%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU762^1 : 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 : n016.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 09:36:59 AM UTC 2026
% Result : Theorem 48.38s 8.19s
% Output : Refutation 48.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 19
% Syntax : Number of formulae : 111 ( 22 unt; 0 typ; 4 def)
% Number of atoms : 5455 (1447 equ; 0 cnn)
% Maximal formula atoms : 285 ( 49 avg)
% Number of connectives : 3210 ( 172 ~; 136 |; 928 &; 800 @)
% ( 14 <=>;1160 =>; 0 <=; 0 <~>)
% Maximal formula depth : 295 ( 23 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 490 ( 487 usr; 301 con; 0-4 aty)
% Number of variables : 194 ( 0 ^; 131 !; 63 ?; 194 :)
% 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_331,type,
sP1: $o > $i > $i > $i > $o ).
thf(func_def_332,type,
sP2: $i > $i > $o ).
thf(func_def_333,type,
sP3: $i > $o ).
thf(func_def_334,type,
sP4: $i > $i > $o ).
thf(func_def_335,type,
sP5: $i > $i > $o ).
thf(func_def_336,type,
sP6: $i > $i > $i > $o ).
thf(func_def_339,type,
sP9: $i > $i > $i > $i > $o ).
thf(func_def_344,type,
sK14: $i > $i ).
thf(func_def_352,type,
sK22: $i > $o ).
thf(func_def_355,type,
sK25: ( $i > $i ) > $i > $i > $i ).
thf(func_def_358,type,
sK28: $i > $i ).
thf(func_def_362,type,
sK32: $i > $o ).
thf(func_def_375,type,
sK45: $i > $i ).
thf(func_def_377,type,
sK47: $i > ( $i > $i ) > $i > $i ).
thf(func_def_383,type,
sK53: $i > $o ).
thf(func_def_432,type,
sK102: $i > $o ).
thf(func_def_434,type,
sK104: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_435,type,
sK105: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_442,type,
sK112: ( $i > $o ) > $i ).
thf(func_def_443,type,
sK113: $i > $o ).
thf(func_def_444,type,
sK114: $i > $i ).
thf(func_def_458,type,
sK128: $i > $i > $i > $i > $i ).
thf(func_def_459,type,
sK129: $i > $i > $i > $i > $i ).
thf(func_def_470,type,
sK140: $i > $i > $i ).
thf(func_def_475,type,
sK145: $i > $i > $o ).
thf(func_def_494,type,
sK164: $i > $o ).
thf(func_def_497,type,
sK167: $i > ( $i > $o ) > $i ).
thf(func_def_498,type,
sK168: $i > $i > $o ).
thf(func_def_526,type,
sK196: $i > $i > $i > $i ).
thf(func_def_530,type,
sK200: $i > $o ).
thf(func_def_532,type,
sK202: $i > ( $i > $o ) > $i ).
thf(func_def_534,type,
sK204: $i > $i ).
thf(func_def_535,type,
sK205: $i > $o ).
thf(func_def_537,type,
sK207: $i > ( $i > $o ) > $i ).
thf(func_def_542,type,
sK212: $i > $i > $i ).
thf(func_def_566,type,
sK236: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_567,type,
sK237: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_570,type,
sK240: $i > $o ).
thf(func_def_571,type,
sK241: $i > $o ).
thf(func_def_579,type,
sK249: $i > $o ).
thf(func_def_587,type,
sK257: $i > $i > $o ).
thf(func_def_596,type,
sK266: $i > $o ).
thf(func_def_605,type,
sK275: ( $i > $o ) > $i ).
thf(func_def_606,type,
sK276: ( $i > $o ) > $i ).
thf(func_def_607,type,
sK277: $i > $o ).
thf(func_def_612,type,
sK282: $i > $o ).
thf(func_def_614,type,
sK284: $i > ( $i > $o ) > $i ).
thf(func_def_625,type,
sK295: $i > $o ).
thf(func_def_636,type,
sK306: $i > $i > $i ).
thf(func_def_647,type,
sK317: $i > $i ).
thf(func_def_648,type,
sK318: $i > $i ).
thf(func_def_651,type,
sK321: $i > $i > ( $i > $i ) > $i ).
thf(func_def_658,type,
sK328: $i > $i > $i ).
thf(func_def_659,type,
sK329: $i > $i > $i ).
thf(func_def_662,type,
sK332: $i > $i > ( $i > $i ) > $i ).
thf(func_def_663,type,
sK333: $i > $i ).
thf(func_def_678,type,
sK348: $i > $i > $i > $i > $i ).
thf(func_def_679,type,
sK349: $i > $o ).
thf(func_def_680,type,
sK350: ( $i > $o ) > $i ).
thf(func_def_685,type,
sK355: $i > $i > $i ).
thf(func_def_709,type,
sK379: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_710,type,
sK380: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_711,type,
sK381: $i > $o ).
thf(func_def_712,type,
sK382: $i > $o ).
thf(func_def_719,type,
sK389: $i > $i > $o ).
thf(func_def_724,type,
sK394: $i > $i > $i > $i ).
thf(func_def_725,type,
sK395: $i > $i > $i > $i ).
thf(func_def_734,type,
sK404: $i > $o ).
thf(func_def_756,type,
sK426: $i > $o ).
thf(func_def_759,type,
sK429: $i > ( $i > $o ) > $i ).
thf(func_def_766,type,
sK436: $i > $i > $i > $i > $i ).
thf(func_def_769,type,
sK439: $i > $i > $o ).
thf(func_def_772,type,
sK442: $i > $i > $i ).
thf(func_def_776,type,
sK446: $i > $o ).
thf(func_def_779,type,
sK449: $i > ( $i > $o ) > $i ).
thf(func_def_806,type,
sK476: ( $i > $o ) > $i > $i ).
thf(func_def_808,type,
sK478: $i > $o ).
thf(func_def_820,type,
sK490: $i > $o ).
thf(func_def_824,type,
sK494: ( $i > $o ) > $i > $i ).
thf(func_def_826,type,
sK496: $i > $o ).
thf(func_def_830,type,
sK500: $i > $i > ( $i > $o ) > $i ).
thf(func_def_831,type,
sK501: $i > $o ).
thf(func_def_873,type,
sK543: $i > $i ).
thf(func_def_878,type,
sK548: $i > $i > $i ).
thf(func_def_882,type,
sK552: $i > $i > $i ).
thf(func_def_883,type,
sK553: $i > $i > $i ).
thf(func_def_884,type,
sK554: $i > $i > $i ).
thf(func_def_885,type,
sK555: $i > $i > $i ).
thf(func_def_886,type,
sK556: $i > $i > $i ).
thf(func_def_887,type,
sK557: $i > $i > $i > $i ).
thf(func_def_888,type,
sK558: $i > $i ).
thf(func_def_889,type,
sK559: $i > $i ).
thf(func_def_890,type,
sK560: $i > $i ).
thf(func_def_891,type,
sK561: $i > $i ).
thf(func_def_892,type,
sK562: $i > $i > $i > $i ).
thf(func_def_893,type,
sK563: $i > $i > $i > $i ).
thf(func_def_894,type,
sK564: $i > $i > $i ).
thf(func_def_895,type,
sK565: $i > $i > $i ).
thf(func_def_896,type,
sK566: $i > $i > $i ).
thf(func_def_898,type,
sK568: $i > $i ).
thf(func_def_899,type,
sK569: $i > $i ).
thf(func_def_900,type,
sK570: $i > $i ).
thf(func_def_916,type,
sK586: $i > $o ).
thf(func_def_917,type,
sK587: $i > $o ).
thf(func_def_918,type,
sK588: $i > $i ).
thf(func_def_919,type,
sK589: ( $i > $o ) > $i ).
thf(func_def_955,type,
sK625: $i > $i ).
thf(func_def_956,type,
sK626: $i > $i ).
thf(func_def_959,type,
sK629: $i > $i > ( $i > $i ) > $i ).
thf(func_def_965,type,
sK635: $i > $o ).
thf(func_def_995,type,
sK665: $i > $i > $i > $i ).
thf(func_def_996,type,
sK666: $i > $i > $i > $i ).
thf(func_def_1000,type,
sK670: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1001,type,
sK671: ( $i > $o ) > $i > $i > $i > $i ).
thf(func_def_1005,type,
sK675: $i > $o ).
thf(func_def_1010,type,
sK680: $i > $i ).
thf(func_def_1012,type,
sK682: $i > $i ).
thf(func_def_1016,type,
sK686: $i > $i > $i ).
thf(func_def_1027,type,
sK697: $i > $o ).
thf(func_def_1051,type,
sK721: $i > $o ).
thf(func_def_1054,type,
sK724: $i > ( $i > $o ) > $i ).
thf(func_def_1055,type,
sK725: $i > ( $i > $o ) > $i ).
thf(func_def_1061,type,
sK731: $i > $i > $i ).
thf(func_def_1067,type,
sK737: $i > $i > $o ).
thf(func_def_1069,type,
sK739: $i > ( $i > $o ) > $i ).
thf(func_def_1070,type,
sK740: $i > $o ).
thf(func_def_1077,type,
sK747: $i > ( $i > $i ) > $i > $i ).
thf(func_def_1079,type,
sK749: $i > $i ).
thf(func_def_1091,type,
sK761: $i > $o ).
thf(func_def_1105,type,
sK775: $i > $i > $i > $i > $i ).
thf(func_def_1106,type,
sK776: $i > $o ).
thf(func_def_1107,type,
sK777: $i > $o ).
thf(func_def_1108,type,
sK778: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1109,type,
sK779: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_1117,type,
sK787: $i > $i > $i > $i > $i ).
thf(func_def_1118,type,
sK788: $i > $i > $i > $i > $i ).
thf(func_def_1119,type,
sK789: $i > $i > $i > $i > $i ).
thf(func_def_1120,type,
sK790: $i > $i > $i > $i > $i ).
thf(func_def_1139,type,
sK809: $i > $i > $o ).
thf(func_def_1143,type,
sK813: $o > $i > $i > $i ).
thf(func_def_1165,type,
sK835: $i > $o ).
thf(func_def_1168,type,
sK838: $i > ( $i > $o ) > $i ).
thf(func_def_1169,type,
sK839: $i > ( $i > $o ) > $i ).
thf(func_def_1182,type,
sK852: $i > $o ).
thf(func_def_1183,type,
sK853: $i > $i > $i > $i ).
thf(func_def_1188,type,
sK858: $i > $i > $o ).
thf(func_def_1189,type,
sK859: $i > $i ).
thf(func_def_1190,type,
sK860: $i > $i ).
thf(func_def_1191,type,
sK861: ( $i > $i > $o ) > $i > $i ).
thf(func_def_1192,type,
sK862: ( $i > $i > $o ) > $i > $i ).
thf(func_def_1193,type,
sK863: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_1236,type,
ph906:
!>[X0: $tType] : X0 ).
thf(f16966,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f10130,f10246,f15201,f15429,f16863]) ).
thf(f16863,plain,
( ~ spl905_35
| spl905_13 ),
inference(avatar_split_clause,[status(thm)],[f16862,f4496,f4790]) ).
thf(f4790,definition,
( spl905_35
<=> ( ( subset @ sK694 @ sK696 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl905_35])],[avatar_definition]) ).
thf(f4496,definition,
( spl905_13
<=> ( $true
= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK696 ) ) ),
introduced(definition,[new_symbols(naming,[spl905_13])],[avatar_definition]) ).
thf(f16862,plain,
( ( ( subset @ sK694 @ sK696 )
!= $true )
| spl905_13 ),
inference(trivial_inequality_removal,[status(thm)],[f16861]) ).
thf(f16861,plain,
( ( $true != $true )
| ( ( subset @ sK694 @ sK696 )
!= $true )
| spl905_13 ),
inference(forward_demodulation,[status(thm)],[f16842,f3547]) ).
thf(f3547,plain,
binintersectRsub = $true,
inference(cnf_transformation,[status(thm)],[f2314]) ).
thf(f2314,plain,
( ( exuE1 = $true )
& ( symdiffI2 = $true )
& ( binintersectI = $true )
& ( setukpairinjR = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( dpsetconstrERa = $true )
& ( cartprodpairmemER = $true )
& ( cartprodmempair = $true )
& ( apProp = $true )
& ( powerset__Cong = $true )
& ( lamProp = $true )
& ( iffalse = $true )
& ( demorgan1a = $true )
& ( omega0Ax = $true )
& ( dpsetconstrSub = $true )
& ( setminusEL = $true )
& ( setminusIRneg = $true )
& ( binunionTILcontra = $true )
& ( demorgan1b = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( ifSingleton = $true )
& ( powersetE1 = $true )
& ( setoftrueEq = $true )
& ( setextAx = $true )
& ( setextT = $true )
& ( dpsetconstrEL1 = $true )
& ( setadjoinE = $true )
& ( doubleComplementSub2 = $true )
& ( complementT_lem = $true )
& ( exuE2 = $true )
& ( woz13rule2 = $true )
& ( emptyinPowerset = $true )
& ( sepInPowerset = $true )
& ( complementTcontraSubset = $true )
& ( woz13rule3 = $true )
& ( complementTI1 = $true )
& ( setukpairinjR11 = $true )
& ( wellorderingAx = $true )
& ( funcGraphProp2 = $true )
& ( funcImageSingleton = $true )
& ( eta2 = $true )
& ( singletoninpowunion = $true )
& ( replAx = $true )
& ( ksndpairEq = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( brelnall2 = $true )
& ( eqinunit = $true )
& ( powersetI1 = $true )
& ( dsetconstrEL = $true )
& ( binintersectER = $true )
& ( singletonsubset = $true )
& ( setadjoinIL = $true )
& ( setunionsingleton1 = $true )
& ( noeltsimpempty = $true )
& ( complementUnionInPowersetComplement = $true )
& ( powersetAx = $true )
& ( setOfPairsIsBReln = $true )
& ( doubleComplementSub1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( kpairsurjEq = $true )
& ( nonemptyI1 = $true )
& ( contrasubsetT2 = $true )
& ( ubforcartprodlem1 = $true )
& ( iftrueProp1 = $true )
& ( woz13rule0 = $true )
& ( exuI3 = $true )
& ( upairsubunion = $true )
& ( iffalseProp2 = $true )
& ( dpsetconstrI = $true )
& ( demorgan2a2 = $true )
& ( binunionIL = $true )
& ( setminusI = $true )
& ( exuI1 = $true )
& ( emptysetAx = $true )
& ( app = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinOr = $true )
& ( complementTnotintersectT = $true )
& ( upairinpowunion = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( descr__Cong = $true )
& ( subPowSU = $true )
& ( funcinfuncset = $true )
& ( kpairiskpair = $true )
& ( binintersectLsub = $true )
& ( eqimpsubset2 = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectSubset5 = $true )
& ( eqbreln = $true )
& ( dsetconstrER = $true )
& ( upairequniteq = $true )
& ( singletoninpowerset = $true )
& ( setadjoinIR = $true )
& ( notsubsetI = $true )
& ( demorgan1 = $true )
& ( binintersectSubset1 = $true )
& ( subsetE2 = $true )
& ( iftrueorfalse = $true )
& ( omegaIndAx = $true )
& ( setminusLsub = $true )
& ( binintersectSubset4 = $true )
& ( binintersectSubset2 = $true )
& ( funcext2 = $true )
& ( setminusERneg = $true )
& ( funcGraphProp3 = $true )
& ( doubleComplementEq = $true )
& ( notequalI2 = $true )
& ( bs114d = $true )
& ( setunion__Cong = $true )
& ( setminusELneg = $true )
& ( notinsingleton = $true )
& ( emptyinunitempty = $true )
& ( upairset2IR = $true )
& ( inIntersectImpInUnion2 = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( setukpairinjR2 = $true )
& ( prop2setE = $true )
& ( setukpairinjL = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodpairin = $true )
& ( subsetE = $true )
& ( ksndsingleton = $true )
& ( setadjoinSub2 = $true )
& ( setukpairinjR1 = $true )
& ( subsetI2 = $true )
& ( cartprodfstin = $true )
& ( ifp = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( emptysetE = $true )
& ( binunionE = $true )
& ( symdiffIneg1 = $true )
& ( kpairp = $true )
& ( complementImpComplementIntersect = $true )
& ( setunionE = $true )
& ( contrasubsetT = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjR12 = $true )
& ( nonemptyI = $true )
& ( singletonprop = $true )
& ( inPowerset = $true )
& ( binunionTIRcontra = $true )
& ( cartprodfstpairEq = $true )
& ( binintersectT_lem = $true )
& ( powersetI = $true )
& ( setunionsingleton = $true )
& ( kfstpairEq = $true )
& ( singletonsswitch = $true )
& ( ubforcartprodlem3 = $true )
& ( setminusER = $true )
& ( upairsetIL = $true )
& ( powersetsubset = $true )
& ( setadjoinSub = $true )
& ( iffalseProp1 = $true )
& ( brelnall1 = $true )
& ( lam2lamEq = $true )
& ( exu__Cong = $true )
& ( upairsetIR = $true )
& ( inIntersectImpInUnion = $true )
& ( ex1I2 = $true )
& ( omegaSAx = $true )
& ( ( in @ sK692 @ ( powerset @ sK693 ) )
= $true )
& ( ( subset @ sK694 @ sK696 )
= $true )
& ( ( subset @ sK692 @ sK695 )
= $true )
& ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ sK695 @ sK696 ) )
!= $true )
& ( $true
= ( in @ sK696 @ ( powerset @ sK693 ) ) )
& ( ( in @ sK695 @ ( powerset @ sK693 ) )
= $true )
& ( ( in @ sK694 @ ( powerset @ sK693 ) )
= $true )
& ( omega__Cong = $true )
& ( setminusSubset2 = $true )
& ( cartprodmempair1 = $true )
& ( quantDeMorgan3 = $true )
& ( lamp = $true )
& ( uniqinunit = $true )
& ( subsetTI = $true )
& ( beta1 = $true )
& ( subbreln = $true )
& ( exuEu = $true )
& ( setadjoin__Cong = $true )
& ( eta1 = $true )
& ( foundationAx = $true )
& ( exuE3e = $true )
& ( prop2setI = $true )
& ( demorgan2a = $true )
& ( demorgan2a1 = $true )
& ( binintersectSubset3 = $true )
& ( quantDeMorgan2 = $true )
& ( setbeta = $true )
& ( dpsetconstrEL2 = $true )
& ( subsetI1 = $true )
& ( dpsetconstrER = $true )
& ( descrp = $true )
& ( ap2p = $true )
& ( binintersectTERcontra = $true )
& ( emptyI = $true )
& ( quantDeMorgan1 = $true )
& ( exuI2 = $true )
& ( funcextLem = $true )
& ( ex1I = $true )
& ( kfstsingleton = $true )
& ( cartprodpairsurjEq = $true )
& ( demorgan2b = $true )
& ( notdallE = $true )
& ( inCongP = $true )
& ( binunionLsub = $true )
& ( setunionI = $true )
& ( powersetTE1 = $true )
& ( doubleComplementI1 = $true )
& ( setextsub = $true )
& ( dsetconstr__Cong = $true )
& ( complementTE1 = $true )
& ( vacuousDall = $true )
& ( ex1E2 = $true )
& ( binunionTEcontra = $true )
& ( powersetTI1 = $true )
& ( secondinupair = $true )
& ( cartprodpairmemEL = $true )
& ( setunionE2 = $true )
& ( quantDeMorgan4 = $true )
& ( binunionEcases = $true )
& ( binunionTE = $true )
& ( theprop = $true )
& ( setminusSubset1 = $true )
& ( theeq = $true )
& ( dsetconstrI = $true )
& ( demorgan2b2 = $true )
& ( sepSubset = $true )
& ( complementSubsetComplementIntersect = $true )
& ( binintersectTELcontra = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( binintersectEL = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjL2 = $true )
& ( emptysetsubset = $true )
& ( ap2apEq2 = $true )
& ( subsetTrans = $true )
& ( nonemptyE1 = $true )
& ( funcext = $true )
& ( emptyInPowerset = $true )
& ( demorgan2 = $true )
& ( binunionIR = $true )
& ( doubleComplementE1 = $true )
& ( powersetT_lem = $true )
& ( subsetemptysetimpeq = $true )
& ( ex1E1 = $true )
& ( setminusILneg = $true )
& ( eqimpsubset1 = $true )
& ( binunionT_lem = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT3 = $true )
& ( notinemptyset = $true )
& ( funcGraphProp1 = $true )
& ( beta2 = $true )
& ( prop2set2propI = $true )
& ( subset2powerset = $true )
& ( disjointsetsI1 = $true )
& ( setunionAx = $true )
& ( setadjoinAx = $true )
& ( setminusT_lem = $true )
& ( setext = $true )
& ( powersetE = $true )
& ( upairsetE = $true )
& ( contraSubsetComplement = $true )
& ( in__Cong = $true )
& ( emptyE1 = $true )
& ( notdexE = $true )
& ( woz13rule1 = $true )
& ( funcGraphProp4 = $true )
& ( subsetRefl = $true )
& ( setukpairIL = $true )
& ( infuncsetfunc = $true )
& ( setukpairIR = $true )
& ( ap2apEq1 = $true )
& ( binunionRsub = $true )
& ( binintersectRsub = $true )
& ( emptysetimpfalse = $true )
& ( iftrueProp2 = $true )
& ( iftrue = $true )
& ( cartprodsndin = $true )
& ( lam2p = $true )
& ( notequalI1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK692,sK693,sK694,sK695,sK696])],[f1100,f2313,f2312,f2311,f2310]) ).
thf(f2310,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( subset @ X2 @ X4 ) )
& ( ( subset @ X0 @ X3 )
= $true )
& ( ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( in @ X4 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) )
=> ( ( ( in @ sK692 @ ( powerset @ sK693 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( subset @ X2 @ X4 ) )
& ( ( subset @ sK692 @ X3 )
= $true )
& ( ( subset @ ( binintersect @ sK692 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( in @ X4 @ ( powerset @ sK693 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ sK693 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK693 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2311,plain,
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( subset @ X2 @ X4 ) )
& ( ( subset @ sK692 @ X3 )
= $true )
& ( ( subset @ ( binintersect @ sK692 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( in @ X4 @ ( powerset @ sK693 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ sK693 ) )
= $true ) )
& ( ( in @ X2 @ ( powerset @ sK693 ) )
= $true ) )
=> ( ? [X3: $i] :
( ? [X4: $i] :
( ( ( subset @ sK694 @ X4 )
= $true )
& ( ( subset @ sK692 @ X3 )
= $true )
& ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( in @ X4 @ ( powerset @ sK693 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ sK693 ) )
= $true ) )
& ( ( in @ sK694 @ ( powerset @ sK693 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2312,plain,
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( subset @ sK694 @ X4 )
= $true )
& ( ( subset @ sK692 @ X3 )
= $true )
& ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( in @ X4 @ ( powerset @ sK693 ) )
= $true ) )
& ( ( in @ X3 @ ( powerset @ sK693 ) )
= $true ) )
=> ( ? [X4: $i] :
( ( ( subset @ sK694 @ X4 )
= $true )
& ( ( subset @ sK692 @ sK695 )
= $true )
& ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ sK695 @ X4 ) ) )
& ( ( in @ X4 @ ( powerset @ sK693 ) )
= $true ) )
& ( ( in @ sK695 @ ( powerset @ sK693 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2313,plain,
( ? [X4: $i] :
( ( ( subset @ sK694 @ X4 )
= $true )
& ( ( subset @ sK692 @ sK695 )
= $true )
& ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ sK695 @ X4 ) ) )
& ( ( in @ X4 @ ( powerset @ sK693 ) )
= $true ) )
=> ( ( ( subset @ sK694 @ sK696 )
= $true )
& ( ( subset @ sK692 @ sK695 )
= $true )
& ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ sK695 @ sK696 ) )
!= $true )
& ( $true
= ( in @ sK696 @ ( powerset @ sK693 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1100,plain,
( ( exuE1 = $true )
& ( symdiffI2 = $true )
& ( binintersectI = $true )
& ( setukpairinjR = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( dpsetconstrERa = $true )
& ( cartprodpairmemER = $true )
& ( cartprodmempair = $true )
& ( apProp = $true )
& ( powerset__Cong = $true )
& ( lamProp = $true )
& ( iffalse = $true )
& ( demorgan1a = $true )
& ( omega0Ax = $true )
& ( dpsetconstrSub = $true )
& ( setminusEL = $true )
& ( setminusIRneg = $true )
& ( binunionTILcontra = $true )
& ( demorgan1b = $true )
& ( upairset2E = $true )
& ( exuE3u = $true )
& ( ifSingleton = $true )
& ( powersetE1 = $true )
& ( setoftrueEq = $true )
& ( setextAx = $true )
& ( setextT = $true )
& ( dpsetconstrEL1 = $true )
& ( setadjoinE = $true )
& ( doubleComplementSub2 = $true )
& ( complementT_lem = $true )
& ( exuE2 = $true )
& ( woz13rule2 = $true )
& ( emptyinPowerset = $true )
& ( sepInPowerset = $true )
& ( complementTcontraSubset = $true )
& ( woz13rule3 = $true )
& ( complementTI1 = $true )
& ( setukpairinjR11 = $true )
& ( wellorderingAx = $true )
& ( funcGraphProp2 = $true )
& ( funcImageSingleton = $true )
& ( eta2 = $true )
& ( singletoninpowunion = $true )
& ( replAx = $true )
& ( ksndpairEq = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( brelnall2 = $true )
& ( eqinunit = $true )
& ( powersetI1 = $true )
& ( dsetconstrEL = $true )
& ( binintersectER = $true )
& ( singletonsubset = $true )
& ( setadjoinIL = $true )
& ( setunionsingleton1 = $true )
& ( noeltsimpempty = $true )
& ( complementUnionInPowersetComplement = $true )
& ( powersetAx = $true )
& ( setOfPairsIsBReln = $true )
& ( doubleComplementSub1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( kpairsurjEq = $true )
& ( nonemptyI1 = $true )
& ( contrasubsetT2 = $true )
& ( ubforcartprodlem1 = $true )
& ( iftrueProp1 = $true )
& ( woz13rule0 = $true )
& ( exuI3 = $true )
& ( upairsubunion = $true )
& ( iffalseProp2 = $true )
& ( dpsetconstrI = $true )
& ( demorgan2a2 = $true )
& ( binunionIL = $true )
& ( setminusI = $true )
& ( exuI1 = $true )
& ( emptysetAx = $true )
& ( app = $true )
& ( setunionsingleton2 = $true )
& ( setadjoinOr = $true )
& ( complementTnotintersectT = $true )
& ( upairinpowunion = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( descr__Cong = $true )
& ( subPowSU = $true )
& ( funcinfuncset = $true )
& ( kpairiskpair = $true )
& ( binintersectLsub = $true )
& ( eqimpsubset2 = $true )
& ( ubforcartprodlem2 = $true )
& ( binintersectSubset5 = $true )
& ( eqbreln = $true )
& ( dsetconstrER = $true )
& ( upairequniteq = $true )
& ( singletoninpowerset = $true )
& ( setadjoinIR = $true )
& ( notsubsetI = $true )
& ( demorgan1 = $true )
& ( binintersectSubset1 = $true )
& ( subsetE2 = $true )
& ( iftrueorfalse = $true )
& ( omegaIndAx = $true )
& ( setminusLsub = $true )
& ( binintersectSubset4 = $true )
& ( binintersectSubset2 = $true )
& ( funcext2 = $true )
& ( setminusERneg = $true )
& ( funcGraphProp3 = $true )
& ( doubleComplementEq = $true )
& ( notequalI2 = $true )
& ( bs114d = $true )
& ( setunion__Cong = $true )
& ( setminusELneg = $true )
& ( notinsingleton = $true )
& ( emptyinunitempty = $true )
& ( upairset2IR = $true )
& ( inIntersectImpInUnion2 = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( setukpairinjR2 = $true )
& ( prop2setE = $true )
& ( setukpairinjL = $true )
& ( nonemptyImpWitness = $true )
& ( cartprodpairin = $true )
& ( subsetE = $true )
& ( ksndsingleton = $true )
& ( setadjoinSub2 = $true )
& ( setukpairinjR1 = $true )
& ( subsetI2 = $true )
& ( cartprodfstin = $true )
& ( ifp = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( emptysetE = $true )
& ( binunionE = $true )
& ( symdiffIneg1 = $true )
& ( kpairp = $true )
& ( complementImpComplementIntersect = $true )
& ( setunionE = $true )
& ( contrasubsetT = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( emptyset__Cong = $true )
& ( setukpairinjR12 = $true )
& ( nonemptyI = $true )
& ( singletonprop = $true )
& ( inPowerset = $true )
& ( binunionTIRcontra = $true )
& ( cartprodfstpairEq = $true )
& ( binintersectT_lem = $true )
& ( powersetI = $true )
& ( setunionsingleton = $true )
& ( kfstpairEq = $true )
& ( singletonsswitch = $true )
& ( ubforcartprodlem3 = $true )
& ( setminusER = $true )
& ( upairsetIL = $true )
& ( powersetsubset = $true )
& ( setadjoinSub = $true )
& ( iffalseProp1 = $true )
& ( brelnall1 = $true )
& ( lam2lamEq = $true )
& ( exu__Cong = $true )
& ( upairsetIR = $true )
& ( inIntersectImpInUnion = $true )
& ( ex1I2 = $true )
& ( omegaSAx = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( $true
= ( subset @ X2 @ X4 ) )
& ( ( subset @ X0 @ X3 )
= $true )
& ( ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( ( in @ X4 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) ) )
& ( omega__Cong = $true )
& ( setminusSubset2 = $true )
& ( cartprodmempair1 = $true )
& ( quantDeMorgan3 = $true )
& ( lamp = $true )
& ( uniqinunit = $true )
& ( subsetTI = $true )
& ( beta1 = $true )
& ( subbreln = $true )
& ( exuEu = $true )
& ( setadjoin__Cong = $true )
& ( eta1 = $true )
& ( foundationAx = $true )
& ( exuE3e = $true )
& ( prop2setI = $true )
& ( demorgan2a = $true )
& ( demorgan2a1 = $true )
& ( binintersectSubset3 = $true )
& ( quantDeMorgan2 = $true )
& ( setbeta = $true )
& ( dpsetconstrEL2 = $true )
& ( subsetI1 = $true )
& ( dpsetconstrER = $true )
& ( descrp = $true )
& ( ap2p = $true )
& ( binintersectTERcontra = $true )
& ( emptyI = $true )
& ( quantDeMorgan1 = $true )
& ( exuI2 = $true )
& ( funcextLem = $true )
& ( ex1I = $true )
& ( kfstsingleton = $true )
& ( cartprodpairsurjEq = $true )
& ( demorgan2b = $true )
& ( notdallE = $true )
& ( inCongP = $true )
& ( binunionLsub = $true )
& ( setunionI = $true )
& ( powersetTE1 = $true )
& ( doubleComplementI1 = $true )
& ( setextsub = $true )
& ( dsetconstr__Cong = $true )
& ( complementTE1 = $true )
& ( vacuousDall = $true )
& ( ex1E2 = $true )
& ( binunionTEcontra = $true )
& ( powersetTI1 = $true )
& ( secondinupair = $true )
& ( cartprodpairmemEL = $true )
& ( setunionE2 = $true )
& ( quantDeMorgan4 = $true )
& ( binunionEcases = $true )
& ( binunionTE = $true )
& ( theprop = $true )
& ( setminusSubset1 = $true )
& ( theeq = $true )
& ( dsetconstrI = $true )
& ( demorgan2b2 = $true )
& ( sepSubset = $true )
& ( complementSubsetComplementIntersect = $true )
& ( binintersectTELcontra = $true )
& ( cartprodsndpairEq = $true )
& ( cartprodmempaircEq = $true )
& ( binintersectEL = $true )
& ( symdiffIneg2 = $true )
& ( setukpairinjL2 = $true )
& ( emptysetsubset = $true )
& ( ap2apEq2 = $true )
& ( subsetTrans = $true )
& ( nonemptyE1 = $true )
& ( funcext = $true )
& ( emptyInPowerset = $true )
& ( demorgan2 = $true )
& ( binunionIR = $true )
& ( doubleComplementE1 = $true )
& ( powersetT_lem = $true )
& ( subsetemptysetimpeq = $true )
& ( ex1E1 = $true )
& ( setminusILneg = $true )
& ( eqimpsubset1 = $true )
& ( binunionT_lem = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT3 = $true )
& ( notinemptyset = $true )
& ( funcGraphProp1 = $true )
& ( beta2 = $true )
& ( prop2set2propI = $true )
& ( subset2powerset = $true )
& ( disjointsetsI1 = $true )
& ( setunionAx = $true )
& ( setadjoinAx = $true )
& ( setminusT_lem = $true )
& ( setext = $true )
& ( powersetE = $true )
& ( upairsetE = $true )
& ( contraSubsetComplement = $true )
& ( in__Cong = $true )
& ( emptyE1 = $true )
& ( notdexE = $true )
& ( woz13rule1 = $true )
& ( funcGraphProp4 = $true )
& ( subsetRefl = $true )
& ( setukpairIL = $true )
& ( infuncsetfunc = $true )
& ( setukpairIR = $true )
& ( ap2apEq1 = $true )
& ( binunionRsub = $true )
& ( binintersectRsub = $true )
& ( emptysetimpfalse = $true )
& ( iftrueProp2 = $true )
& ( iftrue = $true )
& ( cartprodsndin = $true )
& ( lam2p = $true )
& ( notequalI1 = $true ) ),
inference(flattening,[status(thm)],[f1099]) ).
thf(f1099,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
!= $true )
& ( $true
= ( subset @ X2 @ X4 ) )
& ( ( subset @ X0 @ X3 )
= $true )
& ( ( in @ X4 @ ( powerset @ X1 ) )
= $true ) )
& ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) ) )
& ( ( in @ X2 @ ( powerset @ X1 ) )
= $true ) )
& ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
& ( woz13rule3 = $true )
& ( woz13rule2 = $true )
& ( woz13rule1 = $true )
& ( woz13rule0 = $true )
& ( demorgan2 = $true )
& ( demorgan2b = $true )
& ( demorgan2b2 = $true )
& ( demorgan2a = $true )
& ( demorgan1 = $true )
& ( demorgan1b = $true )
& ( demorgan1a = $true )
& ( demorgan2a2 = $true )
& ( complementUnionInPowersetComplement = $true )
& ( demorgan2a1 = $true )
& ( binunionTEcontra = $true )
& ( binunionTE = $true )
& ( inComplementUnionImpInComplement1 = $true )
& ( inComplementUnionImpNotIn1 = $true )
& ( intersectInPowersetIntersectUnions = $true )
& ( inIntersectImpInIntersectUnions = $true )
& ( inIntersectImpInUnion2 = $true )
& ( inIntersectImpInUnion = $true )
& ( binunionTIRcontra = $true )
& ( binunionTILcontra = $true )
& ( complementTcontraSubset = $true )
& ( contraSubsetComplement = $true )
& ( complementInPowersetComplementIntersect = $true )
& ( complementSubsetComplementIntersect = $true )
& ( complementImpComplementIntersect = $true )
& ( complementTnotintersectT = $true )
& ( doubleComplementEq = $true )
& ( doubleComplementSub2 = $true )
& ( doubleComplementSub1 = $true )
& ( doubleComplementE1 = $true )
& ( doubleComplementI1 = $true )
& ( contrasubsetT3 = $true )
& ( contrasubsetT2 = $true )
& ( contrasubsetT1 = $true )
& ( contrasubsetT = $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)],[f721]) ).
thf(f721,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 )
=> ( ( contrasubsetT = $true )
=> ( ( contrasubsetT1 = $true )
=> ( ( contrasubsetT2 = $true )
=> ( ( contrasubsetT3 = $true )
=> ( ( doubleComplementI1 = $true )
=> ( ( doubleComplementE1 = $true )
=> ( ( doubleComplementSub1 = $true )
=> ( ( doubleComplementSub2 = $true )
=> ( ( doubleComplementEq = $true )
=> ( ( complementTnotintersectT = $true )
=> ( ( complementImpComplementIntersect = $true )
=> ( ( complementSubsetComplementIntersect = $true )
=> ( ( complementInPowersetComplementIntersect = $true )
=> ( ( contraSubsetComplement = $true )
=> ( ( complementTcontraSubset = $true )
=> ( ( binunionTILcontra = $true )
=> ( ( binunionTIRcontra = $true )
=> ( ( inIntersectImpInUnion = $true )
=> ( ( inIntersectImpInUnion2 = $true )
=> ( ( inIntersectImpInIntersectUnions = $true )
=> ( ( intersectInPowersetIntersectUnions = $true )
=> ( ( inComplementUnionImpNotIn1 = $true )
=> ( ( inComplementUnionImpInComplement1 = $true )
=> ( ( binunionTE = $true )
=> ( ( binunionTEcontra = $true )
=> ( ( demorgan2a1 = $true )
=> ( ( complementUnionInPowersetComplement = $true )
=> ( ( demorgan2a2 = $true )
=> ( ( demorgan1a = $true )
=> ( ( demorgan1b = $true )
=> ( ( demorgan1 = $true )
=> ( ( demorgan2a = $true )
=> ( ( demorgan2b2 = $true )
=> ( ( demorgan2b = $true )
=> ( ( demorgan2 = $true )
=> ( ( woz13rule0 = $true )
=> ( ( woz13rule1 = $true )
=> ( ( woz13rule2 = $true )
=> ( ( woz13rule3 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ! [X2: $i] :
( ( ( in @ X2 @ ( powerset @ X1 ) )
= $true )
=> ! [X3: $i] :
( ( $true
= ( in @ X3 @ ( powerset @ X1 ) ) )
=> ! [X4: $i] :
( ( ( in @ X4 @ ( powerset @ X1 ) )
= $true )
=> ( ( ( subset @ X0 @ X3 )
= $true )
=> ( ( $true
= ( subset @ X2 @ X4 ) )
=> ( ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f720]) ).
thf(f720,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
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ! [X2: $i] :
( ( in @ X2 @ ( powerset @ X1 ) )
=> ! [X3: $i] :
( ( in @ X3 @ ( powerset @ X1 ) )
=> ! [X4: $i] :
( ( in @ X4 @ ( powerset @ X1 ) )
=> ( ( subset @ X0 @ X3 )
=> ( ( subset @ X2 @ X4 )
=> ( subset @ ( binintersect @ X0 @ X2 ) @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f284]) ).
thf(f284,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
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X17: $i] :
( ( in @ X17 @ ( powerset @ X3 ) )
=> ! [X18: $i] :
( ( in @ X18 @ ( powerset @ X3 ) )
=> ( ( subset @ X11 @ X17 )
=> ( ( subset @ X16 @ X18 )
=> ( subset @ ( binintersect @ X11 @ X16 ) @ ( binintersect @ X17 @ X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f283]) ).
thf(f283,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
=> ( contrasubsetT
=> ( contrasubsetT1
=> ( contrasubsetT2
=> ( contrasubsetT3
=> ( doubleComplementI1
=> ( doubleComplementE1
=> ( doubleComplementSub1
=> ( doubleComplementSub2
=> ( doubleComplementEq
=> ( complementTnotintersectT
=> ( complementImpComplementIntersect
=> ( complementSubsetComplementIntersect
=> ( complementInPowersetComplementIntersect
=> ( contraSubsetComplement
=> ( complementTcontraSubset
=> ( binunionTILcontra
=> ( binunionTIRcontra
=> ( inIntersectImpInUnion
=> ( inIntersectImpInUnion2
=> ( inIntersectImpInIntersectUnions
=> ( intersectInPowersetIntersectUnions
=> ( inComplementUnionImpNotIn1
=> ( inComplementUnionImpInComplement1
=> ( binunionTE
=> ( binunionTEcontra
=> ( demorgan2a1
=> ( complementUnionInPowersetComplement
=> ( demorgan2a2
=> ( demorgan1a
=> ( demorgan1b
=> ( demorgan1
=> ( demorgan2a
=> ( demorgan2b2
=> ( demorgan2b
=> ( demorgan2
=> ( woz13rule0
=> ( woz13rule1
=> ( woz13rule2
=> ( woz13rule3
=> ! [X11: $i,X3: $i] :
( ( in @ X11 @ ( powerset @ X3 ) )
=> ! [X16: $i] :
( ( in @ X16 @ ( powerset @ X3 ) )
=> ! [X17: $i] :
( ( in @ X17 @ ( powerset @ X3 ) )
=> ! [X18: $i] :
( ( in @ X18 @ ( powerset @ X3 ) )
=> ( ( subset @ X11 @ X17 )
=> ( ( subset @ X16 @ X18 )
=> ( subset @ ( binintersect @ X11 @ X16 ) @ ( binintersect @ X17 @ X18 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',woz13rule4) ).
thf(f16842,plain,
( ( binintersectRsub != $true )
| ( ( subset @ sK694 @ sK696 )
!= $true )
| spl905_13 ),
inference(trivial_inequality_removal,[status(thm)],[f16775]) ).
thf(f16775,plain,
( ( $true != $true )
| ( ( subset @ sK694 @ sK696 )
!= $true )
| ( binintersectRsub != $true )
| spl905_13 ),
inference(superposition,[status(thm)],[f15527,f2686]) ).
thf(f2686,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
| ( binintersectRsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f1327]) ).
thf(f1327,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ( $true
!= ( subset @ ( binintersect @ sK55 @ sK56 ) @ sK56 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56])],[f1325,f1326]) ).
thf(f1326,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( subset @ ( binintersect @ X2 @ X3 ) @ X3 ) )
=> ( $true
!= ( subset @ ( binintersect @ sK55 @ sK56 ) @ sK56 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1325,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( subset @ ( binintersect @ X2 @ X3 ) @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f1324]) ).
thf(f1324,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f439]) ).
thf(f439,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
<=> ( binintersectRsub = $true ) ),
inference(fool_elimination,[status(thm)],[f438]) ).
thf(f438,plain,
( binintersectRsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) ) ),
inference(rectify,[status(thm)],[f116]) ).
thf(f116,axiom,
( binintersectRsub
= ( ! [X3: $i,X4: $i] : ( subset @ ( binintersect @ X3 @ X4 ) @ X4 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',binintersectRsub) ).
thf(f15527,plain,
( ! [X0: $i] :
( ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true )
| ( ( subset @ X0 @ sK696 )
!= $true ) )
| spl905_13 ),
inference(trivial_inequality_removal,[status(thm)],[f15526]) ).
thf(f15526,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( subset @ X0 @ sK696 )
!= $true )
| ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true ) )
| spl905_13 ),
inference(forward_demodulation,[status(thm)],[f15501,f3586]) ).
thf(f3586,plain,
subsetTrans = $true,
inference(cnf_transformation,[status(thm)],[f2314]) ).
thf(f15501,plain,
( ! [X0: $i] :
( ( subsetTrans != $true )
| ( ( subset @ X0 @ sK696 )
!= $true )
| ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true ) )
| spl905_13 ),
inference(trivial_inequality_removal,[status(thm)],[f15496]) ).
thf(f15496,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true )
| ( subsetTrans != $true )
| ( ( subset @ X0 @ sK696 )
!= $true ) )
| spl905_13 ),
inference(superposition,[status(thm)],[f4498,f3901]) ).
thf(f3901,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
| ( ( subset @ X4 @ X5 )
!= $true )
| ( ( subset @ X3 @ X4 )
!= $true )
| ( subsetTrans != $true ) ),
inference(cnf_transformation,[status(thm)],[f2400]) ).
thf(f2400,plain,
( ( ( subsetTrans = $true )
| ( ( ( subset @ sK754 @ sK756 )
!= $true )
& ( ( subset @ sK755 @ sK756 )
= $true )
& ( ( subset @ sK754 @ sK755 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
| ( ( subset @ X4 @ X5 )
!= $true )
| ( ( subset @ X3 @ X4 )
!= $true ) )
| ( subsetTrans != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK754,sK755,sK756])],[f2398,f2399]) ).
thf(f2399,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
& ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ X0 @ X1 )
= $true ) )
=> ( ( ( subset @ sK754 @ sK756 )
!= $true )
& ( ( subset @ sK755 @ sK756 )
= $true )
& ( ( subset @ sK754 @ sK755 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2398,plain,
( ( ( subsetTrans = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
& ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ X0 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X5 )
= $true )
| ( ( subset @ X4 @ X5 )
!= $true )
| ( ( subset @ X3 @ X4 )
!= $true ) )
| ( subsetTrans != $true ) ) ),
inference(rectify,[status(thm)],[f2397]) ).
thf(f2397,plain,
( ( ( subsetTrans = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
!= $true )
& ( ( subset @ X1 @ X2 )
= $true )
& ( ( subset @ X0 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
| ( ( subset @ X1 @ X2 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ( subsetTrans != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1189]) ).
thf(f1189,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
| ( ( subset @ X1 @ X2 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f1188]) ).
thf(f1188,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X2 )
= $true )
| ( ( subset @ X1 @ X2 )
!= $true )
| ( ( subset @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f431]) ).
thf(f431,plain,
( ( subsetTrans = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( ( subset @ X1 @ X2 )
= $true )
=> ( ( subset @ X0 @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f430]) ).
thf(f430,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X2 )
=> ( subset @ X0 @ X2 ) ) )
= subsetTrans ),
inference(rectify,[status(thm)],[f89]) ).
thf(f89,axiom,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X5 )
=> ( subset @ X3 @ X5 ) ) )
= subsetTrans ),
file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',subsetTrans) ).
thf(f4498,plain,
( ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK696 ) )
| spl905_13 ),
inference(avatar_component_clause,[status(thm)],[f4496]) ).
thf(f15429,plain,
( ~ spl905_30
| spl905_11 ),
inference(avatar_split_clause,[status(thm)],[f15428,f4485,f4661]) ).
thf(f4661,definition,
( spl905_30
<=> ( ( subset @ sK692 @ sK695 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl905_30])],[avatar_definition]) ).
thf(f4485,definition,
( spl905_11
<=> ( $true
= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK695 ) ) ),
introduced(definition,[new_symbols(naming,[spl905_11])],[avatar_definition]) ).
thf(f15428,plain,
( ( ( subset @ sK692 @ sK695 )
!= $true )
| spl905_11 ),
inference(trivial_inequality_removal,[status(thm)],[f15427]) ).
thf(f15427,plain,
( ( ( subset @ sK692 @ sK695 )
!= $true )
| ( $true != $true )
| spl905_11 ),
inference(forward_demodulation,[status(thm)],[f15275,f3739]) ).
thf(f3739,plain,
binintersectLsub = $true,
inference(cnf_transformation,[status(thm)],[f2314]) ).
thf(f15275,plain,
( ( ( subset @ sK692 @ sK695 )
!= $true )
| ( binintersectLsub != $true )
| spl905_11 ),
inference(trivial_inequality_removal,[status(thm)],[f15238]) ).
thf(f15238,plain,
( ( $true != $true )
| ( binintersectLsub != $true )
| ( ( subset @ sK692 @ sK695 )
!= $true )
| spl905_11 ),
inference(superposition,[status(thm)],[f4850,f3150]) ).
thf(f3150,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ ( binintersect @ X3 @ X2 ) @ X3 )
= $true )
| ( binintersectLsub != $true ) ),
inference(cnf_transformation,[status(thm)],[f1886]) ).
thf(f1886,plain,
( ( ( binintersectLsub = $true )
| ( ( subset @ ( binintersect @ sK421 @ sK420 ) @ sK421 )
!= $true ) )
& ( ! [X2: $i,X3: $i] :
( ( subset @ ( binintersect @ X3 @ X2 ) @ X3 )
= $true )
| ( binintersectLsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK420,sK421])],[f1884,f1885]) ).
thf(f1885,plain,
( ? [X0: $i,X1: $i] :
( $true
!= ( subset @ ( binintersect @ X1 @ X0 ) @ X1 ) )
=> ( ( subset @ ( binintersect @ sK421 @ sK420 ) @ sK421 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1884,plain,
( ( ( binintersectLsub = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( subset @ ( binintersect @ X1 @ X0 ) @ X1 ) ) )
& ( ! [X2: $i,X3: $i] :
( ( subset @ ( binintersect @ X3 @ X2 ) @ X3 )
= $true )
| ( binintersectLsub != $true ) ) ),
inference(rectify,[status(thm)],[f1883]) ).
thf(f1883,plain,
( ( ( binintersectLsub = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( subset @ ( binintersect @ X1 @ X0 ) @ X1 ) ) )
& ( ! [X0: $i,X1: $i] :
( $true
= ( subset @ ( binintersect @ X1 @ X0 ) @ X1 ) )
| ( binintersectLsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f825]) ).
thf(f825,plain,
( ( binintersectLsub = $true )
<=> ! [X0: $i,X1: $i] :
( $true
= ( subset @ ( binintersect @ X1 @ X0 ) @ X1 ) ) ),
inference(fool_elimination,[status(thm)],[f824]) ).
thf(f824,plain,
! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= binintersectLsub ),
inference(rectify,[status(thm)],[f111]) ).
thf(f111,axiom,
! [X4: $i,X3: $i] :
( ( subset @ ( binintersect @ X3 @ X4 ) @ X3 )
= binintersectLsub ),
file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',binintersectLsub) ).
thf(f4850,plain,
( ! [X0: $i] :
( ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true )
| ( ( subset @ X0 @ sK695 )
!= $true ) )
| spl905_11 ),
inference(trivial_inequality_removal,[status(thm)],[f4849]) ).
thf(f4849,plain,
( ! [X0: $i] :
( ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true )
| ( ( subset @ X0 @ sK695 )
!= $true )
| ( $true != $true ) )
| spl905_11 ),
inference(forward_demodulation,[status(thm)],[f4829,f3586]) ).
thf(f4829,plain,
( ! [X0: $i] :
( ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true )
| ( ( subset @ X0 @ sK695 )
!= $true )
| ( subsetTrans != $true ) )
| spl905_11 ),
inference(trivial_inequality_removal,[status(thm)],[f4823]) ).
thf(f4823,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( subsetTrans != $true )
| ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true )
| ( ( subset @ X0 @ sK695 )
!= $true ) )
| spl905_11 ),
inference(superposition,[status(thm)],[f4487,f3901]) ).
thf(f4487,plain,
( ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK695 ) )
| spl905_11 ),
inference(avatar_component_clause,[status(thm)],[f4485]) ).
thf(f15201,plain,
( ~ spl905_11
| ~ spl905_13 ),
inference(avatar_split_clause,[status(thm)],[f15200,f4496,f4485]) ).
thf(f15200,plain,
( ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK695 ) )
| ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK696 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f15199]) ).
thf(f15199,plain,
( ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK696 ) )
| ( $true != $true )
| ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK695 ) ) ),
inference(forward_demodulation,[status(thm)],[f15198,f3736]) ).
thf(f3736,plain,
binintersectSubset5 = $true,
inference(cnf_transformation,[status(thm)],[f2314]) ).
thf(f15198,plain,
( ( binintersectSubset5 != $true )
| ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK696 ) )
| ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK695 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f15186]) ).
thf(f15186,plain,
( ( $true != $true )
| ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK695 ) )
| ( $true
!= ( subset @ ( binintersect @ sK692 @ sK694 ) @ sK696 ) )
| ( binintersectSubset5 != $true ) ),
inference(superposition,[status(thm)],[f5941,f4010]) ).
thf(f4010,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ ( binintersect @ X5 @ X3 ) )
= $true )
| ( binintersectSubset5 != $true )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( ( subset @ X4 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f2513]) ).
thf(f2513,plain,
( ( ( binintersectSubset5 = $true )
| ( ( ( subset @ sK833 @ ( binintersect @ sK834 @ sK832 ) )
!= $true )
& ( ( subset @ sK833 @ sK832 )
= $true )
& ( ( subset @ sK833 @ sK834 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ ( binintersect @ X5 @ X3 ) )
= $true )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( ( subset @ X4 @ X5 )
!= $true ) )
| ( binintersectSubset5 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK832,sK833,sK834])],[f2511,f2512]) ).
thf(f2512,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) )
& ( ( subset @ X1 @ X2 )
= $true ) )
=> ( ( ( subset @ sK833 @ ( binintersect @ sK834 @ sK832 ) )
!= $true )
& ( ( subset @ sK833 @ sK832 )
= $true )
& ( ( subset @ sK833 @ sK834 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2511,plain,
( ( ( binintersectSubset5 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) )
& ( ( subset @ X1 @ X2 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X4 @ ( binintersect @ X5 @ X3 ) )
= $true )
| ( ( subset @ X4 @ X3 )
!= $true )
| ( ( subset @ X4 @ X5 )
!= $true ) )
| ( binintersectSubset5 != $true ) ) ),
inference(rectify,[status(thm)],[f2510]) ).
thf(f2510,plain,
( ( ( binintersectSubset5 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
!= $true )
& ( $true
= ( subset @ X1 @ X0 ) )
& ( ( subset @ X1 @ X2 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( subset @ X1 @ X2 )
!= $true ) )
| ( binintersectSubset5 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f1033]) ).
thf(f1033,plain,
( ( binintersectSubset5 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( subset @ X1 @ X2 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f1032]) ).
thf(f1032,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
= $true )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( subset @ X1 @ X2 )
!= $true ) )
<=> ( binintersectSubset5 = $true ) ),
inference(ennf_transformation,[status(thm)],[f769]) ).
thf(f769,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X1 @ X2 )
= $true )
=> ( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( subset @ X1 @ ( binintersect @ X2 @ X0 ) )
= $true ) ) )
<=> ( binintersectSubset5 = $true ) ),
inference(fool_elimination,[status(thm)],[f768]) ).
thf(f768,plain,
( binintersectSubset5
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( subset @ X1 @ X2 )
=> ( ( subset @ X1 @ X0 )
=> ( subset @ X1 @ ( binintersect @ X2 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f109]) ).
thf(f109,axiom,
( binintersectSubset5
= ( ! [X4: $i,X5: $i,X3: $i] :
( ( subset @ X5 @ X3 )
=> ( ( subset @ X5 @ X4 )
=> ( subset @ X5 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',binintersectSubset5) ).
thf(f5941,plain,
( ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ sK695 @ sK696 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f5940]) ).
thf(f5940,plain,
( ( $true != $true )
| ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ sK695 @ sK696 ) )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f5821,f3575]) ).
thf(f3575,plain,
eqimpsubset1 = $true,
inference(cnf_transformation,[status(thm)],[f2314]) ).
thf(f5821,plain,
( ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ sK695 @ sK696 ) )
!= $true )
| ( eqimpsubset1 != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f5780]) ).
thf(f5780,plain,
( ( eqimpsubset1 != $true )
| ( $true != $true )
| ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ sK695 @ sK696 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f4520,f4157]) ).
thf(f4157,plain,
! [X3: $i] :
( ( ( subset @ X3 @ X3 )
= $true )
| ( eqimpsubset1 != $true ) ),
inference(equality_resolution,[status(thm)],[f3875]) ).
thf(f3875,plain,
! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( $true
= ( subset @ X3 @ X2 ) )
| ( eqimpsubset1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f2370]) ).
thf(f2370,plain,
( ( ( eqimpsubset1 = $true )
| ( ( sK733 = sK732 )
& ( ( subset @ sK733 @ sK732 )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( $true
= ( subset @ X3 @ X2 ) ) )
| ( eqimpsubset1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK732,sK733])],[f2368,f2369]) ).
thf(f2369,plain,
( ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( $true
!= ( subset @ X1 @ X0 ) ) )
=> ( ( sK733 = sK732 )
& ( ( subset @ sK733 @ sK732 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f2368,plain,
( ( ( eqimpsubset1 = $true )
| ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( $true
!= ( subset @ X1 @ X0 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( $true
= ( subset @ X3 @ X2 ) ) )
| ( eqimpsubset1 != $true ) ) ),
inference(rectify,[status(thm)],[f2367]) ).
thf(f2367,plain,
( ( ( eqimpsubset1 = $true )
| ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( $true
!= ( subset @ X1 @ X0 ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( $true
= ( subset @ X1 @ X0 ) ) )
| ( eqimpsubset1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f949]) ).
thf(f949,plain,
( ( eqimpsubset1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( $true
= ( subset @ X1 @ X0 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f443]) ).
thf(f443,plain,
( ( eqimpsubset1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( $true
= ( subset @ X1 @ X0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f442]) ).
thf(f442,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
=> ( subset @ X1 @ X0 ) )
= eqimpsubset1 ),
inference(rectify,[status(thm)],[f80]) ).
thf(f80,axiom,
! [X4: $i,X3: $i] :
( ( ( X3 = X4 )
=> ( subset @ X3 @ X4 ) )
= eqimpsubset1 ),
file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',eqimpsubset1) ).
thf(f4520,plain,
! [X0: $i] :
( ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true )
| ( ( subset @ X0 @ ( binintersect @ sK695 @ sK696 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4519]) ).
thf(f4519,plain,
! [X0: $i] :
( ( ( subset @ X0 @ ( binintersect @ sK695 @ sK696 ) )
!= $true )
| ( $true != $true )
| ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f4474,f3586]) ).
thf(f4474,plain,
! [X0: $i] :
( ( subsetTrans != $true )
| ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true )
| ( ( subset @ X0 @ ( binintersect @ sK695 @ sK696 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f4466]) ).
thf(f4466,plain,
! [X0: $i] :
( ( subsetTrans != $true )
| ( ( subset @ X0 @ ( binintersect @ sK695 @ sK696 ) )
!= $true )
| ( ( subset @ ( binintersect @ sK692 @ sK694 ) @ X0 )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f3658,f3901]) ).
thf(f3658,plain,
( ( subset @ ( binintersect @ sK692 @ sK694 ) @ ( binintersect @ sK695 @ sK696 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f2314]) ).
thf(f10246,plain,
spl905_35,
inference(avatar_contradiction_clause,[status(thm)],[f10245]) ).
thf(f10245,plain,
( $false
| spl905_35 ),
inference(trivial_inequality_removal,[status(thm)],[f10237]) ).
thf(f10237,plain,
( ( $true != $true )
| spl905_35 ),
inference(superposition,[status(thm)],[f4792,f3660]) ).
thf(f3660,plain,
( ( subset @ sK694 @ sK696 )
= $true ),
inference(cnf_transformation,[status(thm)],[f2314]) ).
thf(f4792,plain,
( ( ( subset @ sK694 @ sK696 )
!= $true )
| spl905_35 ),
inference(avatar_component_clause,[status(thm)],[f4790]) ).
thf(f10130,plain,
spl905_30,
inference(avatar_contradiction_clause,[status(thm)],[f10129]) ).
thf(f10129,plain,
( $false
| spl905_30 ),
inference(trivial_inequality_removal,[status(thm)],[f10124]) ).
thf(f10124,plain,
( ( $true != $true )
| spl905_30 ),
inference(superposition,[status(thm)],[f4663,f3659]) ).
thf(f3659,plain,
( ( subset @ sK692 @ sK695 )
= $true ),
inference(cnf_transformation,[status(thm)],[f2314]) ).
thf(f4663,plain,
( ( ( subset @ sK692 @ sK695 )
!= $true )
| spl905_30 ),
inference(avatar_component_clause,[status(thm)],[f4661]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU762^1 : 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
% 0.16/0.34 % Computer : n016.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:33:36 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : SEU762^1 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.46 % Domain : Set Theory
% 0.21/0.46 % Problem : Typed Set Theory - First Wizard of Oz Examples - WoZ1 Lemmas
% 0.21/0.46 % Version : Especial.
