%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU632^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 09:35:46 AM UTC 2026
% Result : Theorem 31.18s 5.90s
% Output : Refutation 31.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 47 ( 11 unt; 0 typ; 4 def)
% Number of atoms : 2592 ( 705 equ; 0 cnn)
% Maximal formula atoms : 150 ( 55 avg)
% Number of connectives : 1506 ( 57 ~; 43 |; 480 &; 315 @)
% ( 7 <=>; 604 =>; 0 <=; 0 <~>)
% Maximal formula depth : 157 ( 27 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 286 ( 283 usr; 162 con; 0-4 aty)
% Number of variables : 116 ( 0 ^; 76 !; 40 ?; 116 :)
% 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_185,type,
sP1: $i > $i > $o ).
thf(func_def_186,type,
sP2: $i > $o ).
thf(func_def_187,type,
sP3: $i > $i > $o ).
thf(func_def_188,type,
sP4: $i > $i > $o ).
thf(func_def_189,type,
sP5: $o > $i > $i > $i > $o ).
thf(func_def_191,type,
sK7: $i > $o ).
thf(func_def_197,type,
sK13: $i > $i > $i ).
thf(func_def_198,type,
sK14: $o > $i > $i > $i ).
thf(func_def_218,type,
sK34: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_219,type,
sK35: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_220,type,
sK36: $i > $o ).
thf(func_def_221,type,
sK37: $i > $o ).
thf(func_def_225,type,
sK41: $i > $o ).
thf(func_def_239,type,
sK55: $i > $o ).
thf(func_def_249,type,
sK65: $i > $o ).
thf(func_def_268,type,
sK84: $i > $i > $i > $i ).
thf(func_def_269,type,
sK85: $i > $i > $i > $i ).
thf(func_def_276,type,
sK92: $i > $i > $i ).
thf(func_def_280,type,
sK96: $i > $o ).
thf(func_def_282,type,
sK98: ( $i > $o ) > $i ).
thf(func_def_283,type,
sK99: ( $i > $o ) > $i ).
thf(func_def_284,type,
sK100: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_285,type,
sK101: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_286,type,
sK102: $i > $o ).
thf(func_def_287,type,
sK103: $i > $o ).
thf(func_def_288,type,
sK104: ( $i > $o ) > $i ).
thf(func_def_289,type,
sK105: $i > $o ).
thf(func_def_290,type,
sK106: $i > $o ).
thf(func_def_294,type,
sK110: $i > $i ).
thf(func_def_310,type,
sK126: $i > $i > $i ).
thf(func_def_319,type,
sK135: $i > $i > $i ).
thf(func_def_323,type,
sK139: $i > $o ).
thf(func_def_333,type,
sK149: $i > $o ).
thf(func_def_342,type,
sK158: $i > $i > $o ).
thf(func_def_343,type,
sK159: $i > $i ).
thf(func_def_344,type,
sK160: $i > $i ).
thf(func_def_345,type,
sK161: ( $i > $i > $o ) > $i > $i ).
thf(func_def_346,type,
sK162: ( $i > $i > $o ) > $i > $i ).
thf(func_def_347,type,
sK163: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_362,type,
sK178: $i > $i ).
thf(func_def_365,type,
sK181: $i > $o ).
thf(func_def_367,type,
sK183: $i > ( $i > $o ) > $i ).
thf(func_def_368,type,
sK184: ( $i > $o ) > $i > $i ).
thf(func_def_370,type,
sK186: $i > $o ).
thf(func_def_400,type,
sK216: $i > $i ).
thf(func_def_403,type,
sK219: $i > $i ).
thf(func_def_404,type,
sK220: ( $i > $o ) > $i ).
thf(func_def_405,type,
sK221: $i > $o ).
thf(func_def_406,type,
sK222: $i > $i ).
thf(func_def_417,type,
sK233: $i > $i > $i ).
thf(func_def_418,type,
sK234: $i > $i > $i ).
thf(func_def_420,type,
sK236: $i > $i ).
thf(func_def_426,type,
sK242: $i > $i > $i ).
thf(func_def_427,type,
sK243: $i > $o ).
thf(func_def_430,type,
sK246: $i > ( $i > $o ) > $i ).
thf(func_def_437,type,
sK253: $i > $i ).
thf(func_def_439,type,
sK255: $i > $i ).
thf(func_def_441,type,
sK257: $i > $o ).
thf(func_def_447,type,
sK263: $i > $i > $i ).
thf(func_def_449,type,
sK265: $i > $o ).
thf(func_def_451,type,
sK267: $i > $o ).
thf(func_def_454,type,
sK270: $i > ( $i > $o ) > $i ).
thf(func_def_477,type,
sK293: ( $i > $o ) > $i ).
thf(func_def_478,type,
sK294: $i > $o ).
thf(func_def_479,type,
sK295: $i > $i ).
thf(func_def_485,type,
sK301: $i > $o ).
thf(func_def_488,type,
sK304: $i > ( $i > $o ) > $i ).
thf(func_def_502,type,
sK318: $i > ( $i > $o ) > $i ).
thf(func_def_503,type,
sK319: $i > $o ).
thf(func_def_506,type,
sK322: $i > $o ).
thf(func_def_507,type,
sK323: $i > $i > $i ).
thf(func_def_508,type,
sK324: $i > $i > $i ).
thf(func_def_509,type,
sK325: $i > $i > $i ).
thf(func_def_510,type,
sK326: $i > $i > $i ).
thf(func_def_511,type,
sK327: $i > $i > $i > $i ).
thf(func_def_512,type,
sK328: $i > $i ).
thf(func_def_513,type,
sK329: $i > $i ).
thf(func_def_514,type,
sK330: $i > $i ).
thf(func_def_515,type,
sK331: $i > $i ).
thf(func_def_516,type,
sK332: $i > $i > $i > $i ).
thf(func_def_517,type,
sK333: $i > $i > $i > $i ).
thf(func_def_518,type,
sK334: $i > $i > $i ).
thf(func_def_519,type,
sK335: $i > $i > $i ).
thf(func_def_520,type,
sK336: $i > $i > $i ).
thf(func_def_522,type,
sK338: $i > $i ).
thf(func_def_523,type,
sK339: $i > $i ).
thf(func_def_524,type,
sK340: $i > $i ).
thf(func_def_525,type,
sK341: $i > $i > $i ).
thf(func_def_526,type,
sK342: $i > $o ).
thf(func_def_548,type,
sK364: $i > $o ).
thf(func_def_566,type,
sK382: $i > $o ).
thf(func_def_568,type,
sK384: $i > ( $i > $o ) > $i ).
thf(func_def_571,type,
sK387: $i > $o ).
thf(func_def_572,type,
sK388: $i > $o ).
thf(func_def_573,type,
sK389: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_574,type,
sK390: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_586,type,
sK402: $i > $i > $i ).
thf(func_def_589,type,
sK405: $i > ( $i > $o ) > $i ).
thf(func_def_590,type,
sK406: $i > $o ).
thf(func_def_600,type,
ph416:
!>[X0: $tType] : X0 ).
thf(func_def_601,type,
sK417: $i > $i ).
thf(func_def_602,type,
sK418: $i > $i ).
thf(f16118,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2936,f3127,f4753,f5318,f16117]) ).
thf(f16117,plain,
( ~ spl415_170
| ~ spl415_214 ),
inference(avatar_contradiction_clause,[status(thm)],[f16116]) ).
thf(f16116,plain,
( $false
| ~ spl415_170
| ~ spl415_214 ),
inference(subsumption_resolution,[status(thm)],[f16115,f1800]) ).
thf(f1800,plain,
( $true
!= ( iskpair @ sK298 ) ),
inference(cnf_transformation,[status(thm)],[f1156]) ).
thf(f1156,plain,
( ( symdiffIneg1 = $true )
& ( emptysetimpfalse = $true )
& ( exuE2 = $true )
& ( powersetE1 = $true )
& ( dsetconstr__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( ubforcartprodlem3 = $true )
& ( setminusELneg = $true )
& ( upairsetIL = $true )
& ( binintersectSubset5 = $true )
& ( upairsetE = $true )
& ( binunionIL = $true )
& ( singletonsubset = $true )
& ( setunionE = $true )
& ( binunionE = $true )
& ( powersetI = $true )
& ( setadjoinE = $true )
& ( exu__Cong = $true )
& ( emptysetE = $true )
& ( symdiffE = $true )
& ( notinsingleton = $true )
& ( powersetI1 = $true )
& ( symdiffI1 = $true )
& ( subsetE2 = $true )
& ( exuE3u = $true )
& ( subPowSU = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinIL = $true )
& ( binunionEcases = $true )
& ( setadjoinOr = $true )
& ( setadjoin__Cong = $true )
& ( binintersectER = $true )
& ( setunionAx = $true )
& ( dsetconstrI = $true )
& ( notdallE = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset4 = $true )
& ( singletoninpowerset = $true )
& ( setunionI = $true )
& ( eqimpsubset1 = $true )
& ( foundationAx = $true )
& ( in__Cong = $true )
& ( exuI1 = $true )
& ( subsetI1 = $true )
& ( nonemptyI = $true )
& ( sepInPowerset = $true )
& ( prop2set2propI = $true )
& ( symdiffIneg2 = $true )
& ( setukpairIL = $true )
& ( cartprodmempair1 = $true )
& ( disjointsetsI1 = $true )
& ( binunionLsub = $true )
& ( eqimpsubset2 = $true )
& ( nonemptyImpWitness = $true )
& ( omega0Ax = $true )
& ( setadjoinIR = $true )
& ( emptysetAx = $true )
& ( setminusEL = $true )
& ( notdexE = $true )
& ( bs114d = $true )
& ( setunion__Cong = $true )
& ( setminusER = $true )
& ( subsetRefl = $true )
& ( cartprodpairin = $true )
& ( notequalI2 = $true )
& ( inPowerset = $true )
& ( upairsubunion = $true )
& ( notsubsetI = $true )
& ( subsetI2 = $true )
& ( kpairp = $true )
& ( exuI2 = $true )
& ( descrp = $true )
& ( singletoninpowunion = $true )
& ( nonemptyE1 = $true )
& ( exuEu = $true )
& ( quantDeMorgan1 = $true )
& ( setminusERneg = $true )
& ( setadjoinSub = $true )
& ( setext = $true )
& ( setminusSubset1 = $true )
& ( quantDeMorgan2 = $true )
& ( subset2powerset = $true )
& ( replAx = $true )
& ( upairinpowunion = $true )
& ( $true
= ( in @ sK298 @ ( cartprod @ sK300 @ sK299 ) ) )
& ( $true
!= ( iskpair @ sK298 ) )
& ( ubforcartprodlem2 = $true )
& ( sepSubset = $true )
& ( powersetAx = $true )
& ( setminusILneg = $true )
& ( emptysetsubset = $true )
& ( emptyinPowerset = $true )
& ( setadjoinAx = $true )
& ( descr__Cong = $true )
& ( binintersectLsub = $true )
& ( upairset2E = $true )
& ( notequalI1 = $true )
& ( symdiffI2 = $true )
& ( setextsub = $true )
& ( setminusI = $true )
& ( omegaSAx = $true )
& ( uniqinunit = $true )
& ( omegaIndAx = $true )
& ( setminusSubset2 = $true )
& ( omega__Cong = $true )
& ( setoftrueEq = $true )
& ( inCongP = $true )
& ( prop2setE = $true )
& ( powerset__Cong = $true )
& ( emptyset__Cong = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( exuE1 = $true )
& ( notinemptyset = $true )
& ( powersetsubset = $true )
& ( binintersectSubset1 = $true )
& ( wellorderingAx = $true )
& ( exuI3 = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionRsub = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrER = $true )
& ( setminusIRneg = $true )
& ( powersetE = $true )
& ( upairsetIR = $true )
& ( noeltsimpempty = $true )
& ( binintersectEL = $true )
& ( prop2setI = $true )
& ( emptyinunitempty = $true )
& ( emptyE1 = $true )
& ( upairset2IR = $true )
& ( exuE3e = $true )
& ( vacuousDall = $true )
& ( subsetTrans = $true )
& ( subsetemptysetimpeq = $true )
& ( kpairiskpair = $true )
& ( setminusLsub = $true )
& ( binintersectSubset2 = $true )
& ( secondinupair = $true )
& ( setukpairIR = $true )
& ( setextAx = $true )
& ( emptyInPowerset = $true )
& ( binunionIR = $true )
& ( eqinunit = $true )
& ( subsetE = $true )
& ( binintersectI = $true )
& ( singletonsswitch = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectRsub = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK298,sK299,sK300])],[f512,f1155]) ).
thf(f1155,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) )
& ( $true
!= ( iskpair @ X0 ) ) )
=> ( ( $true
= ( in @ sK298 @ ( cartprod @ sK300 @ sK299 ) ) )
& ( $true
!= ( iskpair @ sK298 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f512,plain,
( ( symdiffIneg1 = $true )
& ( emptysetimpfalse = $true )
& ( exuE2 = $true )
& ( powersetE1 = $true )
& ( dsetconstr__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( ubforcartprodlem3 = $true )
& ( setminusELneg = $true )
& ( upairsetIL = $true )
& ( binintersectSubset5 = $true )
& ( upairsetE = $true )
& ( binunionIL = $true )
& ( singletonsubset = $true )
& ( setunionE = $true )
& ( binunionE = $true )
& ( powersetI = $true )
& ( setadjoinE = $true )
& ( exu__Cong = $true )
& ( emptysetE = $true )
& ( symdiffE = $true )
& ( notinsingleton = $true )
& ( powersetI1 = $true )
& ( symdiffI1 = $true )
& ( subsetE2 = $true )
& ( exuE3u = $true )
& ( subPowSU = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinIL = $true )
& ( binunionEcases = $true )
& ( setadjoinOr = $true )
& ( setadjoin__Cong = $true )
& ( binintersectER = $true )
& ( setunionAx = $true )
& ( dsetconstrI = $true )
& ( notdallE = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrEL = $true )
& ( binintersectSubset4 = $true )
& ( singletoninpowerset = $true )
& ( setunionI = $true )
& ( eqimpsubset1 = $true )
& ( foundationAx = $true )
& ( in__Cong = $true )
& ( exuI1 = $true )
& ( subsetI1 = $true )
& ( nonemptyI = $true )
& ( sepInPowerset = $true )
& ( prop2set2propI = $true )
& ( symdiffIneg2 = $true )
& ( setukpairIL = $true )
& ( cartprodmempair1 = $true )
& ( disjointsetsI1 = $true )
& ( binunionLsub = $true )
& ( eqimpsubset2 = $true )
& ( nonemptyImpWitness = $true )
& ( omega0Ax = $true )
& ( setadjoinIR = $true )
& ( emptysetAx = $true )
& ( setminusEL = $true )
& ( notdexE = $true )
& ( bs114d = $true )
& ( setunion__Cong = $true )
& ( setminusER = $true )
& ( subsetRefl = $true )
& ( cartprodpairin = $true )
& ( notequalI2 = $true )
& ( inPowerset = $true )
& ( upairsubunion = $true )
& ( notsubsetI = $true )
& ( subsetI2 = $true )
& ( kpairp = $true )
& ( exuI2 = $true )
& ( descrp = $true )
& ( singletoninpowunion = $true )
& ( nonemptyE1 = $true )
& ( exuEu = $true )
& ( quantDeMorgan1 = $true )
& ( setminusERneg = $true )
& ( setadjoinSub = $true )
& ( setext = $true )
& ( setminusSubset1 = $true )
& ( quantDeMorgan2 = $true )
& ( subset2powerset = $true )
& ( replAx = $true )
& ( upairinpowunion = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) )
& ( $true
!= ( iskpair @ X0 ) ) )
& ( ubforcartprodlem2 = $true )
& ( sepSubset = $true )
& ( powersetAx = $true )
& ( setminusILneg = $true )
& ( emptysetsubset = $true )
& ( emptyinPowerset = $true )
& ( setadjoinAx = $true )
& ( descr__Cong = $true )
& ( binintersectLsub = $true )
& ( upairset2E = $true )
& ( notequalI1 = $true )
& ( symdiffI2 = $true )
& ( setextsub = $true )
& ( setminusI = $true )
& ( omegaSAx = $true )
& ( uniqinunit = $true )
& ( omegaIndAx = $true )
& ( setminusSubset2 = $true )
& ( omega__Cong = $true )
& ( setoftrueEq = $true )
& ( inCongP = $true )
& ( prop2setE = $true )
& ( powerset__Cong = $true )
& ( emptyset__Cong = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( exuE1 = $true )
& ( notinemptyset = $true )
& ( powersetsubset = $true )
& ( binintersectSubset1 = $true )
& ( wellorderingAx = $true )
& ( exuI3 = $true )
& ( ubforcartprodlem1 = $true )
& ( binunionRsub = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrER = $true )
& ( setminusIRneg = $true )
& ( powersetE = $true )
& ( upairsetIR = $true )
& ( noeltsimpempty = $true )
& ( binintersectEL = $true )
& ( prop2setI = $true )
& ( emptyinunitempty = $true )
& ( emptyE1 = $true )
& ( upairset2IR = $true )
& ( exuE3e = $true )
& ( vacuousDall = $true )
& ( subsetTrans = $true )
& ( subsetemptysetimpeq = $true )
& ( kpairiskpair = $true )
& ( setminusLsub = $true )
& ( binintersectSubset2 = $true )
& ( secondinupair = $true )
& ( setukpairIR = $true )
& ( setextAx = $true )
& ( emptyInPowerset = $true )
& ( binunionIR = $true )
& ( eqinunit = $true )
& ( subsetE = $true )
& ( binintersectI = $true )
& ( singletonsswitch = $true )
& ( quantDeMorgan3 = $true )
& ( binintersectRsub = $true ) ),
inference(flattening,[status(thm)],[f511]) ).
thf(f511,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) )
& ( $true
!= ( iskpair @ X0 ) ) )
& ( 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)],[f159]) ).
thf(f159,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) )
=> ( $true
= ( iskpair @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f158]) ).
thf(f158,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( cartprod @ X2 @ X1 ) )
=> ( iskpair @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f154]) ).
thf(f154,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
=> ! [X10: $i,X4: $i,X3: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( iskpair @ X10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f153]) ).
thf(f153,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
=> ! [X10: $i,X4: $i,X3: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( iskpair @ X10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qvI7ApaoRY/DTF2THF_26806.p',cartprodmempair) ).
thf(f16115,plain,
( ( $true
= ( iskpair @ sK298 ) )
| ~ spl415_170
| ~ spl415_214 ),
inference(superposition,[status(thm)],[f2931,f12299]) ).
thf(f12299,plain,
( ( sK298
= ( kpair @ ( sK84 @ sK300 @ sK298 @ sK299 ) @ ( sK85 @ sK300 @ sK298 @ sK299 ) ) )
| ~ spl415_214 ),
inference(trivial_inequality_removal,[status(thm)],[f12283]) ).
thf(f12283,plain,
( ( $true != $true )
| ( sK298
= ( kpair @ ( sK84 @ sK300 @ sK298 @ sK299 ) @ ( sK85 @ sK300 @ sK298 @ sK299 ) ) )
| ~ spl415_214 ),
inference(superposition,[status(thm)],[f3126,f1801]) ).
thf(f1801,plain,
( $true
= ( in @ sK298 @ ( cartprod @ sK300 @ sK299 ) ) ),
inference(cnf_transformation,[status(thm)],[f1156]) ).
thf(f3126,plain,
( ! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( cartprod @ X7 @ X5 ) ) )
| ( ( kpair @ ( sK84 @ X7 @ X6 @ X5 ) @ ( sK85 @ X7 @ X6 @ X5 ) )
= X6 ) )
| ~ spl415_214 ),
inference(avatar_component_clause,[status(thm)],[f3125]) ).
thf(f3125,definition,
( spl415_214
<=> ! [X6: $i,X5: $i,X7: $i] :
( ( $true
!= ( in @ X6 @ ( cartprod @ X7 @ X5 ) ) )
| ( ( kpair @ ( sK84 @ X7 @ X6 @ X5 ) @ ( sK85 @ X7 @ X6 @ X5 ) )
= X6 ) ) ),
introduced(definition,[new_symbols(naming,[spl415_214])],[avatar_definition]) ).
thf(f2931,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( kpair @ X0 @ X1 ) ) )
| ~ spl415_170 ),
inference(avatar_component_clause,[status(thm)],[f2930]) ).
thf(f2930,definition,
( spl415_170
<=> ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl415_170])],[avatar_definition]) ).
thf(f5318,plain,
spl415_213,
inference(avatar_split_clause,[status(thm)],[f1836,f3121]) ).
thf(f3121,definition,
( spl415_213
<=> ( cartprodmempair1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl415_213])],[avatar_definition]) ).
thf(f1836,plain,
cartprodmempair1 = $true,
inference(cnf_transformation,[status(thm)],[f1156]) ).
thf(f4753,plain,
spl415_171,
inference(avatar_split_clause,[status(thm)],[f1816,f2933]) ).
thf(f2933,definition,
( spl415_171
<=> ( kpairp = $true ) ),
introduced(definition,[new_symbols(naming,[spl415_171])],[avatar_definition]) ).
thf(f1816,plain,
kpairp = $true,
inference(cnf_transformation,[status(thm)],[f1156]) ).
thf(f3127,plain,
( ~ spl415_213
| spl415_214 ),
inference(avatar_split_clause,[status(thm)],[f1440,f3125,f3121]) ).
thf(f1440,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X6 @ ( cartprod @ X7 @ X5 ) ) )
| ( cartprodmempair1 != $true )
| ( ( kpair @ ( sK84 @ X7 @ X6 @ X5 ) @ ( sK85 @ X7 @ X6 @ X5 ) )
= X6 ) ),
inference(cnf_transformation,[status(thm)],[f788]) ).
thf(f788,plain,
( ( ( cartprodmempair1 = $true )
| ( ( $true
= ( in @ sK82 @ ( cartprod @ sK83 @ sK81 ) ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( sK82
!= ( kpair @ X3 @ X4 ) )
| ( $true
!= ( in @ X4 @ sK81 ) ) )
| ( $true
!= ( in @ X3 @ sK83 ) ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( $true
!= ( in @ X6 @ ( cartprod @ X7 @ X5 ) ) )
| ( ( ( kpair @ ( sK84 @ X7 @ X6 @ X5 ) @ ( sK85 @ X7 @ X6 @ X5 ) )
= X6 )
& ( $true
= ( in @ ( sK85 @ X7 @ X6 @ X5 ) @ X5 ) )
& ( $true
= ( in @ ( sK84 @ X7 @ X6 @ X5 ) @ X7 ) ) ) )
| ( cartprodmempair1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK81,sK82,sK83,sK84,sK85])],[f784,f787,f786,f785]) ).
thf(f785,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= X1 )
| ( $true
!= ( in @ X4 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ X2 ) ) ) )
=> ( ( $true
= ( in @ sK82 @ ( cartprod @ sK83 @ sK81 ) ) )
& ! [X3: $i] :
( ! [X4: $i] :
( ( sK82
!= ( kpair @ X3 @ X4 ) )
| ( $true
!= ( in @ X4 @ sK81 ) ) )
| ( $true
!= ( in @ X3 @ sK83 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f786,plain,
! [X5: $i,X6: $i,X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( ( kpair @ X8 @ X9 )
= X6 )
& ( $true
= ( in @ X9 @ X5 ) ) )
& ( $true
= ( in @ X8 @ X7 ) ) )
=> ( ? [X9: $i] :
( ( ( kpair @ ( sK84 @ X7 @ X6 @ X5 ) @ X9 )
= X6 )
& ( $true
= ( in @ X9 @ X5 ) ) )
& ( $true
= ( in @ ( sK84 @ X7 @ X6 @ X5 ) @ X7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f787,plain,
! [X5: $i,X6: $i,X7: $i] :
( ? [X9: $i] :
( ( ( kpair @ ( sK84 @ X7 @ X6 @ X5 ) @ X9 )
= X6 )
& ( $true
= ( in @ X9 @ X5 ) ) )
=> ( ( ( kpair @ ( sK84 @ X7 @ X6 @ X5 ) @ ( sK85 @ X7 @ X6 @ X5 ) )
= X6 )
& ( $true
= ( in @ ( sK85 @ X7 @ X6 @ X5 ) @ X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f784,plain,
( ( ( cartprodmempair1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= X1 )
| ( $true
!= ( in @ X4 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ X2 ) ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( $true
!= ( in @ X6 @ ( cartprod @ X7 @ X5 ) ) )
| ? [X8: $i] :
( ? [X9: $i] :
( ( ( kpair @ X8 @ X9 )
= X6 )
& ( $true
= ( in @ X9 @ X5 ) ) )
& ( $true
= ( in @ X8 @ X7 ) ) ) )
| ( cartprodmempair1 != $true ) ) ),
inference(rectify,[status(thm)],[f783]) ).
thf(f783,plain,
( ( ( cartprodmempair1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true )
& ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= X1 )
| ( $true
!= ( in @ X4 @ X0 ) ) )
| ( $true
!= ( in @ X3 @ X2 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
!= $true )
| ? [X3: $i] :
( ? [X4: $i] :
( ( ( kpair @ X3 @ X4 )
= X1 )
& ( $true
= ( in @ X4 @ X0 ) ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) )
| ( cartprodmempair1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f615]) ).
thf(f615,plain,
( ( cartprodmempair1 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
!= $true )
| ? [X3: $i] :
( ? [X4: $i] :
( ( ( kpair @ X3 @ X4 )
= X1 )
& ( $true
= ( in @ X4 @ X0 ) ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f205]) ).
thf(f205,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
= $true )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( ( kpair @ X3 @ X4 )
= X1 )
& ( $true
= ( in @ X4 @ X0 ) ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) )
<=> ( cartprodmempair1 = $true ) ),
inference(fool_elimination,[status(thm)],[f204]) ).
thf(f204,plain,
( cartprodmempair1
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( cartprod @ X2 @ X0 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X2 )
& ? [X4: $i] :
( ( in @ X4 @ X0 )
& ( ( kpair @ X3 @ X4 )
= X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f152]) ).
thf(f152,axiom,
( cartprodmempair1
= ( ! [X4: $i,X10: $i,X3: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( ( kpair @ X1 @ X2 )
= X10 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.qvI7ApaoRY/DTF2THF_26806.p',cartprodmempair1) ).
thf(f2936,plain,
( spl415_170
| ~ spl415_171 ),
inference(avatar_split_clause,[status(thm)],[f1437,f2933,f2930]) ).
thf(f1437,plain,
! [X0: $i,X1: $i] :
( ( kpairp != $true )
| ( $true
= ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f782]) ).
thf(f782,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( kpair @ X0 @ X1 ) ) )
| ( kpairp != $true ) )
& ( ( kpairp = $true )
| ( $true
!= ( iskpair @ ( kpair @ sK79 @ sK80 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f780,f781]) ).
thf(f781,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( iskpair @ ( kpair @ X2 @ X3 ) ) )
=> ( $true
!= ( iskpair @ ( kpair @ sK79 @ sK80 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f780,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( kpair @ X0 @ X1 ) ) )
| ( kpairp != $true ) )
& ( ( kpairp = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( iskpair @ ( kpair @ X2 @ X3 ) ) ) ) ),
inference(rectify,[status(thm)],[f779]) ).
thf(f779,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( kpair @ X0 @ X1 ) ) )
| ( kpairp != $true ) )
& ( ( kpairp = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( iskpair @ ( kpair @ X0 @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f203]) ).
thf(f203,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( iskpair @ ( kpair @ X0 @ X1 ) ) )
<=> ( kpairp = $true ) ),
inference(fool_elimination,[status(thm)],[f202]) ).
thf(f202,plain,
! [X0: $i,X1: $i] :
( ( iskpair @ ( kpair @ X0 @ X1 ) )
= kpairp ),
inference(rectify,[status(thm)],[f141]) ).
thf(f141,axiom,
! [X1: $i,X2: $i] :
( ( iskpair @ ( kpair @ X1 @ X2 ) )
= kpairp ),
file('/export/starexec/sandbox/tmp/tmp.qvI7ApaoRY/DTF2THF_26806.p',kpairp) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU632^1 : TPTP v9.2.1. Released v3.7.0.
% 0.13/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n018.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:29:16 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.34/0.48 ---- Original DTF file ---
% 0.34/0.48 thf(spec,logic,$$dhol).
% 0.34/0.48 %------------------------------------------------------------------------------
% 0.34/0.48 % File : SEU632^1 : TPTP v9.2.1. Released v3.7.0.
% 0.34/0.48 % Domain : Set Theory
% 0.34/0.48 % Problem : Ordered Pairs - Cartesian Products
% 0.34/0.48 % Version : Especial.
% 0.34/0.48 % English : (! A:i.! B:i.! u:i.in u (cartprod A B) -> iskpair u)
% 0.34/0.48
% 0.34/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.34/0.48 % Source : [Bro08]
% 0.34/0.48 % Names : ZFC134g [Bro08]
% 0.34/0.48
% 0.34/0.48 % Status : Theorem
% 0.34/0.48 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.43 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, 0.80 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v5.0.0, 1.00 v3.7.0
% 0.34/0.48 % Syntax : Number of formulae : 324 ( 152 unt; 171 typ; 152 def)
% 0.34/0.48 % Number of atoms : 808 ( 213 equ; 0 cnn)
% 0.34/0.48 % Maximal formula atoms : 150 ( 5 avg)
% 0.34/0.48 % Number of connectives : 1392 ( 47 ~; 7 |; 32 &; 936 @)
% 0.34/0.48 % ( 14 <=>; 356 =>; 0 <=; 0 <~>)
% 0.34/0.48 % Maximal formula depth : 156 ( 2 avg)
% 0.34/0.48 % Number of types : 2 ( 0 usr)
% 0.34/0.48 % Number of type conns : 69 ( 69 >; 0 *; 0 +; 0 <<)
% 0.34/0.48 % Number of symbols : 174 ( 171 usr; 152 con; 0-2 aty)
% 0.34/0.48 % Number of variables : 443 ( 33 ^; 377 !; 33 ?; 443 :)
% 0.34/0.48 % SPC : TH0_THM_EQU_NAR
% 0.34/0.48
% 0.34/0.48 % Comments : http://mathgate.info/detsetitem.php?id=189
% 0.34/0.48 %------------------------------------------------------------------------------
% 0.34/0.48 thf(in_type,type,
% 0.34/0.48 in: $i > $i > $o ).
% 0.34/0.48
% 0.34/0.48 thf(exu_type,type,
% 0.34/0.48 exu: ( $i > $o ) > $o ).
% 0.34/0.48
% 0.34/0.48 thf(exu,definition,
% 0.34/0.48 ( exu
% 0.34/0.48 = ( ^ [Xphi: $i > $o] :
% 0.34/0.48 ? [Xx: $i] :
% 0.34/0.48 ( ( Xphi @ Xx )
% 0.34/0.48 & ! [Xy: $i] :
% 0.34/0.48 ( ( Xphi @ Xy )
% 0.34/0.48 => ( Xx = Xy ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setextAx_type,type,
% 0.34/0.48 setextAx: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setextAx,definition,
% 0.34/0.48 ( setextAx
% 0.34/0.48 = ( ! [A: $i,B: $i] :
% 0.34/0.48 ( ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ A )
% 0.34/0.48 <=> ( in @ Xx @ B ) )
% 0.34/0.48 => ( A = B ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(emptyset_type,type,
% 0.34/0.48 emptyset: $i ).
% 0.34/0.48
% 0.34/0.48 thf(emptysetAx_type,type,
% 0.34/0.48 emptysetAx: $o ).
% 0.34/0.48
% 0.34/0.48 thf(emptysetAx,definition,
% 0.34/0.48 ( emptysetAx
% 0.34/0.48 = ( ! [Xx: $i] :
% 0.34/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoin_type,type,
% 0.34/0.48 setadjoin: $i > $i > $i ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoinAx_type,type,
% 0.34/0.48 setadjoinAx: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoinAx,definition,
% 0.34/0.48 ( setadjoinAx
% 0.34/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.34/0.48 <=> ( ( Xy = Xx )
% 0.34/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(powerset_type,type,
% 0.34/0.48 powerset: $i > $i ).
% 0.34/0.48
% 0.34/0.48 thf(powersetAx_type,type,
% 0.34/0.48 powersetAx: $o ).
% 0.34/0.48
% 0.34/0.48 thf(powersetAx,definition,
% 0.34/0.48 ( powersetAx
% 0.34/0.48 = ( ! [A: $i,B: $i] :
% 0.34/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.34/0.48 <=> ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ B )
% 0.34/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setunion_type,type,
% 0.34/0.48 setunion: $i > $i ).
% 0.34/0.48
% 0.34/0.48 thf(setunionAx_type,type,
% 0.34/0.48 setunionAx: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setunionAx,definition,
% 0.34/0.48 ( setunionAx
% 0.34/0.48 = ( ! [A: $i,Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.34/0.48 <=> ? [B: $i] :
% 0.34/0.48 ( ( in @ Xx @ B )
% 0.34/0.48 & ( in @ B @ A ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(omega_type,type,
% 0.34/0.48 omega: $i ).
% 0.34/0.48
% 0.34/0.48 thf(omega0Ax_type,type,
% 0.34/0.48 omega0Ax: $o ).
% 0.34/0.48
% 0.34/0.48 thf(omega0Ax,definition,
% 0.34/0.48 ( omega0Ax
% 0.34/0.48 = ( in @ emptyset @ omega ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(omegaSAx_type,type,
% 0.34/0.48 omegaSAx: $o ).
% 0.34/0.48
% 0.34/0.48 thf(omegaSAx,definition,
% 0.34/0.48 ( omegaSAx
% 0.34/0.48 = ( ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ omega )
% 0.34/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(omegaIndAx_type,type,
% 0.34/0.48 omegaIndAx: $o ).
% 0.34/0.48
% 0.34/0.48 thf(omegaIndAx,definition,
% 0.34/0.48 ( omegaIndAx
% 0.34/0.48 = ( ! [A: $i] :
% 0.34/0.48 ( ( ( in @ emptyset @ A )
% 0.34/0.48 & ! [Xx: $i] :
% 0.34/0.48 ( ( ( in @ Xx @ omega )
% 0.34/0.48 & ( in @ Xx @ A ) )
% 0.34/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.34/0.48 => ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ omega )
% 0.34/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(replAx_type,type,
% 0.34/0.48 replAx: $o ).
