrue = $true) & (nonemptyI1 = $true) & (setminusSubset2 = $true) & (ap2apEq2 = $true) & (funcextLem = $true) & (subPowSU = $true) & (symdiffI1 = $true) & (quantDeMorgan1 = $true) & (cartprodsndpairEq = $true) & (descrp = $true) & (binintersectSubset1 = $true) & (setukpairinjR2 = $true) & (dpsetconstrI = $true) & (notequalI1 = $true) & (complementT_lem = $true) & (ubforcartprodlem1 = $true) & (omega__Cong = $true) & (symdiffIneg1 = $true) & (singletoninpowunion = $true) & (exu__Cong = $true) & (powersetTE1 = $true) & (upairsetE = $true) & (emptyset__Cong = $true) & (upairsubunion = $true) & (cartprodpairmemER = $true) & (setminusILneg = $true) & (theprop = $true) & (inCongP = $true) & (iftrueProp1 = $true) & (dpsetconstrEL2 = $true) & (complementTE1 = $true) & (funcImageSingleton = $true) & (exuE3e = $true) & (setextsub = $true) & (notsubsetI = $true) & (singletonprop = $true) & (setukpairinjR12 = $true) & (binunionIL = $true) & (infuncsetfunc = $true) & (setminusEL = $true) & (setbeta = $true) & (funcGraphProp1 = $true) & (symdiffI2 = $true) & (setminusIRneg = $true) & (lam2p = $true) & (foundationAx = $true) & (powersetE = $true) & (upairsetIL = $true) & (setoftrueEq = $true) & (emptysetAx = $true) & (eqbreln = $true) & (binintersectER = $true) & (setadjoin__Cong = $true)),
% 84.44/13.26 inference(flattening,[status(thm)],[f996])).
% 84.44/13.26 thf(f996,plain,(
% 84.44/13.26 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (((((in @ X3 @ X1) = $true) & ((in @ X3 @ X2) = $true)) & ((subset @ X1 @ (setminus @ X0 @ X2)) = $true)) & ((in @ X3 @ X0) = $true)) & ($true = (in @ X2 @ (powerset @ X0)))) & ((in @ X1 @ (powerset @ X0)) = $true)) & (binintersectTERcontra = $true)) & (binintersectTELcontra = $true)) & (complementTE1 = $true)) & (complementTI1 = $true)) & (powersetTE1 = $true)) & (powersetTI1 = $true)) & (subsetTI = $true)) & (setextT = $true)) & (complementT_lem = $true)) & (setminusT_lem = $true)) & (powersetT_lem = $true)) & (binunionT_lem = $true)) & (binintersectT_lem = $true)) & (iftrueorfalse = $true)) & (iffalse = $true)) & (iftrue = $true)) & (theeq = $true)) & (ifp = $true)) & (ifSingleton = $true)) & (iftrueProp2 = $true)) & (iftrueProp1 = $true)) & (iffalseProp2 = $true)) & (iffalseProp1 = $true)) & (eta2 = $true)) & (beta2 = $true)) & (lam2lamEq = $true)) & (eta1 = $true)) & (beta1 = $true)) & (ap2apEq2 = $true)) & (ap2apEq1 = $true)) & (funcext2 = $true)) & (funcext = $true)) & (eqbreln = $true)) & (subbreln = $true)) & (funcGraphProp4 = $true)) & (funcextLem = $true)) & (funcGraphProp2 = $true)) & (funcGraphProp3 = $true)) & (funcGraphProp1 = $true)) & (ex1E2 = $true)) & (brelnall2 = $true)) & (brelnall1 = $true)) & (lam2p = $true)) & (lamp = $true)) & (lamProp = $true)) & (funcinfuncset = $true)) & (ap2p = $true)) & (infuncsetfunc = $true)) & (app = $true)) & (apProp = $true)) & (funcImageSingleton = $true)) & (dpsetconstrER = $true)) & (dpsetconstrEL2 = $true)) & (dpsetconstrEL1 = $true)) & (dpsetconstrERa = $true)) & (setOfPairsIsBReln = $true)) & (dpsetconstrSub = $true)) & (dpsetconstrI = $true)) & (cartprodpairsurjEq = $true)) & (cartprodsndpairEq = $true)) & (cartprodfstpairEq = $true)) & (cartprodmempaircEq = $true)) & (cartprodpairmemER = $true)) & (cartprodpairmemEL = $true)) & (cartprodsndin = $true)) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 84.44/13.26 inference(ennf_transformation,[status(thm)],[f731])).