% 0.21/0.46 % English : (! A:i.! X:i.in X (powerset A) -> (! Y:i.in Y (powerset A) ->
% 0.21/0.46 % (! Z:i.in Z (powerset A) -> (! W:i.in W (powerset A) ->
% 0.21/0.46 % subset X Z -> subset Y W -> subset (binintersect X Y)
% 0.21/0.46 % (binintersect Z W)))))
% 0.21/0.46
% 0.21/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.46 % Source : [Bro08]
% 0.21/0.46 % Names : ZFC264g [Bro08]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.21/0.46 % Syntax : Number of formulae : 599 ( 282 unt; 316 typ; 282 def)
% 0.21/0.46 % Number of atoms : 1684 ( 410 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 285 ( 5 avg)
% 0.21/0.46 % Number of connectives : 3558 ( 73 ~; 12 |; 44 &;2565 @)
% 0.21/0.46 % ( 14 <=>; 850 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 294 ( 2 avg)
% 0.21/0.46 % Number of types : 2 ( 0 usr)
% 0.21/0.46 % Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 319 ( 316 usr; 282 con; 0-4 aty)
% 0.21/0.46 % Number of variables : 965 ( 74 ^; 856 !; 35 ?; 965 :)
% 0.21/0.46 % SPC : TH0_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments : http://mathgate.info/detsetitem.php?id=323
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 thf(in_type,type,
% 0.21/0.46 in: $i > $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(exu_type,type,
% 0.21/0.46 exu: ( $i > $o ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(exu,definition,
% 0.21/0.46 ( exu
% 0.21/0.46 = ( ^ [Xphi: $i > $o] :
% 0.21/0.46 ? [Xx: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 & ! [Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setextAx_type,type,
% 0.21/0.46 setextAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setextAx,definition,
% 0.21/0.46 ( setextAx
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 <=> ( in @ Xx @ B ) )
% 0.21/0.46 => ( A = B ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyset_type,type,
% 0.21/0.46 emptyset: $i ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetAx_type,type,
% 0.21/0.46 emptysetAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetAx,definition,
% 0.21/0.46 ( emptysetAx
% 0.21/0.46 = ( ! [Xx: $i] :
% 0.21/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoin_type,type,
% 0.21/0.46 setadjoin: $i > $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinAx_type,type,
% 0.21/0.46 setadjoinAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinAx,definition,
% 0.21/0.46 ( setadjoinAx
% 0.21/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.46 <=> ( ( Xy = Xx )
% 0.21/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(powerset_type,type,
% 0.21/0.46 powerset: $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(powersetAx_type,type,
% 0.21/0.46 powersetAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(powersetAx,definition,
% 0.21/0.46 ( powersetAx
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.21/0.46 <=> ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setunion_type,type,
% 0.21/0.46 setunion: $i > $i ).
% 0.21/0.46
% 0.21/0.46 thf(setunionAx_type,type,
% 0.21/0.46 setunionAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setunionAx,definition,
% 0.21/0.46 ( setunionAx
% 0.21/0.46 = ( ! [A: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.21/0.46 <=> ? [B: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(omega_type,type,
% 0.21/0.46 omega: $i ).
% 0.21/0.46
% 0.21/0.46 thf(omega0Ax_type,type,
% 0.21/0.46 omega0Ax: $o ).
% 0.21/0.46
% 0.21/0.46 thf(omega0Ax,definition,
% 0.21/0.46 ( omega0Ax
% 0.21/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(omegaSAx_type,type,
% 0.21/0.46 omegaSAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(omegaSAx,definition,
% 0.21/0.46 ( omegaSAx
% 0.21/0.46 = ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ omega )
% 0.21/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(omegaIndAx_type,type,
% 0.21/0.46 omegaIndAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(omegaIndAx,definition,
% 0.21/0.46 ( omegaIndAx
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ( ( in @ emptyset @ A )
% 0.21/0.46 & ! [Xx: $i] :
% 0.21/0.46 ( ( ( in @ Xx @ omega )
% 0.21/0.46 & ( in @ Xx @ A ) )
% 0.21/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.21/0.46 => ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ omega )
% 0.21/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(replAx_type,type,
% 0.21/0.46 replAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(replAx,definition,
% 0.21/0.46 ( replAx
% 0.21/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( exu
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.21/0.46 => ? [B: $i] :
% 0.21/0.46 ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 <=> ? [Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ A )
% 0.21/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(foundationAx_type,type,
% 0.21/0.46 foundationAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(foundationAx,definition,
% 0.21/0.46 ( foundationAx
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.21/0.46 => ? [B: $i] :
% 0.21/0.46 ( ( in @ B @ A )
% 0.21/0.46 & ~ ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(wellorderingAx_type,type,
% 0.21/0.46 wellorderingAx: $o ).
% 0.21/0.46
% 0.21/0.46 thf(wellorderingAx,definition,
% 0.21/0.46 ( wellorderingAx
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ? [B: $i] :
% 0.21/0.46 ( ! [C: $i] :
% 0.21/0.46 ( ( in @ C @ B )
% 0.21/0.46 => ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ C )
% 0.21/0.46 => ( in @ Xx @ A ) ) )
% 0.21/0.46 & ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( ( in @ Xx @ A )
% 0.21/0.46 & ( in @ Xy @ A ) )
% 0.21/0.46 => ( ! [C: $i] :
% 0.21/0.46 ( ( in @ C @ B )
% 0.21/0.46 => ( ( in @ Xx @ C )
% 0.21/0.46 <=> ( in @ Xy @ C ) ) )
% 0.21/0.46 => ( Xx = Xy ) ) )
% 0.21/0.46 & ! [C: $i,D: $i] :
% 0.21/0.46 ( ( ( in @ C @ B )
% 0.21/0.46 & ( in @ D @ B ) )
% 0.21/0.46 => ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ C )
% 0.21/0.46 => ( in @ Xx @ D ) )
% 0.21/0.46 | ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ D )
% 0.21/0.46 => ( in @ Xx @ C ) ) ) )
% 0.21/0.46 & ! [C: $i] :
% 0.21/0.46 ( ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ C )
% 0.21/0.46 => ( in @ Xx @ A ) )
% 0.21/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.21/0.46 => ? [D: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ D @ B )
% 0.21/0.46 & ( in @ Xx @ C )
% 0.21/0.46 & ~ ? [Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ D )
% 0.21/0.46 & ( in @ Xy @ C ) )
% 0.21/0.46 & ! [E: $i] :
% 0.21/0.46 ( ( in @ E @ B )
% 0.21/0.46 => ( ! [Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ E )
% 0.21/0.46 => ( in @ Xy @ D ) )
% 0.21/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(descr_type,type,
% 0.21/0.46 descr: ( $i > $o ) > $i ).
% 0.21/0.46
% 0.21/0.46 thf(descrp_type,type,
% 0.21/0.46 descrp: $o ).
% 0.21/0.46
% 0.21/0.46 thf(descrp,definition,
% 0.21/0.46 ( descrp
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ( Xphi
% 0.21/0.46 @ ( descr
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstr_type,type,
% 0.21/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrI_type,type,
% 0.21/0.46 dsetconstrI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrI,definition,
% 0.21/0.46 ( dsetconstrI
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( ( Xphi @ Xx )
% 0.21/0.46 => ( in @ Xx
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrEL_type,type,
% 0.21/0.46 dsetconstrEL: $o ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrEL,definition,
% 0.21/0.46 ( dsetconstrEL
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.21/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrER_type,type,
% 0.21/0.46 dsetconstrER: $o ).
% 0.21/0.46
% 0.21/0.46 thf(dsetconstrER,definition,
% 0.21/0.46 ( dsetconstrER
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.21/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuE1_type,type,
% 0.21/0.46 exuE1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuE1,definition,
% 0.21/0.46 ( exuE1
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ? [Xx: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 & ! [Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(prop2set_type,type,
% 0.21/0.46 prop2set: $o > $i ).
% 0.21/0.46
% 0.21/0.46 thf(prop2setE_type,type,
% 0.21/0.46 prop2setE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(prop2setE,definition,
% 0.21/0.46 ( prop2setE
% 0.21/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.21/0.46 => Xphi ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetE_type,type,
% 0.21/0.46 emptysetE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetE,definition,
% 0.21/0.46 ( emptysetE
% 0.21/0.46 = ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ emptyset )
% 0.21/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetimpfalse_type,type,
% 0.21/0.46 emptysetimpfalse: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptysetimpfalse,definition,
% 0.21/0.46 ( emptysetimpfalse
% 0.21/0.46 = ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ emptyset )
% 0.21/0.46 => $false ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notinemptyset_type,type,
% 0.21/0.46 notinemptyset: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notinemptyset,definition,
% 0.21/0.46 ( notinemptyset
% 0.21/0.46 = ( ! [Xx: $i] :
% 0.21/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuE3e_type,type,
% 0.21/0.46 exuE3e: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuE3e,definition,
% 0.21/0.46 ( exuE3e
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setext_type,type,
% 0.21/0.46 setext: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setext,definition,
% 0.21/0.46 ( setext
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( in @ Xx @ B ) )
% 0.21/0.46 => ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( in @ Xx @ A ) )
% 0.21/0.46 => ( A = B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyI_type,type,
% 0.21/0.46 emptyI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyI,definition,
% 0.21/0.46 ( emptyI
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ~ ( in @ Xx @ A )
% 0.21/0.46 => ( A = emptyset ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(noeltsimpempty_type,type,
% 0.21/0.46 noeltsimpempty: $o ).
% 0.21/0.46
% 0.21/0.46 thf(noeltsimpempty,definition,
% 0.21/0.46 ( noeltsimpempty
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ~ ( in @ Xx @ A )
% 0.21/0.46 => ( A = emptyset ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setbeta_type,type,
% 0.21/0.46 setbeta: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setbeta,definition,
% 0.21/0.46 ( setbeta
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( ( in @ Xx
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.21/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(nonempty_type,type,
% 0.21/0.46 nonempty: $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(nonempty,definition,
% 0.21/0.46 ( nonempty
% 0.21/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyE1_type,type,
% 0.21/0.46 nonemptyE1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyE1,definition,
% 0.21/0.46 ( nonemptyE1
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ( nonempty @ A )
% 0.21/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyI_type,type,
% 0.21/0.46 nonemptyI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyI,definition,
% 0.21/0.46 ( nonemptyI
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( ( Xphi @ Xx )
% 0.21/0.46 => ( nonempty
% 0.21/0.46 @ ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyI1_type,type,
% 0.21/0.46 nonemptyI1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyI1,definition,
% 0.21/0.46 ( nonemptyI1
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.21/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinIL_type,type,
% 0.21/0.46 setadjoinIL: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinIL,definition,
% 0.21/0.46 ( setadjoinIL
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyinunitempty_type,type,
% 0.21/0.46 emptyinunitempty: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyinunitempty,definition,
% 0.21/0.46 ( emptyinunitempty
% 0.21/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinIR_type,type,
% 0.21/0.46 setadjoinIR: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinIR,definition,
% 0.21/0.46 ( setadjoinIR
% 0.21/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ A )
% 0.21/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinE_type,type,
% 0.21/0.46 setadjoinE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinE,definition,
% 0.21/0.46 ( setadjoinE
% 0.21/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.46 => ! [Xphi: $o] :
% 0.21/0.46 ( ( ( Xy = Xx )
% 0.21/0.46 => Xphi )
% 0.21/0.46 => ( ( ( in @ Xy @ A )
% 0.21/0.46 => Xphi )
% 0.21/0.46 => Xphi ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinOr_type,type,
% 0.21/0.46 setadjoinOr: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoinOr,definition,
% 0.21/0.46 ( setadjoinOr
% 0.21/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.46 => ( ( Xy = Xx )
% 0.21/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setoftrueEq_type,type,
% 0.21/0.46 setoftrueEq: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setoftrueEq,definition,
% 0.21/0.46 ( setoftrueEq
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xx: $i] : $true )
% 0.21/0.46 = A ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(powersetI_type,type,
% 0.21/0.46 powersetI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(powersetI,definition,
% 0.21/0.46 ( powersetI
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( in @ Xx @ A ) )
% 0.21/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyinPowerset_type,type,
% 0.21/0.46 emptyinPowerset: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyinPowerset,definition,
% 0.21/0.46 ( emptyinPowerset
% 0.21/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyInPowerset_type,type,
% 0.21/0.46 emptyInPowerset: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyInPowerset,definition,
% 0.21/0.46 ( emptyInPowerset
% 0.21/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(powersetE_type,type,
% 0.21/0.46 powersetE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(powersetE,definition,
% 0.21/0.46 ( powersetE
% 0.21/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.21/0.46 => ( ( in @ Xx @ B )
% 0.21/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setunionI_type,type,
% 0.21/0.46 setunionI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setunionI,definition,
% 0.21/0.46 ( setunionI
% 0.21/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( ( in @ B @ A )
% 0.21/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setunionE_type,type,
% 0.21/0.46 setunionE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setunionE,definition,
% 0.21/0.46 ( setunionE
% 0.21/0.46 = ( ! [A: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.21/0.46 => ! [Xphi: $o] :
% 0.21/0.46 ( ! [B: $i] :
% 0.21/0.46 ( ( in @ Xx @ B )
% 0.21/0.46 => ( ( in @ B @ A )
% 0.21/0.46 => Xphi ) )
% 0.21/0.46 => Xphi ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(subPowSU_type,type,
% 0.21/0.46 subPowSU: $o ).
% 0.21/0.46
% 0.21/0.46 thf(subPowSU,definition,
% 0.21/0.46 ( subPowSU
% 0.21/0.46 = ( ! [A: $i,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuE2_type,type,
% 0.21/0.46 exuE2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuE2,definition,
% 0.21/0.46 ( exuE2
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ? [Xx: $i] :
% 0.21/0.46 ! [Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xy )
% 0.21/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyImpWitness_type,type,
% 0.21/0.46 nonemptyImpWitness: $o ).
% 0.21/0.46
% 0.21/0.46 thf(nonemptyImpWitness,definition,
% 0.21/0.46 ( nonemptyImpWitness
% 0.21/0.46 = ( ! [A: $i] :
% 0.21/0.46 ( ( nonempty @ A )
% 0.21/0.46 => ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & $true ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(uniqinunit_type,type,
% 0.21/0.46 uniqinunit: $o ).
% 0.21/0.46
% 0.21/0.46 thf(uniqinunit,definition,
% 0.21/0.46 ( uniqinunit
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.21/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notinsingleton_type,type,
% 0.21/0.46 notinsingleton: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notinsingleton,definition,
% 0.21/0.46 ( notinsingleton
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx != Xy )
% 0.21/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(eqinunit_type,type,
% 0.21/0.46 eqinunit: $o ).
% 0.21/0.46
% 0.21/0.46 thf(eqinunit,definition,
% 0.21/0.46 ( eqinunit
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(singletonsswitch_type,type,
% 0.21/0.46 singletonsswitch: $o ).
% 0.21/0.46
% 0.21/0.46 thf(singletonsswitch,definition,
% 0.21/0.46 ( singletonsswitch
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.21/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetE_type,type,
% 0.21/0.46 upairsetE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetE,definition,
% 0.21/0.46 ( upairsetE
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.21/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.21/0.46 => ( ( Xz = Xx )
% 0.21/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetIL_type,type,
% 0.21/0.46 upairsetIL: $o ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetIL,definition,
% 0.21/0.46 ( upairsetIL
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetIR_type,type,
% 0.21/0.46 upairsetIR: $o ).
% 0.21/0.46
% 0.21/0.46 thf(upairsetIR,definition,
% 0.21/0.46 ( upairsetIR
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyE1_type,type,
% 0.21/0.46 emptyE1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyE1,definition,
% 0.21/0.46 ( emptyE1
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ( Xphi @ Xx ) )
% 0.21/0.46 => ( ( ( dsetconstr @ A
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 = emptyset )
% 0.21/0.46 => $false ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(vacuousDall_type,type,
% 0.21/0.46 vacuousDall: $o ).
% 0.21/0.46
% 0.21/0.46 thf(vacuousDall,definition,
% 0.21/0.46 ( vacuousDall
% 0.21/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ emptyset )
% 0.21/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan1_type,type,
% 0.21/0.46 quantDeMorgan1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan1,definition,
% 0.21/0.46 ( quantDeMorgan1
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ~ ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( Xphi @ Xx ) )
% 0.21/0.46 => ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan2_type,type,
% 0.21/0.46 quantDeMorgan2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan2,definition,
% 0.21/0.46 ( quantDeMorgan2
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ~ ( Xphi @ Xx ) )
% 0.21/0.46 => ~ ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan3_type,type,
% 0.21/0.46 quantDeMorgan3: $o ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan3,definition,
% 0.21/0.46 ( quantDeMorgan3
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ~ ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ( Xphi @ Xx ) )
% 0.21/0.46 => ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan4_type,type,
% 0.21/0.46 quantDeMorgan4: $o ).
% 0.21/0.46
% 0.21/0.46 thf(quantDeMorgan4,definition,
% 0.21/0.46 ( quantDeMorgan4
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ~ ( Xphi @ Xx ) )
% 0.21/0.46 => ~ ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(prop2setI_type,type,
% 0.21/0.46 prop2setI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(prop2setI,definition,
% 0.21/0.46 ( prop2setI
% 0.21/0.46 = ( ! [Xphi: $o] :
% 0.21/0.46 ( Xphi
% 0.21/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(set2prop_type,type,
% 0.21/0.46 set2prop: $i > $o ).
% 0.21/0.46
% 0.21/0.46 thf(prop2set2propI_type,type,
% 0.21/0.46 prop2set2propI: $o ).
% 0.21/0.46
% 0.21/0.46 thf(prop2set2propI,definition,
% 0.21/0.46 ( prop2set2propI
% 0.21/0.46 = ( ! [Xphi: $o] :
% 0.21/0.46 ( Xphi
% 0.21/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notdexE_type,type,
% 0.21/0.46 notdexE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notdexE,definition,
% 0.21/0.46 ( notdexE
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ~ ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ( Xphi @ Xx ) )
% 0.21/0.46 => ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(notdallE_type,type,
% 0.21/0.46 notdallE: $o ).
% 0.21/0.46
% 0.21/0.46 thf(notdallE,definition,
% 0.21/0.46 ( notdallE
% 0.21/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.46 ( ~ ! [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 => ( Xphi @ Xx ) )
% 0.21/0.46 => ? [Xx: $i] :
% 0.21/0.46 ( ( in @ Xx @ A )
% 0.21/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuI1_type,type,
% 0.21/0.46 exuI1: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuI1,definition,
% 0.21/0.46 ( exuI1
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ? [Xx: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 & ! [Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) )
% 0.21/0.46 => ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuI3_type,type,
% 0.21/0.46 exuI3: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuI3,definition,
% 0.21/0.46 ( exuI3
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.21/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 => ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) )
% 0.21/0.46 => ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuI2_type,type,
% 0.21/0.46 exuI2: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuI2,definition,
% 0.21/0.46 ( exuI2
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ? [Xx: $i] :
% 0.21/0.46 ! [Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xy )
% 0.21/0.46 <=> ( Xy = Xx ) )
% 0.21/0.46 => ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(inCongP_type,type,
% 0.21/0.46 inCongP: $o ).
% 0.21/0.46
% 0.21/0.46 thf(inCongP,definition,
% 0.21/0.46 ( inCongP
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ( ( in @ Xx @ A )
% 0.21/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(in__Cong_type,type,
% 0.21/0.46 in__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(in__Cong,definition,
% 0.21/0.46 ( in__Cong
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ( ( in @ Xx @ A )
% 0.21/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuE3u_type,type,
% 0.21/0.46 exuE3u: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuE3u,definition,
% 0.21/0.46 ( exuE3u
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 => ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xphi @ Xx )
% 0.21/0.46 => ( ( Xphi @ Xy )
% 0.21/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exu__Cong_type,type,
% 0.21/0.46 exu__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exu__Cong,definition,
% 0.21/0.46 ( exu__Cong
% 0.21/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.21/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ( ( Xphi @ Xx )
% 0.21/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.21/0.46 => ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.46 <=> ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(emptyset__Cong_type,type,
% 0.21/0.46 emptyset__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(emptyset__Cong,definition,
% 0.21/0.46 ( emptyset__Cong
% 0.21/0.46 = ( emptyset = emptyset ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoin__Cong_type,type,
% 0.21/0.46 setadjoin__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setadjoin__Cong,definition,
% 0.21/0.46 ( setadjoin__Cong
% 0.21/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.46 ( ( Xx = Xy )
% 0.21/0.46 => ! [Xz: $i,Xu: $i] :
% 0.21/0.46 ( ( Xz = Xu )
% 0.21/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.21/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(powerset__Cong_type,type,
% 0.21/0.46 powerset__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(powerset__Cong,definition,
% 0.21/0.46 ( powerset__Cong
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ( ( powerset @ A )
% 0.21/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(setunion__Cong_type,type,
% 0.21/0.46 setunion__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(setunion__Cong,definition,
% 0.21/0.46 ( setunion__Cong
% 0.21/0.46 = ( ! [A: $i,B: $i] :
% 0.21/0.46 ( ( A = B )
% 0.21/0.46 => ( ( setunion @ A )
% 0.21/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(omega__Cong_type,type,
% 0.21/0.46 omega__Cong: $o ).
% 0.21/0.46
% 0.21/0.46 thf(omega__Cong,definition,
% 0.21/0.46 ( omega__Cong
% 0.21/0.46 = ( omega = omega ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(exuEu_type,type,
% 0.21/0.46 exuEu: $o ).
% 0.21/0.46
% 0.21/0.46 thf(exuEu,definition,
% 0.21/0.46 ( exuEu
% 0.21/0.46 = ( ! [Xphi: $i > $o] :
% 0.21/0.46 ( ( exu
% 0.21/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.47 => ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( Xphi @ Xx )
% 0.21/0.47 => ( ( Xphi @ Xy )
% 0.21/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(descr__Cong_type,type,
% 0.21/0.47 descr__Cong: $o ).
% 0.21/0.47
% 0.21/0.47 thf(descr__Cong,definition,
% 0.21/0.47 ( descr__Cong
% 0.21/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.21/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.21/0.47 ( ( Xx = Xy )
% 0.21/0.47 => ( ( Xphi @ Xx )
% 0.21/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.21/0.47 => ( ( exu
% 0.21/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.47 => ( ( exu
% 0.21/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.21/0.47 => ( ( descr
% 0.21/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.47 = ( descr
% 0.21/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(dsetconstr__Cong_type,type,
% 0.21/0.47 dsetconstr__Cong: $o ).
% 0.21/0.47
% 0.21/0.47 thf(dsetconstr__Cong,definition,
% 0.21/0.47 ( dsetconstr__Cong
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( A = B )
% 0.21/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ! [Xy: $i] :
% 0.21/0.47 ( ( in @ Xy @ B )
% 0.21/0.47 => ( ( Xx = Xy )
% 0.21/0.47 => ( ( Xphi @ Xx )
% 0.21/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.21/0.47 => ( ( dsetconstr @ A
% 0.21/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.47 = ( dsetconstr @ B
% 0.21/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(subset_type,type,
% 0.21/0.47 subset: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(disjoint_type,type,
% 0.21/0.47 disjoint: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(setsmeet_type,type,
% 0.21/0.47 setsmeet: $i > $i > $o ).
% 0.21/0.47
% 0.21/0.47 thf(subsetI1_type,type,
% 0.21/0.47 subsetI1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(subsetI1,definition,
% 0.21/0.47 ( subsetI1
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ Xx @ B ) )
% 0.21/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(eqimpsubset2_type,type,
% 0.21/0.47 eqimpsubset2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(eqimpsubset2,definition,
% 0.21/0.47 ( eqimpsubset2
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( A = B )
% 0.21/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(eqimpsubset1_type,type,
% 0.21/0.47 eqimpsubset1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(eqimpsubset1,definition,
% 0.21/0.47 ( eqimpsubset1
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ( A = B )
% 0.21/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(subsetI2_type,type,
% 0.21/0.47 subsetI2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(subsetI2,definition,
% 0.21/0.47 ( subsetI2
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ! [Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ Xx @ B ) )
% 0.21/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(emptysetsubset_type,type,
% 0.21/0.47 emptysetsubset: $o ).
% 0.21/0.47
% 0.21/0.47 thf(emptysetsubset,definition,
% 0.21/0.47 ( emptysetsubset
% 0.21/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(subsetE_type,type,
% 0.21/0.47 subsetE: $o ).
% 0.21/0.47
% 0.21/0.47 thf(subsetE,definition,
% 0.21/0.47 ( subsetE
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( subset @ A @ B )
% 0.21/0.47 => ( ( in @ Xx @ A )
% 0.21/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(subsetE2_type,type,
% 0.21/0.47 subsetE2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(subsetE2,definition,
% 0.21/0.47 ( subsetE2
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( subset @ A @ B )
% 0.21/0.47 => ( ~ ( in @ Xx @ B )
% 0.21/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(notsubsetI_type,type,
% 0.21/0.47 notsubsetI: $o ).
% 0.21/0.47
% 0.21/0.47 thf(notsubsetI,definition,
% 0.21/0.47 ( notsubsetI
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( ~ ( in @ Xx @ B )
% 0.21/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(notequalI1_type,type,
% 0.21/0.47 notequalI1: $o ).
% 0.21/0.47
% 0.21/0.47 thf(notequalI1,definition,
% 0.21/0.47 ( notequalI1
% 0.21/0.47 = ( ! [A: $i,B: $i] :
% 0.21/0.47 ( ~ ( subset @ A @ B )
% 0.21/0.47 => ( A != B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(notequalI2_type,type,
% 0.21/0.47 notequalI2: $o ).
% 0.21/0.47
% 0.21/0.47 thf(notequalI2,definition,
% 0.21/0.47 ( notequalI2
% 0.21/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.47 ( ( in @ Xx @ A )
% 0.21/0.47 => ( ~ ( in @ Xx @ B )
% 0.21/0.47 => ( A != B ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(subsetRefl_type,type,
% 0.21/0.47 subsetRefl: $o ).
% 0.21/0.47
% 0.21/0.47 thf(subsetRefl,definition,
% 0.21/0.47 ( subsetRefl
% 0.21/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(subsetTrans_type,type,
% 0.21/0.47 subsetTrans: $o ).
% 0.21/0.47
% 0.21/0.47 thf(subsetTrans,definition,
% 0.21/0.47 ( subsetTrans
% 0.21/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.21/0.47 ( ( subset @ A @ B )
% 0.21/0.47 => ( ( subset @ B @ C )
% 0.21/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(setadjoinSub_type,type,
% 0.21/0.47 setadjoinSub: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setadjoinSub,definition,
% 0.33/0.47 ( setadjoinSub
% 0.33/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setadjoinSub2_type,type,
% 0.33/0.47 setadjoinSub2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setadjoinSub2,definition,
% 0.33/0.47 ( setadjoinSub2
% 0.33/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.33/0.47 ( ( subset @ A @ B )
% 0.33/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(subset2powerset_type,type,
% 0.33/0.47 subset2powerset: $o ).
% 0.33/0.47
% 0.33/0.47 thf(subset2powerset,definition,
% 0.33/0.47 ( subset2powerset
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( subset @ A @ B )
% 0.33/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setextsub_type,type,
% 0.33/0.47 setextsub: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setextsub,definition,
% 0.33/0.47 ( setextsub
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( subset @ A @ B )
% 0.33/0.47 => ( ( subset @ B @ A )
% 0.33/0.47 => ( A = B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(subsetemptysetimpeq_type,type,
% 0.33/0.47 subsetemptysetimpeq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(subsetemptysetimpeq,definition,
% 0.33/0.47 ( subsetemptysetimpeq
% 0.33/0.47 = ( ! [A: $i] :
% 0.33/0.47 ( ( subset @ A @ emptyset )
% 0.33/0.47 => ( A = emptyset ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(powersetI1_type,type,
% 0.33/0.47 powersetI1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(powersetI1,definition,
% 0.33/0.47 ( powersetI1
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( subset @ B @ A )
% 0.33/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(powersetE1_type,type,
% 0.33/0.47 powersetE1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(powersetE1,definition,
% 0.33/0.47 ( powersetE1
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.33/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(inPowerset_type,type,
% 0.33/0.47 inPowerset: $o ).
% 0.33/0.47
% 0.33/0.47 thf(inPowerset,definition,
% 0.33/0.47 ( inPowerset
% 0.33/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(powersetsubset_type,type,
% 0.33/0.47 powersetsubset: $o ).
% 0.33/0.47
% 0.33/0.47 thf(powersetsubset,definition,
% 0.33/0.47 ( powersetsubset
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( subset @ A @ B )
% 0.33/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(sepInPowerset_type,type,
% 0.33/0.47 sepInPowerset: $o ).
% 0.33/0.47
% 0.33/0.47 thf(sepInPowerset,definition,
% 0.33/0.47 ( sepInPowerset
% 0.33/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.47 ( in
% 0.33/0.47 @ ( dsetconstr @ A
% 0.33/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(sepSubset_type,type,
% 0.33/0.47 sepSubset: $o ).
% 0.33/0.47
% 0.33/0.47 thf(sepSubset,definition,
% 0.33/0.47 ( sepSubset
% 0.33/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.47 ( subset
% 0.33/0.47 @ ( dsetconstr @ A
% 0.33/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.47 @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunion_type,type,
% 0.33/0.47 binunion: $i > $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(binunionIL_type,type,
% 0.33/0.47 binunionIL: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionIL,definition,
% 0.33/0.47 ( binunionIL
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(upairset2IR_type,type,
% 0.33/0.47 upairset2IR: $o ).
% 0.33/0.47
% 0.33/0.47 thf(upairset2IR,definition,
% 0.33/0.47 ( upairset2IR
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunionIR_type,type,
% 0.33/0.47 binunionIR: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionIR,definition,
% 0.33/0.47 ( binunionIR
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ B )
% 0.33/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunionEcases_type,type,
% 0.33/0.47 binunionEcases: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionEcases,definition,
% 0.33/0.47 ( binunionEcases
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.33/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.33/0.47 => ( ( ( in @ Xx @ A )
% 0.33/0.47 => Xphi )
% 0.33/0.47 => ( ( ( in @ Xx @ B )
% 0.33/0.47 => Xphi )
% 0.33/0.47 => Xphi ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunionE_type,type,
% 0.33/0.47 binunionE: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionE,definition,
% 0.33/0.47 ( binunionE
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.33/0.47 => ( ( in @ Xx @ A )
% 0.33/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunionLsub_type,type,
% 0.33/0.47 binunionLsub: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionLsub,definition,
% 0.33/0.47 ( binunionLsub
% 0.33/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunionRsub_type,type,
% 0.33/0.47 binunionRsub: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionRsub,definition,
% 0.33/0.47 ( binunionRsub
% 0.33/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersect_type,type,
% 0.33/0.47 binintersect: $i > $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectI_type,type,
% 0.33/0.47 binintersectI: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectI,definition,
% 0.33/0.47 ( binintersectI
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ B )
% 0.33/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectSubset5_type,type,
% 0.33/0.47 binintersectSubset5: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectSubset5,definition,
% 0.33/0.47 ( binintersectSubset5
% 0.33/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.33/0.47 ( ( subset @ C @ A )
% 0.33/0.47 => ( ( subset @ C @ B )
% 0.33/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectEL_type,type,
% 0.33/0.47 binintersectEL: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectEL,definition,
% 0.33/0.47 ( binintersectEL
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.33/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectLsub_type,type,
% 0.33/0.47 binintersectLsub: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectLsub,definition,
% 0.33/0.47 ( binintersectLsub
% 0.33/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectSubset2_type,type,
% 0.33/0.47 binintersectSubset2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectSubset2,definition,
% 0.33/0.47 ( binintersectSubset2
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( subset @ A @ B )
% 0.33/0.47 => ( ( binintersect @ A @ B )
% 0.33/0.47 = A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectSubset3_type,type,
% 0.33/0.47 binintersectSubset3: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectSubset3,definition,
% 0.33/0.47 ( binintersectSubset3
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( ( binintersect @ A @ B )
% 0.33/0.47 = B )
% 0.33/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectER_type,type,
% 0.33/0.47 binintersectER: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectER,definition,
% 0.33/0.47 ( binintersectER
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.33/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(disjointsetsI1_type,type,
% 0.33/0.47 disjointsetsI1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(disjointsetsI1,definition,
% 0.33/0.47 ( disjointsetsI1
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ~ ? [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 & ( in @ Xx @ B ) )
% 0.33/0.47 => ( ( binintersect @ A @ B )
% 0.33/0.47 = emptyset ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectRsub_type,type,
% 0.33/0.47 binintersectRsub: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectRsub,definition,
% 0.33/0.47 ( binintersectRsub
% 0.33/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectSubset4_type,type,
% 0.33/0.47 binintersectSubset4: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectSubset4,definition,
% 0.33/0.47 ( binintersectSubset4
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( subset @ B @ A )
% 0.33/0.47 => ( ( binintersect @ A @ B )
% 0.33/0.47 = B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectSubset1_type,type,
% 0.33/0.47 binintersectSubset1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectSubset1,definition,
% 0.33/0.47 ( binintersectSubset1
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( ( binintersect @ A @ B )
% 0.33/0.47 = A )
% 0.33/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(bs114d_type,type,
% 0.33/0.47 bs114d: $o ).
% 0.33/0.47
% 0.33/0.47 thf(bs114d,definition,
% 0.33/0.47 ( bs114d
% 0.33/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.33/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.33/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(regular_type,type,
% 0.33/0.47 regular: $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminus_type,type,
% 0.33/0.47 setminus: $i > $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(setminusI_type,type,
% 0.33/0.47 setminusI: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusI,definition,
% 0.33/0.47 ( setminusI
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ~ ( in @ Xx @ B )
% 0.33/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setminusEL_type,type,
% 0.33/0.47 setminusEL: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusEL,definition,
% 0.33/0.47 ( setminusEL
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setminusER_type,type,
% 0.33/0.47 setminusER: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusER,definition,
% 0.33/0.47 ( setminusER
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setminusSubset2_type,type,
% 0.33/0.47 setminusSubset2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusSubset2,definition,
% 0.33/0.47 ( setminusSubset2
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( subset @ A @ B )
% 0.33/0.47 => ( ( setminus @ A @ B )
% 0.33/0.47 = emptyset ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setminusERneg_type,type,
% 0.33/0.47 setminusERneg: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusERneg,definition,
% 0.33/0.47 ( setminusERneg
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/0.47 => ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setminusELneg_type,type,
% 0.33/0.47 setminusELneg: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusELneg,definition,
% 0.33/0.47 ( setminusELneg
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.33/0.47 => ( ~ ( in @ Xx @ B )
% 0.33/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setminusILneg_type,type,
% 0.33/0.47 setminusILneg: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusILneg,definition,
% 0.33/0.47 ( setminusILneg
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ~ ( in @ Xx @ A )
% 0.33/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setminusIRneg_type,type,
% 0.33/0.47 setminusIRneg: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusIRneg,definition,
% 0.33/0.47 ( setminusIRneg
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ B )
% 0.33/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setminusLsub_type,type,
% 0.33/0.47 setminusLsub: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusLsub,definition,
% 0.33/0.47 ( setminusLsub
% 0.33/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setminusSubset1_type,type,
% 0.33/0.47 setminusSubset1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusSubset1,definition,
% 0.33/0.47 ( setminusSubset1
% 0.33/0.47 = ( ! [A: $i,B: $i] :
% 0.33/0.47 ( ( ( setminus @ A @ B )
% 0.33/0.47 = emptyset )
% 0.33/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(symdiff_type,type,
% 0.33/0.47 symdiff: $i > $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(symdiffE_type,type,
% 0.33/0.47 symdiffE: $o ).
% 0.33/0.47
% 0.33/0.47 thf(symdiffE,definition,
% 0.33/0.47 ( symdiffE
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.33/0.47 => ! [Xphi: $o] :
% 0.33/0.47 ( ( ( in @ Xx @ A )
% 0.33/0.47 => ( ~ ( in @ Xx @ B )
% 0.33/0.47 => Xphi ) )
% 0.33/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ B )
% 0.33/0.47 => Xphi ) )
% 0.33/0.47 => Xphi ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(symdiffI1_type,type,
% 0.33/0.47 symdiffI1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(symdiffI1,definition,
% 0.33/0.47 ( symdiffI1
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ~ ( in @ Xx @ B )
% 0.33/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(symdiffI2_type,type,
% 0.33/0.47 symdiffI2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(symdiffI2,definition,
% 0.33/0.47 ( symdiffI2
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ~ ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ B )
% 0.33/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(symdiffIneg1_type,type,
% 0.33/0.47 symdiffIneg1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(symdiffIneg1,definition,
% 0.33/0.47 ( symdiffIneg1
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ B )
% 0.33/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(symdiffIneg2_type,type,
% 0.33/0.47 symdiffIneg2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(symdiffIneg2,definition,
% 0.33/0.47 ( symdiffIneg2
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ~ ( in @ Xx @ A )
% 0.33/0.47 => ( ~ ( in @ Xx @ B )
% 0.33/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(iskpair_type,type,
% 0.33/0.47 iskpair: $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(secondinupair_type,type,
% 0.33/0.47 secondinupair: $o ).
% 0.33/0.47
% 0.33/0.47 thf(secondinupair,definition,
% 0.33/0.47 ( secondinupair
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairIL_type,type,
% 0.33/0.47 setukpairIL: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairIL,definition,
% 0.33/0.47 ( setukpairIL
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairIR_type,type,
% 0.33/0.47 setukpairIR: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairIR,definition,
% 0.33/0.47 ( setukpairIR
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(kpairiskpair_type,type,
% 0.33/0.47 kpairiskpair: $o ).
% 0.33/0.47
% 0.33/0.47 thf(kpairiskpair,definition,
% 0.33/0.47 ( kpairiskpair
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(kpair_type,type,
% 0.33/0.47 kpair: $i > $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(kpairp_type,type,
% 0.33/0.47 kpairp: $o ).
% 0.33/0.47
% 0.33/0.47 thf(kpairp,definition,
% 0.33/0.47 ( kpairp
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprod_type,type,
% 0.33/0.47 cartprod: $i > $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(singletonsubset_type,type,
% 0.33/0.47 singletonsubset: $o ).
% 0.33/0.47
% 0.33/0.47 thf(singletonsubset,definition,
% 0.33/0.47 ( singletonsubset
% 0.33/0.47 = ( ! [A: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(singletoninpowerset_type,type,
% 0.33/0.47 singletoninpowerset: $o ).
% 0.33/0.47
% 0.33/0.47 thf(singletoninpowerset,definition,
% 0.33/0.47 ( singletoninpowerset
% 0.33/0.47 = ( ! [A: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(singletoninpowunion_type,type,
% 0.33/0.47 singletoninpowunion: $o ).
% 0.33/0.47
% 0.33/0.47 thf(singletoninpowunion,definition,
% 0.33/0.47 ( singletoninpowunion
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(upairset2E_type,type,
% 0.33/0.47 upairset2E: $o ).
% 0.33/0.47
% 0.33/0.47 thf(upairset2E,definition,
% 0.33/0.47 ( upairset2E
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.33/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.33/0.47 => ( ( Xz = Xx )
% 0.33/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(upairsubunion_type,type,
% 0.33/0.47 upairsubunion: $o ).
% 0.33/0.47
% 0.33/0.47 thf(upairsubunion,definition,
% 0.33/0.47 ( upairsubunion
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(upairinpowunion_type,type,
% 0.33/0.47 upairinpowunion: $o ).
% 0.33/0.47
% 0.33/0.47 thf(upairinpowunion,definition,
% 0.33/0.47 ( upairinpowunion
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ubforcartprodlem1_type,type,
% 0.33/0.47 ubforcartprodlem1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ubforcartprodlem1,definition,
% 0.33/0.47 ( ubforcartprodlem1
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ubforcartprodlem2_type,type,
% 0.33/0.47 ubforcartprodlem2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ubforcartprodlem2,definition,
% 0.33/0.47 ( ubforcartprodlem2
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ubforcartprodlem3_type,type,
% 0.33/0.47 ubforcartprodlem3: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ubforcartprodlem3,definition,
% 0.33/0.47 ( ubforcartprodlem3
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodpairin_type,type,
% 0.33/0.47 cartprodpairin: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodpairin,definition,
% 0.33/0.47 ( cartprodpairin
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodmempair1_type,type,
% 0.33/0.47 cartprodmempair1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodmempair1,definition,
% 0.33/0.47 ( cartprodmempair1
% 0.33/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.33/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.33/0.47 => ? [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 & ? [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 & ( Xu
% 0.33/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodmempair_type,type,
% 0.33/0.47 cartprodmempair: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodmempair,definition,
% 0.33/0.47 ( cartprodmempair
% 0.33/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.33/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.33/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setunionE2_type,type,
% 0.33/0.47 setunionE2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setunionE2,definition,
% 0.33/0.47 ( setunionE2
% 0.33/0.47 = ( ! [A: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.33/0.47 => ? [X: $i] :
% 0.33/0.47 ( ( in @ X @ A )
% 0.33/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setunionsingleton1_type,type,
% 0.33/0.47 setunionsingleton1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setunionsingleton1,definition,
% 0.33/0.47 ( setunionsingleton1
% 0.33/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setunionsingleton2_type,type,
% 0.33/0.47 setunionsingleton2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setunionsingleton2,definition,
% 0.33/0.47 ( setunionsingleton2
% 0.33/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setunionsingleton_type,type,
% 0.33/0.47 setunionsingleton: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setunionsingleton,definition,
% 0.33/0.47 ( setunionsingleton
% 0.33/0.47 = ( ! [Xx: $i] :
% 0.33/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.33/0.47 = Xx ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(singleton_type,type,
% 0.33/0.47 singleton: $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(singletonprop_type,type,
% 0.33/0.47 singletonprop: $o ).
% 0.33/0.47
% 0.33/0.47 thf(singletonprop,definition,
% 0.33/0.47 ( singletonprop
% 0.33/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( ( Xphi @ Xx )
% 0.33/0.47 => ( ( Xphi @ Xy )
% 0.33/0.47 => ( Xx = Xy ) ) ) ) )
% 0.33/0.47 => ( ? [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 & ( Xphi @ Xx ) )
% 0.33/0.47 => ( singleton
% 0.33/0.47 @ ( dsetconstr @ A
% 0.33/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ex1_type,type,
% 0.33/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.33/0.47
% 0.33/0.47 thf(ex1,definition,
% 0.33/0.47 ( ex1
% 0.33/0.47 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.33/0.47 ( singleton
% 0.33/0.47 @ ( dsetconstr @ A
% 0.33/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ex1E1_type,type,
% 0.33/0.47 ex1E1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ex1E1,definition,
% 0.33/0.47 ( ex1E1
% 0.33/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.47 ( ( ex1 @ A
% 0.33/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.47 => ? [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ex1I_type,type,
% 0.33/0.47 ex1I: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ex1I,definition,
% 0.33/0.47 ( ex1I
% 0.33/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( Xphi @ Xx )
% 0.33/0.47 => ( ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( ( Xphi @ Xy )
% 0.33/0.47 => ( Xy = Xx ) ) )
% 0.33/0.47 => ( ex1 @ A
% 0.33/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ex1I2_type,type,
% 0.33/0.47 ex1I2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ex1I2,definition,
% 0.33/0.47 ( ex1I2
% 0.33/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( ( Xphi @ Xx )
% 0.33/0.47 => ( ( Xphi @ Xy )
% 0.33/0.47 => ( Xx = Xy ) ) ) ) )
% 0.33/0.47 => ( ? [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 & ( Xphi @ Xx ) )
% 0.33/0.47 => ( ex1 @ A
% 0.33/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(singletonsuniq_type,type,
% 0.33/0.47 singletonsuniq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(singletonsuniq,definition,
% 0.33/0.47 ( singletonsuniq
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.33/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.33/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(atmost1p_type,type,
% 0.33/0.47 atmost1p: $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(atleast2p_type,type,
% 0.33/0.47 atleast2p: $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(atmost2p_type,type,
% 0.33/0.47 atmost2p: $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(upairsetp_type,type,
% 0.33/0.47 upairsetp: $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjL1_type,type,
% 0.33/0.47 setukpairinjL1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjL1,definition,
% 0.33/0.47 ( setukpairinjL1
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.33/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.33/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(kfstsingleton_type,type,
% 0.33/0.47 kfstsingleton: $o ).
% 0.33/0.47
% 0.33/0.47 thf(kfstsingleton,definition,
% 0.33/0.47 ( kfstsingleton
% 0.33/0.47 = ( ! [Xu: $i] :
% 0.33/0.47 ( ( iskpair @ Xu )
% 0.33/0.47 => ( singleton
% 0.33/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.33/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(theprop_type,type,
% 0.33/0.47 theprop: $o ).
% 0.33/0.47
% 0.33/0.47 thf(theprop,definition,
% 0.33/0.47 ( theprop
% 0.33/0.47 = ( ! [X: $i] :
% 0.33/0.47 ( ( singleton @ X )
% 0.33/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(kfst_type,type,
% 0.33/0.47 kfst: $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(kfstpairEq_type,type,
% 0.33/0.47 kfstpairEq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(kfstpairEq,definition,
% 0.33/0.47 ( kfstpairEq
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.33/0.47 = Xx ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodfstin_type,type,
% 0.33/0.47 cartprodfstin: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodfstin,definition,
% 0.33/0.47 ( cartprodfstin
% 0.33/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.33/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.33/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjL2_type,type,
% 0.33/0.47 setukpairinjL2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjL2,definition,
% 0.33/0.47 ( setukpairinjL2
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.33/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.33/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjL_type,type,
% 0.33/0.47 setukpairinjL: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjL,definition,
% 0.33/0.47 ( setukpairinjL
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.33/0.47 = ( kpair @ Xz @ Xu ) )
% 0.33/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjR11_type,type,
% 0.33/0.47 setukpairinjR11: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjR11,definition,
% 0.33/0.47 ( setukpairinjR11
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( Xx = Xy )
% 0.33/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.33/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjR12_type,type,
% 0.33/0.47 setukpairinjR12: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjR12,definition,
% 0.33/0.47 ( setukpairinjR12
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( Xx = Xy )
% 0.33/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.33/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjR1_type,type,
% 0.33/0.47 setukpairinjR1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjR1,definition,
% 0.33/0.47 ( setukpairinjR1
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.33/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.33/0.47 => ( ( Xz = Xu )
% 0.33/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(upairequniteq_type,type,
% 0.33/0.47 upairequniteq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(upairequniteq,definition,
% 0.33/0.47 ( upairequniteq
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.33/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.33/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.33/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjR2_type,type,
% 0.33/0.47 setukpairinjR2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjR2,definition,
% 0.33/0.47 ( setukpairinjR2
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.33/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.33/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjR_type,type,
% 0.33/0.47 setukpairinjR: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setukpairinjR,definition,
% 0.33/0.47 ( setukpairinjR
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.33/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.33/0.47 = ( kpair @ Xz @ Xu ) )
% 0.33/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ksndsingleton_type,type,
% 0.33/0.47 ksndsingleton: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ksndsingleton,definition,
% 0.33/0.47 ( ksndsingleton
% 0.33/0.47 = ( ! [Xu: $i] :
% 0.33/0.47 ( ( iskpair @ Xu )
% 0.33/0.47 => ( singleton
% 0.33/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.33/0.47 @ ^ [Xx: $i] :
% 0.33/0.47 ( Xu
% 0.33/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ksnd_type,type,
% 0.33/0.47 ksnd: $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(ksndpairEq_type,type,
% 0.33/0.47 ksndpairEq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ksndpairEq,definition,
% 0.33/0.47 ( ksndpairEq
% 0.33/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.33/0.47 = Xy ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(kpairsurjEq_type,type,
% 0.33/0.47 kpairsurjEq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(kpairsurjEq,definition,
% 0.33/0.47 ( kpairsurjEq
% 0.33/0.47 = ( ! [Xu: $i] :
% 0.33/0.47 ( ( iskpair @ Xu )
% 0.33/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.33/0.47 = Xu ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodsndin_type,type,
% 0.33/0.47 cartprodsndin: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodsndin,definition,
% 0.33/0.47 ( cartprodsndin
% 0.33/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.33/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.33/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodpairmemEL_type,type,
% 0.33/0.47 cartprodpairmemEL: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodpairmemEL,definition,
% 0.33/0.47 ( cartprodpairmemEL
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.33/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodpairmemER_type,type,
% 0.33/0.47 cartprodpairmemER: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodpairmemER,definition,
% 0.33/0.47 ( cartprodpairmemER
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 0.33/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodmempaircEq_type,type,
% 0.33/0.47 cartprodmempaircEq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodmempaircEq,definition,
% 0.33/0.47 ( cartprodmempaircEq
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( kpair @ Xx @ Xy )
% 0.33/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodfstpairEq_type,type,
% 0.33/0.47 cartprodfstpairEq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodfstpairEq,definition,
% 0.33/0.47 ( cartprodfstpairEq
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.33/0.47 = Xx ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodsndpairEq_type,type,
% 0.33/0.47 cartprodsndpairEq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodsndpairEq,definition,
% 0.33/0.47 ( cartprodsndpairEq
% 0.33/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.33/0.47 = Xy ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodpairsurjEq_type,type,
% 0.33/0.47 cartprodpairsurjEq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(cartprodpairsurjEq,definition,
% 0.33/0.47 ( cartprodpairsurjEq
% 0.33/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.33/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.33/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.33/0.47 = Xu ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(breln_type,type,
% 0.33/0.47 breln: $i > $i > $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(breln,definition,
% 0.33/0.47 ( breln
% 0.33/0.47 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstr_type,type,
% 0.33/0.47 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrI_type,type,
% 0.33/0.47 dpsetconstrI: $o ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrI,definition,
% 0.33/0.47 ( dpsetconstrI
% 0.33/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( Xphi @ Xx @ Xy )
% 0.33/0.47 => ( in @ ( kpair @ Xx @ Xy )
% 0.33/0.47 @ ( dpsetconstr @ A @ B
% 0.33/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrSub_type,type,
% 0.33/0.47 dpsetconstrSub: $o ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrSub,definition,
% 0.33/0.47 ( dpsetconstrSub
% 0.33/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.33/0.47 ( subset
% 0.33/0.47 @ ( dpsetconstr @ A @ B
% 0.33/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 0.33/0.47 @ ( cartprod @ A @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setOfPairsIsBReln_type,type,
% 0.33/0.47 setOfPairsIsBReln: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setOfPairsIsBReln,definition,
% 0.33/0.47 ( setOfPairsIsBReln
% 0.33/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 0.33/0.47 ( breln @ A @ B
% 0.33/0.47 @ ( dpsetconstr @ A @ B
% 0.33/0.47 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrERa_type,type,
% 0.33/0.47 dpsetconstrERa: $o ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrERa,definition,
% 0.33/0.47 ( dpsetconstrERa
% 0.33/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( in @ ( kpair @ Xx @ Xy )
% 0.33/0.47 @ ( dpsetconstr @ A @ B
% 0.33/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.33/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrEL1_type,type,
% 0.33/0.47 dpsetconstrEL1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrEL1,definition,
% 0.33/0.47 ( dpsetconstrEL1
% 0.33/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.33/0.47 @ ( dpsetconstr @ A @ B
% 0.33/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.33/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrEL2_type,type,
% 0.33/0.47 dpsetconstrEL2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrEL2,definition,
% 0.33/0.47 ( dpsetconstrEL2
% 0.33/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.33/0.47 @ ( dpsetconstr @ A @ B
% 0.33/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.33/0.47 => ( in @ Xy @ B ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrER_type,type,
% 0.33/0.47 dpsetconstrER: $o ).
% 0.33/0.47
% 0.33/0.47 thf(dpsetconstrER,definition,
% 0.33/0.47 ( dpsetconstrER
% 0.33/0.47 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( in @ ( kpair @ Xx @ Xy )
% 0.33/0.47 @ ( dpsetconstr @ A @ B
% 0.33/0.47 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 0.33/0.47 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(func_type,type,
% 0.33/0.47 func: $i > $i > $i > $o ).
% 0.33/0.47
% 0.33/0.47 thf(funcSet_type,type,
% 0.33/0.47 funcSet: $i > $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(funcImageSingleton_type,type,
% 0.33/0.47 funcImageSingleton: $o ).
% 0.33/0.47
% 0.33/0.47 thf(funcImageSingleton,definition,
% 0.33/0.47 ( funcImageSingleton
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xf )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( singleton
% 0.33/0.47 @ ( dsetconstr @ B
% 0.33/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(apProp_type,type,
% 0.33/0.47 apProp: $o ).
% 0.33/0.47
% 0.33/0.47 thf(apProp,definition,
% 0.33/0.47 ( apProp
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xf )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in
% 0.33/0.47 @ ( setunion
% 0.33/0.47 @ ( dsetconstr @ B
% 0.33/0.47 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 0.33/0.47 @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ap_type,type,
% 0.33/0.47 ap: $i > $i > $i > $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(app_type,type,
% 0.33/0.47 app: $o ).
% 0.33/0.47
% 0.33/0.47 thf(app,definition,
% 0.33/0.47 ( app
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xf )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(infuncsetfunc_type,type,
% 0.33/0.47 infuncsetfunc: $o ).
% 0.33/0.47
% 0.33/0.47 thf(infuncsetfunc,definition,
% 0.33/0.47 ( infuncsetfunc
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/0.47 => ( func @ A @ B @ Xf ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ap2p_type,type,
% 0.33/0.47 ap2p: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ap2p,definition,
% 0.33/0.47 ( ap2p
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(funcinfuncset_type,type,
% 0.33/0.47 funcinfuncset: $o ).
% 0.33/0.47
% 0.33/0.47 thf(funcinfuncset,definition,
% 0.33/0.47 ( funcinfuncset
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xf )
% 0.33/0.47 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(lamProp_type,type,
% 0.33/0.47 lamProp: $o ).
% 0.33/0.47
% 0.33/0.47 thf(lamProp,definition,
% 0.33/0.47 ( lamProp
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/0.47 => ( func @ A @ B
% 0.33/0.47 @ ( dpsetconstr @ A @ B
% 0.33/0.47 @ ^ [Xx: $i,Xy: $i] :
% 0.33/0.47 ( ( Xf @ Xx )
% 0.33/0.47 = Xy ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(lam_type,type,
% 0.33/0.47 lam: $i > $i > ( $i > $i ) > $i ).
% 0.33/0.47
% 0.33/0.47 thf(lamp_type,type,
% 0.33/0.47 lamp: $o ).
% 0.33/0.47
% 0.33/0.47 thf(lamp,definition,
% 0.33/0.47 ( lamp
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/0.47 => ( func @ A @ B
% 0.33/0.47 @ ( lam @ A @ B
% 0.33/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(lam2p_type,type,
% 0.33/0.47 lam2p: $o ).
% 0.33/0.47
% 0.33/0.47 thf(lam2p,definition,
% 0.33/0.47 ( lam2p
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/0.47 => ( in
% 0.33/0.47 @ ( lam @ A @ B
% 0.33/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.33/0.47 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(brelnall1_type,type,
% 0.33/0.47 brelnall1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(brelnall1,definition,
% 0.33/0.47 ( brelnall1
% 0.33/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.33/0.47 ( ( breln @ A @ B @ R )
% 0.33/0.47 => ! [Xphi: $i > $o] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.33/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ R )
% 0.33/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(brelnall2_type,type,
% 0.33/0.47 brelnall2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(brelnall2,definition,
% 0.33/0.47 ( brelnall2
% 0.33/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.33/0.47 ( ( breln @ A @ B @ R )
% 0.33/0.47 => ! [Xphi: $i > $o] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.33/0.47 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ R )
% 0.33/0.47 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ex1E2_type,type,
% 0.33/0.47 ex1E2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ex1E2,definition,
% 0.33/0.47 ( ex1E2
% 0.33/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.33/0.47 ( ( ex1 @ A
% 0.33/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( ( Xphi @ Xx )
% 0.33/0.47 => ( ( Xphi @ Xy )
% 0.33/0.47 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(funcGraphProp1_type,type,
% 0.33/0.47 funcGraphProp1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(funcGraphProp1,definition,
% 0.33/0.47 ( funcGraphProp1
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xf )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(funcGraphProp3_type,type,
% 0.33/0.47 funcGraphProp3: $o ).
% 0.33/0.47
% 0.33/0.47 thf(funcGraphProp3,definition,
% 0.33/0.47 ( funcGraphProp3
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(funcGraphProp2_type,type,
% 0.33/0.47 funcGraphProp2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(funcGraphProp2,definition,
% 0.33/0.47 ( funcGraphProp2
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xf )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.33/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(funcextLem_type,type,
% 0.33/0.47 funcextLem: $o ).