% 0.34/0.48
% 0.34/0.48 thf(replAx,definition,
% 0.34/0.48 ( replAx
% 0.34/0.48 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.34/0.48 ( ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ A )
% 0.34/0.48 => ( exu
% 0.34/0.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.34/0.48 => ? [B: $i] :
% 0.34/0.48 ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ B )
% 0.34/0.48 <=> ? [Xy: $i] :
% 0.34/0.48 ( ( in @ Xy @ A )
% 0.34/0.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(foundationAx_type,type,
% 0.34/0.48 foundationAx: $o ).
% 0.34/0.48
% 0.34/0.48 thf(foundationAx,definition,
% 0.34/0.48 ( foundationAx
% 0.34/0.48 = ( ! [A: $i] :
% 0.34/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.34/0.48 => ? [B: $i] :
% 0.34/0.48 ( ( in @ B @ A )
% 0.34/0.48 & ~ ? [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ B )
% 0.34/0.48 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(wellorderingAx_type,type,
% 0.34/0.48 wellorderingAx: $o ).
% 0.34/0.48
% 0.34/0.48 thf(wellorderingAx,definition,
% 0.34/0.48 ( wellorderingAx
% 0.34/0.48 = ( ! [A: $i] :
% 0.34/0.48 ? [B: $i] :
% 0.34/0.48 ( ! [C: $i] :
% 0.34/0.48 ( ( in @ C @ B )
% 0.34/0.48 => ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ C )
% 0.34/0.48 => ( in @ Xx @ A ) ) )
% 0.34/0.48 & ! [Xx: $i,Xy: $i] :
% 0.34/0.48 ( ( ( in @ Xx @ A )
% 0.34/0.48 & ( in @ Xy @ A ) )
% 0.34/0.48 => ( ! [C: $i] :
% 0.34/0.48 ( ( in @ C @ B )
% 0.34/0.48 => ( ( in @ Xx @ C )
% 0.34/0.48 <=> ( in @ Xy @ C ) ) )
% 0.34/0.48 => ( Xx = Xy ) ) )
% 0.34/0.48 & ! [C: $i,D: $i] :
% 0.34/0.48 ( ( ( in @ C @ B )
% 0.34/0.48 & ( in @ D @ B ) )
% 0.34/0.48 => ( ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ C )
% 0.34/0.48 => ( in @ Xx @ D ) )
% 0.34/0.48 | ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ D )
% 0.34/0.48 => ( in @ Xx @ C ) ) ) )
% 0.34/0.48 & ! [C: $i] :
% 0.34/0.48 ( ( ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ C )
% 0.34/0.48 => ( in @ Xx @ A ) )
% 0.34/0.48 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.34/0.48 => ? [D: $i,Xx: $i] :
% 0.34/0.48 ( ( in @ D @ B )
% 0.34/0.48 & ( in @ Xx @ C )
% 0.34/0.48 & ~ ? [Xy: $i] :
% 0.34/0.48 ( ( in @ Xy @ D )
% 0.34/0.48 & ( in @ Xy @ C ) )
% 0.34/0.48 & ! [E: $i] :
% 0.34/0.48 ( ( in @ E @ B )
% 0.34/0.48 => ( ! [Xy: $i] :
% 0.34/0.48 ( ( in @ Xy @ E )
% 0.34/0.48 => ( in @ Xy @ D ) )
% 0.34/0.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(descr_type,type,
% 0.34/0.48 descr: ( $i > $o ) > $i ).
% 0.34/0.48
% 0.34/0.48 thf(descrp_type,type,
% 0.34/0.48 descrp: $o ).
% 0.34/0.48
% 0.34/0.48 thf(descrp,definition,
% 0.34/0.48 ( descrp
% 0.34/0.48 = ( ! [Xphi: $i > $o] :
% 0.34/0.48 ( ( exu
% 0.34/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.48 => ( Xphi
% 0.34/0.48 @ ( descr
% 0.34/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(dsetconstr_type,type,
% 0.34/0.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.34/0.48
% 0.34/0.48 thf(dsetconstrI_type,type,
% 0.34/0.48 dsetconstrI: $o ).
% 0.34/0.48
% 0.34/0.48 thf(dsetconstrI,definition,
% 0.34/0.48 ( dsetconstrI
% 0.34/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ A )
% 0.34/0.48 => ( ( Xphi @ Xx )
% 0.34/0.48 => ( in @ Xx
% 0.34/0.48 @ ( dsetconstr @ A
% 0.34/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(dsetconstrEL_type,type,
% 0.34/0.48 dsetconstrEL: $o ).
% 0.34/0.48
% 0.34/0.48 thf(dsetconstrEL,definition,
% 0.34/0.48 ( dsetconstrEL
% 0.34/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.48 ( ( in @ Xx
% 0.34/0.48 @ ( dsetconstr @ A
% 0.34/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.34/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(dsetconstrER_type,type,
% 0.34/0.48 dsetconstrER: $o ).
% 0.34/0.48
% 0.34/0.48 thf(dsetconstrER,definition,
% 0.34/0.48 ( dsetconstrER
% 0.34/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.48 ( ( in @ Xx
% 0.34/0.48 @ ( dsetconstr @ A
% 0.34/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.34/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(exuE1_type,type,
% 0.34/0.48 exuE1: $o ).
% 0.34/0.48
% 0.34/0.48 thf(exuE1,definition,
% 0.34/0.48 ( exuE1
% 0.34/0.48 = ( ! [Xphi: $i > $o] :
% 0.34/0.48 ( ( exu
% 0.34/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.48 => ? [Xx: $i] :
% 0.34/0.48 ( ( Xphi @ Xx )
% 0.34/0.48 & ! [Xy: $i] :
% 0.34/0.48 ( ( Xphi @ Xy )
% 0.34/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(prop2set_type,type,
% 0.34/0.48 prop2set: $o > $i ).
% 0.34/0.48
% 0.34/0.48 thf(prop2setE_type,type,
% 0.34/0.48 prop2setE: $o ).
% 0.34/0.48
% 0.34/0.48 thf(prop2setE,definition,
% 0.34/0.48 ( prop2setE
% 0.34/0.48 = ( ! [Xphi: $o,Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.34/0.48 => Xphi ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(emptysetE_type,type,
% 0.34/0.48 emptysetE: $o ).
% 0.34/0.48
% 0.34/0.48 thf(emptysetE,definition,
% 0.34/0.48 ( emptysetE
% 0.34/0.48 = ( ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ emptyset )
% 0.34/0.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(emptysetimpfalse_type,type,
% 0.34/0.48 emptysetimpfalse: $o ).
% 0.34/0.48
% 0.34/0.48 thf(emptysetimpfalse,definition,
% 0.34/0.48 ( emptysetimpfalse
% 0.34/0.48 = ( ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ emptyset )
% 0.34/0.48 => $false ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(notinemptyset_type,type,
% 0.34/0.48 notinemptyset: $o ).
% 0.34/0.48
% 0.34/0.48 thf(notinemptyset,definition,
% 0.34/0.48 ( notinemptyset
% 0.34/0.48 = ( ! [Xx: $i] :
% 0.34/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(exuE3e_type,type,
% 0.34/0.48 exuE3e: $o ).
% 0.34/0.48
% 0.34/0.48 thf(exuE3e,definition,
% 0.34/0.48 ( exuE3e
% 0.34/0.48 = ( ! [Xphi: $i > $o] :
% 0.34/0.48 ( ( exu
% 0.34/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setext_type,type,
% 0.34/0.48 setext: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setext,definition,
% 0.34/0.48 ( setext
% 0.34/0.48 = ( ! [A: $i,B: $i] :
% 0.34/0.48 ( ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ A )
% 0.34/0.48 => ( in @ Xx @ B ) )
% 0.34/0.48 => ( ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ B )
% 0.34/0.48 => ( in @ Xx @ A ) )
% 0.34/0.48 => ( A = B ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(emptyI_type,type,
% 0.34/0.48 emptyI: $o ).
% 0.34/0.48
% 0.34/0.48 thf(emptyI,definition,
% 0.34/0.48 ( emptyI
% 0.34/0.48 = ( ! [A: $i] :
% 0.34/0.48 ( ! [Xx: $i] :
% 0.34/0.48 ~ ( in @ Xx @ A )
% 0.34/0.48 => ( A = emptyset ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(noeltsimpempty_type,type,
% 0.34/0.48 noeltsimpempty: $o ).
% 0.34/0.48
% 0.34/0.48 thf(noeltsimpempty,definition,
% 0.34/0.48 ( noeltsimpempty
% 0.34/0.48 = ( ! [A: $i] :
% 0.34/0.48 ( ! [Xx: $i] :
% 0.34/0.48 ~ ( in @ Xx @ A )
% 0.34/0.48 => ( A = emptyset ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setbeta_type,type,
% 0.34/0.48 setbeta: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setbeta,definition,
% 0.34/0.48 ( setbeta
% 0.34/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ A )
% 0.34/0.48 => ( ( in @ Xx
% 0.34/0.48 @ ( dsetconstr @ A
% 0.34/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.34/0.48 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(nonempty_type,type,
% 0.34/0.48 nonempty: $i > $o ).
% 0.34/0.48
% 0.34/0.48 thf(nonempty,definition,
% 0.34/0.48 ( nonempty
% 0.34/0.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(nonemptyE1_type,type,
% 0.34/0.48 nonemptyE1: $o ).
% 0.34/0.48
% 0.34/0.48 thf(nonemptyE1,definition,
% 0.34/0.48 ( nonemptyE1
% 0.34/0.48 = ( ! [A: $i] :
% 0.34/0.48 ( ( nonempty @ A )
% 0.34/0.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(nonemptyI_type,type,
% 0.34/0.48 nonemptyI: $o ).
% 0.34/0.48
% 0.34/0.48 thf(nonemptyI,definition,
% 0.34/0.48 ( nonemptyI
% 0.34/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ A )
% 0.34/0.48 => ( ( Xphi @ Xx )
% 0.34/0.48 => ( nonempty
% 0.34/0.48 @ ( dsetconstr @ A
% 0.34/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(nonemptyI1_type,type,
% 0.34/0.48 nonemptyI1: $o ).
% 0.34/0.48
% 0.34/0.48 thf(nonemptyI1,definition,
% 0.34/0.48 ( nonemptyI1
% 0.34/0.48 = ( ! [A: $i] :
% 0.34/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.34/0.48 => ( nonempty @ A ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoinIL_type,type,
% 0.34/0.48 setadjoinIL: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoinIL,definition,
% 0.34/0.48 ( setadjoinIL
% 0.34/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(emptyinunitempty_type,type,
% 0.34/0.48 emptyinunitempty: $o ).
% 0.34/0.48
% 0.34/0.48 thf(emptyinunitempty,definition,
% 0.34/0.48 ( emptyinunitempty
% 0.34/0.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoinIR_type,type,
% 0.34/0.48 setadjoinIR: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoinIR,definition,
% 0.34/0.48 ( setadjoinIR
% 0.34/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.48 ( ( in @ Xy @ A )
% 0.34/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoinE_type,type,
% 0.34/0.48 setadjoinE: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoinE,definition,
% 0.34/0.48 ( setadjoinE
% 0.34/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.34/0.48 => ! [Xphi: $o] :
% 0.34/0.48 ( ( ( Xy = Xx )
% 0.34/0.48 => Xphi )
% 0.34/0.48 => ( ( ( in @ Xy @ A )
% 0.34/0.48 => Xphi )
% 0.34/0.48 => Xphi ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoinOr_type,type,
% 0.34/0.48 setadjoinOr: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setadjoinOr,definition,
% 0.34/0.48 ( setadjoinOr
% 0.34/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.34/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.34/0.48 => ( ( Xy = Xx )
% 0.34/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setoftrueEq_type,type,
% 0.34/0.48 setoftrueEq: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setoftrueEq,definition,
% 0.34/0.48 ( setoftrueEq
% 0.34/0.48 = ( ! [A: $i] :
% 0.34/0.48 ( ( dsetconstr @ A
% 0.34/0.48 @ ^ [Xx: $i] : $true )
% 0.34/0.48 = A ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(powersetI_type,type,
% 0.34/0.48 powersetI: $o ).
% 0.34/0.48
% 0.34/0.48 thf(powersetI,definition,
% 0.34/0.48 ( powersetI
% 0.34/0.48 = ( ! [A: $i,B: $i] :
% 0.34/0.48 ( ! [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ B )
% 0.34/0.48 => ( in @ Xx @ A ) )
% 0.34/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(emptyinPowerset_type,type,
% 0.34/0.48 emptyinPowerset: $o ).
% 0.34/0.48
% 0.34/0.48 thf(emptyinPowerset,definition,
% 0.34/0.48 ( emptyinPowerset
% 0.34/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(emptyInPowerset_type,type,
% 0.34/0.48 emptyInPowerset: $o ).
% 0.34/0.48
% 0.34/0.48 thf(emptyInPowerset,definition,
% 0.34/0.48 ( emptyInPowerset
% 0.34/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(powersetE_type,type,
% 0.34/0.48 powersetE: $o ).
% 0.34/0.48
% 0.34/0.48 thf(powersetE,definition,
% 0.34/0.48 ( powersetE
% 0.34/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.34/0.48 => ( ( in @ Xx @ B )
% 0.34/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setunionI_type,type,
% 0.34/0.48 setunionI: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setunionI,definition,
% 0.34/0.48 ( setunionI
% 0.34/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.34/0.48 ( ( in @ Xx @ B )
% 0.34/0.48 => ( ( in @ B @ A )
% 0.34/0.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(setunionE_type,type,
% 0.34/0.48 setunionE: $o ).
% 0.34/0.48
% 0.34/0.48 thf(setunionE,definition,
% 0.34/0.48 ( setunionE
% 0.34/0.48 = ( ! [A: $i,Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.34/0.48 => ! [Xphi: $o] :
% 0.34/0.48 ( ! [B: $i] :
% 0.34/0.48 ( ( in @ Xx @ B )
% 0.34/0.48 => ( ( in @ B @ A )
% 0.34/0.48 => Xphi ) )
% 0.34/0.48 => Xphi ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(subPowSU_type,type,
% 0.34/0.48 subPowSU: $o ).
% 0.34/0.48
% 0.34/0.48 thf(subPowSU,definition,
% 0.34/0.48 ( subPowSU
% 0.34/0.48 = ( ! [A: $i,Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ A )
% 0.34/0.48 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(exuE2_type,type,
% 0.34/0.48 exuE2: $o ).
% 0.34/0.48
% 0.34/0.48 thf(exuE2,definition,
% 0.34/0.48 ( exuE2
% 0.34/0.48 = ( ! [Xphi: $i > $o] :
% 0.34/0.48 ( ( exu
% 0.34/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.48 => ? [Xx: $i] :
% 0.34/0.48 ! [Xy: $i] :
% 0.34/0.48 ( ( Xphi @ Xy )
% 0.34/0.48 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(nonemptyImpWitness_type,type,
% 0.34/0.48 nonemptyImpWitness: $o ).
% 0.34/0.48
% 0.34/0.48 thf(nonemptyImpWitness,definition,
% 0.34/0.48 ( nonemptyImpWitness
% 0.34/0.48 = ( ! [A: $i] :
% 0.34/0.48 ( ( nonempty @ A )
% 0.34/0.48 => ? [Xx: $i] :
% 0.34/0.48 ( ( in @ Xx @ A )
% 0.34/0.48 & $true ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(uniqinunit_type,type,
% 0.34/0.48 uniqinunit: $o ).
% 0.34/0.48
% 0.34/0.48 thf(uniqinunit,definition,
% 0.34/0.48 ( uniqinunit
% 0.34/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.34/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.34/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(notinsingleton_type,type,
% 0.34/0.48 notinsingleton: $o ).
% 0.34/0.48
% 0.34/0.48 thf(notinsingleton,definition,
% 0.34/0.48 ( notinsingleton
% 0.34/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.34/0.48 ( ( Xx != Xy )
% 0.34/0.48 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(eqinunit_type,type,
% 0.34/0.48 eqinunit: $o ).
% 0.34/0.48
% 0.34/0.48 thf(eqinunit,definition,
% 0.34/0.48 ( eqinunit
% 0.34/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.34/0.48 ( ( Xx = Xy )
% 0.34/0.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(singletonsswitch_type,type,
% 0.34/0.48 singletonsswitch: $o ).
% 0.34/0.48
% 0.34/0.48 thf(singletonsswitch,definition,
% 0.34/0.48 ( singletonsswitch
% 0.34/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.34/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.34/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.34/0.48
% 0.34/0.48 thf(upairsetE_type,type,
% 0.34/0.48 upairsetE: $o ).
% 0.34/0.48
% 0.34/0.48 thf(upairsetE,definition,
% 0.34/0.48 ( upairsetE
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.34/0.49 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.34/0.49 => ( ( Xz = Xx )
% 0.34/0.49 | ( Xz = Xy ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(upairsetIL_type,type,
% 0.34/0.49 upairsetIL: $o ).
% 0.34/0.49
% 0.34/0.49 thf(upairsetIL,definition,
% 0.34/0.49 ( upairsetIL
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(upairsetIR_type,type,
% 0.34/0.49 upairsetIR: $o ).
% 0.34/0.49
% 0.34/0.49 thf(upairsetIR,definition,
% 0.34/0.49 ( upairsetIR
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(emptyE1_type,type,
% 0.34/0.49 emptyE1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(emptyE1,definition,
% 0.34/0.49 ( emptyE1
% 0.34/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.49 ( ? [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 & ( Xphi @ Xx ) )
% 0.34/0.49 => ( ( ( dsetconstr @ A
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.49 = emptyset )
% 0.34/0.49 => $false ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(vacuousDall_type,type,
% 0.34/0.49 vacuousDall: $o ).
% 0.34/0.49
% 0.34/0.49 thf(vacuousDall,definition,
% 0.34/0.49 ( vacuousDall
% 0.34/0.49 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ emptyset )
% 0.34/0.49 => ( Xphi @ Xx ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(quantDeMorgan1_type,type,
% 0.34/0.49 quantDeMorgan1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(quantDeMorgan1,definition,
% 0.34/0.49 ( quantDeMorgan1
% 0.34/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.49 ( ~ ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( Xphi @ Xx ) )
% 0.34/0.49 => ? [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(quantDeMorgan2_type,type,
% 0.34/0.49 quantDeMorgan2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(quantDeMorgan2,definition,
% 0.34/0.49 ( quantDeMorgan2
% 0.34/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.49 ( ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ~ ( Xphi @ Xx ) )
% 0.34/0.49 => ~ ? [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(quantDeMorgan3_type,type,
% 0.34/0.49 quantDeMorgan3: $o ).
% 0.34/0.49
% 0.34/0.49 thf(quantDeMorgan3,definition,
% 0.34/0.49 ( quantDeMorgan3
% 0.34/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.49 ( ~ ? [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 & ( Xphi @ Xx ) )
% 0.34/0.49 => ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(quantDeMorgan4_type,type,
% 0.34/0.49 quantDeMorgan4: $o ).
% 0.34/0.49
% 0.34/0.49 thf(quantDeMorgan4,definition,
% 0.34/0.49 ( quantDeMorgan4
% 0.34/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.49 ( ? [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 & ~ ( Xphi @ Xx ) )
% 0.34/0.49 => ~ ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(prop2setI_type,type,
% 0.34/0.49 prop2setI: $o ).
% 0.34/0.49
% 0.34/0.49 thf(prop2setI,definition,
% 0.34/0.49 ( prop2setI
% 0.34/0.49 = ( ! [Xphi: $o] :
% 0.34/0.49 ( Xphi
% 0.34/0.49 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(set2prop_type,type,
% 0.34/0.49 set2prop: $i > $o ).
% 0.34/0.49
% 0.34/0.49 thf(prop2set2propI_type,type,
% 0.34/0.49 prop2set2propI: $o ).
% 0.34/0.49
% 0.34/0.49 thf(prop2set2propI,definition,
% 0.34/0.49 ( prop2set2propI
% 0.34/0.49 = ( ! [Xphi: $o] :
% 0.34/0.49 ( Xphi
% 0.34/0.49 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(notdexE_type,type,
% 0.34/0.49 notdexE: $o ).
% 0.34/0.49
% 0.34/0.49 thf(notdexE,definition,
% 0.34/0.49 ( notdexE
% 0.34/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.49 ( ~ ? [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 & ( Xphi @ Xx ) )
% 0.34/0.49 => ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(notdallE_type,type,
% 0.34/0.49 notdallE: $o ).
% 0.34/0.49
% 0.34/0.49 thf(notdallE,definition,
% 0.34/0.49 ( notdallE
% 0.34/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.49 ( ~ ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( Xphi @ Xx ) )
% 0.34/0.49 => ? [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(exuI1_type,type,
% 0.34/0.49 exuI1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(exuI1,definition,
% 0.34/0.49 ( exuI1
% 0.34/0.49 = ( ! [Xphi: $i > $o] :
% 0.34/0.49 ( ? [Xx: $i] :
% 0.34/0.49 ( ( Xphi @ Xx )
% 0.34/0.49 & ! [Xy: $i] :
% 0.34/0.49 ( ( Xphi @ Xy )
% 0.34/0.49 => ( Xx = Xy ) ) )
% 0.34/0.49 => ( exu
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(exuI3_type,type,
% 0.34/0.49 exuI3: $o ).
% 0.34/0.49
% 0.34/0.49 thf(exuI3,definition,
% 0.34/0.49 ( exuI3
% 0.34/0.49 = ( ! [Xphi: $i > $o] :
% 0.34/0.49 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.34/0.49 => ( ! [Xx: $i,Xy: $i] :
% 0.34/0.49 ( ( Xphi @ Xx )
% 0.34/0.49 => ( ( Xphi @ Xy )
% 0.34/0.49 => ( Xx = Xy ) ) )
% 0.34/0.49 => ( exu
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(exuI2_type,type,
% 0.34/0.49 exuI2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(exuI2,definition,
% 0.34/0.49 ( exuI2
% 0.34/0.49 = ( ! [Xphi: $i > $o] :
% 0.34/0.49 ( ? [Xx: $i] :
% 0.34/0.49 ! [Xy: $i] :
% 0.34/0.49 ( ( Xphi @ Xy )
% 0.34/0.49 <=> ( Xy = Xx ) )
% 0.34/0.49 => ( exu
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(inCongP_type,type,
% 0.34/0.49 inCongP: $o ).
% 0.34/0.49
% 0.34/0.49 thf(inCongP,definition,
% 0.34/0.49 ( inCongP
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( A = B )
% 0.34/0.49 => ! [Xx: $i,Xy: $i] :
% 0.34/0.49 ( ( Xx = Xy )
% 0.34/0.49 => ( ( in @ Xx @ A )
% 0.34/0.49 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(in__Cong_type,type,
% 0.34/0.49 in__Cong: $o ).
% 0.34/0.49
% 0.34/0.49 thf(in__Cong,definition,
% 0.34/0.49 ( in__Cong
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( A = B )
% 0.34/0.49 => ! [Xx: $i,Xy: $i] :
% 0.34/0.49 ( ( Xx = Xy )
% 0.34/0.49 => ( ( in @ Xx @ A )
% 0.34/0.49 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(exuE3u_type,type,
% 0.34/0.49 exuE3u: $o ).
% 0.34/0.49
% 0.34/0.49 thf(exuE3u,definition,
% 0.34/0.49 ( exuE3u
% 0.34/0.49 = ( ! [Xphi: $i > $o] :
% 0.34/0.49 ( ( exu
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.49 => ! [Xx: $i,Xy: $i] :
% 0.34/0.49 ( ( Xphi @ Xx )
% 0.34/0.49 => ( ( Xphi @ Xy )
% 0.34/0.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(exu__Cong_type,type,
% 0.34/0.49 exu__Cong: $o ).
% 0.34/0.49
% 0.34/0.49 thf(exu__Cong,definition,
% 0.34/0.49 ( exu__Cong
% 0.34/0.49 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.34/0.49 ( ! [Xx: $i,Xy: $i] :
% 0.34/0.49 ( ( Xx = Xy )
% 0.34/0.49 => ( ( Xphi @ Xx )
% 0.34/0.49 <=> ( Xpsi @ Xy ) ) )
% 0.34/0.49 => ( ( exu
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.49 <=> ( exu
% 0.34/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(emptyset__Cong_type,type,
% 0.34/0.49 emptyset__Cong: $o ).
% 0.34/0.49
% 0.34/0.49 thf(emptyset__Cong,definition,
% 0.34/0.49 ( emptyset__Cong
% 0.34/0.49 = ( emptyset = emptyset ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setadjoin__Cong_type,type,
% 0.34/0.49 setadjoin__Cong: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setadjoin__Cong,definition,
% 0.34/0.49 ( setadjoin__Cong
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.34/0.49 ( ( Xx = Xy )
% 0.34/0.49 => ! [Xz: $i,Xu: $i] :
% 0.34/0.49 ( ( Xz = Xu )
% 0.34/0.49 => ( ( setadjoin @ Xx @ Xz )
% 0.34/0.49 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(powerset__Cong_type,type,
% 0.34/0.49 powerset__Cong: $o ).
% 0.34/0.49
% 0.34/0.49 thf(powerset__Cong,definition,
% 0.34/0.49 ( powerset__Cong
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( A = B )
% 0.34/0.49 => ( ( powerset @ A )
% 0.34/0.49 = ( powerset @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setunion__Cong_type,type,
% 0.34/0.49 setunion__Cong: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setunion__Cong,definition,
% 0.34/0.49 ( setunion__Cong
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( A = B )
% 0.34/0.49 => ( ( setunion @ A )
% 0.34/0.49 = ( setunion @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(omega__Cong_type,type,
% 0.34/0.49 omega__Cong: $o ).
% 0.34/0.49
% 0.34/0.49 thf(omega__Cong,definition,
% 0.34/0.49 ( omega__Cong
% 0.34/0.49 = ( omega = omega ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(exuEu_type,type,
% 0.34/0.49 exuEu: $o ).
% 0.34/0.49
% 0.34/0.49 thf(exuEu,definition,
% 0.34/0.49 ( exuEu
% 0.34/0.49 = ( ! [Xphi: $i > $o] :
% 0.34/0.49 ( ( exu
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.49 => ! [Xx: $i,Xy: $i] :
% 0.34/0.49 ( ( Xphi @ Xx )
% 0.34/0.49 => ( ( Xphi @ Xy )
% 0.34/0.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(descr__Cong_type,type,
% 0.34/0.49 descr__Cong: $o ).
% 0.34/0.49
% 0.34/0.49 thf(descr__Cong,definition,
% 0.34/0.49 ( descr__Cong
% 0.34/0.49 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.34/0.49 ( ! [Xx: $i,Xy: $i] :
% 0.34/0.49 ( ( Xx = Xy )
% 0.34/0.49 => ( ( Xphi @ Xx )
% 0.34/0.49 <=> ( Xpsi @ Xy ) ) )
% 0.34/0.49 => ( ( exu
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.49 => ( ( exu
% 0.34/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.34/0.49 => ( ( descr
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.49 = ( descr
% 0.34/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(dsetconstr__Cong_type,type,
% 0.34/0.49 dsetconstr__Cong: $o ).
% 0.34/0.49
% 0.34/0.49 thf(dsetconstr__Cong,definition,
% 0.34/0.49 ( dsetconstr__Cong
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( A = B )
% 0.34/0.49 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.34/0.49 ( ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ! [Xy: $i] :
% 0.34/0.49 ( ( in @ Xy @ B )
% 0.34/0.49 => ( ( Xx = Xy )
% 0.34/0.49 => ( ( Xphi @ Xx )
% 0.34/0.49 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.34/0.49 => ( ( dsetconstr @ A
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.49 = ( dsetconstr @ B
% 0.34/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(subset_type,type,
% 0.34/0.49 subset: $i > $i > $o ).
% 0.34/0.49
% 0.34/0.49 thf(disjoint_type,type,
% 0.34/0.49 disjoint: $i > $i > $o ).
% 0.34/0.49
% 0.34/0.49 thf(setsmeet_type,type,
% 0.34/0.49 setsmeet: $i > $i > $o ).
% 0.34/0.49
% 0.34/0.49 thf(subsetI1_type,type,
% 0.34/0.49 subsetI1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(subsetI1,definition,
% 0.34/0.49 ( subsetI1
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( in @ Xx @ B ) )
% 0.34/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(eqimpsubset2_type,type,
% 0.34/0.49 eqimpsubset2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(eqimpsubset2,definition,
% 0.34/0.49 ( eqimpsubset2
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( A = B )
% 0.34/0.49 => ( subset @ B @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(eqimpsubset1_type,type,
% 0.34/0.49 eqimpsubset1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(eqimpsubset1,definition,
% 0.34/0.49 ( eqimpsubset1
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( A = B )
% 0.34/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(subsetI2_type,type,
% 0.34/0.49 subsetI2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(subsetI2,definition,
% 0.34/0.49 ( subsetI2
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ! [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( in @ Xx @ B ) )
% 0.34/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(emptysetsubset_type,type,
% 0.34/0.49 emptysetsubset: $o ).
% 0.34/0.49
% 0.34/0.49 thf(emptysetsubset,definition,
% 0.34/0.49 ( emptysetsubset
% 0.34/0.49 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(subsetE_type,type,
% 0.34/0.49 subsetE: $o ).
% 0.34/0.49
% 0.34/0.49 thf(subsetE,definition,
% 0.34/0.49 ( subsetE
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( subset @ A @ B )
% 0.34/0.49 => ( ( in @ Xx @ A )
% 0.34/0.49 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(subsetE2_type,type,
% 0.34/0.49 subsetE2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(subsetE2,definition,
% 0.34/0.49 ( subsetE2
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( subset @ A @ B )
% 0.34/0.49 => ( ~ ( in @ Xx @ B )
% 0.34/0.49 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(notsubsetI_type,type,
% 0.34/0.49 notsubsetI: $o ).
% 0.34/0.49
% 0.34/0.49 thf(notsubsetI,definition,
% 0.34/0.49 ( notsubsetI
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( ~ ( in @ Xx @ B )
% 0.34/0.49 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(notequalI1_type,type,
% 0.34/0.49 notequalI1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(notequalI1,definition,
% 0.34/0.49 ( notequalI1
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ~ ( subset @ A @ B )
% 0.34/0.49 => ( A != B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(notequalI2_type,type,
% 0.34/0.49 notequalI2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(notequalI2,definition,
% 0.34/0.49 ( notequalI2
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( ~ ( in @ Xx @ B )
% 0.34/0.49 => ( A != B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(subsetRefl_type,type,
% 0.34/0.49 subsetRefl: $o ).
% 0.34/0.49
% 0.34/0.49 thf(subsetRefl,definition,
% 0.34/0.49 ( subsetRefl
% 0.34/0.49 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(subsetTrans_type,type,
% 0.34/0.49 subsetTrans: $o ).
% 0.34/0.49
% 0.34/0.49 thf(subsetTrans,definition,
% 0.34/0.49 ( subsetTrans
% 0.34/0.49 = ( ! [A: $i,B: $i,C: $i] :
% 0.34/0.49 ( ( subset @ A @ B )
% 0.34/0.49 => ( ( subset @ B @ C )
% 0.34/0.49 => ( subset @ A @ C ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setadjoinSub_type,type,
% 0.34/0.49 setadjoinSub: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setadjoinSub,definition,
% 0.34/0.49 ( setadjoinSub
% 0.34/0.49 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setadjoinSub2_type,type,
% 0.34/0.49 setadjoinSub2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setadjoinSub2,definition,
% 0.34/0.49 ( setadjoinSub2
% 0.34/0.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.34/0.49 ( ( subset @ A @ B )
% 0.34/0.49 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(subset2powerset_type,type,
% 0.34/0.49 subset2powerset: $o ).
% 0.34/0.49
% 0.34/0.49 thf(subset2powerset,definition,
% 0.34/0.49 ( subset2powerset
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( subset @ A @ B )
% 0.34/0.49 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setextsub_type,type,
% 0.34/0.49 setextsub: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setextsub,definition,
% 0.34/0.49 ( setextsub
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( subset @ A @ B )
% 0.34/0.49 => ( ( subset @ B @ A )
% 0.34/0.49 => ( A = B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(subsetemptysetimpeq_type,type,
% 0.34/0.49 subsetemptysetimpeq: $o ).
% 0.34/0.49
% 0.34/0.49 thf(subsetemptysetimpeq,definition,
% 0.34/0.49 ( subsetemptysetimpeq
% 0.34/0.49 = ( ! [A: $i] :
% 0.34/0.49 ( ( subset @ A @ emptyset )
% 0.34/0.49 => ( A = emptyset ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(powersetI1_type,type,
% 0.34/0.49 powersetI1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(powersetI1,definition,
% 0.34/0.49 ( powersetI1
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( subset @ B @ A )
% 0.34/0.49 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(powersetE1_type,type,
% 0.34/0.49 powersetE1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(powersetE1,definition,
% 0.34/0.49 ( powersetE1
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( in @ B @ ( powerset @ A ) )
% 0.34/0.49 => ( subset @ B @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(inPowerset_type,type,
% 0.34/0.49 inPowerset: $o ).
% 0.34/0.49
% 0.34/0.49 thf(inPowerset,definition,
% 0.34/0.49 ( inPowerset
% 0.34/0.49 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(powersetsubset_type,type,
% 0.34/0.49 powersetsubset: $o ).
% 0.34/0.49
% 0.34/0.49 thf(powersetsubset,definition,
% 0.34/0.49 ( powersetsubset
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( subset @ A @ B )
% 0.34/0.49 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sepInPowerset_type,type,
% 0.34/0.49 sepInPowerset: $o ).
% 0.34/0.49
% 0.34/0.49 thf(sepInPowerset,definition,
% 0.34/0.49 ( sepInPowerset
% 0.34/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.49 ( in
% 0.34/0.49 @ ( dsetconstr @ A
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.49 @ ( powerset @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(sepSubset_type,type,
% 0.34/0.49 sepSubset: $o ).
% 0.34/0.49
% 0.34/0.49 thf(sepSubset,definition,
% 0.34/0.49 ( sepSubset
% 0.34/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.34/0.49 ( subset
% 0.34/0.49 @ ( dsetconstr @ A
% 0.34/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.34/0.49 @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binunion_type,type,
% 0.34/0.49 binunion: $i > $i > $i ).