% 84.44/13.26 thf(f731,plain,(
% 84.44/13.26 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((subset @ X1 @ (setminus @ X0 @ X2)) = $true) => (((in @ X3 @ X2) = $true) => ((in @ X3 @ X1) != $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 84.44/13.26 inference(flattening,[status(thm)],[f449])).
% 84.44/13.26 thf(f449,plain,(
% 84.44/13.26 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ((cartprodsndin = $true) => ((cartprodpairmemEL = $true) => ((cartprodpairmemER = $true) => ((cartprodmempaircEq = $true) => ((cartprodfstpairEq = $true) => ((cartprodsndpairEq = $true) => ((cartprodpairsurjEq = $true) => ((dpsetconstrI = $true) => ((dpsetconstrSub = $true) => ((setOfPairsIsBReln = $true) => ((dpsetconstrERa = $true) => ((dpsetconstrEL1 = $true) => ((dpsetconstrEL2 = $true) => ((dpsetconstrER = $true) => ((funcImageSingleton = $true) => ((apProp = $true) => ((app = $true) => ((infuncsetfunc = $true) => ((ap2p = $true) => ((funcinfuncset = $true) => ((lamProp = $true) => ((lamp = $true) => ((lam2p = $true) => ((brelnall1 = $true) => ((brelnall2 = $true) => ((ex1E2 = $true) => ((funcGraphProp1 = $true) => ((funcGraphProp3 = $true) => ((funcGraphProp2 = $true) => ((funcextLem = $true) => ((funcGraphProp4 = $true) => ((subbreln = $true) => ((eqbreln = $true) => ((funcext = $true) => ((funcext2 = $true) => ((ap2apEq1 = $true) => ((ap2apEq2 = $true) => ((beta1 = $true) => ((eta1 = $true) => ((lam2lamEq = $true) => ((beta2 = $true) => ((eta2 = $true) => ((iffalseProp1 = $true) => ((iffalseProp2 = $true) => ((iftrueProp1 = $true) => ((iftrueProp2 = $true) => ((ifSingleton = $true) => ((ifp = $true) => ((theeq = $true) => ((iftrue = $true) => ((iffalse = $true) => ((iftrueorfalse = $true) => ((binintersectT_lem = $true) => ((binunionT_lem = $true) => ((powersetT_lem = $true) => ((setminusT_lem = $true) => ((complementT_lem = $true) => ((setextT = $true) => ((subsetTI = $true) => ((powersetTI1 = $true) => ((powersetTE1 = $true) => ((complementTI1 = $true) => ((complementTE1 = $true) => ((binintersectTELcontra = $true) => ((binintersectTERcontra = $true) => ! [X0 : $i,X1 : $i] : (((in @ X1 @ (powerset @ X0)) = $true) => ! [X2 : $i] : (($true = (in @ X2 @ (powerset @ X0))) => ! [X3 : $i] : (((in @ X3 @ X0) = $true) => (((subset @ X1 @ (setminus @ X0 @ X2)) = $true) => (((in @ X3 @ X2) = $true) => ~((in @ X3 @ X1) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 84.44/13.26 inference(fool_elimination,[status(thm)],[f448])).
% 84.44/13.26 thf(f448,plain,(
% 84.44/13.26 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X0)) => ! [X3 : $i] : ((in @ X3 @ X0) => ((subset @ X1 @ (setminus @ X0 @ X2)) => ((in @ X3 @ X2) => ~(in @ X3 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 84.44/13.26 inference(rectify,[status(thm)],[f245])).
% 84.44/13.26 thf(f245,negated_conjecture,(
% 84.44/13.26 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => ! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X1 : $i] : ((in @ X1 @ X3) => ((subset @ X11 @ (setminus @ X3 @ X16)) => ((in @ X1 @ X16) => ~(in @ X1 @ X11)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 84.44/13.26 inference(negated_conjecture,[status(cth)],[f244])).