% 0.33/0.47
% 0.33/0.47 thf(funcextLem,definition,
% 0.33/0.47 ( funcextLem
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xf )
% 0.33/0.47 => ! [Xg: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xg )
% 0.33/0.47 => ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 0.33/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(funcGraphProp4_type,type,
% 0.33/0.47 funcGraphProp4: $o ).
% 0.33/0.47
% 0.33/0.47 thf(funcGraphProp4,definition,
% 0.33/0.47 ( funcGraphProp4
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 0.33/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/0.47 = Xy ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(subbreln_type,type,
% 0.33/0.47 subbreln: $o ).
% 0.33/0.47
% 0.33/0.47 thf(subbreln,definition,
% 0.33/0.47 ( subbreln
% 0.33/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.33/0.47 ( ( breln @ A @ B @ R )
% 0.33/0.47 => ! [S: $i] :
% 0.33/0.47 ( ( breln @ A @ B @ S )
% 0.33/0.47 => ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.33/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.33/0.47 => ( subset @ R @ S ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(eqbreln_type,type,
% 0.33/0.47 eqbreln: $o ).
% 0.33/0.47
% 0.33/0.47 thf(eqbreln,definition,
% 0.33/0.47 ( eqbreln
% 0.33/0.47 = ( ! [A: $i,B: $i,R: $i] :
% 0.33/0.47 ( ( breln @ A @ B @ R )
% 0.33/0.47 => ! [S: $i] :
% 0.33/0.47 ( ( breln @ A @ B @ S )
% 0.33/0.47 => ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 0.33/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 0.33/0.47 => ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ B )
% 0.33/0.47 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 0.33/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 0.33/0.47 => ( R = S ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(funcext_type,type,
% 0.33/0.47 funcext: $o ).
% 0.33/0.47
% 0.33/0.47 thf(funcext,definition,
% 0.33/0.47 ( funcext
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xf )
% 0.33/0.47 => ! [Xg: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xg )
% 0.33/0.47 => ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.33/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(funcext2_type,type,
% 0.33/0.47 funcext2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(funcext2,definition,
% 0.33/0.47 ( funcext2
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/0.47 => ! [Xg: $i] :
% 0.33/0.47 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 0.33/0.47 => ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/0.47 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 0.33/0.47 => ( Xf = Xg ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ap2apEq1_type,type,
% 0.33/0.47 ap2apEq1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ap2apEq1,definition,
% 0.33/0.47 ( ap2apEq1
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ap2apEq2_type,type,
% 0.33/0.47 ap2apEq2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ap2apEq2,definition,
% 0.33/0.47 ( ap2apEq2
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xf )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( ap @ A @ B @ Xf @ Xx )
% 0.33/0.47 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(beta1_type,type,
% 0.33/0.47 beta1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(beta1,definition,
% 0.33/0.47 ( beta1
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( ap @ A @ B
% 0.33/0.47 @ ( lam @ A @ B
% 0.33/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.33/0.47 @ Xx )
% 0.33/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(eta1_type,type,
% 0.33/0.47 eta1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(eta1,definition,
% 0.33/0.47 ( eta1
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( func @ A @ B @ Xf )
% 0.33/0.47 => ( ( lam @ A @ B
% 0.33/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.33/0.47 = Xf ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(lam2lamEq_type,type,
% 0.33/0.47 lam2lamEq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(lam2lamEq,definition,
% 0.33/0.47 ( lam2lamEq
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/0.47 => ( ( lam @ A @ B
% 0.33/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 0.33/0.47 = ( lam @ A @ B
% 0.33/0.47 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(beta2_type,type,
% 0.33/0.47 beta2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(beta2,definition,
% 0.33/0.47 ( beta2
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 0.33/0.47 ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( in @ ( Xf @ Xx ) @ B ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( ap @ A @ B
% 0.33/0.47 @ ( lam @ A @ B
% 0.33/0.47 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 0.33/0.47 @ Xx )
% 0.33/0.47 = ( Xf @ Xx ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(eta2_type,type,
% 0.33/0.47 eta2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(eta2,definition,
% 0.33/0.47 ( eta2
% 0.33/0.47 = ( ! [A: $i,B: $i,Xf: $i] :
% 0.33/0.47 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 0.33/0.47 => ( ( lam @ A @ B
% 0.33/0.47 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 0.33/0.47 = Xf ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(iffalseProp1_type,type,
% 0.33/0.47 iffalseProp1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(iffalseProp1,definition,
% 0.33/0.47 ( iffalseProp1
% 0.33/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( ~ Xphi
% 0.33/0.47 => ( in @ Xy
% 0.33/0.47 @ ( dsetconstr @ A
% 0.33/0.47 @ ^ [Xz: $i] :
% 0.33/0.47 ( ( Xphi
% 0.33/0.47 & ( Xz = Xx ) )
% 0.33/0.47 | ( ~ Xphi
% 0.33/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(iffalseProp2_type,type,
% 0.33/0.47 iffalseProp2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(iffalseProp2,definition,
% 0.33/0.47 ( iffalseProp2
% 0.33/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( ~ Xphi
% 0.33/0.47 => ( ( dsetconstr @ A
% 0.33/0.47 @ ^ [Xz: $i] :
% 0.33/0.47 ( ( Xphi
% 0.33/0.47 & ( Xz = Xx ) )
% 0.33/0.47 | ( ~ Xphi
% 0.33/0.47 & ( Xz = Xy ) ) ) )
% 0.33/0.47 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(iftrueProp1_type,type,
% 0.33/0.47 iftrueProp1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(iftrueProp1,definition,
% 0.33/0.47 ( iftrueProp1
% 0.33/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( Xphi
% 0.33/0.47 => ( in @ Xx
% 0.33/0.47 @ ( dsetconstr @ A
% 0.33/0.47 @ ^ [Xz: $i] :
% 0.33/0.47 ( ( Xphi
% 0.33/0.47 & ( Xz = Xx ) )
% 0.33/0.47 | ( ~ Xphi
% 0.33/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(iftrueProp2_type,type,
% 0.33/0.47 iftrueProp2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(iftrueProp2,definition,
% 0.33/0.47 ( iftrueProp2
% 0.33/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( Xphi
% 0.33/0.47 => ( ( dsetconstr @ A
% 0.33/0.47 @ ^ [Xz: $i] :
% 0.33/0.47 ( ( Xphi
% 0.33/0.47 & ( Xz = Xx ) )
% 0.33/0.47 | ( ~ Xphi
% 0.33/0.47 & ( Xz = Xy ) ) ) )
% 0.33/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(ifSingleton_type,type,
% 0.33/0.47 ifSingleton: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ifSingleton,definition,
% 0.33/0.47 ( ifSingleton
% 0.33/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( singleton
% 0.33/0.47 @ ( dsetconstr @ A
% 0.33/0.47 @ ^ [Xz: $i] :
% 0.33/0.47 ( ( Xphi
% 0.33/0.47 & ( Xz = Xx ) )
% 0.33/0.47 | ( ~ Xphi
% 0.33/0.47 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(if_type,type,
% 0.33/0.47 if: $i > $o > $i > $i > $i ).
% 0.33/0.47
% 0.33/0.47 thf(ifp_type,type,
% 0.33/0.47 ifp: $o ).
% 0.33/0.47
% 0.33/0.47 thf(ifp,definition,
% 0.33/0.47 ( ifp
% 0.33/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(theeq_type,type,
% 0.33/0.47 theeq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(theeq,definition,
% 0.33/0.47 ( theeq
% 0.33/0.47 = ( ! [X: $i] :
% 0.33/0.47 ( ( singleton @ X )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ X )
% 0.33/0.47 => ( ( setunion @ X )
% 0.33/0.47 = Xx ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(iftrue_type,type,
% 0.33/0.47 iftrue: $o ).
% 0.33/0.47
% 0.33/0.47 thf(iftrue,definition,
% 0.33/0.47 ( iftrue
% 0.33/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( Xphi
% 0.33/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.33/0.47 = Xx ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(iffalse_type,type,
% 0.33/0.47 iffalse: $o ).
% 0.33/0.47
% 0.33/0.47 thf(iffalse,definition,
% 0.33/0.47 ( iffalse
% 0.33/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( ~ Xphi
% 0.33/0.47 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 0.33/0.47 = Xy ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(iftrueorfalse_type,type,
% 0.33/0.47 iftrueorfalse: $o ).
% 0.33/0.47
% 0.33/0.47 thf(iftrueorfalse,definition,
% 0.33/0.47 ( iftrueorfalse
% 0.33/0.47 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ! [Xy: $i] :
% 0.33/0.47 ( ( in @ Xy @ A )
% 0.33/0.47 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectT_lem_type,type,
% 0.33/0.47 binintersectT_lem: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectT_lem,definition,
% 0.33/0.47 ( binintersectT_lem
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunionT_lem_type,type,
% 0.33/0.47 binunionT_lem: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionT_lem,definition,
% 0.33/0.47 ( binunionT_lem
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(powersetT_lem_type,type,
% 0.33/0.47 powersetT_lem: $o ).
% 0.33/0.47
% 0.33/0.47 thf(powersetT_lem,definition,
% 0.33/0.47 ( powersetT_lem
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setminusT_lem_type,type,
% 0.33/0.47 setminusT_lem: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setminusT_lem,definition,
% 0.33/0.47 ( setminusT_lem
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(complementT_lem_type,type,
% 0.33/0.47 complementT_lem: $o ).
% 0.33/0.47
% 0.33/0.47 thf(complementT_lem,definition,
% 0.33/0.47 ( complementT_lem
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(setextT_type,type,
% 0.33/0.47 setextT: $o ).
% 0.33/0.47
% 0.33/0.47 thf(setextT,definition,
% 0.33/0.47 ( setextT
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ X )
% 0.33/0.47 => ( in @ Xx @ Y ) ) )
% 0.33/0.47 => ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ Y )
% 0.33/0.47 => ( in @ Xx @ X ) ) )
% 0.33/0.47 => ( X = Y ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(subsetTI_type,type,
% 0.33/0.47 subsetTI: $o ).
% 0.33/0.47
% 0.33/0.47 thf(subsetTI,definition,
% 0.33/0.47 ( subsetTI
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ X )
% 0.33/0.47 => ( in @ Xx @ Y ) ) )
% 0.33/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(powersetTI1_type,type,
% 0.33/0.47 powersetTI1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(powersetTI1,definition,
% 0.33/0.47 ( powersetTI1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ X )
% 0.33/0.47 => ( in @ Xx @ Y ) ) )
% 0.33/0.47 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(powersetTE1_type,type,
% 0.33/0.47 powersetTE1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(powersetTE1,definition,
% 0.33/0.47 ( powersetTE1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ X @ ( powerset @ Y ) )
% 0.33/0.47 => ( ( in @ Xx @ X )
% 0.33/0.47 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(complementTI1_type,type,
% 0.33/0.47 complementTI1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(complementTI1,definition,
% 0.33/0.47 ( complementTI1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ X )
% 0.33/0.47 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(complementTE1_type,type,
% 0.33/0.47 complementTE1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(complementTE1,definition,
% 0.33/0.47 ( complementTE1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 0.33/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectTELcontra_type,type,
% 0.33/0.47 binintersectTELcontra: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectTELcontra,definition,
% 0.33/0.47 ( binintersectTELcontra
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ~ ( in @ Xx @ X )
% 0.33/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectTERcontra_type,type,
% 0.33/0.47 binintersectTERcontra: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binintersectTERcontra,definition,
% 0.33/0.47 ( binintersectTERcontra
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ~ ( in @ Xx @ Y )
% 0.33/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(contrasubsetT_type,type,
% 0.33/0.47 contrasubsetT: $o ).
% 0.33/0.47
% 0.33/0.47 thf(contrasubsetT,definition,
% 0.33/0.47 ( contrasubsetT
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.33/0.47 => ( ( in @ Xx @ Y )
% 0.33/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(contrasubsetT1_type,type,
% 0.33/0.47 contrasubsetT1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(contrasubsetT1,definition,
% 0.33/0.47 ( contrasubsetT1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( subset @ X @ Y )
% 0.33/0.47 => ( ~ ( in @ Xx @ Y )
% 0.33/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(contrasubsetT2_type,type,
% 0.33/0.47 contrasubsetT2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(contrasubsetT2,definition,
% 0.33/0.47 ( contrasubsetT2
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( ( subset @ X @ Y )
% 0.33/0.47 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(contrasubsetT3_type,type,
% 0.33/0.47 contrasubsetT3: $o ).
% 0.33/0.47
% 0.33/0.47 thf(contrasubsetT3,definition,
% 0.33/0.47 ( contrasubsetT3
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 0.33/0.47 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(doubleComplementI1_type,type,
% 0.33/0.47 doubleComplementI1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(doubleComplementI1,definition,
% 0.33/0.47 ( doubleComplementI1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ X )
% 0.33/0.47 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(doubleComplementE1_type,type,
% 0.33/0.47 doubleComplementE1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(doubleComplementE1,definition,
% 0.33/0.47 ( doubleComplementE1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 0.33/0.47 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(doubleComplementSub1_type,type,
% 0.33/0.47 doubleComplementSub1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(doubleComplementSub1,definition,
% 0.33/0.47 ( doubleComplementSub1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(doubleComplementSub2_type,type,
% 0.33/0.47 doubleComplementSub2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(doubleComplementSub2,definition,
% 0.33/0.47 ( doubleComplementSub2
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(doubleComplementEq_type,type,
% 0.33/0.47 doubleComplementEq: $o ).
% 0.33/0.47
% 0.33/0.47 thf(doubleComplementEq,definition,
% 0.33/0.47 ( doubleComplementEq
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ( X
% 0.33/0.47 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(complementTnotintersectT_type,type,
% 0.33/0.47 complementTnotintersectT: $o ).
% 0.33/0.47
% 0.33/0.47 thf(complementTnotintersectT,definition,
% 0.33/0.47 ( complementTnotintersectT
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.33/0.47 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(complementImpComplementIntersect_type,type,
% 0.33/0.47 complementImpComplementIntersect: $o ).
% 0.33/0.47
% 0.33/0.47 thf(complementImpComplementIntersect,definition,
% 0.33/0.47 ( complementImpComplementIntersect
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.33/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(complementSubsetComplementIntersect_type,type,
% 0.33/0.47 complementSubsetComplementIntersect: $o ).
% 0.33/0.47
% 0.33/0.47 thf(complementSubsetComplementIntersect,definition,
% 0.33/0.47 ( complementSubsetComplementIntersect
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(complementInPowersetComplementIntersect_type,type,
% 0.33/0.47 complementInPowersetComplementIntersect: $o ).
% 0.33/0.47
% 0.33/0.47 thf(complementInPowersetComplementIntersect,definition,
% 0.33/0.47 ( complementInPowersetComplementIntersect
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(contraSubsetComplement_type,type,
% 0.33/0.47 contraSubsetComplement: $o ).
% 0.33/0.47
% 0.33/0.47 thf(contraSubsetComplement,definition,
% 0.33/0.47 ( contraSubsetComplement
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ Y )
% 0.33/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(complementTcontraSubset_type,type,
% 0.33/0.47 complementTcontraSubset: $o ).
% 0.33/0.47
% 0.33/0.47 thf(complementTcontraSubset,definition,
% 0.33/0.47 ( complementTcontraSubset
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 0.33/0.47 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunionTILcontra_type,type,
% 0.33/0.47 binunionTILcontra: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionTILcontra,definition,
% 0.33/0.47 ( binunionTILcontra
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.33/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunionTIRcontra_type,type,
% 0.33/0.47 binunionTIRcontra: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionTIRcontra,definition,
% 0.33/0.47 ( binunionTIRcontra
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.33/0.47 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(inIntersectImpInUnion_type,type,
% 0.33/0.47 inIntersectImpInUnion: $o ).
% 0.33/0.47
% 0.33/0.47 thf(inIntersectImpInUnion,definition,
% 0.33/0.47 ( inIntersectImpInUnion
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Z: $i] :
% 0.33/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.33/0.47 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(inIntersectImpInUnion2_type,type,
% 0.33/0.47 inIntersectImpInUnion2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(inIntersectImpInUnion2,definition,
% 0.33/0.47 ( inIntersectImpInUnion2
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Z: $i] :
% 0.33/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.33/0.47 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(inIntersectImpInIntersectUnions_type,type,
% 0.33/0.47 inIntersectImpInIntersectUnions: $o ).
% 0.33/0.47
% 0.33/0.47 thf(inIntersectImpInIntersectUnions,definition,
% 0.33/0.47 ( inIntersectImpInIntersectUnions
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Z: $i] :
% 0.33/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.33/0.47 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(intersectInPowersetIntersectUnions_type,type,
% 0.33/0.47 intersectInPowersetIntersectUnions: $o ).
% 0.33/0.47
% 0.33/0.47 thf(intersectInPowersetIntersectUnions,definition,
% 0.33/0.47 ( intersectInPowersetIntersectUnions
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Z: $i] :
% 0.33/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/0.47 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(inComplementUnionImpNotIn1_type,type,
% 0.33/0.47 inComplementUnionImpNotIn1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(inComplementUnionImpNotIn1,definition,
% 0.33/0.47 ( inComplementUnionImpNotIn1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.33/0.47 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(inComplementUnionImpInComplement1_type,type,
% 0.33/0.47 inComplementUnionImpInComplement1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(inComplementUnionImpInComplement1,definition,
% 0.33/0.47 ( inComplementUnionImpInComplement1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.33/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunionTE_type,type,
% 0.33/0.47 binunionTE: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionTE,definition,
% 0.33/0.47 ( binunionTE
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xphi: $o,Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 0.33/0.47 => ( ( ( in @ Xx @ X )
% 0.33/0.47 => Xphi )
% 0.33/0.47 => ( ( ( in @ Xx @ Y )
% 0.33/0.47 => Xphi )
% 0.33/0.47 => Xphi ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(binunionTEcontra_type,type,
% 0.33/0.47 binunionTEcontra: $o ).
% 0.33/0.47
% 0.33/0.47 thf(binunionTEcontra,definition,
% 0.33/0.47 ( binunionTEcontra
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ~ ( in @ Xx @ X )
% 0.33/0.47 => ( ~ ( in @ Xx @ Y )
% 0.33/0.47 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2a1_type,type,
% 0.33/0.47 demorgan2a1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2a1,definition,
% 0.33/0.47 ( demorgan2a1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.33/0.47 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(complementUnionInPowersetComplement_type,type,
% 0.33/0.47 complementUnionInPowersetComplement: $o ).
% 0.33/0.47
% 0.33/0.47 thf(complementUnionInPowersetComplement,definition,
% 0.33/0.47 ( complementUnionInPowersetComplement
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2a2_type,type,
% 0.33/0.47 demorgan2a2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2a2,definition,
% 0.33/0.47 ( demorgan2a2
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.33/0.47 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan1a_type,type,
% 0.33/0.47 demorgan1a: $o ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan1a,definition,
% 0.33/0.47 ( demorgan1a
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 0.33/0.47 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan1b_type,type,
% 0.33/0.47 demorgan1b: $o ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan1b,definition,
% 0.33/0.47 ( demorgan1b
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.33/0.47 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan1_type,type,
% 0.33/0.47 demorgan1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan1,definition,
% 0.33/0.47 ( demorgan1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 0.33/0.47 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2a_type,type,
% 0.33/0.47 demorgan2a: $o ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2a,definition,
% 0.33/0.47 ( demorgan2a
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 0.33/0.47 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2b2_type,type,
% 0.33/0.47 demorgan2b2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2b2,definition,
% 0.33/0.47 ( demorgan2b2
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 0.33/0.47 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 0.33/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2b_type,type,
% 0.33/0.47 demorgan2b: $o ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2b,definition,
% 0.33/0.47 ( demorgan2b
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ A )
% 0.33/0.47 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 0.33/0.47 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2_type,type,
% 0.33/0.47 demorgan2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(demorgan2,definition,
% 0.33/0.47 ( demorgan2
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 0.33/0.47 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(woz13rule0_type,type,
% 0.33/0.47 woz13rule0: $o ).
% 0.33/0.47
% 0.33/0.47 thf(woz13rule0,definition,
% 0.33/0.47 ( woz13rule0
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Xx: $i] :
% 0.33/0.47 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 0.33/0.47 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(woz13rule1_type,type,
% 0.33/0.47 woz13rule1: $o ).
% 0.33/0.47
% 0.33/0.47 thf(woz13rule1,definition,
% 0.33/0.47 ( woz13rule1
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Z: $i] :
% 0.33/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/0.47 => ( ( subset @ X @ Z )
% 0.33/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(woz13rule2_type,type,
% 0.33/0.47 woz13rule2: $o ).
% 0.33/0.47
% 0.33/0.47 thf(woz13rule2,definition,
% 0.33/0.47 ( woz13rule2
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Z: $i] :
% 0.33/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/0.47 => ( ( subset @ Y @ Z )
% 0.33/0.47 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(woz13rule3_type,type,
% 0.33/0.47 woz13rule3: $o ).
% 0.33/0.47
% 0.33/0.47 thf(woz13rule3,definition,
% 0.33/0.47 ( woz13rule3
% 0.33/0.47 = ( ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Z: $i] :
% 0.33/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/0.47 => ( ( subset @ X @ Y )
% 0.33/0.47 => ( ( subset @ X @ Z )
% 0.33/0.47 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 thf(woz13rule4,conjecture,
% 0.33/0.47 ( setextAx
% 0.33/0.47 => ( emptysetAx
% 0.33/0.47 => ( setadjoinAx
% 0.33/0.47 => ( powersetAx
% 0.33/0.47 => ( setunionAx
% 0.33/0.47 => ( omega0Ax
% 0.33/0.47 => ( omegaSAx
% 0.33/0.47 => ( omegaIndAx
% 0.33/0.47 => ( replAx
% 0.33/0.47 => ( foundationAx
% 0.33/0.47 => ( wellorderingAx
% 0.33/0.47 => ( descrp
% 0.33/0.47 => ( dsetconstrI
% 0.33/0.47 => ( dsetconstrEL
% 0.33/0.47 => ( dsetconstrER
% 0.33/0.47 => ( exuE1
% 0.33/0.47 => ( prop2setE
% 0.33/0.47 => ( emptysetE
% 0.33/0.47 => ( emptysetimpfalse
% 0.33/0.47 => ( notinemptyset
% 0.33/0.47 => ( exuE3e
% 0.33/0.47 => ( setext
% 0.33/0.47 => ( emptyI
% 0.33/0.47 => ( noeltsimpempty
% 0.33/0.47 => ( setbeta
% 0.33/0.47 => ( nonemptyE1
% 0.33/0.47 => ( nonemptyI
% 0.33/0.47 => ( nonemptyI1
% 0.33/0.47 => ( setadjoinIL
% 0.33/0.47 => ( emptyinunitempty
% 0.33/0.47 => ( setadjoinIR
% 0.33/0.47 => ( setadjoinE
% 0.33/0.47 => ( setadjoinOr
% 0.33/0.47 => ( setoftrueEq
% 0.33/0.47 => ( powersetI
% 0.33/0.47 => ( emptyinPowerset
% 0.33/0.47 => ( emptyInPowerset
% 0.33/0.47 => ( powersetE
% 0.33/0.47 => ( setunionI
% 0.33/0.47 => ( setunionE
% 0.33/0.47 => ( subPowSU
% 0.33/0.47 => ( exuE2
% 0.33/0.47 => ( nonemptyImpWitness
% 0.33/0.47 => ( uniqinunit
% 0.33/0.47 => ( notinsingleton
% 0.33/0.47 => ( eqinunit
% 0.33/0.47 => ( singletonsswitch
% 0.33/0.47 => ( upairsetE
% 0.33/0.47 => ( upairsetIL
% 0.33/0.47 => ( upairsetIR
% 0.33/0.47 => ( emptyE1
% 0.33/0.47 => ( vacuousDall
% 0.33/0.47 => ( quantDeMorgan1
% 0.33/0.47 => ( quantDeMorgan2
% 0.33/0.47 => ( quantDeMorgan3
% 0.33/0.47 => ( quantDeMorgan4
% 0.33/0.47 => ( prop2setI
% 0.33/0.47 => ( prop2set2propI
% 0.33/0.47 => ( notdexE
% 0.33/0.47 => ( notdallE
% 0.33/0.47 => ( exuI1
% 0.33/0.47 => ( exuI3
% 0.33/0.47 => ( exuI2
% 0.33/0.47 => ( inCongP
% 0.33/0.47 => ( in__Cong
% 0.33/0.47 => ( exuE3u
% 0.33/0.47 => ( exu__Cong
% 0.33/0.47 => ( emptyset__Cong
% 0.33/0.47 => ( setadjoin__Cong
% 0.33/0.47 => ( powerset__Cong
% 0.33/0.47 => ( setunion__Cong
% 0.33/0.47 => ( omega__Cong
% 0.33/0.47 => ( exuEu
% 0.33/0.47 => ( descr__Cong
% 0.33/0.47 => ( dsetconstr__Cong
% 0.33/0.47 => ( subsetI1
% 0.33/0.47 => ( eqimpsubset2
% 0.33/0.47 => ( eqimpsubset1
% 0.33/0.47 => ( subsetI2
% 0.33/0.47 => ( emptysetsubset
% 0.33/0.47 => ( subsetE
% 0.33/0.47 => ( subsetE2
% 0.33/0.47 => ( notsubsetI
% 0.33/0.47 => ( notequalI1
% 0.33/0.47 => ( notequalI2
% 0.33/0.47 => ( subsetRefl
% 0.33/0.47 => ( subsetTrans
% 0.33/0.47 => ( setadjoinSub
% 0.33/0.47 => ( setadjoinSub2
% 0.33/0.47 => ( subset2powerset
% 0.33/0.47 => ( setextsub
% 0.33/0.47 => ( subsetemptysetimpeq
% 0.33/0.47 => ( powersetI1
% 0.33/0.47 => ( powersetE1
% 0.33/0.47 => ( inPowerset
% 0.33/0.47 => ( powersetsubset
% 0.33/0.47 => ( sepInPowerset
% 0.33/0.47 => ( sepSubset
% 0.33/0.47 => ( binunionIL
% 0.33/0.47 => ( upairset2IR
% 0.33/0.47 => ( binunionIR
% 0.33/0.47 => ( binunionEcases
% 0.33/0.47 => ( binunionE
% 0.33/0.47 => ( binunionLsub
% 0.33/0.47 => ( binunionRsub
% 0.33/0.47 => ( binintersectI
% 0.33/0.47 => ( binintersectSubset5
% 0.33/0.47 => ( binintersectEL
% 0.33/0.47 => ( binintersectLsub
% 0.33/0.47 => ( binintersectSubset2
% 0.33/0.47 => ( binintersectSubset3
% 0.33/0.47 => ( binintersectER
% 0.33/0.47 => ( disjointsetsI1
% 0.33/0.47 => ( binintersectRsub
% 0.33/0.47 => ( binintersectSubset4
% 0.33/0.47 => ( binintersectSubset1
% 0.33/0.47 => ( bs114d
% 0.33/0.47 => ( setminusI
% 0.33/0.47 => ( setminusEL
% 0.33/0.47 => ( setminusER
% 0.33/0.47 => ( setminusSubset2
% 0.33/0.47 => ( setminusERneg
% 0.33/0.47 => ( setminusELneg
% 0.33/0.47 => ( setminusILneg
% 0.33/0.47 => ( setminusIRneg
% 0.33/0.47 => ( setminusLsub
% 0.33/0.47 => ( setminusSubset1
% 0.33/0.47 => ( symdiffE
% 0.33/0.47 => ( symdiffI1
% 0.33/0.47 => ( symdiffI2
% 0.33/0.47 => ( symdiffIneg1
% 0.33/0.47 => ( symdiffIneg2
% 0.33/0.47 => ( secondinupair
% 0.33/0.47 => ( setukpairIL
% 0.33/0.47 => ( setukpairIR
% 0.33/0.47 => ( kpairiskpair
% 0.33/0.47 => ( kpairp
% 0.33/0.47 => ( singletonsubset
% 0.33/0.47 => ( singletoninpowerset
% 0.33/0.47 => ( singletoninpowunion
% 0.33/0.47 => ( upairset2E
% 0.33/0.47 => ( upairsubunion
% 0.33/0.47 => ( upairinpowunion
% 0.33/0.47 => ( ubforcartprodlem1
% 0.33/0.47 => ( ubforcartprodlem2
% 0.33/0.47 => ( ubforcartprodlem3
% 0.33/0.47 => ( cartprodpairin
% 0.33/0.47 => ( cartprodmempair1
% 0.33/0.47 => ( cartprodmempair
% 0.33/0.47 => ( setunionE2
% 0.33/0.47 => ( setunionsingleton1
% 0.33/0.47 => ( setunionsingleton2
% 0.33/0.47 => ( setunionsingleton
% 0.33/0.47 => ( singletonprop
% 0.33/0.47 => ( ex1E1
% 0.33/0.47 => ( ex1I
% 0.33/0.47 => ( ex1I2
% 0.33/0.47 => ( singletonsuniq
% 0.33/0.47 => ( setukpairinjL1
% 0.33/0.47 => ( kfstsingleton
% 0.33/0.47 => ( theprop
% 0.33/0.47 => ( kfstpairEq
% 0.33/0.47 => ( cartprodfstin
% 0.33/0.47 => ( setukpairinjL2
% 0.33/0.47 => ( setukpairinjL
% 0.33/0.47 => ( setukpairinjR11
% 0.33/0.47 => ( setukpairinjR12
% 0.33/0.47 => ( setukpairinjR1
% 0.33/0.47 => ( upairequniteq
% 0.33/0.47 => ( setukpairinjR2
% 0.33/0.47 => ( setukpairinjR
% 0.33/0.47 => ( ksndsingleton
% 0.33/0.47 => ( ksndpairEq
% 0.33/0.47 => ( kpairsurjEq
% 0.33/0.47 => ( cartprodsndin
% 0.33/0.47 => ( cartprodpairmemEL
% 0.33/0.47 => ( cartprodpairmemER
% 0.33/0.47 => ( cartprodmempaircEq
% 0.33/0.47 => ( cartprodfstpairEq
% 0.33/0.47 => ( cartprodsndpairEq
% 0.33/0.47 => ( cartprodpairsurjEq
% 0.33/0.47 => ( dpsetconstrI
% 0.33/0.47 => ( dpsetconstrSub
% 0.33/0.47 => ( setOfPairsIsBReln
% 0.33/0.47 => ( dpsetconstrERa
% 0.33/0.47 => ( dpsetconstrEL1
% 0.33/0.47 => ( dpsetconstrEL2
% 0.33/0.47 => ( dpsetconstrER
% 0.33/0.47 => ( funcImageSingleton
% 0.33/0.47 => ( apProp
% 0.33/0.47 => ( app
% 0.33/0.47 => ( infuncsetfunc
% 0.33/0.47 => ( ap2p
% 0.33/0.47 => ( funcinfuncset
% 0.33/0.47 => ( lamProp
% 0.33/0.47 => ( lamp
% 0.33/0.47 => ( lam2p
% 0.33/0.47 => ( brelnall1
% 0.33/0.47 => ( brelnall2
% 0.33/0.47 => ( ex1E2
% 0.33/0.47 => ( funcGraphProp1
% 0.33/0.47 => ( funcGraphProp3
% 0.33/0.47 => ( funcGraphProp2
% 0.33/0.47 => ( funcextLem
% 0.33/0.47 => ( funcGraphProp4
% 0.33/0.47 => ( subbreln
% 0.33/0.47 => ( eqbreln
% 0.33/0.47 => ( funcext
% 0.33/0.47 => ( funcext2
% 0.33/0.47 => ( ap2apEq1
% 0.33/0.47 => ( ap2apEq2
% 0.33/0.47 => ( beta1
% 0.33/0.47 => ( eta1
% 0.33/0.47 => ( lam2lamEq
% 0.33/0.47 => ( beta2
% 0.33/0.47 => ( eta2
% 0.33/0.47 => ( iffalseProp1
% 0.33/0.47 => ( iffalseProp2
% 0.33/0.47 => ( iftrueProp1
% 0.33/0.47 => ( iftrueProp2
% 0.33/0.47 => ( ifSingleton
% 0.33/0.47 => ( ifp
% 0.33/0.47 => ( theeq
% 0.33/0.47 => ( iftrue
% 0.33/0.47 => ( iffalse
% 0.33/0.47 => ( iftrueorfalse
% 0.33/0.47 => ( binintersectT_lem
% 0.33/0.47 => ( binunionT_lem
% 0.33/0.47 => ( powersetT_lem
% 0.33/0.47 => ( setminusT_lem
% 0.33/0.47 => ( complementT_lem
% 0.33/0.47 => ( setextT
% 0.33/0.47 => ( subsetTI
% 0.33/0.47 => ( powersetTI1
% 0.33/0.47 => ( powersetTE1
% 0.33/0.47 => ( complementTI1
% 0.33/0.47 => ( complementTE1
% 0.33/0.47 => ( binintersectTELcontra
% 0.33/0.47 => ( binintersectTERcontra
% 0.33/0.47 => ( contrasubsetT
% 0.33/0.47 => ( contrasubsetT1
% 0.33/0.47 => ( contrasubsetT2
% 0.33/0.47 => ( contrasubsetT3
% 0.33/0.47 => ( doubleComplementI1
% 0.33/0.47 => ( doubleComplementE1
% 0.33/0.47 => ( doubleComplementSub1
% 0.33/0.47 => ( doubleComplementSub2
% 0.33/0.47 => ( doubleComplementEq
% 0.33/0.47 => ( complementTnotintersectT
% 0.33/0.47 => ( complementImpComplementIntersect
% 0.33/0.47 => ( complementSubsetComplementIntersect
% 0.33/0.47 => ( complementInPowersetComplementIntersect
% 0.33/0.47 => ( contraSubsetComplement
% 0.33/0.47 => ( complementTcontraSubset
% 0.33/0.47 => ( binunionTILcontra
% 0.33/0.47 => ( binunionTIRcontra
% 0.33/0.47 => ( inIntersectImpInUnion
% 0.33/0.47 => ( inIntersectImpInUnion2
% 0.33/0.47 => ( inIntersectImpInIntersectUnions
% 0.33/0.47 => ( intersectInPowersetIntersectUnions
% 0.33/0.47 => ( inComplementUnionImpNotIn1
% 0.33/0.47 => ( inComplementUnionImpInComplement1
% 0.33/0.47 => ( binunionTE
% 0.33/0.47 => ( binunionTEcontra
% 0.33/0.47 => ( demorgan2a1
% 0.33/0.47 => ( complementUnionInPowersetComplement
% 0.33/0.47 => ( demorgan2a2
% 0.33/0.47 => ( demorgan1a
% 0.33/0.47 => ( demorgan1b
% 0.33/0.47 => ( demorgan1
% 0.33/0.47 => ( demorgan2a
% 0.33/0.47 => ( demorgan2b2
% 0.33/0.47 => ( demorgan2b
% 0.33/0.47 => ( demorgan2
% 0.33/0.47 => ( woz13rule0
% 0.33/0.47 => ( woz13rule1
% 0.33/0.47 => ( woz13rule2
% 0.33/0.47 => ( woz13rule3
% 0.33/0.47 => ! [A: $i,X: $i] :
% 0.33/0.47 ( ( in @ X @ ( powerset @ A ) )
% 0.33/0.47 => ! [Y: $i] :
% 0.33/0.47 ( ( in @ Y @ ( powerset @ A ) )
% 0.33/0.47 => ! [Z: $i] :
% 0.33/0.47 ( ( in @ Z @ ( powerset @ A ) )
% 0.33/0.47 => ! [W: $i] :
% 0.33/0.47 ( ( in @ W @ ( powerset @ A ) )
% 0.33/0.47 => ( ( subset @ X @ Z )
% 0.33/0.47 => ( ( subset @ Y @ W )
% 0.33/0.47 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.33/0.47
% 0.33/0.47 %------------------------------------------------------------------------------
% 0.33/0.47 ------------------------
% 2.86/1.58 ---- Embedded in THF ---
% 2.86/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.86/1.58 %%% Generated on Tue Feb 24 12:33:37 EST 2026
% 2.86/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.86/1.58 %%% Logic specification used:
% 2.86/1.58 %%% thf(spec, logic, $$dhol).
% 2.86/1.58
% 2.86/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2DTF31785.p
% See solution above
% 2.86/1.58 ------------------------
% 3.13/1.64 ---- Cleaned THF ---
% 3.13/1.64 thf(in_type,type,
% 3.13/1.64 in: $i > $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(exu_type,type,
% 3.13/1.64 exu: ( $i > $o ) > $o ).
% 3.13/1.64
% 3.13/1.64 thf(exu,definition,
% 3.13/1.64 ( exu
% 3.13/1.64 = ( ^ [Xphi: $i > $o] :
% 3.13/1.64 ? [Xx: $i] :
% 3.13/1.64 ( ( Xphi @ Xx )
% 3.13/1.64 & ! [Xy: $i] :
% 3.13/1.64 ( ( Xphi @ Xy )
% 3.13/1.64 => ( Xx = Xy ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setextAx_type,type,
% 3.13/1.64 setextAx: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setextAx,definition,
% 3.13/1.64 ( setextAx
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 <=> ( in @ Xx @ B ) )
% 3.13/1.64 => ( A = B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(emptyset_type,type,
% 3.13/1.64 emptyset: $i ).
% 3.13/1.64
% 3.13/1.64 thf(emptysetAx_type,type,
% 3.13/1.64 emptysetAx: $o ).
% 3.13/1.64
% 3.13/1.64 thf(emptysetAx,definition,
% 3.13/1.64 ( emptysetAx
% 3.13/1.64 = ( ! [Xx: $i] :
% 3.13/1.64 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoin_type,type,
% 3.13/1.64 setadjoin: $i > $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinAx_type,type,
% 3.13/1.64 setadjoinAx: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinAx,definition,
% 3.13/1.64 ( setadjoinAx
% 3.13/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.13/1.64 <=> ( ( Xy = Xx )
% 3.13/1.64 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(powerset_type,type,
% 3.13/1.64 powerset: $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(powersetAx_type,type,
% 3.13/1.64 powersetAx: $o ).
% 3.13/1.64
% 3.13/1.64 thf(powersetAx,definition,
% 3.13/1.64 ( powersetAx
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( in @ B @ ( powerset @ A ) )
% 3.13/1.64 <=> ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ B )
% 3.13/1.64 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setunion_type,type,
% 3.13/1.64 setunion: $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(setunionAx_type,type,
% 3.13/1.64 setunionAx: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setunionAx,definition,
% 3.13/1.64 ( setunionAx
% 3.13/1.64 = ( ! [A: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( setunion @ A ) )
% 3.13/1.64 <=> ? [B: $i] :
% 3.13/1.64 ( ( in @ Xx @ B )
% 3.13/1.64 & ( in @ B @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(omega_type,type,
% 3.13/1.64 omega: $i ).
% 3.13/1.64
% 3.13/1.64 thf(omega0Ax_type,type,
% 3.13/1.64 omega0Ax: $o ).
% 3.13/1.64
% 3.13/1.64 thf(omega0Ax,definition,
% 3.13/1.64 ( omega0Ax
% 3.13/1.64 = ( in @ emptyset @ omega ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(omegaSAx_type,type,
% 3.13/1.64 omegaSAx: $o ).
% 3.13/1.64
% 3.13/1.64 thf(omegaSAx,definition,
% 3.13/1.64 ( omegaSAx
% 3.13/1.64 = ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ omega )
% 3.13/1.64 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(omegaIndAx_type,type,
% 3.13/1.64 omegaIndAx: $o ).
% 3.13/1.64
% 3.13/1.64 thf(omegaIndAx,definition,
% 3.13/1.64 ( omegaIndAx
% 3.13/1.64 = ( ! [A: $i] :
% 3.13/1.64 ( ( ( in @ emptyset @ A )
% 3.13/1.64 & ! [Xx: $i] :
% 3.13/1.64 ( ( ( in @ Xx @ omega )
% 3.13/1.64 & ( in @ Xx @ A ) )
% 3.13/1.64 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 3.13/1.64 => ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ omega )
% 3.13/1.64 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(replAx_type,type,
% 3.13/1.64 replAx: $o ).
% 3.13/1.64
% 3.13/1.64 thf(replAx,definition,
% 3.13/1.64 ( replAx
% 3.13/1.64 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( exu
% 3.13/1.64 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 3.13/1.64 => ? [B: $i] :
% 3.13/1.64 ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ B )
% 3.13/1.64 <=> ? [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ A )
% 3.13/1.64 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(foundationAx_type,type,
% 3.13/1.64 foundationAx: $o ).
% 3.13/1.64
% 3.13/1.64 thf(foundationAx,definition,
% 3.13/1.64 ( foundationAx
% 3.13/1.64 = ( ! [A: $i] :
% 3.13/1.64 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.13/1.64 => ? [B: $i] :
% 3.13/1.64 ( ( in @ B @ A )
% 3.13/1.64 & ~ ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ B )
% 3.13/1.64 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(wellorderingAx_type,type,
% 3.13/1.64 wellorderingAx: $o ).
% 3.13/1.64
% 3.13/1.64 thf(wellorderingAx,definition,
% 3.13/1.64 ( wellorderingAx
% 3.13/1.64 = ( ! [A: $i] :
% 3.13/1.64 ? [B: $i] :
% 3.13/1.64 ( ! [C: $i] :
% 3.13/1.64 ( ( in @ C @ B )
% 3.13/1.64 => ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ C )
% 3.13/1.64 => ( in @ Xx @ A ) ) )
% 3.13/1.64 & ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( ( in @ Xx @ A )
% 3.13/1.64 & ( in @ Xy @ A ) )
% 3.13/1.64 => ( ! [C: $i] :
% 3.13/1.64 ( ( in @ C @ B )
% 3.13/1.64 => ( ( in @ Xx @ C )
% 3.13/1.64 <=> ( in @ Xy @ C ) ) )
% 3.13/1.64 => ( Xx = Xy ) ) )
% 3.13/1.64 & ! [C: $i,D: $i] :
% 3.13/1.64 ( ( ( in @ C @ B )
% 3.13/1.64 & ( in @ D @ B ) )
% 3.13/1.64 => ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ C )
% 3.13/1.64 => ( in @ Xx @ D ) )
% 3.13/1.64 | ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ D )
% 3.13/1.64 => ( in @ Xx @ C ) ) ) )
% 3.13/1.64 & ! [C: $i] :
% 3.13/1.64 ( ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ C )
% 3.13/1.64 => ( in @ Xx @ A ) )
% 3.13/1.64 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 3.13/1.64 => ? [D: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ D @ B )
% 3.13/1.64 & ( in @ Xx @ C )
% 3.13/1.64 & ~ ? [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ D )
% 3.13/1.64 & ( in @ Xy @ C ) )
% 3.13/1.64 & ! [E: $i] :
% 3.13/1.64 ( ( in @ E @ B )
% 3.13/1.64 => ( ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ E )
% 3.13/1.64 => ( in @ Xy @ D ) )
% 3.13/1.64 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(descr_type,type,
% 3.13/1.64 descr: ( $i > $o ) > $i ).
% 3.13/1.64
% 3.13/1.64 thf(descrp_type,type,
% 3.13/1.64 descrp: $o ).
% 3.13/1.64
% 3.13/1.64 thf(descrp,definition,
% 3.13/1.64 ( descrp
% 3.13/1.64 = ( ! [Xphi: $i > $o] :
% 3.13/1.64 ( ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 => ( Xphi
% 3.13/1.64 @ ( descr
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(dsetconstr_type,type,
% 3.13/1.64 dsetconstr: $i > ( $i > $o ) > $i ).
% 3.13/1.64
% 3.13/1.64 thf(dsetconstrI_type,type,
% 3.13/1.64 dsetconstrI: $o ).
% 3.13/1.64
% 3.13/1.64 thf(dsetconstrI,definition,
% 3.13/1.64 ( dsetconstrI
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( ( Xphi @ Xx )
% 3.13/1.64 => ( in @ Xx
% 3.13/1.64 @ ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(dsetconstrEL_type,type,
% 3.13/1.64 dsetconstrEL: $o ).
% 3.13/1.64
% 3.13/1.64 thf(dsetconstrEL,definition,
% 3.13/1.64 ( dsetconstrEL
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx
% 3.13/1.64 @ ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.13/1.64 => ( in @ Xx @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(dsetconstrER_type,type,
% 3.13/1.64 dsetconstrER: $o ).
% 3.13/1.64
% 3.13/1.64 thf(dsetconstrER,definition,
% 3.13/1.64 ( dsetconstrER
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx
% 3.13/1.64 @ ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.13/1.64 => ( Xphi @ Xx ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(exuE1_type,type,
% 3.13/1.64 exuE1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(exuE1,definition,
% 3.13/1.64 ( exuE1
% 3.13/1.64 = ( ! [Xphi: $i > $o] :
% 3.13/1.64 ( ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 => ? [Xx: $i] :
% 3.13/1.64 ( ( Xphi @ Xx )
% 3.13/1.64 & ! [Xy: $i] :
% 3.13/1.64 ( ( Xphi @ Xy )
% 3.13/1.64 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(prop2set_type,type,
% 3.13/1.64 prop2set: $o > $i ).
% 3.13/1.64
% 3.13/1.64 thf(prop2setE_type,type,
% 3.13/1.64 prop2setE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(prop2setE,definition,
% 3.13/1.64 ( prop2setE
% 3.13/1.64 = ( ! [Xphi: $o,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 3.13/1.64 => Xphi ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(emptysetE_type,type,
% 3.13/1.64 emptysetE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(emptysetE,definition,
% 3.13/1.64 ( emptysetE
% 3.13/1.64 = ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ emptyset )
% 3.13/1.64 => ! [Xphi: $o] : Xphi ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(emptysetimpfalse_type,type,
% 3.13/1.64 emptysetimpfalse: $o ).
% 3.13/1.64
% 3.13/1.64 thf(emptysetimpfalse,definition,
% 3.13/1.64 ( emptysetimpfalse
% 3.13/1.64 = ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ emptyset )
% 3.13/1.64 => $false ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(notinemptyset_type,type,
% 3.13/1.64 notinemptyset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(notinemptyset,definition,
% 3.13/1.64 ( notinemptyset
% 3.13/1.64 = ( ! [Xx: $i] :
% 3.13/1.64 ~ ( in @ Xx @ emptyset ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(exuE3e_type,type,
% 3.13/1.64 exuE3e: $o ).
% 3.13/1.64
% 3.13/1.64 thf(exuE3e,definition,
% 3.13/1.64 ( exuE3e
% 3.13/1.64 = ( ! [Xphi: $i > $o] :
% 3.13/1.64 ( ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setext_type,type,
% 3.13/1.64 setext: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setext,definition,
% 3.13/1.64 ( setext
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( in @ Xx @ B ) )
% 3.13/1.64 => ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ B )
% 3.13/1.64 => ( in @ Xx @ A ) )
% 3.13/1.64 => ( A = B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(emptyI_type,type,
% 3.13/1.64 emptyI: $o ).
% 3.13/1.64
% 3.13/1.64 thf(emptyI,definition,
% 3.13/1.64 ( emptyI
% 3.13/1.64 = ( ! [A: $i] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ~ ( in @ Xx @ A )
% 3.13/1.64 => ( A = emptyset ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(noeltsimpempty_type,type,
% 3.13/1.64 noeltsimpempty: $o ).
% 3.13/1.64
% 3.13/1.64 thf(noeltsimpempty,definition,
% 3.13/1.64 ( noeltsimpempty
% 3.13/1.64 = ( ! [A: $i] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ~ ( in @ Xx @ A )
% 3.13/1.64 => ( A = emptyset ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setbeta_type,type,
% 3.13/1.64 setbeta: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setbeta,definition,
% 3.13/1.64 ( setbeta
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( ( in @ Xx
% 3.13/1.64 @ ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 3.13/1.64 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(nonempty_type,type,
% 3.13/1.64 nonempty: $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(nonempty,definition,
% 3.13/1.64 ( nonempty
% 3.13/1.64 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(nonemptyE1_type,type,
% 3.13/1.64 nonemptyE1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(nonemptyE1,definition,
% 3.13/1.64 ( nonemptyE1
% 3.13/1.64 = ( ! [A: $i] :
% 3.13/1.64 ( ( nonempty @ A )
% 3.13/1.64 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(nonemptyI_type,type,
% 3.13/1.64 nonemptyI: $o ).
% 3.13/1.64
% 3.13/1.64 thf(nonemptyI,definition,
% 3.13/1.64 ( nonemptyI
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( ( Xphi @ Xx )
% 3.13/1.64 => ( nonempty
% 3.13/1.64 @ ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(nonemptyI1_type,type,
% 3.13/1.64 nonemptyI1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(nonemptyI1,definition,
% 3.13/1.64 ( nonemptyI1
% 3.13/1.64 = ( ! [A: $i] :
% 3.13/1.64 ( ? [Xx: $i] : ( in @ Xx @ A )
% 3.13/1.64 => ( nonempty @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinIL_type,type,
% 3.13/1.64 setadjoinIL: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinIL,definition,
% 3.13/1.64 ( setadjoinIL
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(emptyinunitempty_type,type,
% 3.13/1.64 emptyinunitempty: $o ).
% 3.13/1.64
% 3.13/1.64 thf(emptyinunitempty,definition,
% 3.13/1.64 ( emptyinunitempty
% 3.13/1.64 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinIR_type,type,
% 3.13/1.64 setadjoinIR: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinIR,definition,
% 3.13/1.64 ( setadjoinIR
% 3.13/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ A )
% 3.13/1.64 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinE_type,type,
% 3.13/1.64 setadjoinE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinE,definition,
% 3.13/1.64 ( setadjoinE
% 3.13/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.13/1.64 => ! [Xphi: $o] :
% 3.13/1.64 ( ( ( Xy = Xx )
% 3.13/1.64 => Xphi )
% 3.13/1.64 => ( ( ( in @ Xy @ A )
% 3.13/1.64 => Xphi )
% 3.13/1.64 => Xphi ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinOr_type,type,
% 3.13/1.64 setadjoinOr: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinOr,definition,
% 3.13/1.64 ( setadjoinOr
% 3.13/1.64 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 3.13/1.64 => ( ( Xy = Xx )
% 3.13/1.64 | ( in @ Xy @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setoftrueEq_type,type,
% 3.13/1.64 setoftrueEq: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setoftrueEq,definition,
% 3.13/1.64 ( setoftrueEq
% 3.13/1.64 = ( ! [A: $i] :
% 3.13/1.64 ( ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xx: $i] : $true )
% 3.13/1.64 = A ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(powersetI_type,type,
% 3.13/1.64 powersetI: $o ).
% 3.13/1.64
% 3.13/1.64 thf(powersetI,definition,
% 3.13/1.64 ( powersetI
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ B )
% 3.13/1.64 => ( in @ Xx @ A ) )
% 3.13/1.64 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(emptyinPowerset_type,type,
% 3.13/1.64 emptyinPowerset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(emptyinPowerset,definition,
% 3.13/1.64 ( emptyinPowerset
% 3.13/1.64 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(emptyInPowerset_type,type,
% 3.13/1.64 emptyInPowerset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(emptyInPowerset,definition,
% 3.13/1.64 ( emptyInPowerset
% 3.13/1.64 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(powersetE_type,type,
% 3.13/1.64 powersetE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(powersetE,definition,
% 3.13/1.64 ( powersetE
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ B @ ( powerset @ A ) )
% 3.13/1.64 => ( ( in @ Xx @ B )
% 3.13/1.64 => ( in @ Xx @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setunionI_type,type,
% 3.13/1.64 setunionI: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setunionI,definition,
% 3.13/1.64 ( setunionI
% 3.13/1.64 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.13/1.64 ( ( in @ Xx @ B )
% 3.13/1.64 => ( ( in @ B @ A )
% 3.13/1.64 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setunionE_type,type,
% 3.13/1.64 setunionE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setunionE,definition,
% 3.13/1.64 ( setunionE
% 3.13/1.64 = ( ! [A: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( setunion @ A ) )
% 3.13/1.64 => ! [Xphi: $o] :
% 3.13/1.64 ( ! [B: $i] :
% 3.13/1.64 ( ( in @ Xx @ B )
% 3.13/1.64 => ( ( in @ B @ A )
% 3.13/1.64 => Xphi ) )
% 3.13/1.64 => Xphi ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(subPowSU_type,type,
% 3.13/1.64 subPowSU: $o ).
% 3.13/1.64
% 3.13/1.64 thf(subPowSU,definition,
% 3.13/1.64 ( subPowSU
% 3.13/1.64 = ( ! [A: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(exuE2_type,type,
% 3.13/1.64 exuE2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(exuE2,definition,
% 3.13/1.64 ( exuE2
% 3.13/1.64 = ( ! [Xphi: $i > $o] :
% 3.13/1.64 ( ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 => ? [Xx: $i] :
% 3.13/1.64 ! [Xy: $i] :
% 3.13/1.64 ( ( Xphi @ Xy )
% 3.13/1.64 <=> ( Xy = Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(nonemptyImpWitness_type,type,
% 3.13/1.64 nonemptyImpWitness: $o ).
% 3.13/1.64
% 3.13/1.64 thf(nonemptyImpWitness,definition,
% 3.13/1.64 ( nonemptyImpWitness
% 3.13/1.64 = ( ! [A: $i] :
% 3.13/1.64 ( ( nonempty @ A )
% 3.13/1.64 => ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & $true ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(uniqinunit_type,type,
% 3.13/1.64 uniqinunit: $o ).
% 3.13/1.64
% 3.13/1.64 thf(uniqinunit,definition,
% 3.13/1.64 ( uniqinunit
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.13/1.64 => ( Xx = Xy ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(notinsingleton_type,type,
% 3.13/1.64 notinsingleton: $o ).
% 3.13/1.64
% 3.13/1.64 thf(notinsingleton,definition,
% 3.13/1.64 ( notinsingleton
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xx != Xy )
% 3.13/1.64 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(eqinunit_type,type,
% 3.13/1.64 eqinunit: $o ).
% 3.13/1.64
% 3.13/1.64 thf(eqinunit,definition,
% 3.13/1.64 ( eqinunit
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xx = Xy )
% 3.13/1.64 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(singletonsswitch_type,type,
% 3.13/1.64 singletonsswitch: $o ).
% 3.13/1.64
% 3.13/1.64 thf(singletonsswitch,definition,
% 3.13/1.64 ( singletonsswitch
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.13/1.64 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(upairsetE_type,type,
% 3.13/1.64 upairsetE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(upairsetE,definition,
% 3.13/1.64 ( upairsetE
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.13/1.64 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.13/1.64 => ( ( Xz = Xx )
% 3.13/1.64 | ( Xz = Xy ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(upairsetIL_type,type,
% 3.13/1.64 upairsetIL: $o ).
% 3.13/1.64
% 3.13/1.64 thf(upairsetIL,definition,
% 3.13/1.64 ( upairsetIL
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(upairsetIR_type,type,
% 3.13/1.64 upairsetIR: $o ).
% 3.13/1.64
% 3.13/1.64 thf(upairsetIR,definition,
% 3.13/1.64 ( upairsetIR
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(emptyE1_type,type,
% 3.13/1.64 emptyE1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(emptyE1,definition,
% 3.13/1.64 ( emptyE1
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ( Xphi @ Xx ) )
% 3.13/1.64 => ( ( ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 = emptyset )
% 3.13/1.64 => $false ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(vacuousDall_type,type,
% 3.13/1.64 vacuousDall: $o ).
% 3.13/1.64
% 3.13/1.64 thf(vacuousDall,definition,
% 3.13/1.64 ( vacuousDall
% 3.13/1.64 = ( ! [Xphi: $i > $o,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ emptyset )
% 3.13/1.64 => ( Xphi @ Xx ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(quantDeMorgan1_type,type,
% 3.13/1.64 quantDeMorgan1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(quantDeMorgan1,definition,
% 3.13/1.64 ( quantDeMorgan1
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( ~ ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( Xphi @ Xx ) )
% 3.13/1.64 => ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(quantDeMorgan2_type,type,
% 3.13/1.64 quantDeMorgan2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(quantDeMorgan2,definition,
% 3.13/1.64 ( quantDeMorgan2
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ~ ( Xphi @ Xx ) )
% 3.13/1.64 => ~ ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(quantDeMorgan3_type,type,
% 3.13/1.64 quantDeMorgan3: $o ).
% 3.13/1.64
% 3.13/1.64 thf(quantDeMorgan3,definition,
% 3.13/1.64 ( quantDeMorgan3
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( ~ ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ( Xphi @ Xx ) )
% 3.13/1.64 => ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(quantDeMorgan4_type,type,
% 3.13/1.64 quantDeMorgan4: $o ).
% 3.13/1.64
% 3.13/1.64 thf(quantDeMorgan4,definition,
% 3.13/1.64 ( quantDeMorgan4
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ~ ( Xphi @ Xx ) )
% 3.13/1.64 => ~ ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(prop2setI_type,type,
% 3.13/1.64 prop2setI: $o ).
% 3.13/1.64
% 3.13/1.64 thf(prop2setI,definition,
% 3.13/1.64 ( prop2setI
% 3.13/1.64 = ( ! [Xphi: $o] :
% 3.13/1.64 ( Xphi
% 3.13/1.64 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(set2prop_type,type,
% 3.13/1.64 set2prop: $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(prop2set2propI_type,type,
% 3.13/1.64 prop2set2propI: $o ).