% 0.34/0.49
% 0.34/0.49 thf(binunionIL_type,type,
% 0.34/0.49 binunionIL: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binunionIL,definition,
% 0.34/0.49 ( binunionIL
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(upairset2IR_type,type,
% 0.34/0.49 upairset2IR: $o ).
% 0.34/0.49
% 0.34/0.49 thf(upairset2IR,definition,
% 0.34/0.49 ( upairset2IR
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binunionIR_type,type,
% 0.34/0.49 binunionIR: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binunionIR,definition,
% 0.34/0.49 ( binunionIR
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ B )
% 0.34/0.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binunionEcases_type,type,
% 0.34/0.49 binunionEcases: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binunionEcases,definition,
% 0.34/0.49 ( binunionEcases
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.34/0.49 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.34/0.49 => ( ( ( in @ Xx @ A )
% 0.34/0.49 => Xphi )
% 0.34/0.49 => ( ( ( in @ Xx @ B )
% 0.34/0.49 => Xphi )
% 0.34/0.49 => Xphi ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binunionE_type,type,
% 0.34/0.49 binunionE: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binunionE,definition,
% 0.34/0.49 ( binunionE
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.34/0.49 => ( ( in @ Xx @ A )
% 0.34/0.49 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binunionLsub_type,type,
% 0.34/0.49 binunionLsub: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binunionLsub,definition,
% 0.34/0.49 ( binunionLsub
% 0.34/0.49 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binunionRsub_type,type,
% 0.34/0.49 binunionRsub: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binunionRsub,definition,
% 0.34/0.49 ( binunionRsub
% 0.34/0.49 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binintersect_type,type,
% 0.34/0.49 binintersect: $i > $i > $i ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectI_type,type,
% 0.34/0.49 binintersectI: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectI,definition,
% 0.34/0.49 ( binintersectI
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( ( in @ Xx @ B )
% 0.34/0.49 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectSubset5_type,type,
% 0.34/0.49 binintersectSubset5: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectSubset5,definition,
% 0.34/0.49 ( binintersectSubset5
% 0.34/0.49 = ( ! [A: $i,B: $i,C: $i] :
% 0.34/0.49 ( ( subset @ C @ A )
% 0.34/0.49 => ( ( subset @ C @ B )
% 0.34/0.49 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectEL_type,type,
% 0.34/0.49 binintersectEL: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectEL,definition,
% 0.34/0.49 ( binintersectEL
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.34/0.49 => ( in @ Xx @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectLsub_type,type,
% 0.34/0.49 binintersectLsub: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectLsub,definition,
% 0.34/0.49 ( binintersectLsub
% 0.34/0.49 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectSubset2_type,type,
% 0.34/0.49 binintersectSubset2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectSubset2,definition,
% 0.34/0.49 ( binintersectSubset2
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( subset @ A @ B )
% 0.34/0.49 => ( ( binintersect @ A @ B )
% 0.34/0.49 = A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectSubset3_type,type,
% 0.34/0.49 binintersectSubset3: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectSubset3,definition,
% 0.34/0.49 ( binintersectSubset3
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( ( binintersect @ A @ B )
% 0.34/0.49 = B )
% 0.34/0.49 => ( subset @ B @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectER_type,type,
% 0.34/0.49 binintersectER: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectER,definition,
% 0.34/0.49 ( binintersectER
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.34/0.49 => ( in @ Xx @ B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(disjointsetsI1_type,type,
% 0.34/0.49 disjointsetsI1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(disjointsetsI1,definition,
% 0.34/0.49 ( disjointsetsI1
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ~ ? [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 & ( in @ Xx @ B ) )
% 0.34/0.49 => ( ( binintersect @ A @ B )
% 0.34/0.49 = emptyset ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectRsub_type,type,
% 0.34/0.49 binintersectRsub: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectRsub,definition,
% 0.34/0.49 ( binintersectRsub
% 0.34/0.49 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectSubset4_type,type,
% 0.34/0.49 binintersectSubset4: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectSubset4,definition,
% 0.34/0.49 ( binintersectSubset4
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( subset @ B @ A )
% 0.34/0.49 => ( ( binintersect @ A @ B )
% 0.34/0.49 = B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectSubset1_type,type,
% 0.34/0.49 binintersectSubset1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(binintersectSubset1,definition,
% 0.34/0.49 ( binintersectSubset1
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( ( binintersect @ A @ B )
% 0.34/0.49 = A )
% 0.34/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(bs114d_type,type,
% 0.34/0.49 bs114d: $o ).
% 0.34/0.49
% 0.34/0.49 thf(bs114d,definition,
% 0.34/0.49 ( bs114d
% 0.34/0.49 = ( ! [A: $i,B: $i,C: $i] :
% 0.34/0.49 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.34/0.49 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(regular_type,type,
% 0.34/0.49 regular: $i > $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminus_type,type,
% 0.34/0.49 setminus: $i > $i > $i ).
% 0.34/0.49
% 0.34/0.49 thf(setminusI_type,type,
% 0.34/0.49 setminusI: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminusI,definition,
% 0.34/0.49 ( setminusI
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( ~ ( in @ Xx @ B )
% 0.34/0.49 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setminusEL_type,type,
% 0.34/0.49 setminusEL: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminusEL,definition,
% 0.34/0.49 ( setminusEL
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.34/0.49 => ( in @ Xx @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setminusER_type,type,
% 0.34/0.49 setminusER: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminusER,definition,
% 0.34/0.49 ( setminusER
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.34/0.49 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setminusSubset2_type,type,
% 0.34/0.49 setminusSubset2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminusSubset2,definition,
% 0.34/0.49 ( setminusSubset2
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( subset @ A @ B )
% 0.34/0.49 => ( ( setminus @ A @ B )
% 0.34/0.49 = emptyset ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setminusERneg_type,type,
% 0.34/0.49 setminusERneg: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminusERneg,definition,
% 0.34/0.49 ( setminusERneg
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.34/0.49 => ( ( in @ Xx @ A )
% 0.34/0.49 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setminusELneg_type,type,
% 0.34/0.49 setminusELneg: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminusELneg,definition,
% 0.34/0.49 ( setminusELneg
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.34/0.49 => ( ~ ( in @ Xx @ B )
% 0.34/0.49 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setminusILneg_type,type,
% 0.34/0.49 setminusILneg: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminusILneg,definition,
% 0.34/0.49 ( setminusILneg
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ~ ( in @ Xx @ A )
% 0.34/0.49 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setminusIRneg_type,type,
% 0.34/0.49 setminusIRneg: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminusIRneg,definition,
% 0.34/0.49 ( setminusIRneg
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ B )
% 0.34/0.49 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setminusLsub_type,type,
% 0.34/0.49 setminusLsub: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminusLsub,definition,
% 0.34/0.49 ( setminusLsub
% 0.34/0.49 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setminusSubset1_type,type,
% 0.34/0.49 setminusSubset1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setminusSubset1,definition,
% 0.34/0.49 ( setminusSubset1
% 0.34/0.49 = ( ! [A: $i,B: $i] :
% 0.34/0.49 ( ( ( setminus @ A @ B )
% 0.34/0.49 = emptyset )
% 0.34/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(symdiff_type,type,
% 0.34/0.49 symdiff: $i > $i > $i ).
% 0.34/0.49
% 0.34/0.49 thf(symdiffE_type,type,
% 0.34/0.49 symdiffE: $o ).
% 0.34/0.49
% 0.34/0.49 thf(symdiffE,definition,
% 0.34/0.49 ( symdiffE
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.34/0.49 => ! [Xphi: $o] :
% 0.34/0.49 ( ( ( in @ Xx @ A )
% 0.34/0.49 => ( ~ ( in @ Xx @ B )
% 0.34/0.49 => Xphi ) )
% 0.34/0.49 => ( ( ~ ( in @ Xx @ A )
% 0.34/0.49 => ( ( in @ Xx @ B )
% 0.34/0.49 => Xphi ) )
% 0.34/0.49 => Xphi ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(symdiffI1_type,type,
% 0.34/0.49 symdiffI1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(symdiffI1,definition,
% 0.34/0.49 ( symdiffI1
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( ~ ( in @ Xx @ B )
% 0.34/0.49 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(symdiffI2_type,type,
% 0.34/0.49 symdiffI2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(symdiffI2,definition,
% 0.34/0.49 ( symdiffI2
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ~ ( in @ Xx @ A )
% 0.34/0.49 => ( ( in @ Xx @ B )
% 0.34/0.49 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(symdiffIneg1_type,type,
% 0.34/0.49 symdiffIneg1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(symdiffIneg1,definition,
% 0.34/0.49 ( symdiffIneg1
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( ( in @ Xx @ B )
% 0.34/0.49 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(symdiffIneg2_type,type,
% 0.34/0.49 symdiffIneg2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(symdiffIneg2,definition,
% 0.34/0.49 ( symdiffIneg2
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ~ ( in @ Xx @ A )
% 0.34/0.49 => ( ~ ( in @ Xx @ B )
% 0.34/0.49 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(iskpair_type,type,
% 0.34/0.49 iskpair: $i > $o ).
% 0.34/0.49
% 0.34/0.49 thf(iskpair,definition,
% 0.34/0.49 ( iskpair
% 0.34/0.49 = ( ^ [A: $i] :
% 0.34/0.49 ? [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ ( setunion @ A ) )
% 0.34/0.49 & ? [Xy: $i] :
% 0.34/0.49 ( ( in @ Xy @ ( setunion @ A ) )
% 0.34/0.49 & ( A
% 0.34/0.49 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(secondinupair_type,type,
% 0.34/0.49 secondinupair: $o ).
% 0.34/0.49
% 0.34/0.49 thf(secondinupair,definition,
% 0.34/0.49 ( secondinupair
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setukpairIL_type,type,
% 0.34/0.49 setukpairIL: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setukpairIL,definition,
% 0.34/0.49 ( setukpairIL
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(setukpairIR_type,type,
% 0.34/0.49 setukpairIR: $o ).
% 0.34/0.49
% 0.34/0.49 thf(setukpairIR,definition,
% 0.34/0.49 ( setukpairIR
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(kpairiskpair_type,type,
% 0.34/0.49 kpairiskpair: $o ).
% 0.34/0.49
% 0.34/0.49 thf(kpairiskpair,definition,
% 0.34/0.49 ( kpairiskpair
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(kpair_type,type,
% 0.34/0.49 kpair: $i > $i > $i ).
% 0.34/0.49
% 0.34/0.49 thf(kpair,definition,
% 0.34/0.49 ( kpair
% 0.34/0.49 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(kpairp_type,type,
% 0.34/0.49 kpairp: $o ).
% 0.34/0.49
% 0.34/0.49 thf(kpairp,definition,
% 0.34/0.49 ( kpairp
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(cartprod_type,type,
% 0.34/0.49 cartprod: $i > $i > $i ).
% 0.34/0.49
% 0.34/0.49 thf(singletonsubset_type,type,
% 0.34/0.49 singletonsubset: $o ).
% 0.34/0.49
% 0.34/0.49 thf(singletonsubset,definition,
% 0.34/0.49 ( singletonsubset
% 0.34/0.49 = ( ! [A: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(singletoninpowerset_type,type,
% 0.34/0.49 singletoninpowerset: $o ).
% 0.34/0.49
% 0.34/0.49 thf(singletoninpowerset,definition,
% 0.34/0.49 ( singletoninpowerset
% 0.34/0.49 = ( ! [A: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(singletoninpowunion_type,type,
% 0.34/0.49 singletoninpowunion: $o ).
% 0.34/0.49
% 0.34/0.49 thf(singletoninpowunion,definition,
% 0.34/0.49 ( singletoninpowunion
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(upairset2E_type,type,
% 0.34/0.49 upairset2E: $o ).
% 0.34/0.49
% 0.34/0.49 thf(upairset2E,definition,
% 0.34/0.49 ( upairset2E
% 0.34/0.49 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.34/0.49 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.34/0.49 => ( ( Xz = Xx )
% 0.34/0.49 | ( Xz = Xy ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(upairsubunion_type,type,
% 0.34/0.49 upairsubunion: $o ).
% 0.34/0.49
% 0.34/0.49 thf(upairsubunion,definition,
% 0.34/0.49 ( upairsubunion
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ! [Xy: $i] :
% 0.34/0.49 ( ( in @ Xy @ B )
% 0.34/0.49 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(upairinpowunion_type,type,
% 0.34/0.49 upairinpowunion: $o ).
% 0.34/0.49
% 0.34/0.49 thf(upairinpowunion,definition,
% 0.34/0.49 ( upairinpowunion
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ! [Xy: $i] :
% 0.34/0.49 ( ( in @ Xy @ B )
% 0.34/0.49 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(ubforcartprodlem1_type,type,
% 0.34/0.49 ubforcartprodlem1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(ubforcartprodlem1,definition,
% 0.34/0.49 ( ubforcartprodlem1
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ! [Xy: $i] :
% 0.34/0.49 ( ( in @ Xy @ B )
% 0.34/0.49 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(ubforcartprodlem2_type,type,
% 0.34/0.49 ubforcartprodlem2: $o ).
% 0.34/0.49
% 0.34/0.49 thf(ubforcartprodlem2,definition,
% 0.34/0.49 ( ubforcartprodlem2
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ! [Xy: $i] :
% 0.34/0.49 ( ( in @ Xy @ B )
% 0.34/0.49 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(ubforcartprodlem3_type,type,
% 0.34/0.49 ubforcartprodlem3: $o ).
% 0.34/0.49
% 0.34/0.49 thf(ubforcartprodlem3,definition,
% 0.34/0.49 ( ubforcartprodlem3
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ! [Xy: $i] :
% 0.34/0.49 ( ( in @ Xy @ B )
% 0.34/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(cartprodpairin_type,type,
% 0.34/0.49 cartprodpairin: $o ).
% 0.34/0.49
% 0.34/0.49 thf(cartprodpairin,definition,
% 0.34/0.49 ( cartprodpairin
% 0.34/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 => ! [Xy: $i] :
% 0.34/0.49 ( ( in @ Xy @ B )
% 0.34/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(cartprodmempair1_type,type,
% 0.34/0.49 cartprodmempair1: $o ).
% 0.34/0.49
% 0.34/0.49 thf(cartprodmempair1,definition,
% 0.34/0.49 ( cartprodmempair1
% 0.34/0.49 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.34/0.49 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.34/0.49 => ? [Xx: $i] :
% 0.34/0.49 ( ( in @ Xx @ A )
% 0.34/0.49 & ? [Xy: $i] :
% 0.34/0.49 ( ( in @ Xy @ B )
% 0.34/0.49 & ( Xu
% 0.34/0.49 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 thf(cartprodmempair,conjecture,
% 0.34/0.49 ( setextAx
% 0.34/0.49 => ( emptysetAx
% 0.34/0.49 => ( setadjoinAx
% 0.34/0.49 => ( powersetAx
% 0.34/0.49 => ( setunionAx
% 0.34/0.49 => ( omega0Ax
% 0.34/0.49 => ( omegaSAx
% 0.34/0.49 => ( omegaIndAx
% 0.34/0.49 => ( replAx
% 0.34/0.49 => ( foundationAx
% 0.34/0.49 => ( wellorderingAx
% 0.34/0.49 => ( descrp
% 0.34/0.49 => ( dsetconstrI
% 0.34/0.49 => ( dsetconstrEL
% 0.34/0.49 => ( dsetconstrER
% 0.34/0.49 => ( exuE1
% 0.34/0.49 => ( prop2setE
% 0.34/0.49 => ( emptysetE
% 0.34/0.49 => ( emptysetimpfalse
% 0.34/0.49 => ( notinemptyset
% 0.34/0.49 => ( exuE3e
% 0.34/0.49 => ( setext
% 0.34/0.49 => ( emptyI
% 0.34/0.49 => ( noeltsimpempty
% 0.34/0.49 => ( setbeta
% 0.34/0.49 => ( nonemptyE1
% 0.34/0.49 => ( nonemptyI
% 0.34/0.49 => ( nonemptyI1
% 0.34/0.49 => ( setadjoinIL
% 0.34/0.49 => ( emptyinunitempty
% 0.34/0.49 => ( setadjoinIR
% 0.34/0.49 => ( setadjoinE
% 0.34/0.49 => ( setadjoinOr
% 0.34/0.49 => ( setoftrueEq
% 0.34/0.49 => ( powersetI
% 0.34/0.49 => ( emptyinPowerset
% 0.34/0.49 => ( emptyInPowerset
% 0.34/0.49 => ( powersetE
% 0.34/0.49 => ( setunionI
% 0.34/0.49 => ( setunionE
% 0.34/0.49 => ( subPowSU
% 0.34/0.49 => ( exuE2
% 0.34/0.49 => ( nonemptyImpWitness
% 0.34/0.49 => ( uniqinunit
% 0.34/0.49 => ( notinsingleton
% 0.34/0.49 => ( eqinunit
% 0.34/0.49 => ( singletonsswitch
% 0.34/0.49 => ( upairsetE
% 0.34/0.49 => ( upairsetIL
% 0.34/0.49 => ( upairsetIR
% 0.34/0.49 => ( emptyE1
% 0.34/0.49 => ( vacuousDall
% 0.34/0.49 => ( quantDeMorgan1
% 0.34/0.49 => ( quantDeMorgan2
% 0.34/0.49 => ( quantDeMorgan3
% 0.34/0.49 => ( quantDeMorgan4
% 0.34/0.49 => ( prop2setI
% 0.34/0.49 => ( prop2set2propI
% 0.34/0.49 => ( notdexE
% 0.34/0.49 => ( notdallE
% 0.34/0.49 => ( exuI1
% 0.34/0.49 => ( exuI3
% 0.34/0.49 => ( exuI2
% 0.34/0.49 => ( inCongP
% 0.34/0.49 => ( in__Cong
% 0.34/0.49 => ( exuE3u
% 0.34/0.49 => ( exu__Cong
% 0.34/0.49 => ( emptyset__Cong
% 0.34/0.49 => ( setadjoin__Cong
% 0.34/0.49 => ( powerset__Cong
% 0.34/0.49 => ( setunion__Cong
% 0.34/0.49 => ( omega__Cong
% 0.34/0.49 => ( exuEu
% 0.34/0.49 => ( descr__Cong
% 0.34/0.49 => ( dsetconstr__Cong
% 0.34/0.49 => ( subsetI1
% 0.34/0.49 => ( eqimpsubset2
% 0.34/0.49 => ( eqimpsubset1
% 0.34/0.49 => ( subsetI2
% 0.34/0.49 => ( emptysetsubset
% 0.34/0.49 => ( subsetE
% 0.34/0.49 => ( subsetE2
% 0.34/0.49 => ( notsubsetI
% 0.34/0.49 => ( notequalI1
% 0.34/0.49 => ( notequalI2
% 0.34/0.49 => ( subsetRefl
% 0.34/0.49 => ( subsetTrans
% 0.34/0.49 => ( setadjoinSub
% 0.34/0.49 => ( setadjoinSub2
% 0.34/0.49 => ( subset2powerset
% 0.34/0.49 => ( setextsub
% 0.34/0.49 => ( subsetemptysetimpeq
% 0.34/0.49 => ( powersetI1
% 0.34/0.49 => ( powersetE1
% 0.34/0.49 => ( inPowerset
% 0.34/0.49 => ( powersetsubset
% 0.34/0.49 => ( sepInPowerset
% 0.34/0.49 => ( sepSubset
% 0.34/0.49 => ( binunionIL
% 0.34/0.49 => ( upairset2IR
% 0.34/0.49 => ( binunionIR
% 0.34/0.49 => ( binunionEcases
% 0.34/0.49 => ( binunionE
% 0.34/0.49 => ( binunionLsub
% 0.34/0.49 => ( binunionRsub
% 0.34/0.49 => ( binintersectI
% 0.34/0.49 => ( binintersectSubset5
% 0.34/0.49 => ( binintersectEL
% 0.34/0.49 => ( binintersectLsub
% 0.34/0.49 => ( binintersectSubset2
% 0.34/0.49 => ( binintersectSubset3
% 0.34/0.49 => ( binintersectER
% 0.34/0.49 => ( disjointsetsI1
% 0.34/0.49 => ( binintersectRsub
% 0.34/0.49 => ( binintersectSubset4
% 0.34/0.49 => ( binintersectSubset1
% 0.34/0.49 => ( bs114d
% 0.34/0.49 => ( setminusI
% 0.34/0.49 => ( setminusEL
% 0.34/0.49 => ( setminusER
% 0.34/0.49 => ( setminusSubset2
% 0.34/0.49 => ( setminusERneg
% 0.34/0.49 => ( setminusELneg
% 0.34/0.49 => ( setminusILneg
% 0.34/0.49 => ( setminusIRneg
% 0.34/0.49 => ( setminusLsub
% 0.34/0.49 => ( setminusSubset1
% 0.34/0.49 => ( symdiffE
% 0.34/0.49 => ( symdiffI1
% 0.34/0.49 => ( symdiffI2
% 0.34/0.49 => ( symdiffIneg1
% 0.34/0.49 => ( symdiffIneg2
% 0.34/0.49 => ( secondinupair
% 0.34/0.49 => ( setukpairIL
% 0.34/0.49 => ( setukpairIR
% 0.34/0.49 => ( kpairiskpair
% 0.34/0.49 => ( kpairp
% 0.34/0.49 => ( singletonsubset
% 0.34/0.49 => ( singletoninpowerset
% 0.34/0.49 => ( singletoninpowunion
% 0.34/0.49 => ( upairset2E
% 0.34/0.49 => ( upairsubunion
% 0.34/0.49 => ( upairinpowunion
% 0.34/0.49 => ( ubforcartprodlem1
% 0.34/0.49 => ( ubforcartprodlem2
% 0.34/0.49 => ( ubforcartprodlem3
% 0.34/0.49 => ( cartprodpairin
% 0.34/0.49 => ( cartprodmempair1
% 0.34/0.49 => ! [A: $i,B: $i,Xu: $i] :
% 0.34/0.49 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.34/0.49 => ( iskpair @ Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.34/0.49
% 0.34/0.49 %------------------------------------------------------------------------------
% 0.34/0.49 ------------------------
% 2.56/1.69 ---- Embedded in THF ---
% 2.56/1.69 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.56/1.69 %%% Generated on Tue Feb 24 12:29:17 EST 2026
% 2.56/1.69 %%% using '$$dhol' embedding, version 1.3.0.
% 2.56/1.69 %%% Logic specification used:
% 2.56/1.69 %%% thf(spec, logic, $$dhol).
% 2.56/1.69
% 2.56/1.69 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.qvI7ApaoRY/DTF2DTF26806.p
% See solution above
% 2.56/1.69 ------------------------
% 2.83/1.72 ---- Cleaned THF ---
% 2.83/1.72 thf(in_type,type,
% 2.83/1.72 in: $i > $i > $o ).
% 2.83/1.72
% 2.83/1.72 thf(exu_type,type,
% 2.83/1.72 exu: ( $i > $o ) > $o ).
% 2.83/1.72
% 2.83/1.72 thf(exu,definition,
% 2.83/1.72 ( exu
% 2.83/1.72 = ( ^ [Xphi: $i > $o] :
% 2.83/1.72 ? [Xx: $i] :
% 2.83/1.72 ( ( Xphi @ Xx )
% 2.83/1.72 & ! [Xy: $i] :
% 2.83/1.72 ( ( Xphi @ Xy )
% 2.83/1.72 => ( Xx = Xy ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setextAx_type,type,
% 2.83/1.72 setextAx: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setextAx,definition,
% 2.83/1.72 ( setextAx
% 2.83/1.72 = ( ! [A: $i,B: $i] :
% 2.83/1.72 ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 <=> ( in @ Xx @ B ) )
% 2.83/1.72 => ( A = B ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(emptyset_type,type,
% 2.83/1.72 emptyset: $i ).
% 2.83/1.72
% 2.83/1.72 thf(emptysetAx_type,type,
% 2.83/1.72 emptysetAx: $o ).
% 2.83/1.72
% 2.83/1.72 thf(emptysetAx,definition,
% 2.83/1.72 ( emptysetAx
% 2.83/1.72 = ( ! [Xx: $i] :
% 2.83/1.72 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoin_type,type,
% 2.83/1.72 setadjoin: $i > $i > $i ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoinAx_type,type,
% 2.83/1.72 setadjoinAx: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoinAx,definition,
% 2.83/1.72 ( setadjoinAx
% 2.83/1.72 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.83/1.72 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.83/1.72 <=> ( ( Xy = Xx )
% 2.83/1.72 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(powerset_type,type,
% 2.83/1.72 powerset: $i > $i ).
% 2.83/1.72
% 2.83/1.72 thf(powersetAx_type,type,
% 2.83/1.72 powersetAx: $o ).
% 2.83/1.72
% 2.83/1.72 thf(powersetAx,definition,
% 2.83/1.72 ( powersetAx
% 2.83/1.72 = ( ! [A: $i,B: $i] :
% 2.83/1.72 ( ( in @ B @ ( powerset @ A ) )
% 2.83/1.72 <=> ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ B )
% 2.83/1.72 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setunion_type,type,
% 2.83/1.72 setunion: $i > $i ).
% 2.83/1.72
% 2.83/1.72 thf(setunionAx_type,type,
% 2.83/1.72 setunionAx: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setunionAx,definition,
% 2.83/1.72 ( setunionAx
% 2.83/1.72 = ( ! [A: $i,Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ ( setunion @ A ) )
% 2.83/1.72 <=> ? [B: $i] :
% 2.83/1.72 ( ( in @ Xx @ B )
% 2.83/1.72 & ( in @ B @ A ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(omega_type,type,
% 2.83/1.72 omega: $i ).
% 2.83/1.72
% 2.83/1.72 thf(omega0Ax_type,type,
% 2.83/1.72 omega0Ax: $o ).
% 2.83/1.72
% 2.83/1.72 thf(omega0Ax,definition,
% 2.83/1.72 ( omega0Ax
% 2.83/1.72 = ( in @ emptyset @ omega ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(omegaSAx_type,type,
% 2.83/1.72 omegaSAx: $o ).
% 2.83/1.72
% 2.83/1.72 thf(omegaSAx,definition,
% 2.83/1.72 ( omegaSAx
% 2.83/1.72 = ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ omega )
% 2.83/1.72 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(omegaIndAx_type,type,
% 2.83/1.72 omegaIndAx: $o ).
% 2.83/1.72
% 2.83/1.72 thf(omegaIndAx,definition,
% 2.83/1.72 ( omegaIndAx
% 2.83/1.72 = ( ! [A: $i] :
% 2.83/1.72 ( ( ( in @ emptyset @ A )
% 2.83/1.72 & ! [Xx: $i] :
% 2.83/1.72 ( ( ( in @ Xx @ omega )
% 2.83/1.72 & ( in @ Xx @ A ) )
% 2.83/1.72 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.83/1.72 => ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ omega )
% 2.83/1.72 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(replAx_type,type,
% 2.83/1.72 replAx: $o ).
% 2.83/1.72
% 2.83/1.72 thf(replAx,definition,
% 2.83/1.72 ( replAx
% 2.83/1.72 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.83/1.72 ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ( exu
% 2.83/1.72 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.83/1.72 => ? [B: $i] :
% 2.83/1.72 ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ B )
% 2.83/1.72 <=> ? [Xy: $i] :
% 2.83/1.72 ( ( in @ Xy @ A )
% 2.83/1.72 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(foundationAx_type,type,
% 2.83/1.72 foundationAx: $o ).
% 2.83/1.72
% 2.83/1.72 thf(foundationAx,definition,
% 2.83/1.72 ( foundationAx
% 2.83/1.72 = ( ! [A: $i] :
% 2.83/1.72 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.83/1.72 => ? [B: $i] :
% 2.83/1.72 ( ( in @ B @ A )
% 2.83/1.72 & ~ ? [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ B )
% 2.83/1.72 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(wellorderingAx_type,type,
% 2.83/1.72 wellorderingAx: $o ).
% 2.83/1.72
% 2.83/1.72 thf(wellorderingAx,definition,
% 2.83/1.72 ( wellorderingAx
% 2.83/1.72 = ( ! [A: $i] :
% 2.83/1.72 ? [B: $i] :
% 2.83/1.72 ( ! [C: $i] :
% 2.83/1.72 ( ( in @ C @ B )
% 2.83/1.72 => ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ C )
% 2.83/1.72 => ( in @ Xx @ A ) ) )
% 2.83/1.72 & ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( ( in @ Xx @ A )
% 2.83/1.72 & ( in @ Xy @ A ) )
% 2.83/1.72 => ( ! [C: $i] :
% 2.83/1.72 ( ( in @ C @ B )
% 2.83/1.72 => ( ( in @ Xx @ C )
% 2.83/1.72 <=> ( in @ Xy @ C ) ) )
% 2.83/1.72 => ( Xx = Xy ) ) )
% 2.83/1.72 & ! [C: $i,D: $i] :
% 2.83/1.72 ( ( ( in @ C @ B )
% 2.83/1.72 & ( in @ D @ B ) )
% 2.83/1.72 => ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ C )
% 2.83/1.72 => ( in @ Xx @ D ) )
% 2.83/1.72 | ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ D )
% 2.83/1.72 => ( in @ Xx @ C ) ) ) )
% 2.83/1.72 & ! [C: $i] :
% 2.83/1.72 ( ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ C )
% 2.83/1.72 => ( in @ Xx @ A ) )
% 2.83/1.72 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.83/1.72 => ? [D: $i,Xx: $i] :
% 2.83/1.72 ( ( in @ D @ B )
% 2.83/1.72 & ( in @ Xx @ C )
% 2.83/1.72 & ~ ? [Xy: $i] :
% 2.83/1.72 ( ( in @ Xy @ D )
% 2.83/1.72 & ( in @ Xy @ C ) )
% 2.83/1.72 & ! [E: $i] :
% 2.83/1.72 ( ( in @ E @ B )
% 2.83/1.72 => ( ! [Xy: $i] :
% 2.83/1.72 ( ( in @ Xy @ E )
% 2.83/1.72 => ( in @ Xy @ D ) )
% 2.83/1.72 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(descr_type,type,
% 2.83/1.72 descr: ( $i > $o ) > $i ).
% 2.83/1.72
% 2.83/1.72 thf(descrp_type,type,
% 2.83/1.72 descrp: $o ).
% 2.83/1.72
% 2.83/1.72 thf(descrp,definition,
% 2.83/1.72 ( descrp
% 2.83/1.72 = ( ! [Xphi: $i > $o] :
% 2.83/1.72 ( ( exu
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.72 => ( Xphi
% 2.83/1.72 @ ( descr
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(dsetconstr_type,type,
% 2.83/1.72 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.83/1.72
% 2.83/1.72 thf(dsetconstrI_type,type,
% 2.83/1.72 dsetconstrI: $o ).
% 2.83/1.72
% 2.83/1.72 thf(dsetconstrI,definition,
% 2.83/1.72 ( dsetconstrI
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ( ( Xphi @ Xx )
% 2.83/1.72 => ( in @ Xx
% 2.83/1.72 @ ( dsetconstr @ A
% 2.83/1.72 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(dsetconstrEL_type,type,
% 2.83/1.72 dsetconstrEL: $o ).
% 2.83/1.72
% 2.83/1.72 thf(dsetconstrEL,definition,
% 2.83/1.72 ( dsetconstrEL
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.83/1.72 ( ( in @ Xx
% 2.83/1.72 @ ( dsetconstr @ A
% 2.83/1.72 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.83/1.72 => ( in @ Xx @ A ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(dsetconstrER_type,type,
% 2.83/1.72 dsetconstrER: $o ).
% 2.83/1.72
% 2.83/1.72 thf(dsetconstrER,definition,
% 2.83/1.72 ( dsetconstrER
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.83/1.72 ( ( in @ Xx
% 2.83/1.72 @ ( dsetconstr @ A
% 2.83/1.72 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.83/1.72 => ( Xphi @ Xx ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(exuE1_type,type,
% 2.83/1.72 exuE1: $o ).
% 2.83/1.72
% 2.83/1.72 thf(exuE1,definition,
% 2.83/1.72 ( exuE1
% 2.83/1.72 = ( ! [Xphi: $i > $o] :
% 2.83/1.72 ( ( exu
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.72 => ? [Xx: $i] :
% 2.83/1.72 ( ( Xphi @ Xx )
% 2.83/1.72 & ! [Xy: $i] :
% 2.83/1.72 ( ( Xphi @ Xy )
% 2.83/1.72 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(prop2set_type,type,
% 2.83/1.72 prop2set: $o > $i ).
% 2.83/1.72
% 2.83/1.72 thf(prop2setE_type,type,
% 2.83/1.72 prop2setE: $o ).
% 2.83/1.72
% 2.83/1.72 thf(prop2setE,definition,
% 2.83/1.72 ( prop2setE
% 2.83/1.72 = ( ! [Xphi: $o,Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.83/1.72 => Xphi ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(emptysetE_type,type,
% 2.83/1.72 emptysetE: $o ).
% 2.83/1.72
% 2.83/1.72 thf(emptysetE,definition,
% 2.83/1.72 ( emptysetE
% 2.83/1.72 = ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ emptyset )
% 2.83/1.72 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(emptysetimpfalse_type,type,
% 2.83/1.72 emptysetimpfalse: $o ).
% 2.83/1.72
% 2.83/1.72 thf(emptysetimpfalse,definition,
% 2.83/1.72 ( emptysetimpfalse
% 2.83/1.72 = ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ emptyset )
% 2.83/1.72 => $false ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(notinemptyset_type,type,
% 2.83/1.72 notinemptyset: $o ).
% 2.83/1.72
% 2.83/1.72 thf(notinemptyset,definition,
% 2.83/1.72 ( notinemptyset
% 2.83/1.72 = ( ! [Xx: $i] :
% 2.83/1.72 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(exuE3e_type,type,
% 2.83/1.72 exuE3e: $o ).
% 2.83/1.72
% 2.83/1.72 thf(exuE3e,definition,
% 2.83/1.72 ( exuE3e
% 2.83/1.72 = ( ! [Xphi: $i > $o] :
% 2.83/1.72 ( ( exu
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.72 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setext_type,type,
% 2.83/1.72 setext: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setext,definition,
% 2.83/1.72 ( setext
% 2.83/1.72 = ( ! [A: $i,B: $i] :
% 2.83/1.72 ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ( in @ Xx @ B ) )
% 2.83/1.72 => ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ B )
% 2.83/1.72 => ( in @ Xx @ A ) )
% 2.83/1.72 => ( A = B ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(emptyI_type,type,
% 2.83/1.72 emptyI: $o ).