% 84.44/13.26 thf(f244,conjecture,(
% 84.44/13.26 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => (cartprodsndin => (cartprodpairmemEL => (cartprodpairmemER => (cartprodmempaircEq => (cartprodfstpairEq => (cartprodsndpairEq => (cartprodpairsurjEq => (dpsetconstrI => (dpsetconstrSub => (setOfPairsIsBReln => (dpsetconstrERa => (dpsetconstrEL1 => (dpsetconstrEL2 => (dpsetconstrER => (funcImageSingleton => (apProp => (app => (infuncsetfunc => (ap2p => (funcinfuncset => (lamProp => (lamp => (lam2p => (brelnall1 => (brelnall2 => (ex1E2 => (funcGraphProp1 => (funcGraphProp3 => (funcGraphProp2 => (funcextLem => (funcGraphProp4 => (subbreln => (eqbreln => (funcext => (funcext2 => (ap2apEq1 => (ap2apEq2 => (beta1 => (eta1 => (lam2lamEq => (beta2 => (eta2 => (iffalseProp1 => (iffalseProp2 => (iftrueProp1 => (iftrueProp2 => (ifSingleton => (ifp => (theeq => (iftrue => (iffalse => (iftrueorfalse => (binintersectT_lem => (binunionT_lem => (powersetT_lem => (setminusT_lem => (complementT_lem => (setextT => (subsetTI => (powersetTI1 => (powersetTE1 => (complementTI1 => (complementTE1 => (binintersectTELcontra => (binintersectTERcontra => ! [X3 : $i,X11 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X1 : $i] : ((in @ X1 @ X3) => ((subset @ X11 @ (setminus @ X3 @ X16)) => ((in @ X1 @ X16) => ~(in @ X1 @ X11))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 84.44/13.26 file('/export/starexec/sandbox2/tmp/tmp.BaQAZpWnWT/DTF2THF_13872.p',contrasubsetT)).
% 84.44/13.26 thf(f20098,plain,(
% 84.44/13.26 ($true != (in @ sK741 @ sK740))),
% 84.44/13.26 inference(trivial_inequality_removal,[status(thm)],[f20048])).
% 84.44/13.26 thf(f20048,plain,(
% 84.44/13.26 ($true != $true) | ($true != (in @ sK741 @ sK740))),
% 84.44/13.26 inference(superposition,[status(thm)],[f4569,f18938])).
% 84.44/13.26 thf(f18938,plain,(
% 84.44/13.26 ($true = (in @ sK741 @ (setminus @ sK738 @ sK740)))),
% 84.44/13.26 inference(trivial_inequality_removal,[status(thm)],[f18919])).
% 84.44/13.26 thf(f18919,plain,(
% 84.44/13.26 ($true != $true) | ($true = (in @ sK741 @ (setminus @ sK738 @ sK740)))),
% 84.44/13.26 inference(superposition,[status(thm)],[f8537,f3302])).
% 84.44/13.26 thf(f3302,plain,(
% 84.44/13.26 ((subset @ sK739 @ (setminus @ sK738 @ sK740)) = $true)),
% 84.44/13.26 inference(cnf_transformation,[status(thm)],[f2186])).
% 84.44/13.26 thf(f8537,plain,(
% 84.44/13.26 ( ! [X0 : $i] : (($true != (subset @ sK739 @ X0)) | ((in @ sK741 @ X0) = $true)) )),
% 84.44/13.26 inference(trivial_inequality_removal,[status(thm)],[f8520])).
% 84.44/13.26 thf(f8520,plain,(
% 84.44/13.26 ( ! [X0 : $i] : (($true != (subset @ sK739 @ X0)) | ($true != $true) | ((in @ sK741 @ X0) = $true)) )),
% 84.44/13.26 inference(superposition,[status(thm)],[f4732,f3300])).
% 84.44/13.26 thf(f3300,plain,(
% 84.44/13.26 ((in @ sK741 @ sK739) = $true)),
% 84.44/13.26 inference(cnf_transformation,[status(thm)],[f2186])).
% 84.44/13.26 thf(f4732,plain,(
% 84.44/13.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X2)) | ((subset @ X2 @ X1) != $true) | ((in @ X0 @ X1) = $true)) )),
% 84.44/13.26 inference(trivial_inequality_removal,[status(thm)],[f3723])).
% 84.44/13.26 thf(f3723,plain,(
% 84.44/13.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((subset @ X2 @ X1) != $true) | ($true != (in @ X0 @ X2)) | ($true != $true) | ((in @ X0 @ X1) = $true)) )),
% 84.44/13.26 inference(definition_unfolding,[status(thm)],[f2565,f3272])).