% 3.13/1.64
% 3.13/1.64 thf(prop2set2propI,definition,
% 3.13/1.64 ( prop2set2propI
% 3.13/1.64 = ( ! [Xphi: $o] :
% 3.13/1.64 ( Xphi
% 3.13/1.64 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(notdexE_type,type,
% 3.13/1.64 notdexE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(notdexE,definition,
% 3.13/1.64 ( notdexE
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( ~ ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ( Xphi @ Xx ) )
% 3.13/1.64 => ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(notdallE_type,type,
% 3.13/1.64 notdallE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(notdallE,definition,
% 3.13/1.64 ( notdallE
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( ~ ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( Xphi @ Xx ) )
% 3.13/1.64 => ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(exuI1_type,type,
% 3.13/1.64 exuI1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(exuI1,definition,
% 3.13/1.64 ( exuI1
% 3.13/1.64 = ( ! [Xphi: $i > $o] :
% 3.13/1.64 ( ? [Xx: $i] :
% 3.13/1.64 ( ( Xphi @ Xx )
% 3.13/1.64 & ! [Xy: $i] :
% 3.13/1.64 ( ( Xphi @ Xy )
% 3.13/1.64 => ( Xx = Xy ) ) )
% 3.13/1.64 => ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(exuI3_type,type,
% 3.13/1.64 exuI3: $o ).
% 3.13/1.64
% 3.13/1.64 thf(exuI3,definition,
% 3.13/1.64 ( exuI3
% 3.13/1.64 = ( ! [Xphi: $i > $o] :
% 3.13/1.64 ( ? [Xx: $i] : ( Xphi @ Xx )
% 3.13/1.64 => ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xphi @ Xx )
% 3.13/1.64 => ( ( Xphi @ Xy )
% 3.13/1.64 => ( Xx = Xy ) ) )
% 3.13/1.64 => ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(exuI2_type,type,
% 3.13/1.64 exuI2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(exuI2,definition,
% 3.13/1.64 ( exuI2
% 3.13/1.64 = ( ! [Xphi: $i > $o] :
% 3.13/1.64 ( ? [Xx: $i] :
% 3.13/1.64 ! [Xy: $i] :
% 3.13/1.64 ( ( Xphi @ Xy )
% 3.13/1.64 <=> ( Xy = Xx ) )
% 3.13/1.64 => ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(inCongP_type,type,
% 3.13/1.64 inCongP: $o ).
% 3.13/1.64
% 3.13/1.64 thf(inCongP,definition,
% 3.13/1.64 ( inCongP
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( A = B )
% 3.13/1.64 => ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xx = Xy )
% 3.13/1.64 => ( ( in @ Xx @ A )
% 3.13/1.64 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(in__Cong_type,type,
% 3.13/1.64 in__Cong: $o ).
% 3.13/1.64
% 3.13/1.64 thf(in__Cong,definition,
% 3.13/1.64 ( in__Cong
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( A = B )
% 3.13/1.64 => ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xx = Xy )
% 3.13/1.64 => ( ( in @ Xx @ A )
% 3.13/1.64 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(exuE3u_type,type,
% 3.13/1.64 exuE3u: $o ).
% 3.13/1.64
% 3.13/1.64 thf(exuE3u,definition,
% 3.13/1.64 ( exuE3u
% 3.13/1.64 = ( ! [Xphi: $i > $o] :
% 3.13/1.64 ( ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 => ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xphi @ Xx )
% 3.13/1.64 => ( ( Xphi @ Xy )
% 3.13/1.64 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(exu__Cong_type,type,
% 3.13/1.64 exu__Cong: $o ).
% 3.13/1.64
% 3.13/1.64 thf(exu__Cong,definition,
% 3.13/1.64 ( exu__Cong
% 3.13/1.64 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.13/1.64 ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xx = Xy )
% 3.13/1.64 => ( ( Xphi @ Xx )
% 3.13/1.64 <=> ( Xpsi @ Xy ) ) )
% 3.13/1.64 => ( ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 <=> ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(emptyset__Cong_type,type,
% 3.13/1.64 emptyset__Cong: $o ).
% 3.13/1.64
% 3.13/1.64 thf(emptyset__Cong,definition,
% 3.13/1.64 ( emptyset__Cong
% 3.13/1.64 = ( emptyset = emptyset ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoin__Cong_type,type,
% 3.13/1.64 setadjoin__Cong: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoin__Cong,definition,
% 3.13/1.64 ( setadjoin__Cong
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xx = Xy )
% 3.13/1.64 => ! [Xz: $i,Xu: $i] :
% 3.13/1.64 ( ( Xz = Xu )
% 3.13/1.64 => ( ( setadjoin @ Xx @ Xz )
% 3.13/1.64 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(powerset__Cong_type,type,
% 3.13/1.64 powerset__Cong: $o ).
% 3.13/1.64
% 3.13/1.64 thf(powerset__Cong,definition,
% 3.13/1.64 ( powerset__Cong
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( A = B )
% 3.13/1.64 => ( ( powerset @ A )
% 3.13/1.64 = ( powerset @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setunion__Cong_type,type,
% 3.13/1.64 setunion__Cong: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setunion__Cong,definition,
% 3.13/1.64 ( setunion__Cong
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( A = B )
% 3.13/1.64 => ( ( setunion @ A )
% 3.13/1.64 = ( setunion @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(omega__Cong_type,type,
% 3.13/1.64 omega__Cong: $o ).
% 3.13/1.64
% 3.13/1.64 thf(omega__Cong,definition,
% 3.13/1.64 ( omega__Cong
% 3.13/1.64 = ( omega = omega ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(exuEu_type,type,
% 3.13/1.64 exuEu: $o ).
% 3.13/1.64
% 3.13/1.64 thf(exuEu,definition,
% 3.13/1.64 ( exuEu
% 3.13/1.64 = ( ! [Xphi: $i > $o] :
% 3.13/1.64 ( ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 => ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xphi @ Xx )
% 3.13/1.64 => ( ( Xphi @ Xy )
% 3.13/1.64 => ( Xx = Xy ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(descr__Cong_type,type,
% 3.13/1.64 descr__Cong: $o ).
% 3.13/1.64
% 3.13/1.64 thf(descr__Cong,definition,
% 3.13/1.64 ( descr__Cong
% 3.13/1.64 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.13/1.64 ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xx = Xy )
% 3.13/1.64 => ( ( Xphi @ Xx )
% 3.13/1.64 <=> ( Xpsi @ Xy ) ) )
% 3.13/1.64 => ( ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 => ( ( exu
% 3.13/1.64 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 3.13/1.64 => ( ( descr
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 = ( descr
% 3.13/1.64 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(dsetconstr__Cong_type,type,
% 3.13/1.64 dsetconstr__Cong: $o ).
% 3.13/1.64
% 3.13/1.64 thf(dsetconstr__Cong,definition,
% 3.13/1.64 ( dsetconstr__Cong
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( A = B )
% 3.13/1.64 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 => ( ( Xx = Xy )
% 3.13/1.64 => ( ( Xphi @ Xx )
% 3.13/1.64 <=> ( Xpsi @ Xy ) ) ) ) )
% 3.13/1.64 => ( ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 = ( dsetconstr @ B
% 3.13/1.64 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(subset_type,type,
% 3.13/1.64 subset: $i > $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(disjoint_type,type,
% 3.13/1.64 disjoint: $i > $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(setsmeet_type,type,
% 3.13/1.64 setsmeet: $i > $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(subsetI1_type,type,
% 3.13/1.64 subsetI1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(subsetI1,definition,
% 3.13/1.64 ( subsetI1
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( in @ Xx @ B ) )
% 3.13/1.64 => ( subset @ A @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(eqimpsubset2_type,type,
% 3.13/1.64 eqimpsubset2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(eqimpsubset2,definition,
% 3.13/1.64 ( eqimpsubset2
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( A = B )
% 3.13/1.64 => ( subset @ B @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(eqimpsubset1_type,type,
% 3.13/1.64 eqimpsubset1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(eqimpsubset1,definition,
% 3.13/1.64 ( eqimpsubset1
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( A = B )
% 3.13/1.64 => ( subset @ A @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(subsetI2_type,type,
% 3.13/1.64 subsetI2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(subsetI2,definition,
% 3.13/1.64 ( subsetI2
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( in @ Xx @ B ) )
% 3.13/1.64 => ( subset @ A @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(emptysetsubset_type,type,
% 3.13/1.64 emptysetsubset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(emptysetsubset,definition,
% 3.13/1.64 ( emptysetsubset
% 3.13/1.64 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(subsetE_type,type,
% 3.13/1.64 subsetE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(subsetE,definition,
% 3.13/1.64 ( subsetE
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( subset @ A @ B )
% 3.13/1.64 => ( ( in @ Xx @ A )
% 3.13/1.64 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(subsetE2_type,type,
% 3.13/1.64 subsetE2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(subsetE2,definition,
% 3.13/1.64 ( subsetE2
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( subset @ A @ B )
% 3.13/1.64 => ( ~ ( in @ Xx @ B )
% 3.13/1.64 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(notsubsetI_type,type,
% 3.13/1.64 notsubsetI: $o ).
% 3.13/1.64
% 3.13/1.64 thf(notsubsetI,definition,
% 3.13/1.64 ( notsubsetI
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( ~ ( in @ Xx @ B )
% 3.13/1.64 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(notequalI1_type,type,
% 3.13/1.64 notequalI1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(notequalI1,definition,
% 3.13/1.64 ( notequalI1
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ~ ( subset @ A @ B )
% 3.13/1.64 => ( A != B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(notequalI2_type,type,
% 3.13/1.64 notequalI2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(notequalI2,definition,
% 3.13/1.64 ( notequalI2
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( ~ ( in @ Xx @ B )
% 3.13/1.64 => ( A != B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(subsetRefl_type,type,
% 3.13/1.64 subsetRefl: $o ).
% 3.13/1.64
% 3.13/1.64 thf(subsetRefl,definition,
% 3.13/1.64 ( subsetRefl
% 3.13/1.64 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(subsetTrans_type,type,
% 3.13/1.64 subsetTrans: $o ).
% 3.13/1.64
% 3.13/1.64 thf(subsetTrans,definition,
% 3.13/1.64 ( subsetTrans
% 3.13/1.64 = ( ! [A: $i,B: $i,C: $i] :
% 3.13/1.64 ( ( subset @ A @ B )
% 3.13/1.64 => ( ( subset @ B @ C )
% 3.13/1.64 => ( subset @ A @ C ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinSub_type,type,
% 3.13/1.64 setadjoinSub: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinSub,definition,
% 3.13/1.64 ( setadjoinSub
% 3.13/1.64 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinSub2_type,type,
% 3.13/1.64 setadjoinSub2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setadjoinSub2,definition,
% 3.13/1.64 ( setadjoinSub2
% 3.13/1.64 = ( ! [A: $i,Xx: $i,B: $i] :
% 3.13/1.64 ( ( subset @ A @ B )
% 3.13/1.64 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(subset2powerset_type,type,
% 3.13/1.64 subset2powerset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(subset2powerset,definition,
% 3.13/1.64 ( subset2powerset
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( subset @ A @ B )
% 3.13/1.64 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setextsub_type,type,
% 3.13/1.64 setextsub: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setextsub,definition,
% 3.13/1.64 ( setextsub
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( subset @ A @ B )
% 3.13/1.64 => ( ( subset @ B @ A )
% 3.13/1.64 => ( A = B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(subsetemptysetimpeq_type,type,
% 3.13/1.64 subsetemptysetimpeq: $o ).
% 3.13/1.64
% 3.13/1.64 thf(subsetemptysetimpeq,definition,
% 3.13/1.64 ( subsetemptysetimpeq
% 3.13/1.64 = ( ! [A: $i] :
% 3.13/1.64 ( ( subset @ A @ emptyset )
% 3.13/1.64 => ( A = emptyset ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(powersetI1_type,type,
% 3.13/1.64 powersetI1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(powersetI1,definition,
% 3.13/1.64 ( powersetI1
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( subset @ B @ A )
% 3.13/1.64 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(powersetE1_type,type,
% 3.13/1.64 powersetE1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(powersetE1,definition,
% 3.13/1.64 ( powersetE1
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( in @ B @ ( powerset @ A ) )
% 3.13/1.64 => ( subset @ B @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(inPowerset_type,type,
% 3.13/1.64 inPowerset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(inPowerset,definition,
% 3.13/1.64 ( inPowerset
% 3.13/1.64 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(powersetsubset_type,type,
% 3.13/1.64 powersetsubset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(powersetsubset,definition,
% 3.13/1.64 ( powersetsubset
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( subset @ A @ B )
% 3.13/1.64 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(sepInPowerset_type,type,
% 3.13/1.64 sepInPowerset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(sepInPowerset,definition,
% 3.13/1.64 ( sepInPowerset
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( in
% 3.13/1.64 @ ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 @ ( powerset @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(sepSubset_type,type,
% 3.13/1.64 sepSubset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(sepSubset,definition,
% 3.13/1.64 ( sepSubset
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( subset
% 3.13/1.64 @ ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 @ A ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binunion_type,type,
% 3.13/1.64 binunion: $i > $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(binunionIL_type,type,
% 3.13/1.64 binunionIL: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binunionIL,definition,
% 3.13/1.64 ( binunionIL
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(upairset2IR_type,type,
% 3.13/1.64 upairset2IR: $o ).
% 3.13/1.64
% 3.13/1.64 thf(upairset2IR,definition,
% 3.13/1.64 ( upairset2IR
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binunionIR_type,type,
% 3.13/1.64 binunionIR: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binunionIR,definition,
% 3.13/1.64 ( binunionIR
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ B )
% 3.13/1.64 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binunionEcases_type,type,
% 3.13/1.64 binunionEcases: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binunionEcases,definition,
% 3.13/1.64 ( binunionEcases
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 3.13/1.64 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.13/1.64 => ( ( ( in @ Xx @ A )
% 3.13/1.64 => Xphi )
% 3.13/1.64 => ( ( ( in @ Xx @ B )
% 3.13/1.64 => Xphi )
% 3.13/1.64 => Xphi ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binunionE_type,type,
% 3.13/1.64 binunionE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binunionE,definition,
% 3.13/1.64 ( binunionE
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 3.13/1.64 => ( ( in @ Xx @ A )
% 3.13/1.64 | ( in @ Xx @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binunionLsub_type,type,
% 3.13/1.64 binunionLsub: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binunionLsub,definition,
% 3.13/1.64 ( binunionLsub
% 3.13/1.64 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binunionRsub_type,type,
% 3.13/1.64 binunionRsub: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binunionRsub,definition,
% 3.13/1.64 ( binunionRsub
% 3.13/1.64 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binintersect_type,type,
% 3.13/1.64 binintersect: $i > $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectI_type,type,
% 3.13/1.64 binintersectI: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectI,definition,
% 3.13/1.64 ( binintersectI
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( ( in @ Xx @ B )
% 3.13/1.64 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectSubset5_type,type,
% 3.13/1.64 binintersectSubset5: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectSubset5,definition,
% 3.13/1.64 ( binintersectSubset5
% 3.13/1.64 = ( ! [A: $i,B: $i,C: $i] :
% 3.13/1.64 ( ( subset @ C @ A )
% 3.13/1.64 => ( ( subset @ C @ B )
% 3.13/1.64 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectEL_type,type,
% 3.13/1.64 binintersectEL: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectEL,definition,
% 3.13/1.64 ( binintersectEL
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.13/1.64 => ( in @ Xx @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectLsub_type,type,
% 3.13/1.64 binintersectLsub: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectLsub,definition,
% 3.13/1.64 ( binintersectLsub
% 3.13/1.64 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectSubset2_type,type,
% 3.13/1.64 binintersectSubset2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectSubset2,definition,
% 3.13/1.64 ( binintersectSubset2
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( subset @ A @ B )
% 3.13/1.64 => ( ( binintersect @ A @ B )
% 3.13/1.64 = A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectSubset3_type,type,
% 3.13/1.64 binintersectSubset3: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectSubset3,definition,
% 3.13/1.64 ( binintersectSubset3
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( ( binintersect @ A @ B )
% 3.13/1.64 = B )
% 3.13/1.64 => ( subset @ B @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectER_type,type,
% 3.13/1.64 binintersectER: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectER,definition,
% 3.13/1.64 ( binintersectER
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 3.13/1.64 => ( in @ Xx @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(disjointsetsI1_type,type,
% 3.13/1.64 disjointsetsI1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(disjointsetsI1,definition,
% 3.13/1.64 ( disjointsetsI1
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ~ ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ( in @ Xx @ B ) )
% 3.13/1.64 => ( ( binintersect @ A @ B )
% 3.13/1.64 = emptyset ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectRsub_type,type,
% 3.13/1.64 binintersectRsub: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectRsub,definition,
% 3.13/1.64 ( binintersectRsub
% 3.13/1.64 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectSubset4_type,type,
% 3.13/1.64 binintersectSubset4: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectSubset4,definition,
% 3.13/1.64 ( binintersectSubset4
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( subset @ B @ A )
% 3.13/1.64 => ( ( binintersect @ A @ B )
% 3.13/1.64 = B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectSubset1_type,type,
% 3.13/1.64 binintersectSubset1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(binintersectSubset1,definition,
% 3.13/1.64 ( binintersectSubset1
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( ( binintersect @ A @ B )
% 3.13/1.64 = A )
% 3.13/1.64 => ( subset @ A @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(bs114d_type,type,
% 3.13/1.64 bs114d: $o ).
% 3.13/1.64
% 3.13/1.64 thf(bs114d,definition,
% 3.13/1.64 ( bs114d
% 3.13/1.64 = ( ! [A: $i,B: $i,C: $i] :
% 3.13/1.64 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 3.13/1.64 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(regular_type,type,
% 3.13/1.64 regular: $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminus_type,type,
% 3.13/1.64 setminus: $i > $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(setminusI_type,type,
% 3.13/1.64 setminusI: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminusI,definition,
% 3.13/1.64 ( setminusI
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( ~ ( in @ Xx @ B )
% 3.13/1.64 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setminusEL_type,type,
% 3.13/1.64 setminusEL: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminusEL,definition,
% 3.13/1.64 ( setminusEL
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.13/1.64 => ( in @ Xx @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setminusER_type,type,
% 3.13/1.64 setminusER: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminusER,definition,
% 3.13/1.64 ( setminusER
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 3.13/1.64 => ~ ( in @ Xx @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setminusSubset2_type,type,
% 3.13/1.64 setminusSubset2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminusSubset2,definition,
% 3.13/1.64 ( setminusSubset2
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( subset @ A @ B )
% 3.13/1.64 => ( ( setminus @ A @ B )
% 3.13/1.64 = emptyset ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setminusERneg_type,type,
% 3.13/1.64 setminusERneg: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminusERneg,definition,
% 3.13/1.64 ( setminusERneg
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.13/1.64 => ( ( in @ Xx @ A )
% 3.13/1.64 => ( in @ Xx @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setminusELneg_type,type,
% 3.13/1.64 setminusELneg: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminusELneg,definition,
% 3.13/1.64 ( setminusELneg
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 3.13/1.64 => ( ~ ( in @ Xx @ B )
% 3.13/1.64 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setminusILneg_type,type,
% 3.13/1.64 setminusILneg: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminusILneg,definition,
% 3.13/1.64 ( setminusILneg
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ~ ( in @ Xx @ A )
% 3.13/1.64 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setminusIRneg_type,type,
% 3.13/1.64 setminusIRneg: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminusIRneg,definition,
% 3.13/1.64 ( setminusIRneg
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ B )
% 3.13/1.64 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setminusLsub_type,type,
% 3.13/1.64 setminusLsub: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminusLsub,definition,
% 3.13/1.64 ( setminusLsub
% 3.13/1.64 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setminusSubset1_type,type,
% 3.13/1.64 setminusSubset1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setminusSubset1,definition,
% 3.13/1.64 ( setminusSubset1
% 3.13/1.64 = ( ! [A: $i,B: $i] :
% 3.13/1.64 ( ( ( setminus @ A @ B )
% 3.13/1.64 = emptyset )
% 3.13/1.64 => ( subset @ A @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(symdiff_type,type,
% 3.13/1.64 symdiff: $i > $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(symdiffE_type,type,
% 3.13/1.64 symdiffE: $o ).
% 3.13/1.64
% 3.13/1.64 thf(symdiffE,definition,
% 3.13/1.64 ( symdiffE
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 3.13/1.64 => ! [Xphi: $o] :
% 3.13/1.64 ( ( ( in @ Xx @ A )
% 3.13/1.64 => ( ~ ( in @ Xx @ B )
% 3.13/1.64 => Xphi ) )
% 3.13/1.64 => ( ( ~ ( in @ Xx @ A )
% 3.13/1.64 => ( ( in @ Xx @ B )
% 3.13/1.64 => Xphi ) )
% 3.13/1.64 => Xphi ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(symdiffI1_type,type,
% 3.13/1.64 symdiffI1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(symdiffI1,definition,
% 3.13/1.64 ( symdiffI1
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( ~ ( in @ Xx @ B )
% 3.13/1.64 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(symdiffI2_type,type,
% 3.13/1.64 symdiffI2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(symdiffI2,definition,
% 3.13/1.64 ( symdiffI2
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ~ ( in @ Xx @ A )
% 3.13/1.64 => ( ( in @ Xx @ B )
% 3.13/1.64 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(symdiffIneg1_type,type,
% 3.13/1.64 symdiffIneg1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(symdiffIneg1,definition,
% 3.13/1.64 ( symdiffIneg1
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( ( in @ Xx @ B )
% 3.13/1.64 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(symdiffIneg2_type,type,
% 3.13/1.64 symdiffIneg2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(symdiffIneg2,definition,
% 3.13/1.64 ( symdiffIneg2
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ~ ( in @ Xx @ A )
% 3.13/1.64 => ( ~ ( in @ Xx @ B )
% 3.13/1.64 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(iskpair_type,type,
% 3.13/1.64 iskpair: $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(secondinupair_type,type,
% 3.13/1.64 secondinupair: $o ).
% 3.13/1.64
% 3.13/1.64 thf(secondinupair,definition,
% 3.13/1.64 ( secondinupair
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairIL_type,type,
% 3.13/1.64 setukpairIL: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairIL,definition,
% 3.13/1.64 ( setukpairIL
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairIR_type,type,
% 3.13/1.64 setukpairIR: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairIR,definition,
% 3.13/1.64 ( setukpairIR
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(kpairiskpair_type,type,
% 3.13/1.64 kpairiskpair: $o ).
% 3.13/1.64
% 3.13/1.64 thf(kpairiskpair,definition,
% 3.13/1.64 ( kpairiskpair
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(kpair_type,type,
% 3.13/1.64 kpair: $i > $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(kpairp_type,type,
% 3.13/1.64 kpairp: $o ).
% 3.13/1.64
% 3.13/1.64 thf(kpairp,definition,
% 3.13/1.64 ( kpairp
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprod_type,type,
% 3.13/1.64 cartprod: $i > $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(singletonsubset_type,type,
% 3.13/1.64 singletonsubset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(singletonsubset,definition,
% 3.13/1.64 ( singletonsubset
% 3.13/1.64 = ( ! [A: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(singletoninpowerset_type,type,
% 3.13/1.64 singletoninpowerset: $o ).
% 3.13/1.64
% 3.13/1.64 thf(singletoninpowerset,definition,
% 3.13/1.64 ( singletoninpowerset
% 3.13/1.64 = ( ! [A: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(singletoninpowunion_type,type,
% 3.13/1.64 singletoninpowunion: $o ).
% 3.13/1.64
% 3.13/1.64 thf(singletoninpowunion,definition,
% 3.13/1.64 ( singletoninpowunion
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(upairset2E_type,type,
% 3.13/1.64 upairset2E: $o ).
% 3.13/1.64
% 3.13/1.64 thf(upairset2E,definition,
% 3.13/1.64 ( upairset2E
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.13/1.64 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 3.13/1.64 => ( ( Xz = Xx )
% 3.13/1.64 | ( Xz = Xy ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(upairsubunion_type,type,
% 3.13/1.64 upairsubunion: $o ).
% 3.13/1.64
% 3.13/1.64 thf(upairsubunion,definition,
% 3.13/1.64 ( upairsubunion
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(upairinpowunion_type,type,
% 3.13/1.64 upairinpowunion: $o ).
% 3.13/1.64
% 3.13/1.64 thf(upairinpowunion,definition,
% 3.13/1.64 ( upairinpowunion
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(ubforcartprodlem1_type,type,
% 3.13/1.64 ubforcartprodlem1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(ubforcartprodlem1,definition,
% 3.13/1.64 ( ubforcartprodlem1
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(ubforcartprodlem2_type,type,
% 3.13/1.64 ubforcartprodlem2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(ubforcartprodlem2,definition,
% 3.13/1.64 ( ubforcartprodlem2
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(ubforcartprodlem3_type,type,
% 3.13/1.64 ubforcartprodlem3: $o ).
% 3.13/1.64
% 3.13/1.64 thf(ubforcartprodlem3,definition,
% 3.13/1.64 ( ubforcartprodlem3
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodpairin_type,type,
% 3.13/1.64 cartprodpairin: $o ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodpairin,definition,
% 3.13/1.64 ( cartprodpairin
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodmempair1_type,type,
% 3.13/1.64 cartprodmempair1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodmempair1,definition,
% 3.13/1.64 ( cartprodmempair1
% 3.13/1.64 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.13/1.64 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.13/1.64 => ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ? [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 & ( Xu
% 3.13/1.64 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodmempair_type,type,
% 3.13/1.64 cartprodmempair: $o ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodmempair,definition,
% 3.13/1.64 ( cartprodmempair
% 3.13/1.64 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.13/1.64 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.13/1.64 => ( iskpair @ Xu ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setunionE2_type,type,
% 3.13/1.64 setunionE2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setunionE2,definition,
% 3.13/1.64 ( setunionE2
% 3.13/1.64 = ( ! [A: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ ( setunion @ A ) )
% 3.13/1.64 => ? [X: $i] :
% 3.13/1.64 ( ( in @ X @ A )
% 3.13/1.64 & ( in @ Xx @ X ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setunionsingleton1_type,type,
% 3.13/1.64 setunionsingleton1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setunionsingleton1,definition,
% 3.13/1.64 ( setunionsingleton1
% 3.13/1.64 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setunionsingleton2_type,type,
% 3.13/1.64 setunionsingleton2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setunionsingleton2,definition,
% 3.13/1.64 ( setunionsingleton2
% 3.13/1.64 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setunionsingleton_type,type,
% 3.13/1.64 setunionsingleton: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setunionsingleton,definition,
% 3.13/1.64 ( setunionsingleton
% 3.13/1.64 = ( ! [Xx: $i] :
% 3.13/1.64 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 3.13/1.64 = Xx ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(singleton_type,type,
% 3.13/1.64 singleton: $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(singletonprop_type,type,
% 3.13/1.64 singletonprop: $o ).
% 3.13/1.64
% 3.13/1.64 thf(singletonprop,definition,
% 3.13/1.64 ( singletonprop
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ A )
% 3.13/1.64 => ( ( Xphi @ Xx )
% 3.13/1.64 => ( ( Xphi @ Xy )
% 3.13/1.64 => ( Xx = Xy ) ) ) ) )
% 3.13/1.64 => ( ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ( Xphi @ Xx ) )
% 3.13/1.64 => ( singleton
% 3.13/1.64 @ ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(ex1_type,type,
% 3.13/1.64 ex1: $i > ( $i > $o ) > $o ).
% 3.13/1.64
% 3.13/1.64 thf(ex1,definition,
% 3.13/1.64 ( ex1
% 3.13/1.64 = ( ^ [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( singleton
% 3.13/1.64 @ ( dsetconstr @ A
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(ex1E1_type,type,
% 3.13/1.64 ex1E1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(ex1E1,definition,
% 3.13/1.64 ( ex1E1
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( ( ex1 @ A
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.64 => ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ( Xphi @ Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(ex1I_type,type,
% 3.13/1.64 ex1I: $o ).
% 3.13/1.64
% 3.13/1.64 thf(ex1I,definition,
% 3.13/1.64 ( ex1I
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ( ( Xphi @ Xx )
% 3.13/1.64 => ( ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ A )
% 3.13/1.64 => ( ( Xphi @ Xy )
% 3.13/1.64 => ( Xy = Xx ) ) )
% 3.13/1.64 => ( ex1 @ A
% 3.13/1.64 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(ex1I2_type,type,
% 3.13/1.64 ex1I2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(ex1I2,definition,
% 3.13/1.64 ( ex1I2
% 3.13/1.64 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.64 ( ! [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ A )
% 3.13/1.64 => ( ( Xphi @ Xx )
% 3.13/1.64 => ( ( Xphi @ Xy )
% 3.13/1.64 => ( Xx = Xy ) ) ) ) )
% 3.13/1.64 => ( ? [Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 & ( Xphi @ Xx ) )
% 3.13/1.64 => ( ex1 @ A
% 3.13/1.64 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(singletonsuniq_type,type,
% 3.13/1.64 singletonsuniq: $o ).
% 3.13/1.64
% 3.13/1.64 thf(singletonsuniq,definition,
% 3.13/1.64 ( singletonsuniq
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( ( setadjoin @ Xx @ emptyset )
% 3.13/1.64 = ( setadjoin @ Xy @ emptyset ) )
% 3.13/1.64 => ( Xx = Xy ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(atmost1p_type,type,
% 3.13/1.64 atmost1p: $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(atleast2p_type,type,
% 3.13/1.64 atleast2p: $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(atmost2p_type,type,
% 3.13/1.64 atmost2p: $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(upairsetp_type,type,
% 3.13/1.64 upairsetp: $i > $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjL1_type,type,
% 3.13/1.64 setukpairinjL1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjL1,definition,
% 3.13/1.64 ( setukpairinjL1
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.13/1.64 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 3.13/1.64 => ( Xx = Xz ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(kfstsingleton_type,type,
% 3.13/1.64 kfstsingleton: $o ).
% 3.13/1.64
% 3.13/1.64 thf(kfstsingleton,definition,
% 3.13/1.64 ( kfstsingleton
% 3.13/1.64 = ( ! [Xu: $i] :
% 3.13/1.64 ( ( iskpair @ Xu )
% 3.13/1.64 => ( singleton
% 3.13/1.64 @ ( dsetconstr @ ( setunion @ Xu )
% 3.13/1.64 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(theprop_type,type,
% 3.13/1.64 theprop: $o ).
% 3.13/1.64
% 3.13/1.64 thf(theprop,definition,
% 3.13/1.64 ( theprop
% 3.13/1.64 = ( ! [X: $i] :
% 3.13/1.64 ( ( singleton @ X )
% 3.13/1.64 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(kfst_type,type,
% 3.13/1.64 kfst: $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(kfstpairEq_type,type,
% 3.13/1.64 kfstpairEq: $o ).
% 3.13/1.64
% 3.13/1.64 thf(kfstpairEq,definition,
% 3.13/1.64 ( kfstpairEq
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.13/1.64 = Xx ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodfstin_type,type,
% 3.13/1.64 cartprodfstin: $o ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodfstin,definition,
% 3.13/1.64 ( cartprodfstin
% 3.13/1.64 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.13/1.64 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.13/1.64 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjL2_type,type,
% 3.13/1.64 setukpairinjL2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjL2,definition,
% 3.13/1.64 ( setukpairinjL2
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.13/1.64 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.13/1.64 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.13/1.64 => ( Xx = Xz ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjL_type,type,
% 3.13/1.64 setukpairinjL: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjL,definition,
% 3.13/1.64 ( setukpairinjL
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.13/1.64 ( ( ( kpair @ Xx @ Xy )
% 3.13/1.64 = ( kpair @ Xz @ Xu ) )
% 3.13/1.64 => ( Xx = Xz ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjR11_type,type,
% 3.13/1.64 setukpairinjR11: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjR11,definition,
% 3.13/1.64 ( setukpairinjR11
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xx = Xy )
% 3.13/1.64 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.13/1.64 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjR12_type,type,
% 3.13/1.64 setukpairinjR12: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjR12,definition,
% 3.13/1.64 ( setukpairinjR12
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( Xx = Xy )
% 3.13/1.64 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.13/1.64 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjR1_type,type,
% 3.13/1.64 setukpairinjR1: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjR1,definition,
% 3.13/1.64 ( setukpairinjR1
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.13/1.64 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.13/1.64 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.13/1.64 => ( ( Xz = Xu )
% 3.13/1.64 => ( Xy = Xu ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(upairequniteq_type,type,
% 3.13/1.64 upairequniteq: $o ).
% 3.13/1.64
% 3.13/1.64 thf(upairequniteq,definition,
% 3.13/1.64 ( upairequniteq
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 3.13/1.64 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 3.13/1.64 = ( setadjoin @ Xz @ emptyset ) )
% 3.13/1.64 => ( Xx = Xy ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjR2_type,type,
% 3.13/1.64 setukpairinjR2: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjR2,definition,
% 3.13/1.64 ( setukpairinjR2
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.13/1.64 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 3.13/1.64 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 3.13/1.64 => ( Xy = Xu ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjR_type,type,
% 3.13/1.64 setukpairinjR: $o ).
% 3.13/1.64
% 3.13/1.64 thf(setukpairinjR,definition,
% 3.13/1.64 ( setukpairinjR
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 3.13/1.64 ( ( ( kpair @ Xx @ Xy )
% 3.13/1.64 = ( kpair @ Xz @ Xu ) )
% 3.13/1.64 => ( Xy = Xu ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(ksndsingleton_type,type,
% 3.13/1.64 ksndsingleton: $o ).
% 3.13/1.64
% 3.13/1.64 thf(ksndsingleton,definition,
% 3.13/1.64 ( ksndsingleton
% 3.13/1.64 = ( ! [Xu: $i] :
% 3.13/1.64 ( ( iskpair @ Xu )
% 3.13/1.64 => ( singleton
% 3.13/1.64 @ ( dsetconstr @ ( setunion @ Xu )
% 3.13/1.64 @ ^ [Xx: $i] :
% 3.13/1.64 ( Xu
% 3.13/1.64 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(ksnd_type,type,
% 3.13/1.64 ksnd: $i > $i ).
% 3.13/1.64
% 3.13/1.64 thf(ksndpairEq_type,type,
% 3.13/1.64 ksndpairEq: $o ).
% 3.13/1.64
% 3.13/1.64 thf(ksndpairEq,definition,
% 3.13/1.64 ( ksndpairEq
% 3.13/1.64 = ( ! [Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.13/1.64 = Xy ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(kpairsurjEq_type,type,
% 3.13/1.64 kpairsurjEq: $o ).
% 3.13/1.64
% 3.13/1.64 thf(kpairsurjEq,definition,
% 3.13/1.64 ( kpairsurjEq
% 3.13/1.64 = ( ! [Xu: $i] :
% 3.13/1.64 ( ( iskpair @ Xu )
% 3.13/1.64 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.13/1.64 = Xu ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodsndin_type,type,
% 3.13/1.64 cartprodsndin: $o ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodsndin,definition,
% 3.13/1.64 ( cartprodsndin
% 3.13/1.64 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.13/1.64 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.13/1.64 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodpairmemEL_type,type,
% 3.13/1.64 cartprodpairmemEL: $o ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodpairmemEL,definition,
% 3.13/1.64 ( cartprodpairmemEL
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.13/1.64 => ( in @ Xx @ A ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodpairmemER_type,type,
% 3.13/1.64 cartprodpairmemER: $o ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodpairmemER,definition,
% 3.13/1.64 ( cartprodpairmemER
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
% 3.13/1.64 ( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
% 3.13/1.64 => ( in @ Xy @ B ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodmempaircEq_type,type,
% 3.13/1.64 cartprodmempaircEq: $o ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodmempaircEq,definition,
% 3.13/1.64 ( cartprodmempaircEq
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 => ( ( kpair @ Xx @ Xy )
% 3.13/1.64 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodfstpairEq_type,type,
% 3.13/1.64 cartprodfstpairEq: $o ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodfstpairEq,definition,
% 3.13/1.64 ( cartprodfstpairEq
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 => ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 3.13/1.64 = Xx ) ) ) ) ) ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodsndpairEq_type,type,
% 3.13/1.64 cartprodsndpairEq: $o ).
% 3.13/1.64
% 3.13/1.64 thf(cartprodsndpairEq,definition,
% 3.13/1.64 ( cartprodsndpairEq
% 3.13/1.64 = ( ! [A: $i,B: $i,Xx: $i] :
% 3.13/1.64 ( ( in @ Xx @ A )
% 3.13/1.64 => ! [Xy: $i] :
% 3.13/1.64 ( ( in @ Xy @ B )
% 3.13/1.64 => ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 3.13/1.64 = Xy ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(cartprodpairsurjEq_type,type,
% 3.13/1.65 cartprodpairsurjEq: $o ).
% 3.13/1.65
% 3.13/1.65 thf(cartprodpairsurjEq,definition,
% 3.13/1.65 ( cartprodpairsurjEq
% 3.13/1.65 = ( ! [A: $i,B: $i,Xu: $i] :
% 3.13/1.65 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 3.13/1.65 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 3.13/1.65 = Xu ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(breln_type,type,
% 3.13/1.65 breln: $i > $i > $i > $o ).
% 3.13/1.65
% 3.13/1.65 thf(breln,definition,
% 3.13/1.65 ( breln
% 3.13/1.65 = ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstr_type,type,
% 3.13/1.65 dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrI_type,type,
% 3.13/1.65 dpsetconstrI: $o ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrI,definition,
% 3.13/1.65 ( dpsetconstrI
% 3.13/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ B )
% 3.13/1.65 => ( ( Xphi @ Xx @ Xy )
% 3.13/1.65 => ( in @ ( kpair @ Xx @ Xy )
% 3.13/1.65 @ ( dpsetconstr @ A @ B
% 3.13/1.65 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrSub_type,type,
% 3.13/1.65 dpsetconstrSub: $o ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrSub,definition,
% 3.13/1.65 ( dpsetconstrSub
% 3.13/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.13/1.65 ( subset
% 3.13/1.65 @ ( dpsetconstr @ A @ B
% 3.13/1.65 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
% 3.13/1.65 @ ( cartprod @ A @ B ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(setOfPairsIsBReln_type,type,
% 3.13/1.65 setOfPairsIsBReln: $o ).
% 3.13/1.65
% 3.13/1.65 thf(setOfPairsIsBReln,definition,
% 3.13/1.65 ( setOfPairsIsBReln
% 3.13/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
% 3.13/1.65 ( breln @ A @ B
% 3.13/1.65 @ ( dpsetconstr @ A @ B
% 3.13/1.65 @ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrERa_type,type,
% 3.13/1.65 dpsetconstrERa: $o ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrERa,definition,
% 3.13/1.65 ( dpsetconstrERa
% 3.13/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ B )
% 3.13/1.65 => ( ( in @ ( kpair @ Xx @ Xy )
% 3.13/1.65 @ ( dpsetconstr @ A @ B
% 3.13/1.65 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.13/1.65 => ( Xphi @ Xx @ Xy ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrEL1_type,type,
% 3.13/1.65 dpsetconstrEL1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrEL1,definition,
% 3.13/1.65 ( dpsetconstrEL1
% 3.13/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.13/1.65 ( ( in @ ( kpair @ Xx @ Xy )
% 3.13/1.65 @ ( dpsetconstr @ A @ B
% 3.13/1.65 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.13/1.65 => ( in @ Xx @ A ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrEL2_type,type,
% 3.13/1.65 dpsetconstrEL2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrEL2,definition,
% 3.13/1.65 ( dpsetconstrEL2
% 3.13/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.13/1.65 ( ( in @ ( kpair @ Xx @ Xy )
% 3.13/1.65 @ ( dpsetconstr @ A @ B
% 3.13/1.65 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.13/1.65 => ( in @ Xy @ B ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrER_type,type,
% 3.13/1.65 dpsetconstrER: $o ).
% 3.13/1.65
% 3.13/1.65 thf(dpsetconstrER,definition,
% 3.13/1.65 ( dpsetconstrER
% 3.13/1.65 = ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
% 3.13/1.65 ( ( in @ ( kpair @ Xx @ Xy )
% 3.13/1.65 @ ( dpsetconstr @ A @ B
% 3.13/1.65 @ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
% 3.13/1.65 => ( Xphi @ Xx @ Xy ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(func_type,type,
% 3.13/1.65 func: $i > $i > $i > $o ).
% 3.13/1.65
% 3.13/1.65 thf(funcSet_type,type,
% 3.13/1.65 funcSet: $i > $i > $i ).
% 3.13/1.65
% 3.13/1.65 thf(funcImageSingleton_type,type,
% 3.13/1.65 funcImageSingleton: $o ).
% 3.13/1.65
% 3.13/1.65 thf(funcImageSingleton,definition,
% 3.13/1.65 ( funcImageSingleton
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xf )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( singleton
% 3.13/1.65 @ ( dsetconstr @ B
% 3.13/1.65 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(apProp_type,type,
% 3.13/1.65 apProp: $o ).
% 3.13/1.65
% 3.13/1.65 thf(apProp,definition,
% 3.13/1.65 ( apProp
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xf )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in
% 3.13/1.65 @ ( setunion
% 3.13/1.65 @ ( dsetconstr @ B
% 3.13/1.65 @ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
% 3.13/1.65 @ B ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(ap_type,type,
% 3.13/1.65 ap: $i > $i > $i > $i > $i ).
% 3.13/1.65
% 3.13/1.65 thf(app_type,type,
% 3.13/1.65 app: $o ).
% 3.13/1.65
% 3.13/1.65 thf(app,definition,
% 3.13/1.65 ( app
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xf )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(infuncsetfunc_type,type,
% 3.13/1.65 infuncsetfunc: $o ).
% 3.13/1.65
% 3.13/1.65 thf(infuncsetfunc,definition,
% 3.13/1.65 ( infuncsetfunc
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.13/1.65 => ( func @ A @ B @ Xf ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(ap2p_type,type,
% 3.13/1.65 ap2p: $o ).
% 3.13/1.65
% 3.13/1.65 thf(ap2p,definition,
% 3.13/1.65 ( ap2p
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(funcinfuncset_type,type,
% 3.13/1.65 funcinfuncset: $o ).
% 3.13/1.65
% 3.13/1.65 thf(funcinfuncset,definition,
% 3.13/1.65 ( funcinfuncset
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xf )
% 3.13/1.65 => ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(lamProp_type,type,
% 3.13/1.65 lamProp: $o ).
% 3.13/1.65
% 3.13/1.65 thf(lamProp,definition,
% 3.13/1.65 ( lamProp
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.13/1.65 ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.13/1.65 => ( func @ A @ B
% 3.13/1.65 @ ( dpsetconstr @ A @ B
% 3.13/1.65 @ ^ [Xx: $i,Xy: $i] :
% 3.13/1.65 ( ( Xf @ Xx )
% 3.13/1.65 = Xy ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(lam_type,type,
% 3.13/1.65 lam: $i > $i > ( $i > $i ) > $i ).
% 3.13/1.65
% 3.13/1.65 thf(lamp_type,type,
% 3.13/1.65 lamp: $o ).
% 3.13/1.65
% 3.13/1.65 thf(lamp,definition,
% 3.13/1.65 ( lamp
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.13/1.65 ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.13/1.65 => ( func @ A @ B
% 3.13/1.65 @ ( lam @ A @ B
% 3.13/1.65 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(lam2p_type,type,
% 3.13/1.65 lam2p: $o ).
% 3.13/1.65
% 3.13/1.65 thf(lam2p,definition,
% 3.13/1.65 ( lam2p
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.13/1.65 ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.13/1.65 => ( in
% 3.13/1.65 @ ( lam @ A @ B
% 3.13/1.65 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.13/1.65 @ ( funcSet @ A @ B ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(brelnall1_type,type,
% 3.13/1.65 brelnall1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(brelnall1,definition,
% 3.13/1.65 ( brelnall1
% 3.13/1.65 = ( ! [A: $i,B: $i,R: $i] :
% 3.13/1.65 ( ( breln @ A @ B @ R )
% 3.13/1.65 => ! [Xphi: $i > $o] :
% 3.13/1.65 ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ B )
% 3.13/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.13/1.65 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ R )
% 3.13/1.65 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(brelnall2_type,type,
% 3.13/1.65 brelnall2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(brelnall2,definition,
% 3.13/1.65 ( brelnall2
% 3.13/1.65 = ( ! [A: $i,B: $i,R: $i] :
% 3.13/1.65 ( ( breln @ A @ B @ R )
% 3.13/1.65 => ! [Xphi: $i > $o] :
% 3.13/1.65 ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ B )
% 3.13/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.13/1.65 => ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ R )
% 3.13/1.65 => ( Xphi @ Xx ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(ex1E2_type,type,
% 3.13/1.65 ex1E2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(ex1E2,definition,
% 3.13/1.65 ( ex1E2
% 3.13/1.65 = ( ! [A: $i,Xphi: $i > $o] :
% 3.13/1.65 ( ( ex1 @ A
% 3.13/1.65 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ A )
% 3.13/1.65 => ( ( Xphi @ Xx )
% 3.13/1.65 => ( ( Xphi @ Xy )
% 3.13/1.65 => ( Xx = Xy ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(funcGraphProp1_type,type,
% 3.13/1.65 funcGraphProp1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(funcGraphProp1,definition,
% 3.13/1.65 ( funcGraphProp1
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xf )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(funcGraphProp3_type,type,
% 3.13/1.65 funcGraphProp3: $o ).
% 3.13/1.65
% 3.13/1.65 thf(funcGraphProp3,definition,
% 3.13/1.65 ( funcGraphProp3
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(funcGraphProp2_type,type,
% 3.13/1.65 funcGraphProp2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(funcGraphProp2,definition,
% 3.13/1.65 ( funcGraphProp2
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xf )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ B )
% 3.13/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.13/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.13/1.65 = Xy ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(funcextLem_type,type,
% 3.13/1.65 funcextLem: $o ).
% 3.13/1.65
% 3.13/1.65 thf(funcextLem,definition,
% 3.13/1.65 ( funcextLem
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xf )
% 3.13/1.65 => ! [Xg: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xg )
% 3.13/1.65 => ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.13/1.65 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ B )
% 3.13/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
% 3.13/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(funcGraphProp4_type,type,
% 3.13/1.65 funcGraphProp4: $o ).
% 3.13/1.65
% 3.13/1.65 thf(funcGraphProp4,definition,
% 3.13/1.65 ( funcGraphProp4
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ B )
% 3.13/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
% 3.13/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.13/1.65 = Xy ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(subbreln_type,type,
% 3.13/1.65 subbreln: $o ).
% 3.13/1.65
% 3.13/1.65 thf(subbreln,definition,
% 3.13/1.65 ( subbreln
% 3.13/1.65 = ( ! [A: $i,B: $i,R: $i] :
% 3.13/1.65 ( ( breln @ A @ B @ R )
% 3.13/1.65 => ! [S: $i] :
% 3.13/1.65 ( ( breln @ A @ B @ S )
% 3.13/1.65 => ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ B )
% 3.13/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.13/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.13/1.65 => ( subset @ R @ S ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(eqbreln_type,type,
% 3.13/1.65 eqbreln: $o ).
% 3.13/1.65
% 3.13/1.65 thf(eqbreln,definition,
% 3.13/1.65 ( eqbreln
% 3.13/1.65 = ( ! [A: $i,B: $i,R: $i] :
% 3.13/1.65 ( ( breln @ A @ B @ R )
% 3.13/1.65 => ! [S: $i] :
% 3.13/1.65 ( ( breln @ A @ B @ S )
% 3.13/1.65 => ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ B )
% 3.13/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ R )
% 3.13/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
% 3.13/1.65 => ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ B )
% 3.13/1.65 => ( ( in @ ( kpair @ Xx @ Xy ) @ S )
% 3.13/1.65 => ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
% 3.13/1.65 => ( R = S ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(funcext_type,type,
% 3.13/1.65 funcext: $o ).
% 3.13/1.65
% 3.13/1.65 thf(funcext,definition,
% 3.13/1.65 ( funcext
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xf )
% 3.13/1.65 => ! [Xg: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xg )
% 3.13/1.65 => ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.13/1.65 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.13/1.65 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(funcext2_type,type,
% 3.13/1.65 funcext2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(funcext2,definition,
% 3.13/1.65 ( funcext2
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.13/1.65 => ! [Xg: $i] :
% 3.13/1.65 ( ( in @ Xg @ ( funcSet @ A @ B ) )
% 3.13/1.65 => ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.13/1.65 = ( ap @ A @ B @ Xg @ Xx ) ) )
% 3.13/1.65 => ( Xf = Xg ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(ap2apEq1_type,type,
% 3.13/1.65 ap2apEq1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(ap2apEq1,definition,
% 3.13/1.65 ( ap2apEq1
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.13/1.65 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(ap2apEq2_type,type,
% 3.13/1.65 ap2apEq2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(ap2apEq2,definition,
% 3.13/1.65 ( ap2apEq2
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xf )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( ap @ A @ B @ Xf @ Xx )
% 3.13/1.65 = ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(beta1_type,type,
% 3.13/1.65 beta1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(beta1,definition,
% 3.13/1.65 ( beta1
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.13/1.65 ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( ap @ A @ B
% 3.13/1.65 @ ( lam @ A @ B
% 3.13/1.65 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.13/1.65 @ Xx )
% 3.13/1.65 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(eta1_type,type,
% 3.13/1.65 eta1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(eta1,definition,
% 3.13/1.65 ( eta1
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( func @ A @ B @ Xf )
% 3.13/1.65 => ( ( lam @ A @ B
% 3.13/1.65 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.13/1.65 = Xf ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(lam2lamEq_type,type,
% 3.13/1.65 lam2lamEq: $o ).
% 3.13/1.65
% 3.13/1.65 thf(lam2lamEq,definition,
% 3.13/1.65 ( lam2lamEq
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.13/1.65 ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.13/1.65 => ( ( lam @ A @ B
% 3.13/1.65 @ ^ [Xx: $i] : ( Xf @ Xx ) )
% 3.13/1.65 = ( lam @ A @ B
% 3.13/1.65 @ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(beta2_type,type,
% 3.13/1.65 beta2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(beta2,definition,
% 3.13/1.65 ( beta2
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i > $i] :
% 3.13/1.65 ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( in @ ( Xf @ Xx ) @ B ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( ap @ A @ B
% 3.13/1.65 @ ( lam @ A @ B
% 3.13/1.65 @ ^ [Xy: $i] : ( Xf @ Xy ) )
% 3.13/1.65 @ Xx )
% 3.13/1.65 = ( Xf @ Xx ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(eta2_type,type,
% 3.13/1.65 eta2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(eta2,definition,
% 3.13/1.65 ( eta2
% 3.13/1.65 = ( ! [A: $i,B: $i,Xf: $i] :
% 3.13/1.65 ( ( in @ Xf @ ( funcSet @ A @ B ) )
% 3.13/1.65 => ( ( lam @ A @ B
% 3.13/1.65 @ ^ [Xx: $i] : ( ap @ A @ B @ Xf @ Xx ) )
% 3.13/1.65 = Xf ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(iffalseProp1_type,type,
% 3.13/1.65 iffalseProp1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(iffalseProp1,definition,
% 3.13/1.65 ( iffalseProp1
% 3.13/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ A )
% 3.13/1.65 => ( ~ Xphi
% 3.13/1.65 => ( in @ Xy
% 3.13/1.65 @ ( dsetconstr @ A
% 3.13/1.65 @ ^ [Xz: $i] :
% 3.13/1.65 ( ( Xphi
% 3.13/1.65 & ( Xz = Xx ) )
% 3.13/1.65 | ( ~ Xphi
% 3.13/1.65 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(iffalseProp2_type,type,
% 3.13/1.65 iffalseProp2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(iffalseProp2,definition,
% 3.13/1.65 ( iffalseProp2
% 3.13/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ A )
% 3.13/1.65 => ( ~ Xphi
% 3.13/1.65 => ( ( dsetconstr @ A
% 3.13/1.65 @ ^ [Xz: $i] :
% 3.13/1.65 ( ( Xphi
% 3.13/1.65 & ( Xz = Xx ) )
% 3.13/1.65 | ( ~ Xphi
% 3.13/1.65 & ( Xz = Xy ) ) ) )
% 3.13/1.65 = ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(iftrueProp1_type,type,
% 3.13/1.65 iftrueProp1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(iftrueProp1,definition,
% 3.13/1.65 ( iftrueProp1
% 3.13/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ A )
% 3.13/1.65 => ( Xphi
% 3.13/1.65 => ( in @ Xx
% 3.13/1.65 @ ( dsetconstr @ A
% 3.13/1.65 @ ^ [Xz: $i] :
% 3.13/1.65 ( ( Xphi
% 3.13/1.65 & ( Xz = Xx ) )
% 3.13/1.65 | ( ~ Xphi
% 3.13/1.65 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(iftrueProp2_type,type,
% 3.13/1.65 iftrueProp2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(iftrueProp2,definition,
% 3.13/1.65 ( iftrueProp2
% 3.13/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ A )
% 3.13/1.65 => ( Xphi
% 3.13/1.65 => ( ( dsetconstr @ A
% 3.13/1.65 @ ^ [Xz: $i] :
% 3.13/1.65 ( ( Xphi
% 3.13/1.65 & ( Xz = Xx ) )
% 3.13/1.65 | ( ~ Xphi
% 3.13/1.65 & ( Xz = Xy ) ) ) )
% 3.13/1.65 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(ifSingleton_type,type,
% 3.13/1.65 ifSingleton: $o ).
% 3.13/1.65
% 3.13/1.65 thf(ifSingleton,definition,
% 3.13/1.65 ( ifSingleton
% 3.13/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ A )
% 3.13/1.65 => ( singleton
% 3.13/1.65 @ ( dsetconstr @ A
% 3.13/1.65 @ ^ [Xz: $i] :
% 3.13/1.65 ( ( Xphi
% 3.13/1.65 & ( Xz = Xx ) )
% 3.13/1.65 | ( ~ Xphi
% 3.13/1.65 & ( Xz = Xy ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(if_type,type,
% 3.13/1.65 if: $i > $o > $i > $i > $i ).
% 3.13/1.65
% 3.13/1.65 thf(ifp_type,type,
% 3.13/1.65 ifp: $o ).
% 3.13/1.65
% 3.13/1.65 thf(ifp,definition,
% 3.13/1.65 ( ifp
% 3.13/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ A )
% 3.13/1.65 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ A ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(theeq_type,type,
% 3.13/1.65 theeq: $o ).
% 3.13/1.65
% 3.13/1.65 thf(theeq,definition,
% 3.13/1.65 ( theeq
% 3.13/1.65 = ( ! [X: $i] :
% 3.13/1.65 ( ( singleton @ X )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ X )
% 3.13/1.65 => ( ( setunion @ X )
% 3.13/1.65 = Xx ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(iftrue_type,type,
% 3.13/1.65 iftrue: $o ).
% 3.13/1.65
% 3.13/1.65 thf(iftrue,definition,
% 3.13/1.65 ( iftrue
% 3.13/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ A )
% 3.13/1.65 => ( Xphi
% 3.13/1.65 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.13/1.65 = Xx ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(iffalse_type,type,
% 3.13/1.65 iffalse: $o ).
% 3.13/1.65
% 3.13/1.65 thf(iffalse,definition,
% 3.13/1.65 ( iffalse
% 3.13/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ A )
% 3.13/1.65 => ( ~ Xphi
% 3.13/1.65 => ( ( if @ A @ Xphi @ Xx @ Xy )
% 3.13/1.65 = Xy ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(iftrueorfalse_type,type,
% 3.13/1.65 iftrueorfalse: $o ).
% 3.13/1.65
% 3.13/1.65 thf(iftrueorfalse,definition,
% 3.13/1.65 ( iftrueorfalse
% 3.13/1.65 = ( ! [A: $i,Xphi: $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ! [Xy: $i] :
% 3.13/1.65 ( ( in @ Xy @ A )
% 3.13/1.65 => ( in @ ( if @ A @ Xphi @ Xx @ Xy ) @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(binintersectT_lem_type,type,
% 3.13/1.65 binintersectT_lem: $o ).
% 3.13/1.65
% 3.13/1.65 thf(binintersectT_lem,definition,
% 3.13/1.65 ( binintersectT_lem
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(binunionT_lem_type,type,
% 3.13/1.65 binunionT_lem: $o ).
% 3.13/1.65
% 3.13/1.65 thf(binunionT_lem,definition,
% 3.13/1.65 ( binunionT_lem
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( in @ ( binunion @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(powersetT_lem_type,type,
% 3.13/1.65 powersetT_lem: $o ).
% 3.13/1.65
% 3.13/1.65 thf(powersetT_lem,definition,
% 3.13/1.65 ( powersetT_lem
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ( in @ ( powerset @ X ) @ ( powerset @ ( powerset @ A ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(setminusT_lem_type,type,
% 3.13/1.65 setminusT_lem: $o ).
% 3.13/1.65
% 3.13/1.65 thf(setminusT_lem,definition,
% 3.13/1.65 ( setminusT_lem
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( in @ ( setminus @ X @ Y ) @ ( powerset @ A ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(complementT_lem_type,type,
% 3.13/1.65 complementT_lem: $o ).
% 3.13/1.65
% 3.13/1.65 thf(complementT_lem,definition,
% 3.13/1.65 ( complementT_lem
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ( in @ ( setminus @ A @ X ) @ ( powerset @ A ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(setextT_type,type,
% 3.13/1.65 setextT: $o ).
% 3.13/1.65
% 3.13/1.65 thf(setextT,definition,
% 3.13/1.65 ( setextT
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ X )
% 3.13/1.65 => ( in @ Xx @ Y ) ) )
% 3.13/1.65 => ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ Y )
% 3.13/1.65 => ( in @ Xx @ X ) ) )
% 3.13/1.65 => ( X = Y ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(subsetTI_type,type,
% 3.13/1.65 subsetTI: $o ).
% 3.13/1.65
% 3.13/1.65 thf(subsetTI,definition,
% 3.13/1.65 ( subsetTI
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ X )
% 3.13/1.65 => ( in @ Xx @ Y ) ) )
% 3.13/1.65 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(powersetTI1_type,type,
% 3.13/1.65 powersetTI1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(powersetTI1,definition,
% 3.13/1.65 ( powersetTI1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ X )
% 3.13/1.65 => ( in @ Xx @ Y ) ) )
% 3.13/1.65 => ( in @ X @ ( powerset @ Y ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(powersetTE1_type,type,
% 3.13/1.65 powersetTE1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(powersetTE1,definition,
% 3.13/1.65 ( powersetTE1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ X @ ( powerset @ Y ) )
% 3.13/1.65 => ( ( in @ Xx @ X )
% 3.13/1.65 => ( in @ Xx @ Y ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(complementTI1_type,type,
% 3.13/1.65 complementTI1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(complementTI1,definition,
% 3.13/1.65 ( complementTI1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ X )
% 3.13/1.65 => ~ ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(complementTE1_type,type,
% 3.13/1.65 complementTE1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(complementTE1,definition,
% 3.13/1.65 ( complementTE1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ~ ( in @ Xx @ ( setminus @ A @ X ) )
% 3.13/1.65 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(binintersectTELcontra_type,type,
% 3.13/1.65 binintersectTELcontra: $o ).