% 2.83/1.72
% 2.83/1.72 thf(emptyI,definition,
% 2.83/1.72 ( emptyI
% 2.83/1.72 = ( ! [A: $i] :
% 2.83/1.72 ( ! [Xx: $i] :
% 2.83/1.72 ~ ( in @ Xx @ A )
% 2.83/1.72 => ( A = emptyset ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(noeltsimpempty_type,type,
% 2.83/1.72 noeltsimpempty: $o ).
% 2.83/1.72
% 2.83/1.72 thf(noeltsimpempty,definition,
% 2.83/1.72 ( noeltsimpempty
% 2.83/1.72 = ( ! [A: $i] :
% 2.83/1.72 ( ! [Xx: $i] :
% 2.83/1.72 ~ ( in @ Xx @ A )
% 2.83/1.72 => ( A = emptyset ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setbeta_type,type,
% 2.83/1.72 setbeta: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setbeta,definition,
% 2.83/1.72 ( setbeta
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ( ( in @ Xx
% 2.83/1.72 @ ( dsetconstr @ A
% 2.83/1.72 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.83/1.72 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(nonempty_type,type,
% 2.83/1.72 nonempty: $i > $o ).
% 2.83/1.72
% 2.83/1.72 thf(nonempty,definition,
% 2.83/1.72 ( nonempty
% 2.83/1.72 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(nonemptyE1_type,type,
% 2.83/1.72 nonemptyE1: $o ).
% 2.83/1.72
% 2.83/1.72 thf(nonemptyE1,definition,
% 2.83/1.72 ( nonemptyE1
% 2.83/1.72 = ( ! [A: $i] :
% 2.83/1.72 ( ( nonempty @ A )
% 2.83/1.72 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(nonemptyI_type,type,
% 2.83/1.72 nonemptyI: $o ).
% 2.83/1.72
% 2.83/1.72 thf(nonemptyI,definition,
% 2.83/1.72 ( nonemptyI
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ( ( Xphi @ Xx )
% 2.83/1.72 => ( nonempty
% 2.83/1.72 @ ( dsetconstr @ A
% 2.83/1.72 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(nonemptyI1_type,type,
% 2.83/1.72 nonemptyI1: $o ).
% 2.83/1.72
% 2.83/1.72 thf(nonemptyI1,definition,
% 2.83/1.72 ( nonemptyI1
% 2.83/1.72 = ( ! [A: $i] :
% 2.83/1.72 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.83/1.72 => ( nonempty @ A ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoinIL_type,type,
% 2.83/1.72 setadjoinIL: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoinIL,definition,
% 2.83/1.72 ( setadjoinIL
% 2.83/1.72 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(emptyinunitempty_type,type,
% 2.83/1.72 emptyinunitempty: $o ).
% 2.83/1.72
% 2.83/1.72 thf(emptyinunitempty,definition,
% 2.83/1.72 ( emptyinunitempty
% 2.83/1.72 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoinIR_type,type,
% 2.83/1.72 setadjoinIR: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoinIR,definition,
% 2.83/1.72 ( setadjoinIR
% 2.83/1.72 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.83/1.72 ( ( in @ Xy @ A )
% 2.83/1.72 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoinE_type,type,
% 2.83/1.72 setadjoinE: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoinE,definition,
% 2.83/1.72 ( setadjoinE
% 2.83/1.72 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.83/1.72 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.83/1.72 => ! [Xphi: $o] :
% 2.83/1.72 ( ( ( Xy = Xx )
% 2.83/1.72 => Xphi )
% 2.83/1.72 => ( ( ( in @ Xy @ A )
% 2.83/1.72 => Xphi )
% 2.83/1.72 => Xphi ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoinOr_type,type,
% 2.83/1.72 setadjoinOr: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoinOr,definition,
% 2.83/1.72 ( setadjoinOr
% 2.83/1.72 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.83/1.72 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.83/1.72 => ( ( Xy = Xx )
% 2.83/1.72 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setoftrueEq_type,type,
% 2.83/1.72 setoftrueEq: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setoftrueEq,definition,
% 2.83/1.72 ( setoftrueEq
% 2.83/1.72 = ( ! [A: $i] :
% 2.83/1.72 ( ( dsetconstr @ A
% 2.83/1.72 @ ^ [Xx: $i] : $true )
% 2.83/1.72 = A ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(powersetI_type,type,
% 2.83/1.72 powersetI: $o ).
% 2.83/1.72
% 2.83/1.72 thf(powersetI,definition,
% 2.83/1.72 ( powersetI
% 2.83/1.72 = ( ! [A: $i,B: $i] :
% 2.83/1.72 ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ B )
% 2.83/1.72 => ( in @ Xx @ A ) )
% 2.83/1.72 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(emptyinPowerset_type,type,
% 2.83/1.72 emptyinPowerset: $o ).
% 2.83/1.72
% 2.83/1.72 thf(emptyinPowerset,definition,
% 2.83/1.72 ( emptyinPowerset
% 2.83/1.72 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(emptyInPowerset_type,type,
% 2.83/1.72 emptyInPowerset: $o ).
% 2.83/1.72
% 2.83/1.72 thf(emptyInPowerset,definition,
% 2.83/1.72 ( emptyInPowerset
% 2.83/1.72 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(powersetE_type,type,
% 2.83/1.72 powersetE: $o ).
% 2.83/1.72
% 2.83/1.72 thf(powersetE,definition,
% 2.83/1.72 ( powersetE
% 2.83/1.72 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.72 ( ( in @ B @ ( powerset @ A ) )
% 2.83/1.72 => ( ( in @ Xx @ B )
% 2.83/1.72 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setunionI_type,type,
% 2.83/1.72 setunionI: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setunionI,definition,
% 2.83/1.72 ( setunionI
% 2.83/1.72 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.83/1.72 ( ( in @ Xx @ B )
% 2.83/1.72 => ( ( in @ B @ A )
% 2.83/1.72 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setunionE_type,type,
% 2.83/1.72 setunionE: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setunionE,definition,
% 2.83/1.72 ( setunionE
% 2.83/1.72 = ( ! [A: $i,Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ ( setunion @ A ) )
% 2.83/1.72 => ! [Xphi: $o] :
% 2.83/1.72 ( ! [B: $i] :
% 2.83/1.72 ( ( in @ Xx @ B )
% 2.83/1.72 => ( ( in @ B @ A )
% 2.83/1.72 => Xphi ) )
% 2.83/1.72 => Xphi ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(subPowSU_type,type,
% 2.83/1.72 subPowSU: $o ).
% 2.83/1.72
% 2.83/1.72 thf(subPowSU,definition,
% 2.83/1.72 ( subPowSU
% 2.83/1.72 = ( ! [A: $i,Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(exuE2_type,type,
% 2.83/1.72 exuE2: $o ).
% 2.83/1.72
% 2.83/1.72 thf(exuE2,definition,
% 2.83/1.72 ( exuE2
% 2.83/1.72 = ( ! [Xphi: $i > $o] :
% 2.83/1.72 ( ( exu
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.72 => ? [Xx: $i] :
% 2.83/1.72 ! [Xy: $i] :
% 2.83/1.72 ( ( Xphi @ Xy )
% 2.83/1.72 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(nonemptyImpWitness_type,type,
% 2.83/1.72 nonemptyImpWitness: $o ).
% 2.83/1.72
% 2.83/1.72 thf(nonemptyImpWitness,definition,
% 2.83/1.72 ( nonemptyImpWitness
% 2.83/1.72 = ( ! [A: $i] :
% 2.83/1.72 ( ( nonempty @ A )
% 2.83/1.72 => ? [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 & $true ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(uniqinunit_type,type,
% 2.83/1.72 uniqinunit: $o ).
% 2.83/1.72
% 2.83/1.72 thf(uniqinunit,definition,
% 2.83/1.72 ( uniqinunit
% 2.83/1.72 = ( ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.83/1.72 => ( Xx = Xy ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(notinsingleton_type,type,
% 2.83/1.72 notinsingleton: $o ).
% 2.83/1.72
% 2.83/1.72 thf(notinsingleton,definition,
% 2.83/1.72 ( notinsingleton
% 2.83/1.72 = ( ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( Xx != Xy )
% 2.83/1.72 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(eqinunit_type,type,
% 2.83/1.72 eqinunit: $o ).
% 2.83/1.72
% 2.83/1.72 thf(eqinunit,definition,
% 2.83/1.72 ( eqinunit
% 2.83/1.72 = ( ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( Xx = Xy )
% 2.83/1.72 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(singletonsswitch_type,type,
% 2.83/1.72 singletonsswitch: $o ).
% 2.83/1.72
% 2.83/1.72 thf(singletonsswitch,definition,
% 2.83/1.72 ( singletonsswitch
% 2.83/1.72 = ( ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.83/1.72 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(upairsetE_type,type,
% 2.83/1.72 upairsetE: $o ).
% 2.83/1.72
% 2.83/1.72 thf(upairsetE,definition,
% 2.83/1.72 ( upairsetE
% 2.83/1.72 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.83/1.72 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.83/1.72 => ( ( Xz = Xx )
% 2.83/1.72 | ( Xz = Xy ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(upairsetIL_type,type,
% 2.83/1.72 upairsetIL: $o ).
% 2.83/1.72
% 2.83/1.72 thf(upairsetIL,definition,
% 2.83/1.72 ( upairsetIL
% 2.83/1.72 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(upairsetIR_type,type,
% 2.83/1.72 upairsetIR: $o ).
% 2.83/1.72
% 2.83/1.72 thf(upairsetIR,definition,
% 2.83/1.72 ( upairsetIR
% 2.83/1.72 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(emptyE1_type,type,
% 2.83/1.72 emptyE1: $o ).
% 2.83/1.72
% 2.83/1.72 thf(emptyE1,definition,
% 2.83/1.72 ( emptyE1
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o] :
% 2.83/1.72 ( ? [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 & ( Xphi @ Xx ) )
% 2.83/1.72 => ( ( ( dsetconstr @ A
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.72 = emptyset )
% 2.83/1.72 => $false ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(vacuousDall_type,type,
% 2.83/1.72 vacuousDall: $o ).
% 2.83/1.72
% 2.83/1.72 thf(vacuousDall,definition,
% 2.83/1.72 ( vacuousDall
% 2.83/1.72 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ emptyset )
% 2.83/1.72 => ( Xphi @ Xx ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(quantDeMorgan1_type,type,
% 2.83/1.72 quantDeMorgan1: $o ).
% 2.83/1.72
% 2.83/1.72 thf(quantDeMorgan1,definition,
% 2.83/1.72 ( quantDeMorgan1
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o] :
% 2.83/1.72 ( ~ ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ( Xphi @ Xx ) )
% 2.83/1.72 => ? [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(quantDeMorgan2_type,type,
% 2.83/1.72 quantDeMorgan2: $o ).
% 2.83/1.72
% 2.83/1.72 thf(quantDeMorgan2,definition,
% 2.83/1.72 ( quantDeMorgan2
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o] :
% 2.83/1.72 ( ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ~ ( Xphi @ Xx ) )
% 2.83/1.72 => ~ ? [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(quantDeMorgan3_type,type,
% 2.83/1.72 quantDeMorgan3: $o ).
% 2.83/1.72
% 2.83/1.72 thf(quantDeMorgan3,definition,
% 2.83/1.72 ( quantDeMorgan3
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o] :
% 2.83/1.72 ( ~ ? [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 & ( Xphi @ Xx ) )
% 2.83/1.72 => ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(quantDeMorgan4_type,type,
% 2.83/1.72 quantDeMorgan4: $o ).
% 2.83/1.72
% 2.83/1.72 thf(quantDeMorgan4,definition,
% 2.83/1.72 ( quantDeMorgan4
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o] :
% 2.83/1.72 ( ? [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 & ~ ( Xphi @ Xx ) )
% 2.83/1.72 => ~ ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(prop2setI_type,type,
% 2.83/1.72 prop2setI: $o ).
% 2.83/1.72
% 2.83/1.72 thf(prop2setI,definition,
% 2.83/1.72 ( prop2setI
% 2.83/1.72 = ( ! [Xphi: $o] :
% 2.83/1.72 ( Xphi
% 2.83/1.72 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(set2prop_type,type,
% 2.83/1.72 set2prop: $i > $o ).
% 2.83/1.72
% 2.83/1.72 thf(prop2set2propI_type,type,
% 2.83/1.72 prop2set2propI: $o ).
% 2.83/1.72
% 2.83/1.72 thf(prop2set2propI,definition,
% 2.83/1.72 ( prop2set2propI
% 2.83/1.72 = ( ! [Xphi: $o] :
% 2.83/1.72 ( Xphi
% 2.83/1.72 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(notdexE_type,type,
% 2.83/1.72 notdexE: $o ).
% 2.83/1.72
% 2.83/1.72 thf(notdexE,definition,
% 2.83/1.72 ( notdexE
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o] :
% 2.83/1.72 ( ~ ? [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 & ( Xphi @ Xx ) )
% 2.83/1.72 => ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(notdallE_type,type,
% 2.83/1.72 notdallE: $o ).
% 2.83/1.72
% 2.83/1.72 thf(notdallE,definition,
% 2.83/1.72 ( notdallE
% 2.83/1.72 = ( ! [A: $i,Xphi: $i > $o] :
% 2.83/1.72 ( ~ ! [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 => ( Xphi @ Xx ) )
% 2.83/1.72 => ? [Xx: $i] :
% 2.83/1.72 ( ( in @ Xx @ A )
% 2.83/1.72 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(exuI1_type,type,
% 2.83/1.72 exuI1: $o ).
% 2.83/1.72
% 2.83/1.72 thf(exuI1,definition,
% 2.83/1.72 ( exuI1
% 2.83/1.72 = ( ! [Xphi: $i > $o] :
% 2.83/1.72 ( ? [Xx: $i] :
% 2.83/1.72 ( ( Xphi @ Xx )
% 2.83/1.72 & ! [Xy: $i] :
% 2.83/1.72 ( ( Xphi @ Xy )
% 2.83/1.72 => ( Xx = Xy ) ) )
% 2.83/1.72 => ( exu
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(exuI3_type,type,
% 2.83/1.72 exuI3: $o ).
% 2.83/1.72
% 2.83/1.72 thf(exuI3,definition,
% 2.83/1.72 ( exuI3
% 2.83/1.72 = ( ! [Xphi: $i > $o] :
% 2.83/1.72 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.83/1.72 => ( ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( Xphi @ Xx )
% 2.83/1.72 => ( ( Xphi @ Xy )
% 2.83/1.72 => ( Xx = Xy ) ) )
% 2.83/1.72 => ( exu
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(exuI2_type,type,
% 2.83/1.72 exuI2: $o ).
% 2.83/1.72
% 2.83/1.72 thf(exuI2,definition,
% 2.83/1.72 ( exuI2
% 2.83/1.72 = ( ! [Xphi: $i > $o] :
% 2.83/1.72 ( ? [Xx: $i] :
% 2.83/1.72 ! [Xy: $i] :
% 2.83/1.72 ( ( Xphi @ Xy )
% 2.83/1.72 <=> ( Xy = Xx ) )
% 2.83/1.72 => ( exu
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(inCongP_type,type,
% 2.83/1.72 inCongP: $o ).
% 2.83/1.72
% 2.83/1.72 thf(inCongP,definition,
% 2.83/1.72 ( inCongP
% 2.83/1.72 = ( ! [A: $i,B: $i] :
% 2.83/1.72 ( ( A = B )
% 2.83/1.72 => ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( Xx = Xy )
% 2.83/1.72 => ( ( in @ Xx @ A )
% 2.83/1.72 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(in__Cong_type,type,
% 2.83/1.72 in__Cong: $o ).
% 2.83/1.72
% 2.83/1.72 thf(in__Cong,definition,
% 2.83/1.72 ( in__Cong
% 2.83/1.72 = ( ! [A: $i,B: $i] :
% 2.83/1.72 ( ( A = B )
% 2.83/1.72 => ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( Xx = Xy )
% 2.83/1.72 => ( ( in @ Xx @ A )
% 2.83/1.72 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(exuE3u_type,type,
% 2.83/1.72 exuE3u: $o ).
% 2.83/1.72
% 2.83/1.72 thf(exuE3u,definition,
% 2.83/1.72 ( exuE3u
% 2.83/1.72 = ( ! [Xphi: $i > $o] :
% 2.83/1.72 ( ( exu
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.72 => ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( Xphi @ Xx )
% 2.83/1.72 => ( ( Xphi @ Xy )
% 2.83/1.72 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(exu__Cong_type,type,
% 2.83/1.72 exu__Cong: $o ).
% 2.83/1.72
% 2.83/1.72 thf(exu__Cong,definition,
% 2.83/1.72 ( exu__Cong
% 2.83/1.72 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.83/1.72 ( ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( Xx = Xy )
% 2.83/1.72 => ( ( Xphi @ Xx )
% 2.83/1.72 <=> ( Xpsi @ Xy ) ) )
% 2.83/1.72 => ( ( exu
% 2.83/1.72 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.72 <=> ( exu
% 2.83/1.72 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(emptyset__Cong_type,type,
% 2.83/1.72 emptyset__Cong: $o ).
% 2.83/1.72
% 2.83/1.72 thf(emptyset__Cong,definition,
% 2.83/1.72 ( emptyset__Cong
% 2.83/1.72 = ( emptyset = emptyset ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoin__Cong_type,type,
% 2.83/1.72 setadjoin__Cong: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setadjoin__Cong,definition,
% 2.83/1.72 ( setadjoin__Cong
% 2.83/1.72 = ( ! [Xx: $i,Xy: $i] :
% 2.83/1.72 ( ( Xx = Xy )
% 2.83/1.72 => ! [Xz: $i,Xu: $i] :
% 2.83/1.72 ( ( Xz = Xu )
% 2.83/1.72 => ( ( setadjoin @ Xx @ Xz )
% 2.83/1.72 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(powerset__Cong_type,type,
% 2.83/1.72 powerset__Cong: $o ).
% 2.83/1.72
% 2.83/1.72 thf(powerset__Cong,definition,
% 2.83/1.72 ( powerset__Cong
% 2.83/1.72 = ( ! [A: $i,B: $i] :
% 2.83/1.72 ( ( A = B )
% 2.83/1.72 => ( ( powerset @ A )
% 2.83/1.72 = ( powerset @ B ) ) ) ) ) ).
% 2.83/1.72
% 2.83/1.72 thf(setunion__Cong_type,type,
% 2.83/1.72 setunion__Cong: $o ).
% 2.83/1.72
% 2.83/1.72 thf(setunion__Cong,definition,
% 2.83/1.72 ( setunion__Cong
% 2.83/1.72 = ( ! [A: $i,B: $i] :
% 2.83/1.72 ( ( A = B )
% 2.83/1.72 => ( ( setunion @ A )
% 2.83/1.73 = ( setunion @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(omega__Cong_type,type,
% 2.83/1.73 omega__Cong: $o ).
% 2.83/1.73
% 2.83/1.73 thf(omega__Cong,definition,
% 2.83/1.73 ( omega__Cong
% 2.83/1.73 = ( omega = omega ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(exuEu_type,type,
% 2.83/1.73 exuEu: $o ).
% 2.83/1.73
% 2.83/1.73 thf(exuEu,definition,
% 2.83/1.73 ( exuEu
% 2.83/1.73 = ( ! [Xphi: $i > $o] :
% 2.83/1.73 ( ( exu
% 2.83/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.73 => ! [Xx: $i,Xy: $i] :
% 2.83/1.73 ( ( Xphi @ Xx )
% 2.83/1.73 => ( ( Xphi @ Xy )
% 2.83/1.73 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(descr__Cong_type,type,
% 2.83/1.73 descr__Cong: $o ).
% 2.83/1.73
% 2.83/1.73 thf(descr__Cong,definition,
% 2.83/1.73 ( descr__Cong
% 2.83/1.73 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.83/1.73 ( ! [Xx: $i,Xy: $i] :
% 2.83/1.73 ( ( Xx = Xy )
% 2.83/1.73 => ( ( Xphi @ Xx )
% 2.83/1.73 <=> ( Xpsi @ Xy ) ) )
% 2.83/1.73 => ( ( exu
% 2.83/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.73 => ( ( exu
% 2.83/1.73 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.83/1.73 => ( ( descr
% 2.83/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.73 = ( descr
% 2.83/1.73 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(dsetconstr__Cong_type,type,
% 2.83/1.73 dsetconstr__Cong: $o ).
% 2.83/1.73
% 2.83/1.73 thf(dsetconstr__Cong,definition,
% 2.83/1.73 ( dsetconstr__Cong
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( A = B )
% 2.83/1.73 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.83/1.73 ( ! [Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ! [Xy: $i] :
% 2.83/1.73 ( ( in @ Xy @ B )
% 2.83/1.73 => ( ( Xx = Xy )
% 2.83/1.73 => ( ( Xphi @ Xx )
% 2.83/1.73 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.83/1.73 => ( ( dsetconstr @ A
% 2.83/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.73 = ( dsetconstr @ B
% 2.83/1.73 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(subset_type,type,
% 2.83/1.73 subset: $i > $i > $o ).
% 2.83/1.73
% 2.83/1.73 thf(disjoint_type,type,
% 2.83/1.73 disjoint: $i > $i > $o ).
% 2.83/1.73
% 2.83/1.73 thf(setsmeet_type,type,
% 2.83/1.73 setsmeet: $i > $i > $o ).
% 2.83/1.73
% 2.83/1.73 thf(subsetI1_type,type,
% 2.83/1.73 subsetI1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(subsetI1,definition,
% 2.83/1.73 ( subsetI1
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ! [Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( in @ Xx @ B ) )
% 2.83/1.73 => ( subset @ A @ B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(eqimpsubset2_type,type,
% 2.83/1.73 eqimpsubset2: $o ).
% 2.83/1.73
% 2.83/1.73 thf(eqimpsubset2,definition,
% 2.83/1.73 ( eqimpsubset2
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( A = B )
% 2.83/1.73 => ( subset @ B @ A ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(eqimpsubset1_type,type,
% 2.83/1.73 eqimpsubset1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(eqimpsubset1,definition,
% 2.83/1.73 ( eqimpsubset1
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( A = B )
% 2.83/1.73 => ( subset @ A @ B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(subsetI2_type,type,
% 2.83/1.73 subsetI2: $o ).
% 2.83/1.73
% 2.83/1.73 thf(subsetI2,definition,
% 2.83/1.73 ( subsetI2
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ! [Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( in @ Xx @ B ) )
% 2.83/1.73 => ( subset @ A @ B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(emptysetsubset_type,type,
% 2.83/1.73 emptysetsubset: $o ).
% 2.83/1.73
% 2.83/1.73 thf(emptysetsubset,definition,
% 2.83/1.73 ( emptysetsubset
% 2.83/1.73 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(subsetE_type,type,
% 2.83/1.73 subsetE: $o ).
% 2.83/1.73
% 2.83/1.73 thf(subsetE,definition,
% 2.83/1.73 ( subsetE
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( subset @ A @ B )
% 2.83/1.73 => ( ( in @ Xx @ A )
% 2.83/1.73 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(subsetE2_type,type,
% 2.83/1.73 subsetE2: $o ).
% 2.83/1.73
% 2.83/1.73 thf(subsetE2,definition,
% 2.83/1.73 ( subsetE2
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( subset @ A @ B )
% 2.83/1.73 => ( ~ ( in @ Xx @ B )
% 2.83/1.73 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(notsubsetI_type,type,
% 2.83/1.73 notsubsetI: $o ).
% 2.83/1.73
% 2.83/1.73 thf(notsubsetI,definition,
% 2.83/1.73 ( notsubsetI
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( ~ ( in @ Xx @ B )
% 2.83/1.73 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(notequalI1_type,type,
% 2.83/1.73 notequalI1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(notequalI1,definition,
% 2.83/1.73 ( notequalI1
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ~ ( subset @ A @ B )
% 2.83/1.73 => ( A != B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(notequalI2_type,type,
% 2.83/1.73 notequalI2: $o ).
% 2.83/1.73
% 2.83/1.73 thf(notequalI2,definition,
% 2.83/1.73 ( notequalI2
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( ~ ( in @ Xx @ B )
% 2.83/1.73 => ( A != B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(subsetRefl_type,type,
% 2.83/1.73 subsetRefl: $o ).
% 2.83/1.73
% 2.83/1.73 thf(subsetRefl,definition,
% 2.83/1.73 ( subsetRefl
% 2.83/1.73 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(subsetTrans_type,type,
% 2.83/1.73 subsetTrans: $o ).
% 2.83/1.73
% 2.83/1.73 thf(subsetTrans,definition,
% 2.83/1.73 ( subsetTrans
% 2.83/1.73 = ( ! [A: $i,B: $i,C: $i] :
% 2.83/1.73 ( ( subset @ A @ B )
% 2.83/1.73 => ( ( subset @ B @ C )
% 2.83/1.73 => ( subset @ A @ C ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setadjoinSub_type,type,
% 2.83/1.73 setadjoinSub: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setadjoinSub,definition,
% 2.83/1.73 ( setadjoinSub
% 2.83/1.73 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setadjoinSub2_type,type,
% 2.83/1.73 setadjoinSub2: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setadjoinSub2,definition,
% 2.83/1.73 ( setadjoinSub2
% 2.83/1.73 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.83/1.73 ( ( subset @ A @ B )
% 2.83/1.73 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(subset2powerset_type,type,
% 2.83/1.73 subset2powerset: $o ).
% 2.83/1.73
% 2.83/1.73 thf(subset2powerset,definition,
% 2.83/1.73 ( subset2powerset
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( subset @ A @ B )
% 2.83/1.73 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setextsub_type,type,
% 2.83/1.73 setextsub: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setextsub,definition,
% 2.83/1.73 ( setextsub
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( subset @ A @ B )
% 2.83/1.73 => ( ( subset @ B @ A )
% 2.83/1.73 => ( A = B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(subsetemptysetimpeq_type,type,
% 2.83/1.73 subsetemptysetimpeq: $o ).
% 2.83/1.73
% 2.83/1.73 thf(subsetemptysetimpeq,definition,
% 2.83/1.73 ( subsetemptysetimpeq
% 2.83/1.73 = ( ! [A: $i] :
% 2.83/1.73 ( ( subset @ A @ emptyset )
% 2.83/1.73 => ( A = emptyset ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(powersetI1_type,type,
% 2.83/1.73 powersetI1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(powersetI1,definition,
% 2.83/1.73 ( powersetI1
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( subset @ B @ A )
% 2.83/1.73 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(powersetE1_type,type,
% 2.83/1.73 powersetE1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(powersetE1,definition,
% 2.83/1.73 ( powersetE1
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( in @ B @ ( powerset @ A ) )
% 2.83/1.73 => ( subset @ B @ A ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(inPowerset_type,type,
% 2.83/1.73 inPowerset: $o ).
% 2.83/1.73
% 2.83/1.73 thf(inPowerset,definition,
% 2.83/1.73 ( inPowerset
% 2.83/1.73 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(powersetsubset_type,type,
% 2.83/1.73 powersetsubset: $o ).
% 2.83/1.73
% 2.83/1.73 thf(powersetsubset,definition,
% 2.83/1.73 ( powersetsubset
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( subset @ A @ B )
% 2.83/1.73 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(sepInPowerset_type,type,
% 2.83/1.73 sepInPowerset: $o ).
% 2.83/1.73
% 2.83/1.73 thf(sepInPowerset,definition,
% 2.83/1.73 ( sepInPowerset
% 2.83/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.83/1.73 ( in
% 2.83/1.73 @ ( dsetconstr @ A
% 2.83/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.73 @ ( powerset @ A ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(sepSubset_type,type,
% 2.83/1.73 sepSubset: $o ).
% 2.83/1.73
% 2.83/1.73 thf(sepSubset,definition,
% 2.83/1.73 ( sepSubset
% 2.83/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.83/1.73 ( subset
% 2.83/1.73 @ ( dsetconstr @ A
% 2.83/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.83/1.73 @ A ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binunion_type,type,
% 2.83/1.73 binunion: $i > $i > $i ).
% 2.83/1.73
% 2.83/1.73 thf(binunionIL_type,type,
% 2.83/1.73 binunionIL: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binunionIL,definition,
% 2.83/1.73 ( binunionIL
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(upairset2IR_type,type,
% 2.83/1.73 upairset2IR: $o ).
% 2.83/1.73
% 2.83/1.73 thf(upairset2IR,definition,
% 2.83/1.73 ( upairset2IR
% 2.83/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binunionIR_type,type,
% 2.83/1.73 binunionIR: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binunionIR,definition,
% 2.83/1.73 ( binunionIR
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ B )
% 2.83/1.73 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binunionEcases_type,type,
% 2.83/1.73 binunionEcases: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binunionEcases,definition,
% 2.83/1.73 ( binunionEcases
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.83/1.73 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.83/1.73 => ( ( ( in @ Xx @ A )
% 2.83/1.73 => Xphi )
% 2.83/1.73 => ( ( ( in @ Xx @ B )
% 2.83/1.73 => Xphi )
% 2.83/1.73 => Xphi ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binunionE_type,type,
% 2.83/1.73 binunionE: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binunionE,definition,
% 2.83/1.73 ( binunionE
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.83/1.73 => ( ( in @ Xx @ A )
% 2.83/1.73 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binunionLsub_type,type,
% 2.83/1.73 binunionLsub: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binunionLsub,definition,
% 2.83/1.73 ( binunionLsub
% 2.83/1.73 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binunionRsub_type,type,
% 2.83/1.73 binunionRsub: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binunionRsub,definition,
% 2.83/1.73 ( binunionRsub
% 2.83/1.73 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binintersect_type,type,
% 2.83/1.73 binintersect: $i > $i > $i ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectI_type,type,
% 2.83/1.73 binintersectI: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectI,definition,
% 2.83/1.73 ( binintersectI
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( ( in @ Xx @ B )
% 2.83/1.73 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectSubset5_type,type,
% 2.83/1.73 binintersectSubset5: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectSubset5,definition,
% 2.83/1.73 ( binintersectSubset5
% 2.83/1.73 = ( ! [A: $i,B: $i,C: $i] :
% 2.83/1.73 ( ( subset @ C @ A )
% 2.83/1.73 => ( ( subset @ C @ B )
% 2.83/1.73 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectEL_type,type,
% 2.83/1.73 binintersectEL: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectEL,definition,
% 2.83/1.73 ( binintersectEL
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.83/1.73 => ( in @ Xx @ A ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectLsub_type,type,
% 2.83/1.73 binintersectLsub: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectLsub,definition,
% 2.83/1.73 ( binintersectLsub
% 2.83/1.73 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectSubset2_type,type,
% 2.83/1.73 binintersectSubset2: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectSubset2,definition,
% 2.83/1.73 ( binintersectSubset2
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( subset @ A @ B )
% 2.83/1.73 => ( ( binintersect @ A @ B )
% 2.83/1.73 = A ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectSubset3_type,type,
% 2.83/1.73 binintersectSubset3: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectSubset3,definition,
% 2.83/1.73 ( binintersectSubset3
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( ( binintersect @ A @ B )
% 2.83/1.73 = B )
% 2.83/1.73 => ( subset @ B @ A ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectER_type,type,
% 2.83/1.73 binintersectER: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectER,definition,
% 2.83/1.73 ( binintersectER
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.83/1.73 => ( in @ Xx @ B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(disjointsetsI1_type,type,
% 2.83/1.73 disjointsetsI1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(disjointsetsI1,definition,
% 2.83/1.73 ( disjointsetsI1
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ~ ? [Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 & ( in @ Xx @ B ) )
% 2.83/1.73 => ( ( binintersect @ A @ B )
% 2.83/1.73 = emptyset ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectRsub_type,type,
% 2.83/1.73 binintersectRsub: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectRsub,definition,
% 2.83/1.73 ( binintersectRsub
% 2.83/1.73 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectSubset4_type,type,
% 2.83/1.73 binintersectSubset4: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectSubset4,definition,
% 2.83/1.73 ( binintersectSubset4
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( subset @ B @ A )
% 2.83/1.73 => ( ( binintersect @ A @ B )
% 2.83/1.73 = B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectSubset1_type,type,
% 2.83/1.73 binintersectSubset1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(binintersectSubset1,definition,
% 2.83/1.73 ( binintersectSubset1
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( ( binintersect @ A @ B )
% 2.83/1.73 = A )
% 2.83/1.73 => ( subset @ A @ B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(bs114d_type,type,
% 2.83/1.73 bs114d: $o ).
% 2.83/1.73
% 2.83/1.73 thf(bs114d,definition,
% 2.83/1.73 ( bs114d
% 2.83/1.73 = ( ! [A: $i,B: $i,C: $i] :
% 2.83/1.73 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.83/1.73 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(regular_type,type,
% 2.83/1.73 regular: $i > $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminus_type,type,
% 2.83/1.73 setminus: $i > $i > $i ).
% 2.83/1.73
% 2.83/1.73 thf(setminusI_type,type,
% 2.83/1.73 setminusI: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminusI,definition,
% 2.83/1.73 ( setminusI
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( ~ ( in @ Xx @ B )
% 2.83/1.73 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setminusEL_type,type,
% 2.83/1.73 setminusEL: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminusEL,definition,
% 2.83/1.73 ( setminusEL
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.83/1.73 => ( in @ Xx @ A ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setminusER_type,type,
% 2.83/1.73 setminusER: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminusER,definition,
% 2.83/1.73 ( setminusER
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.83/1.73 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setminusSubset2_type,type,
% 2.83/1.73 setminusSubset2: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminusSubset2,definition,
% 2.83/1.73 ( setminusSubset2
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( subset @ A @ B )
% 2.83/1.73 => ( ( setminus @ A @ B )
% 2.83/1.73 = emptyset ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setminusERneg_type,type,
% 2.83/1.73 setminusERneg: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminusERneg,definition,
% 2.83/1.73 ( setminusERneg
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.83/1.73 => ( ( in @ Xx @ A )
% 2.83/1.73 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setminusELneg_type,type,
% 2.83/1.73 setminusELneg: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminusELneg,definition,
% 2.83/1.73 ( setminusELneg
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.83/1.73 => ( ~ ( in @ Xx @ B )
% 2.83/1.73 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setminusILneg_type,type,
% 2.83/1.73 setminusILneg: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminusILneg,definition,
% 2.83/1.73 ( setminusILneg
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ~ ( in @ Xx @ A )
% 2.83/1.73 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setminusIRneg_type,type,
% 2.83/1.73 setminusIRneg: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminusIRneg,definition,
% 2.83/1.73 ( setminusIRneg
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ B )
% 2.83/1.73 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setminusLsub_type,type,
% 2.83/1.73 setminusLsub: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminusLsub,definition,
% 2.83/1.73 ( setminusLsub
% 2.83/1.73 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setminusSubset1_type,type,
% 2.83/1.73 setminusSubset1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setminusSubset1,definition,
% 2.83/1.73 ( setminusSubset1
% 2.83/1.73 = ( ! [A: $i,B: $i] :
% 2.83/1.73 ( ( ( setminus @ A @ B )
% 2.83/1.73 = emptyset )
% 2.83/1.73 => ( subset @ A @ B ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(symdiff_type,type,
% 2.83/1.73 symdiff: $i > $i > $i ).