% 84.44/13.26 thf(f3272,plain,(
% 84.44/13.26 (subsetE2 = $true)),
% 84.44/13.26 inference(cnf_transformation,[status(thm)],[f2186])).
% 84.44/13.26 thf(f2565,plain,(
% 84.44/13.26 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true) | (subsetE2 != $true)) )),
% 84.44/13.26 inference(cnf_transformation,[status(thm)],[f1454])).
% 84.44/13.26 thf(f1454,plain,(
% 84.44/13.26 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true)) | (subsetE2 != $true)) & ((subsetE2 = $true) | (($true = (in @ sK265 @ sK267)) & ((in @ sK265 @ sK266) != $true) & ((subset @ sK267 @ sK266) = $true)))),
% 84.44/13.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK265,sK266,sK267])],[f1452,f1453])).
% 84.44/13.26 thf(f1453,plain,(
% 84.44/13.26 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) = $true) & ($true != (in @ X3 @ X4)) & ((subset @ X5 @ X4) = $true)) => (($true = (in @ sK265 @ sK267)) & ((in @ sK265 @ sK266) != $true) & ((subset @ sK267 @ sK266) = $true))),
% 84.44/13.26 introduced(definition,[],[choice_axiom])).
% 84.44/13.26 thf(f1452,plain,(
% 84.44/13.26 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true)) | (subsetE2 != $true)) & ((subsetE2 = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X3 @ X5) = $true) & ($true != (in @ X3 @ X4)) & ((subset @ X5 @ X4) = $true)))),
% 84.44/13.26 inference(rectify,[status(thm)],[f1451])).
% 84.44/13.26 thf(f1451,plain,(
% 84.44/13.26 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true)) | (subsetE2 != $true)) & ((subsetE2 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ X2)) & ((in @ X0 @ X1) != $true) & ((subset @ X2 @ X1) = $true)))),
% 84.44/13.26 inference(nnf_transformation,[status(thm)],[f781])).
% 84.44/13.26 thf(f781,plain,(
% 84.44/13.26 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) | ((in @ X0 @ X1) = $true) | ((subset @ X2 @ X1) != $true)) <=> (subsetE2 = $true)),
% 84.44/13.26 inference(flattening,[status(thm)],[f780])).
% 84.44/13.26 thf(f780,plain,(
% 84.44/13.26 (subsetE2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((($true != (in @ X0 @ X2)) | ((in @ X0 @ X1) = $true)) | ((subset @ X2 @ X1) != $true))),
% 84.44/13.26 inference(ennf_transformation,[status(thm)],[f754])).
% 84.44/13.26 thf(f754,plain,(
% 84.44/13.26 (subsetE2 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) = $true) => (((in @ X0 @ X1) != $true) => ($true != (in @ X0 @ X2))))),
% 84.44/13.26 inference(flattening,[status(thm)],[f419])).
% 84.44/13.26 thf(f419,plain,(
% 84.44/13.26 ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X1) = $true) => (~((in @ X0 @ X1) = $true) => ~($true = (in @ X0 @ X2)))) <=> (subsetE2 = $true)),
% 84.44/13.26 inference(fool_elimination,[status(thm)],[f418])).
% 84.44/13.26 thf(f418,plain,(
% 84.44/13.26 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X1) => (~(in @ X0 @ X1) => ~(in @ X0 @ X2))) = subsetE2)),
% 84.44/13.26 inference(rectify,[status(thm)],[f84])).
% 84.44/13.26 thf(f84,axiom,(
% 84.44/13.26 (! [X1 : $i,X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => (~(in @ X1 @ X4) => ~(in @ X1 @ X3))) = subsetE2)),
% 84.44/13.26 file('/export/starexec/sandbox2/tmp/tmp.BaQAZpWnWT/DTF2THF_13872.p',subsetE2)).
% 84.44/13.26 thf(f4569,plain,(
% 84.44/13.26 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X3) != $true)) )),
% 84.44/13.26 inference(trivial_inequality_removal,[status(thm)],[f3949])).