% 3.13/1.65
% 3.13/1.65 thf(binintersectTELcontra,definition,
% 3.13/1.65 ( binintersectTELcontra
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ~ ( in @ Xx @ X )
% 3.13/1.65 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(binintersectTERcontra_type,type,
% 3.13/1.65 binintersectTERcontra: $o ).
% 3.13/1.65
% 3.13/1.65 thf(binintersectTERcontra,definition,
% 3.13/1.65 ( binintersectTERcontra
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ~ ( in @ Xx @ Y )
% 3.13/1.65 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(contrasubsetT_type,type,
% 3.13/1.65 contrasubsetT: $o ).
% 3.13/1.65
% 3.13/1.65 thf(contrasubsetT,definition,
% 3.13/1.65 ( contrasubsetT
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.13/1.65 => ( ( in @ Xx @ Y )
% 3.13/1.65 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(contrasubsetT1_type,type,
% 3.13/1.65 contrasubsetT1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(contrasubsetT1,definition,
% 3.13/1.65 ( contrasubsetT1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( subset @ X @ Y )
% 3.13/1.65 => ( ~ ( in @ Xx @ Y )
% 3.13/1.65 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(contrasubsetT2_type,type,
% 3.13/1.65 contrasubsetT2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(contrasubsetT2,definition,
% 3.13/1.65 ( contrasubsetT2
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( ( subset @ X @ Y )
% 3.13/1.65 => ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(contrasubsetT3_type,type,
% 3.13/1.65 contrasubsetT3: $o ).
% 3.13/1.65
% 3.13/1.65 thf(contrasubsetT3,definition,
% 3.13/1.65 ( contrasubsetT3
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( ( subset @ ( setminus @ A @ Y ) @ ( setminus @ A @ X ) )
% 3.13/1.65 => ( subset @ X @ Y ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(doubleComplementI1_type,type,
% 3.13/1.65 doubleComplementI1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(doubleComplementI1,definition,
% 3.13/1.65 ( doubleComplementI1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ X )
% 3.13/1.65 => ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(doubleComplementE1_type,type,
% 3.13/1.65 doubleComplementE1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(doubleComplementE1,definition,
% 3.13/1.65 ( doubleComplementE1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( setminus @ A @ X ) ) )
% 3.13/1.65 => ( in @ Xx @ X ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(doubleComplementSub1_type,type,
% 3.13/1.65 doubleComplementSub1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(doubleComplementSub1,definition,
% 3.13/1.65 ( doubleComplementSub1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ( subset @ X @ ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(doubleComplementSub2_type,type,
% 3.13/1.65 doubleComplementSub2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(doubleComplementSub2,definition,
% 3.13/1.65 ( doubleComplementSub2
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ( subset @ ( setminus @ A @ ( setminus @ A @ X ) ) @ X ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(doubleComplementEq_type,type,
% 3.13/1.65 doubleComplementEq: $o ).
% 3.13/1.65
% 3.13/1.65 thf(doubleComplementEq,definition,
% 3.13/1.65 ( doubleComplementEq
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ( X
% 3.13/1.65 = ( setminus @ A @ ( setminus @ A @ X ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(complementTnotintersectT_type,type,
% 3.13/1.65 complementTnotintersectT: $o ).
% 3.13/1.65
% 3.13/1.65 thf(complementTnotintersectT,definition,
% 3.13/1.65 ( complementTnotintersectT
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.13/1.65 => ~ ( in @ Xx @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(complementImpComplementIntersect_type,type,
% 3.13/1.65 complementImpComplementIntersect: $o ).
% 3.13/1.65
% 3.13/1.65 thf(complementImpComplementIntersect,definition,
% 3.13/1.65 ( complementImpComplementIntersect
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.13/1.65 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(complementSubsetComplementIntersect_type,type,
% 3.13/1.65 complementSubsetComplementIntersect: $o ).
% 3.13/1.65
% 3.13/1.65 thf(complementSubsetComplementIntersect,definition,
% 3.13/1.65 ( complementSubsetComplementIntersect
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( subset @ ( setminus @ A @ X ) @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(complementInPowersetComplementIntersect_type,type,
% 3.13/1.65 complementInPowersetComplementIntersect: $o ).
% 3.13/1.65
% 3.13/1.65 thf(complementInPowersetComplementIntersect,definition,
% 3.13/1.65 ( complementInPowersetComplementIntersect
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( in @ ( setminus @ A @ X ) @ ( powerset @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(contraSubsetComplement_type,type,
% 3.13/1.65 contraSubsetComplement: $o ).
% 3.13/1.65
% 3.13/1.65 thf(contraSubsetComplement,definition,
% 3.13/1.65 ( contraSubsetComplement
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ Y )
% 3.13/1.65 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(complementTcontraSubset_type,type,
% 3.13/1.65 complementTcontraSubset: $o ).
% 3.13/1.65
% 3.13/1.65 thf(complementTcontraSubset,definition,
% 3.13/1.65 ( complementTcontraSubset
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( ( subset @ X @ ( setminus @ A @ Y ) )
% 3.13/1.65 => ( subset @ Y @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(binunionTILcontra_type,type,
% 3.13/1.65 binunionTILcontra: $o ).
% 3.13/1.65
% 3.13/1.65 thf(binunionTILcontra,definition,
% 3.13/1.65 ( binunionTILcontra
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.13/1.65 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(binunionTIRcontra_type,type,
% 3.13/1.65 binunionTIRcontra: $o ).
% 3.13/1.65
% 3.13/1.65 thf(binunionTIRcontra,definition,
% 3.13/1.65 ( binunionTIRcontra
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ~ ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.13/1.65 => ~ ( in @ Xx @ Y ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(inIntersectImpInUnion_type,type,
% 3.13/1.65 inIntersectImpInUnion: $o ).
% 3.13/1.65
% 3.13/1.65 thf(inIntersectImpInUnion,definition,
% 3.13/1.65 ( inIntersectImpInUnion
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Z: $i] :
% 3.13/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.13/1.65 => ( in @ Xx @ ( binunion @ X @ Z ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(inIntersectImpInUnion2_type,type,
% 3.13/1.65 inIntersectImpInUnion2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(inIntersectImpInUnion2,definition,
% 3.13/1.65 ( inIntersectImpInUnion2
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Z: $i] :
% 3.13/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.13/1.65 => ( in @ Xx @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(inIntersectImpInIntersectUnions_type,type,
% 3.13/1.65 inIntersectImpInIntersectUnions: $o ).
% 3.13/1.65
% 3.13/1.65 thf(inIntersectImpInIntersectUnions,definition,
% 3.13/1.65 ( inIntersectImpInIntersectUnions
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Z: $i] :
% 3.13/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.13/1.65 => ( in @ Xx @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(intersectInPowersetIntersectUnions_type,type,
% 3.13/1.65 intersectInPowersetIntersectUnions: $o ).
% 3.13/1.65
% 3.13/1.65 thf(intersectInPowersetIntersectUnions,definition,
% 3.13/1.65 ( intersectInPowersetIntersectUnions
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Z: $i] :
% 3.13/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.13/1.65 => ( in @ ( binintersect @ X @ Y ) @ ( powerset @ ( binintersect @ ( binunion @ X @ Z ) @ ( binunion @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(inComplementUnionImpNotIn1_type,type,
% 3.13/1.65 inComplementUnionImpNotIn1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(inComplementUnionImpNotIn1,definition,
% 3.13/1.65 ( inComplementUnionImpNotIn1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.13/1.65 => ~ ( in @ Xx @ X ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(inComplementUnionImpInComplement1_type,type,
% 3.13/1.65 inComplementUnionImpInComplement1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(inComplementUnionImpInComplement1,definition,
% 3.13/1.65 ( inComplementUnionImpInComplement1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.13/1.65 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(binunionTE_type,type,
% 3.13/1.65 binunionTE: $o ).
% 3.13/1.65
% 3.13/1.65 thf(binunionTE,definition,
% 3.13/1.65 ( binunionTE
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xphi: $o,Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( binunion @ X @ Y ) )
% 3.13/1.65 => ( ( ( in @ Xx @ X )
% 3.13/1.65 => Xphi )
% 3.13/1.65 => ( ( ( in @ Xx @ Y )
% 3.13/1.65 => Xphi )
% 3.13/1.65 => Xphi ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(binunionTEcontra_type,type,
% 3.13/1.65 binunionTEcontra: $o ).
% 3.13/1.65
% 3.13/1.65 thf(binunionTEcontra,definition,
% 3.13/1.65 ( binunionTEcontra
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ~ ( in @ Xx @ X )
% 3.13/1.65 => ( ~ ( in @ Xx @ Y )
% 3.13/1.65 => ~ ( in @ Xx @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2a1_type,type,
% 3.13/1.65 demorgan2a1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2a1,definition,
% 3.13/1.65 ( demorgan2a1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.13/1.65 => ( in @ Xx @ ( setminus @ A @ X ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(complementUnionInPowersetComplement_type,type,
% 3.13/1.65 complementUnionInPowersetComplement: $o ).
% 3.13/1.65
% 3.13/1.65 thf(complementUnionInPowersetComplement,definition,
% 3.13/1.65 ( complementUnionInPowersetComplement
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( in @ ( setminus @ A @ ( binunion @ X @ Y ) ) @ ( powerset @ ( setminus @ A @ X ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2a2_type,type,
% 3.13/1.65 demorgan2a2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2a2,definition,
% 3.13/1.65 ( demorgan2a2
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.13/1.65 => ( in @ Xx @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan1a_type,type,
% 3.13/1.65 demorgan1a: $o ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan1a,definition,
% 3.13/1.65 ( demorgan1a
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) )
% 3.13/1.65 => ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan1b_type,type,
% 3.13/1.65 demorgan1b: $o ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan1b,definition,
% 3.13/1.65 ( demorgan1b
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.13/1.65 => ( in @ Xx @ ( setminus @ A @ ( binintersect @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan1_type,type,
% 3.13/1.65 demorgan1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan1,definition,
% 3.13/1.65 ( demorgan1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( ( setminus @ A @ ( binintersect @ X @ Y ) )
% 3.13/1.65 = ( binunion @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2a_type,type,
% 3.13/1.65 demorgan2a: $o ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2a,definition,
% 3.13/1.65 ( demorgan2a
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) )
% 3.13/1.65 => ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2b2_type,type,
% 3.13/1.65 demorgan2b2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2b2,definition,
% 3.13/1.65 ( demorgan2b2
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ X ) )
% 3.13/1.65 => ( ( in @ Xx @ ( setminus @ A @ Y ) )
% 3.13/1.65 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2b_type,type,
% 3.13/1.65 demorgan2b: $o ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2b,definition,
% 3.13/1.65 ( demorgan2b
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ A )
% 3.13/1.65 => ( ( in @ Xx @ ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) )
% 3.13/1.65 => ( in @ Xx @ ( setminus @ A @ ( binunion @ X @ Y ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2_type,type,
% 3.13/1.65 demorgan2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(demorgan2,definition,
% 3.13/1.65 ( demorgan2
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ( ( setminus @ A @ ( binunion @ X @ Y ) )
% 3.13/1.65 = ( binintersect @ ( setminus @ A @ X ) @ ( setminus @ A @ Y ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(woz13rule0_type,type,
% 3.13/1.65 woz13rule0: $o ).
% 3.13/1.65
% 3.13/1.65 thf(woz13rule0,definition,
% 3.13/1.65 ( woz13rule0
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Xx: $i] :
% 3.13/1.65 ( ( in @ Xx @ ( binintersect @ X @ Y ) )
% 3.13/1.65 => ( in @ Xx @ A ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(woz13rule1_type,type,
% 3.13/1.65 woz13rule1: $o ).
% 3.13/1.65
% 3.13/1.65 thf(woz13rule1,definition,
% 3.13/1.65 ( woz13rule1
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Z: $i] :
% 3.13/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.13/1.65 => ( ( subset @ X @ Z )
% 3.13/1.65 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(woz13rule2_type,type,
% 3.13/1.65 woz13rule2: $o ).
% 3.13/1.65
% 3.13/1.65 thf(woz13rule2,definition,
% 3.13/1.65 ( woz13rule2
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Z: $i] :
% 3.13/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.13/1.65 => ( ( subset @ Y @ Z )
% 3.13/1.65 => ( subset @ ( binintersect @ X @ Y ) @ Z ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(woz13rule3_type,type,
% 3.13/1.65 woz13rule3: $o ).
% 3.13/1.65
% 3.13/1.65 thf(woz13rule3,definition,
% 3.13/1.65 ( woz13rule3
% 3.13/1.65 = ( ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Z: $i] :
% 3.13/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.13/1.65 => ( ( subset @ X @ Y )
% 3.13/1.65 => ( ( subset @ X @ Z )
% 3.13/1.65 => ( subset @ X @ ( binintersect @ Y @ Z ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65
% 3.13/1.65 thf(woz13rule4,conjecture,
% 3.13/1.65 ( setextAx
% 3.13/1.65 => ( emptysetAx
% 3.13/1.65 => ( setadjoinAx
% 3.13/1.65 => ( powersetAx
% 3.13/1.65 => ( setunionAx
% 3.13/1.65 => ( omega0Ax
% 3.13/1.65 => ( omegaSAx
% 3.13/1.65 => ( omegaIndAx
% 3.13/1.65 => ( replAx
% 3.13/1.65 => ( foundationAx
% 3.13/1.65 => ( wellorderingAx
% 3.13/1.65 => ( descrp
% 3.13/1.65 => ( dsetconstrI
% 3.13/1.65 => ( dsetconstrEL
% 3.13/1.65 => ( dsetconstrER
% 3.13/1.65 => ( exuE1
% 3.13/1.65 => ( prop2setE
% 3.13/1.65 => ( emptysetE
% 3.13/1.65 => ( emptysetimpfalse
% 3.13/1.65 => ( notinemptyset
% 3.13/1.65 => ( exuE3e
% 3.13/1.65 => ( setext
% 3.13/1.65 => ( emptyI
% 3.13/1.65 => ( noeltsimpempty
% 3.13/1.65 => ( setbeta
% 3.13/1.65 => ( nonemptyE1
% 3.13/1.65 => ( nonemptyI
% 3.13/1.65 => ( nonemptyI1
% 3.13/1.65 => ( setadjoinIL
% 3.13/1.65 => ( emptyinunitempty
% 3.13/1.65 => ( setadjoinIR
% 3.13/1.65 => ( setadjoinE
% 3.13/1.65 => ( setadjoinOr
% 3.13/1.65 => ( setoftrueEq
% 3.13/1.65 => ( powersetI
% 3.13/1.65 => ( emptyinPowerset
% 3.13/1.65 => ( emptyInPowerset
% 3.13/1.65 => ( powersetE
% 3.13/1.65 => ( setunionI
% 3.13/1.65 => ( setunionE
% 3.13/1.65 => ( subPowSU
% 3.13/1.65 => ( exuE2
% 3.13/1.65 => ( nonemptyImpWitness
% 3.13/1.65 => ( uniqinunit
% 3.13/1.65 => ( notinsingleton
% 3.13/1.65 => ( eqinunit
% 3.13/1.65 => ( singletonsswitch
% 3.13/1.65 => ( upairsetE
% 3.13/1.65 => ( upairsetIL
% 3.13/1.65 => ( upairsetIR
% 3.13/1.65 => ( emptyE1
% 3.13/1.65 => ( vacuousDall
% 3.13/1.65 => ( quantDeMorgan1
% 3.13/1.65 => ( quantDeMorgan2
% 3.13/1.65 => ( quantDeMorgan3
% 3.13/1.65 => ( quantDeMorgan4
% 3.13/1.65 => ( prop2setI
% 3.13/1.65 => ( prop2set2propI
% 3.13/1.65 => ( notdexE
% 3.13/1.65 => ( notdallE
% 3.13/1.65 => ( exuI1
% 3.13/1.65 => ( exuI3
% 3.13/1.65 => ( exuI2
% 3.13/1.65 => ( inCongP
% 3.13/1.65 => ( in__Cong
% 3.13/1.65 => ( exuE3u
% 3.13/1.65 => ( exu__Cong
% 3.13/1.65 => ( emptyset__Cong
% 3.13/1.65 => ( setadjoin__Cong
% 3.13/1.65 => ( powerset__Cong
% 3.13/1.65 => ( setunion__Cong
% 3.13/1.65 => ( omega__Cong
% 3.13/1.65 => ( exuEu
% 3.13/1.65 => ( descr__Cong
% 3.13/1.65 => ( dsetconstr__Cong
% 3.13/1.65 => ( subsetI1
% 3.13/1.65 => ( eqimpsubset2
% 3.13/1.65 => ( eqimpsubset1
% 3.13/1.65 => ( subsetI2
% 3.13/1.65 => ( emptysetsubset
% 3.13/1.65 => ( subsetE
% 3.13/1.65 => ( subsetE2
% 3.13/1.65 => ( notsubsetI
% 3.13/1.65 => ( notequalI1
% 3.13/1.65 => ( notequalI2
% 3.13/1.65 => ( subsetRefl
% 3.13/1.65 => ( subsetTrans
% 3.13/1.65 => ( setadjoinSub
% 3.13/1.65 => ( setadjoinSub2
% 3.13/1.65 => ( subset2powerset
% 3.13/1.65 => ( setextsub
% 3.13/1.65 => ( subsetemptysetimpeq
% 3.13/1.65 => ( powersetI1
% 3.13/1.65 => ( powersetE1
% 3.13/1.65 => ( inPowerset
% 3.13/1.65 => ( powersetsubset
% 3.13/1.65 => ( sepInPowerset
% 3.13/1.65 => ( sepSubset
% 3.13/1.65 => ( binunionIL
% 3.13/1.65 => ( upairset2IR
% 3.13/1.65 => ( binunionIR
% 3.13/1.65 => ( binunionEcases
% 3.13/1.65 => ( binunionE
% 3.13/1.65 => ( binunionLsub
% 3.13/1.65 => ( binunionRsub
% 3.13/1.65 => ( binintersectI
% 3.13/1.65 => ( binintersectSubset5
% 3.13/1.65 => ( binintersectEL
% 3.13/1.65 => ( binintersectLsub
% 3.13/1.65 => ( binintersectSubset2
% 3.13/1.65 => ( binintersectSubset3
% 3.13/1.65 => ( binintersectER
% 3.13/1.65 => ( disjointsetsI1
% 3.13/1.65 => ( binintersectRsub
% 3.13/1.65 => ( binintersectSubset4
% 3.13/1.65 => ( binintersectSubset1
% 3.13/1.65 => ( bs114d
% 3.13/1.65 => ( setminusI
% 3.13/1.65 => ( setminusEL
% 3.13/1.65 => ( setminusER
% 3.13/1.65 => ( setminusSubset2
% 3.13/1.65 => ( setminusERneg
% 3.13/1.65 => ( setminusELneg
% 3.13/1.65 => ( setminusILneg
% 3.13/1.65 => ( setminusIRneg
% 3.13/1.65 => ( setminusLsub
% 3.13/1.65 => ( setminusSubset1
% 3.13/1.65 => ( symdiffE
% 3.13/1.65 => ( symdiffI1
% 3.13/1.65 => ( symdiffI2
% 3.13/1.65 => ( symdiffIneg1
% 3.13/1.65 => ( symdiffIneg2
% 3.13/1.65 => ( secondinupair
% 3.13/1.65 => ( setukpairIL
% 3.13/1.65 => ( setukpairIR
% 3.13/1.65 => ( kpairiskpair
% 3.13/1.65 => ( kpairp
% 3.13/1.65 => ( singletonsubset
% 3.13/1.65 => ( singletoninpowerset
% 3.13/1.65 => ( singletoninpowunion
% 3.13/1.65 => ( upairset2E
% 3.13/1.65 => ( upairsubunion
% 3.13/1.65 => ( upairinpowunion
% 3.13/1.65 => ( ubforcartprodlem1
% 3.13/1.65 => ( ubforcartprodlem2
% 3.13/1.65 => ( ubforcartprodlem3
% 3.13/1.65 => ( cartprodpairin
% 3.13/1.65 => ( cartprodmempair1
% 3.13/1.65 => ( cartprodmempair
% 3.13/1.65 => ( setunionE2
% 3.13/1.65 => ( setunionsingleton1
% 3.13/1.65 => ( setunionsingleton2
% 3.13/1.65 => ( setunionsingleton
% 3.13/1.65 => ( singletonprop
% 3.13/1.65 => ( ex1E1
% 3.13/1.65 => ( ex1I
% 3.13/1.65 => ( ex1I2
% 3.13/1.65 => ( singletonsuniq
% 3.13/1.65 => ( setukpairinjL1
% 3.13/1.65 => ( kfstsingleton
% 3.13/1.65 => ( theprop
% 3.13/1.65 => ( kfstpairEq
% 3.13/1.65 => ( cartprodfstin
% 3.13/1.65 => ( setukpairinjL2
% 3.13/1.65 => ( setukpairinjL
% 3.13/1.65 => ( setukpairinjR11
% 3.13/1.65 => ( setukpairinjR12
% 3.13/1.65 => ( setukpairinjR1
% 3.13/1.65 => ( upairequniteq
% 3.13/1.65 => ( setukpairinjR2
% 3.13/1.65 => ( setukpairinjR
% 3.13/1.65 => ( ksndsingleton
% 3.13/1.65 => ( ksndpairEq
% 3.13/1.65 => ( kpairsurjEq
% 3.13/1.65 => ( cartprodsndin
% 3.13/1.65 => ( cartprodpairmemEL
% 3.13/1.65 => ( cartprodpairmemER
% 3.13/1.65 => ( cartprodmempaircEq
% 3.13/1.65 => ( cartprodfstpairEq
% 3.13/1.65 => ( cartprodsndpairEq
% 3.13/1.65 => ( cartprodpairsurjEq
% 3.13/1.65 => ( dpsetconstrI
% 3.13/1.65 => ( dpsetconstrSub
% 3.13/1.65 => ( setOfPairsIsBReln
% 3.13/1.65 => ( dpsetconstrERa
% 3.13/1.65 => ( dpsetconstrEL1
% 3.13/1.65 => ( dpsetconstrEL2
% 3.13/1.65 => ( dpsetconstrER
% 3.13/1.65 => ( funcImageSingleton
% 3.13/1.65 => ( apProp
% 3.13/1.65 => ( app
% 3.13/1.65 => ( infuncsetfunc
% 3.13/1.65 => ( ap2p
% 3.13/1.65 => ( funcinfuncset
% 3.13/1.65 => ( lamProp
% 3.13/1.65 => ( lamp
% 3.13/1.65 => ( lam2p
% 3.13/1.65 => ( brelnall1
% 3.13/1.65 => ( brelnall2
% 3.13/1.65 => ( ex1E2
% 3.13/1.65 => ( funcGraphProp1
% 3.13/1.65 => ( funcGraphProp3
% 3.13/1.65 => ( funcGraphProp2
% 3.13/1.65 => ( funcextLem
% 3.13/1.65 => ( funcGraphProp4
% 3.13/1.65 => ( subbreln
% 3.13/1.65 => ( eqbreln
% 3.13/1.65 => ( funcext
% 3.13/1.65 => ( funcext2
% 3.13/1.65 => ( ap2apEq1
% 3.13/1.65 => ( ap2apEq2
% 3.13/1.65 => ( beta1
% 3.13/1.65 => ( eta1
% 3.13/1.65 => ( lam2lamEq
% 3.13/1.65 => ( beta2
% 3.13/1.65 => ( eta2
% 3.13/1.65 => ( iffalseProp1
% 3.13/1.65 => ( iffalseProp2
% 3.13/1.65 => ( iftrueProp1
% 3.13/1.65 => ( iftrueProp2
% 3.13/1.65 => ( ifSingleton
% 3.13/1.65 => ( ifp
% 3.13/1.65 => ( theeq
% 3.13/1.65 => ( iftrue
% 3.13/1.65 => ( iffalse
% 3.13/1.65 => ( iftrueorfalse
% 3.13/1.65 => ( binintersectT_lem
% 3.13/1.65 => ( binunionT_lem
% 3.13/1.65 => ( powersetT_lem
% 3.13/1.65 => ( setminusT_lem
% 3.13/1.65 => ( complementT_lem
% 3.13/1.65 => ( setextT
% 3.13/1.65 => ( subsetTI
% 3.13/1.65 => ( powersetTI1
% 3.13/1.65 => ( powersetTE1
% 3.13/1.65 => ( complementTI1
% 3.13/1.65 => ( complementTE1
% 3.13/1.65 => ( binintersectTELcontra
% 3.13/1.65 => ( binintersectTERcontra
% 3.13/1.65 => ( contrasubsetT
% 3.13/1.65 => ( contrasubsetT1
% 3.13/1.65 => ( contrasubsetT2
% 3.13/1.65 => ( contrasubsetT3
% 3.13/1.65 => ( doubleComplementI1
% 3.13/1.65 => ( doubleComplementE1
% 3.13/1.65 => ( doubleComplementSub1
% 3.13/1.65 => ( doubleComplementSub2
% 3.13/1.65 => ( doubleComplementEq
% 3.13/1.65 => ( complementTnotintersectT
% 3.13/1.65 => ( complementImpComplementIntersect
% 3.13/1.65 => ( complementSubsetComplementIntersect
% 3.13/1.65 => ( complementInPowersetComplementIntersect
% 3.13/1.65 => ( contraSubsetComplement
% 3.13/1.65 => ( complementTcontraSubset
% 3.13/1.65 => ( binunionTILcontra
% 3.13/1.65 => ( binunionTIRcontra
% 3.13/1.65 => ( inIntersectImpInUnion
% 3.13/1.65 => ( inIntersectImpInUnion2
% 3.13/1.65 => ( inIntersectImpInIntersectUnions
% 3.13/1.65 => ( intersectInPowersetIntersectUnions
% 3.13/1.65 => ( inComplementUnionImpNotIn1
% 3.13/1.65 => ( inComplementUnionImpInComplement1
% 3.13/1.65 => ( binunionTE
% 3.13/1.65 => ( binunionTEcontra
% 3.13/1.65 => ( demorgan2a1
% 3.13/1.65 => ( complementUnionInPowersetComplement
% 3.13/1.65 => ( demorgan2a2
% 3.13/1.65 => ( demorgan1a
% 3.13/1.65 => ( demorgan1b
% 3.13/1.65 => ( demorgan1
% 3.13/1.65 => ( demorgan2a
% 3.13/1.65 => ( demorgan2b2
% 3.13/1.65 => ( demorgan2b
% 3.13/1.65 => ( demorgan2
% 3.13/1.65 => ( woz13rule0
% 3.13/1.65 => ( woz13rule1
% 3.13/1.65 => ( woz13rule2
% 3.13/1.65 => ( woz13rule3
% 3.13/1.65 => ! [A: $i,X: $i] :
% 3.13/1.65 ( ( in @ X @ ( powerset @ A ) )
% 3.13/1.65 => ! [Y: $i] :
% 3.13/1.65 ( ( in @ Y @ ( powerset @ A ) )
% 3.13/1.65 => ! [Z: $i] :
% 3.13/1.65 ( ( in @ Z @ ( powerset @ A ) )
% 3.13/1.65 => ! [W: $i] :
% 3.13/1.65 ( ( in @ W @ ( powerset @ A ) )
% 3.13/1.65 => ( ( subset @ X @ Z )
% 3.13/1.65 => ( ( subset @ Y @ W )
% 3.13/1.65 => ( subset @ ( binintersect @ X @ Y ) @ ( binintersect @ Z @ W ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 3.13/1.65 ------------------------
% 3.13/1.69 % (32117)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/18Mi)
% 3.13/1.69 % (32111)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/183Mi)
% 3.13/1.69 % (32113)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_31785 for (2999ds/27Mi)
% 3.13/1.69 % (32117)Instruction limit reached!
% 3.13/1.69 % (32117)------------------------------
% 3.13/1.69 % (32117)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.69 % (32117)Termination reason: Unknown
% 3.13/1.69 % (32117)Termination phase: shuffling
% 3.13/1.69
% 3.13/1.69 % (32117)Memory used [KB]: 1918
% 3.13/1.69 % (32117)Time elapsed: 0.008 s
% 3.13/1.69 % (32117)Instructions burned: 20 (million)
% 3.13/1.69 % (32117)------------------------------
% 3.13/1.69 % (32117)------------------------------
% 3.13/1.69 % (32112)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_31785 for (2999ds/4Mi)
% 3.13/1.69 % (32114)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/2Mi)
% 3.13/1.69 % (32115)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_31785 for (2999ds/2Mi)
% 3.13/1.69 % (32116)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_31785 for (2999ds/275Mi)
% 3.13/1.70 % (32113)Instruction limit reached!
% 3.13/1.70 % (32113)------------------------------
% 3.13/1.70 % (32113)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.70 % (32113)Termination reason: Unknown
% 3.13/1.70 % (32113)Termination phase: shuffling
% 3.13/1.70
% 3.13/1.70 % (32113)Memory used [KB]: 2046
% 3.13/1.70 % (32113)Time elapsed: 0.010 s
% 3.13/1.70 % (32113)Instructions burned: 29 (million)
% 3.13/1.70 % (32113)------------------------------
% 3.13/1.70 % (32113)------------------------------
% 3.13/1.70 % (32114)Instruction limit reached!
% 3.13/1.70 % (32114)------------------------------
% 3.13/1.70 % (32114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.70 % (32114)Termination reason: Unknown
% 3.13/1.70 % (32114)Termination phase: shuffling
% 3.13/1.70
% 3.13/1.70 % (32114)Memory used [KB]: 1535
% 3.13/1.70 % (32114)Time elapsed: 0.003 s
% 3.13/1.70 % (32114)Instructions burned: 3 (million)
% 3.13/1.70 % (32114)------------------------------
% 3.13/1.70 % (32114)------------------------------
% 3.13/1.70 % (32115)Instruction limit reached!
% 3.13/1.70 % (32115)------------------------------
% 3.13/1.70 % (32115)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.13/1.70 % (32115)Termination reason: Unknown
% 3.13/1.70 % (32115)Termination phase: shuffling
% 3.13/1.70
% 3.13/1.70 % (32115)Memory used [KB]: 1535
% 3.13/1.70 % (32115)Time elapsed: 0.003 s
% 3.13/1.70 % (32115)Instructions burned: 2 (million)
% 3.13/1.70 % (32115)------------------------------
% 3.13/1.70 % (32115)------------------------------
% 3.19/1.70 % (32112)Instruction limit reached!
% 3.19/1.70 % (32112)------------------------------
% 3.19/1.70 % (32112)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.70 % (32112)Termination reason: Unknown
% 3.19/1.70 % (32112)Termination phase: shuffling
% 3.19/1.70
% 3.19/1.70 % (32112)Memory used [KB]: 1535
% 3.19/1.70 % (32112)Time elapsed: 0.004 s
% 3.19/1.70 % (32112)Instructions burned: 4 (million)
% 3.19/1.70 % (32112)------------------------------
% 3.19/1.70 % (32112)------------------------------
% 3.19/1.70 % (32121)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/3Mi)
% 3.19/1.70 % (32121)Instruction limit reached!
% 3.19/1.70 % (32121)------------------------------
% 3.19/1.70 % (32121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.70 % (32121)Termination reason: Unknown
% 3.19/1.70 % (32121)Termination phase: shuffling
% 3.19/1.70
% 3.19/1.70 % (32121)Memory used [KB]: 1535
% 3.19/1.70 % (32121)Time elapsed: 0.002 s
% 3.19/1.70 % (32121)Instructions burned: 3 (million)
% 3.19/1.70 % (32121)------------------------------
% 3.19/1.70 % (32121)------------------------------
% 3.19/1.71 % (32123)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_31785 for (2999ds/37Mi)
% 3.19/1.71 % (32132)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/7Mi)
% 3.19/1.71 % (32124)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_31785 for (2999ds/15Mi)
% 3.19/1.71 % (32126)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_31785 for (2999ds/3Mi)
% 3.19/1.71 % (32127)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_31785 for (2999ds/1041Mi)
% 3.19/1.72 % (32126)Instruction limit reached!
% 3.19/1.72 % (32126)------------------------------
% 3.19/1.72 % (32126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.72 % (32126)Termination reason: Unknown
% 3.19/1.72 % (32126)Termination phase: shuffling
% 3.19/1.72
% 3.19/1.72 % (32126)Memory used [KB]: 1535
% 3.19/1.72 % (32126)Time elapsed: 0.004 s
% 3.19/1.72 % (32126)Instructions burned: 3 (million)
% 3.19/1.72 % (32126)------------------------------
% 3.19/1.72 % (32126)------------------------------
% 3.19/1.72 % (32132)Instruction limit reached!
% 3.19/1.72 % (32132)------------------------------
% 3.19/1.72 % (32132)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.72 % (32132)Termination reason: Unknown
% 3.19/1.72 % (32132)Termination phase: shuffling
% 3.19/1.72
% 3.19/1.72 % (32132)Memory used [KB]: 1663
% 3.19/1.72 % (32132)Time elapsed: 0.004 s
% 3.19/1.72 % (32132)Instructions burned: 10 (million)
% 3.19/1.72 % (32132)------------------------------
% 3.19/1.72 % (32132)------------------------------
% 3.19/1.72 % (32123)Instruction limit reached!
% 3.19/1.72 % (32123)------------------------------
% 3.19/1.72 % (32123)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.72 % (32123)Termination reason: Unknown
% 3.19/1.72 % (32123)Termination phase: shuffling
% 3.19/1.72
% 3.19/1.72 % (32123)Memory used [KB]: 2302
% 3.19/1.72 % (32123)Time elapsed: 0.012 s
% 3.19/1.72 % (32123)Instructions burned: 37 (million)
% 3.19/1.72 % (32123)------------------------------
% 3.19/1.72 % (32123)------------------------------
% 3.19/1.72 % (32124)Instruction limit reached!
% 3.19/1.72 % (32124)------------------------------
% 3.19/1.72 % (32124)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.72 % (32124)Termination reason: Unknown
% 3.19/1.72 % (32124)Termination phase: shuffling
% 3.19/1.72
% 3.19/1.72 % (32124)Memory used [KB]: 1791
% 3.19/1.72 % (32124)Time elapsed: 0.012 s
% 3.19/1.72 % (32124)Instructions burned: 16 (million)
% 3.19/1.72 % (32124)------------------------------
% 3.19/1.72 % (32124)------------------------------
% 3.19/1.73 % (32136)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_31785 for (2999ds/3Mi)
% 3.19/1.73 % (32136)Instruction limit reached!
% 3.19/1.73 % (32136)------------------------------
% 3.19/1.73 % (32136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.73 % (32136)Termination reason: Unknown
% 3.19/1.73 % (32136)Termination phase: shuffling
% 3.19/1.73
% 3.19/1.73 % (32136)Memory used [KB]: 1535
% 3.19/1.73 % (32136)Time elapsed: 0.002 s
% 3.19/1.73 % (32136)Instructions burned: 3 (million)
% 3.19/1.73 % (32136)------------------------------
% 3.19/1.73 % (32136)------------------------------
% 3.19/1.73 % (32138)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_31785 for (2999ds/3Mi)
% 3.19/1.73 % (32138)Instruction limit reached!
% 3.19/1.73 % (32138)------------------------------
% 3.19/1.73 % (32138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.73 % (32138)Termination reason: Unknown
% 3.19/1.73 % (32138)Termination phase: shuffling
% 3.19/1.73
% 3.19/1.73 % (32138)Memory used [KB]: 1535
% 3.19/1.73 % (32138)Time elapsed: 0.002 s
% 3.19/1.73 % (32138)Instructions burned: 3 (million)
% 3.19/1.73 % (32138)------------------------------
% 3.19/1.73 % (32138)------------------------------
% 3.19/1.73 % (32135)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/16Mi)
% 3.19/1.74 % (32111)Instruction limit reached!
% 3.19/1.74 % (32111)------------------------------
% 3.19/1.74 % (32111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.74 % (32111)Termination reason: Unknown
% 3.19/1.74 % (32111)Termination phase: Saturation
% 3.19/1.74
% 3.19/1.74 % (32111)Memory used [KB]: 7419
% 3.19/1.74 % (32111)Time elapsed: 0.052 s
% 3.19/1.74 % (32111)Instructions burned: 183 (million)
% 3.19/1.74 % (32111)------------------------------
% 3.19/1.74 % (32111)------------------------------
% 3.19/1.74 % (32144)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/4Mi)
% 3.19/1.74 % (32144)Instruction limit reached!
% 3.19/1.74 % (32144)------------------------------
% 3.19/1.74 % (32144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.74 % (32144)Termination reason: Unknown
% 3.19/1.74 % (32144)Termination phase: shuffling
% 3.19/1.74
% 3.19/1.74 % (32144)Memory used [KB]: 1535
% 3.19/1.74 % (32144)Time elapsed: 0.002 s
% 3.19/1.74 % (32144)Instructions burned: 4 (million)
% 3.19/1.74 % (32144)------------------------------
% 3.19/1.74 % (32144)------------------------------
% 3.19/1.74 % (32141)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/7Mi)
% 3.19/1.74 % (32135)Instruction limit reached!
% 3.19/1.74 % (32135)------------------------------
% 3.19/1.74 % (32135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.74 % (32135)Termination reason: Unknown
% 3.19/1.74 % (32135)Termination phase: shuffling
% 3.19/1.74
% 3.19/1.74 % (32135)Memory used [KB]: 1918
% 3.19/1.74 % (32135)Time elapsed: 0.011 s
% 3.19/1.74 % (32135)Instructions burned: 17 (million)
% 3.19/1.74 % (32135)------------------------------
% 3.19/1.74 % (32135)------------------------------
% 3.19/1.74 % (32143)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/3Mi)
% 3.19/1.74 % (32141)Instruction limit reached!
% 3.19/1.74 % (32141)------------------------------
% 3.19/1.74 % (32141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.74 % (32141)Termination reason: Unknown
% 3.19/1.74 % (32141)Termination phase: shuffling
% 3.19/1.74
% 3.19/1.74 % (32141)Memory used [KB]: 1535
% 3.19/1.74 % (32141)Time elapsed: 0.006 s
% 3.19/1.74 % (32141)Instructions burned: 7 (million)
% 3.19/1.74 % (32141)------------------------------
% 3.19/1.74 % (32141)------------------------------
% 3.19/1.75 % (32143)Instruction limit reached!
% 3.19/1.75 % (32143)------------------------------
% 3.19/1.75 % (32143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.75 % (32143)Termination reason: Unknown
% 3.19/1.75 % (32143)Termination phase: shuffling
% 3.19/1.75
% 3.19/1.75 % (32143)Memory used [KB]: 1535
% 3.19/1.75 % (32143)Time elapsed: 0.004 s
% 3.19/1.75 % (32143)Instructions burned: 3 (million)
% 3.19/1.75 % (32143)------------------------------
% 3.19/1.75 % (32143)------------------------------
% 3.19/1.75 % (32148)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/18Mi)
% 3.19/1.75 % (32149)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/710Mi)
% 3.19/1.75 % (32148)Instruction limit reached!
% 3.19/1.75 % (32148)------------------------------
% 3.19/1.75 % (32148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.75 % (32148)Termination reason: Unknown
% 3.19/1.75 % (32148)Termination phase: shuffling
% 3.19/1.75
% 3.19/1.75 % (32148)Memory used [KB]: 1918
% 3.19/1.75 % (32148)Time elapsed: 0.007 s
% 3.19/1.75 % (32148)Instructions burned: 20 (million)
% 3.19/1.75 % (32148)------------------------------
% 3.19/1.75 % (32148)------------------------------
% 3.19/1.76 % (32151)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_31785 for (2999ds/902Mi)
% 3.19/1.76 % (32150)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/6Mi)
% 3.19/1.76 % (32152)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_31785 for (2999ds/21Mi)
% 3.19/1.76 % (32150)Instruction limit reached!
% 3.19/1.76 % (32150)------------------------------
% 3.19/1.76 % (32150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.76 % (32150)Termination reason: Unknown
% 3.19/1.76 % (32150)Termination phase: shuffling
% 3.19/1.76
% 3.19/1.76 % (32150)Memory used [KB]: 1535
% 3.19/1.76 % (32150)Time elapsed: 0.006 s
% 3.19/1.76 % (32150)Instructions burned: 7 (million)
% 3.19/1.76 % (32150)------------------------------
% 3.19/1.76 % (32150)------------------------------
% 3.19/1.76 % (32157)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_31785 for (2999ds/5Mi)
% 3.19/1.77 % (32157)Instruction limit reached!
% 3.19/1.77 % (32157)------------------------------
% 3.19/1.77 % (32157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.77 % (32157)Termination reason: Unknown
% 3.19/1.77 % (32157)Termination phase: shuffling
% 3.19/1.77
% 3.19/1.77 % (32157)Memory used [KB]: 1535
% 3.19/1.77 % (32157)Time elapsed: 0.003 s
% 3.19/1.77 % (32157)Instructions burned: 7 (million)
% 3.19/1.77 % (32157)------------------------------
% 3.19/1.77 % (32157)------------------------------
% 3.19/1.77 % (32152)Instruction limit reached!
% 3.19/1.77 % (32152)------------------------------
% 3.19/1.77 % (32152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.77 % (32152)Termination reason: Unknown
% 3.19/1.77 % (32152)Termination phase: shuffling
% 3.19/1.77
% 3.19/1.77 % (32152)Memory used [KB]: 1918
% 3.19/1.77 % (32152)Time elapsed: 0.011 s
% 3.19/1.77 % (32152)Instructions burned: 23 (million)
% 3.19/1.77 % (32152)------------------------------
% 3.19/1.77 % (32152)------------------------------
% 3.19/1.78 % (32166)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_31785 for (2998ds/377Mi)
% 3.19/1.78 % (32169)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_31785 for (2998ds/779Mi)
% 3.19/1.78 % (32163)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_31785 for (2998ds/6Mi)
% 3.19/1.79 % (32163)Instruction limit reached!
% 3.19/1.79 % (32163)------------------------------
% 3.19/1.79 % (32163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.79 % (32163)Termination reason: Unknown
% 3.19/1.79 % (32163)Termination phase: shuffling
% 3.19/1.79
% 3.19/1.79 % (32163)Memory used [KB]: 1535
% 3.19/1.79 % (32163)Time elapsed: 0.006 s
% 3.19/1.79 % (32163)Instructions burned: 7 (million)
% 3.19/1.79 % (32163)------------------------------
% 3.19/1.79 % (32163)------------------------------
% 3.19/1.80 % (32178)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_31785 for (2998ds/19Mi)
% 3.19/1.81 % (32116)Instruction limit reached!
% 3.19/1.81 % (32116)------------------------------
% 3.19/1.81 % (32116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.81 % (32116)Termination reason: Unknown
% 3.19/1.81 % (32116)Termination phase: Saturation
% 3.19/1.81
% 3.19/1.81 % (32116)Memory used [KB]: 9978
% 3.19/1.81 % (32116)Time elapsed: 0.115 s
% 3.19/1.81 % (32116)Instructions burned: 277 (million)
% 3.19/1.81 % (32116)------------------------------
% 3.19/1.81 % (32116)------------------------------
% 3.19/1.81 % (32178)Instruction limit reached!
% 3.19/1.81 % (32178)------------------------------
% 3.19/1.81 % (32178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.81 % (32178)Termination reason: Unknown
% 3.19/1.81 % (32178)Termination phase: shuffling
% 3.19/1.81
% 3.19/1.81 % (32178)Memory used [KB]: 1791
% 3.19/1.81 % (32178)Time elapsed: 0.010 s
% 3.19/1.81 % (32178)Instructions burned: 19 (million)
% 3.19/1.81 % (32178)------------------------------
% 3.19/1.81 % (32178)------------------------------
% 3.19/1.82 % (32191)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_31785 for (2998ds/879Mi)
% 3.19/1.82 % (32194)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_31785 for (2998ds/17Mi)
% 3.19/1.83 % (32194)Instruction limit reached!
% 3.19/1.83 % (32194)------------------------------
% 3.19/1.83 % (32194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.83 % (32194)Termination reason: Unknown
% 3.19/1.83 % (32194)Termination phase: shuffling
% 3.19/1.83
% 3.19/1.83 % (32194)Memory used [KB]: 1791
% 3.19/1.83 % (32194)Time elapsed: 0.006 s
% 3.19/1.83 % (32194)Instructions burned: 17 (million)
% 3.19/1.83 % (32194)------------------------------
% 3.19/1.83 % (32194)------------------------------
% 3.19/1.84 % (32197)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_31785 for (2998ds/3Mi)
% 3.19/1.84 % (32197)Instruction limit reached!
% 3.19/1.84 % (32197)------------------------------
% 3.19/1.84 % (32197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.84 % (32197)Termination reason: Unknown
% 3.19/1.84 % (32197)Termination phase: shuffling
% 3.19/1.84
% 3.19/1.84 % (32197)Memory used [KB]: 1535
% 3.19/1.84 % (32197)Time elapsed: 0.002 s
% 3.19/1.84 % (32197)Instructions burned: 4 (million)
% 3.19/1.84 % (32197)------------------------------
% 3.19/1.84 % (32197)------------------------------
% 3.19/1.85 % (32201)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_31785 for (2998ds/30Mi)
% 3.19/1.86 % (32201)Instruction limit reached!
% 3.19/1.86 % (32201)------------------------------
% 3.19/1.86 % (32201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.86 % (32201)Termination reason: Unknown
% 3.19/1.86 % (32201)Termination phase: shuffling
% 3.19/1.86
% 3.19/1.86 % (32201)Memory used [KB]: 2046
% 3.19/1.86 % (32201)Time elapsed: 0.010 s
% 3.19/1.86 % (32201)Instructions burned: 31 (million)
% 3.19/1.86 % (32201)------------------------------
% 3.19/1.86 % (32201)------------------------------
% 3.19/1.87 % (32202)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_31785 for (2998ds/127Mi)
% 3.19/1.88 % (32166)Instruction limit reached!
% 3.19/1.88 % (32166)------------------------------
% 3.19/1.88 % (32166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.88 % (32166)Termination reason: Unknown
% 3.19/1.88 % (32166)Termination phase: Saturation
% 3.19/1.88
% 3.19/1.88 % (32166)Memory used [KB]: 9466
% 3.19/1.88 % (32166)Time elapsed: 0.103 s
% 3.19/1.88 % (32166)Instructions burned: 377 (million)
% 3.19/1.88 % (32166)------------------------------
% 3.19/1.88 % (32166)------------------------------
% 3.19/1.89 % (32203)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_31785 for (2997ds/100Mi)
% 3.19/1.90 % (32202)Instruction limit reached!
% 3.19/1.90 % (32202)------------------------------
% 3.19/1.90 % (32202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.90 % (32202)Termination reason: Unknown
% 3.19/1.90 % (32202)Termination phase: Property scanning
% 3.19/1.90
% 3.19/1.90 % (32202)Memory used [KB]: 2686
% 3.19/1.90 % (32202)Time elapsed: 0.037 s
% 3.19/1.90 % (32202)Instructions burned: 130 (million)
% 3.19/1.90 % (32202)------------------------------
% 3.19/1.90 % (32202)------------------------------
% 3.19/1.91 % (32203)Instruction limit reached!
% 3.19/1.91 % (32203)------------------------------
% 3.19/1.91 % (32203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.91 % (32203)Termination reason: Unknown
% 3.19/1.91 % (32203)Termination phase: Property scanning
% 3.19/1.91
% 3.19/1.91 % (32203)Memory used [KB]: 2686
% 3.19/1.91 % (32203)Time elapsed: 0.027 s
% 3.19/1.91 % (32203)Instructions burned: 101 (million)
% 3.19/1.91 % (32203)------------------------------
% 3.19/1.91 % (32203)------------------------------
% 3.19/1.91 % (32204)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_31785 for (2997ds/3Mi)
% 3.19/1.91 % (32204)Instruction limit reached!
% 3.19/1.91 % (32204)------------------------------
% 3.19/1.91 % (32204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.91 % (32204)Termination reason: Unknown
% 3.19/1.91 % (32204)Termination phase: shuffling
% 3.19/1.91
% 3.19/1.91 % (32204)Memory used [KB]: 1535
% 3.19/1.91 % (32204)Time elapsed: 0.002 s
% 3.19/1.91 % (32204)Instructions burned: 3 (million)
% 3.19/1.91 % (32204)------------------------------
% 3.19/1.91 % (32204)------------------------------
% 3.19/1.92 % (32205)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_31785 for (2997ds/20Mi)
% 3.19/1.93 % (32206)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_31785 for (2997ds/86Mi)
% 3.19/1.93 % (32205)Instruction limit reached!
% 3.19/1.93 % (32205)------------------------------
% 3.19/1.93 % (32205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.93 % (32205)Termination reason: Unknown
% 3.19/1.93 % (32205)Termination phase: shuffling
% 3.19/1.93
% 3.19/1.93 % (32205)Memory used [KB]: 1791
% 3.19/1.93 % (32205)Time elapsed: 0.008 s
% 3.19/1.93 % (32205)Instructions burned: 20 (million)
% 3.19/1.93 % (32205)------------------------------
% 3.19/1.93 % (32205)------------------------------
% 3.19/1.94 % (32207)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_31785 for (2997ds/107Mi)
% 3.19/1.95 % (32206)Instruction limit reached!
% 3.19/1.95 % (32206)------------------------------
% 3.19/1.95 % (32206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.95 % (32206)Termination reason: Unknown
% 3.19/1.95 % (32206)Termination phase: Property scanning
% 3.19/1.95
% 3.19/1.95 % (32206)Memory used [KB]: 2686
% 3.19/1.95 % (32206)Time elapsed: 0.026 s
% 3.19/1.95 % (32206)Instructions burned: 89 (million)
% 3.19/1.95 % (32206)------------------------------
% 3.19/1.95 % (32206)------------------------------
% 3.19/1.96 % (32208)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_31785 for (2997ds/39Mi)
% 3.19/1.97 % (32149)Instruction limit reached!
% 3.19/1.97 % (32149)------------------------------
% 3.19/1.97 % (32149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.97 % (32149)Termination reason: Unknown
% 3.19/1.97 % (32149)Termination phase: Saturation
% 3.19/1.97
% 3.19/1.97 % (32149)Memory used [KB]: 10618
% 3.19/1.97 % (32149)Time elapsed: 0.219 s
% 3.19/1.97 % (32149)Instructions burned: 710 (million)
% 3.19/1.97 % (32149)------------------------------
% 3.19/1.97 % (32149)------------------------------
% 3.19/1.97 % (32207)Instruction limit reached!
% 3.19/1.97 % (32207)------------------------------
% 3.19/1.97 % (32207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.97 % (32207)Termination reason: Unknown
% 3.19/1.97 % (32207)Termination phase: Preprocessing 3
% 3.19/1.97
% 3.19/1.97 % (32207)Memory used [KB]: 2686
% 3.19/1.97 % (32207)Time elapsed: 0.029 s
% 3.19/1.97 % (32207)Instructions burned: 108 (million)
% 3.19/1.97 % (32207)------------------------------
% 3.19/1.97 % (32207)------------------------------
% 3.19/1.97 % (32208)Instruction limit reached!
% 3.19/1.97 % (32208)------------------------------
% 3.19/1.97 % (32208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.97 % (32208)Termination reason: Unknown
% 3.19/1.97 % (32208)Termination phase: shuffling
% 3.19/1.97
% 3.19/1.97 % (32208)Memory used [KB]: 2302
% 3.19/1.97 % (32208)Time elapsed: 0.012 s
% 3.19/1.97 % (32208)Instructions burned: 39 (million)
% 3.19/1.97 % (32208)------------------------------
% 3.19/1.97 % (32208)------------------------------
% 3.19/1.98 % (32209)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_31785 for (2996ds/448Mi)
% 3.19/1.98 % (32210)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_31785 for (2996ds/46Mi)
% 3.19/1.98 % (32211)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_31785 for (2996ds/98Mi)
% 3.19/1.99 % (32169)Instruction limit reached!
% 3.19/1.99 % (32169)------------------------------
% 3.19/1.99 % (32169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.99 % (32169)Termination reason: Unknown
% 3.19/1.99 % (32169)Termination phase: Saturation
% 3.19/1.99
% 3.19/1.99 % (32169)Memory used [KB]: 7675
% 3.19/1.99 % (32169)Time elapsed: 0.209 s
% 3.19/1.99 % (32169)Instructions burned: 781 (million)
% 3.19/1.99 % (32169)------------------------------
% 3.19/1.99 % (32169)------------------------------
% 3.19/1.99 % (32210)Instruction limit reached!
% 3.19/1.99 % (32210)------------------------------
% 3.19/1.99 % (32210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/1.99 % (32210)Termination reason: Unknown
% 3.19/1.99 % (32210)Termination phase: shuffling
% 3.19/1.99
% 3.19/1.99 % (32210)Memory used [KB]: 2430
% 3.19/1.99 % (32210)Time elapsed: 0.014 s
% 3.19/1.99 % (32210)Instructions burned: 47 (million)
% 3.19/1.99 % (32210)------------------------------
% 3.19/1.99 % (32210)------------------------------
% 3.19/2.00 % (32212)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_31785 for (2996ds/507Mi)
% 3.19/2.00 % (32213)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_31785 for (2996ds/149Mi)
% 3.19/2.01 % (32211)Instruction limit reached!
% 3.19/2.01 % (32211)------------------------------
% 3.19/2.01 % (32211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.19/2.01 % (32211)Termination reason: Unknown
% 3.19/2.01 % (32211)Termination phase: Property scanning
% 3.19/2.01
% 3.19/2.01 % (32211)Memory used [KB]: 2558
% 3.19/2.01 % (32211)Time elapsed: 0.028 s
% 3.19/2.01 % (32211)Instructions burned: 98 (million)
% 3.19/2.01 % (32211)------------------------------
% 3.19/2.01 % (32211)------------------------------
% 5.50/2.02 % (32214)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_31785 for (2996ds/39Mi)
% 5.50/2.02 % (32127)Instruction limit reached!
% 5.50/2.02 % (32127)------------------------------
% 5.50/2.02 % (32127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.02 % (32127)Termination reason: Unknown
% 5.50/2.02 % (32127)Termination phase: Saturation
% 5.50/2.02
% 5.50/2.02 % (32127)Memory used [KB]: 15607
% 5.50/2.02 % (32127)Time elapsed: 0.307 s
% 5.50/2.02 % (32127)Instructions burned: 1042 (million)
% 5.50/2.02 % (32127)------------------------------
% 5.50/2.02 % (32127)------------------------------
% 5.50/2.03 % (32214)Instruction limit reached!
% 5.50/2.03 % (32214)------------------------------
% 5.50/2.03 % (32214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.03 % (32214)Termination reason: Unknown
% 5.50/2.03 % (32214)Termination phase: shuffling
% 5.50/2.03
% 5.50/2.03 % (32214)Memory used [KB]: 2302
% 5.50/2.03 % (32214)Time elapsed: 0.013 s
% 5.50/2.03 % (32214)Instructions burned: 41 (million)
% 5.50/2.03 % (32214)------------------------------
% 5.50/2.03 % (32214)------------------------------
% 5.50/2.04 % (32213)Instruction limit reached!
% 5.50/2.04 % (32213)------------------------------
% 5.50/2.04 % (32213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.04 % (32213)Termination reason: Unknown
% 5.50/2.04 % (32213)Termination phase: Twee Goal Transformation
% 5.50/2.04
% 5.50/2.04 % (32213)Memory used [KB]: 3326
% 5.50/2.04 % (32213)Time elapsed: 0.041 s
% 5.50/2.04 % (32213)Instructions burned: 151 (million)
% 5.50/2.04 % (32213)------------------------------
% 5.50/2.04 % (32213)------------------------------
% 5.50/2.04 % (32215)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_31785 for (2996ds/6Mi)
% 5.50/2.04 % (32216)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_31785 for (2996ds/1087Mi)
% 5.50/2.05 % (32215)Instruction limit reached!
% 5.50/2.05 % (32215)------------------------------
% 5.50/2.05 % (32215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.05 % (32215)Termination reason: Unknown
% 5.50/2.05 % (32215)Termination phase: shuffling
% 5.50/2.05
% 5.50/2.05 % (32215)Memory used [KB]: 1535
% 5.50/2.05 % (32215)Time elapsed: 0.006 s
% 5.50/2.05 % (32215)Instructions burned: 7 (million)
% 5.50/2.05 % (32215)------------------------------
% 5.50/2.05 % (32215)------------------------------
% 5.50/2.05 % (32151)Instruction limit reached!
% 5.50/2.05 % (32151)------------------------------
% 5.50/2.05 % (32151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.05 % (32151)Termination reason: Unknown
% 5.50/2.05 % (32151)Termination phase: Saturation
% 5.50/2.05
% 5.50/2.05 % (32151)Memory used [KB]: 12792
% 5.50/2.05 % (32151)Time elapsed: 0.287 s
% 5.50/2.05 % (32151)Instructions burned: 904 (million)
% 5.50/2.05 % (32151)------------------------------
% 5.50/2.05 % (32151)------------------------------
% 5.50/2.05 % (32217)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_31785 for (2996ds/47Mi)
% 5.50/2.06 % (32219)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_31785 for (2996ds/432Mi)
% 5.50/2.06 % (32217)Instruction limit reached!