% 2.83/1.73
% 2.83/1.73 thf(symdiffE_type,type,
% 2.83/1.73 symdiffE: $o ).
% 2.83/1.73
% 2.83/1.73 thf(symdiffE,definition,
% 2.83/1.73 ( symdiffE
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.83/1.73 => ! [Xphi: $o] :
% 2.83/1.73 ( ( ( in @ Xx @ A )
% 2.83/1.73 => ( ~ ( in @ Xx @ B )
% 2.83/1.73 => Xphi ) )
% 2.83/1.73 => ( ( ~ ( in @ Xx @ A )
% 2.83/1.73 => ( ( in @ Xx @ B )
% 2.83/1.73 => Xphi ) )
% 2.83/1.73 => Xphi ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(symdiffI1_type,type,
% 2.83/1.73 symdiffI1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(symdiffI1,definition,
% 2.83/1.73 ( symdiffI1
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( ~ ( in @ Xx @ B )
% 2.83/1.73 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(symdiffI2_type,type,
% 2.83/1.73 symdiffI2: $o ).
% 2.83/1.73
% 2.83/1.73 thf(symdiffI2,definition,
% 2.83/1.73 ( symdiffI2
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ~ ( in @ Xx @ A )
% 2.83/1.73 => ( ( in @ Xx @ B )
% 2.83/1.73 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(symdiffIneg1_type,type,
% 2.83/1.73 symdiffIneg1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(symdiffIneg1,definition,
% 2.83/1.73 ( symdiffIneg1
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( ( in @ Xx @ B )
% 2.83/1.73 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(symdiffIneg2_type,type,
% 2.83/1.73 symdiffIneg2: $o ).
% 2.83/1.73
% 2.83/1.73 thf(symdiffIneg2,definition,
% 2.83/1.73 ( symdiffIneg2
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ~ ( in @ Xx @ A )
% 2.83/1.73 => ( ~ ( in @ Xx @ B )
% 2.83/1.73 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(iskpair_type,type,
% 2.83/1.73 iskpair: $i > $o ).
% 2.83/1.73
% 2.83/1.73 thf(iskpair,definition,
% 2.83/1.73 ( iskpair
% 2.83/1.73 = ( ^ [A: $i] :
% 2.83/1.73 ? [Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ ( setunion @ A ) )
% 2.83/1.73 & ? [Xy: $i] :
% 2.83/1.73 ( ( in @ Xy @ ( setunion @ A ) )
% 2.83/1.73 & ( A
% 2.83/1.73 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(secondinupair_type,type,
% 2.83/1.73 secondinupair: $o ).
% 2.83/1.73
% 2.83/1.73 thf(secondinupair,definition,
% 2.83/1.73 ( secondinupair
% 2.83/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setukpairIL_type,type,
% 2.83/1.73 setukpairIL: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setukpairIL,definition,
% 2.83/1.73 ( setukpairIL
% 2.83/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(setukpairIR_type,type,
% 2.83/1.73 setukpairIR: $o ).
% 2.83/1.73
% 2.83/1.73 thf(setukpairIR,definition,
% 2.83/1.73 ( setukpairIR
% 2.83/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(kpairiskpair_type,type,
% 2.83/1.73 kpairiskpair: $o ).
% 2.83/1.73
% 2.83/1.73 thf(kpairiskpair,definition,
% 2.83/1.73 ( kpairiskpair
% 2.83/1.73 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(kpair_type,type,
% 2.83/1.73 kpair: $i > $i > $i ).
% 2.83/1.73
% 2.83/1.73 thf(kpair,definition,
% 2.83/1.73 ( kpair
% 2.83/1.73 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(kpairp_type,type,
% 2.83/1.73 kpairp: $o ).
% 2.83/1.73
% 2.83/1.73 thf(kpairp,definition,
% 2.83/1.73 ( kpairp
% 2.83/1.73 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(cartprod_type,type,
% 2.83/1.73 cartprod: $i > $i > $i ).
% 2.83/1.73
% 2.83/1.73 thf(singletonsubset_type,type,
% 2.83/1.73 singletonsubset: $o ).
% 2.83/1.73
% 2.83/1.73 thf(singletonsubset,definition,
% 2.83/1.73 ( singletonsubset
% 2.83/1.73 = ( ! [A: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(singletoninpowerset_type,type,
% 2.83/1.73 singletoninpowerset: $o ).
% 2.83/1.73
% 2.83/1.73 thf(singletoninpowerset,definition,
% 2.83/1.73 ( singletoninpowerset
% 2.83/1.73 = ( ! [A: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(singletoninpowunion_type,type,
% 2.83/1.73 singletoninpowunion: $o ).
% 2.83/1.73
% 2.83/1.73 thf(singletoninpowunion,definition,
% 2.83/1.73 ( singletoninpowunion
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(upairset2E_type,type,
% 2.83/1.73 upairset2E: $o ).
% 2.83/1.73
% 2.83/1.73 thf(upairset2E,definition,
% 2.83/1.73 ( upairset2E
% 2.83/1.73 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.83/1.73 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.83/1.73 => ( ( Xz = Xx )
% 2.83/1.73 | ( Xz = Xy ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(upairsubunion_type,type,
% 2.83/1.73 upairsubunion: $o ).
% 2.83/1.73
% 2.83/1.73 thf(upairsubunion,definition,
% 2.83/1.73 ( upairsubunion
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ! [Xy: $i] :
% 2.83/1.73 ( ( in @ Xy @ B )
% 2.83/1.73 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(upairinpowunion_type,type,
% 2.83/1.73 upairinpowunion: $o ).
% 2.83/1.73
% 2.83/1.73 thf(upairinpowunion,definition,
% 2.83/1.73 ( upairinpowunion
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ! [Xy: $i] :
% 2.83/1.73 ( ( in @ Xy @ B )
% 2.83/1.73 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(ubforcartprodlem1_type,type,
% 2.83/1.73 ubforcartprodlem1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(ubforcartprodlem1,definition,
% 2.83/1.73 ( ubforcartprodlem1
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ! [Xy: $i] :
% 2.83/1.73 ( ( in @ Xy @ B )
% 2.83/1.73 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(ubforcartprodlem2_type,type,
% 2.83/1.73 ubforcartprodlem2: $o ).
% 2.83/1.73
% 2.83/1.73 thf(ubforcartprodlem2,definition,
% 2.83/1.73 ( ubforcartprodlem2
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ! [Xy: $i] :
% 2.83/1.73 ( ( in @ Xy @ B )
% 2.83/1.73 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(ubforcartprodlem3_type,type,
% 2.83/1.73 ubforcartprodlem3: $o ).
% 2.83/1.73
% 2.83/1.73 thf(ubforcartprodlem3,definition,
% 2.83/1.73 ( ubforcartprodlem3
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ! [Xy: $i] :
% 2.83/1.73 ( ( in @ Xy @ B )
% 2.83/1.73 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(cartprodpairin_type,type,
% 2.83/1.73 cartprodpairin: $o ).
% 2.83/1.73
% 2.83/1.73 thf(cartprodpairin,definition,
% 2.83/1.73 ( cartprodpairin
% 2.83/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 => ! [Xy: $i] :
% 2.83/1.73 ( ( in @ Xy @ B )
% 2.83/1.73 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(cartprodmempair1_type,type,
% 2.83/1.73 cartprodmempair1: $o ).
% 2.83/1.73
% 2.83/1.73 thf(cartprodmempair1,definition,
% 2.83/1.73 ( cartprodmempair1
% 2.83/1.73 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.83/1.73 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.83/1.73 => ? [Xx: $i] :
% 2.83/1.73 ( ( in @ Xx @ A )
% 2.83/1.73 & ? [Xy: $i] :
% 2.83/1.73 ( ( in @ Xy @ B )
% 2.83/1.73 & ( Xu
% 2.83/1.73 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.83/1.73
% 2.83/1.73 thf(cartprodmempair,conjecture,
% 2.83/1.73 ( setextAx
% 2.83/1.73 => ( emptysetAx
% 2.83/1.73 => ( setadjoinAx
% 2.83/1.73 => ( powersetAx
% 2.83/1.73 => ( setunionAx
% 2.83/1.73 => ( omega0Ax
% 2.83/1.73 => ( omegaSAx
% 2.83/1.73 => ( omegaIndAx
% 2.83/1.73 => ( replAx
% 2.83/1.73 => ( foundationAx
% 2.83/1.73 => ( wellorderingAx
% 2.83/1.73 => ( descrp
% 2.83/1.73 => ( dsetconstrI
% 2.83/1.73 => ( dsetconstrEL
% 2.83/1.73 => ( dsetconstrER
% 2.83/1.73 => ( exuE1
% 2.83/1.73 => ( prop2setE
% 2.83/1.73 => ( emptysetE
% 2.83/1.73 => ( emptysetimpfalse
% 2.83/1.73 => ( notinemptyset
% 2.83/1.73 => ( exuE3e
% 2.83/1.73 => ( setext
% 2.83/1.73 => ( emptyI
% 2.83/1.73 => ( noeltsimpempty
% 2.83/1.73 => ( setbeta
% 2.83/1.73 => ( nonemptyE1
% 2.83/1.73 => ( nonemptyI
% 2.83/1.73 => ( nonemptyI1
% 2.83/1.73 => ( setadjoinIL
% 2.83/1.73 => ( emptyinunitempty
% 2.83/1.73 => ( setadjoinIR
% 2.83/1.73 => ( setadjoinE
% 2.83/1.73 => ( setadjoinOr
% 2.83/1.73 => ( setoftrueEq
% 2.83/1.73 => ( powersetI
% 2.83/1.73 => ( emptyinPowerset
% 2.83/1.73 => ( emptyInPowerset
% 2.83/1.73 => ( powersetE
% 2.83/1.73 => ( setunionI
% 2.83/1.73 => ( setunionE
% 2.83/1.73 => ( subPowSU
% 2.83/1.73 => ( exuE2
% 2.83/1.73 => ( nonemptyImpWitness
% 2.83/1.73 => ( uniqinunit
% 2.83/1.73 => ( notinsingleton
% 2.83/1.73 => ( eqinunit
% 2.83/1.73 => ( singletonsswitch
% 2.83/1.73 => ( upairsetE
% 2.83/1.73 => ( upairsetIL
% 2.83/1.73 => ( upairsetIR
% 2.83/1.73 => ( emptyE1
% 2.83/1.73 => ( vacuousDall
% 2.83/1.73 => ( quantDeMorgan1
% 2.83/1.73 => ( quantDeMorgan2
% 2.83/1.73 => ( quantDeMorgan3
% 2.83/1.73 => ( quantDeMorgan4
% 2.83/1.73 => ( prop2setI
% 2.83/1.73 => ( prop2set2propI
% 2.83/1.73 => ( notdexE
% 2.83/1.73 => ( notdallE
% 2.83/1.73 => ( exuI1
% 2.83/1.73 => ( exuI3
% 2.83/1.73 => ( exuI2
% 2.83/1.73 => ( inCongP
% 2.83/1.73 => ( in__Cong
% 2.83/1.73 => ( exuE3u
% 2.83/1.73 => ( exu__Cong
% 2.83/1.73 => ( emptyset__Cong
% 2.83/1.73 => ( setadjoin__Cong
% 2.83/1.73 => ( powerset__Cong
% 2.83/1.73 => ( setunion__Cong
% 2.83/1.73 => ( omega__Cong
% 2.83/1.73 => ( exuEu
% 2.83/1.73 => ( descr__Cong
% 2.83/1.73 => ( dsetconstr__Cong
% 2.83/1.73 => ( subsetI1
% 2.83/1.73 => ( eqimpsubset2
% 2.83/1.73 => ( eqimpsubset1
% 2.83/1.73 => ( subsetI2
% 2.83/1.73 => ( emptysetsubset
% 2.83/1.73 => ( subsetE
% 2.83/1.73 => ( subsetE2
% 2.83/1.73 => ( notsubsetI
% 2.83/1.73 => ( notequalI1
% 2.83/1.73 => ( notequalI2
% 2.83/1.73 => ( subsetRefl
% 2.83/1.73 => ( subsetTrans
% 2.83/1.73 => ( setadjoinSub
% 2.83/1.73 => ( setadjoinSub2
% 2.83/1.73 => ( subset2powerset
% 2.83/1.73 => ( setextsub
% 2.83/1.73 => ( subsetemptysetimpeq
% 2.83/1.73 => ( powersetI1
% 2.83/1.73 => ( powersetE1
% 2.83/1.73 => ( inPowerset
% 2.83/1.73 => ( powersetsubset
% 2.83/1.73 => ( sepInPowerset
% 2.83/1.73 => ( sepSubset
% 2.83/1.73 => ( binunionIL
% 2.83/1.73 => ( upairset2IR
% 2.83/1.73 => ( binunionIR
% 2.83/1.73 => ( binunionEcases
% 2.83/1.73 => ( binunionE
% 2.83/1.73 => ( binunionLsub
% 2.83/1.73 => ( binunionRsub
% 2.83/1.73 => ( binintersectI
% 2.83/1.73 => ( binintersectSubset5
% 2.83/1.73 => ( binintersectEL
% 2.83/1.73 => ( binintersectLsub
% 2.83/1.73 => ( binintersectSubset2
% 2.83/1.73 => ( binintersectSubset3
% 2.83/1.73 => ( binintersectER
% 2.83/1.73 => ( disjointsetsI1
% 2.83/1.73 => ( binintersectRsub
% 2.83/1.73 => ( binintersectSubset4
% 2.83/1.73 => ( binintersectSubset1
% 2.83/1.73 => ( bs114d
% 2.83/1.73 => ( setminusI
% 2.83/1.73 => ( setminusEL
% 2.83/1.73 => ( setminusER
% 2.83/1.73 => ( setminusSubset2
% 2.83/1.73 => ( setminusERneg
% 2.83/1.73 => ( setminusELneg
% 2.83/1.73 => ( setminusILneg
% 2.83/1.73 => ( setminusIRneg
% 2.83/1.73 => ( setminusLsub
% 2.83/1.73 => ( setminusSubset1
% 2.83/1.73 => ( symdiffE
% 2.83/1.73 => ( symdiffI1
% 2.83/1.73 => ( symdiffI2
% 2.83/1.73 => ( symdiffIneg1
% 2.83/1.73 => ( symdiffIneg2
% 2.83/1.73 => ( secondinupair
% 2.83/1.73 => ( setukpairIL
% 2.83/1.73 => ( setukpairIR
% 2.83/1.73 => ( kpairiskpair
% 2.83/1.73 => ( kpairp
% 2.83/1.73 => ( singletonsubset
% 2.83/1.73 => ( singletoninpowerset
% 2.83/1.73 => ( singletoninpowunion
% 2.83/1.73 => ( upairset2E
% 2.83/1.73 => ( upairsubunion
% 2.83/1.73 => ( upairinpowunion
% 2.83/1.73 => ( ubforcartprodlem1
% 2.83/1.73 => ( ubforcartprodlem2
% 2.83/1.73 => ( ubforcartprodlem3
% 2.83/1.73 => ( cartprodpairin
% 2.83/1.73 => ( cartprodmempair1
% 2.83/1.73 => ! [A: $i,B: $i,Xu: $i] :
% 2.83/1.73 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.83/1.73 => ( iskpair @ Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.83/1.73 ------------------------
% 2.83/1.75 % (26914)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/2Mi)
% 2.83/1.75 % (26912)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_26806 for (2999ds/4Mi)
% 2.83/1.75 % (26913)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_26806 for (2999ds/27Mi)
% 2.83/1.75 % (26915)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_26806 for (2999ds/2Mi)
% 2.83/1.75 % (26911)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/183Mi)
% 2.83/1.75 % (26916)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_26806 for (2999ds/275Mi)
% 2.83/1.75 % (26917)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/18Mi)
% 2.83/1.75 % (26914)Instruction limit reached!
% 2.83/1.75 % (26914)------------------------------
% 2.83/1.75 % (26914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.75 % (26914)Termination reason: Unknown
% 2.83/1.75 % (26915)Instruction limit reached!
% 2.83/1.75 % (26915)------------------------------
% 2.83/1.75 % (26915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.75 % (26914)Termination phase: shuffling
% 2.83/1.75
% 2.83/1.75 % (26914)Memory used [KB]: 1279
% 2.83/1.75 % (26914)Time elapsed: 0.003 s
% 2.83/1.75 % (26914)Instructions burned: 2 (million)
% 2.83/1.75 % (26914)------------------------------
% 2.83/1.75 % (26914)------------------------------
% 2.83/1.75 % (26915)Termination reason: Unknown
% 2.83/1.75 % (26915)Termination phase: shuffling
% 2.83/1.75
% 2.83/1.75 % (26915)Memory used [KB]: 1279
% 2.83/1.75 % (26915)Time elapsed: 0.003 s
% 2.83/1.75 % (26915)Instructions burned: 3 (million)
% 2.83/1.75 % (26915)------------------------------
% 2.83/1.75 % (26915)------------------------------
% 2.83/1.75 % (26912)Instruction limit reached!
% 2.83/1.75 % (26912)------------------------------
% 2.83/1.75 % (26912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.75 % (26912)Termination reason: Unknown
% 2.83/1.75 % (26912)Termination phase: shuffling
% 2.83/1.75
% 2.83/1.75 % (26912)Memory used [KB]: 1279
% 2.83/1.75 % (26912)Time elapsed: 0.004 s
% 2.83/1.75 % (26912)Instructions burned: 4 (million)
% 2.83/1.75 % (26912)------------------------------
% 2.83/1.75 % (26912)------------------------------
% 2.83/1.76 % (26917)Instruction limit reached!
% 2.83/1.76 % (26917)------------------------------
% 2.83/1.76 % (26917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.76 % (26917)Termination reason: Unknown
% 2.83/1.76 % (26917)Termination phase: Property scanning
% 2.83/1.76
% 2.83/1.76 % (26917)Memory used [KB]: 1535
% 2.83/1.76 % (26917)Time elapsed: 0.010 s
% 2.83/1.76 % (26917)Instructions burned: 18 (million)
% 2.83/1.76 % (26917)------------------------------
% 2.83/1.76 % (26917)------------------------------
% 2.83/1.77 % (26913)Instruction limit reached!
% 2.83/1.77 % (26913)------------------------------
% 2.83/1.77 % (26913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.77 % (26913)Termination reason: Unknown
% 2.83/1.77 % (26913)Termination phase: Property scanning
% 2.83/1.77
% 2.83/1.77 % (26913)Memory used [KB]: 1791
% 2.83/1.77 % (26913)Time elapsed: 0.015 s
% 2.83/1.77 % (26913)Instructions burned: 29 (million)
% 2.83/1.77 % (26913)------------------------------
% 2.83/1.77 % (26913)------------------------------
% 2.83/1.77 % (26918)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/3Mi)
% 2.83/1.77 % (26919)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_26806 for (2999ds/37Mi)
% 2.83/1.77 % (26920)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_26806 for (2999ds/15Mi)
% 2.83/1.77 % (26918)Instruction limit reached!
% 2.83/1.77 % (26918)------------------------------
% 2.83/1.77 % (26918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.77 % (26918)Termination reason: Unknown
% 2.83/1.77 % (26918)Termination phase: shuffling
% 2.83/1.77
% 2.83/1.77 % (26918)Memory used [KB]: 1279
% 2.83/1.77 % (26918)Time elapsed: 0.003 s
% 2.83/1.77 % (26918)Instructions burned: 3 (million)
% 2.83/1.77 % (26918)------------------------------
% 2.83/1.77 % (26918)------------------------------
% 2.83/1.78 % (26921)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_26806 for (2999ds/3Mi)
% 2.83/1.78 % (26920)Instruction limit reached!
% 2.83/1.78 % (26920)------------------------------
% 2.83/1.78 % (26920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.78 % (26920)Termination reason: Unknown
% 2.83/1.78 % (26920)Termination phase: Property scanning
% 2.83/1.78
% 2.83/1.78 % (26920)Memory used [KB]: 1535
% 2.83/1.78 % (26920)Time elapsed: 0.009 s
% 2.83/1.78 % (26920)Instructions burned: 15 (million)
% 2.83/1.78 % (26920)------------------------------
% 2.83/1.78 % (26920)------------------------------
% 2.83/1.78 % (26921)Instruction limit reached!
% 2.83/1.78 % (26921)------------------------------
% 2.83/1.78 % (26921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.78 % (26921)Termination reason: Unknown
% 2.83/1.78 % (26921)Termination phase: shuffling
% 2.83/1.78
% 2.83/1.78 % (26921)Memory used [KB]: 1279
% 2.83/1.78 % (26921)Time elapsed: 0.003 s
% 2.83/1.78 % (26921)Instructions burned: 3 (million)
% 2.83/1.78 % (26921)------------------------------
% 2.83/1.78 % (26921)------------------------------
% 2.83/1.78 % (26922)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_26806 for (2999ds/1041Mi)
% 2.83/1.79 % (26919)Instruction limit reached!
% 2.83/1.79 % (26919)------------------------------
% 2.83/1.79 % (26919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.79 % (26919)Termination reason: Unknown
% 2.83/1.79 % (26919)Termination phase: Property scanning
% 2.83/1.79
% 2.83/1.79 % (26919)Memory used [KB]: 1663
% 2.83/1.79 % (26919)Time elapsed: 0.018 s
% 2.83/1.79 % (26919)Instructions burned: 37 (million)
% 2.83/1.79 % (26919)------------------------------
% 2.83/1.79 % (26919)------------------------------
% 2.83/1.79 % (26923)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/7Mi)
% 2.83/1.79 % (26923)Instruction limit reached!
% 2.83/1.79 % (26923)------------------------------
% 2.83/1.79 % (26923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.83/1.79 % (26923)Termination reason: Unknown
% 2.83/1.79 % (26923)Termination phase: shuffling
% 2.83/1.79
% 2.83/1.79 % (26923)Memory used [KB]: 1407
% 2.83/1.79 % (26923)Time elapsed: 0.005 s
% 2.83/1.79 % (26923)Instructions burned: 7 (million)
% 2.83/1.79 % (26923)------------------------------
% 2.83/1.79 % (26923)------------------------------
% 2.83/1.79 % (26924)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/16Mi)
% 2.83/1.79 % (26925)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_26806 for (2999ds/3Mi)
% 2.86/1.80 % (26925)Instruction limit reached!
% 2.86/1.80 % (26925)------------------------------
% 2.86/1.80 % (26925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.80 % (26925)Termination reason: Unknown
% 2.86/1.80 % (26925)Termination phase: shuffling
% 2.86/1.80
% 2.86/1.80 % (26925)Memory used [KB]: 1279
% 2.86/1.80 % (26925)Time elapsed: 0.003 s
% 2.86/1.80 % (26925)Instructions burned: 3 (million)
% 2.86/1.80 % (26925)------------------------------
% 2.86/1.80 % (26925)------------------------------
% 2.86/1.80 % (26924)Instruction limit reached!
% 2.86/1.80 % (26924)------------------------------
% 2.86/1.80 % (26924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.80 % (26924)Termination reason: Unknown
% 2.86/1.80 % (26924)Termination phase: shuffling
% 2.86/1.80
% 2.86/1.80 % (26924)Memory used [KB]: 1535
% 2.86/1.80 % (26924)Time elapsed: 0.010 s
% 2.86/1.80 % (26924)Instructions burned: 17 (million)
% 2.86/1.80 % (26924)------------------------------
% 2.86/1.80 % (26924)------------------------------
% 2.86/1.80 % (26926)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_26806 for (2999ds/3Mi)
% 2.86/1.80 % (26926)Instruction limit reached!
% 2.86/1.80 % (26926)------------------------------
% 2.86/1.80 % (26926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.80 % (26926)Termination reason: Unknown
% 2.86/1.80 % (26926)Termination phase: shuffling
% 2.86/1.80
% 2.86/1.80 % (26926)Memory used [KB]: 1279
% 2.86/1.80 % (26926)Time elapsed: 0.003 s
% 2.86/1.80 % (26926)Instructions burned: 3 (million)
% 2.86/1.80 % (26926)------------------------------
% 2.86/1.80 % (26926)------------------------------
% 2.86/1.81 % (26927)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/7Mi)
% 2.86/1.81 % (26927)Instruction limit reached!
% 2.86/1.81 % (26927)------------------------------
% 2.86/1.81 % (26927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.81 % (26927)Termination reason: Unknown
% 2.86/1.81 % (26927)Termination phase: shuffling
% 2.86/1.81
% 2.86/1.81 % (26927)Memory used [KB]: 1407
% 2.86/1.81 % (26927)Time elapsed: 0.005 s
% 2.86/1.81 % (26927)Instructions burned: 7 (million)
% 2.86/1.81 % (26927)------------------------------
% 2.86/1.81 % (26927)------------------------------
% 2.86/1.81 % (26928)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/3Mi)
% 2.86/1.81 % (26928)Instruction limit reached!
% 2.86/1.81 % (26928)------------------------------
% 2.86/1.81 % (26928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.81 % (26928)Termination reason: Unknown
% 2.86/1.81 % (26928)Termination phase: shuffling
% 2.86/1.81
% 2.86/1.81 % (26928)Memory used [KB]: 1279
% 2.86/1.81 % (26928)Time elapsed: 0.003 s
% 2.86/1.81 % (26928)Instructions burned: 3 (million)
% 2.86/1.81 % (26928)------------------------------
% 2.86/1.81 % (26928)------------------------------
% 2.86/1.82 % (26929)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/4Mi)
% 2.86/1.82 % (26930)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/18Mi)
% 2.86/1.82 % (26929)Instruction limit reached!
% 2.86/1.82 % (26929)------------------------------
% 2.86/1.82 % (26929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.82 % (26929)Termination reason: Unknown
% 2.86/1.82 % (26929)Termination phase: shuffling
% 2.86/1.82
% 2.86/1.82 % (26929)Memory used [KB]: 1279
% 2.86/1.82 % (26929)Time elapsed: 0.004 s
% 2.86/1.82 % (26929)Instructions burned: 5 (million)
% 2.86/1.82 % (26929)------------------------------
% 2.86/1.82 % (26929)------------------------------
% 2.86/1.83 % (26931)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/710Mi)
% 2.86/1.83 % (26930)Instruction limit reached!
% 2.86/1.83 % (26930)------------------------------
% 2.86/1.83 % (26930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.83 % (26930)Termination reason: Unknown
% 2.86/1.83 % (26930)Termination phase: shuffling
% 2.86/1.83
% 2.86/1.83 % (26930)Memory used [KB]: 1663
% 2.86/1.83 % (26930)Time elapsed: 0.010 s
% 2.86/1.83 % (26930)Instructions burned: 18 (million)
% 2.86/1.83 % (26930)------------------------------
% 2.86/1.83 % (26930)------------------------------
% 2.86/1.83 % (26932)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/6Mi)
% 2.86/1.83 % (26932)Instruction limit reached!
% 2.86/1.83 % (26932)------------------------------
% 2.86/1.83 % (26932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.83 % (26932)Termination reason: Unknown
% 2.86/1.83 % (26932)Termination phase: shuffling
% 2.86/1.83
% 2.86/1.83 % (26932)Memory used [KB]: 1279
% 2.86/1.83 % (26932)Time elapsed: 0.004 s
% 2.86/1.83 % (26932)Instructions burned: 6 (million)
% 2.86/1.83 % (26932)------------------------------
% 2.86/1.83 % (26932)------------------------------
% 2.86/1.84 % (26911)Instruction limit reached!
% 2.86/1.84 % (26911)------------------------------
% 2.86/1.84 % (26911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.84 % (26911)Termination reason: Unknown
% 2.86/1.84 % (26911)Termination phase: Saturation
% 2.86/1.84
% 2.86/1.84 % (26911)Memory used [KB]: 7164
% 2.86/1.84 % (26911)Time elapsed: 0.087 s
% 2.86/1.84 % (26911)Instructions burned: 184 (million)
% 2.86/1.84 % (26933)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_26806 for (2999ds/902Mi)
% 2.86/1.84 % (26911)------------------------------
% 2.86/1.84 % (26911)------------------------------
% 2.86/1.85 % (26934)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_26806 for (2999ds/21Mi)
% 2.86/1.85 % (26935)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26806 for (2999ds/5Mi)
% 2.86/1.85 % (26935)Instruction limit reached!
% 2.86/1.85 % (26935)------------------------------
% 2.86/1.85 % (26935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.85 % (26935)Termination reason: Unknown
% 2.86/1.85 % (26935)Termination phase: shuffling
% 2.86/1.85
% 2.86/1.85 % (26935)Memory used [KB]: 1279
% 2.86/1.85 % (26935)Time elapsed: 0.004 s
% 2.86/1.85 % (26935)Instructions burned: 5 (million)
% 2.86/1.85 % (26935)------------------------------
% 2.86/1.85 % (26935)------------------------------
% 2.86/1.85 % (26936)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_26806 for (2999ds/6Mi)
% 2.86/1.86 % (26934)Instruction limit reached!
% 2.86/1.86 % (26934)------------------------------
% 2.86/1.86 % (26934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.86 % (26934)Termination reason: Unknown
% 2.86/1.86 % (26934)Termination phase: shuffling
% 2.86/1.86
% 2.86/1.86 % (26934)Memory used [KB]: 1663
% 2.86/1.86 % (26934)Time elapsed: 0.012 s
% 2.86/1.86 % (26934)Instructions burned: 22 (million)
% 2.86/1.86 % (26934)------------------------------
% 2.86/1.86 % (26934)------------------------------
% 2.86/1.86 % (26936)Instruction limit reached!
% 2.86/1.86 % (26936)------------------------------
% 2.86/1.86 % (26936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.86 % (26936)Termination reason: Unknown
% 2.86/1.86 % (26936)Termination phase: shuffling
% 2.86/1.86
% 2.86/1.86 % (26936)Memory used [KB]: 1407
% 2.86/1.86 % (26936)Time elapsed: 0.005 s
% 2.86/1.86 % (26936)Instructions burned: 6 (million)
% 2.86/1.86 % (26936)------------------------------
% 2.86/1.86 % (26936)------------------------------
% 2.86/1.87 % (26937)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26806 for (2998ds/377Mi)
% 2.86/1.87 % (26938)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_26806 for (2998ds/779Mi)
% 2.86/1.87 % (26939)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_26806 for (2998ds/19Mi)
% 2.86/1.88 % (26939)Instruction limit reached!
% 2.86/1.88 % (26939)------------------------------
% 2.86/1.88 % (26939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.88 % (26939)Termination reason: Unknown
% 2.86/1.88 % (26939)Termination phase: shuffling
% 2.86/1.88
% 2.86/1.88 % (26939)Memory used [KB]: 1663
% 2.86/1.88 % (26939)Time elapsed: 0.011 s
% 2.86/1.88 % (26939)Instructions burned: 20 (million)
% 2.86/1.88 % (26939)------------------------------
% 2.86/1.88 % (26939)------------------------------
% 2.86/1.89 % (26916)Instruction limit reached!
% 2.86/1.89 % (26916)------------------------------
% 2.86/1.89 % (26916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.89 % (26916)Termination reason: Unknown
% 2.86/1.89 % (26916)Termination phase: Saturation
% 2.86/1.89
% 2.86/1.89 % (26916)Memory used [KB]: 8059
% 2.86/1.89 % (26916)Time elapsed: 0.137 s
% 2.86/1.89 % (26916)Instructions burned: 276 (million)
% 2.86/1.89 % (26916)------------------------------
% 2.86/1.89 % (26916)------------------------------
% 2.86/1.90 % (26940)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26806 for (2998ds/879Mi)
% 2.86/1.90 % (26941)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26806 for (2998ds/17Mi)
% 2.86/1.91 % (26941)Instruction limit reached!
% 2.86/1.91 % (26941)------------------------------
% 2.86/1.91 % (26941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.91 % (26941)Termination reason: Unknown
% 2.86/1.91 % (26941)Termination phase: shuffling
% 2.86/1.91
% 2.86/1.91 % (26941)Memory used [KB]: 1663
% 2.86/1.91 % (26941)Time elapsed: 0.010 s
% 2.86/1.91 % (26941)Instructions burned: 18 (million)
% 2.86/1.91 % (26941)------------------------------
% 2.86/1.91 % (26941)------------------------------
% 2.86/1.91 % (26933)Refutation not found, incomplete strategy
% 2.86/1.91 % (26933)------------------------------
% 2.86/1.91 % (26933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.91 % (26933)Termination reason: Refutation not found, incomplete strategy
% 2.86/1.91
% 2.86/1.91
% 2.86/1.91 % (26933)Memory used [KB]: 7675
% 2.86/1.91 % (26933)Time elapsed: 0.077 s
% 2.86/1.91 % (26933)Instructions burned: 155 (million)
% 2.86/1.91 % (26933)------------------------------
% 2.86/1.91 % (26933)------------------------------
% 2.86/1.93 % (26942)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26806 for (2998ds/3Mi)
% 2.86/1.93 % (26942)Instruction limit reached!
% 2.86/1.93 % (26942)------------------------------
% 2.86/1.93 % (26942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.93 % (26942)Termination reason: Unknown
% 2.86/1.93 % (26942)Termination phase: shuffling
% 2.86/1.93
% 2.86/1.93 % (26942)Memory used [KB]: 1279
% 2.86/1.93 % (26942)Time elapsed: 0.003 s
% 2.86/1.93 % (26942)Instructions burned: 3 (million)
% 2.86/1.93 % (26942)------------------------------
% 2.86/1.93 % (26942)------------------------------
% 2.86/1.93 % (26943)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26806 for (2998ds/30Mi)
% 2.86/1.94 % (26943)Instruction limit reached!