% 84.44/13.26 thf(f3949,plain,(
% 84.44/13.26 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ X3) != $true) | ($true != $true) | ((in @ X4 @ (setminus @ X5 @ X3)) != $true)) )),
% 84.44/13.26 inference(definition_unfolding,[status(thm)],[f2794,f3386])).
% 84.44/13.26 thf(f3386,plain,(
% 84.44/13.26 (setminusER = $true)),
% 84.44/13.26 inference(cnf_transformation,[status(thm)],[f2186])).
% 84.44/13.26 thf(f2794,plain,(
% 84.44/13.26 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X3) != $true) | (setminusER != $true)) )),
% 84.44/13.26 inference(cnf_transformation,[status(thm)],[f1721])).
% 84.44/13.26 thf(f1721,plain,(
% 84.44/13.26 ((setminusER = $true) | (((in @ sK439 @ (setminus @ sK440 @ sK438)) = $true) & ((in @ sK439 @ sK438) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X3) != $true)) | (setminusER != $true))),
% 84.44/13.26 inference(skolemisation,[status(esa),new_symbols(skolem,[sK438,sK439,sK440])],[f1719,f1720])).
% 84.44/13.26 thf(f1720,plain,(
% 84.44/13.26 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setminus @ X2 @ X0))) & ((in @ X1 @ X0) = $true)) => (((in @ sK439 @ (setminus @ sK440 @ sK438)) = $true) & ((in @ sK439 @ sK438) = $true))),
% 84.44/13.26 introduced(definition,[],[choice_axiom])).
% 84.44/13.26 thf(f1719,plain,(
% 84.44/13.26 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setminus @ X2 @ X0))) & ((in @ X1 @ X0) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((in @ X4 @ (setminus @ X5 @ X3)) != $true) | ((in @ X4 @ X3) != $true)) | (setminusER != $true))),
% 84.44/13.26 inference(rectify,[status(thm)],[f1718])).
% 84.44/13.26 thf(f1718,plain,(
% 84.44/13.26 ((setminusER = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setminus @ X2 @ X0))) & ((in @ X1 @ X0) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setminus @ X2 @ X0))) | ((in @ X1 @ X0) != $true)) | (setminusER != $true))),
% 84.44/13.26 inference(nnf_transformation,[status(thm)],[f1009])).
% 84.44/13.26 thf(f1009,plain,(
% 84.44/13.26 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X1 @ (setminus @ X2 @ X0))) | ((in @ X1 @ X0) != $true))),
% 84.44/13.26 inference(ennf_transformation,[status(thm)],[f759])).
% 84.44/13.26 thf(f759,plain,(
% 84.44/13.26 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setminus @ X2 @ X0))) => ((in @ X1 @ X0) != $true))),
% 84.44/13.26 inference(flattening,[status(thm)],[f710])).
% 84.44/13.26 thf(f710,plain,(
% 84.44/13.26 (setminusER = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X1 @ (setminus @ X2 @ X0))) => ~((in @ X1 @ X0) = $true))),
% 84.44/13.26 inference(fool_elimination,[status(thm)],[f709])).
% 84.44/13.26 thf(f709,plain,(
% 84.44/13.26 (setminusER = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (setminus @ X2 @ X0)) => ~(in @ X1 @ X0)))),
% 84.44/13.26 inference(rectify,[status(thm)],[f122])).
% 84.44/13.26 thf(f122,axiom,(
% 84.44/13.26 (setminusER = ! [X4 : $i,X1 : $i,X3 : $i] : ((in @ X1 @ (setminus @ X3 @ X4)) => ~(in @ X1 @ X4)))),
% 84.44/13.26 file('/export/starexec/sandbox2/tmp/tmp.BaQAZpWnWT/DTF2THF_13872.p',setminusER)).
% 84.44/13.26 % SZS output end Proof for DTF2THF_13872
% 84.44/13.26 % (14330)------------------------------
% 84.44/13.26 % (14330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 84.44/13.26 % (14330)Termination reason: Refutation
% 84.44/13.26
% 84.44/13.26 % (14330)Memory used [KB]: 20596
% 84.44/13.26 % (14330)Time elapsed: 2.167 s
% 84.44/13.26 % (14330)Instructions burned: 6775 (million)
% 84.44/13.26 % (14330)------------------------------
% 84.44/13.26 % (14330)------------------------------
% 84.44/13.26 % (14091)Success in time 11.718 s
%------------------------------------------------------------------------------