% 5.50/2.06 % (32217)------------------------------
% 5.50/2.06 % (32217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.06 % (32217)Termination reason: Unknown
% 5.50/2.06 % (32217)Termination phase: shuffling
% 5.50/2.06
% 5.50/2.06 % (32217)Memory used [KB]: 2430
% 5.50/2.06 % (32217)Time elapsed: 0.015 s
% 5.50/2.06 % (32217)Instructions burned: 50 (million)
% 5.50/2.06 % (32217)------------------------------
% 5.50/2.06 % (32217)------------------------------
% 5.50/2.06 % (32218)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_31785 for (2996ds/44Mi)
% 5.50/2.07 % (32220)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_31785 for (2995ds/62Mi)
% 5.50/2.08 % (32191)Instruction limit reached!
% 5.50/2.08 % (32191)------------------------------
% 5.50/2.08 % (32191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.08 % (32191)Termination reason: Unknown
% 5.50/2.08 % (32191)Termination phase: Saturation
% 5.50/2.08
% 5.50/2.08 % (32191)Memory used [KB]: 9978
% 5.50/2.08 % (32191)Time elapsed: 0.263 s
% 5.50/2.08 % (32191)Instructions burned: 881 (million)
% 5.50/2.08 % (32191)------------------------------
% 5.50/2.08 % (32191)------------------------------
% 5.50/2.08 % (32218)Instruction limit reached!
% 5.50/2.08 % (32218)------------------------------
% 5.50/2.08 % (32218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.08 % (32218)Termination reason: Unknown
% 5.50/2.08 % (32218)Termination phase: shuffling
% 5.50/2.08
% 5.50/2.08 % (32218)Memory used [KB]: 2430
% 5.50/2.08 % (32218)Time elapsed: 0.024 s
% 5.50/2.08 % (32218)Instructions burned: 45 (million)
% 5.50/2.08 % (32218)------------------------------
% 5.50/2.08 % (32218)------------------------------
% 5.50/2.09 % (32209)Instruction limit reached!
% 5.50/2.09 % (32209)------------------------------
% 5.50/2.09 % (32209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.09 % (32209)Termination reason: Unknown
% 5.50/2.09 % (32209)Termination phase: Saturation
% 5.50/2.09
% 5.50/2.09 % (32209)Memory used [KB]: 7547
% 5.50/2.09 % (32209)Time elapsed: 0.112 s
% 5.50/2.09 % (32209)Instructions burned: 449 (million)
% 5.50/2.09 % (32209)------------------------------
% 5.50/2.09 % (32209)------------------------------
% 5.50/2.09 % (32220)Instruction limit reached!
% 5.50/2.09 % (32220)------------------------------
% 5.50/2.09 % (32220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.09 % (32220)Termination reason: Unknown
% 5.50/2.09 % (32220)Termination phase: Property scanning
% 5.50/2.09
% 5.50/2.09 % (32220)Memory used [KB]: 2430
% 5.50/2.09 % (32220)Time elapsed: 0.018 s
% 5.50/2.09 % (32220)Instructions burned: 64 (million)
% 5.50/2.09 % (32220)------------------------------
% 5.50/2.09 % (32220)------------------------------
% 5.50/2.09 % (32221)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_31785 for (2995ds/31Mi)
% 5.50/2.10 % (32222)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_31785 for (2995ds/96Mi)
% 5.50/2.10 % (32223)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_31785 for (2995ds/453Mi)
% 5.50/2.10 % (32221)Instruction limit reached!
% 5.50/2.10 % (32221)------------------------------
% 5.50/2.10 % (32221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.50/2.10 % (32221)Termination reason: Unknown
% 5.50/2.10 % (32221)Termination phase: shuffling
% 5.50/2.10
% 5.50/2.10 % (32221)Memory used [KB]: 2046
% 5.50/2.10 % (32221)Time elapsed: 0.010 s
% 5.50/2.10 % (32221)Instructions burned: 32 (million)
% 5.50/2.10 % (32221)------------------------------
% 5.50/2.10 % (32221)------------------------------
% 5.50/2.10 % (32224)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_31785 for (2995ds/71Mi)
% 5.50/2.11 % (32225)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_31785 for (2995ds/83Mi)
% 6.02/2.12 % (32224)Instruction limit reached!
% 6.02/2.12 % (32224)------------------------------
% 6.02/2.12 % (32224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.12 % (32224)Termination reason: Unknown
% 6.02/2.12 % (32224)Termination phase: Property scanning
% 6.02/2.12
% 6.02/2.12 % (32224)Memory used [KB]: 2558
% 6.02/2.12 % (32224)Time elapsed: 0.020 s
% 6.02/2.12 % (32224)Instructions burned: 71 (million)
% 6.02/2.12 % (32224)------------------------------
% 6.02/2.12 % (32224)------------------------------
% 6.02/2.12 % (32222)Instruction limit reached!
% 6.02/2.12 % (32222)------------------------------
% 6.02/2.12 % (32222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.12 % (32222)Termination reason: Unknown
% 6.02/2.12 % (32222)Termination phase: Property scanning
% 6.02/2.12
% 6.02/2.12 % (32222)Memory used [KB]: 2686
% 6.02/2.12 % (32222)Time elapsed: 0.029 s
% 6.02/2.12 % (32222)Instructions burned: 96 (million)
% 6.02/2.12 % (32222)------------------------------
% 6.02/2.12 % (32222)------------------------------
% 6.02/2.13 % (32226)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_31785 for (2995ds/11Mi)
% 6.02/2.13 % (32225)Instruction limit reached!
% 6.02/2.13 % (32225)------------------------------
% 6.02/2.13 % (32225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.13 % (32225)Termination reason: Unknown
% 6.02/2.13 % (32225)Termination phase: Property scanning
% 6.02/2.13
% 6.02/2.13 % (32225)Memory used [KB]: 2558
% 6.02/2.13 % (32225)Time elapsed: 0.023 s
% 6.02/2.13 % (32225)Instructions burned: 83 (million)
% 6.02/2.13 % (32225)------------------------------
% 6.02/2.13 % (32225)------------------------------
% 6.02/2.13 % (32226)Instruction limit reached!
% 6.02/2.13 % (32226)------------------------------
% 6.02/2.13 % (32226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.13 % (32226)Termination reason: Unknown
% 6.02/2.13 % (32226)Termination phase: shuffling
% 6.02/2.13
% 6.02/2.13 % (32226)Memory used [KB]: 1791
% 6.02/2.13 % (32226)Time elapsed: 0.005 s
% 6.02/2.13 % (32226)Instructions burned: 14 (million)
% 6.02/2.13 % (32226)------------------------------
% 6.02/2.13 % (32226)------------------------------
% 6.02/2.13 % (32227)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_31785 for (2995ds/41Mi)
% 6.02/2.14 % (32228)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_31785 for (2995ds/6Mi)
% 6.02/2.14 % (32229)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_31785 for (2995ds/150Mi)
% 6.02/2.14 % (32228)Instruction limit reached!
% 6.02/2.14 % (32228)------------------------------
% 6.02/2.14 % (32228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.14 % (32228)Termination reason: Unknown
% 6.02/2.14 % (32228)Termination phase: shuffling
% 6.02/2.14
% 6.02/2.14 % (32228)Memory used [KB]: 1535
% 6.02/2.14 % (32228)Time elapsed: 0.003 s
% 6.02/2.14 % (32228)Instructions burned: 7 (million)
% 6.02/2.14 % (32228)------------------------------
% 6.02/2.14 % (32228)------------------------------
% 6.02/2.14 % (32212)Instruction limit reached!
% 6.02/2.14 % (32212)------------------------------
% 6.02/2.14 % (32212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.14 % (32212)Termination reason: Unknown
% 6.02/2.14 % (32212)Termination phase: Saturation
% 6.02/2.14
% 6.02/2.14 % (32212)Memory used [KB]: 8187
% 6.02/2.14 % (32212)Time elapsed: 0.168 s
% 6.02/2.14 % (32212)Instructions burned: 508 (million)
% 6.02/2.14 % (32212)------------------------------
% 6.02/2.14 % (32212)------------------------------
% 6.02/2.15 % (32227)Instruction limit reached!
% 6.02/2.15 % (32227)------------------------------
% 6.02/2.15 % (32227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.15 % (32227)Termination reason: Unknown
% 6.02/2.15 % (32227)Termination phase: shuffling
% 6.02/2.15
% 6.02/2.15 % (32227)Memory used [KB]: 2302
% 6.02/2.15 % (32227)Time elapsed: 0.013 s
% 6.02/2.15 % (32227)Instructions burned: 42 (million)
% 6.02/2.15 % (32227)------------------------------
% 6.02/2.15 % (32227)------------------------------
% 6.02/2.15 % (32230)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_31785 for (2995ds/343Mi)
% 6.02/2.15 % (32231)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_31785 for (2995ds/109Mi)
% 6.02/2.16 % (32232)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_31785 for (2995ds/253Mi)
% 6.02/2.16 % (32219)Instruction limit reached!
% 6.02/2.16 % (32219)------------------------------
% 6.02/2.16 % (32219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.16 % (32219)Termination reason: Unknown
% 6.02/2.16 % (32219)Termination phase: Saturation
% 6.02/2.16
% 6.02/2.16 % (32219)Memory used [KB]: 3070
% 6.02/2.16 % (32219)Time elapsed: 0.109 s
% 6.02/2.16 % (32219)Instructions burned: 433 (million)
% 6.02/2.16 % (32219)------------------------------
% 6.02/2.16 % (32219)------------------------------
% 6.02/2.17 % (32233)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_31785 for (2994ds/140Mi)
% 6.02/2.18 % (32231)Instruction limit reached!
% 6.02/2.18 % (32231)------------------------------
% 6.02/2.18 % (32231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.18 % (32231)Termination reason: Unknown
% 6.02/2.18 % (32231)Termination phase: Property scanning
% 6.02/2.18
% 6.02/2.18 % (32231)Memory used [KB]: 2686
% 6.02/2.18 % (32231)Time elapsed: 0.030 s
% 6.02/2.18 % (32231)Instructions burned: 110 (million)
% 6.02/2.18 % (32231)------------------------------
% 6.02/2.18 % (32231)------------------------------
% 6.02/2.18 % (32229)Instruction limit reached!
% 6.02/2.18 % (32229)------------------------------
% 6.02/2.18 % (32229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.02/2.18 % (32229)Termination reason: Unknown
% 6.02/2.18 % (32229)Termination phase: Property scanning
% 6.02/2.18
% 6.02/2.18 % (32229)Memory used [KB]: 4733
% 6.02/2.18 % (32229)Time elapsed: 0.045 s
% 6.02/2.18 % (32229)Instructions burned: 151 (million)
% 6.02/2.18 % (32229)------------------------------
% 6.02/2.18 % (32229)------------------------------
% 6.02/2.19 % (32234)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_31785 for (2994ds/614Mi)
% 6.02/2.19 % (32235)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_31785 for (2994ds/202Mi)
% 6.41/2.21 % (32233)Instruction limit reached!
% 6.41/2.21 % (32233)------------------------------
% 6.41/2.21 % (32233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.21 % (32233)Termination reason: Unknown
% 6.41/2.21 % (32233)Termination phase: Property scanning
% 6.41/2.21
% 6.41/2.21 % (32233)Memory used [KB]: 2814
% 6.41/2.21 % (32233)Time elapsed: 0.038 s
% 6.41/2.21 % (32233)Instructions burned: 140 (million)
% 6.41/2.21 % (32233)------------------------------
% 6.41/2.21 % (32233)------------------------------
% 6.41/2.21 % (32223)Instruction limit reached!
% 6.41/2.21 % (32223)------------------------------
% 6.41/2.21 % (32223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.21 % (32223)Termination reason: Unknown
% 6.41/2.21 % (32223)Termination phase: Saturation
% 6.41/2.21
% 6.41/2.21 % (32223)Memory used [KB]: 7547
% 6.41/2.21 % (32223)Time elapsed: 0.115 s
% 6.41/2.21 % (32223)Instructions burned: 455 (million)
% 6.41/2.21 % (32223)------------------------------
% 6.41/2.21 % (32223)------------------------------
% 6.41/2.22 % (32236)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_31785 for (2994ds/339Mi)
% 6.41/2.22 % (32237)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_31785 for (2994ds/283Mi)
% 6.41/2.23 % (32232)Instruction limit reached!
% 6.41/2.23 % (32232)------------------------------
% 6.41/2.23 % (32232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.23 % (32232)Termination reason: Unknown
% 6.41/2.23 % (32232)Termination phase: Saturation
% 6.41/2.23
% 6.41/2.23 % (32232)Memory used [KB]: 9978
% 6.41/2.23 % (32232)Time elapsed: 0.077 s
% 6.41/2.23 % (32232)Instructions burned: 254 (million)
% 6.41/2.23 % (32232)------------------------------
% 6.41/2.23 % (32232)------------------------------
% 6.41/2.24 % (32230)Instruction limit reached!
% 6.41/2.24 % (32230)------------------------------
% 6.41/2.24 % (32230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.24 % (32230)Termination reason: Unknown
% 6.41/2.24 % (32230)Termination phase: Saturation
% 6.41/2.24
% 6.41/2.24 % (32230)Memory used [KB]: 8571
% 6.41/2.24 % (32230)Time elapsed: 0.091 s
% 6.41/2.24 % (32230)Instructions burned: 343 (million)
% 6.41/2.24 % (32230)------------------------------
% 6.41/2.24 % (32230)------------------------------
% 6.41/2.24 % (32238)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_31785 for (2994ds/134Mi)
% 6.41/2.25 % (32239)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_31785 for (2994ds/298Mi)
% 6.41/2.25 % (32235)Instruction limit reached!
% 6.41/2.25 % (32235)------------------------------
% 6.41/2.25 % (32235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.25 % (32235)Termination reason: Unknown
% 6.41/2.25 % (32235)Termination phase: Property scanning
% 6.41/2.25
% 6.41/2.25 % (32235)Memory used [KB]: 4989
% 6.41/2.25 % (32235)Time elapsed: 0.059 s
% 6.41/2.25 % (32235)Instructions burned: 205 (million)
% 6.41/2.25 % (32235)------------------------------
% 6.41/2.25 % (32235)------------------------------
% 6.41/2.26 % (32240)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_31785 for (2994ds/192Mi)
% 6.41/2.28 % (32238)Instruction limit reached!
% 6.41/2.28 % (32238)------------------------------
% 6.41/2.28 % (32238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.28 % (32238)Termination reason: Unknown
% 6.41/2.28 % (32238)Termination phase: Property scanning
% 6.41/2.28
% 6.41/2.28 % (32238)Memory used [KB]: 2814
% 6.41/2.28 % (32238)Time elapsed: 0.036 s
% 6.41/2.28 % (32238)Instructions burned: 135 (million)
% 6.41/2.28 % (32238)------------------------------
% 6.41/2.28 % (32238)------------------------------
% 6.41/2.29 % (32241)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_31785 for (2993ds/258Mi)
% 6.41/2.29 % (32237)Instruction limit reached!
% 6.41/2.29 % (32237)------------------------------
% 6.41/2.29 % (32237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.41/2.29 % (32237)Termination reason: Unknown
% 6.41/2.29 % (32237)Termination phase: Saturation
% 6.41/2.29
% 6.41/2.29 % (32237)Memory used [KB]: 7419
% 6.41/2.29 % (32237)Time elapsed: 0.072 s
% 6.41/2.29 % (32237)Instructions burned: 286 (million)
% 6.41/2.29 % (32237)------------------------------
% 6.41/2.29 % (32237)------------------------------
% 6.96/2.30 % (32242)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_31785 for (2993ds/90Mi)
% 6.96/2.31 % (32236)Instruction limit reached!
% 6.96/2.31 % (32236)------------------------------
% 6.96/2.31 % (32236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.31 % (32236)Termination reason: Unknown
% 6.96/2.31 % (32236)Termination phase: Saturation
% 6.96/2.31
% 6.96/2.31 % (32236)Memory used [KB]: 7931
% 6.96/2.31 % (32236)Time elapsed: 0.093 s
% 6.96/2.31 % (32236)Instructions burned: 340 (million)
% 6.96/2.31 % (32236)------------------------------
% 6.96/2.31 % (32236)------------------------------
% 6.96/2.31 % (32240)Instruction limit reached!
% 6.96/2.31 % (32240)------------------------------
% 6.96/2.31 % (32240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.31 % (32240)Termination reason: Unknown
% 6.96/2.31 % (32240)Termination phase: Saturation
% 6.96/2.31
% 6.96/2.31 % (32240)Memory used [KB]: 7547
% 6.96/2.31 % (32240)Time elapsed: 0.051 s
% 6.96/2.31 % (32240)Instructions burned: 194 (million)
% 6.96/2.31 % (32240)------------------------------
% 6.96/2.31 % (32240)------------------------------
% 6.96/2.32 % (32244)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_31785 for (2993ds/458Mi)
% 6.96/2.32 % (32239)Instruction limit reached!
% 6.96/2.32 % (32239)------------------------------
% 6.96/2.32 % (32239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.32 % (32239)Termination reason: Unknown
% 6.96/2.32 % (32239)Termination phase: Saturation
% 6.96/2.32
% 6.96/2.32 % (32239)Memory used [KB]: 7419
% 6.96/2.32 % (32239)Time elapsed: 0.075 s
% 6.96/2.32 % (32239)Instructions burned: 298 (million)
% 6.96/2.32 % (32239)------------------------------
% 6.96/2.32 % (32239)------------------------------
% 6.96/2.33 % (32242)Instruction limit reached!
% 6.96/2.33 % (32242)------------------------------
% 6.96/2.33 % (32242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.33 % (32242)Termination reason: Unknown
% 6.96/2.33 % (32242)Termination phase: Property scanning
% 6.96/2.33
% 6.96/2.33 % (32242)Memory used [KB]: 2686
% 6.96/2.33 % (32242)Time elapsed: 0.025 s
% 6.96/2.33 % (32242)Instructions burned: 92 (million)
% 6.96/2.33 % (32242)------------------------------
% 6.96/2.33 % (32242)------------------------------
% 6.96/2.33 % (32243)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_31785 for (2993ds/231Mi)
% 6.96/2.33 % (32245)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_31785 for (2993ds/31Mi)
% 6.96/2.34 % (32246)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_31785 for (2993ds/297Mi)
% 6.96/2.34 % (32245)Instruction limit reached!
% 6.96/2.34 % (32245)------------------------------
% 6.96/2.34 % (32245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.34 % (32245)Termination reason: Unknown
% 6.96/2.34 % (32245)Termination phase: shuffling
% 6.96/2.34
% 6.96/2.34 % (32245)Memory used [KB]: 2046
% 6.96/2.34 % (32245)Time elapsed: 0.010 s
% 6.96/2.34 % (32245)Instructions burned: 33 (million)
% 6.96/2.34 % (32245)------------------------------
% 6.96/2.34 % (32245)------------------------------
% 6.96/2.35 % (32247)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_31785 for (2993ds/987Mi)
% 6.96/2.35 % (32241)Instruction limit reached!
% 6.96/2.35 % (32241)------------------------------
% 6.96/2.35 % (32241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.35 % (32241)Termination reason: Unknown
% 6.96/2.35 % (32241)Termination phase: Saturation
% 6.96/2.35
% 6.96/2.35 % (32241)Memory used [KB]: 7931
% 6.96/2.35 % (32241)Time elapsed: 0.068 s
% 6.96/2.35 % (32241)Instructions burned: 259 (million)
% 6.96/2.35 % (32241)------------------------------
% 6.96/2.35 % (32241)------------------------------
% 6.96/2.36 % (32248)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_31785 for (2993ds/182Mi)
% 6.96/2.37 % (32234)Instruction limit reached!
% 6.96/2.37 % (32234)------------------------------
% 6.96/2.37 % (32234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.37 % (32234)Termination reason: Unknown
% 6.96/2.37 % (32234)Termination phase: Saturation
% 6.96/2.37
% 6.96/2.37 % (32234)Memory used [KB]: 10106
% 6.96/2.37 % (32234)Time elapsed: 0.179 s
% 6.96/2.37 % (32234)Instructions burned: 614 (million)
% 6.96/2.37 % (32234)------------------------------
% 6.96/2.37 % (32234)------------------------------
% 6.96/2.38 % (32249)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_31785 for (2992ds/182Mi)
% 6.96/2.39 % (32216)Instruction limit reached!
% 6.96/2.39 % (32216)------------------------------
% 6.96/2.39 % (32216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.96/2.39 % (32216)Termination reason: Unknown
% 6.96/2.39 % (32216)Termination phase: Saturation
% 6.96/2.39
% 6.96/2.39 % (32216)Memory used [KB]: 12409
% 6.96/2.39 % (32216)Time elapsed: 0.353 s
% 6.96/2.39 % (32216)Instructions burned: 1089 (million)
% 6.96/2.39 % (32216)------------------------------
% 6.96/2.39 % (32216)------------------------------
% 7.89/2.40 % (32250)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_31785 for (2992ds/154Mi)
% 7.89/2.41 % (32246)Instruction limit reached!
% 7.89/2.41 % (32246)------------------------------
% 7.89/2.41 % (32246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.41 % (32246)Termination reason: Unknown
% 7.89/2.41 % (32246)Termination phase: Saturation
% 7.89/2.41
% 7.89/2.41 % (32246)Memory used [KB]: 7547
% 7.89/2.41 % (32246)Time elapsed: 0.077 s
% 7.89/2.41 % (32246)Instructions burned: 299 (million)
% 7.89/2.41 % (32246)------------------------------
% 7.89/2.41 % (32246)------------------------------
% 7.89/2.41 % (32248)Instruction limit reached!
% 7.89/2.41 % (32248)------------------------------
% 7.89/2.41 % (32248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.41 % (32248)Termination reason: Unknown
% 7.89/2.41 % (32248)Termination phase: Saturation
% 7.89/2.41
% 7.89/2.41 % (32248)Memory used [KB]: 7419
% 7.89/2.41 % (32248)Time elapsed: 0.050 s
% 7.89/2.41 % (32248)Instructions burned: 184 (million)
% 7.89/2.41 % (32248)------------------------------
% 7.89/2.41 % (32248)------------------------------
% 7.89/2.42 % (32243)Instruction limit reached!
% 7.89/2.42 % (32243)------------------------------
% 7.89/2.42 % (32243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.42 % (32243)Termination reason: Unknown
% 7.89/2.42 % (32243)Termination phase: Saturation
% 7.89/2.42
% 7.89/2.42 % (32243)Memory used [KB]: 8443
% 7.89/2.42 % (32243)Time elapsed: 0.091 s
% 7.89/2.42 % (32243)Instructions burned: 234 (million)
% 7.89/2.42 % (32243)------------------------------
% 7.89/2.42 % (32243)------------------------------
% 7.89/2.42 % (32251)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_31785 for (2992ds/79Mi)
% 7.89/2.42 % (32252)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_31785 for (2992ds/216Mi)
% 7.89/2.43 % (32253)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_31785 for (2992ds/114Mi)
% 7.89/2.43 % (32249)Instruction limit reached!
% 7.89/2.43 % (32249)------------------------------
% 7.89/2.43 % (32249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.43 % (32249)Termination reason: Unknown
% 7.89/2.43 % (32249)Termination phase: Property scanning
% 7.89/2.43
% 7.89/2.43 % (32249)Memory used [KB]: 4989
% 7.89/2.43 % (32249)Time elapsed: 0.054 s
% 7.89/2.43 % (32249)Instructions burned: 185 (million)
% 7.89/2.43 % (32249)------------------------------
% 7.89/2.43 % (32249)------------------------------
% 7.89/2.44 % (32251)Instruction limit reached!
% 7.89/2.44 % (32251)------------------------------
% 7.89/2.44 % (32251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.44 % (32251)Termination reason: Unknown
% 7.89/2.44 % (32251)Termination phase: Property scanning
% 7.89/2.44
% 7.89/2.44 % (32251)Memory used [KB]: 2558
% 7.89/2.44 % (32251)Time elapsed: 0.022 s
% 7.89/2.44 % (32251)Instructions burned: 80 (million)
% 7.89/2.44 % (32251)------------------------------
% 7.89/2.44 % (32251)------------------------------
% 7.89/2.44 % (32254)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_31785 for (2992ds/922Mi)
% 7.89/2.44 % (32250)Instruction limit reached!
% 7.89/2.44 % (32250)------------------------------
% 7.89/2.44 % (32250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.44 % (32250)Termination reason: Unknown
% 7.89/2.44 % (32250)Termination phase: Property scanning
% 7.89/2.44
% 7.89/2.44 % (32250)Memory used [KB]: 2686
% 7.89/2.44 % (32250)Time elapsed: 0.040 s
% 7.89/2.44 % (32250)Instructions burned: 155 (million)
% 7.89/2.44 % (32250)------------------------------
% 7.89/2.44 % (32250)------------------------------
% 7.89/2.45 % (32244)Instruction limit reached!
% 7.89/2.45 % (32244)------------------------------
% 7.89/2.45 % (32244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.45 % (32244)Termination reason: Unknown
% 7.89/2.45 % (32244)Termination phase: Saturation
% 7.89/2.45
% 7.89/2.45 % (32244)Memory used [KB]: 9594
% 7.89/2.45 % (32244)Time elapsed: 0.127 s
% 7.89/2.45 % (32244)Instructions burned: 458 (million)
% 7.89/2.45 % (32244)------------------------------
% 7.89/2.45 % (32244)------------------------------
% 7.89/2.45 % (32255)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_31785 for (2992ds/182Mi)
% 7.89/2.45 % (32256)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_31785 for (2992ds/164Mi)
% 7.89/2.46 % (32257)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_31785 for (2992ds/50Mi)
% 7.89/2.46 % (32253)Instruction limit reached!
% 7.89/2.46 % (32253)------------------------------
% 7.89/2.46 % (32253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.46 % (32253)Termination reason: Unknown
% 7.89/2.46 % (32253)Termination phase: Property scanning
% 7.89/2.46
% 7.89/2.46 % (32253)Memory used [KB]: 2686
% 7.89/2.46 % (32253)Time elapsed: 0.033 s
% 7.89/2.46 % (32253)Instructions burned: 115 (million)
% 7.89/2.46 % (32253)------------------------------
% 7.89/2.46 % (32253)------------------------------
% 7.89/2.47 % (32258)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_31785 for (2992ds/368Mi)
% 7.89/2.47 % (32257)Instruction limit reached!
% 7.89/2.47 % (32257)------------------------------
% 7.89/2.47 % (32257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.47 % (32257)Termination reason: Unknown
% 7.89/2.47 % (32257)Termination phase: shuffling
% 7.89/2.47
% 7.89/2.47 % (32257)Memory used [KB]: 2430
% 7.89/2.47 % (32257)Time elapsed: 0.016 s
% 7.89/2.47 % (32257)Instructions burned: 52 (million)
% 7.89/2.47 % (32257)------------------------------
% 7.89/2.47 % (32257)------------------------------
% 7.89/2.48 % (32252)Instruction limit reached!
% 7.89/2.48 % (32252)------------------------------
% 7.89/2.48 % (32252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.48 % (32252)Termination reason: Unknown
% 7.89/2.48 % (32252)Termination phase: Saturation
% 7.89/2.48
% 7.89/2.48 % (32252)Memory used [KB]: 7547
% 7.89/2.48 % (32252)Time elapsed: 0.055 s
% 7.89/2.48 % (32252)Instructions burned: 218 (million)
% 7.89/2.48 % (32252)------------------------------
% 7.89/2.48 % (32252)------------------------------
% 7.89/2.48 % (32259)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_31785 for (2991ds/1021Mi)
% 7.89/2.49 % (32260)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_31785 for (2991ds/267Mi)
% 7.89/2.50 % (32256)Instruction limit reached!
% 7.89/2.50 % (32256)------------------------------
% 7.89/2.50 % (32256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.89/2.50 % (32256)Termination reason: Unknown
% 7.89/2.50 % (32256)Termination phase: Property scanning
% 7.89/2.50
% 7.89/2.50 % (32256)Memory used [KB]: 2814
% 7.89/2.50 % (32256)Time elapsed: 0.044 s
% 7.89/2.50 % (32256)Instructions burned: 165 (million)
% 7.89/2.50 % (32256)------------------------------
% 7.89/2.50 % (32256)------------------------------
% 8.55/2.50 % (32255)Instruction limit reached!
% 8.55/2.50 % (32255)------------------------------
% 8.55/2.50 % (32255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.50 % (32255)Termination reason: Unknown
% 8.55/2.50 % (32255)Termination phase: Saturation
% 8.55/2.50
% 8.55/2.50 % (32255)Memory used [KB]: 7419
% 8.55/2.50 % (32255)Time elapsed: 0.048 s
% 8.55/2.50 % (32255)Instructions burned: 182 (million)
% 8.55/2.50 % (32255)------------------------------
% 8.55/2.50 % (32255)------------------------------
% 8.55/2.51 % (32261)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_31785 for (2991ds/204Mi)
% 8.55/2.51 % (32262)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_31785 for (2991ds/26Mi)
% 8.55/2.52 % (32262)Instruction limit reached!
% 8.55/2.52 % (32262)------------------------------
% 8.55/2.52 % (32262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.52 % (32262)Termination reason: Unknown
% 8.55/2.52 % (32262)Termination phase: shuffling
% 8.55/2.52
% 8.55/2.52 % (32262)Memory used [KB]: 2174
% 8.55/2.52 % (32262)Time elapsed: 0.009 s
% 8.55/2.52 % (32262)Instructions burned: 29 (million)
% 8.55/2.52 % (32262)------------------------------
% 8.55/2.52 % (32262)------------------------------
% 8.55/2.53 % (32263)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_31785 for (2991ds/53Mi)
% 8.55/2.54 % (32263)Instruction limit reached!
% 8.55/2.54 % (32263)------------------------------
% 8.55/2.54 % (32263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.54 % (32263)Termination reason: Unknown
% 8.55/2.54 % (32263)Termination phase: Property scanning
% 8.55/2.54
% 8.55/2.54 % (32263)Memory used [KB]: 2430
% 8.55/2.54 % (32263)Time elapsed: 0.015 s
% 8.55/2.54 % (32263)Instructions burned: 53 (million)
% 8.55/2.54 % (32263)------------------------------
% 8.55/2.54 % (32263)------------------------------
% 8.55/2.55 % (32264)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_31785 for (2991ds/4436Mi)
% 8.55/2.55 % (32260)Instruction limit reached!
% 8.55/2.55 % (32260)------------------------------
% 8.55/2.55 % (32260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.55 % (32260)Termination reason: Unknown
% 8.55/2.55 % (32260)Termination phase: Saturation
% 8.55/2.55
% 8.55/2.55 % (32260)Memory used [KB]: 7547
% 8.55/2.55 % (32260)Time elapsed: 0.069 s
% 8.55/2.55 % (32260)Instructions burned: 268 (million)
% 8.55/2.55 % (32260)------------------------------
% 8.55/2.55 % (32260)------------------------------
% 8.55/2.56 % (32261)Instruction limit reached!
% 8.55/2.56 % (32261)------------------------------
% 8.55/2.56 % (32261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.56 % (32261)Termination reason: Unknown
% 8.55/2.56 % (32261)Termination phase: Saturation
% 8.55/2.56
% 8.55/2.56 % (32261)Memory used [KB]: 7291
% 8.55/2.56 % (32261)Time elapsed: 0.052 s
% 8.55/2.56 % (32261)Instructions burned: 205 (million)
% 8.55/2.56 % (32261)------------------------------
% 8.55/2.56 % (32261)------------------------------
% 8.55/2.56 % (32265)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_31785 for (2990ds/1539Mi)
% 8.55/2.57 % (32266)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_31785 for (2990ds/408Mi)
% 8.55/2.57 % (32258)Instruction limit reached!
% 8.55/2.57 % (32258)------------------------------
% 8.55/2.57 % (32258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.55/2.57 % (32258)Termination reason: Unknown
% 8.55/2.57 % (32258)Termination phase: Saturation
% 8.55/2.57
% 8.55/2.57 % (32258)Memory used [KB]: 9466
% 8.55/2.57 % (32258)Time elapsed: 0.101 s
% 8.55/2.57 % (32258)Instructions burned: 368 (million)
% 8.55/2.57 % (32258)------------------------------
% 8.55/2.57 % (32258)------------------------------
% 8.55/2.58 % (32267)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_31785 for (2990ds/5205Mi)
% 8.94/2.61 % (32247)Instruction limit reached!
% 8.94/2.61 % (32247)------------------------------
% 8.94/2.61 % (32247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.94/2.61 % (32247)Termination reason: Unknown
% 8.94/2.61 % (32247)Termination phase: Saturation
% 8.94/2.61
% 8.94/2.61 % (32247)Memory used [KB]: 15735
% 8.94/2.61 % (32247)Time elapsed: 0.255 s
% 8.94/2.61 % (32247)Instructions burned: 987 (million)
% 8.94/2.61 % (32247)------------------------------
% 8.94/2.61 % (32247)------------------------------
% 8.94/2.62 % (32268)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_31785 for (2990ds/1913Mi)
% 8.94/2.69 % (32266)Instruction limit reached!
% 8.94/2.69 % (32266)------------------------------
% 8.94/2.69 % (32266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.94/2.69 % (32266)Termination reason: Unknown
% 8.94/2.69 % (32266)Termination phase: Saturation
% 8.94/2.69
% 8.94/2.69 % (32266)Memory used [KB]: 11129
% 8.94/2.69 % (32266)Time elapsed: 0.123 s
% 8.94/2.69 % (32266)Instructions burned: 411 (million)
% 8.94/2.69 % (32266)------------------------------
% 8.94/2.69 % (32266)------------------------------
% 9.33/2.70 % (32269)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_31785 for (2989ds/4350Mi)
% 9.33/2.73 % (32254)Instruction limit reached!
% 9.33/2.73 % (32254)------------------------------
% 9.33/2.73 % (32254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.73 % (32254)Termination reason: Unknown
% 9.33/2.73 % (32254)Termination phase: Saturation
% 9.33/2.73
% 9.33/2.73 % (32254)Memory used [KB]: 12281
% 9.33/2.73 % (32254)Time elapsed: 0.287 s
% 9.33/2.73 % (32254)Instructions burned: 924 (million)
% 9.33/2.73 % (32254)------------------------------
% 9.33/2.73 % (32254)------------------------------
% 9.33/2.74 % (32270)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_31785 for (2989ds/68Mi)
% 9.33/2.76 % (32270)Instruction limit reached!
% 9.33/2.76 % (32270)------------------------------
% 9.33/2.76 % (32270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.33/2.76 % (32270)Termination reason: Unknown
% 9.33/2.76 % (32270)Termination phase: Property scanning
% 9.33/2.76
% 9.33/2.76 % (32270)Memory used [KB]: 2558
% 9.33/2.76 % (32270)Time elapsed: 0.020 s
% 9.33/2.76 % (32270)Instructions burned: 70 (million)
% 9.33/2.76 % (32270)------------------------------
% 9.33/2.76 % (32270)------------------------------
% 9.33/2.77 % (32271)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_31785 for (2988ds/358Mi)
% 9.67/2.80 % (32259)Instruction limit reached!
% 9.67/2.80 % (32259)------------------------------
% 9.67/2.80 % (32259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.80 % (32259)Termination reason: Unknown
% 9.67/2.80 % (32259)Termination phase: Saturation
% 9.67/2.80
% 9.67/2.80 % (32259)Memory used [KB]: 12792
% 9.67/2.80 % (32259)Time elapsed: 0.344 s
% 9.67/2.80 % (32259)Instructions burned: 1024 (million)
% 9.67/2.80 % (32259)------------------------------
% 9.67/2.80 % (32259)------------------------------
% 9.67/2.81 % (32272)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_31785 for (2988ds/31Mi)
% 9.67/2.82 % (32272)Instruction limit reached!
% 9.67/2.82 % (32272)------------------------------
% 9.67/2.82 % (32272)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.82 % (32272)Termination reason: Unknown
% 9.67/2.82 % (32272)Termination phase: shuffling
% 9.67/2.82
% 9.67/2.82 % (32272)Memory used [KB]: 2046
% 9.67/2.82 % (32272)Time elapsed: 0.010 s
% 9.67/2.82 % (32272)Instructions burned: 32 (million)
% 9.67/2.82 % (32272)------------------------------
% 9.67/2.82 % (32272)------------------------------
% 9.67/2.83 % (32273)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_31785 for (2988ds/279Mi)
% 9.67/2.86 % (32271)Instruction limit reached!
% 9.67/2.86 % (32271)------------------------------
% 9.67/2.86 % (32271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.67/2.86 % (32271)Termination reason: Unknown
% 9.67/2.86 % (32271)Termination phase: Saturation
% 9.67/2.86
% 9.67/2.86 % (32271)Memory used [KB]: 8571
% 9.67/2.86 % (32271)Time elapsed: 0.094 s
% 9.67/2.86 % (32271)Instructions burned: 358 (million)
% 9.67/2.86 % (32271)------------------------------
% 9.67/2.86 % (32271)------------------------------
% 9.67/2.87 % (32274)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_31785 for (2987ds/258Mi)
% 10.12/2.90 % (32273)Instruction limit reached!
% 10.12/2.90 % (32273)------------------------------
% 10.12/2.90 % (32273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.90 % (32273)Termination reason: Unknown
% 10.12/2.90 % (32273)Termination phase: Saturation
% 10.12/2.90
% 10.12/2.90 % (32273)Memory used [KB]: 7547
% 10.12/2.90 % (32273)Time elapsed: 0.073 s
% 10.12/2.90 % (32273)Instructions burned: 281 (million)
% 10.12/2.90 % (32273)------------------------------
% 10.12/2.90 % (32273)------------------------------
% 10.12/2.91 % (32275)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_31785 for (2987ds/26Mi)
% 10.12/2.92 % (32275)Instruction limit reached!
% 10.12/2.92 % (32275)------------------------------
% 10.12/2.92 % (32275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.92 % (32275)Termination reason: Unknown
% 10.12/2.92 % (32275)Termination phase: shuffling
% 10.12/2.92
% 10.12/2.92 % (32275)Memory used [KB]: 2046
% 10.12/2.92 % (32275)Time elapsed: 0.009 s
% 10.12/2.92 % (32275)Instructions burned: 29 (million)
% 10.12/2.92 % (32275)------------------------------
% 10.12/2.92 % (32275)------------------------------
% 10.12/2.93 % (32276)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_31785 for (2987ds/995Mi)
% 10.12/2.94 % (32274)Instruction limit reached!
% 10.12/2.94 % (32274)------------------------------
% 10.12/2.94 % (32274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.12/2.94 % (32274)Termination reason: Unknown
% 10.12/2.94 % (32274)Termination phase: Saturation
% 10.12/2.94
% 10.12/2.94 % (32274)Memory used [KB]: 8315
% 10.12/2.94 % (32274)Time elapsed: 0.070 s
% 10.12/2.94 % (32274)Instructions burned: 259 (million)
% 10.12/2.94 % (32274)------------------------------
% 10.12/2.94 % (32274)------------------------------
% 10.12/2.95 % (32277)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_31785 for (2987ds/373Mi)
% 12.50/3.03 % (32265)Instruction limit reached!
% 12.50/3.03 % (32265)------------------------------
% 12.50/3.03 % (32265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.50/3.03 % (32265)Termination reason: Unknown
% 12.50/3.03 % (32265)Termination phase: Saturation
% 12.50/3.03
% 12.50/3.03 % (32265)Memory used [KB]: 11129
% 12.50/3.03 % (32265)Time elapsed: 0.472 s
% 12.50/3.03 % (32265)Instructions burned: 1541 (million)
% 12.50/3.03 % (32265)------------------------------
% 12.50/3.03 % (32265)------------------------------
% 12.50/3.05 % (32278)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_31785 for (2986ds/253Mi)
% 12.50/3.05 % (32277)Instruction limit reached!
% 12.50/3.05 % (32277)------------------------------
% 12.50/3.05 % (32277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.50/3.05 % (32277)Termination reason: Unknown
% 12.50/3.05 % (32277)Termination phase: Saturation
% 12.50/3.05
% 12.50/3.05 % (32277)Memory used [KB]: 9466
% 12.50/3.05 % (32277)Time elapsed: 0.101 s
% 12.50/3.05 % (32277)Instructions burned: 374 (million)
% 12.50/3.05 % (32277)------------------------------
% 12.50/3.05 % (32277)------------------------------
% 12.50/3.06 % (32279)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_31785 for (2986ds/832Mi)
% 12.50/3.11 % (32278)Instruction limit reached!
% 12.50/3.11 % (32278)------------------------------
% 12.50/3.11 % (32278)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.50/3.11 % (32278)Termination reason: Unknown
% 12.50/3.11 % (32278)Termination phase: Saturation
% 12.50/3.11
% 12.50/3.11 % (32278)Memory used [KB]: 7419
% 12.50/3.11 % (32278)Time elapsed: 0.065 s
% 12.50/3.11 % (32278)Instructions burned: 256 (million)
% 12.50/3.11 % (32278)------------------------------
% 12.50/3.11 % (32278)------------------------------
% 13.15/3.12 % (32280)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_31785 for (2985ds/668Mi)
% 13.15/3.18 % (32276)Instruction limit reached!
% 13.15/3.18 % (32276)------------------------------
% 13.15/3.18 % (32276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.15/3.18 % (32276)Termination reason: Unknown
% 13.15/3.18 % (32276)Termination phase: Saturation
% 13.15/3.18
% 13.15/3.18 % (32276)Memory used [KB]: 15735
% 13.15/3.18 % (32276)Time elapsed: 0.254 s
% 13.15/3.18 % (32276)Instructions burned: 998 (million)
% 13.15/3.18 % (32276)------------------------------
% 13.15/3.18 % (32276)------------------------------
% 13.15/3.19 % (32281)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_31785 for (2984ds/40Mi)
% 13.57/3.20 % (32281)Instruction limit reached!
% 13.57/3.20 % (32281)------------------------------
% 13.57/3.20 % (32281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.57/3.20 % (32268)Instruction limit reached!
% 13.57/3.20 % (32268)------------------------------
% 13.57/3.20 % (32268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.57/3.20 % (32268)Termination reason: Unknown
% 13.57/3.20 % (32268)Termination phase: Saturation
% 13.57/3.20
% 13.57/3.20 % (32268)Memory used [KB]: 6396
% 13.57/3.20 % (32268)Time elapsed: 0.587 s
% 13.57/3.20 % (32268)Instructions burned: 1914 (million)
% 13.57/3.20 % (32268)------------------------------
% 13.57/3.20 % (32268)------------------------------
% 13.57/3.20 % (32281)Termination reason: Unknown
% 13.57/3.20 % (32281)Termination phase: shuffling
% 13.57/3.20
% 13.57/3.20 % (32281)Memory used [KB]: 2302
% 13.57/3.20 % (32281)Time elapsed: 0.012 s
% 13.57/3.20 % (32281)Instructions burned: 40 (million)
% 13.57/3.20 % (32281)------------------------------
% 13.57/3.20 % (32281)------------------------------
% 13.57/3.21 % (32282)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_31785 for (2984ds/294Mi)
% 13.57/3.21 % (32283)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_31785 for (2984ds/187Mi)
% 13.57/3.26 % (32283)Instruction limit reached!
% 13.57/3.26 % (32283)------------------------------
% 13.57/3.26 % (32283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.57/3.26 % (32283)Termination reason: Unknown
% 13.57/3.26 % (32283)Termination phase: Saturation
% 13.57/3.26
% 13.57/3.26 % (32283)Memory used [KB]: 7419
% 13.57/3.26 % (32283)Time elapsed: 0.049 s
% 13.57/3.26 % (32283)Instructions burned: 189 (million)
% 13.57/3.26 % (32283)------------------------------
% 13.57/3.26 % (32283)------------------------------
% 13.57/3.27 % (32284)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_31785 for (2984ds/371Mi)
% 13.57/3.29 % (32282)Instruction limit reached!
% 13.57/3.29 % (32282)------------------------------
% 13.57/3.29 % (32282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.57/3.29 % (32282)Termination reason: Unknown
% 13.57/3.29 % (32282)Termination phase: Saturation
% 13.57/3.29
% 13.57/3.29 % (32282)Memory used [KB]: 7547
% 13.57/3.29 % (32282)Time elapsed: 0.075 s
% 13.57/3.29 % (32282)Instructions burned: 296 (million)
% 13.57/3.29 % (32282)------------------------------
% 13.57/3.29 % (32282)------------------------------
% 13.57/3.29 % (32280)Instruction limit reached!
% 13.57/3.29 % (32280)------------------------------
% 13.57/3.29 % (32280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.57/3.29 % (32280)Termination reason: Unknown
% 13.57/3.29 % (32280)Termination phase: Saturation
% 13.57/3.29
% 13.57/3.29 % (32280)Memory used [KB]: 16247
% 13.57/3.29 % (32280)Time elapsed: 0.170 s
% 13.57/3.29 % (32280)Instructions burned: 670 (million)
% 13.57/3.29 % (32280)------------------------------
% 13.57/3.29 % (32280)------------------------------
% 13.57/3.30 % (32285)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_31785 for (2983ds/1827Mi)
% 14.23/3.30 % (32286)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_31785 for (2983ds/70Mi)
% 14.23/3.31 % (32279)Instruction limit reached!
% 14.23/3.31 % (32279)------------------------------
% 14.23/3.31 % (32279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.23/3.31 % (32279)Termination reason: Unknown
% 14.23/3.31 % (32279)Termination phase: Saturation
% 14.23/3.31
% 14.23/3.31 % (32279)Memory used [KB]: 11513
% 14.23/3.31 % (32279)Time elapsed: 0.276 s
% 14.23/3.31 % (32279)Instructions burned: 833 (million)
% 14.23/3.31 % (32279)------------------------------
% 14.23/3.31 % (32279)------------------------------
% 14.23/3.32 % (32286)Instruction limit reached!
% 14.23/3.32 % (32286)------------------------------
% 14.23/3.32 % (32286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.23/3.32 % (32286)Termination reason: Unknown
% 14.23/3.32 % (32286)Termination phase: Property scanning
% 14.23/3.32
% 14.23/3.32 % (32286)Memory used [KB]: 2558
% 14.23/3.32 % (32286)Time elapsed: 0.020 s
% 14.23/3.32 % (32286)Instructions burned: 73 (million)
% 14.23/3.32 % (32286)------------------------------
% 14.23/3.32 % (32286)------------------------------
% 14.23/3.32 % (32287)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_31785 for (2983ds/316Mi)
% 14.23/3.33 % (32288)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_31785 for (2983ds/932Mi)
% 14.23/3.37 % (32284)Instruction limit reached!
% 14.23/3.37 % (32284)------------------------------
% 14.23/3.37 % (32284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.23/3.37 % (32284)Termination reason: Unknown
% 14.23/3.37 % (32284)Termination phase: Saturation
% 14.23/3.37
% 14.23/3.37 % (32284)Memory used [KB]: 9338
% 14.23/3.37 % (32284)Time elapsed: 0.099 s
% 14.23/3.37 % (32284)Instructions burned: 373 (million)
% 14.23/3.37 % (32284)------------------------------
% 14.23/3.37 % (32284)------------------------------
% 14.23/3.38 % (32289)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_31785 for (2982ds/4714Mi)
% 14.93/3.40 % (32287)Instruction limit reached!
% 14.93/3.40 % (32287)------------------------------
% 14.93/3.40 % (32287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.93/3.40 % (32287)Termination reason: Unknown
% 14.93/3.40 % (32287)Termination phase: Saturation
% 14.93/3.40
% 14.93/3.40 % (32287)Memory used [KB]: 7547
% 14.93/3.40 % (32287)Time elapsed: 0.080 s
% 14.93/3.40 % (32287)Instructions burned: 319 (million)
% 14.93/3.40 % (32287)------------------------------
% 14.93/3.40 % (32287)------------------------------
% 14.93/3.41 % (32290)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_31785 for (2982ds/8250Mi)
% 15.32/3.56 % (32288)Instruction limit reached!
% 15.32/3.56 % (32288)------------------------------
% 15.32/3.56 % (32288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.32/3.56 % (32288)Termination reason: Unknown
% 15.32/3.56 % (32288)Termination phase: Saturation
% 15.32/3.56
% 15.32/3.56 % (32288)Memory used [KB]: 16375
% 15.32/3.56 % (32288)Time elapsed: 0.236 s
% 15.32/3.56 % (32288)Instructions burned: 933 (million)
% 15.32/3.56 % (32288)------------------------------
% 15.32/3.56 % (32288)------------------------------
% 15.32/3.57 % (32291)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_31785 for (2980ds/770Mi)
% 16.18/3.79 % (32291)Instruction limit reached!
% 16.18/3.79 % (32291)------------------------------
% 16.18/3.79 % (32291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.18/3.79 % (32291)Termination reason: Unknown
% 16.18/3.79 % (32291)Termination phase: Saturation
% 16.18/3.79
% 16.18/3.79 % (32291)Memory used [KB]: 7675
% 16.18/3.79 % (32291)Time elapsed: 0.218 s
% 16.18/3.79 % (32291)Instructions burned: 770 (million)
% 16.18/3.79 % (32291)------------------------------
% 16.18/3.79 % (32291)------------------------------
% 16.70/3.80 % (32292)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_31785 for (2978ds/794Mi)
% 16.70/3.82 % (32285)Instruction limit reached!
% 16.70/3.82 % (32285)------------------------------
% 16.70/3.82 % (32285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.70/3.82 % (32285)Termination reason: Unknown
% 16.70/3.82 % (32285)Termination phase: Saturation
% 16.70/3.82
% 16.70/3.82 % (32285)Memory used [KB]: 20852
% 16.70/3.82 % (32285)Time elapsed: 0.530 s
% 16.70/3.82 % (32285)Instructions burned: 1829 (million)
% 16.70/3.82 % (32285)------------------------------
% 16.70/3.82 % (32285)------------------------------
% 16.70/3.84 % (32293)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_31785 for (2978ds/464Mi)
% 17.55/3.94 % (32264)Instruction limit reached!
% 17.55/3.94 % (32264)------------------------------
% 17.55/3.94 % (32264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.55/3.94 % (32264)Termination reason: Unknown
% 17.55/3.94 % (32264)Termination phase: Saturation
% 17.55/3.94
% 17.55/3.94 % (32264)Memory used [KB]: 18166
% 17.55/3.94 % (32264)Time elapsed: 1.394 s
% 17.55/3.94 % (32264)Instructions burned: 4439 (million)
% 17.55/3.94 % (32264)------------------------------
% 17.55/3.94 % (32264)------------------------------
% 17.55/3.95 % (32267)Instruction limit reached!
% 17.55/3.95 % (32267)------------------------------
% 17.55/3.95 % (32267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.55/3.95 % (32267)Termination reason: Unknown
% 17.55/3.95 % (32267)Termination phase: Saturation
% 17.55/3.95
% 17.55/3.95 % (32267)Memory used [KB]: 17014
% 17.55/3.95 % (32267)Time elapsed: 1.373 s
% 17.55/3.95 % (32267)Instructions burned: 5206 (million)
% 17.55/3.95 % (32267)------------------------------
% 17.55/3.95 % (32267)------------------------------
% 17.55/3.95 % (32294)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_31785 for (2977ds/1376Mi)
% 17.55/3.96 % (32295)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_31785 for (2976ds/906Mi)
% 17.55/3.96 % (32293)Instruction limit reached!
% 17.55/3.96 % (32293)------------------------------
% 17.55/3.96 % (32293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.55/3.96 % (32293)Termination reason: Unknown
% 17.55/3.96 % (32293)Termination phase: Saturation
% 17.55/3.96
% 17.55/3.96 % (32293)Memory used [KB]: 9594
% 17.55/3.96 % (32293)Time elapsed: 0.129 s
% 17.55/3.96 % (32293)Instructions burned: 464 (million)
% 17.55/3.96 % (32293)------------------------------
% 17.55/3.96 % (32293)------------------------------
% 17.55/3.97 % (32296)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_31785 for (2976ds/434Mi)
% 19.62/4.03 % (32292)Instruction limit reached!
% 19.62/4.03 % (32292)------------------------------
% 19.62/4.03 % (32292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.62/4.03 % (32292)Termination reason: Unknown
% 19.62/4.03 % (32292)Termination phase: Saturation
% 19.62/4.03
% 19.62/4.03 % (32292)Memory used [KB]: 5884
% 19.62/4.03 % (32292)Time elapsed: 0.235 s
% 19.62/4.03 % (32292)Instructions burned: 796 (million)
% 19.62/4.03 % (32292)------------------------------
% 19.62/4.03 % (32292)------------------------------
% 19.62/4.04 % (32269)Instruction limit reached!
% 19.62/4.04 % (32269)------------------------------
% 19.62/4.04 % (32269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.62/4.04 % (32269)Termination reason: Unknown
% 19.62/4.04 % (32269)Termination phase: Saturation
% 19.62/4.04
% 19.62/4.04 % (32269)Memory used [KB]: 13944
% 19.62/4.04 % (32269)Time elapsed: 1.345 s
% 19.62/4.04 % (32269)Instructions burned: 4351 (million)
% 19.62/4.04 % (32269)------------------------------
% 19.62/4.04 % (32269)------------------------------
% 19.62/4.04 % (32297)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_31785 for (2976ds/865Mi)
% 19.62/4.05 % (32298)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_31785 for (2976ds/593Mi)
% 19.62/4.10 % (32296)Instruction limit reached!
% 19.62/4.10 % (32296)------------------------------
% 19.62/4.10 % (32296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.62/4.10 % (32296)Termination reason: Unknown
% 19.62/4.10 % (32296)Termination phase: Saturation
% 19.62/4.10
% 19.62/4.10 % (32296)Memory used [KB]: 11001
% 19.62/4.10 % (32296)Time elapsed: 0.131 s
% 19.62/4.10 % (32296)Instructions burned: 436 (million)
% 19.62/4.10 % (32296)------------------------------
% 19.62/4.10 % (32296)------------------------------
% 19.62/4.11 % (32299)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_31785 for (2975ds/443Mi)
% 20.43/4.21 % (32298)Instruction limit reached!
% 20.43/4.21 % (32298)------------------------------
% 20.43/4.21 % (32298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.21 % (32298)Termination reason: Unknown
% 20.43/4.21 % (32298)Termination phase: Saturation
% 20.43/4.21
% 20.43/4.21 % (32298)Memory used [KB]: 7675
% 20.43/4.21 % (32298)Time elapsed: 0.155 s
% 20.43/4.21 % (32298)Instructions burned: 596 (million)
% 20.43/4.21 % (32298)------------------------------
% 20.43/4.21 % (32298)------------------------------
% 20.43/4.22 % (32300)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_31785 for (2974ds/594Mi)
% 20.43/4.24 % (32299)Instruction limit reached!
% 20.43/4.24 % (32299)------------------------------
% 20.43/4.24 % (32299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.24 % (32299)Termination reason: Unknown
% 20.43/4.24 % (32299)Termination phase: Saturation
% 20.43/4.24
% 20.43/4.24 % (32299)Memory used [KB]: 9594
% 20.43/4.24 % (32299)Time elapsed: 0.125 s
% 20.43/4.24 % (32299)Instructions burned: 443 (million)
% 20.43/4.24 % (32299)------------------------------
% 20.43/4.24 % (32299)------------------------------
% 20.43/4.24 % (32295)Instruction limit reached!
% 20.43/4.24 % (32295)------------------------------
% 20.43/4.24 % (32295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.43/4.24 % (32295)Termination reason: Unknown
% 20.43/4.24 % (32295)Termination phase: Saturation
% 20.43/4.24
% 20.43/4.24 % (32295)Memory used [KB]: 11257
% 20.43/4.24 % (32295)Time elapsed: 0.279 s
% 20.43/4.24 % (32295)Instructions burned: 906 (million)
% 20.43/4.24 % (32295)------------------------------
% 20.43/4.24 % (32295)------------------------------
% 20.43/4.25 % (32301)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_31785 for (2974ds/327Mi)
% 20.43/4.25 % (32302)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_31785 for (2974ds/5411Mi)
% 21.09/4.30 % (32297)Instruction limit reached!
% 21.09/4.30 % (32297)------------------------------
% 21.09/4.30 % (32297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.09/4.30 % (32297)Termination reason: Unknown
% 21.09/4.30 % (32297)Termination phase: Saturation
% 21.09/4.30
% 21.09/4.30 % (32297)Memory used [KB]: 9978
% 21.09/4.30 % (32297)Time elapsed: 0.260 s
% 21.09/4.30 % (32297)Instructions burned: 867 (million)
% 21.09/4.30 % (32297)------------------------------
% 21.09/4.30 % (32297)------------------------------
% 21.09/4.31 % (32294)Instruction limit reached!
% 21.09/4.31 % (32294)------------------------------
% 21.09/4.31 % (32294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.09/4.31 % (32294)Termination reason: Unknown
% 21.09/4.31 % (32294)Termination phase: Saturation
% 21.09/4.31
% 21.09/4.31 % (32294)Memory used [KB]: 10106
% 21.09/4.31 % (32294)Time elapsed: 0.355 s
% 21.09/4.31 % (32294)Instructions burned: 1377 (million)
% 21.09/4.31 % (32294)------------------------------
% 21.09/4.31 % (32294)------------------------------
% 21.09/4.31 % (32303)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_31785 for (2973ds/1762Mi)
% 21.09/4.32 % (32304)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_31785 for (2973ds/96Mi)
% 21.09/4.34 % (32304)Instruction limit reached!
% 21.09/4.34 % (32304)------------------------------
% 21.09/4.34 % (32304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.09/4.34 % (32304)Termination reason: Unknown
% 21.09/4.34 % (32304)Termination phase: Property scanning
% 21.09/4.34
% 21.09/4.34 % (32304)Memory used [KB]: 2558
% 21.09/4.34 % (32304)Time elapsed: 0.026 s
% 21.09/4.34 % (32304)Instructions burned: 98 (million)
% 21.09/4.34 % (32304)------------------------------
% 21.09/4.34 % (32304)------------------------------
% 21.09/4.34 % (32301)Instruction limit reached!