% 2.86/1.94 % (26943)------------------------------
% 2.86/1.94 % (26943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/1.94 % (26943)Termination reason: Unknown
% 2.86/1.94 % (26943)Termination phase: Property scanning
% 2.86/1.94
% 2.86/1.94 % (26943)Memory used [KB]: 1663
% 2.86/1.94 % (26943)Time elapsed: 0.016 s
% 2.86/1.94 % (26943)Instructions burned: 32 (million)
% 2.86/1.94 % (26943)------------------------------
% 2.86/1.94 % (26943)------------------------------
% 2.86/1.95 % (26944)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26806 for (2997ds/127Mi)
% 2.86/1.96 % (26945)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26806 for (2997ds/100Mi)
% 2.86/2.00 % (26944)Instruction limit reached!
% 2.86/2.00 % (26944)------------------------------
% 2.86/2.00 % (26944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/2.00 % (26944)Termination reason: Unknown
% 2.86/2.00 % (26944)Termination phase: Saturation
% 2.86/2.00
% 2.86/2.00 % (26944)Memory used [KB]: 6780
% 2.86/2.00 % (26944)Time elapsed: 0.057 s
% 2.86/2.00 % (26944)Instructions burned: 127 (million)
% 2.86/2.00 % (26944)------------------------------
% 2.86/2.00 % (26944)------------------------------
% 2.86/2.01 % (26945)Instruction limit reached!
% 2.86/2.01 % (26945)------------------------------
% 2.86/2.01 % (26945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/2.01 % (26945)Termination reason: Unknown
% 2.86/2.01 % (26945)Termination phase: Saturation
% 2.86/2.01
% 2.86/2.01 % (26945)Memory used [KB]: 6652
% 2.86/2.01 % (26945)Time elapsed: 0.048 s
% 2.86/2.01 % (26945)Instructions burned: 101 (million)
% 2.86/2.01 % (26945)------------------------------
% 2.86/2.01 % (26945)------------------------------
% 2.86/2.02 % (26946)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_26806 for (2997ds/3Mi)
% 2.86/2.02 % (26946)Instruction limit reached!
% 2.86/2.02 % (26946)------------------------------
% 2.86/2.02 % (26946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.86/2.02 % (26946)Termination reason: Unknown
% 2.86/2.02 % (26946)Termination phase: shuffling
% 2.86/2.02
% 2.86/2.02 % (26946)Memory used [KB]: 1279
% 2.86/2.02 % (26946)Time elapsed: 0.003 s
% 2.86/2.02 % (26946)Instructions burned: 3 (million)
% 2.86/2.02 % (26946)------------------------------
% 2.86/2.02 % (26946)------------------------------
% 2.86/2.02 % (26947)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_26806 for (2997ds/20Mi)
% 4.80/2.03 % (26947)Instruction limit reached!
% 4.80/2.03 % (26947)------------------------------
% 4.80/2.03 % (26947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.80/2.03 % (26947)Termination reason: Unknown
% 4.80/2.03 % (26947)Termination phase: SInE selection
% 4.80/2.03
% 4.80/2.03 % (26947)Memory used [KB]: 1535
% 4.80/2.03 % (26947)Time elapsed: 0.012 s
% 4.80/2.03 % (26947)Instructions burned: 20 (million)
% 4.80/2.03 % (26947)------------------------------
% 4.80/2.03 % (26947)------------------------------
% 4.80/2.04 % (26948)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_26806 for (2997ds/86Mi)
% 4.80/2.05 % (26949)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_26806 for (2997ds/107Mi)
% 4.80/2.06 % (26937)Instruction limit reached!
% 4.80/2.06 % (26937)------------------------------
% 4.80/2.06 % (26937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.80/2.06 % (26937)Termination reason: Unknown
% 4.80/2.06 % (26937)Termination phase: Saturation
% 4.80/2.06
% 4.80/2.06 % (26937)Memory used [KB]: 7803
% 4.80/2.06 % (26937)Time elapsed: 0.214 s
% 4.80/2.06 % (26937)Instructions burned: 377 (million)
% 4.80/2.06 % (26937)------------------------------
% 4.80/2.06 % (26937)------------------------------
% 4.80/2.08 % (26948)Instruction limit reached!
% 4.80/2.08 % (26948)------------------------------
% 4.80/2.08 % (26948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.80/2.08 % (26948)Termination reason: Unknown
% 4.80/2.08 % (26948)Termination phase: Saturation
% 4.80/2.08
% 4.80/2.08 % (26948)Memory used [KB]: 6524
% 4.80/2.08 % (26948)Time elapsed: 0.040 s
% 4.80/2.08 % (26948)Instructions burned: 86 (million)
% 4.80/2.08 % (26948)------------------------------
% 4.80/2.08 % (26948)------------------------------
% 4.80/2.08 % (26950)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_26806 for (2996ds/39Mi)
% 4.80/2.09 % (26951)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_26806 for (2996ds/448Mi)
% 4.80/2.09 % (26950)Instruction limit reached!
% 4.80/2.09 % (26950)------------------------------
% 4.80/2.09 % (26950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.80/2.09 % (26950)Termination reason: Unknown
% 4.80/2.09 % (26950)Termination phase: Property scanning
% 4.80/2.09
% 4.80/2.09 % (26950)Memory used [KB]: 1791
% 4.80/2.09 % (26950)Time elapsed: 0.019 s
% 4.80/2.09 % (26950)Instructions burned: 39 (million)
% 4.80/2.09 % (26950)------------------------------
% 4.80/2.09 % (26950)------------------------------
% 4.80/2.10 % (26949)Instruction limit reached!
% 4.80/2.10 % (26949)------------------------------
% 4.80/2.10 % (26949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.80/2.10 % (26949)Termination reason: Unknown
% 4.80/2.10 % (26949)Termination phase: Saturation
% 4.80/2.10
% 4.80/2.10 % (26949)Memory used [KB]: 6780
% 4.80/2.10 % (26949)Time elapsed: 0.050 s
% 4.80/2.10 % (26949)Instructions burned: 107 (million)
% 4.80/2.10 % (26949)------------------------------
% 4.80/2.10 % (26949)------------------------------
% 4.80/2.11 % (26952)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_26806 for (2996ds/46Mi)
% 4.80/2.11 % (26953)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_26806 for (2996ds/98Mi)
% 5.43/2.13 % (26952)Instruction limit reached!
% 5.43/2.13 % (26952)------------------------------
% 5.43/2.13 % (26952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.43/2.13 % (26952)Termination reason: Unknown
% 5.43/2.13 % (26952)Termination phase: Clausification
% 5.43/2.13
% 5.43/2.13 % (26952)Memory used [KB]: 1791
% 5.43/2.13 % (26952)Time elapsed: 0.022 s
% 5.43/2.13 % (26952)Instructions burned: 46 (million)
% 5.43/2.13 % (26952)------------------------------
% 5.43/2.13 % (26952)------------------------------
% 5.43/2.15 % (26954)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_26806 for (2996ds/507Mi)
% 5.43/2.15 % (26938)Instruction limit reached!
% 5.43/2.15 % (26938)------------------------------
% 5.43/2.15 % (26938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.43/2.15 % (26938)Termination reason: Unknown
% 5.43/2.15 % (26938)Termination phase: Saturation
% 5.43/2.15
% 5.43/2.15 % (26938)Memory used [KB]: 6652
% 5.43/2.15 % (26938)Time elapsed: 0.281 s
% 5.43/2.15 % (26938)Instructions burned: 780 (million)
% 5.43/2.15 % (26938)------------------------------
% 5.43/2.15 % (26938)------------------------------
% 5.43/2.16 % (26953)Instruction limit reached!
% 5.43/2.16 % (26953)------------------------------
% 5.43/2.16 % (26953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.43/2.16 % (26953)Termination reason: Unknown
% 5.43/2.16 % (26953)Termination phase: Saturation
% 5.43/2.16
% 5.43/2.16 % (26953)Memory used [KB]: 2046
% 5.43/2.16 % (26953)Time elapsed: 0.044 s
% 5.43/2.16 % (26953)Instructions burned: 99 (million)
% 5.43/2.16 % (26953)------------------------------
% 5.43/2.16 % (26953)------------------------------
% 5.43/2.17 % (26955)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_26806 for (2995ds/149Mi)
% 5.43/2.17 % (26956)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_26806 for (2995ds/39Mi)
% 5.43/2.18 % (26922)Instruction limit reached!
% 5.43/2.18 % (26922)------------------------------
% 5.43/2.18 % (26922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.43/2.18 % (26922)Termination reason: Unknown
% 5.43/2.18 % (26922)Termination phase: Saturation
% 5.43/2.18
% 5.43/2.18 % (26922)Memory used [KB]: 9338
% 5.43/2.18 % (26922)Time elapsed: 0.396 s
% 5.43/2.18 % (26922)Instructions burned: 1041 (million)
% 5.43/2.18 % (26922)------------------------------
% 5.43/2.18 % (26922)------------------------------
% 5.43/2.19 % (26931)Instruction limit reached!
% 5.43/2.19 % (26931)------------------------------
% 5.43/2.19 % (26931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.43/2.19 % (26931)Termination reason: Unknown
% 5.43/2.19 % (26931)Termination phase: Saturation
% 5.43/2.19
% 5.43/2.19 % (26931)Memory used [KB]: 9083
% 5.43/2.19 % (26931)Time elapsed: 0.362 s
% 5.43/2.19 % (26931)Instructions burned: 711 (million)
% 5.43/2.19 % (26931)------------------------------
% 5.43/2.19 % (26931)------------------------------
% 5.43/2.19 % (26956)Instruction limit reached!
% 5.43/2.19 % (26956)------------------------------
% 5.43/2.19 % (26956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.43/2.19 % (26956)Termination reason: Unknown
% 5.43/2.19 % (26956)Termination phase: Property scanning
% 5.43/2.19
% 5.43/2.19 % (26956)Memory used [KB]: 1791
% 5.43/2.19 % (26956)Time elapsed: 0.020 s
% 5.43/2.19 % (26956)Instructions burned: 40 (million)
% 5.43/2.19 % (26956)------------------------------
% 5.43/2.19 % (26956)------------------------------
% 5.43/2.19 % (26957)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_26806 for (2995ds/6Mi)
% 5.43/2.20 % (26957)Instruction limit reached!
% 5.43/2.20 % (26957)------------------------------
% 5.43/2.20 % (26957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.43/2.20 % (26957)Termination reason: Unknown
% 5.43/2.20 % (26957)Termination phase: shuffling
% 5.43/2.20
% 5.43/2.20 % (26957)Memory used [KB]: 1407
% 5.43/2.20 % (26957)Time elapsed: 0.005 s
% 5.43/2.20 % (26957)Instructions burned: 7 (million)
% 5.43/2.20 % (26957)------------------------------
% 5.43/2.20 % (26957)------------------------------
% 5.78/2.20 % (26958)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_26806 for (2995ds/1087Mi)
% 5.78/2.21 % (26959)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_26806 for (2995ds/47Mi)
% 5.78/2.21 % (26960)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_26806 for (2995ds/44Mi)
% 5.78/2.23 % (26959)Instruction limit reached!
% 5.78/2.23 % (26959)------------------------------
% 5.78/2.23 % (26959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.23 % (26959)Termination reason: Unknown
% 5.78/2.23 % (26959)Termination phase: Property scanning
% 5.78/2.23
% 5.78/2.23 % (26959)Memory used [KB]: 1791
% 5.78/2.23 % (26959)Time elapsed: 0.023 s
% 5.78/2.23 % (26959)Instructions burned: 49 (million)
% 5.78/2.23 % (26959)------------------------------
% 5.78/2.23 % (26959)------------------------------
% 5.78/2.23 % (26960)Instruction limit reached!
% 5.78/2.23 % (26960)------------------------------
% 5.78/2.23 % (26960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.23 % (26960)Termination reason: Unknown
% 5.78/2.23 % (26960)Termination phase: SInE selection
% 5.78/2.23
% 5.78/2.23 % (26960)Memory used [KB]: 1791
% 5.78/2.23 % (26960)Time elapsed: 0.021 s
% 5.78/2.23 % (26960)Instructions burned: 45 (million)
% 5.78/2.23 % (26960)------------------------------
% 5.78/2.23 % (26960)------------------------------
% 5.78/2.24 % (26955)Instruction limit reached!
% 5.78/2.24 % (26955)------------------------------
% 5.78/2.24 % (26955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.24 % (26955)Termination reason: Unknown
% 5.78/2.24 % (26955)Termination phase: Saturation
% 5.78/2.24
% 5.78/2.24 % (26955)Memory used [KB]: 7036
% 5.78/2.24 % (26955)Time elapsed: 0.094 s
% 5.78/2.24 % (26955)Instructions burned: 150 (million)
% 5.78/2.24 % (26955)------------------------------
% 5.78/2.24 % (26955)------------------------------
% 5.78/2.24 % (26961)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_26806 for (2995ds/432Mi)
% 5.78/2.25 % (26962)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_26806 for (2994ds/62Mi)
% 5.78/2.26 % (26963)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_26806 for (2994ds/31Mi)
% 5.78/2.26 % (26951)Instruction limit reached!
% 5.78/2.26 % (26951)------------------------------
% 5.78/2.26 % (26951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.26 % (26951)Termination reason: Unknown
% 5.78/2.26 % (26951)Termination phase: Saturation
% 5.78/2.26
% 5.78/2.26 % (26951)Memory used [KB]: 6524
% 5.78/2.26 % (26951)Time elapsed: 0.166 s
% 5.78/2.26 % (26951)Instructions burned: 451 (million)
% 5.78/2.26 % (26951)------------------------------
% 5.78/2.26 % (26951)------------------------------
% 5.78/2.27 % (26963)Instruction limit reached!
% 5.78/2.27 % (26963)------------------------------
% 5.78/2.27 % (26963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.27 % (26963)Termination reason: Unknown
% 5.78/2.27 % (26963)Termination phase: Property scanning
% 5.78/2.27
% 5.78/2.27 % (26963)Memory used [KB]: 1663
% 5.78/2.27 % (26963)Time elapsed: 0.016 s
% 5.78/2.27 % (26963)Instructions burned: 32 (million)
% 5.78/2.27 % (26963)------------------------------
% 5.78/2.27 % (26963)------------------------------
% 5.78/2.27 % (26964)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_26806 for (2994ds/96Mi)
% 5.78/2.27 % (26962)Instruction limit reached!
% 5.78/2.27 % (26962)------------------------------
% 5.78/2.27 % (26962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.27 % (26962)Termination reason: Unknown
% 5.78/2.27 % (26962)Termination phase: Property scanning
% 5.78/2.27
% 5.78/2.27 % (26962)Memory used [KB]: 1791
% 5.78/2.27 % (26962)Time elapsed: 0.029 s
% 5.78/2.27 % (26962)Instructions burned: 63 (million)
% 5.78/2.27 % (26962)------------------------------
% 5.78/2.27 % (26962)------------------------------
% 5.78/2.29 % (26965)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_26806 for (2994ds/453Mi)
% 5.78/2.29 % (26966)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_26806 for (2994ds/71Mi)
% 6.32/2.32 % (26964)Instruction limit reached!
% 6.32/2.32 % (26964)------------------------------
% 6.32/2.32 % (26964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.32 % (26964)Termination reason: Unknown
% 6.32/2.32 % (26964)Termination phase: Saturation
% 6.32/2.32
% 6.32/2.32 % (26964)Memory used [KB]: 6652
% 6.32/2.32 % (26964)Time elapsed: 0.045 s
% 6.32/2.32 % (26964)Instructions burned: 96 (million)
% 6.32/2.32 % (26964)------------------------------
% 6.32/2.32 % (26964)------------------------------
% 6.32/2.32 % (26966)Instruction limit reached!
% 6.32/2.32 % (26966)------------------------------
% 6.32/2.32 % (26966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.32 % (26966)Termination reason: Unknown
% 6.32/2.32 % (26966)Termination phase: Saturation
% 6.32/2.32
% 6.32/2.32 % (26966)Memory used [KB]: 6396
% 6.32/2.32 % (26966)Time elapsed: 0.034 s
% 6.32/2.32 % (26966)Instructions burned: 71 (million)
% 6.32/2.32 % (26966)------------------------------
% 6.32/2.32 % (26966)------------------------------
% 6.32/2.33 % (26940)Refutation not found, non-redundant clauses discarded% (26940)------------------------------
% 6.32/2.33 % (26940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.33 % (26940)Termination reason: Refutation not found, non-redundant clauses discarded
% 6.32/2.33
% 6.32/2.33 % (26940)Memory used [KB]: 8187
% 6.32/2.33 % (26940)Time elapsed: 0.434 s
% 6.32/2.33 % (26940)Instructions burned: 864 (million)
% 6.32/2.33 % (26940)------------------------------
% 6.32/2.33 % (26940)------------------------------
% 6.32/2.33 % (26967)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_26806 for (2994ds/83Mi)
% 6.32/2.34 % (26968)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_26806 for (2994ds/11Mi)
% 6.32/2.34 % (26968)Instruction limit reached!
% 6.32/2.34 % (26968)------------------------------
% 6.32/2.34 % (26968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.34 % (26968)Termination reason: Unknown
% 6.32/2.34 % (26968)Termination phase: shuffling
% 6.32/2.34
% 6.32/2.34 % (26968)Memory used [KB]: 1407
% 6.32/2.34 % (26968)Time elapsed: 0.007 s
% 6.32/2.34 % (26968)Instructions burned: 11 (million)
% 6.32/2.34 % (26968)------------------------------
% 6.32/2.34 % (26968)------------------------------
% 6.32/2.35 % (26969)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_26806 for (2993ds/41Mi)
% 6.32/2.36 % (26970)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26806 for (2993ds/6Mi)
% 6.32/2.36 % (26970)Instruction limit reached!
% 6.32/2.36 % (26970)------------------------------
% 6.32/2.36 % (26970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.36 % (26970)Termination reason: Unknown
% 6.32/2.36 % (26970)Termination phase: shuffling
% 6.32/2.36
% 6.32/2.36 % (26970)Memory used [KB]: 1279
% 6.32/2.36 % (26970)Time elapsed: 0.005 s
% 6.32/2.36 % (26970)Instructions burned: 6 (million)
% 6.32/2.36 % (26970)------------------------------
% 6.32/2.36 % (26970)------------------------------
% 6.32/2.37 % (26967)Instruction limit reached!
% 6.32/2.37 % (26967)------------------------------
% 6.32/2.37 % (26967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.37 % (26967)Termination reason: Unknown
% 6.32/2.37 % (26967)Termination phase: Saturation
% 6.32/2.37
% 6.32/2.37 % (26967)Memory used [KB]: 1918
% 6.32/2.37 % (26967)Time elapsed: 0.037 s
% 6.32/2.37 % (26967)Instructions burned: 83 (million)
% 6.32/2.37 % (26967)------------------------------
% 6.32/2.37 % (26967)------------------------------
% 6.32/2.37 % (26969)Instruction limit reached!
% 6.32/2.37 % (26969)------------------------------
% 6.32/2.37 % (26969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.37 % (26969)Termination reason: Unknown
% 6.32/2.37 % (26969)Termination phase: Property scanning
% 6.32/2.37
% 6.32/2.37 % (26969)Memory used [KB]: 1791
% 6.32/2.37 % (26969)Time elapsed: 0.020 s
% 6.32/2.37 % (26969)Instructions burned: 42 (million)
% 6.32/2.37 % (26969)------------------------------
% 6.32/2.37 % (26969)------------------------------
% 6.32/2.38 % (26971)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_26806 for (2993ds/150Mi)
% 6.32/2.38 % (26972)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_26806 for (2993ds/343Mi)
% 6.32/2.39 % (26973)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_26806 for (2993ds/109Mi)
% 6.32/2.39 % (26954)Instruction limit reached!
% 6.32/2.39 % (26954)------------------------------
% 6.32/2.39 % (26954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.32/2.39 % (26954)Termination reason: Unknown
% 6.32/2.39 % (26954)Termination phase: Saturation
% 6.32/2.39
% 6.32/2.39 % (26954)Memory used [KB]: 7291
% 6.32/2.39 % (26954)Time elapsed: 0.264 s
% 6.32/2.39 % (26954)Instructions burned: 507 (million)
% 6.32/2.39 % (26954)------------------------------
% 6.32/2.39 % (26954)------------------------------
% 6.86/2.41 % (26974)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_26806 for (2993ds/253Mi)
% 6.86/2.41 % (26961)Instruction limit reached!
% 6.86/2.41 % (26961)------------------------------
% 6.86/2.41 % (26961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.41 % (26961)Termination reason: Unknown
% 6.86/2.41 % (26961)Termination phase: Saturation
% 6.86/2.41
% 6.86/2.41 % (26961)Memory used [KB]: 2942
% 6.86/2.41 % (26961)Time elapsed: 0.172 s
% 6.86/2.41 % (26961)Instructions burned: 434 (million)
% 6.86/2.41 % (26961)------------------------------
% 6.86/2.41 % (26961)------------------------------
% 6.86/2.43 % (26975)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_26806 for (2993ds/140Mi)
% 6.86/2.43 % (26973)Instruction limit reached!
% 6.86/2.43 % (26973)------------------------------
% 6.86/2.43 % (26973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.43 % (26973)Termination reason: Unknown
% 6.86/2.43 % (26973)Termination phase: Saturation
% 6.86/2.43
% 6.86/2.43 % (26973)Memory used [KB]: 6652
% 6.86/2.43 % (26973)Time elapsed: 0.051 s
% 6.86/2.43 % (26973)Instructions burned: 109 (million)
% 6.86/2.43 % (26973)------------------------------
% 6.86/2.43 % (26973)------------------------------
% 6.86/2.45 % (26971)Instruction limit reached!
% 6.86/2.45 % (26971)------------------------------
% 6.86/2.45 % (26971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.45 % (26971)Termination reason: Unknown
% 6.86/2.45 % (26971)Termination phase: Saturation
% 6.86/2.45
% 6.86/2.45 % (26971)Memory used [KB]: 7803
% 6.86/2.45 % (26971)Time elapsed: 0.074 s
% 6.86/2.45 % (26971)Instructions burned: 151 (million)
% 6.86/2.45 % (26971)------------------------------
% 6.86/2.45 % (26971)------------------------------
% 6.86/2.45 % (26976)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_26806 for (2992ds/614Mi)
% 6.86/2.45 % (26965)Instruction limit reached!
% 6.86/2.45 % (26965)------------------------------
% 6.86/2.45 % (26965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.45 % (26965)Termination reason: Unknown
% 6.86/2.45 % (26965)Termination phase: Saturation
% 6.86/2.45
% 6.86/2.45 % (26965)Memory used [KB]: 6524
% 6.86/2.45 % (26965)Time elapsed: 0.170 s
% 6.86/2.45 % (26965)Instructions burned: 455 (million)
% 6.86/2.45 % (26965)------------------------------
% 6.86/2.45 % (26965)------------------------------
% 6.86/2.47 % (26977)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_26806 for (2992ds/202Mi)
% 6.86/2.47 % (26978)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_26806 for (2992ds/339Mi)
% 6.86/2.49 % (26975)Instruction limit reached!
% 6.86/2.49 % (26975)------------------------------
% 6.86/2.49 % (26975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.86/2.49 % (26975)Termination reason: Unknown
% 6.86/2.49 % (26975)Termination phase: Saturation
% 6.86/2.49
% 6.86/2.49 % (26975)Memory used [KB]: 6524
% 6.86/2.49 % (26975)Time elapsed: 0.064 s
% 6.86/2.49 % (26975)Instructions burned: 141 (million)
% 6.86/2.49 % (26975)------------------------------
% 6.86/2.49 % (26975)------------------------------
% 7.47/2.51 % (26979)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_26806 for (2992ds/283Mi)
% 7.47/2.53 % (26974)Instruction limit reached!
% 7.47/2.53 % (26974)------------------------------
% 7.47/2.53 % (26974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.53 % (26974)Termination reason: Unknown
% 7.47/2.53 % (26974)Termination phase: Saturation
% 7.47/2.53
% 7.47/2.53 % (26974)Memory used [KB]: 8059
% 7.47/2.53 % (26974)Time elapsed: 0.128 s
% 7.47/2.53 % (26974)Instructions burned: 253 (million)
% 7.47/2.53 % (26974)------------------------------
% 7.47/2.53 % (26974)------------------------------
% 7.47/2.55 % (26972)Instruction limit reached!
% 7.47/2.55 % (26972)------------------------------
% 7.47/2.55 % (26972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.55 % (26972)Termination reason: Unknown
% 7.47/2.55 % (26972)Termination phase: Saturation
% 7.47/2.55
% 7.47/2.55 % (26972)Memory used [KB]: 7675
% 7.47/2.55 % (26972)Time elapsed: 0.163 s
% 7.47/2.55 % (26972)Instructions burned: 344 (million)
% 7.47/2.55 % (26972)------------------------------
% 7.47/2.55 % (26972)------------------------------
% 7.47/2.55 % (26980)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_26806 for (2992ds/134Mi)
% 7.47/2.56 % (26981)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_26806 for (2991ds/298Mi)
% 7.47/2.57 % (26977)Instruction limit reached!
% 7.47/2.57 % (26977)------------------------------
% 7.47/2.57 % (26977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.57 % (26977)Termination reason: Unknown
% 7.47/2.57 % (26977)Termination phase: Saturation
% 7.47/2.57
% 7.47/2.57 % (26977)Memory used [KB]: 8443
% 7.47/2.57 % (26977)Time elapsed: 0.103 s
% 7.47/2.57 % (26977)Instructions burned: 203 (million)
% 7.47/2.57 % (26977)------------------------------
% 7.47/2.57 % (26977)------------------------------
% 7.47/2.58 % (26982)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_26806 for (2991ds/192Mi)
% 7.91/2.61 % (26980)Instruction limit reached!
% 7.91/2.61 % (26980)------------------------------
% 7.91/2.61 % (26980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.61 % (26980)Termination reason: Unknown
% 7.91/2.61 % (26980)Termination phase: Saturation
% 7.91/2.61
% 7.91/2.61 % (26980)Memory used [KB]: 6908
% 7.91/2.61 % (26980)Time elapsed: 0.063 s
% 7.91/2.61 % (26980)Instructions burned: 135 (million)
% 7.91/2.61 % (26980)------------------------------
% 7.91/2.61 % (26980)------------------------------
% 7.91/2.62 % (26979)Instruction limit reached!
% 7.91/2.62 % (26979)------------------------------
% 7.91/2.62 % (26979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.62 % (26979)Termination reason: Unknown
% 7.91/2.62 % (26979)Termination phase: Saturation
% 7.91/2.62
% 7.91/2.62 % (26979)Memory used [KB]: 8955
% 7.91/2.62 % (26979)Time elapsed: 0.111 s
% 7.91/2.62 % (26979)Instructions burned: 283 (million)
% 7.91/2.62 % (26979)------------------------------
% 7.91/2.62 % (26979)------------------------------
% 7.91/2.63 % (26983)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_26806 for (2991ds/258Mi)
% 7.91/2.63 % (26978)Instruction limit reached!
% 7.91/2.63 % (26978)------------------------------
% 7.91/2.63 % (26978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.63 % (26978)Termination reason: Unknown
% 7.91/2.63 % (26978)Termination phase: Saturation
% 7.91/2.63
% 7.91/2.63 % (26978)Memory used [KB]: 7547
% 7.91/2.63 % (26978)Time elapsed: 0.161 s
% 7.91/2.63 % (26978)Instructions burned: 339 (million)
% 7.91/2.63 % (26978)------------------------------
% 7.91/2.63 % (26978)------------------------------
% 7.91/2.64 % (26984)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_26806 for (2991ds/90Mi)
% 7.91/2.65 % (26985)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_26806 for (2991ds/231Mi)
% 7.91/2.67 % (26982)Instruction limit reached!
% 7.91/2.67 % (26982)------------------------------
% 7.91/2.67 % (26982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.67 % (26982)Termination reason: Unknown
% 7.91/2.67 % (26982)Termination phase: Saturation
% 7.91/2.67
% 7.91/2.67 % (26982)Memory used [KB]: 7164
% 7.91/2.67 % (26982)Time elapsed: 0.089 s
% 7.91/2.67 % (26982)Instructions burned: 192 (million)
% 7.91/2.67 % (26982)------------------------------
% 7.91/2.67 % (26982)------------------------------
% 7.91/2.68 % (26984)Instruction limit reached!
% 7.91/2.68 % (26984)------------------------------
% 7.91/2.68 % (26984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.68 % (26984)Termination reason: Unknown
% 7.91/2.68 % (26984)Termination phase: Saturation
% 7.91/2.68
% 7.91/2.68 % (26984)Memory used [KB]: 6780
% 7.91/2.68 % (26984)Time elapsed: 0.042 s
% 7.91/2.68 % (26984)Instructions burned: 91 (million)
% 7.91/2.68 % (26984)------------------------------
% 7.91/2.68 % (26984)------------------------------
% 7.91/2.69 % (26981)Instruction limit reached!
% 7.91/2.69 % (26981)------------------------------
% 7.91/2.69 % (26981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.91/2.69 % (26981)Termination reason: Unknown
% 7.91/2.69 % (26981)Termination phase: Saturation
% 7.91/2.69
% 7.91/2.69 % (26981)Memory used [KB]: 6652
% 7.91/2.69 % (26981)Time elapsed: 0.127 s
% 7.91/2.69 % (26981)Instructions burned: 299 (million)
% 7.91/2.69 % (26981)------------------------------
% 7.91/2.69 % (26981)------------------------------
% 7.91/2.69 % (26986)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_26806 for (2990ds/458Mi)
% 7.91/2.69 % (26987)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_26806 for (2990ds/31Mi)
% 8.59/2.70 % (26988)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_26806 for (2990ds/297Mi)
% 8.59/2.71 % (26987)Instruction limit reached!
% 8.59/2.71 % (26987)------------------------------
% 8.59/2.71 % (26987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.71 % (26987)Termination reason: Unknown
% 8.59/2.71 % (26987)Termination phase: Property scanning
% 8.59/2.71
% 8.59/2.71 % (26987)Memory used [KB]: 1663
% 8.59/2.71 % (26987)Time elapsed: 0.016 s
% 8.59/2.71 % (26987)Instructions burned: 31 (million)
% 8.59/2.71 % (26987)------------------------------
% 8.59/2.71 % (26987)------------------------------
% 8.59/2.72 % (26989)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_26806 for (2990ds/987Mi)
% 8.59/2.75 % (26983)Instruction limit reached!
% 8.59/2.75 % (26983)------------------------------
% 8.59/2.75 % (26983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.75 % (26983)Termination reason: Unknown
% 8.59/2.75 % (26983)Termination phase: Saturation
% 8.59/2.75
% 8.59/2.75 % (26983)Memory used [KB]: 7547
% 8.59/2.75 % (26983)Time elapsed: 0.122 s
% 8.59/2.75 % (26983)Instructions burned: 258 (million)
% 8.59/2.75 % (26983)------------------------------
% 8.59/2.75 % (26983)------------------------------
% 8.59/2.75 % (26976)Instruction limit reached!
% 8.59/2.75 % (26976)------------------------------
% 8.59/2.75 % (26976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.75 % (26976)Termination reason: Unknown
% 8.59/2.75 % (26976)Termination phase: Saturation
% 8.59/2.75
% 8.59/2.75 % (26976)Memory used [KB]: 8315
% 8.59/2.75 % (26976)Time elapsed: 0.303 s
% 8.59/2.75 % (26976)Instructions burned: 615 (million)
% 8.59/2.75 % (26958)Instruction limit reached!
% 8.59/2.75 % (26958)------------------------------
% 8.59/2.75 % (26958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.75 % (26976)------------------------------
% 8.59/2.75 % (26976)------------------------------
% 8.59/2.75 % (26958)Termination reason: Unknown
% 8.59/2.75 % (26958)Termination phase: Saturation
% 8.59/2.75
% 8.59/2.75 % (26958)Memory used [KB]: 10490
% 8.59/2.75 % (26958)Time elapsed: 0.572 s
% 8.59/2.75 % (26958)Instructions burned: 1088 (million)
% 8.59/2.75 % (26958)------------------------------
% 8.59/2.75 % (26958)------------------------------
% 8.59/2.76 % (26985)Instruction limit reached!
% 8.59/2.76 % (26985)------------------------------
% 8.59/2.76 % (26985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.76 % (26985)Termination reason: Unknown
% 8.59/2.76 % (26985)Termination phase: Saturation
% 8.59/2.76
% 8.59/2.76 % (26985)Memory used [KB]: 10618
% 8.59/2.76 % (26985)Time elapsed: 0.111 s
% 8.59/2.76 % (26985)Instructions burned: 232 (million)
% 8.59/2.76 % (26985)------------------------------
% 8.59/2.76 % (26985)------------------------------
% 8.59/2.76 % (26990)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_26806 for (2989ds/182Mi)
% 8.59/2.77 % (26991)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_26806 for (2989ds/182Mi)
% 8.59/2.77 % (26992)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_26806 for (2989ds/154Mi)
% 8.59/2.77 % (26993)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_26806 for (2989ds/79Mi)
% 9.76/2.81 % (26993)Instruction limit reached!
% 9.76/2.81 % (26993)------------------------------
% 9.76/2.81 % (26993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.76/2.81 % (26993)Termination reason: Unknown
% 9.76/2.81 % (26993)Termination phase: Saturation
% 9.76/2.81
% 9.76/2.81 % (26993)Memory used [KB]: 6396
% 9.76/2.81 % (26993)Time elapsed: 0.036 s
% 9.76/2.81 % (26993)Instructions burned: 79 (million)
% 9.76/2.81 % (26993)------------------------------
% 9.76/2.81 % (26993)------------------------------
% 9.76/2.82 % (26988)Instruction limit reached!