% 21.09/4.34 % (32301)------------------------------
% 21.09/4.34 % (32301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.09/4.34 % (32301)Termination reason: Unknown
% 21.09/4.34 % (32301)Termination phase: Saturation
% 21.09/4.34
% 21.09/4.34 % (32301)Memory used [KB]: 11257
% 21.09/4.34 % (32301)Time elapsed: 0.098 s
% 21.09/4.34 % (32301)Instructions burned: 329 (million)
% 21.09/4.34 % (32301)------------------------------
% 21.09/4.34 % (32301)------------------------------
% 21.09/4.35 % (32305)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_31785 for (2973ds/503Mi)
% 21.09/4.35 % (32306)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_31785 for (2973ds/90Mi)
% 21.09/4.38 % (32306)Instruction limit reached!
% 21.09/4.38 % (32306)------------------------------
% 21.09/4.38 % (32306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.09/4.38 % (32306)Termination reason: Unknown
% 21.09/4.38 % (32306)Termination phase: Property scanning
% 21.09/4.38
% 21.09/4.38 % (32306)Memory used [KB]: 2686
% 21.09/4.38 % (32306)Time elapsed: 0.025 s
% 21.09/4.38 % (32306)Instructions burned: 91 (million)
% 21.09/4.38 % (32306)------------------------------
% 21.09/4.38 % (32306)------------------------------
% 21.09/4.38 % (32300)Instruction limit reached!
% 21.09/4.38 % (32300)------------------------------
% 21.09/4.38 % (32300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.09/4.38 % (32300)Termination reason: Unknown
% 21.09/4.38 % (32300)Termination phase: Saturation
% 21.09/4.38
% 21.09/4.38 % (32300)Memory used [KB]: 9722
% 21.09/4.38 % (32300)Time elapsed: 0.169 s
% 21.09/4.38 % (32300)Instructions burned: 594 (million)
% 21.09/4.38 % (32300)------------------------------
% 21.09/4.38 % (32300)------------------------------
% 21.09/4.39 % (32307)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_31785 for (2972ds/593Mi)
% 21.09/4.39 % (32308)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_31785 for (2972ds/1512Mi)
% 21.94/4.49 % (32305)Instruction limit reached!
% 21.94/4.49 % (32305)------------------------------
% 21.94/4.49 % (32305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.94/4.49 % (32305)Termination reason: Unknown
% 21.94/4.49 % (32305)Termination phase: Saturation
% 21.94/4.49
% 21.94/4.49 % (32305)Memory used [KB]: 9850
% 21.94/4.49 % (32305)Time elapsed: 0.140 s
% 21.94/4.49 % (32305)Instructions burned: 503 (million)
% 21.94/4.49 % (32305)------------------------------
% 21.94/4.49 % (32305)------------------------------
% 22.27/4.50 % (32309)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_31785 for (2971ds/569Mi)
% 22.27/4.56 % (32307)Instruction limit reached!
% 22.27/4.56 % (32307)------------------------------
% 22.27/4.56 % (32307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.27/4.56 % (32307)Termination reason: Unknown
% 22.27/4.56 % (32307)Termination phase: Saturation
% 22.27/4.56
% 22.27/4.56 % (32307)Memory used [KB]: 10106
% 22.27/4.56 % (32307)Time elapsed: 0.172 s
% 22.27/4.56 % (32307)Instructions burned: 593 (million)
% 22.27/4.56 % (32307)------------------------------
% 22.27/4.56 % (32307)------------------------------
% 22.27/4.56 % (32289)Instruction limit reached!
% 22.27/4.56 % (32289)------------------------------
% 22.27/4.56 % (32289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.27/4.56 % (32289)Termination reason: Unknown
% 22.27/4.56 % (32289)Termination phase: Saturation
% 22.27/4.56
% 22.27/4.56 % (32289)Memory used [KB]: 7675
% 22.27/4.56 % (32289)Time elapsed: 1.183 s
% 22.27/4.56 % (32289)Instructions burned: 4714 (million)
% 22.27/4.56 % (32289)------------------------------
% 22.27/4.56 % (32289)------------------------------
% 22.27/4.57 % (32310)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_31785 for (2970ds/501Mi)
% 22.27/4.57 % (32311)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_31785 for (2970ds/562Mi)
% 22.63/4.64 % (32309)Instruction limit reached!
% 22.63/4.64 % (32309)------------------------------
% 22.63/4.64 % (32309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.63/4.64 % (32309)Termination reason: Unknown
% 22.63/4.64 % (32309)Termination phase: Saturation
% 22.63/4.64
% 22.63/4.64 % (32309)Memory used [KB]: 8571
% 22.63/4.64 % (32309)Time elapsed: 0.145 s
% 22.63/4.64 % (32309)Instructions burned: 569 (million)
% 22.63/4.64 % (32309)------------------------------
% 22.63/4.64 % (32309)------------------------------
% 22.63/4.65 % (32312)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_31785 for (2970ds/406Mi)
% 22.90/4.72 % (32310)Instruction limit reached!
% 22.90/4.72 % (32310)------------------------------
% 22.90/4.72 % (32310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.90/4.72 % (32310)Termination reason: Unknown
% 22.90/4.72 % (32310)Termination phase: Saturation
% 22.90/4.72
% 22.90/4.72 % (32310)Memory used [KB]: 10490
% 22.90/4.72 % (32310)Time elapsed: 0.150 s
% 22.90/4.72 % (32310)Instructions burned: 502 (million)
% 22.90/4.72 % (32310)------------------------------
% 22.90/4.72 % (32310)------------------------------
% 22.90/4.73 % (32313)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_31785 for (2969ds/582Mi)
% 22.90/4.73 % (32311)Instruction limit reached!
% 22.90/4.73 % (32311)------------------------------
% 22.90/4.73 % (32311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.90/4.73 % (32311)Termination reason: Unknown
% 22.90/4.73 % (32311)Termination phase: Saturation
% 22.90/4.73
% 22.90/4.73 % (32311)Memory used [KB]: 8699
% 22.90/4.73 % (32311)Time elapsed: 0.163 s
% 22.90/4.73 % (32311)Instructions burned: 563 (million)
% 22.90/4.73 % (32311)------------------------------
% 22.90/4.73 % (32311)------------------------------
% 22.90/4.74 % (32303)Instruction limit reached!
% 22.90/4.74 % (32303)------------------------------
% 22.90/4.74 % (32303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.90/4.74 % (32303)Termination reason: Unknown
% 22.90/4.74 % (32303)Termination phase: Saturation
% 22.90/4.74
% 22.90/4.74 % (32303)Memory used [KB]: 23411
% 22.90/4.74 % (32303)Time elapsed: 0.432 s
% 22.90/4.74 % (32303)Instructions burned: 1763 (million)
% 22.90/4.74 % (32303)------------------------------
% 22.90/4.74 % (32303)------------------------------
% 22.90/4.74 % (32314)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_31785 for (2969ds/456Mi)
% 22.90/4.75 % (32315)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_31785 for (2969ds/393Mi)
% 22.90/4.76 % (32312)Instruction limit reached!
% 22.90/4.76 % (32312)------------------------------
% 22.90/4.76 % (32312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.90/4.76 % (32312)Termination reason: Unknown
% 22.90/4.76 % (32312)Termination phase: Saturation
% 22.90/4.76
% 22.90/4.76 % (32312)Memory used [KB]: 7803
% 22.90/4.76 % (32312)Time elapsed: 0.110 s
% 22.90/4.76 % (32312)Instructions burned: 406 (million)
% 22.90/4.76 % (32312)------------------------------
% 22.90/4.76 % (32312)------------------------------
% 22.90/4.77 % (32316)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_31785 for (2968ds/1335Mi)
% 23.89/4.85 % (32315)Instruction limit reached!
% 23.89/4.85 % (32315)------------------------------
% 23.89/4.85 % (32315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.89/4.85 % (32315)Termination reason: Unknown
% 23.89/4.85 % (32315)Termination phase: Saturation
% 23.89/4.85
% 23.89/4.85 % (32315)Memory used [KB]: 9722
% 23.89/4.85 % (32315)Time elapsed: 0.101 s
% 23.89/4.85 % (32315)Instructions burned: 393 (million)
% 23.89/4.85 % (32315)------------------------------
% 23.89/4.85 % (32315)------------------------------
% 23.89/4.86 % (32317)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_31785 for (2968ds/3373Mi)
% 23.89/4.86 % (32308)Instruction limit reached!
% 23.89/4.86 % (32308)------------------------------
% 23.89/4.86 % (32308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.89/4.86 % (32308)Termination reason: Unknown
% 23.89/4.86 % (32308)Termination phase: Saturation
% 23.89/4.86
% 23.89/4.86 % (32308)Memory used [KB]: 14072
% 23.89/4.86 % (32308)Time elapsed: 0.472 s
% 23.89/4.86 % (32308)Instructions burned: 1512 (million)
% 23.89/4.86 % (32308)------------------------------
% 23.89/4.86 % (32308)------------------------------
% 23.89/4.87 % (32314)Instruction limit reached!
% 23.89/4.87 % (32314)------------------------------
% 23.89/4.87 % (32314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 23.89/4.87 % (32314)Termination reason: Unknown
% 23.89/4.87 % (32314)Termination phase: Saturation
% 23.89/4.87
% 23.89/4.87 % (32314)Memory used [KB]: 9722
% 23.89/4.87 % (32314)Time elapsed: 0.126 s
% 23.89/4.87 % (32314)Instructions burned: 458 (million)
% 23.89/4.87 % (32314)------------------------------
% 23.89/4.87 % (32314)------------------------------
% 23.89/4.88 % (32318)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_31785 for (2967ds/474Mi)
% 23.89/4.88 % (32319)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_31785 for (2967ds/157Mi)
% 24.71/4.91 % (32313)Instruction limit reached!
% 24.71/4.91 % (32313)------------------------------
% 24.71/4.91 % (32313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.91 % (32313)Termination reason: Unknown
% 24.71/4.91 % (32313)Termination phase: Saturation
% 24.71/4.91
% 24.71/4.91 % (32313)Memory used [KB]: 10746
% 24.71/4.91 % (32313)Time elapsed: 0.179 s
% 24.71/4.91 % (32313)Instructions burned: 584 (million)
% 24.71/4.91 % (32313)------------------------------
% 24.71/4.91 % (32313)------------------------------
% 24.71/4.92 % (32320)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_31785 for (2967ds/590Mi)
% 24.71/4.92 % (32319)Instruction limit reached!
% 24.71/4.92 % (32319)------------------------------
% 24.71/4.92 % (32319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.92 % (32319)Termination reason: Unknown
% 24.71/4.92 % (32319)Termination phase: Property scanning
% 24.71/4.92
% 24.71/4.92 % (32319)Memory used [KB]: 2686
% 24.71/4.92 % (32319)Time elapsed: 0.041 s
% 24.71/4.92 % (32319)Instructions burned: 160 (million)
% 24.71/4.92 % (32319)------------------------------
% 24.71/4.92 % (32319)------------------------------
% 24.71/4.93 % (32321)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_31785 for (2967ds/104Mi)
% 24.71/4.95 % (32321)Instruction limit reached!
% 24.71/4.95 % (32321)------------------------------
% 24.71/4.95 % (32321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.95 % (32321)Termination reason: Unknown
% 24.71/4.95 % (32321)Termination phase: Property scanning
% 24.71/4.95
% 24.71/4.95 % (32321)Memory used [KB]: 2686
% 24.71/4.95 % (32321)Time elapsed: 0.028 s
% 24.71/4.95 % (32321)Instructions burned: 105 (million)
% 24.71/4.95 % (32321)------------------------------
% 24.71/4.95 % (32321)------------------------------
% 24.71/4.96 % (32322)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_31785 for (2967ds/414Mi)
% 24.71/4.99 % (32318)Instruction limit reached!
% 24.71/4.99 % (32318)------------------------------
% 24.71/4.99 % (32318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.71/4.99 % (32318)Termination reason: Unknown
% 24.71/4.99 % (32318)Termination phase: Saturation
% 24.71/4.99
% 24.71/4.99 % (32318)Memory used [KB]: 7547
% 24.71/4.99 % (32318)Time elapsed: 0.119 s
% 24.71/4.99 % (32318)Instructions burned: 476 (million)
% 24.71/4.99 % (32318)------------------------------
% 24.71/4.99 % (32318)------------------------------
% 24.71/5.00 % (32323)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_31785 for (2966ds/715Mi)
% 26.63/5.07 % (32322)Instruction limit reached!
% 26.63/5.07 % (32322)------------------------------
% 26.63/5.07 % (32322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.63/5.07 % (32322)Termination reason: Unknown
% 26.63/5.07 % (32322)Termination phase: Saturation
% 26.63/5.07
% 26.63/5.07 % (32322)Memory used [KB]: 7547
% 26.63/5.07 % (32322)Time elapsed: 0.104 s
% 26.63/5.07 % (32322)Instructions burned: 417 (million)
% 26.63/5.07 % (32322)------------------------------
% 26.63/5.07 % (32322)------------------------------
% 26.63/5.07 % (32324)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_31785 for (2965ds/961Mi)
% 26.63/5.08 % (32320)Instruction limit reached!
% 26.63/5.08 % (32320)------------------------------
% 26.63/5.08 % (32320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.63/5.08 % (32320)Termination reason: Unknown
% 26.63/5.08 % (32320)Termination phase: Saturation
% 26.63/5.08
% 26.63/5.08 % (32320)Memory used [KB]: 8955
% 26.63/5.08 % (32320)Time elapsed: 0.165 s
% 26.63/5.08 % (32320)Instructions burned: 592 (million)
% 26.63/5.08 % (32320)------------------------------
% 26.63/5.08 % (32320)------------------------------
% 26.63/5.09 % (32325)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_31785 for (2965ds/1213Mi)
% 27.25/5.14 % (32316)Instruction limit reached!
% 27.25/5.14 % (32316)------------------------------
% 27.25/5.14 % (32316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.25/5.14 % (32316)Termination reason: Unknown
% 27.25/5.14 % (32316)Termination phase: Saturation
% 27.25/5.14
% 27.25/5.14 % (32316)Memory used [KB]: 9594
% 27.25/5.14 % (32316)Time elapsed: 0.365 s
% 27.25/5.14 % (32316)Instructions burned: 1336 (million)
% 27.25/5.14 % (32316)------------------------------
% 27.25/5.14 % (32316)------------------------------
% 27.25/5.15 % (32326)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_31785 for (2965ds/1979Mi)
% 27.55/5.21 % (32323)Instruction limit reached!
% 27.55/5.21 % (32323)------------------------------
% 27.55/5.21 % (32323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.55/5.21 % (32323)Termination reason: Unknown
% 27.55/5.21 % (32323)Termination phase: Saturation
% 27.55/5.21
% 27.55/5.21 % (32323)Memory used [KB]: 5500
% 27.55/5.21 % (32323)Time elapsed: 0.210 s
% 27.55/5.21 % (32323)Instructions burned: 717 (million)
% 27.55/5.21 % (32323)------------------------------
% 27.55/5.21 % (32323)------------------------------
% 27.55/5.22 % (32327)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_31785 for (2964ds/481Mi)
% 27.88/5.35 % (32327)Instruction limit reached!
% 27.88/5.35 % (32327)------------------------------
% 27.88/5.35 % (32327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.88/5.35 % (32327)Termination reason: Unknown
% 27.88/5.35 % (32327)Termination phase: Saturation
% 27.88/5.35
% 27.88/5.35 % (32327)Memory used [KB]: 7547
% 27.88/5.35 % (32327)Time elapsed: 0.125 s
% 27.88/5.35 % (32327)Instructions burned: 483 (million)
% 27.88/5.35 % (32327)------------------------------
% 27.88/5.35 % (32327)------------------------------
% 27.88/5.36 % (32328)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_31785 for (2963ds/783Mi)
% 27.88/5.36 % (32324)Instruction limit reached!
% 27.88/5.36 % (32324)------------------------------
% 27.88/5.36 % (32324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.88/5.36 % (32324)Termination reason: Unknown
% 27.88/5.36 % (32324)Termination phase: Saturation
% 27.88/5.36
% 27.88/5.36 % (32324)Memory used [KB]: 10234
% 27.88/5.36 % (32324)Time elapsed: 0.290 s
% 27.88/5.36 % (32324)Instructions burned: 961 (million)
% 27.88/5.36 % (32324)------------------------------
% 27.88/5.36 % (32324)------------------------------
% 27.88/5.37 % (32329)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_31785 for (2962ds/432Mi)
% 28.61/5.47 % (32325)Instruction limit reached!
% 28.61/5.47 % (32325)------------------------------
% 28.61/5.47 % (32325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.61/5.47 % (32325)Termination reason: Unknown
% 28.61/5.47 % (32325)Termination phase: Saturation
% 28.61/5.47
% 28.61/5.47 % (32325)Memory used [KB]: 14967
% 28.61/5.47 % (32325)Time elapsed: 0.382 s
% 28.61/5.47 % (32325)Instructions burned: 1216 (million)
% 28.61/5.47 % (32325)------------------------------
% 28.61/5.47 % (32325)------------------------------
% 28.61/5.48 % (32330)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_31785 for (2961ds/1670Mi)
% 28.61/5.49 % (32329)Instruction limit reached!
% 28.61/5.49 % (32329)------------------------------
% 28.61/5.49 % (32329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.61/5.49 % (32329)Termination reason: Unknown
% 28.61/5.49 % (32329)Termination phase: Saturation
% 28.61/5.49
% 28.61/5.49 % (32329)Memory used [KB]: 9594
% 28.61/5.49 % (32329)Time elapsed: 0.120 s
% 28.61/5.49 % (32329)Instructions burned: 433 (million)
% 28.61/5.49 % (32329)------------------------------
% 28.61/5.49 % (32329)------------------------------
% 29.44/5.50 % (32331)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_31785 for (2961ds/90Mi)
% 29.44/5.53 % (32331)Instruction limit reached!
% 29.44/5.53 % (32331)------------------------------
% 29.44/5.53 % (32331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.44/5.53 % (32331)Termination reason: Unknown
% 29.44/5.53 % (32331)Termination phase: Property scanning
% 29.44/5.53
% 29.44/5.53 % (32331)Memory used [KB]: 2686
% 29.44/5.53 % (32331)Time elapsed: 0.026 s
% 29.44/5.53 % (32331)Instructions burned: 91 (million)
% 29.44/5.53 % (32331)------------------------------
% 29.44/5.53 % (32331)------------------------------
% 29.44/5.54 % (32332)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_31785 for (2961ds/346Mi)
% 29.78/5.60 % (32328)Instruction limit reached!
% 29.78/5.60 % (32328)------------------------------
% 29.78/5.60 % (32328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.78/5.60 % (32328)Termination reason: Unknown
% 29.78/5.60 % (32328)Termination phase: Saturation
% 29.78/5.60
% 29.78/5.60 % (32328)Memory used [KB]: 11897
% 29.78/5.60 % (32328)Time elapsed: 0.243 s
% 29.78/5.60 % (32328)Instructions burned: 784 (million)
% 29.78/5.60 % (32328)------------------------------
% 29.78/5.60 % (32328)------------------------------
% 29.78/5.61 % (32333)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_31785 for (2960ds/401Mi)
% 29.78/5.62 % (32332)Instruction limit reached!
% 29.78/5.62 % (32332)------------------------------
% 29.78/5.62 % (32332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.78/5.62 % (32332)Termination reason: Unknown
% 29.78/5.62 % (32332)Termination phase: Saturation
% 29.78/5.62
% 29.78/5.62 % (32332)Memory used [KB]: 7547
% 29.78/5.62 % (32332)Time elapsed: 0.086 s
% 29.78/5.62 % (32332)Instructions burned: 346 (million)
% 29.78/5.62 % (32332)------------------------------
% 29.78/5.62 % (32332)------------------------------
% 29.78/5.63 % (32334)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_31785 for (2960ds/6454Mi)
% 30.42/5.71 % (32333)Instruction limit reached!
% 30.42/5.71 % (32333)------------------------------
% 30.42/5.71 % (32333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.42/5.71 % (32333)Termination reason: Unknown
% 30.42/5.71 % (32333)Termination phase: Saturation
% 30.42/5.71
% 30.42/5.71 % (32333)Memory used [KB]: 7547
% 30.42/5.71 % (32333)Time elapsed: 0.104 s
% 30.42/5.71 % (32333)Instructions burned: 404 (million)
% 30.42/5.71 % (32333)------------------------------
% 30.42/5.71 % (32333)------------------------------
% 30.42/5.72 % (32335)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_31785 for (2959ds/283Mi)
% 30.42/5.75 % (32326)Refutation not found, non-redundant clauses discarded% (32326)------------------------------
% 30.42/5.75 % (32326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.42/5.75 % (32326)Termination reason: Refutation not found, non-redundant clauses discarded
% 30.42/5.75
% 30.42/5.75 % (32326)Memory used [KB]: 10618
% 30.42/5.75 % (32326)Time elapsed: 0.608 s
% 30.42/5.75 % (32326)Instructions burned: 1974 (million)
% 30.42/5.75 % (32326)------------------------------
% 30.42/5.75 % (32326)------------------------------
% 30.42/5.76 % (32336)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_31785 for (2958ds/865Mi)
% 30.42/5.79 % (32335)Instruction limit reached!
% 30.42/5.79 % (32335)------------------------------
% 30.42/5.79 % (32335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.42/5.79 % (32335)Termination reason: Unknown
% 30.42/5.79 % (32335)Termination phase: Saturation
% 30.42/5.79
% 30.42/5.79 % (32335)Memory used [KB]: 8187
% 30.42/5.79 % (32335)Time elapsed: 0.075 s
% 30.42/5.79 % (32335)Instructions burned: 285 (million)
% 30.42/5.79 % (32335)------------------------------
% 30.42/5.79 % (32335)------------------------------
% 31.55/5.80 % (32337)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_31785 for (2958ds/4528Mi)
% 31.55/5.88 % (32317)Instruction limit reached!
% 31.55/5.88 % (32317)------------------------------
% 31.55/5.88 % (32317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.55/5.88 % (32317)Termination reason: Unknown
% 31.55/5.88 % (32317)Termination phase: Saturation
% 31.55/5.88
% 31.55/5.88 % (32317)Memory used [KB]: 12920
% 31.55/5.88 % (32317)Time elapsed: 1.017 s
% 31.55/5.88 % (32317)Instructions burned: 3373 (million)
% 31.55/5.88 % (32317)------------------------------
% 31.55/5.88 % (32317)------------------------------
% 31.55/5.89 % (32338)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_31785 for (2957ds/1001Mi)
% 31.86/5.91 % (32330)Instruction limit reached!
% 31.86/5.91 % (32330)------------------------------
% 31.86/5.91 % (32330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.86/5.91 % (32330)Termination reason: Unknown
% 31.86/5.91 % (32330)Termination phase: Saturation
% 31.86/5.91
% 31.86/5.91 % (32330)Memory used [KB]: 17270
% 31.86/5.91 % (32330)Time elapsed: 0.433 s
% 31.86/5.91 % (32330)Instructions burned: 1670 (million)
% 31.86/5.91 % (32330)------------------------------
% 31.86/5.91 % (32330)------------------------------
% 31.86/5.92 % (32339)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_31785 for (2957ds/102Mi)
% 31.86/5.95 % (32339)Instruction limit reached!
% 31.86/5.95 % (32339)------------------------------
% 31.86/5.95 % (32339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.86/5.95 % (32339)Termination reason: Unknown
% 31.86/5.95 % (32339)Termination phase: Property scanning
% 31.86/5.95
% 31.86/5.95 % (32339)Memory used [KB]: 2686
% 31.86/5.95 % (32339)Time elapsed: 0.028 s
% 31.86/5.95 % (32339)Instructions burned: 105 (million)
% 31.86/5.95 % (32339)------------------------------
% 31.86/5.95 % (32339)------------------------------
% 31.86/5.95 % (32302)Instruction limit reached!
% 31.86/5.95 % (32302)------------------------------
% 31.86/5.95 % (32302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.86/5.95 % (32302)Termination reason: Unknown
% 31.86/5.95 % (32302)Termination phase: Saturation
% 31.86/5.95
% 31.86/5.95 % (32302)Memory used [KB]: 17398
% 31.86/5.95 % (32302)Time elapsed: 1.701 s
% 31.86/5.95 % (32302)Instructions burned: 5411 (million)
% 31.86/5.95 % (32302)------------------------------
% 31.86/5.95 % (32302)------------------------------
% 31.86/5.96 % (32340)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_31785 for (2957ds/952Mi)
% 31.86/5.96 % (32341)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_31785 for (2957ds/578Mi)
% 31.86/5.99 % (32337)Refutation not found, incomplete strategy
% 31.86/5.99 % (32337)------------------------------
% 31.86/5.99 % (32337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.86/5.99 % (32337)Termination reason: Refutation not found, incomplete strategy
% 31.86/5.99
% 31.86/5.99
% 31.86/5.99 % (32337)Memory used [KB]: 3198
% 31.86/5.99 % (32337)Time elapsed: 0.189 s
% 31.86/5.99 % (32337)Instructions burned: 711 (million)
% 31.86/5.99 % (32337)------------------------------
% 31.86/5.99 % (32337)------------------------------
% 31.86/6.00 % (32336)Instruction limit reached!
% 31.86/6.00 % (32336)------------------------------
% 31.86/6.00 % (32336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.86/6.00 % (32336)Termination reason: Unknown
% 31.86/6.00 % (32336)Termination phase: Saturation
% 31.86/6.00
% 31.86/6.00 % (32336)Memory used [KB]: 7931
% 31.86/6.00 % (32336)Time elapsed: 0.237 s
% 31.86/6.00 % (32336)Instructions burned: 868 (million)
% 31.86/6.00 % (32336)------------------------------
% 31.86/6.00 % (32336)------------------------------
% 31.86/6.00 % (32342)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_31785 for (2956ds/643Mi)
% 31.86/6.01 % (32343)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_31785 for (2956ds/865Mi)
% 31.86/6.02 % (32290)Instruction limit reached!
% 31.86/6.02 % (32290)------------------------------
% 31.86/6.02 % (32290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.86/6.02 % (32290)Termination reason: Unknown
% 31.86/6.02 % (32290)Termination phase: Saturation
% 31.86/6.02
% 31.86/6.02 % (32290)Memory used [KB]: 30703
% 31.86/6.02 % (32290)Time elapsed: 2.615 s
% 31.86/6.02 % (32290)Instructions burned: 8252 (million)
% 31.86/6.02 % (32290)------------------------------
% 31.86/6.02 % (32290)------------------------------
% 33.65/6.04 % (32344)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_31785 for (2956ds/1174Mi)
% 33.65/6.10 % (32341)Instruction limit reached!
% 33.65/6.10 % (32341)------------------------------
% 33.65/6.10 % (32341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.65/6.10 % (32341)Termination reason: Unknown
% 33.65/6.10 % (32341)Termination phase: Saturation
% 33.65/6.10
% 33.65/6.10 % (32341)Memory used [KB]: 10490
% 33.65/6.10 % (32341)Time elapsed: 0.139 s
% 33.65/6.10 % (32341)Instructions burned: 580 (million)
% 33.65/6.10 % (32341)------------------------------
% 33.65/6.10 % (32341)------------------------------
% 33.65/6.11 % (32345)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_31785 for (2955ds/644Mi)
% 34.14/6.16 % (32342)Instruction limit reached!
% 34.14/6.16 % (32342)------------------------------
% 34.14/6.16 % (32342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.14/6.16 % (32342)Termination reason: Unknown
% 34.14/6.16 % (32342)Termination phase: Saturation
% 34.14/6.16
% 34.14/6.16 % (32342)Memory used [KB]: 7675
% 34.14/6.16 % (32342)Time elapsed: 0.160 s
% 34.14/6.16 % (32342)Instructions burned: 645 (million)
% 34.14/6.16 % (32342)------------------------------
% 34.14/6.16 % (32342)------------------------------
% 34.14/6.17 % (32346)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_31785 for (2954ds/1201Mi)
% 34.14/6.19 % (32338)Instruction limit reached!
% 34.14/6.19 % (32338)------------------------------
% 34.14/6.19 % (32338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.14/6.19 % (32338)Termination reason: Unknown
% 34.14/6.19 % (32338)Termination phase: Saturation
% 34.14/6.19
% 34.14/6.19 % (32338)Memory used [KB]: 11513
% 34.14/6.19 % (32338)Time elapsed: 0.301 s
% 34.14/6.19 % (32338)Instructions burned: 1001 (million)
% 34.14/6.19 % (32338)------------------------------
% 34.14/6.19 % (32338)------------------------------
% 34.40/6.20 % (32347)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_31785 for (2954ds/1046Mi)
% 34.40/6.24 % (32343)Instruction limit reached!
% 34.40/6.24 % (32343)------------------------------
% 34.40/6.24 % (32343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.40/6.24 % (32343)Termination reason: Unknown
% 34.40/6.24 % (32343)Termination phase: Saturation
% 34.40/6.24
% 34.40/6.24 % (32343)Memory used [KB]: 7931
% 34.40/6.24 % (32343)Time elapsed: 0.234 s
% 34.40/6.24 % (32343)Instructions burned: 865 (million)
% 34.40/6.24 % (32343)------------------------------
% 34.40/6.24 % (32343)------------------------------
% 34.40/6.25 % (32348)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_31785 for (2954ds/222Mi)
% 34.40/6.28 % (32340)Instruction limit reached!
% 34.40/6.28 % (32340)------------------------------
% 34.40/6.28 % (32340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.40/6.28 % (32340)Termination reason: Unknown
% 34.40/6.28 % (32340)Termination phase: Saturation
% 34.40/6.28
% 34.40/6.28 % (32340)Memory used [KB]: 10234
% 34.40/6.28 % (32340)Time elapsed: 0.324 s
% 34.40/6.28 % (32340)Instructions burned: 953 (million)
% 34.40/6.28 % (32340)------------------------------
% 34.40/6.28 % (32340)------------------------------
% 34.40/6.30 % (32345)Instruction limit reached!
% 34.40/6.30 % (32345)------------------------------
% 34.40/6.30 % (32345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.40/6.30 % (32345)Termination reason: Unknown
% 34.40/6.30 % (32345)Termination phase: Saturation
% 34.40/6.30
% 34.40/6.30 % (32345)Memory used [KB]: 8187
% 34.40/6.30 % (32345)Time elapsed: 0.187 s
% 34.40/6.30 % (32345)Instructions burned: 646 (million)
% 34.40/6.30 % (32345)------------------------------
% 34.40/6.30 % (32345)------------------------------
% 35.04/6.30 % (32349)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_31785 for (2953ds/68Mi)
% 35.04/6.30 % (32350)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_31785 for (2953ds/454Mi)
% 35.04/6.31 % (32348)Instruction limit reached!
% 35.04/6.31 % (32348)------------------------------
% 35.04/6.31 % (32348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.31 % (32348)Termination reason: Unknown
% 35.04/6.31 % (32348)Termination phase: Saturation
% 35.04/6.31
% 35.04/6.31 % (32348)Memory used [KB]: 7419
% 35.04/6.31 % (32348)Time elapsed: 0.058 s
% 35.04/6.31 % (32348)Instructions burned: 223 (million)
% 35.04/6.31 % (32348)------------------------------
% 35.04/6.31 % (32348)------------------------------
% 35.04/6.32 % (32351)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_31785 for (2953ds/360Mi)
% 35.04/6.33 % (32349)Instruction limit reached!
% 35.04/6.33 % (32349)------------------------------
% 35.04/6.33 % (32349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.33 % (32349)Termination reason: Unknown
% 35.04/6.33 % (32349)Termination phase: Property scanning
% 35.04/6.33
% 35.04/6.33 % (32349)Memory used [KB]: 2558
% 35.04/6.33 % (32349)Time elapsed: 0.029 s
% 35.04/6.33 % (32349)Instructions burned: 70 (million)
% 35.04/6.33 % (32349)------------------------------
% 35.04/6.33 % (32349)------------------------------
% 35.04/6.34 % (32352)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_31785 for (2953ds/157Mi)
% 35.04/6.39 % (32344)Instruction limit reached!
% 35.04/6.39 % (32344)------------------------------
% 35.04/6.39 % (32344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.04/6.39 % (32344)Termination reason: Unknown
% 35.04/6.39 % (32344)Termination phase: Saturation
% 35.04/6.39
% 35.04/6.39 % (32344)Memory used [KB]: 10362
% 35.04/6.39 % (32344)Time elapsed: 0.355 s
% 35.04/6.39 % (32344)Instructions burned: 1176 (million)
% 35.04/6.39 % (32344)------------------------------
% 35.04/6.39 % (32344)------------------------------
% 35.62/6.40 % (32353)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_31785 for (2952ds/5061Mi)
% 35.62/6.40 % (32352)Instruction limit reached!
% 35.62/6.40 % (32352)------------------------------
% 35.62/6.40 % (32352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.62/6.40 % (32352)Termination reason: Unknown
% 35.62/6.40 % (32352)Termination phase: Property scanning
% 35.62/6.40
% 35.62/6.40 % (32352)Memory used [KB]: 2686
% 35.62/6.40 % (32352)Time elapsed: 0.060 s
% 35.62/6.40 % (32352)Instructions burned: 157 (million)
% 35.62/6.40 % (32352)------------------------------
% 35.62/6.40 % (32352)------------------------------
% 35.62/6.41 % (32351)Instruction limit reached!
% 35.62/6.41 % (32351)------------------------------
% 35.62/6.41 % (32351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.62/6.41 % (32351)Termination reason: Unknown
% 35.62/6.41 % (32351)Termination phase: Saturation
% 35.62/6.41
% 35.62/6.41 % (32351)Memory used [KB]: 7547
% 35.62/6.41 % (32351)Time elapsed: 0.090 s
% 35.62/6.41 % (32351)Instructions burned: 361 (million)
% 35.62/6.41 % (32351)------------------------------
% 35.62/6.41 % (32351)------------------------------
% 35.62/6.42 % (32355)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_31785 for (2952ds/5798Mi)
% 35.62/6.42 % (32354)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_31785 for (2952ds/2401Mi)
% 35.62/6.42 % (32350)Instruction limit reached!
% 35.62/6.42 % (32350)------------------------------
% 35.62/6.42 % (32350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.62/6.42 % (32350)Termination reason: Unknown
% 35.62/6.42 % (32350)Termination phase: Saturation
% 35.62/6.42
% 35.62/6.42 % (32350)Memory used [KB]: 12025
% 35.62/6.42 % (32350)Time elapsed: 0.114 s
% 35.62/6.42 % (32350)Instructions burned: 456 (million)
% 35.62/6.42 % (32350)------------------------------
% 35.62/6.42 % (32350)------------------------------
% 35.62/6.43 % (32356)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_31785 for (2952ds/346Mi)
% 35.62/6.46 % (32347)Instruction limit reached!
% 35.62/6.46 % (32347)------------------------------
% 35.62/6.46 % (32347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.62/6.46 % (32347)Termination reason: Unknown
% 35.62/6.46 % (32347)Termination phase: Saturation
% 35.62/6.46
% 35.62/6.46 % (32347)Memory used [KB]: 7675
% 35.62/6.46 % (32347)Time elapsed: 0.264 s
% 35.62/6.46 % (32347)Instructions burned: 1047 (million)
% 35.62/6.46 % (32347)------------------------------
% 35.62/6.46 % (32347)------------------------------
% 35.62/6.47 % (32357)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_31785 for (2952ds/1321Mi)
% 36.28/6.51 % (32346)Instruction limit reached!
% 36.28/6.51 % (32346)------------------------------
% 36.28/6.51 % (32346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.28/6.51 % (32346)Termination reason: Unknown
% 36.28/6.51 % (32346)Termination phase: Saturation
% 36.28/6.51
% 36.28/6.51 % (32346)Memory used [KB]: 11001
% 36.28/6.51 % (32346)Time elapsed: 0.341 s
% 36.28/6.51 % (32346)Instructions burned: 1202 (million)
% 36.28/6.51 % (32346)------------------------------
% 36.28/6.51 % (32346)------------------------------
% 36.28/6.51 % (32356)Instruction limit reached!
% 36.28/6.51 % (32356)------------------------------
% 36.28/6.51 % (32356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.28/6.51 % (32356)Termination reason: Unknown
% 36.28/6.51 % (32356)Termination phase: Saturation
% 36.28/6.51
% 36.28/6.51 % (32356)Memory used [KB]: 7547
% 36.28/6.51 % (32356)Time elapsed: 0.088 s
% 36.28/6.51 % (32356)Instructions burned: 347 (million)
% 36.28/6.51 % (32356)------------------------------
% 36.28/6.51 % (32356)------------------------------
% 36.28/6.52 % (32359)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_31785 for (2951ds/672Mi)
% 36.28/6.53 % (32358)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_31785 for (2951ds/1312Mi)
% 36.94/6.73 % (32359)Instruction limit reached!
% 36.94/6.73 % (32359)------------------------------
% 36.94/6.73 % (32359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.94/6.73 % (32359)Termination reason: Unknown
% 36.94/6.73 % (32359)Termination phase: Saturation
% 36.94/6.73
% 36.94/6.73 % (32359)Memory used [KB]: 11001
% 36.94/6.73 % (32359)Time elapsed: 0.203 s
% 36.94/6.73 % (32359)Instructions burned: 675 (million)
% 36.94/6.73 % (32359)------------------------------
% 36.94/6.73 % (32359)------------------------------
% 36.94/6.74 % (32360)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_31785 for (2949ds/1897Mi)
% 37.25/6.86 % (32357)Instruction limit reached!
% 37.25/6.86 % (32357)------------------------------
% 37.25/6.86 % (32357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.25/6.86 % (32357)Termination reason: Unknown
% 37.25/6.86 % (32357)Termination phase: Saturation
% 37.25/6.86
% 37.25/6.86 % (32357)Memory used [KB]: 8699
% 37.25/6.86 % (32357)Time elapsed: 0.417 s
% 37.25/6.86 % (32357)Instructions burned: 1323 (million)
% 37.25/6.86 % (32357)------------------------------
% 37.25/6.86 % (32357)------------------------------
% 37.25/6.88 % (32361)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_31785 for (2947ds/1202Mi)
% 37.76/6.94 % (32358)Instruction limit reached!
% 37.76/6.94 % (32358)------------------------------
% 37.76/6.94 % (32358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 37.76/6.94 % (32358)Termination reason: Unknown
% 37.76/6.94 % (32358)Termination phase: Saturation
% 37.76/6.94
% 37.76/6.94 % (32358)Memory used [KB]: 16375
% 37.76/6.94 % (32358)Time elapsed: 0.437 s
% 37.76/6.94 % (32358)Instructions burned: 1314 (million)
% 37.76/6.94 % (32358)------------------------------
% 37.76/6.94 % (32358)------------------------------
% 37.76/6.95 % (32362)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_31785 for (2947ds/1493Mi)
% 41.29/7.17 % (32354)Instruction limit reached!
% 41.29/7.17 % (32354)------------------------------
% 41.29/7.17 % (32354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.29/7.17 % (32354)Termination reason: Unknown
% 41.29/7.17 % (32354)Termination phase: Saturation
% 41.29/7.17
% 41.29/7.17 % (32354)Memory used [KB]: 10874
% 41.29/7.17 % (32354)Time elapsed: 0.776 s
% 41.29/7.17 % (32354)Instructions burned: 2403 (million)
% 41.29/7.17 % (32354)------------------------------
% 41.29/7.17 % (32354)------------------------------
% 41.29/7.18 % (32363)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_31785 for (2944ds/7679Mi)
% 41.86/7.22 % (32361)Instruction limit reached!
% 41.86/7.22 % (32361)------------------------------
% 41.86/7.22 % (32361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.86/7.22 % (32361)Termination reason: Unknown
% 41.86/7.22 % (32361)Termination phase: Saturation
% 41.86/7.22
% 41.86/7.22 % (32361)Memory used [KB]: 9466
% 41.86/7.22 % (32361)Time elapsed: 0.348 s
% 41.86/7.22 % (32361)Instructions burned: 1204 (million)
% 41.86/7.22 % (32361)------------------------------
% 41.86/7.22 % (32361)------------------------------
% 41.86/7.23 % (32364)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_31785 for (2944ds/340Mi)
% 42.41/7.33 % (32364)Instruction limit reached!
% 42.41/7.33 % (32364)------------------------------
% 42.41/7.33 % (32364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.41/7.33 % (32364)Termination reason: Unknown
% 42.41/7.33 % (32364)Termination phase: Saturation
% 42.41/7.33
% 42.41/7.33 % (32364)Memory used [KB]: 11001
% 42.41/7.33 % (32364)Time elapsed: 0.098 s
% 42.41/7.33 % (32364)Instructions burned: 342 (million)
% 42.41/7.33 % (32364)------------------------------
% 42.41/7.33 % (32364)------------------------------
% 42.41/7.34 % (32360)Instruction limit reached!
% 42.41/7.34 % (32360)------------------------------
% 42.41/7.34 % (32360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.41/7.34 % (32360)Termination reason: Unknown
% 42.41/7.34 % (32360)Termination phase: Saturation
% 42.41/7.34
% 42.41/7.34 % (32360)Memory used [KB]: 14072
% 42.41/7.34 % (32360)Time elapsed: 0.601 s
% 42.41/7.34 % (32360)Instructions burned: 1899 (million)
% 42.41/7.34 % (32360)------------------------------
% 42.41/7.34 % (32360)------------------------------
% 42.41/7.34 % (32365)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_31785 for (2943ds/3672Mi)
% 42.41/7.35 % (32366)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_31785 for (2943ds/1535Mi)
% 42.41/7.37 % (32362)Instruction limit reached!
% 42.41/7.37 % (32362)------------------------------
% 42.41/7.37 % (32362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.41/7.37 % (32362)Termination reason: Unknown
% 42.41/7.37 % (32362)Termination phase: Saturation
% 42.41/7.37
% 42.41/7.37 % (32362)Memory used [KB]: 8059
% 42.41/7.37 % (32362)Time elapsed: 0.421 s
% 42.41/7.37 % (32362)Instructions burned: 1495 (million)
% 42.41/7.37 % (32362)------------------------------
% 42.41/7.37 % (32362)------------------------------
% 42.41/7.38 % (32367)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_31785 for (2942ds/4637Mi)
% 43.55/7.65 % (32334)Refutation not found, non-redundant clauses discarded% (32334)------------------------------
% 43.55/7.65 % (32334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.55/7.65 % (32334)Termination reason: Refutation not found, non-redundant clauses discarded
% 43.55/7.65
% 43.55/7.65 % (32334)Memory used [KB]: 14967
% 43.55/7.65 % (32334)Time elapsed: 2.016 s
% 43.55/7.65 % (32334)Instructions burned: 6442 (million)
% 43.55/7.65 % (32334)------------------------------
% 43.55/7.65 % (32334)------------------------------
% 43.55/7.65 % (32353)Instruction limit reached!
% 43.55/7.65 % (32353)------------------------------
% 43.55/7.65 % (32353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.55/7.65 % (32353)Termination reason: Unknown
% 43.55/7.65 % (32353)Termination phase: Saturation
% 43.55/7.65
% 43.55/7.65 % (32353)Memory used [KB]: 7931
% 43.55/7.65 % (32353)Time elapsed: 1.257 s
% 43.55/7.65 % (32353)Instructions burned: 5062 (million)
% 43.55/7.65 % (32353)------------------------------
% 43.55/7.65 % (32353)------------------------------
% 43.55/7.66 % (32368)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_31785 for (2940ds/3174Mi)
% 43.55/7.66 % (32369)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_31785 for (2939ds/307Mi)
% 43.79/7.72 % (32366)Instruction limit reached!
% 43.79/7.72 % (32366)------------------------------
% 43.79/7.72 % (32366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.79/7.72 % (32366)Termination reason: Unknown
% 43.79/7.72 % (32366)Termination phase: Saturation
% 43.79/7.72
% 43.79/7.72 % (32366)Memory used [KB]: 15607
% 43.79/7.72 % (32366)Time elapsed: 0.377 s
% 43.79/7.72 % (32366)Instructions burned: 1536 (million)
% 43.79/7.72 % (32366)------------------------------
% 43.79/7.72 % (32366)------------------------------
% 43.79/7.73 % (32370)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_31785 for (2939ds/3619Mi)
% 43.79/7.74 % (32369)Instruction limit reached!
% 43.79/7.74 % (32369)------------------------------
% 43.79/7.74 % (32369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 43.79/7.74 % (32369)Termination reason: Unknown
% 43.79/7.74 % (32369)Termination phase: Saturation
% 43.79/7.74
% 43.79/7.74 % (32369)Memory used [KB]: 7547
% 43.79/7.74 % (32369)Time elapsed: 0.081 s
% 43.79/7.74 % (32369)Instructions burned: 310 (million)
% 43.79/7.74 % (32369)------------------------------
% 43.79/7.74 % (32369)------------------------------
% 43.79/7.75 % (32371)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_31785 for (2939ds/2325Mi)
% 48.38/8.18 % (32370)First to succeed.
% 48.38/8.19 % (32370)Refutation found. Thanks to Tanya!
% 48.38/8.19 % SZS status Theorem for DTF2THF_31785
% 48.38/8.19 % SZS output start Proof for DTF2THF_31785
% 48.38/8.19 thf(func_def_0, type, in: $i > $i > $o).
% 48.38/8.19 thf(func_def_1, type, exu: ($i > $o) > $o).
% 48.38/8.19 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 48.38/8.19 thf(func_def_8, type, powerset: $i > $i).
% 48.38/8.19 thf(func_def_10, type, setunion: $i > $i).
% 48.38/8.19 thf(func_def_19, type, descr: ($i > $o) > $i).
% 48.38/8.19 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_26, type, prop2set: $o > $i).
% 48.38/8.19 thf(func_def_36, type, nonempty: $i > $o).
% 48.38/8.19 thf(func_def_69, type, set2prop: $i > $o).
% 48.38/8.19 thf(func_def_88, type, subset: $i > $i > $o).
% 48.38/8.19 thf(func_def_89, type, disjoint: $i > $i > $o).
% 48.38/8.19 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 48.38/8.19 thf(func_def_114, type, binunion: $i > $i > $i).
% 48.38/8.19 thf(func_def_122, type, binintersect: $i > $i > $i).
% 48.38/8.19 thf(func_def_135, type, regular: $i > $o).
% 48.38/8.19 thf(func_def_136, type, setminus: $i > $i > $i).
% 48.38/8.19 thf(func_def_147, type, symdiff: $i > $i > $i).
% 48.38/8.19 thf(func_def_153, type, iskpair: $i > $o).
% 48.38/8.19 thf(func_def_158, type, kpair: $i > $i > $i).
% 48.38/8.19 thf(func_def_160, type, cartprod: $i > $i > $i).
% 48.38/8.19 thf(func_def_177, type, singleton: $i > $o).
% 48.38/8.19 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 48.38/8.19 thf(func_def_184, type, atmost1p: $i > $o).
% 48.38/8.19 thf(func_def_185, type, atleast2p: $i > $o).
% 48.38/8.19 thf(func_def_186, type, atmost2p: $i > $o).
% 48.38/8.19 thf(func_def_187, type, upairsetp: $i > $o).
% 48.38/8.19 thf(func_def_191, type, kfst: $i > $i).
% 48.38/8.19 thf(func_def_203, type, ksnd: $i > $i).
% 48.38/8.19 thf(func_def_213, type, breln: $i > $i > $i > $o).
% 48.38/8.19 thf(func_def_214, type, dpsetconstr: $i > $i > ($i > $i > $o) > $i).
% 48.38/8.19 thf(func_def_222, type, func: $i > $i > $i > $o).
% 48.38/8.19 thf(func_def_223, type, funcSet: $i > $i > $i).
% 48.38/8.19 thf(func_def_226, type, ap: $i > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_232, type, lam: $i > $i > ($i > $i) > $i).
% 48.38/8.19 thf(func_def_259, type, if: $i > $o > $i > $i > $i).
% 48.38/8.19 thf(func_def_331, type, sP1: $o > $i > $i > $i > $o).
% 48.38/8.19 thf(func_def_332, type, sP2: $i > $i > $o).
% 48.38/8.19 thf(func_def_333, type, sP3: $i > $o).
% 48.38/8.19 thf(func_def_334, type, sP4: $i > $i > $o).
% 48.38/8.19 thf(func_def_335, type, sP5: $i > $i > $o).
% 48.38/8.19 thf(func_def_336, type, sP6: $i > $i > $i > $o).
% 48.38/8.19 thf(func_def_339, type, sP9: $i > $i > $i > $i > $o).
% 48.38/8.19 thf(func_def_344, type, sK14: $i > $i).
% 48.38/8.19 thf(func_def_352, type, sK22: $i > $o).
% 48.38/8.19 thf(func_def_355, type, sK25: ($i > $i) > $i > $i > $i).
% 48.38/8.19 thf(func_def_358, type, sK28: $i > $i).
% 48.38/8.19 thf(func_def_362, type, sK32: $i > $o).
% 48.38/8.19 thf(func_def_375, type, sK45: $i > $i).
% 48.38/8.19 thf(func_def_377, type, sK47: $i > ($i > $i) > $i > $i).
% 48.38/8.19 thf(func_def_383, type, sK53: $i > $o).
% 48.38/8.19 thf(func_def_432, type, sK102: $i > $o).
% 48.38/8.19 thf(func_def_434, type, sK104: ($i > $o) > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_435, type, sK105: ($i > $o) > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_442, type, sK112: ($i > $o) > $i).
% 48.38/8.19 thf(func_def_443, type, sK113: $i > $o).
% 48.38/8.19 thf(func_def_444, type, sK114: $i > $i).
% 48.38/8.19 thf(func_def_458, type, sK128: $i > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_459, type, sK129: $i > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_470, type, sK140: $i > $i > $i).
% 48.38/8.19 thf(func_def_475, type, sK145: $i > $i > $o).
% 48.38/8.19 thf(func_def_494, type, sK164: $i > $o).
% 48.38/8.19 thf(func_def_497, type, sK167: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_498, type, sK168: $i > $i > $o).
% 48.38/8.19 thf(func_def_526, type, sK196: $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_530, type, sK200: $i > $o).
% 48.38/8.19 thf(func_def_532, type, sK202: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_534, type, sK204: $i > $i).
% 48.38/8.19 thf(func_def_535, type, sK205: $i > $o).
% 48.38/8.19 thf(func_def_537, type, sK207: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_542, type, sK212: $i > $i > $i).
% 48.38/8.19 thf(func_def_566, type, sK236: ($i > $o) > ($i > $o) > $i > $i > $i).
% 48.38/8.19 thf(func_def_567, type, sK237: ($i > $o) > ($i > $o) > $i > $i > $i).
% 48.38/8.19 thf(func_def_570, type, sK240: $i > $o).
% 48.38/8.19 thf(func_def_571, type, sK241: $i > $o).
% 48.38/8.19 thf(func_def_579, type, sK249: $i > $o).
% 48.38/8.19 thf(func_def_587, type, sK257: $i > $i > $o).
% 48.38/8.19 thf(func_def_596, type, sK266: $i > $o).
% 48.38/8.19 thf(func_def_605, type, sK275: ($i > $o) > $i).
% 48.38/8.19 thf(func_def_606, type, sK276: ($i > $o) > $i).
% 48.38/8.19 thf(func_def_607, type, sK277: $i > $o).
% 48.38/8.19 thf(func_def_612, type, sK282: $i > $o).
% 48.38/8.19 thf(func_def_614, type, sK284: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_625, type, sK295: $i > $o).
% 48.38/8.19 thf(func_def_636, type, sK306: $i > $i > $i).
% 48.38/8.19 thf(func_def_647, type, sK317: $i > $i).
% 48.38/8.19 thf(func_def_648, type, sK318: $i > $i).
% 48.38/8.19 thf(func_def_651, type, sK321: $i > $i > ($i > $i) > $i).
% 48.38/8.19 thf(func_def_658, type, sK328: $i > $i > $i).
% 48.38/8.19 thf(func_def_659, type, sK329: $i > $i > $i).
% 48.38/8.19 thf(func_def_662, type, sK332: $i > $i > ($i > $i) > $i).
% 48.38/8.19 thf(func_def_663, type, sK333: $i > $i).
% 48.38/8.19 thf(func_def_678, type, sK348: $i > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_679, type, sK349: $i > $o).
% 48.38/8.19 thf(func_def_680, type, sK350: ($i > $o) > $i).
% 48.38/8.19 thf(func_def_685, type, sK355: $i > $i > $i).
% 48.38/8.19 thf(func_def_709, type, sK379: ($i > $o) > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_710, type, sK380: ($i > $o) > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_711, type, sK381: $i > $o).
% 48.38/8.19 thf(func_def_712, type, sK382: $i > $o).
% 48.38/8.19 thf(func_def_719, type, sK389: $i > $i > $o).
% 48.38/8.19 thf(func_def_724, type, sK394: $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_725, type, sK395: $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_734, type, sK404: $i > $o).
% 48.38/8.19 thf(func_def_756, type, sK426: $i > $o).
% 48.38/8.19 thf(func_def_759, type, sK429: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_766, type, sK436: $i > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_769, type, sK439: $i > $i > $o).
% 48.38/8.19 thf(func_def_772, type, sK442: $i > $i > $i).
% 48.38/8.19 thf(func_def_776, type, sK446: $i > $o).
% 48.38/8.19 thf(func_def_779, type, sK449: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_806, type, sK476: ($i > $o) > $i > $i).
% 48.38/8.19 thf(func_def_808, type, sK478: $i > $o).
% 48.38/8.19 thf(func_def_820, type, sK490: $i > $o).
% 48.38/8.19 thf(func_def_824, type, sK494: ($i > $o) > $i > $i).
% 48.38/8.19 thf(func_def_826, type, sK496: $i > $o).
% 48.38/8.19 thf(func_def_830, type, sK500: $i > $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_831, type, sK501: $i > $o).
% 48.38/8.19 thf(func_def_873, type, sK543: $i > $i).
% 48.38/8.19 thf(func_def_878, type, sK548: $i > $i > $i).
% 48.38/8.19 thf(func_def_882, type, sK552: $i > $i > $i).
% 48.38/8.19 thf(func_def_883, type, sK553: $i > $i > $i).
% 48.38/8.19 thf(func_def_884, type, sK554: $i > $i > $i).
% 48.38/8.19 thf(func_def_885, type, sK555: $i > $i > $i).
% 48.38/8.19 thf(func_def_886, type, sK556: $i > $i > $i).
% 48.38/8.19 thf(func_def_887, type, sK557: $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_888, type, sK558: $i > $i).
% 48.38/8.19 thf(func_def_889, type, sK559: $i > $i).
% 48.38/8.19 thf(func_def_890, type, sK560: $i > $i).
% 48.38/8.19 thf(func_def_891, type, sK561: $i > $i).
% 48.38/8.19 thf(func_def_892, type, sK562: $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_893, type, sK563: $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_894, type, sK564: $i > $i > $i).
% 48.38/8.19 thf(func_def_895, type, sK565: $i > $i > $i).
% 48.38/8.19 thf(func_def_896, type, sK566: $i > $i > $i).
% 48.38/8.19 thf(func_def_898, type, sK568: $i > $i).
% 48.38/8.19 thf(func_def_899, type, sK569: $i > $i).
% 48.38/8.19 thf(func_def_900, type, sK570: $i > $i).
% 48.38/8.19 thf(func_def_916, type, sK586: $i > $o).
% 48.38/8.19 thf(func_def_917, type, sK587: $i > $o).
% 48.38/8.19 thf(func_def_918, type, sK588: $i > $i).
% 48.38/8.19 thf(func_def_919, type, sK589: ($i > $o) > $i).
% 48.38/8.19 thf(func_def_955, type, sK625: $i > $i).
% 48.38/8.19 thf(func_def_956, type, sK626: $i > $i).
% 48.38/8.19 thf(func_def_959, type, sK629: $i > $i > ($i > $i) > $i).
% 48.38/8.19 thf(func_def_965, type, sK635: $i > $o).
% 48.38/8.19 thf(func_def_995, type, sK665: $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_996, type, sK666: $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_1000, type, sK670: ($i > $o) > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_1001, type, sK671: ($i > $o) > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_1005, type, sK675: $i > $o).
% 48.38/8.19 thf(func_def_1010, type, sK680: $i > $i).
% 48.38/8.19 thf(func_def_1012, type, sK682: $i > $i).
% 48.38/8.19 thf(func_def_1016, type, sK686: $i > $i > $i).
% 48.38/8.19 thf(func_def_1027, type, sK697: $i > $o).
% 48.38/8.19 thf(func_def_1051, type, sK721: $i > $o).
% 48.38/8.19 thf(func_def_1054, type, sK724: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_1055, type, sK725: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_1061, type, sK731: $i > $i > $i).
% 48.38/8.19 thf(func_def_1067, type, sK737: $i > $i > $o).
% 48.38/8.19 thf(func_def_1069, type, sK739: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_1070, type, sK740: $i > $o).
% 48.38/8.19 thf(func_def_1077, type, sK747: $i > ($i > $i) > $i > $i).
% 48.38/8.19 thf(func_def_1079, type, sK749: $i > $i).
% 48.38/8.19 thf(func_def_1091, type, sK761: $i > $o).
% 48.38/8.19 thf(func_def_1105, type, sK775: $i > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_1106, type, sK776: $i > $o).
% 48.38/8.19 thf(func_def_1107, type, sK777: $i > $o).
% 48.38/8.19 thf(func_def_1108, type, sK778: ($i > $o) > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_1109, type, sK779: ($i > $o) > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_1117, type, sK787: $i > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_1118, type, sK788: $i > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_1119, type, sK789: $i > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_1120, type, sK790: $i > $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_1139, type, sK809: $i > $i > $o).
% 48.38/8.19 thf(func_def_1143, type, sK813: $o > $i > $i > $i).
% 48.38/8.19 thf(func_def_1165, type, sK835: $i > $o).
% 48.38/8.19 thf(func_def_1168, type, sK838: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_1169, type, sK839: $i > ($i > $o) > $i).
% 48.38/8.19 thf(func_def_1182, type, sK852: $i > $o).
% 48.38/8.19 thf(func_def_1183, type, sK853: $i > $i > $i > $i).
% 48.38/8.19 thf(func_def_1188, type, sK858: $i > $i > $o).
% 48.38/8.19 thf(func_def_1189, type, sK859: $i > $i).
% 48.38/8.19 thf(func_def_1190, type, sK860: $i > $i).
% 48.38/8.19 thf(func_def_1191, type, sK861: ($i > $i > $o) > $i > $i).
% 48.38/8.19 thf(func_def_1192, type, sK862: ($i > $i > $o) > $i > $i).
% 48.38/8.19 thf(func_def_1193, type, sK863: $i > ($i > $i > $o) > $i > $i).
% 48.38/8.19 thf(func_def_1236, type, ph906: !>[X0: $tType]:(X0)).
% 48.38/8.19 thf(f16966,plain,(
% 48.38/8.19 $false),
% 48.38/8.19 inference(avatar_sat_refutation,[status(thm)],[f10130,f10246,f15201,f15429,f16863])).
% 48.38/8.19 thf(f16863,plain,(
% 48.38/8.19 ~spl905_35 | spl905_13),
% 48.38/8.19 inference(avatar_split_clause,[status(thm)],[f16862,f4496,f4790])).
% 48.38/8.19 thf(f4790,definition,(
% 48.38/8.19 spl905_35 <=> ((subset @ sK694 @ sK696) = $true)),
% 48.38/8.19 introduced(definition,[new_symbols(naming,[spl905_35])],[avatar_definition])).
% 48.38/8.19 thf(f4496,definition,(
% 48.38/8.19 spl905_13 <=> ($true = (subset @ (binintersect @ sK692 @ sK694) @ sK696))),
% 48.38/8.19 introduced(definition,[new_symbols(naming,[spl905_13])],[avatar_definition])).
% 48.38/8.19 thf(f16862,plain,(
% 48.38/8.19 ((subset @ sK694 @ sK696) != $true) | spl905_13),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f16861])).
% 48.38/8.19 thf(f16861,plain,(
% 48.38/8.19 ($true != $true) | ((subset @ sK694 @ sK696) != $true) | spl905_13),
% 48.38/8.19 inference(forward_demodulation,[status(thm)],[f16842,f3547])).
% 48.38/8.19 thf(f3547,plain,(
% 48.38/8.19 (binintersectRsub = $true)),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2314])).
% 48.38/8.19 thf(f2314,plain,(
% 48.38/8.19 (exuE1 = $true) & (symdiffI2 = $true) & (binintersectI = $true) & (setukpairinjR = $true) & (inComplementUnionImpInComplement1 = $true) & (dpsetconstrERa = $true) & (cartprodpairmemER = $true) & (cartprodmempair = $true) & (apProp = $true) & (powerset__Cong = $true) & (lamProp = $true) & (iffalse = $true) & (demorgan1a = $true) & (omega0Ax = $true) & (dpsetconstrSub = $true) & (setminusEL = $true) & (setminusIRneg = $true) & (binunionTILcontra = $true) & (demorgan1b = $true) & (upairset2E = $true) & (exuE3u = $true) & (ifSingleton = $true) & (powersetE1 = $true) & (setoftrueEq = $true) & (setextAx = $true) & (setextT = $true) & (dpsetconstrEL1 = $true) & (setadjoinE = $true) & (doubleComplementSub2 = $true) & (complementT_lem = $true) & (exuE2 = $true) & (woz13rule2 = $true) & (emptyinPowerset = $true) & (sepInPowerset = $true) & (complementTcontraSubset = $true) & (woz13rule3 = $true) & (complementTI1 = $true) & (setukpairinjR11 = $true) & (wellorderingAx = $true) & (funcGraphProp2 = $true) & (funcImageSingleton = $true) & (eta2 = $true) & (singletoninpowunion = $true) & (replAx = $true) & (ksndpairEq = $true) & (complementInPowersetComplementIntersect = $true) & (brelnall2 = $true) & (eqinunit = $true) & (powersetI1 = $true) & (dsetconstrEL = $true) & (binintersectER = $true) & (singletonsubset = $true) & (setadjoinIL = $true) & (setunionsingleton1 = $true) & (noeltsimpempty = $true) & (complementUnionInPowersetComplement = $true) & (powersetAx = $true) & (setOfPairsIsBReln = $true) & (doubleComplementSub1 = $true) & (intersectInPowersetIntersectUnions = $true) & (kpairsurjEq = $true) & (nonemptyI1 = $true) & (contrasubsetT2 = $true) & (ubforcartprodlem1 = $true) & (iftrueProp1 = $true) & (woz13rule0 = $true) & (exuI3 = $true) & (upairsubunion = $true) & (iffalseProp2 = $true) & (dpsetconstrI = $true) & (demorgan2a2 = $true) & (binunionIL = $true) & (setminusI = $true) & (exuI1 = $true) & (emptysetAx = $true) & (app = $true) & (setunionsingleton2 = $true) & (setadjoinOr = $true) & (complementTnotintersectT = $true) & (upairinpowunion = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (descr__Cong = $true) & (subPowSU = $true) & (funcinfuncset = $true) & (kpairiskpair = $true) & (binintersectLsub = $true) & (eqimpsubset2 = $true) & (ubforcartprodlem2 = $true) & (binintersectSubset5 = $true) & (eqbreln = $true) & (dsetconstrER = $true) & (upairequniteq = $true) & (singletoninpowerset = $true) & (setadjoinIR = $true) & (notsubsetI = $true) & (demorgan1 = $true) & (binintersectSubset1 = $true) & (subsetE2 = $true) & (iftrueorfalse = $true) & (omegaIndAx = $true) & (setminusLsub = $true) & (binintersectSubset4 = $true) & (binintersectSubset2 = $true) & (funcext2 = $true) & (setminusERneg = $true) & (funcGraphProp3 = $true) & (doubleComplementEq = $true) & (notequalI2 = $true) & (bs114d = $true) & (setunion__Cong = $true) & (setminusELneg = $true) & (notinsingleton = $true) & (emptyinunitempty = $true) & (upairset2IR = $true) & (inIntersectImpInUnion2 = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (setukpairinjR2 = $true) & (prop2setE = $true) & (setukpairinjL = $true) & (nonemptyImpWitness = $true) & (cartprodpairin = $true) & (subsetE = $true) & (ksndsingleton = $true) & (setadjoinSub2 = $true) & (setukpairinjR1 = $true) & (subsetI2 = $true) & (cartprodfstin = $true) & (ifp = $true) & (inComplementUnionImpNotIn1 = $true) & (emptysetE = $true) & (binunionE = $true) & (symdiffIneg1 = $true) & (kpairp = $true) & (complementImpComplementIntersect = $true) & (setunionE = $true) & (contrasubsetT = $true) & (inIntersectImpInIntersectUnions = $true) & (emptyset__Cong = $true) & (setukpairinjR12 = $true) & (nonemptyI = $true) & (singletonprop = $true) & (inPowerset = $true) & (binunionTIRcontra = $true) & (cartprodfstpairEq = $true) & (binintersectT_lem = $true) & (powersetI = $true) & (setunionsingleton = $true) & (kfstpairEq = $true) & (singletonsswitch = $true) & (ubforcartprodlem3 = $true) & (setminusER = $true) & (upairsetIL = $true) & (powersetsubset = $true) & (setadjoinSub = $true) & (iffalseProp1 = $true) & (brelnall1 = $true) & (lam2lamEq = $true) & (exu__Cong = $true) & (upairsetIR = $true) & (inIntersectImpInUnion = $true) & (ex1I2 = $true) & (omegaSAx = $true) & (((in @ sK692 @ (powerset @ sK693)) = $true) & (((((subset @ sK694 @ sK696) = $true) & ((subset @ sK692 @ sK695) = $true) & ((subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ sK695 @ sK696)) != $true) & ($true = (in @ sK696 @ (powerset @ sK693)))) & ((in @ sK695 @ (powerset @ sK693)) = $true)) & ((in @ sK694 @ (powerset @ sK693)) = $true))) & (omega__Cong = $true) & (setminusSubset2 = $true) & (cartprodmempair1 = $true) & (quantDeMorgan3 = $true) & (lamp = $true) & (uniqinunit = $true) & (subsetTI = $true) & (beta1 = $true) & (subbreln = $true) & (exuEu = $true) & (setadjoin__Cong = $true) & (eta1 = $true) & (foundationAx = $true) & (exuE3e = $true) & (prop2setI = $true) & (demorgan2a = $true) & (demorgan2a1 = $true) & (binintersectSubset3 = $true) & (quantDeMorgan2 = $true) & (setbeta = $true) & (dpsetconstrEL2 = $true) & (subsetI1 = $true) & (dpsetconstrER = $true) & (descrp = $true) & (ap2p = $true) & (binintersectTERcontra = $true) & (emptyI = $true) & (quantDeMorgan1 = $true) & (exuI2 = $true) & (funcextLem = $true) & (ex1I = $true) & (kfstsingleton = $true) & (cartprodpairsurjEq = $true) & (demorgan2b = $true) & (notdallE = $true) & (inCongP = $true) & (binunionLsub = $true) & (setunionI = $true) & (powersetTE1 = $true) & (doubleComplementI1 = $true) & (setextsub = $true) & (dsetconstr__Cong = $true) & (complementTE1 = $true) & (vacuousDall = $true) & (ex1E2 = $true) & (binunionTEcontra = $true) & (powersetTI1 = $true) & (secondinupair = $true) & (cartprodpairmemEL = $true) & (setunionE2 = $true) & (quantDeMorgan4 = $true) & (binunionEcases = $true) & (binunionTE = $true) & (theprop = $true) & (setminusSubset1 = $true) & (theeq = $true) & (dsetconstrI = $true) & (demorgan2b2 = $true) & (sepSubset = $true) & (complementSubsetComplementIntersect = $true) & (binintersectTELcontra = $true) & (cartprodsndpairEq = $true) & (cartprodmempaircEq = $true) & (binintersectEL = $true) & (symdiffIneg2 = $true) & (setukpairinjL2 = $true) & (emptysetsubset = $true) & (ap2apEq2 = $true) & (subsetTrans = $true) & (nonemptyE1 = $true) & (funcext = $true) & (emptyInPowerset = $true) & (demorgan2 = $true) & (binunionIR = $true) & (doubleComplementE1 = $true) & (powersetT_lem = $true) & (subsetemptysetimpeq = $true) & (ex1E1 = $true) & (setminusILneg = $true) & (eqimpsubset1 = $true) & (binunionT_lem = $true) & (contrasubsetT1 = $true) & (contrasubsetT3 = $true) & (notinemptyset = $true) & (funcGraphProp1 = $true) & (beta2 = $true) & (prop2set2propI = $true) & (subset2powerset = $true) & (disjointsetsI1 = $true) & (setunionAx = $true) & (setadjoinAx = $true) & (setminusT_lem = $true) & (setext = $true) & (powersetE = $true) & (upairsetE = $true) & (contraSubsetComplement = $true) & (in__Cong = $true) & (emptyE1 = $true) & (notdexE = $true) & (woz13rule1 = $true) & (funcGraphProp4 = $true) & (subsetRefl = $true) & (setukpairIL = $true) & (infuncsetfunc = $true) & (setukpairIR = $true) & (ap2apEq1 = $true) & (binunionRsub = $true) & (binintersectRsub = $true) & (emptysetimpfalse = $true) & (iftrueProp2 = $true) & (iftrue = $true) & (cartprodsndin = $true) & (lam2p = $true) & (notequalI1 = $true)),
% 48.38/8.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK692,sK693,sK694,sK695,sK696])],[f1100,f2313,f2312,f2311,f2310])).
% 48.38/8.19 thf(f2310,plain,(
% 48.38/8.19 ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (subset @ X2 @ X4)) & ((subset @ X0 @ X3) = $true) & ((subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4)) != $true) & ((in @ X4 @ (powerset @ X1)) = $true)) & ($true = (in @ X3 @ (powerset @ X1)))) & ((in @ X2 @ (powerset @ X1)) = $true))) => (((in @ sK692 @ (powerset @ sK693)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (subset @ X2 @ X4)) & ((subset @ sK692 @ X3) = $true) & ((subset @ (binintersect @ sK692 @ X2) @ (binintersect @ X3 @ X4)) != $true) & ((in @ X4 @ (powerset @ sK693)) = $true)) & ((in @ X3 @ (powerset @ sK693)) = $true)) & ((in @ X2 @ (powerset @ sK693)) = $true)))),
% 48.38/8.19 introduced(definition,[],[choice_axiom])).
% 48.38/8.19 thf(f2311,plain,(
% 48.38/8.19 ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (subset @ X2 @ X4)) & ((subset @ sK692 @ X3) = $true) & ((subset @ (binintersect @ sK692 @ X2) @ (binintersect @ X3 @ X4)) != $true) & ((in @ X4 @ (powerset @ sK693)) = $true)) & ((in @ X3 @ (powerset @ sK693)) = $true)) & ((in @ X2 @ (powerset @ sK693)) = $true)) => (? [X3 : $i] : (? [X4 : $i] : (((subset @ sK694 @ X4) = $true) & ((subset @ sK692 @ X3) = $true) & ((subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ X3 @ X4)) != $true) & ((in @ X4 @ (powerset @ sK693)) = $true)) & ((in @ X3 @ (powerset @ sK693)) = $true)) & ((in @ sK694 @ (powerset @ sK693)) = $true))),
% 48.38/8.19 introduced(definition,[],[choice_axiom])).
% 48.38/8.19 thf(f2312,plain,(
% 48.38/8.19 ? [X3 : $i] : (? [X4 : $i] : (((subset @ sK694 @ X4) = $true) & ((subset @ sK692 @ X3) = $true) & ((subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ X3 @ X4)) != $true) & ((in @ X4 @ (powerset @ sK693)) = $true)) & ((in @ X3 @ (powerset @ sK693)) = $true)) => (? [X4 : $i] : (((subset @ sK694 @ X4) = $true) & ((subset @ sK692 @ sK695) = $true) & ($true != (subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ sK695 @ X4))) & ((in @ X4 @ (powerset @ sK693)) = $true)) & ((in @ sK695 @ (powerset @ sK693)) = $true))),
% 48.38/8.19 introduced(definition,[],[choice_axiom])).
% 48.38/8.19 thf(f2313,plain,(
% 48.38/8.19 ? [X4 : $i] : (((subset @ sK694 @ X4) = $true) & ((subset @ sK692 @ sK695) = $true) & ($true != (subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ sK695 @ X4))) & ((in @ X4 @ (powerset @ sK693)) = $true)) => (((subset @ sK694 @ sK696) = $true) & ((subset @ sK692 @ sK695) = $true) & ((subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ sK695 @ sK696)) != $true) & ($true = (in @ sK696 @ (powerset @ sK693))))),
% 48.38/8.19 introduced(definition,[],[choice_axiom])).
% 48.38/8.19 thf(f1100,plain,(
% 48.38/8.19 (exuE1 = $true) & (symdiffI2 = $true) & (binintersectI = $true) & (setukpairinjR = $true) & (inComplementUnionImpInComplement1 = $true) & (dpsetconstrERa = $true) & (cartprodpairmemER = $true) & (cartprodmempair = $true) & (apProp = $true) & (powerset__Cong = $true) & (lamProp = $true) & (iffalse = $true) & (demorgan1a = $true) & (omega0Ax = $true) & (dpsetconstrSub = $true) & (setminusEL = $true) & (setminusIRneg = $true) & (binunionTILcontra = $true) & (demorgan1b = $true) & (upairset2E = $true) & (exuE3u = $true) & (ifSingleton = $true) & (powersetE1 = $true) & (setoftrueEq = $true) & (setextAx = $true) & (setextT = $true) & (dpsetconstrEL1 = $true) & (setadjoinE = $true) & (doubleComplementSub2 = $true) & (complementT_lem = $true) & (exuE2 = $true) & (woz13rule2 = $true) & (emptyinPowerset = $true) & (sepInPowerset = $true) & (complementTcontraSubset = $true) & (woz13rule3 = $true) & (complementTI1 = $true) & (setukpairinjR11 = $true) & (wellorderingAx = $true) & (funcGraphProp2 = $true) & (funcImageSingleton = $true) & (eta2 = $true) & (singletoninpowunion = $true) & (replAx = $true) & (ksndpairEq = $true) & (complementInPowersetComplementIntersect = $true) & (brelnall2 = $true) & (eqinunit = $true) & (powersetI1 = $true) & (dsetconstrEL = $true) & (binintersectER = $true) & (singletonsubset = $true) & (setadjoinIL = $true) & (setunionsingleton1 = $true) & (noeltsimpempty = $true) & (complementUnionInPowersetComplement = $true) & (powersetAx = $true) & (setOfPairsIsBReln = $true) & (doubleComplementSub1 = $true) & (intersectInPowersetIntersectUnions = $true) & (kpairsurjEq = $true) & (nonemptyI1 = $true) & (contrasubsetT2 = $true) & (ubforcartprodlem1 = $true) & (iftrueProp1 = $true) & (woz13rule0 = $true) & (exuI3 = $true) & (upairsubunion = $true) & (iffalseProp2 = $true) & (dpsetconstrI = $true) & (demorgan2a2 = $true) & (binunionIL = $true) & (setminusI = $true) & (exuI1 = $true) & (emptysetAx = $true) & (app = $true) & (setunionsingleton2 = $true) & (setadjoinOr = $true) & (complementTnotintersectT = $true) & (upairinpowunion = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (descr__Cong = $true) & (subPowSU = $true) & (funcinfuncset = $true) & (kpairiskpair = $true) & (binintersectLsub = $true) & (eqimpsubset2 = $true) & (ubforcartprodlem2 = $true) & (binintersectSubset5 = $true) & (eqbreln = $true) & (dsetconstrER = $true) & (upairequniteq = $true) & (singletoninpowerset = $true) & (setadjoinIR = $true) & (notsubsetI = $true) & (demorgan1 = $true) & (binintersectSubset1 = $true) & (subsetE2 = $true) & (iftrueorfalse = $true) & (omegaIndAx = $true) & (setminusLsub = $true) & (binintersectSubset4 = $true) & (binintersectSubset2 = $true) & (funcext2 = $true) & (setminusERneg = $true) & (funcGraphProp3 = $true) & (doubleComplementEq = $true) & (notequalI2 = $true) & (bs114d = $true) & (setunion__Cong = $true) & (setminusELneg = $true) & (notinsingleton = $true) & (emptyinunitempty = $true) & (upairset2IR = $true) & (inIntersectImpInUnion2 = $true) & (setukpairinjL1 = $true) & (singletonsuniq = $true) & (setukpairinjR2 = $true) & (prop2setE = $true) & (setukpairinjL = $true) & (nonemptyImpWitness = $true) & (cartprodpairin = $true) & (subsetE = $true) & (ksndsingleton = $true) & (setadjoinSub2 = $true) & (setukpairinjR1 = $true) & (subsetI2 = $true) & (cartprodfstin = $true) & (ifp = $true) & (inComplementUnionImpNotIn1 = $true) & (emptysetE = $true) & (binunionE = $true) & (symdiffIneg1 = $true) & (kpairp = $true) & (complementImpComplementIntersect = $true) & (setunionE = $true) & (contrasubsetT = $true) & (inIntersectImpInIntersectUnions = $true) & (emptyset__Cong = $true) & (setukpairinjR12 = $true) & (nonemptyI = $true) & (singletonprop = $true) & (inPowerset = $true) & (binunionTIRcontra = $true) & (cartprodfstpairEq = $true) & (binintersectT_lem = $true) & (powersetI = $true) & (setunionsingleton = $true) & (kfstpairEq = $true) & (singletonsswitch = $true) & (ubforcartprodlem3 = $true) & (setminusER = $true) & (upairsetIL = $true) & (powersetsubset = $true) & (setadjoinSub = $true) & (iffalseProp1 = $true) & (brelnall1 = $true) & (lam2lamEq = $true) & (exu__Cong = $true) & (upairsetIR = $true) & (inIntersectImpInUnion = $true) & (ex1I2 = $true) & (omegaSAx = $true) & ? [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) & ? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (($true = (subset @ X2 @ X4)) & ((subset @ X0 @ X3) = $true) & ((subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4)) != $true) & ((in @ X4 @ (powerset @ X1)) = $true)) & ($true = (in @ X3 @ (powerset @ X1)))) & ((in @ X2 @ (powerset @ X1)) = $true))) & (omega__Cong = $true) & (setminusSubset2 = $true) & (cartprodmempair1 = $true) & (quantDeMorgan3 = $true) & (lamp = $true) & (uniqinunit = $true) & (subsetTI = $true) & (beta1 = $true) & (subbreln = $true) & (exuEu = $true) & (setadjoin__Cong = $true) & (eta1 = $true) & (foundationAx = $true) & (exuE3e = $true) & (prop2setI = $true) & (demorgan2a = $true) & (demorgan2a1 = $true) & (binintersectSubset3 = $true) & (quantDeMorgan2 = $true) & (setbeta = $true) & (dpsetconstrEL2 = $true) & (subsetI1 = $true) & (dpsetconstrER = $true) & (descrp = $true) & (ap2p = $true) & (binintersectTERcontra = $true) & (emptyI = $true) & (quantDeMorgan1 = $true) & (exuI2 = $true) & (funcextLem = $true) & (ex1I = $true) & (kfstsingleton = $true) & (cartprodpairsurjEq = $true) & (demorgan2b = $true) & (notdallE = $true) & (inCongP = $true) & (binunionLsub = $true) & (setunionI = $true) & (powersetTE1 = $true) & (doubleComplementI1 = $true) & (setextsub = $true) & (dsetconstr__Cong = $true) & (complementTE1 = $true) & (vacuousDall = $true) & (ex1E2 = $true) & (binunionTEcontra = $true) & (powersetTI1 = $true) & (secondinupair = $true) & (cartprodpairmemEL = $true) & (setunionE2 = $true) & (quantDeMorgan4 = $true) & (binunionEcases = $true) & (binunionTE = $true) & (theprop = $true) & (setminusSubset1 = $true) & (theeq = $true) & (dsetconstrI = $true) & (demorgan2b2 = $true) & (sepSubset = $true) & (complementSubsetComplementIntersect = $true) & (binintersectTELcontra = $true) & (cartprodsndpairEq = $true) & (cartprodmempaircEq = $true) & (binintersectEL = $true) & (symdiffIneg2 = $true) & (setukpairinjL2 = $true) & (emptysetsubset = $true) & (ap2apEq2 = $true) & (subsetTrans = $true) & (nonemptyE1 = $true) & (funcext = $true) & (emptyInPowerset = $true) & (demorgan2 = $true) & (binunionIR = $true) & (doubleComplementE1 = $true) & (powersetT_lem = $true) & (subsetemptysetimpeq = $true) & (ex1E1 = $true) & (setminusILneg = $true) & (eqimpsubset1 = $true) & (binunionT_lem = $true) & (contrasubsetT1 = $true) & (contrasubsetT3 = $true) & (notinemptyset = $true) & (funcGraphProp1 = $true) & (beta2 = $true) & (prop2set2propI = $true) & (subset2powerset = $true) & (disjointsetsI1 = $true) & (setunionAx = $true) & (setadjoinAx = $true) & (setminusT_lem = $true) & (setext = $true) & (powersetE = $true) & (upairsetE = $true) & (contraSubsetComplement = $true) & (in__Cong = $true) & (emptyE1 = $true) & (notdexE = $true) & (woz13rule1 = $true) & (funcGraphProp4 = $true) & (subsetRefl = $true) & (setukpairIL = $true) & (infuncsetfunc = $true) & (setukpairIR = $true) & (ap2apEq1 = $true) & (binunionRsub = $true) & (binintersectRsub = $true) & (emptysetimpfalse = $true) & (iftrueProp2 = $true) & (iftrue = $true) & (cartprodsndin = $true) & (lam2p = $true) & (notequalI1 = $true)),
% 48.38/8.19 inference(flattening,[status(thm)],[f1099])).
% 48.38/8.19 thf(f1099,plain,(
% 48.38/8.19 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (? [X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((((subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4)) != $true) & ($true = (subset @ X2 @ X4))) & ((subset @ X0 @ X3) = $true)) & ((in @ X4 @ (powerset @ X1)) = $true)) & ($true = (in @ X3 @ (powerset @ X1)))) & ((in @ X2 @ (powerset @ X1)) = $true)) & ((in @ X0 @ (powerset @ X1)) = $true)) & (woz13rule3 = $true)) & (woz13rule2 = $true)) & (woz13rule1 = $true)) & (woz13rule0 = $true)) & (demorgan2 = $true)) & (demorgan2b = $true)) & (demorgan2b2 = $true)) & (demorgan2a = $true)) & (demorgan1 = $true)) & (demorgan1b = $true)) & (demorgan1a = $true)) & (demorgan2a2 = $true)) & (complementUnionInPowersetComplement = $true)) & (demorgan2a1 = $true)) & (binunionTEcontra = $true)) & (binunionTE = $true)) & (inComplementUnionImpInComplement1 = $true)) & (inComplementUnionImpNotIn1 = $true)) & (intersectInPowersetIntersectUnions = $true)) & (inIntersectImpInIntersectUnions = $true)) & (inIntersectImpInUnion2 = $true)) & (inIntersectImpInUnion = $true)) & (binunionTIRcontra = $true)) & (binunionTILcontra = $true)) & (complementTcontraSubset = $true)) & (contraSubsetComplement = $true)) & (complementInPowersetComplementIntersect = $true)) & (complementSubsetComplementIntersect = $true)) & (complementImpComplementIntersect = $true)) & (complementTnotintersectT = $true)) & (doubleComplementEq = $true)) & (doubleComplementSub2 = $true)) & (doubleComplementSub1 = $true)) & (doubleComplementE1 = $true)) & (doubleComplementI1 = $true)) & (contrasubsetT3 = $true)) & (contrasubsetT2 = $true)) & (contrasubsetT1 = $true)) & (contrasubsetT = $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)),
% 48.38/8.19 inference(ennf_transformation,[status(thm)],[f721])).
% 48.38/8.19 thf(f721,plain,(
% 48.38/8.19 ~((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) => ((contrasubsetT = $true) => ((contrasubsetT1 = $true) => ((contrasubsetT2 = $true) => ((contrasubsetT3 = $true) => ((doubleComplementI1 = $true) => ((doubleComplementE1 = $true) => ((doubleComplementSub1 = $true) => ((doubleComplementSub2 = $true) => ((doubleComplementEq = $true) => ((complementTnotintersectT = $true) => ((complementImpComplementIntersect = $true) => ((complementSubsetComplementIntersect = $true) => ((complementInPowersetComplementIntersect = $true) => ((contraSubsetComplement = $true) => ((complementTcontraSubset = $true) => ((binunionTILcontra = $true) => ((binunionTIRcontra = $true) => ((inIntersectImpInUnion = $true) => ((inIntersectImpInUnion2 = $true) => ((inIntersectImpInIntersectUnions = $true) => ((intersectInPowersetIntersectUnions = $true) => ((inComplementUnionImpNotIn1 = $true) => ((inComplementUnionImpInComplement1 = $true) => ((binunionTE = $true) => ((binunionTEcontra = $true) => ((demorgan2a1 = $true) => ((complementUnionInPowersetComplement = $true) => ((demorgan2a2 = $true) => ((demorgan1a = $true) => ((demorgan1b = $true) => ((demorgan1 = $true) => ((demorgan2a = $true) => ((demorgan2b2 = $true) => ((demorgan2b = $true) => ((demorgan2 = $true) => ((woz13rule0 = $true) => ((woz13rule1 = $true) => ((woz13rule2 = $true) => ((woz13rule3 = $true) => ! [X0 : $i,X1 : $i] : (((in @ X0 @ (powerset @ X1)) = $true) => ! [X2 : $i] : (((in @ X2 @ (powerset @ X1)) = $true) => ! [X3 : $i] : (($true = (in @ X3 @ (powerset @ X1))) => ! [X4 : $i] : (((in @ X4 @ (powerset @ X1)) = $true) => (((subset @ X0 @ X3) = $true) => (($true = (subset @ X2 @ X4)) => ((subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4)) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 48.38/8.19 inference(fool_elimination,[status(thm)],[f720])).
% 48.38/8.19 thf(f720,plain,(
% 48.38/8.19 ~(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 => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X0 : $i,X1 : $i] : ((in @ X0 @ (powerset @ X1)) => ! [X2 : $i] : ((in @ X2 @ (powerset @ X1)) => ! [X3 : $i] : ((in @ X3 @ (powerset @ X1)) => ! [X4 : $i] : ((in @ X4 @ (powerset @ X1)) => ((subset @ X0 @ X3) => ((subset @ X2 @ X4) => (subset @ (binintersect @ X0 @ X2) @ (binintersect @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 48.38/8.19 inference(rectify,[status(thm)],[f284])).
% 48.38/8.19 thf(f284,negated_conjecture,(
% 48.38/8.19 ~(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 => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X17 : $i] : ((in @ X17 @ (powerset @ X3)) => ! [X18 : $i] : ((in @ X18 @ (powerset @ X3)) => ((subset @ X11 @ X17) => ((subset @ X16 @ X18) => (subset @ (binintersect @ X11 @ X16) @ (binintersect @ X17 @ X18))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 48.38/8.19 inference(negated_conjecture,[status(cth)],[f283])).
% 48.38/8.19 thf(f283,conjecture,(
% 48.38/8.19 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 => (contrasubsetT => (contrasubsetT1 => (contrasubsetT2 => (contrasubsetT3 => (doubleComplementI1 => (doubleComplementE1 => (doubleComplementSub1 => (doubleComplementSub2 => (doubleComplementEq => (complementTnotintersectT => (complementImpComplementIntersect => (complementSubsetComplementIntersect => (complementInPowersetComplementIntersect => (contraSubsetComplement => (complementTcontraSubset => (binunionTILcontra => (binunionTIRcontra => (inIntersectImpInUnion => (inIntersectImpInUnion2 => (inIntersectImpInIntersectUnions => (intersectInPowersetIntersectUnions => (inComplementUnionImpNotIn1 => (inComplementUnionImpInComplement1 => (binunionTE => (binunionTEcontra => (demorgan2a1 => (complementUnionInPowersetComplement => (demorgan2a2 => (demorgan1a => (demorgan1b => (demorgan1 => (demorgan2a => (demorgan2b2 => (demorgan2b => (demorgan2 => (woz13rule0 => (woz13rule1 => (woz13rule2 => (woz13rule3 => ! [X11 : $i,X3 : $i] : ((in @ X11 @ (powerset @ X3)) => ! [X16 : $i] : ((in @ X16 @ (powerset @ X3)) => ! [X17 : $i] : ((in @ X17 @ (powerset @ X3)) => ! [X18 : $i] : ((in @ X18 @ (powerset @ X3)) => ((subset @ X11 @ X17) => ((subset @ X16 @ X18) => (subset @ (binintersect @ X11 @ X16) @ (binintersect @ X17 @ X18)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 48.38/8.19 file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',woz13rule4)).
% 48.38/8.19 thf(f16842,plain,(
% 48.38/8.19 (binintersectRsub != $true) | ((subset @ sK694 @ sK696) != $true) | spl905_13),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f16775])).
% 48.38/8.19 thf(f16775,plain,(
% 48.38/8.19 ($true != $true) | ((subset @ sK694 @ sK696) != $true) | (binintersectRsub != $true) | spl905_13),
% 48.38/8.19 inference(superposition,[status(thm)],[f15527,f2686])).
% 48.38/8.19 thf(f2686,plain,(
% 48.38/8.19 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X1) = $true) | (binintersectRsub != $true)) )),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f1327])).
% 48.38/8.19 thf(f1327,plain,(
% 48.38/8.19 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) = $true) | (binintersectRsub != $true)) & ((binintersectRsub = $true) | ($true != (subset @ (binintersect @ sK55 @ sK56) @ sK56)))),
% 48.38/8.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56])],[f1325,f1326])).
% 48.38/8.19 thf(f1326,plain,(
% 48.38/8.19 ? [X2 : $i,X3 : $i] : ($true != (subset @ (binintersect @ X2 @ X3) @ X3)) => ($true != (subset @ (binintersect @ sK55 @ sK56) @ sK56))),
% 48.38/8.19 introduced(definition,[],[choice_axiom])).
% 48.38/8.19 thf(f1325,plain,(
% 48.38/8.19 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) = $true) | (binintersectRsub != $true)) & ((binintersectRsub = $true) | ? [X2 : $i,X3 : $i] : ($true != (subset @ (binintersect @ X2 @ X3) @ X3)))),
% 48.38/8.19 inference(rectify,[status(thm)],[f1324])).
% 48.38/8.19 thf(f1324,plain,(
% 48.38/8.19 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) = $true) | (binintersectRsub != $true)) & ((binintersectRsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) != $true))),
% 48.38/8.19 inference(nnf_transformation,[status(thm)],[f439])).
% 48.38/8.19 thf(f439,plain,(
% 48.38/8.19 ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X1) = $true) <=> (binintersectRsub = $true)),
% 48.38/8.19 inference(fool_elimination,[status(thm)],[f438])).
% 48.38/8.19 thf(f438,plain,(
% 48.38/8.19 (binintersectRsub = ! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X1))),
% 48.38/8.19 inference(rectify,[status(thm)],[f116])).
% 48.38/8.19 thf(f116,axiom,(
% 48.38/8.19 (binintersectRsub = ! [X3 : $i,X4 : $i] : (subset @ (binintersect @ X3 @ X4) @ X4))),
% 48.38/8.19 file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',binintersectRsub)).
% 48.38/8.19 thf(f15527,plain,(
% 48.38/8.19 ( ! [X0 : $i] : (((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true) | ((subset @ X0 @ sK696) != $true)) ) | spl905_13),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f15526])).
% 48.38/8.19 thf(f15526,plain,(
% 48.38/8.19 ( ! [X0 : $i] : (($true != $true) | ((subset @ X0 @ sK696) != $true) | ((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true)) ) | spl905_13),
% 48.38/8.19 inference(forward_demodulation,[status(thm)],[f15501,f3586])).
% 48.38/8.19 thf(f3586,plain,(
% 48.38/8.19 (subsetTrans = $true)),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2314])).
% 48.38/8.19 thf(f15501,plain,(
% 48.38/8.19 ( ! [X0 : $i] : ((subsetTrans != $true) | ((subset @ X0 @ sK696) != $true) | ((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true)) ) | spl905_13),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f15496])).
% 48.38/8.19 thf(f15496,plain,(
% 48.38/8.19 ( ! [X0 : $i] : (($true != $true) | ((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true) | (subsetTrans != $true) | ((subset @ X0 @ sK696) != $true)) ) | spl905_13),
% 48.38/8.19 inference(superposition,[status(thm)],[f4498,f3901])).
% 48.38/8.19 thf(f3901,plain,(
% 48.38/8.19 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X5) = $true) | ((subset @ X4 @ X5) != $true) | ((subset @ X3 @ X4) != $true) | (subsetTrans != $true)) )),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2400])).
% 48.38/8.19 thf(f2400,plain,(
% 48.38/8.19 ((subsetTrans = $true) | (((subset @ sK754 @ sK756) != $true) & ((subset @ sK755 @ sK756) = $true) & ((subset @ sK754 @ sK755) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X5) = $true) | ((subset @ X4 @ X5) != $true) | ((subset @ X3 @ X4) != $true)) | (subsetTrans != $true))),
% 48.38/8.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK754,sK755,sK756])],[f2398,f2399])).
% 48.38/8.19 thf(f2399,plain,(
% 48.38/8.19 ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) != $true) & ((subset @ X1 @ X2) = $true) & ((subset @ X0 @ X1) = $true)) => (((subset @ sK754 @ sK756) != $true) & ((subset @ sK755 @ sK756) = $true) & ((subset @ sK754 @ sK755) = $true))),
% 48.38/8.19 introduced(definition,[],[choice_axiom])).
% 48.38/8.19 thf(f2398,plain,(
% 48.38/8.19 ((subsetTrans = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) != $true) & ((subset @ X1 @ X2) = $true) & ((subset @ X0 @ X1) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X3 @ X5) = $true) | ((subset @ X4 @ X5) != $true) | ((subset @ X3 @ X4) != $true)) | (subsetTrans != $true))),
% 48.38/8.19 inference(rectify,[status(thm)],[f2397])).
% 48.38/8.19 thf(f2397,plain,(
% 48.38/8.19 ((subsetTrans = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) != $true) & ((subset @ X1 @ X2) = $true) & ((subset @ X0 @ X1) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) = $true) | ((subset @ X1 @ X2) != $true) | ((subset @ X0 @ X1) != $true)) | (subsetTrans != $true))),
% 48.38/8.19 inference(nnf_transformation,[status(thm)],[f1189])).
% 48.38/8.19 thf(f1189,plain,(
% 48.38/8.19 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X2) = $true) | ((subset @ X1 @ X2) != $true) | ((subset @ X0 @ X1) != $true))),
% 48.38/8.19 inference(flattening,[status(thm)],[f1188])).
% 48.38/8.19 thf(f1188,plain,(
% 48.38/8.19 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X0 @ X2) = $true) | ((subset @ X1 @ X2) != $true)) | ((subset @ X0 @ X1) != $true))),
% 48.38/8.19 inference(ennf_transformation,[status(thm)],[f431])).
% 48.38/8.19 thf(f431,plain,(
% 48.38/8.19 (subsetTrans = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X0 @ X1) = $true) => (((subset @ X1 @ X2) = $true) => ((subset @ X0 @ X2) = $true)))),
% 48.38/8.19 inference(fool_elimination,[status(thm)],[f430])).
% 48.38/8.19 thf(f430,plain,(
% 48.38/8.19 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X2) => (subset @ X0 @ X2))) = subsetTrans)),
% 48.38/8.19 inference(rectify,[status(thm)],[f89])).
% 48.38/8.19 thf(f89,axiom,(
% 48.38/8.19 (! [X3 : $i,X4 : $i,X5 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X5) => (subset @ X3 @ X5))) = subsetTrans)),
% 48.38/8.19 file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',subsetTrans)).
% 48.38/8.19 thf(f4498,plain,(
% 48.38/8.19 ($true != (subset @ (binintersect @ sK692 @ sK694) @ sK696)) | spl905_13),
% 48.38/8.19 inference(avatar_component_clause,[status(thm)],[f4496])).
% 48.38/8.19 thf(f15429,plain,(
% 48.38/8.19 ~spl905_30 | spl905_11),
% 48.38/8.19 inference(avatar_split_clause,[status(thm)],[f15428,f4485,f4661])).
% 48.38/8.19 thf(f4661,definition,(
% 48.38/8.19 spl905_30 <=> ((subset @ sK692 @ sK695) = $true)),
% 48.38/8.19 introduced(definition,[new_symbols(naming,[spl905_30])],[avatar_definition])).
% 48.38/8.19 thf(f4485,definition,(
% 48.38/8.19 spl905_11 <=> ($true = (subset @ (binintersect @ sK692 @ sK694) @ sK695))),
% 48.38/8.19 introduced(definition,[new_symbols(naming,[spl905_11])],[avatar_definition])).
% 48.38/8.19 thf(f15428,plain,(
% 48.38/8.19 ((subset @ sK692 @ sK695) != $true) | spl905_11),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f15427])).
% 48.38/8.19 thf(f15427,plain,(
% 48.38/8.19 ((subset @ sK692 @ sK695) != $true) | ($true != $true) | spl905_11),
% 48.38/8.19 inference(forward_demodulation,[status(thm)],[f15275,f3739])).
% 48.38/8.19 thf(f3739,plain,(
% 48.38/8.19 (binintersectLsub = $true)),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2314])).
% 48.38/8.19 thf(f15275,plain,(
% 48.38/8.19 ((subset @ sK692 @ sK695) != $true) | (binintersectLsub != $true) | spl905_11),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f15238])).
% 48.38/8.19 thf(f15238,plain,(
% 48.38/8.19 ($true != $true) | (binintersectLsub != $true) | ((subset @ sK692 @ sK695) != $true) | spl905_11),
% 48.38/8.19 inference(superposition,[status(thm)],[f4850,f3150])).
% 48.38/8.19 thf(f3150,plain,(
% 48.38/8.19 ( ! [X2 : $i,X3 : $i] : (((subset @ (binintersect @ X3 @ X2) @ X3) = $true) | (binintersectLsub != $true)) )),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f1886])).
% 48.38/8.19 thf(f1886,plain,(
% 48.38/8.19 ((binintersectLsub = $true) | ((subset @ (binintersect @ sK421 @ sK420) @ sK421) != $true)) & (! [X2 : $i,X3 : $i] : ((subset @ (binintersect @ X3 @ X2) @ X3) = $true) | (binintersectLsub != $true))),
% 48.38/8.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK420,sK421])],[f1884,f1885])).
% 48.38/8.19 thf(f1885,plain,(
% 48.38/8.19 ? [X0 : $i,X1 : $i] : ($true != (subset @ (binintersect @ X1 @ X0) @ X1)) => ((subset @ (binintersect @ sK421 @ sK420) @ sK421) != $true)),
% 48.38/8.19 introduced(definition,[],[choice_axiom])).
% 48.38/8.19 thf(f1884,plain,(
% 48.38/8.19 ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : ($true != (subset @ (binintersect @ X1 @ X0) @ X1))) & (! [X2 : $i,X3 : $i] : ((subset @ (binintersect @ X3 @ X2) @ X3) = $true) | (binintersectLsub != $true))),
% 48.38/8.19 inference(rectify,[status(thm)],[f1883])).
% 48.38/8.19 thf(f1883,plain,(
% 48.38/8.19 ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : ($true != (subset @ (binintersect @ X1 @ X0) @ X1))) & (! [X0 : $i,X1 : $i] : ($true = (subset @ (binintersect @ X1 @ X0) @ X1)) | (binintersectLsub != $true))),
% 48.38/8.19 inference(nnf_transformation,[status(thm)],[f825])).
% 48.38/8.19 thf(f825,plain,(
% 48.38/8.19 (binintersectLsub = $true) <=> ! [X0 : $i,X1 : $i] : ($true = (subset @ (binintersect @ X1 @ X0) @ X1))),
% 48.38/8.19 inference(fool_elimination,[status(thm)],[f824])).
% 48.38/8.19 thf(f824,plain,(
% 48.38/8.19 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X1 @ X0) @ X1) = binintersectLsub)),
% 48.38/8.19 inference(rectify,[status(thm)],[f111])).
% 48.38/8.19 thf(f111,axiom,(
% 48.38/8.19 (! [X4 : $i,X3 : $i] : (subset @ (binintersect @ X3 @ X4) @ X3) = binintersectLsub)),
% 48.38/8.19 file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',binintersectLsub)).
% 48.38/8.19 thf(f4850,plain,(
% 48.38/8.19 ( ! [X0 : $i] : (((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true) | ((subset @ X0 @ sK695) != $true)) ) | spl905_11),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f4849])).
% 48.38/8.19 thf(f4849,plain,(
% 48.38/8.19 ( ! [X0 : $i] : (((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true) | ((subset @ X0 @ sK695) != $true) | ($true != $true)) ) | spl905_11),
% 48.38/8.19 inference(forward_demodulation,[status(thm)],[f4829,f3586])).
% 48.38/8.19 thf(f4829,plain,(
% 48.38/8.19 ( ! [X0 : $i] : (((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true) | ((subset @ X0 @ sK695) != $true) | (subsetTrans != $true)) ) | spl905_11),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f4823])).
% 48.38/8.19 thf(f4823,plain,(
% 48.38/8.19 ( ! [X0 : $i] : (($true != $true) | (subsetTrans != $true) | ((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true) | ((subset @ X0 @ sK695) != $true)) ) | spl905_11),
% 48.38/8.19 inference(superposition,[status(thm)],[f4487,f3901])).
% 48.38/8.19 thf(f4487,plain,(
% 48.38/8.19 ($true != (subset @ (binintersect @ sK692 @ sK694) @ sK695)) | spl905_11),
% 48.38/8.19 inference(avatar_component_clause,[status(thm)],[f4485])).
% 48.38/8.19 thf(f15201,plain,(
% 48.38/8.19 ~spl905_11 | ~spl905_13),
% 48.38/8.19 inference(avatar_split_clause,[status(thm)],[f15200,f4496,f4485])).
% 48.38/8.19 thf(f15200,plain,(
% 48.38/8.19 ($true != (subset @ (binintersect @ sK692 @ sK694) @ sK695)) | ($true != (subset @ (binintersect @ sK692 @ sK694) @ sK696))),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f15199])).
% 48.38/8.19 thf(f15199,plain,(
% 48.38/8.19 ($true != (subset @ (binintersect @ sK692 @ sK694) @ sK696)) | ($true != $true) | ($true != (subset @ (binintersect @ sK692 @ sK694) @ sK695))),
% 48.38/8.19 inference(forward_demodulation,[status(thm)],[f15198,f3736])).
% 48.38/8.19 thf(f3736,plain,(
% 48.38/8.19 (binintersectSubset5 = $true)),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2314])).
% 48.38/8.19 thf(f15198,plain,(
% 48.38/8.19 (binintersectSubset5 != $true) | ($true != (subset @ (binintersect @ sK692 @ sK694) @ sK696)) | ($true != (subset @ (binintersect @ sK692 @ sK694) @ sK695))),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f15186])).
% 48.38/8.19 thf(f15186,plain,(
% 48.38/8.19 ($true != $true) | ($true != (subset @ (binintersect @ sK692 @ sK694) @ sK695)) | ($true != (subset @ (binintersect @ sK692 @ sK694) @ sK696)) | (binintersectSubset5 != $true)),
% 48.38/8.19 inference(superposition,[status(thm)],[f5941,f4010])).
% 48.38/8.19 thf(f4010,plain,(
% 48.38/8.19 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ (binintersect @ X5 @ X3)) = $true) | (binintersectSubset5 != $true) | ((subset @ X4 @ X3) != $true) | ((subset @ X4 @ X5) != $true)) )),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2513])).
% 48.38/8.19 thf(f2513,plain,(
% 48.38/8.19 ((binintersectSubset5 = $true) | (((subset @ sK833 @ (binintersect @ sK834 @ sK832)) != $true) & ((subset @ sK833 @ sK832) = $true) & ((subset @ sK833 @ sK834) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ (binintersect @ X5 @ X3)) = $true) | ((subset @ X4 @ X3) != $true) | ((subset @ X4 @ X5) != $true)) | (binintersectSubset5 != $true))),
% 48.38/8.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK832,sK833,sK834])],[f2511,f2512])).
% 48.38/8.19 thf(f2512,plain,(
% 48.38/8.19 ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ (binintersect @ X2 @ X0)) != $true) & ($true = (subset @ X1 @ X0)) & ((subset @ X1 @ X2) = $true)) => (((subset @ sK833 @ (binintersect @ sK834 @ sK832)) != $true) & ((subset @ sK833 @ sK832) = $true) & ((subset @ sK833 @ sK834) = $true))),
% 48.38/8.19 introduced(definition,[],[choice_axiom])).
% 48.38/8.19 thf(f2511,plain,(
% 48.38/8.19 ((binintersectSubset5 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ (binintersect @ X2 @ X0)) != $true) & ($true = (subset @ X1 @ X0)) & ((subset @ X1 @ X2) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X4 @ (binintersect @ X5 @ X3)) = $true) | ((subset @ X4 @ X3) != $true) | ((subset @ X4 @ X5) != $true)) | (binintersectSubset5 != $true))),
% 48.38/8.19 inference(rectify,[status(thm)],[f2510])).
% 48.38/8.19 thf(f2510,plain,(
% 48.38/8.19 ((binintersectSubset5 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ (binintersect @ X2 @ X0)) != $true) & ($true = (subset @ X1 @ X0)) & ((subset @ X1 @ X2) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ (binintersect @ X2 @ X0)) = $true) | ($true != (subset @ X1 @ X0)) | ((subset @ X1 @ X2) != $true)) | (binintersectSubset5 != $true))),
% 48.38/8.19 inference(nnf_transformation,[status(thm)],[f1033])).
% 48.38/8.19 thf(f1033,plain,(
% 48.38/8.19 (binintersectSubset5 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ (binintersect @ X2 @ X0)) = $true) | ($true != (subset @ X1 @ X0)) | ((subset @ X1 @ X2) != $true))),
% 48.38/8.19 inference(flattening,[status(thm)],[f1032])).
% 48.38/8.19 thf(f1032,plain,(
% 48.38/8.19 ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X1 @ (binintersect @ X2 @ X0)) = $true) | ($true != (subset @ X1 @ X0))) | ((subset @ X1 @ X2) != $true)) <=> (binintersectSubset5 = $true)),
% 48.38/8.19 inference(ennf_transformation,[status(thm)],[f769])).
% 48.38/8.19 thf(f769,plain,(
% 48.38/8.19 ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X1 @ X2) = $true) => (($true = (subset @ X1 @ X0)) => ((subset @ X1 @ (binintersect @ X2 @ X0)) = $true))) <=> (binintersectSubset5 = $true)),
% 48.38/8.19 inference(fool_elimination,[status(thm)],[f768])).
% 48.38/8.19 thf(f768,plain,(
% 48.38/8.19 (binintersectSubset5 = ! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X1 @ X2) => ((subset @ X1 @ X0) => (subset @ X1 @ (binintersect @ X2 @ X0)))))),
% 48.38/8.19 inference(rectify,[status(thm)],[f109])).
% 48.38/8.19 thf(f109,axiom,(
% 48.38/8.19 (binintersectSubset5 = ! [X4 : $i,X5 : $i,X3 : $i] : ((subset @ X5 @ X3) => ((subset @ X5 @ X4) => (subset @ X5 @ (binintersect @ X3 @ X4)))))),
% 48.38/8.19 file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',binintersectSubset5)).
% 48.38/8.19 thf(f5941,plain,(
% 48.38/8.19 ((subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ sK695 @ sK696)) != $true)),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f5940])).
% 48.38/8.19 thf(f5940,plain,(
% 48.38/8.19 ($true != $true) | ((subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ sK695 @ sK696)) != $true)),
% 48.38/8.19 inference(forward_demodulation,[status(thm)],[f5821,f3575])).
% 48.38/8.19 thf(f3575,plain,(
% 48.38/8.19 (eqimpsubset1 = $true)),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2314])).
% 48.38/8.19 thf(f5821,plain,(
% 48.38/8.19 ((subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ sK695 @ sK696)) != $true) | (eqimpsubset1 != $true)),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f5780])).
% 48.38/8.19 thf(f5780,plain,(
% 48.38/8.19 (eqimpsubset1 != $true) | ($true != $true) | ((subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ sK695 @ sK696)) != $true)),
% 48.38/8.19 inference(superposition,[status(thm)],[f4520,f4157])).
% 48.38/8.19 thf(f4157,plain,(
% 48.38/8.19 ( ! [X3 : $i] : (((subset @ X3 @ X3) = $true) | (eqimpsubset1 != $true)) )),
% 48.38/8.19 inference(equality_resolution,[status(thm)],[f3875])).
% 48.38/8.19 thf(f3875,plain,(
% 48.38/8.19 ( ! [X2 : $i,X3 : $i] : ((X2 != X3) | ($true = (subset @ X3 @ X2)) | (eqimpsubset1 != $true)) )),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2370])).
% 48.38/8.19 thf(f2370,plain,(
% 48.38/8.19 ((eqimpsubset1 = $true) | ((sK733 = sK732) & ((subset @ sK733 @ sK732) != $true))) & (! [X2 : $i,X3 : $i] : ((X2 != X3) | ($true = (subset @ X3 @ X2))) | (eqimpsubset1 != $true))),
% 48.38/8.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK732,sK733])],[f2368,f2369])).
% 48.38/8.19 thf(f2369,plain,(
% 48.38/8.19 ? [X0 : $i,X1 : $i] : ((X0 = X1) & ($true != (subset @ X1 @ X0))) => ((sK733 = sK732) & ((subset @ sK733 @ sK732) != $true))),
% 48.38/8.19 introduced(definition,[],[choice_axiom])).
% 48.38/8.19 thf(f2368,plain,(
% 48.38/8.19 ((eqimpsubset1 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & ($true != (subset @ X1 @ X0)))) & (! [X2 : $i,X3 : $i] : ((X2 != X3) | ($true = (subset @ X3 @ X2))) | (eqimpsubset1 != $true))),
% 48.38/8.19 inference(rectify,[status(thm)],[f2367])).
% 48.38/8.19 thf(f2367,plain,(
% 48.38/8.19 ((eqimpsubset1 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & ($true != (subset @ X1 @ X0)))) & (! [X0 : $i,X1 : $i] : ((X0 != X1) | ($true = (subset @ X1 @ X0))) | (eqimpsubset1 != $true))),
% 48.38/8.19 inference(nnf_transformation,[status(thm)],[f949])).
% 48.38/8.19 thf(f949,plain,(
% 48.38/8.19 (eqimpsubset1 = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 != X1) | ($true = (subset @ X1 @ X0)))),
% 48.38/8.19 inference(ennf_transformation,[status(thm)],[f443])).
% 48.38/8.19 thf(f443,plain,(
% 48.38/8.19 (eqimpsubset1 = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 = X1) => ($true = (subset @ X1 @ X0)))),
% 48.38/8.19 inference(fool_elimination,[status(thm)],[f442])).
% 48.38/8.19 thf(f442,plain,(
% 48.38/8.19 (! [X0 : $i,X1 : $i] : ((X0 = X1) => (subset @ X1 @ X0)) = eqimpsubset1)),
% 48.38/8.19 inference(rectify,[status(thm)],[f80])).
% 48.38/8.19 thf(f80,axiom,(
% 48.38/8.19 (! [X4 : $i,X3 : $i] : ((X3 = X4) => (subset @ X3 @ X4)) = eqimpsubset1)),
% 48.38/8.19 file('/export/starexec/sandbox2/tmp/tmp.X9tg9JOzFs/DTF2THF_31785.p',eqimpsubset1)).
% 48.38/8.19 thf(f4520,plain,(
% 48.38/8.19 ( ! [X0 : $i] : (((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true) | ((subset @ X0 @ (binintersect @ sK695 @ sK696)) != $true)) )),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f4519])).
% 48.38/8.19 thf(f4519,plain,(
% 48.38/8.19 ( ! [X0 : $i] : (((subset @ X0 @ (binintersect @ sK695 @ sK696)) != $true) | ($true != $true) | ((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true)) )),
% 48.38/8.19 inference(forward_demodulation,[status(thm)],[f4474,f3586])).
% 48.38/8.19 thf(f4474,plain,(
% 48.38/8.19 ( ! [X0 : $i] : ((subsetTrans != $true) | ((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true) | ((subset @ X0 @ (binintersect @ sK695 @ sK696)) != $true)) )),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f4466])).
% 48.38/8.19 thf(f4466,plain,(
% 48.38/8.19 ( ! [X0 : $i] : ((subsetTrans != $true) | ((subset @ X0 @ (binintersect @ sK695 @ sK696)) != $true) | ((subset @ (binintersect @ sK692 @ sK694) @ X0) != $true) | ($true != $true)) )),
% 48.38/8.19 inference(superposition,[status(thm)],[f3658,f3901])).
% 48.38/8.19 thf(f3658,plain,(
% 48.38/8.19 ((subset @ (binintersect @ sK692 @ sK694) @ (binintersect @ sK695 @ sK696)) != $true)),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2314])).
% 48.38/8.19 thf(f10246,plain,(
% 48.38/8.19 spl905_35),
% 48.38/8.19 inference(avatar_contradiction_clause,[status(thm)],[f10245])).
% 48.38/8.19 thf(f10245,plain,(
% 48.38/8.19 $false | spl905_35),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f10237])).
% 48.38/8.19 thf(f10237,plain,(
% 48.38/8.19 ($true != $true) | spl905_35),
% 48.38/8.19 inference(superposition,[status(thm)],[f4792,f3660])).
% 48.38/8.19 thf(f3660,plain,(
% 48.38/8.19 ((subset @ sK694 @ sK696) = $true)),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2314])).
% 48.38/8.19 thf(f4792,plain,(
% 48.38/8.19 ((subset @ sK694 @ sK696) != $true) | spl905_35),
% 48.38/8.19 inference(avatar_component_clause,[status(thm)],[f4790])).
% 48.38/8.19 thf(f10130,plain,(
% 48.38/8.19 spl905_30),
% 48.38/8.19 inference(avatar_contradiction_clause,[status(thm)],[f10129])).
% 48.38/8.19 thf(f10129,plain,(
% 48.38/8.19 $false | spl905_30),
% 48.38/8.19 inference(trivial_inequality_removal,[status(thm)],[f10124])).
% 48.38/8.19 thf(f10124,plain,(
% 48.38/8.19 ($true != $true) | spl905_30),
% 48.38/8.19 inference(superposition,[status(thm)],[f4663,f3659])).
% 48.38/8.19 thf(f3659,plain,(
% 48.38/8.19 ((subset @ sK692 @ sK695) = $true)),
% 48.38/8.19 inference(cnf_transformation,[status(thm)],[f2314])).
% 48.38/8.19 thf(f4663,plain,(
% 48.38/8.19 ((subset @ sK692 @ sK695) != $true) | spl905_30),
% 48.38/8.19 inference(avatar_component_clause,[status(thm)],[f4661])).
% 48.38/8.19 % SZS output end Proof for DTF2THF_31785
% 48.38/8.19 % (32370)------------------------------
% 48.38/8.19 % (32370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.38/8.19 % (32370)Termination reason: Refutation
% 48.38/8.19
% 48.38/8.19 % (32370)Memory used [KB]: 15607
% 48.38/8.19 % (32370)Time elapsed: 0.456 s
% 48.38/8.19 % (32370)Instructions burned: 1503 (million)
% 48.38/8.19 % (32370)------------------------------
% 48.38/8.19 % (32370)------------------------------
% 48.38/8.19 % (32102)Success in time 6.51 s
%------------------------------------------------------------------------------