% 9.76/2.82 % (26988)------------------------------
% 9.76/2.82 % (26988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.76/2.82 % (26988)Termination reason: Unknown
% 9.76/2.82 % (26988)Termination phase: Saturation
% 9.76/2.82
% 9.76/2.82 % (26988)Memory used [KB]: 8187
% 9.76/2.82 % (26988)Time elapsed: 0.117 s
% 9.76/2.82 % (26988)Instructions burned: 298 (million)
% 9.76/2.82 % (26988)------------------------------
% 9.76/2.82 % (26988)------------------------------
% 9.76/2.82 % (26994)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_26806 for (2989ds/216Mi)
% 9.76/2.83 % (26992)Instruction limit reached!
% 9.76/2.83 % (26992)------------------------------
% 9.76/2.83 % (26992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.76/2.83 % (26992)Termination reason: Unknown
% 9.76/2.83 % (26992)Termination phase: Saturation
% 9.76/2.83
% 9.76/2.83 % (26992)Memory used [KB]: 6524
% 9.76/2.84 % (26992)Time elapsed: 0.067 s
% 9.76/2.84 % (26992)Instructions burned: 154 (million)
% 9.76/2.84 % (26992)------------------------------
% 9.76/2.84 % (26992)------------------------------
% 9.76/2.84 % (26995)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_26806 for (2989ds/114Mi)
% 9.76/2.85 % (26990)Instruction limit reached!
% 9.76/2.85 % (26990)------------------------------
% 9.76/2.85 % (26990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.76/2.85 % (26990)Termination reason: Unknown
% 9.76/2.85 % (26990)Termination phase: Saturation
% 9.76/2.85
% 9.76/2.85 % (26990)Memory used [KB]: 7164
% 9.76/2.85 % (26990)Time elapsed: 0.087 s
% 9.76/2.85 % (26990)Instructions burned: 183 (million)
% 9.76/2.85 % (26990)------------------------------
% 9.76/2.85 % (26990)------------------------------
% 9.76/2.85 % (26996)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_26806 for (2989ds/922Mi)
% 9.76/2.86 % (26991)Instruction limit reached!
% 9.76/2.86 % (26991)------------------------------
% 9.76/2.86 % (26991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.76/2.86 % (26991)Termination reason: Unknown
% 9.76/2.86 % (26991)Termination phase: Saturation
% 9.76/2.86
% 9.76/2.86 % (26991)Memory used [KB]: 9338
% 9.76/2.86 % (26991)Time elapsed: 0.089 s
% 9.76/2.86 % (26991)Instructions burned: 182 (million)
% 9.76/2.86 % (26991)------------------------------
% 9.76/2.86 % (26991)------------------------------
% 9.76/2.87 % (26997)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_26806 for (2988ds/182Mi)
% 9.76/2.87 % (26998)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_26806 for (2988ds/164Mi)
% 9.76/2.89 % (26995)Instruction limit reached!
% 9.76/2.89 % (26995)------------------------------
% 9.76/2.89 % (26995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.76/2.89 % (26995)Termination reason: Unknown
% 9.76/2.89 % (26995)Termination phase: Saturation
% 9.76/2.89
% 9.76/2.89 % (26995)Memory used [KB]: 6780
% 9.76/2.89 % (26995)Time elapsed: 0.052 s
% 9.76/2.89 % (26995)Instructions burned: 115 (million)
% 9.76/2.89 % (26995)------------------------------
% 9.76/2.89 % (26995)------------------------------
% 10.30/2.90 % (26999)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_26806 for (2988ds/50Mi)
% 10.30/2.91 % (26986)Instruction limit reached!
% 10.30/2.91 % (26986)------------------------------
% 10.30/2.91 % (26986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.91 % (26986)Termination reason: Unknown
% 10.30/2.91 % (26986)Termination phase: Saturation
% 10.30/2.91
% 10.30/2.91 % (26986)Memory used [KB]: 7803
% 10.30/2.91 % (26986)Time elapsed: 0.222 s
% 10.30/2.91 % (26986)Instructions burned: 459 (million)
% 10.30/2.91 % (26986)------------------------------
% 10.30/2.91 % (26986)------------------------------
% 10.30/2.91 % (26994)Instruction limit reached!
% 10.30/2.91 % (26994)------------------------------
% 10.30/2.91 % (26994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.91 % (26994)Termination reason: Unknown
% 10.30/2.91 % (26994)Termination phase: Saturation
% 10.30/2.91
% 10.30/2.91 % (26994)Memory used [KB]: 6652
% 10.30/2.91 % (26994)Time elapsed: 0.086 s
% 10.30/2.91 % (26994)Instructions burned: 217 (million)
% 10.30/2.91 % (26994)------------------------------
% 10.30/2.91 % (26994)------------------------------
% 10.30/2.92 % (26999)Instruction limit reached!
% 10.30/2.92 % (26999)------------------------------
% 10.30/2.92 % (26999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.92 % (26999)Termination reason: Unknown
% 10.30/2.92 % (26999)Termination phase: Property scanning
% 10.30/2.92
% 10.30/2.92 % (26999)Memory used [KB]: 1791
% 10.30/2.92 % (26999)Time elapsed: 0.023 s
% 10.30/2.92 % (26999)Instructions burned: 51 (million)
% 10.30/2.92 % (26999)------------------------------
% 10.30/2.92 % (26999)------------------------------
% 10.30/2.92 % (27000)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_26806 for (2988ds/368Mi)
% 10.30/2.93 % (27001)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_26806 for (2988ds/1021Mi)
% 10.30/2.94 % (26997)Instruction limit reached!
% 10.30/2.94 % (26997)------------------------------
% 10.30/2.94 % (26997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.94 % (26997)Termination reason: Unknown
% 10.30/2.94 % (26997)Termination phase: Saturation
% 10.30/2.94
% 10.30/2.94 % (26997)Memory used [KB]: 6524
% 10.30/2.94 % (26997)Time elapsed: 0.076 s
% 10.30/2.94 % (26997)Instructions burned: 182 (million)
% 10.30/2.94 % (26997)------------------------------
% 10.30/2.94 % (26997)------------------------------
% 10.30/2.94 % (27002)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_26806 for (2988ds/267Mi)
% 10.30/2.95 % (26998)Instruction limit reached!
% 10.30/2.95 % (26998)------------------------------
% 10.30/2.95 % (26998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.95 % (26998)Termination reason: Unknown
% 10.30/2.95 % (26998)Termination phase: Saturation
% 10.30/2.95
% 10.30/2.95 % (26998)Memory used [KB]: 2302
% 10.30/2.95 % (26998)Time elapsed: 0.075 s
% 10.30/2.95 % (26998)Instructions burned: 164 (million)
% 10.30/2.95 % (26998)------------------------------
% 10.30/2.95 % (26998)------------------------------
% 10.30/2.96 % (27003)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_26806 for (2987ds/204Mi)
% 10.30/2.96 % (27004)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_26806 for (2987ds/26Mi)
% 10.30/2.97 % (27004)Instruction limit reached!
% 10.30/2.97 % (27004)------------------------------
% 10.30/2.97 % (27004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/2.97 % (27004)Termination reason: Unknown
% 10.30/2.97 % (27004)Termination phase: Property scanning
% 10.30/2.97
% 10.30/2.97 % (27004)Memory used [KB]: 1663
% 10.30/2.97 % (27004)Time elapsed: 0.014 s
% 10.30/2.97 % (27004)Instructions burned: 27 (million)
% 10.30/2.97 % (27004)------------------------------
% 10.30/2.97 % (27004)------------------------------
% 10.30/2.99 % (27005)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_26806 for (2987ds/53Mi)
% 10.30/3.01 % (27005)Instruction limit reached!
% 10.30/3.01 % (27005)------------------------------
% 10.30/3.01 % (27005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.30/3.01 % (27005)Termination reason: Unknown
% 10.30/3.01 % (27005)Termination phase: Function definition elimination
% 10.30/3.01
% 10.30/3.01 % (27005)Memory used [KB]: 1791
% 10.30/3.01 % (27005)Time elapsed: 0.026 s
% 10.30/3.01 % (27005)Instructions burned: 55 (million)
% 10.30/3.01 % (27005)------------------------------
% 10.30/3.01 % (27005)------------------------------
% 10.30/3.03 % (27006)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_26806 for (2987ds/4436Mi)
% 11.84/3.05 % (27003)Instruction limit reached!
% 11.84/3.05 % (27003)------------------------------
% 11.84/3.05 % (27003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.84/3.05 % (27003)Termination reason: Unknown
% 11.84/3.05 % (27003)Termination phase: Saturation
% 11.84/3.05
% 11.84/3.05 % (27003)Memory used [KB]: 7164
% 11.84/3.05 % (27003)Time elapsed: 0.094 s
% 11.84/3.05 % (27003)Instructions burned: 205 (million)
% 11.84/3.05 % (27003)------------------------------
% 11.84/3.05 % (27003)------------------------------
% 11.84/3.06 % (27002)Instruction limit reached!
% 11.84/3.06 % (27002)------------------------------
% 11.84/3.06 % (27002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.84/3.06 % (27002)Termination reason: Unknown
% 11.84/3.06 % (27002)Termination phase: Saturation
% 11.84/3.06
% 11.84/3.06 % (27002)Memory used [KB]: 8827
% 11.84/3.06 % (27002)Time elapsed: 0.110 s
% 11.84/3.06 % (27002)Instructions burned: 267 (million)
% 11.84/3.06 % (27002)------------------------------
% 11.84/3.06 % (27002)------------------------------
% 11.84/3.06 % (27007)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_26806 for (2986ds/1539Mi)
% 11.84/3.08 % (27008)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_26806 for (2986ds/408Mi)
% 11.84/3.10 % (26989)Instruction limit reached!
% 11.84/3.10 % (26989)------------------------------
% 11.84/3.10 % (26989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.84/3.10 % (26989)Termination reason: Unknown
% 11.84/3.10 % (26989)Termination phase: Saturation
% 11.84/3.10
% 11.84/3.10 % (26989)Memory used [KB]: 9466
% 11.84/3.10 % (26989)Time elapsed: 0.374 s
% 11.84/3.10 % (26989)Instructions burned: 988 (million)
% 11.84/3.10 % (26989)------------------------------
% 11.84/3.10 % (26989)------------------------------
% 11.84/3.10 % (27000)Instruction limit reached!
% 11.84/3.10 % (27000)------------------------------
% 11.84/3.10 % (27000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.84/3.10 % (27000)Termination reason: Unknown
% 11.84/3.10 % (27000)Termination phase: Saturation
% 11.84/3.10
% 11.84/3.10 % (27000)Memory used [KB]: 7803
% 11.84/3.10 % (27000)Time elapsed: 0.205 s
% 11.84/3.10 % (27000)Instructions burned: 368 (million)
% 11.84/3.10 % (27000)------------------------------
% 11.84/3.10 % (27000)------------------------------
% 11.84/3.11 % (27009)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_26806 for (2986ds/5205Mi)
% 11.84/3.12 % (27010)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_26806 for (2986ds/1913Mi)
% 12.36/3.29 % (27008)Instruction limit reached!
% 12.36/3.29 % (27008)------------------------------
% 12.36/3.29 % (27008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.36/3.29 % (27008)Termination reason: Unknown
% 12.36/3.29 % (27008)Termination phase: Saturation
% 12.36/3.29
% 12.36/3.29 % (27008)Memory used [KB]: 9210
% 12.36/3.29 % (27008)Time elapsed: 0.207 s
% 12.36/3.29 % (27008)Instructions burned: 408 (million)
% 12.36/3.29 % (27008)------------------------------
% 12.36/3.29 % (27008)------------------------------
% 12.80/3.30 % (27011)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_26806 for (2984ds/4350Mi)
% 12.80/3.32 % (26996)Instruction limit reached!
% 12.80/3.32 % (26996)------------------------------
% 12.80/3.32 % (26996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.80/3.32 % (26996)Termination reason: Unknown
% 12.80/3.32 % (26996)Termination phase: Saturation
% 12.80/3.32
% 12.80/3.32 % (26996)Memory used [KB]: 9466
% 12.80/3.32 % (26996)Time elapsed: 0.489 s
% 12.80/3.32 % (26996)Instructions burned: 922 (million)
% 12.80/3.32 % (26996)------------------------------
% 12.80/3.32 % (26996)------------------------------
% 12.80/3.34 % (27012)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_26806 for (2984ds/68Mi)
% 12.80/3.37 % (27012)Instruction limit reached!
% 12.80/3.37 % (27012)------------------------------
% 12.80/3.37 % (27012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.80/3.37 % (27012)Termination reason: Unknown
% 12.80/3.37 % (27012)Termination phase: Property scanning
% 12.80/3.37
% 12.80/3.37 % (27012)Memory used [KB]: 1918
% 12.80/3.37 % (27012)Time elapsed: 0.032 s
% 12.80/3.37 % (27012)Instructions burned: 69 (million)
% 12.80/3.37 % (27012)------------------------------
% 12.80/3.37 % (27012)------------------------------
% 12.80/3.38 % (27013)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_26806 for (2983ds/358Mi)
% 12.99/3.44 % (27001)Instruction limit reached!
% 12.99/3.44 % (27001)------------------------------
% 12.99/3.44 % (27001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.99/3.44 % (27001)Termination reason: Unknown
% 12.99/3.44 % (27001)Termination phase: Saturation
% 12.99/3.44
% 12.99/3.44 % (27001)Memory used [KB]: 9594
% 12.99/3.44 % (27001)Time elapsed: 0.538 s
% 12.99/3.44 % (27001)Instructions burned: 1022 (million)
% 12.99/3.44 % (27001)------------------------------
% 12.99/3.44 % (27001)------------------------------
% 12.99/3.45 % (27014)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_26806 for (2982ds/31Mi)
% 12.99/3.47 % (27014)Instruction limit reached!
% 12.99/3.47 % (27014)------------------------------
% 12.99/3.47 % (27014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.99/3.47 % (27014)Termination reason: Unknown
% 12.99/3.47 % (27014)Termination phase: Property scanning
% 12.99/3.47
% 12.99/3.47 % (27014)Memory used [KB]: 1663
% 12.99/3.47 % (27014)Time elapsed: 0.016 s
% 12.99/3.47 % (27014)Instructions burned: 31 (million)
% 12.99/3.47 % (27014)------------------------------
% 12.99/3.47 % (27014)------------------------------
% 12.99/3.49 % (27015)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_26806 for (2982ds/279Mi)
% 13.06/3.55 % (27013)Instruction limit reached!
% 13.06/3.55 % (27013)------------------------------
% 13.06/3.55 % (27013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.06/3.55 % (27013)Termination reason: Unknown
% 13.06/3.55 % (27013)Termination phase: Saturation
% 13.06/3.55
% 13.06/3.55 % (27013)Memory used [KB]: 7547
% 13.06/3.55 % (27013)Time elapsed: 0.166 s
% 13.06/3.55 % (27013)Instructions burned: 359 (million)
% 13.06/3.55 % (27013)------------------------------
% 13.06/3.55 % (27013)------------------------------
% 13.06/3.56 % (27016)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_26806 for (2981ds/258Mi)
% 13.06/3.59 % (27015)Instruction limit reached!
% 13.06/3.59 % (27015)------------------------------
% 13.06/3.59 % (27015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.06/3.59 % (27015)Termination reason: Unknown
% 13.06/3.59 % (27015)Termination phase: Saturation
% 13.06/3.59
% 13.06/3.59 % (27015)Memory used [KB]: 6524
% 13.06/3.59 % (27015)Time elapsed: 0.111 s
% 13.06/3.59 % (27015)Instructions burned: 280 (million)
% 13.06/3.59 % (27015)------------------------------
% 13.06/3.59 % (27015)------------------------------
% 13.38/3.61 % (27017)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_26806 for (2981ds/26Mi)
% 13.38/3.62 % (27017)Instruction limit reached!
% 13.38/3.62 % (27017)------------------------------
% 13.38/3.62 % (27017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.38/3.62 % (27017)Termination reason: Unknown
% 13.38/3.62 % (27017)Termination phase: Property scanning
% 13.38/3.62
% 13.38/3.62 % (27017)Memory used [KB]: 1663
% 13.38/3.62 % (27017)Time elapsed: 0.013 s
% 13.38/3.62 % (27017)Instructions burned: 26 (million)
% 13.38/3.62 % (27017)------------------------------
% 13.38/3.62 % (27017)------------------------------
% 13.38/3.64 % (27018)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_26806 for (2981ds/995Mi)
% 13.38/3.68 % (27016)Instruction limit reached!
% 13.38/3.68 % (27016)------------------------------
% 13.38/3.68 % (27016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.38/3.68 % (27016)Termination reason: Unknown
% 13.38/3.68 % (27016)Termination phase: Saturation
% 13.38/3.68
% 13.38/3.68 % (27016)Memory used [KB]: 7547
% 13.38/3.68 % (27016)Time elapsed: 0.115 s
% 13.38/3.68 % (27016)Instructions burned: 259 (million)
% 13.38/3.68 % (27016)------------------------------
% 13.38/3.68 % (27016)------------------------------
% 13.38/3.69 % (27019)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_26806 for (2980ds/373Mi)
% 13.52/3.75 % (27007)Instruction limit reached!
% 13.52/3.75 % (27007)------------------------------
% 13.52/3.75 % (27007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.52/3.75 % (27007)Termination reason: Unknown
% 13.52/3.75 % (27007)Termination phase: Saturation
% 13.52/3.75
% 13.52/3.75 % (27007)Memory used [KB]: 8571
% 13.52/3.75 % (27007)Time elapsed: 0.693 s
% 13.52/3.75 % (27007)Instructions burned: 1539 (million)
% 13.52/3.75 % (27007)------------------------------
% 13.52/3.75 % (27007)------------------------------
% 13.52/3.77 % (27020)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_26806 for (2979ds/253Mi)
% 14.23/3.87 % (27020)Instruction limit reached!
% 14.23/3.87 % (27020)------------------------------
% 14.23/3.87 % (27020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.23/3.87 % (27020)Termination reason: Unknown
% 14.23/3.87 % (27020)Termination phase: Saturation
% 14.23/3.87
% 14.23/3.87 % (27020)Memory used [KB]: 6652
% 14.23/3.87 % (27020)Time elapsed: 0.100 s
% 14.23/3.87 % (27020)Instructions burned: 253 (million)
% 14.23/3.87 % (27020)------------------------------
% 14.23/3.87 % (27020)------------------------------
% 14.23/3.87 % (27019)Instruction limit reached!
% 14.23/3.87 % (27019)------------------------------
% 14.23/3.87 % (27019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.23/3.87 % (27019)Termination reason: Unknown
% 14.23/3.87 % (27019)Termination phase: Saturation
% 14.23/3.87
% 14.23/3.87 % (27019)Memory used [KB]: 7675
% 14.23/3.87 % (27019)Time elapsed: 0.181 s
% 14.23/3.87 % (27019)Instructions burned: 374 (million)
% 14.23/3.87 % (27019)------------------------------
% 14.23/3.87 % (27019)------------------------------
% 14.23/3.89 % (27021)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_26806 for (2978ds/832Mi)
% 14.23/3.89 % (27022)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_26806 for (2978ds/668Mi)
% 14.55/3.97 % (27021)Refutation not found, incomplete strategy
% 14.55/3.97 % (27021)------------------------------
% 14.55/3.97 % (27021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/3.97 % (27021)Termination reason: Refutation not found, incomplete strategy
% 14.55/3.97
% 14.55/3.97
% 14.55/3.97 % (27021)Memory used [KB]: 7931
% 14.55/3.97 % (27021)Time elapsed: 0.086 s
% 14.55/3.97 % (27021)Instructions burned: 170 (million)
% 14.55/3.97 % (27021)------------------------------
% 14.55/3.97 % (27021)------------------------------
% 14.55/3.99 % (27023)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_26806 for (2977ds/40Mi)
% 14.55/4.00 % (27018)Instruction limit reached!
% 14.55/4.00 % (27018)------------------------------
% 14.55/4.00 % (27018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/4.00 % (27018)Termination reason: Unknown
% 14.55/4.00 % (27018)Termination phase: Saturation
% 14.55/4.00
% 14.55/4.00 % (27018)Memory used [KB]: 8955
% 14.55/4.00 % (27018)Time elapsed: 0.369 s
% 14.55/4.00 % (27018)Instructions burned: 995 (million)
% 14.55/4.00 % (27018)------------------------------
% 14.55/4.00 % (27018)------------------------------
% 14.55/4.01 % (27023)Instruction limit reached!
% 14.55/4.01 % (27023)------------------------------
% 14.55/4.01 % (27023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.55/4.01 % (27023)Termination reason: Unknown
% 14.55/4.01 % (27023)Termination phase: Property scanning
% 14.55/4.01
% 14.55/4.01 % (27023)Memory used [KB]: 1791
% 14.55/4.01 % (27023)Time elapsed: 0.020 s
% 14.55/4.01 % (27023)Instructions burned: 40 (million)
% 14.55/4.01 % (27023)------------------------------
% 14.55/4.01 % (27023)------------------------------
% 14.55/4.02 % (27024)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_26806 for (2977ds/294Mi)
% 18.76/4.02 % (27025)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_26806 for (2977ds/187Mi)
% 18.76/4.03 % (27010)Instruction limit reached!
% 18.76/4.03 % (27010)------------------------------
% 18.76/4.03 % (27010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.76/4.03 % (27010)Termination reason: Unknown
% 18.76/4.03 % (27010)Termination phase: Saturation
% 18.76/4.03
% 18.76/4.03 % (27010)Memory used [KB]: 4093
% 18.76/4.03 % (27010)Time elapsed: 0.909 s
% 18.76/4.03 % (27010)Instructions burned: 1914 (million)
% 18.76/4.03 % (27010)------------------------------
% 18.76/4.03 % (27010)------------------------------
% 18.76/4.04 % (27026)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_26806 for (2977ds/371Mi)
% 18.76/4.11 % (27025)Instruction limit reached!
% 18.76/4.11 % (27025)------------------------------
% 18.76/4.11 % (27025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.76/4.11 % (27025)Termination reason: Unknown
% 18.76/4.11 % (27025)Termination phase: Saturation
% 18.76/4.11
% 18.76/4.11 % (27025)Memory used [KB]: 7547
% 18.76/4.11 % (27025)Time elapsed: 0.089 s
% 18.76/4.11 % (27025)Instructions burned: 187 (million)
% 18.76/4.11 % (27025)------------------------------
% 18.76/4.11 % (27025)------------------------------
% 19.27/4.13 % (27027)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_26806 for (2976ds/1827Mi)
% 19.27/4.13 % (27022)Instruction limit reached!
% 19.27/4.13 % (27022)------------------------------
% 19.27/4.13 % (27022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.27/4.13 % (27022)Termination reason: Unknown
% 19.27/4.13 % (27022)Termination phase: Saturation
% 19.27/4.13
% 19.27/4.13 % (27022)Memory used [KB]: 13560
% 19.27/4.13 % (27022)Time elapsed: 0.247 s
% 19.27/4.13 % (27022)Instructions burned: 668 (million)
% 19.27/4.13 % (27022)------------------------------
% 19.27/4.13 % (27022)------------------------------
% 19.27/4.14 % (27024)Instruction limit reached!
% 19.27/4.14 % (27024)------------------------------
% 19.27/4.14 % (27024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.27/4.14 % (27024)Termination reason: Unknown
% 19.27/4.14 % (27024)Termination phase: Saturation
% 19.27/4.14
% 19.27/4.14 % (27024)Memory used [KB]: 6524
% 19.27/4.14 % (27024)Time elapsed: 0.123 s
% 19.27/4.14 % (27024)Instructions burned: 294 (million)
% 19.27/4.14 % (27024)------------------------------
% 19.27/4.14 % (27024)------------------------------
% 19.27/4.15 % (27028)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_26806 for (2976ds/70Mi)
% 19.27/4.16 % (27029)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_26806 for (2975ds/316Mi)
% 19.27/4.18 % (27028)Instruction limit reached!
% 19.27/4.18 % (27028)------------------------------
% 19.27/4.18 % (27028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.27/4.18 % (27028)Termination reason: Unknown
% 19.27/4.18 % (27028)Termination phase: Property scanning
% 19.27/4.18
% 19.27/4.18 % (27028)Memory used [KB]: 1791
% 19.27/4.18 % (27028)Time elapsed: 0.033 s
% 19.27/4.18 % (27028)Instructions burned: 71 (million)
% 19.27/4.18 % (27028)------------------------------
% 19.27/4.18 % (27028)------------------------------
% 19.70/4.20 % (27030)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_26806 for (2975ds/932Mi)
% 19.70/4.22 % (27026)Instruction limit reached!
% 19.70/4.22 % (27026)------------------------------
% 19.70/4.22 % (27026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.70/4.22 % (27026)Termination reason: Unknown
% 19.70/4.22 % (27026)Termination phase: Saturation
% 19.70/4.22
% 19.70/4.22 % (27026)Memory used [KB]: 7675
% 19.70/4.22 % (27026)Time elapsed: 0.178 s
% 19.70/4.22 % (27026)Instructions burned: 371 (million)
% 19.70/4.22 % (27026)------------------------------
% 19.70/4.22 % (27026)------------------------------
% 19.70/4.24 % (27031)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_26806 for (2975ds/4714Mi)
% 19.70/4.29 % (27029)Instruction limit reached!
% 19.70/4.29 % (27029)------------------------------
% 19.70/4.29 % (27029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.70/4.29 % (27029)Termination reason: Unknown
% 19.70/4.29 % (27029)Termination phase: Saturation
% 19.70/4.29
% 19.70/4.29 % (27029)Memory used [KB]: 7419
% 19.70/4.29 % (27029)Time elapsed: 0.130 s
% 19.70/4.29 % (27029)Instructions burned: 318 (million)
% 19.70/4.29 % (27029)------------------------------
% 19.70/4.29 % (27029)------------------------------
% 20.34/4.31 % (27032)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_26806 for (2974ds/8250Mi)
% 20.94/4.57 % (27030)Instruction limit reached!
% 20.94/4.57 % (27030)------------------------------
% 20.94/4.57 % (27030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.94/4.57 % (27030)Termination reason: Unknown
% 20.94/4.57 % (27030)Termination phase: Saturation
% 20.94/4.57
% 20.94/4.57 % (27030)Memory used [KB]: 9850
% 20.94/4.57 % (27030)Time elapsed: 0.372 s
% 20.94/4.57 % (27030)Instructions burned: 934 (million)
% 20.94/4.57 % (27030)------------------------------
% 20.94/4.57 % (27030)------------------------------
% 20.94/4.59 % (27033)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_26806 for (2971ds/770Mi)
% 22.52/4.93 % (27033)Instruction limit reached!
% 22.52/4.93 % (27033)------------------------------
% 22.52/4.93 % (27033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.52/4.93 % (27033)Termination reason: Unknown
% 22.52/4.93 % (27033)Termination phase: Saturation
% 22.52/4.93
% 22.52/4.93 % (27033)Memory used [KB]: 6780
% 22.52/4.93 % (27033)Time elapsed: 0.364 s
% 22.52/4.93 % (27033)Instructions burned: 770 (million)
% 22.52/4.93 % (27033)------------------------------
% 22.52/4.93 % (27033)------------------------------
% 22.52/4.94 % (27034)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_26806 for (2968ds/794Mi)
% 25.77/5.04 % (27027)Instruction limit reached!
% 25.77/5.04 % (27027)------------------------------
% 25.77/5.04 % (27027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.77/5.04 % (27027)Termination reason: Unknown
% 25.77/5.04 % (27027)Termination phase: Saturation
% 25.77/5.04
% 25.77/5.04 % (27027)Memory used [KB]: 15863
% 25.77/5.04 % (27027)Time elapsed: 0.906 s
% 25.77/5.04 % (27027)Instructions burned: 1827 (million)
% 25.77/5.04 % (27027)------------------------------
% 25.77/5.04 % (27027)------------------------------
% 25.77/5.05 % (27035)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_26806 for (2967ds/464Mi)
% 25.77/5.07 % (27009)Instruction limit reached!
% 25.77/5.07 % (27009)------------------------------
% 25.77/5.07 % (27009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.77/5.07 % (27009)Termination reason: Unknown
% 25.77/5.07 % (27009)Termination phase: Saturation
% 25.77/5.07
% 25.77/5.07 % (27009)Memory used [KB]: 9722
% 25.77/5.07 % (27009)Time elapsed: 1.958 s
% 25.77/5.07 % (27009)Instructions burned: 5205 (million)
% 25.77/5.07 % (27009)------------------------------
% 25.77/5.07 % (27009)------------------------------
% 25.77/5.09 % (27036)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_26806 for (2966ds/1376Mi)
% 26.72/5.27 % (27006)Instruction limit reached!
% 26.72/5.27 % (27006)------------------------------
% 26.72/5.27 % (27006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.72/5.27 % (27006)Termination reason: Unknown
% 26.72/5.27 % (27006)Termination phase: Saturation
% 26.72/5.27
% 26.72/5.27 % (27006)Memory used [KB]: 16119
% 26.72/5.27 % (27006)Time elapsed: 2.241 s
% 26.72/5.27 % (27006)Instructions burned: 4436 (million)
% 26.72/5.27 % (27006)------------------------------
% 26.72/5.27 % (27006)------------------------------
% 26.72/5.28 % (27035)Instruction limit reached!
% 26.72/5.28 % (27035)------------------------------
% 26.72/5.28 % (27035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.72/5.28 % (27035)Termination reason: Unknown
% 26.72/5.28 % (27035)Termination phase: Saturation
% 26.72/5.28
% 26.72/5.28 % (27035)Memory used [KB]: 8059
% 26.72/5.28 % (27035)Time elapsed: 0.255 s
% 26.72/5.28 % (27035)Instructions burned: 465 (million)
% 26.72/5.28 % (27035)------------------------------
% 26.72/5.28 % (27035)------------------------------
% 26.72/5.29 % (27037)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_26806 for (2964ds/906Mi)
% 27.44/5.30 % (27038)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_26806 for (2964ds/434Mi)
% 27.44/5.33 % (27034)Instruction limit reached!
% 27.44/5.33 % (27034)------------------------------
% 27.44/5.33 % (27034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.44/5.33 % (27034)Termination reason: Unknown
% 27.44/5.33 % (27034)Termination phase: Saturation
% 27.44/5.33
% 27.44/5.33 % (27034)Memory used [KB]: 3965
% 27.44/5.33 % (27034)Time elapsed: 0.416 s
% 27.44/5.33 % (27034)Instructions burned: 795 (million)
% 27.44/5.33 % (27034)------------------------------
% 27.44/5.33 % (27034)------------------------------
% 27.44/5.35 % (27039)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_26806 for (2963ds/865Mi)
% 27.78/5.45 % (27011)Instruction limit reached!
% 27.78/5.45 % (27011)------------------------------
% 27.78/5.45 % (27011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.78/5.45 % (27011)Termination reason: Unknown
% 27.78/5.45 % (27011)Termination phase: Saturation
% 27.78/5.45
% 27.78/5.45 % (27011)Memory used [KB]: 10490
% 27.78/5.45 % (27011)Time elapsed: 2.153 s
% 27.78/5.45 % (27011)Instructions burned: 4351 (million)
% 27.78/5.45 % (27011)------------------------------
% 27.78/5.45 % (27011)------------------------------
% 27.78/5.47 % (27040)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_26806 for (2962ds/593Mi)
% 28.05/5.51 % (27038)Instruction limit reached!
% 28.05/5.51 % (27038)------------------------------
% 28.05/5.51 % (27038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.05/5.51 % (27038)Termination reason: Unknown
% 28.05/5.51 % (27038)Termination phase: Saturation
% 28.05/5.51
% 28.05/5.51 % (27038)Memory used [KB]: 8955
% 28.05/5.51 % (27038)Time elapsed: 0.239 s
% 28.05/5.51 % (27038)Instructions burned: 434 (million)
% 28.05/5.51 % (27038)------------------------------
% 28.05/5.51 % (27038)------------------------------
% 28.05/5.53 % (27041)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_26806 for (2962ds/443Mi)
% 28.47/5.63 % (27036)Instruction limit reached!
% 28.47/5.63 % (27036)------------------------------
% 28.47/5.63 % (27036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.47/5.63 % (27036)Termination reason: Unknown
% 28.47/5.63 % (27036)Termination phase: Saturation
% 28.47/5.63
% 28.47/5.63 % (27036)Memory used [KB]: 8187
% 28.47/5.63 % (27036)Time elapsed: 0.566 s
% 28.47/5.63 % (27036)Instructions burned: 1378 (million)
% 28.47/5.63 % (27036)------------------------------
% 28.47/5.63 % (27036)------------------------------
% 28.47/5.65 % (27042)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_26806 for (2960ds/594Mi)
% 28.47/5.68 % (27040)Instruction limit reached!
% 28.47/5.68 % (27040)------------------------------
% 28.47/5.68 % (27040)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.47/5.68 % (27040)Termination reason: Unknown
% 28.47/5.68 % (27040)Termination phase: Saturation
% 28.47/5.68
% 28.47/5.68 % (27040)Memory used [KB]: 6652
% 28.47/5.68 % (27040)Time elapsed: 0.216 s
% 28.47/5.68 % (27040)Instructions burned: 593 (million)
% 28.47/5.68 % (27040)------------------------------
% 28.47/5.68 % (27040)------------------------------
% 29.47/5.70 % (27043)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_26806 for (2960ds/327Mi)
% 29.47/5.72 % (27037)Instruction limit reached!
% 29.47/5.72 % (27037)------------------------------
% 29.47/5.72 % (27037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.47/5.72 % (27037)Termination reason: Unknown
% 29.47/5.72 % (27037)Termination phase: Saturation
% 29.47/5.72
% 29.47/5.72 % (27037)Memory used [KB]: 9722
% 29.47/5.72 % (27037)Time elapsed: 0.457 s
% 29.47/5.72 % (27037)Instructions burned: 907 (million)
% 29.47/5.72 % (27037)------------------------------
% 29.47/5.72 % (27037)------------------------------
% 29.47/5.74 % (27044)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_26806 for (2960ds/5411Mi)
% 29.47/5.74 % (27041)Instruction limit reached!
% 29.47/5.74 % (27041)------------------------------
% 29.47/5.74 % (27041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.47/5.74 % (27041)Termination reason: Unknown
% 29.47/5.74 % (27041)Termination phase: Saturation
% 29.47/5.74
% 29.47/5.74 % (27041)Memory used [KB]: 7803
% 29.47/5.74 % (27041)Time elapsed: 0.219 s
% 29.47/5.74 % (27041)Instructions burned: 444 (million)
% 29.47/5.74 % (27041)------------------------------
% 29.47/5.74 % (27041)------------------------------
% 29.47/5.76 % (27045)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_26806 for (2959ds/1762Mi)
% 29.47/5.77 % (27039)Instruction limit reached!
% 29.47/5.77 % (27039)------------------------------
% 29.47/5.77 % (27039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.47/5.77 % (27039)Termination reason: Unknown
% 29.47/5.77 % (27039)Termination phase: Saturation
% 29.47/5.77
% 29.47/5.77 % (27039)Memory used [KB]: 8699
% 29.47/5.77 % (27039)Time elapsed: 0.423 s
% 29.47/5.77 % (27039)Instructions burned: 866 (million)
% 29.47/5.77 % (27039)------------------------------
% 29.47/5.77 % (27039)------------------------------
% 29.47/5.78 % (27031)Refutation not found, non-redundant clauses discarded% (27031)------------------------------
% 29.47/5.78 % (27031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.47/5.78 % (27031)Termination reason: Refutation not found, non-redundant clauses discarded
% 29.47/5.78
% 29.47/5.78 % (27031)Memory used [KB]: 7036
% 29.47/5.78 % (27031)Time elapsed: 1.561 s
% 29.47/5.78 % (27031)Instructions burned: 4473 (million)
% 29.47/5.78 % (27031)------------------------------
% 29.47/5.78 % (27031)------------------------------
% 29.47/5.79 % (27046)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_26806 for (2959ds/96Mi)
% 29.47/5.79 % (27047)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_26806 for (2959ds/503Mi)
% 30.78/5.83 % (27046)Instruction limit reached!
% 30.78/5.83 % (27046)------------------------------
% 30.78/5.83 % (27046)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.78/5.83 % (27046)Termination reason: Unknown
% 30.78/5.83 % (27046)Termination phase: Saturation
% 30.78/5.83
% 30.78/5.83 % (27046)Memory used [KB]: 6524
% 30.78/5.83 % (27046)Time elapsed: 0.043 s
% 30.78/5.83 % (27046)Instructions burned: 97 (million)
% 30.78/5.83 % (27046)------------------------------
% 30.78/5.83 % (27046)------------------------------
% 30.78/5.85 % (27048)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_26806 for (2958ds/90Mi)
% 30.78/5.87 % (27043)Instruction limit reached!
% 30.78/5.87 % (27043)------------------------------
% 30.78/5.87 % (27043)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.78/5.87 % (27043)Termination reason: Unknown
% 30.78/5.87 % (27043)Termination phase: Saturation
% 30.78/5.87
% 30.78/5.87 % (27043)Memory used [KB]: 9210
% 30.78/5.87 % (27043)Time elapsed: 0.170 s
% 30.78/5.87 % (27043)Instructions burned: 328 (million)
% 30.78/5.87 % (27043)------------------------------
% 30.78/5.87 % (27043)------------------------------
% 30.78/5.89 % (27048)Instruction limit reached!
% 30.78/5.89 % (27048)------------------------------
% 30.78/5.89 % (27048)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.78/5.89 % (27048)Termination reason: Unknown
% 30.78/5.89 % (27048)Termination phase: Saturation
% 30.78/5.89
% 30.78/5.89 % (27048)Memory used [KB]: 6908
% 30.78/5.89 % (27048)Time elapsed: 0.043 s
% 30.78/5.89 % (27048)Instructions burned: 91 (million)
% 30.78/5.89 % (27048)------------------------------
% 30.78/5.89 % (27048)------------------------------
% 30.78/5.89 % (27049)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_26806 for (2958ds/593Mi)
% 30.78/5.89 % (27032)First to succeed.
% 31.18/5.90 % (27032)Refutation found. Thanks to Tanya!
% 31.18/5.90 % SZS status Theorem for DTF2THF_26806
% 31.18/5.90 % SZS output start Proof for DTF2THF_26806
% 31.18/5.90 thf(func_def_0, type, in: $i > $i > $o).
% 31.18/5.90 thf(func_def_1, type, exu: ($i > $o) > $o).
% 31.18/5.90 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 31.18/5.90 thf(func_def_8, type, powerset: $i > $i).
% 31.18/5.90 thf(func_def_10, type, setunion: $i > $i).
% 31.18/5.90 thf(func_def_19, type, descr: ($i > $o) > $i).
% 31.18/5.90 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_26, type, prop2set: $o > $i).
% 31.18/5.90 thf(func_def_36, type, nonempty: $i > $o).
% 31.18/5.90 thf(func_def_69, type, set2prop: $i > $o).
% 31.18/5.90 thf(func_def_88, type, subset: $i > $i > $o).
% 31.18/5.90 thf(func_def_89, type, disjoint: $i > $i > $o).
% 31.18/5.90 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 31.18/5.90 thf(func_def_114, type, binunion: $i > $i > $i).
% 31.18/5.90 thf(func_def_122, type, binintersect: $i > $i > $i).
% 31.18/5.90 thf(func_def_135, type, regular: $i > $o).
% 31.18/5.90 thf(func_def_136, type, setminus: $i > $i > $i).
% 31.18/5.90 thf(func_def_147, type, symdiff: $i > $i > $i).
% 31.18/5.90 thf(func_def_153, type, iskpair: $i > $o).
% 31.18/5.90 thf(func_def_158, type, kpair: $i > $i > $i).
% 31.18/5.90 thf(func_def_160, type, cartprod: $i > $i > $i).
% 31.18/5.90 thf(func_def_185, type, sP1: $i > $i > $o).
% 31.18/5.90 thf(func_def_186, type, sP2: $i > $o).
% 31.18/5.90 thf(func_def_187, type, sP3: $i > $i > $o).
% 31.18/5.90 thf(func_def_188, type, sP4: $i > $i > $o).
% 31.18/5.90 thf(func_def_189, type, sP5: $o > $i > $i > $i > $o).
% 31.18/5.90 thf(func_def_191, type, sK7: $i > $o).
% 31.18/5.90 thf(func_def_197, type, sK13: $i > $i > $i).
% 31.18/5.90 thf(func_def_198, type, sK14: $o > $i > $i > $i).
% 31.18/5.90 thf(func_def_218, type, sK34: ($i > $o) > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_219, type, sK35: ($i > $o) > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_220, type, sK36: $i > $o).
% 31.18/5.90 thf(func_def_221, type, sK37: $i > $o).
% 31.18/5.90 thf(func_def_225, type, sK41: $i > $o).
% 31.18/5.90 thf(func_def_239, type, sK55: $i > $o).
% 31.18/5.90 thf(func_def_249, type, sK65: $i > $o).
% 31.18/5.90 thf(func_def_268, type, sK84: $i > $i > $i > $i).
% 31.18/5.90 thf(func_def_269, type, sK85: $i > $i > $i > $i).
% 31.18/5.90 thf(func_def_276, type, sK92: $i > $i > $i).
% 31.18/5.90 thf(func_def_280, type, sK96: $i > $o).
% 31.18/5.90 thf(func_def_282, type, sK98: ($i > $o) > $i).
% 31.18/5.90 thf(func_def_283, type, sK99: ($i > $o) > $i).
% 31.18/5.90 thf(func_def_284, type, sK100: ($i > $o) > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_285, type, sK101: ($i > $o) > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_286, type, sK102: $i > $o).
% 31.18/5.90 thf(func_def_287, type, sK103: $i > $o).
% 31.18/5.90 thf(func_def_288, type, sK104: ($i > $o) > $i).
% 31.18/5.90 thf(func_def_289, type, sK105: $i > $o).
% 31.18/5.90 thf(func_def_290, type, sK106: $i > $o).
% 31.18/5.90 thf(func_def_294, type, sK110: $i > $i).
% 31.18/5.90 thf(func_def_310, type, sK126: $i > $i > $i).
% 31.18/5.90 thf(func_def_319, type, sK135: $i > $i > $i).
% 31.18/5.90 thf(func_def_323, type, sK139: $i > $o).
% 31.18/5.90 thf(func_def_333, type, sK149: $i > $o).
% 31.18/5.90 thf(func_def_342, type, sK158: $i > $i > $o).
% 31.18/5.90 thf(func_def_343, type, sK159: $i > $i).
% 31.18/5.90 thf(func_def_344, type, sK160: $i > $i).
% 31.18/5.90 thf(func_def_345, type, sK161: ($i > $i > $o) > $i > $i).
% 31.18/5.90 thf(func_def_346, type, sK162: ($i > $i > $o) > $i > $i).
% 31.18/5.90 thf(func_def_347, type, sK163: $i > ($i > $i > $o) > $i > $i).
% 31.18/5.90 thf(func_def_362, type, sK178: $i > $i).
% 31.18/5.90 thf(func_def_365, type, sK181: $i > $o).
% 31.18/5.90 thf(func_def_367, type, sK183: $i > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_368, type, sK184: ($i > $o) > $i > $i).
% 31.18/5.90 thf(func_def_370, type, sK186: $i > $o).
% 31.18/5.90 thf(func_def_400, type, sK216: $i > $i).
% 31.18/5.90 thf(func_def_403, type, sK219: $i > $i).
% 31.18/5.90 thf(func_def_404, type, sK220: ($i > $o) > $i).
% 31.18/5.90 thf(func_def_405, type, sK221: $i > $o).
% 31.18/5.90 thf(func_def_406, type, sK222: $i > $i).
% 31.18/5.90 thf(func_def_417, type, sK233: $i > $i > $i).
% 31.18/5.90 thf(func_def_418, type, sK234: $i > $i > $i).
% 31.18/5.90 thf(func_def_420, type, sK236: $i > $i).
% 31.18/5.90 thf(func_def_426, type, sK242: $i > $i > $i).
% 31.18/5.90 thf(func_def_427, type, sK243: $i > $o).
% 31.18/5.90 thf(func_def_430, type, sK246: $i > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_437, type, sK253: $i > $i).
% 31.18/5.90 thf(func_def_439, type, sK255: $i > $i).
% 31.18/5.90 thf(func_def_441, type, sK257: $i > $o).
% 31.18/5.90 thf(func_def_447, type, sK263: $i > $i > $i).
% 31.18/5.90 thf(func_def_449, type, sK265: $i > $o).
% 31.18/5.90 thf(func_def_451, type, sK267: $i > $o).
% 31.18/5.90 thf(func_def_454, type, sK270: $i > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_477, type, sK293: ($i > $o) > $i).
% 31.18/5.90 thf(func_def_478, type, sK294: $i > $o).
% 31.18/5.90 thf(func_def_479, type, sK295: $i > $i).
% 31.18/5.90 thf(func_def_485, type, sK301: $i > $o).
% 31.18/5.90 thf(func_def_488, type, sK304: $i > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_502, type, sK318: $i > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_503, type, sK319: $i > $o).
% 31.18/5.90 thf(func_def_506, type, sK322: $i > $o).
% 31.18/5.90 thf(func_def_507, type, sK323: $i > $i > $i).
% 31.18/5.90 thf(func_def_508, type, sK324: $i > $i > $i).
% 31.18/5.90 thf(func_def_509, type, sK325: $i > $i > $i).
% 31.18/5.90 thf(func_def_510, type, sK326: $i > $i > $i).
% 31.18/5.90 thf(func_def_511, type, sK327: $i > $i > $i > $i).
% 31.18/5.90 thf(func_def_512, type, sK328: $i > $i).
% 31.18/5.90 thf(func_def_513, type, sK329: $i > $i).
% 31.18/5.90 thf(func_def_514, type, sK330: $i > $i).
% 31.18/5.90 thf(func_def_515, type, sK331: $i > $i).
% 31.18/5.90 thf(func_def_516, type, sK332: $i > $i > $i > $i).
% 31.18/5.90 thf(func_def_517, type, sK333: $i > $i > $i > $i).
% 31.18/5.90 thf(func_def_518, type, sK334: $i > $i > $i).
% 31.18/5.90 thf(func_def_519, type, sK335: $i > $i > $i).
% 31.18/5.90 thf(func_def_520, type, sK336: $i > $i > $i).
% 31.18/5.90 thf(func_def_522, type, sK338: $i > $i).
% 31.18/5.90 thf(func_def_523, type, sK339: $i > $i).
% 31.18/5.90 thf(func_def_524, type, sK340: $i > $i).
% 31.18/5.90 thf(func_def_525, type, sK341: $i > $i > $i).
% 31.18/5.90 thf(func_def_526, type, sK342: $i > $o).
% 31.18/5.90 thf(func_def_548, type, sK364: $i > $o).
% 31.18/5.90 thf(func_def_566, type, sK382: $i > $o).
% 31.18/5.90 thf(func_def_568, type, sK384: $i > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_571, type, sK387: $i > $o).
% 31.18/5.90 thf(func_def_572, type, sK388: $i > $o).
% 31.18/5.90 thf(func_def_573, type, sK389: ($i > $o) > ($i > $o) > $i > $i > $i).
% 31.18/5.90 thf(func_def_574, type, sK390: ($i > $o) > ($i > $o) > $i > $i > $i).
% 31.18/5.90 thf(func_def_586, type, sK402: $i > $i > $i).
% 31.18/5.90 thf(func_def_589, type, sK405: $i > ($i > $o) > $i).
% 31.18/5.90 thf(func_def_590, type, sK406: $i > $o).
% 31.18/5.90 thf(func_def_600, type, ph416: !>[X0: $tType]:(X0)).
% 31.18/5.90 thf(func_def_601, type, sK417: $i > $i).
% 31.18/5.90 thf(func_def_602, type, sK418: $i > $i).
% 31.18/5.90 thf(f16118,plain,(
% 31.18/5.90 $false),
% 31.18/5.90 inference(avatar_sat_refutation,[status(thm)],[f2936,f3127,f4753,f5318,f16117])).
% 31.18/5.90 thf(f16117,plain,(
% 31.18/5.90 ~spl415_170 | ~spl415_214),
% 31.18/5.90 inference(avatar_contradiction_clause,[status(thm)],[f16116])).
% 31.18/5.90 thf(f16116,plain,(
% 31.18/5.90 $false | (~spl415_170 | ~spl415_214)),
% 31.18/5.90 inference(subsumption_resolution,[status(thm)],[f16115,f1800])).
% 31.18/5.90 thf(f1800,plain,(
% 31.18/5.90 ($true != (iskpair @ sK298))),
% 31.18/5.90 inference(cnf_transformation,[status(thm)],[f1156])).
% 31.18/5.90 thf(f1156,plain,(
% 31.18/5.90 (symdiffIneg1 = $true) & (emptysetimpfalse = $true) & (exuE2 = $true) & (powersetE1 = $true) & (dsetconstr__Cong = $true) & (quantDeMorgan4 = $true) & (ubforcartprodlem3 = $true) & (setminusELneg = $true) & (upairsetIL = $true) & (binintersectSubset5 = $true) & (upairsetE = $true) & (binunionIL = $true) & (singletonsubset = $true) & (setunionE = $true) & (binunionE = $true) & (powersetI = $true) & (setadjoinE = $true) & (exu__Cong = $true) & (emptysetE = $true) & (symdiffE = $true) & (notinsingleton = $true) & (powersetI1 = $true) & (symdiffI1 = $true) & (subsetE2 = $true) & (exuE3u = $true) & (subPowSU = $true) & (setadjoinSub2 = $true) & (setadjoinIL = $true) & (binunionEcases = $true) & (setadjoinOr = $true) & (setadjoin__Cong = $true) & (binintersectER = $true) & (setunionAx = $true) & (dsetconstrI = $true) & (notdallE = $true) & (binintersectSubset3 = $true) & (dsetconstrEL = $true) & (binintersectSubset4 = $true) & (singletoninpowerset = $true) & (setunionI = $true) & (eqimpsubset1 = $true) & (foundationAx = $true) & (in__Cong = $true) & (exuI1 = $true) & (subsetI1 = $true) & (nonemptyI = $true) & (sepInPowerset = $true) & (prop2set2propI = $true) & (symdiffIneg2 = $true) & (setukpairIL = $true) & (cartprodmempair1 = $true) & (disjointsetsI1 = $true) & (binunionLsub = $true) & (eqimpsubset2 = $true) & (nonemptyImpWitness = $true) & (omega0Ax = $true) & (setadjoinIR = $true) & (emptysetAx = $true) & (setminusEL = $true) & (notdexE = $true) & (bs114d = $true) & (setunion__Cong = $true) & (setminusER = $true) & (subsetRefl = $true) & (cartprodpairin = $true) & (notequalI2 = $true) & (inPowerset = $true) & (upairsubunion = $true) & (notsubsetI = $true) & (subsetI2 = $true) & (kpairp = $true) & (exuI2 = $true) & (descrp = $true) & (singletoninpowunion = $true) & (nonemptyE1 = $true) & (exuEu = $true) & (quantDeMorgan1 = $true) & (setminusERneg = $true) & (setadjoinSub = $true) & (setext = $true) & (setminusSubset1 = $true) & (quantDeMorgan2 = $true) & (subset2powerset = $true) & (replAx = $true) & (upairinpowunion = $true) & (($true = (in @ sK298 @ (cartprod @ sK300 @ sK299))) & ($true != (iskpair @ sK298))) & (ubforcartprodlem2 = $true) & (sepSubset = $true) & (powersetAx = $true) & (setminusILneg = $true) & (emptysetsubset = $true) & (emptyinPowerset = $true) & (setadjoinAx = $true) & (descr__Cong = $true) & (binintersectLsub = $true) & (upairset2E = $true) & (notequalI1 = $true) & (symdiffI2 = $true) & (setextsub = $true) & (setminusI = $true) & (omegaSAx = $true) & (uniqinunit = $true) & (omegaIndAx = $true) & (setminusSubset2 = $true) & (omega__Cong = $true) & (setoftrueEq = $true) & (inCongP = $true) & (prop2setE = $true) & (powerset__Cong = $true) & (emptyset__Cong = $true) & (emptyI = $true) & (setbeta = $true) & (exuE1 = $true) & (notinemptyset = $true) & (powersetsubset = $true) & (binintersectSubset1 = $true) & (wellorderingAx = $true) & (exuI3 = $true) & (ubforcartprodlem1 = $true) & (binunionRsub = $true) & (nonemptyI1 = $true) & (dsetconstrER = $true) & (setminusIRneg = $true) & (powersetE = $true) & (upairsetIR = $true) & (noeltsimpempty = $true) & (binintersectEL = $true) & (prop2setI = $true) & (emptyinunitempty = $true) & (emptyE1 = $true) & (upairset2IR = $true) & (exuE3e = $true) & (vacuousDall = $true) & (subsetTrans = $true) & (subsetemptysetimpeq = $true) & (kpairiskpair = $true) & (setminusLsub = $true) & (binintersectSubset2 = $true) & (secondinupair = $true) & (setukpairIR = $true) & (setextAx = $true) & (emptyInPowerset = $true) & (binunionIR = $true) & (eqinunit = $true) & (subsetE = $true) & (binintersectI = $true) & (singletonsswitch = $true) & (quantDeMorgan3 = $true) & (binintersectRsub = $true)),
% 31.18/5.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK298,sK299,sK300])],[f512,f1155])).
% 31.18/5.90 thf(f1155,plain,(
% 31.18/5.90 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X2 @ X1))) & ($true != (iskpair @ X0))) => (($true = (in @ sK298 @ (cartprod @ sK300 @ sK299))) & ($true != (iskpair @ sK298)))),
% 31.18/5.90 introduced(definition,[],[choice_axiom])).
% 31.18/5.90 thf(f512,plain,(
% 31.18/5.90 (symdiffIneg1 = $true) & (emptysetimpfalse = $true) & (exuE2 = $true) & (powersetE1 = $true) & (dsetconstr__Cong = $true) & (quantDeMorgan4 = $true) & (ubforcartprodlem3 = $true) & (setminusELneg = $true) & (upairsetIL = $true) & (binintersectSubset5 = $true) & (upairsetE = $true) & (binunionIL = $true) & (singletonsubset = $true) & (setunionE = $true) & (binunionE = $true) & (powersetI = $true) & (setadjoinE = $true) & (exu__Cong = $true) & (emptysetE = $true) & (symdiffE = $true) & (notinsingleton = $true) & (powersetI1 = $true) & (symdiffI1 = $true) & (subsetE2 = $true) & (exuE3u = $true) & (subPowSU = $true) & (setadjoinSub2 = $true) & (setadjoinIL = $true) & (binunionEcases = $true) & (setadjoinOr = $true) & (setadjoin__Cong = $true) & (binintersectER = $true) & (setunionAx = $true) & (dsetconstrI = $true) & (notdallE = $true) & (binintersectSubset3 = $true) & (dsetconstrEL = $true) & (binintersectSubset4 = $true) & (singletoninpowerset = $true) & (setunionI = $true) & (eqimpsubset1 = $true) & (foundationAx = $true) & (in__Cong = $true) & (exuI1 = $true) & (subsetI1 = $true) & (nonemptyI = $true) & (sepInPowerset = $true) & (prop2set2propI = $true) & (symdiffIneg2 = $true) & (setukpairIL = $true) & (cartprodmempair1 = $true) & (disjointsetsI1 = $true) & (binunionLsub = $true) & (eqimpsubset2 = $true) & (nonemptyImpWitness = $true) & (omega0Ax = $true) & (setadjoinIR = $true) & (emptysetAx = $true) & (setminusEL = $true) & (notdexE = $true) & (bs114d = $true) & (setunion__Cong = $true) & (setminusER = $true) & (subsetRefl = $true) & (cartprodpairin = $true) & (notequalI2 = $true) & (inPowerset = $true) & (upairsubunion = $true) & (notsubsetI = $true) & (subsetI2 = $true) & (kpairp = $true) & (exuI2 = $true) & (descrp = $true) & (singletoninpowunion = $true) & (nonemptyE1 = $true) & (exuEu = $true) & (quantDeMorgan1 = $true) & (setminusERneg = $true) & (setadjoinSub = $true) & (setext = $true) & (setminusSubset1 = $true) & (quantDeMorgan2 = $true) & (subset2powerset = $true) & (replAx = $true) & (upairinpowunion = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X2 @ X1))) & ($true != (iskpair @ X0))) & (ubforcartprodlem2 = $true) & (sepSubset = $true) & (powersetAx = $true) & (setminusILneg = $true) & (emptysetsubset = $true) & (emptyinPowerset = $true) & (setadjoinAx = $true) & (descr__Cong = $true) & (binintersectLsub = $true) & (upairset2E = $true) & (notequalI1 = $true) & (symdiffI2 = $true) & (setextsub = $true) & (setminusI = $true) & (omegaSAx = $true) & (uniqinunit = $true) & (omegaIndAx = $true) & (setminusSubset2 = $true) & (omega__Cong = $true) & (setoftrueEq = $true) & (inCongP = $true) & (prop2setE = $true) & (powerset__Cong = $true) & (emptyset__Cong = $true) & (emptyI = $true) & (setbeta = $true) & (exuE1 = $true) & (notinemptyset = $true) & (powersetsubset = $true) & (binintersectSubset1 = $true) & (wellorderingAx = $true) & (exuI3 = $true) & (ubforcartprodlem1 = $true) & (binunionRsub = $true) & (nonemptyI1 = $true) & (dsetconstrER = $true) & (setminusIRneg = $true) & (powersetE = $true) & (upairsetIR = $true) & (noeltsimpempty = $true) & (binintersectEL = $true) & (prop2setI = $true) & (emptyinunitempty = $true) & (emptyE1 = $true) & (upairset2IR = $true) & (exuE3e = $true) & (vacuousDall = $true) & (subsetTrans = $true) & (subsetemptysetimpeq = $true) & (kpairiskpair = $true) & (setminusLsub = $true) & (binintersectSubset2 = $true) & (secondinupair = $true) & (setukpairIR = $true) & (setextAx = $true) & (emptyInPowerset = $true) & (binunionIR = $true) & (eqinunit = $true) & (subsetE = $true) & (binintersectI = $true) & (singletonsswitch = $true) & (quantDeMorgan3 = $true) & (binintersectRsub = $true)),
% 31.18/5.90 inference(flattening,[status(thm)],[f511])).
% 31.18/5.90 thf(f511,plain,(
% 31.18/5.90 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X2 @ X1))) & ($true != (iskpair @ X0))) & (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)),
% 31.18/5.90 inference(ennf_transformation,[status(thm)],[f159])).
% 31.18/5.90 thf(f159,plain,(
% 31.18/5.90 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X2 @ X1))) => ($true = (iskpair @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.18/5.90 inference(fool_elimination,[status(thm)],[f158])).
% 31.18/5.90 thf(f158,plain,(
% 31.18/5.90 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X2 @ X1)) => (iskpair @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.18/5.90 inference(rectify,[status(thm)],[f154])).
% 31.18/5.90 thf(f154,negated_conjecture,(
% 31.18/5.90 ~(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 => ! [X10 : $i,X4 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (iskpair @ X10))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.18/5.90 inference(negated_conjecture,[status(cth)],[f153])).
% 31.18/5.90 thf(f153,conjecture,(
% 31.18/5.90 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 => ! [X10 : $i,X4 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (iskpair @ X10)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 31.18/5.90 file('/export/starexec/sandbox/tmp/tmp.qvI7ApaoRY/DTF2THF_26806.p',cartprodmempair)).
% 31.18/5.90 thf(f16115,plain,(
% 31.18/5.90 ($true = (iskpair @ sK298)) | (~spl415_170 | ~spl415_214)),
% 31.18/5.90 inference(superposition,[status(thm)],[f2931,f12299])).
% 31.18/5.90 thf(f12299,plain,(
% 31.18/5.90 (sK298 = (kpair @ (sK84 @ sK300 @ sK298 @ sK299) @ (sK85 @ sK300 @ sK298 @ sK299))) | ~spl415_214),
% 31.18/5.90 inference(trivial_inequality_removal,[status(thm)],[f12283])).
% 31.18/5.90 thf(f12283,plain,(
% 31.18/5.90 ($true != $true) | (sK298 = (kpair @ (sK84 @ sK300 @ sK298 @ sK299) @ (sK85 @ sK300 @ sK298 @ sK299))) | ~spl415_214),
% 31.18/5.90 inference(superposition,[status(thm)],[f3126,f1801])).
% 31.18/5.90 thf(f1801,plain,(
% 31.18/5.90 ($true = (in @ sK298 @ (cartprod @ sK300 @ sK299)))),
% 31.18/5.90 inference(cnf_transformation,[status(thm)],[f1156])).
% 31.18/5.90 thf(f3126,plain,(
% 31.18/5.90 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X6 @ (cartprod @ X7 @ X5))) | ((kpair @ (sK84 @ X7 @ X6 @ X5) @ (sK85 @ X7 @ X6 @ X5)) = X6)) ) | ~spl415_214),
% 31.18/5.90 inference(avatar_component_clause,[status(thm)],[f3125])).
% 31.18/5.90 thf(f3125,definition,(
% 31.18/5.90 spl415_214 <=> ! [X6 : $i,X5 : $i,X7 : $i] : (($true != (in @ X6 @ (cartprod @ X7 @ X5))) | ((kpair @ (sK84 @ X7 @ X6 @ X5) @ (sK85 @ X7 @ X6 @ X5)) = X6))),
% 31.18/5.90 introduced(definition,[new_symbols(naming,[spl415_214])],[avatar_definition])).
% 31.18/5.90 thf(f2931,plain,(
% 31.18/5.90 ( ! [X0 : $i,X1 : $i] : (($true = (iskpair @ (kpair @ X0 @ X1)))) ) | ~spl415_170),
% 31.18/5.90 inference(avatar_component_clause,[status(thm)],[f2930])).
% 31.18/5.90 thf(f2930,definition,(
% 31.18/5.90 spl415_170 <=> ! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X0 @ X1)))),
% 31.18/5.90 introduced(definition,[new_symbols(naming,[spl415_170])],[avatar_definition])).
% 31.18/5.90 thf(f5318,plain,(
% 31.18/5.90 spl415_213),
% 31.18/5.90 inference(avatar_split_clause,[status(thm)],[f1836,f3121])).
% 31.18/5.90 thf(f3121,definition,(
% 31.18/5.90 spl415_213 <=> (cartprodmempair1 = $true)),
% 31.18/5.90 introduced(definition,[new_symbols(naming,[spl415_213])],[avatar_definition])).
% 31.18/5.90 thf(f1836,plain,(
% 31.18/5.90 (cartprodmempair1 = $true)),
% 31.18/5.90 inference(cnf_transformation,[status(thm)],[f1156])).
% 31.18/5.90 thf(f4753,plain,(
% 31.18/5.90 spl415_171),
% 31.18/5.90 inference(avatar_split_clause,[status(thm)],[f1816,f2933])).
% 31.18/5.90 thf(f2933,definition,(
% 31.18/5.90 spl415_171 <=> (kpairp = $true)),
% 31.18/5.90 introduced(definition,[new_symbols(naming,[spl415_171])],[avatar_definition])).
% 31.18/5.90 thf(f1816,plain,(
% 31.18/5.90 (kpairp = $true)),
% 31.18/5.90 inference(cnf_transformation,[status(thm)],[f1156])).
% 31.18/5.90 thf(f3127,plain,(
% 31.18/5.90 ~spl415_213 | spl415_214),
% 31.18/5.90 inference(avatar_split_clause,[status(thm)],[f1440,f3125,f3121])).
% 31.18/5.90 thf(f1440,plain,(
% 31.18/5.90 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X6 @ (cartprod @ X7 @ X5))) | (cartprodmempair1 != $true) | ((kpair @ (sK84 @ X7 @ X6 @ X5) @ (sK85 @ X7 @ X6 @ X5)) = X6)) )),
% 31.18/5.90 inference(cnf_transformation,[status(thm)],[f788])).
% 31.18/5.90 thf(f788,plain,(
% 31.18/5.90 ((cartprodmempair1 = $true) | (($true = (in @ sK82 @ (cartprod @ sK83 @ sK81))) & ! [X3 : $i] : (! [X4 : $i] : ((sK82 != (kpair @ X3 @ X4)) | ($true != (in @ X4 @ sK81))) | ($true != (in @ X3 @ sK83))))) & (! [X5 : $i,X6 : $i,X7 : $i] : (($true != (in @ X6 @ (cartprod @ X7 @ X5))) | ((((kpair @ (sK84 @ X7 @ X6 @ X5) @ (sK85 @ X7 @ X6 @ X5)) = X6) & ($true = (in @ (sK85 @ X7 @ X6 @ X5) @ X5))) & ($true = (in @ (sK84 @ X7 @ X6 @ X5) @ X7)))) | (cartprodmempair1 != $true))),
% 31.18/5.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK81,sK82,sK83,sK84,sK85])],[f784,f787,f786,f785])).
% 31.18/5.90 thf(f785,plain,(
% 31.18/5.90 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (cartprod @ X2 @ X0)) = $true) & ! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != X1) | ($true != (in @ X4 @ X0))) | ($true != (in @ X3 @ X2)))) => (($true = (in @ sK82 @ (cartprod @ sK83 @ sK81))) & ! [X3 : $i] : (! [X4 : $i] : ((sK82 != (kpair @ X3 @ X4)) | ($true != (in @ X4 @ sK81))) | ($true != (in @ X3 @ sK83))))),
% 31.18/5.90 introduced(definition,[],[choice_axiom])).
% 31.18/5.90 thf(f786,plain,(
% 31.18/5.90 ! [X5 : $i,X6 : $i,X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : (((kpair @ X8 @ X9) = X6) & ($true = (in @ X9 @ X5))) & ($true = (in @ X8 @ X7))) => (? [X9 : $i] : (((kpair @ (sK84 @ X7 @ X6 @ X5) @ X9) = X6) & ($true = (in @ X9 @ X5))) & ($true = (in @ (sK84 @ X7 @ X6 @ X5) @ X7))))),
% 31.18/5.90 introduced(definition,[],[choice_axiom])).
% 31.18/5.90 thf(f787,plain,(
% 31.18/5.90 ! [X5 : $i,X6 : $i,X7 : $i] : (? [X9 : $i] : (((kpair @ (sK84 @ X7 @ X6 @ X5) @ X9) = X6) & ($true = (in @ X9 @ X5))) => (((kpair @ (sK84 @ X7 @ X6 @ X5) @ (sK85 @ X7 @ X6 @ X5)) = X6) & ($true = (in @ (sK85 @ X7 @ X6 @ X5) @ X5))))),
% 31.18/5.90 introduced(definition,[],[choice_axiom])).
% 31.18/5.90 thf(f784,plain,(
% 31.18/5.90 ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (cartprod @ X2 @ X0)) = $true) & ! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != X1) | ($true != (in @ X4 @ X0))) | ($true != (in @ X3 @ X2))))) & (! [X5 : $i,X6 : $i,X7 : $i] : (($true != (in @ X6 @ (cartprod @ X7 @ X5))) | ? [X8 : $i] : (? [X9 : $i] : (((kpair @ X8 @ X9) = X6) & ($true = (in @ X9 @ X5))) & ($true = (in @ X8 @ X7)))) | (cartprodmempair1 != $true))),
% 31.18/5.90 inference(rectify,[status(thm)],[f783])).
% 31.18/5.90 thf(f783,plain,(
% 31.18/5.90 ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (cartprod @ X2 @ X0)) = $true) & ! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != X1) | ($true != (in @ X4 @ X0))) | ($true != (in @ X3 @ X2))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (cartprod @ X2 @ X0)) != $true) | ? [X3 : $i] : (? [X4 : $i] : (((kpair @ X3 @ X4) = X1) & ($true = (in @ X4 @ X0))) & ($true = (in @ X3 @ X2)))) | (cartprodmempair1 != $true))),
% 31.18/5.90 inference(nnf_transformation,[status(thm)],[f615])).
% 31.18/5.90 thf(f615,plain,(
% 31.18/5.90 (cartprodmempair1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (cartprod @ X2 @ X0)) != $true) | ? [X3 : $i] : (? [X4 : $i] : (((kpair @ X3 @ X4) = X1) & ($true = (in @ X4 @ X0))) & ($true = (in @ X3 @ X2))))),
% 31.18/5.90 inference(ennf_transformation,[status(thm)],[f205])).
% 31.18/5.90 thf(f205,plain,(
% 31.18/5.90 ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X1 @ (cartprod @ X2 @ X0)) = $true) => ? [X3 : $i] : (? [X4 : $i] : (((kpair @ X3 @ X4) = X1) & ($true = (in @ X4 @ X0))) & ($true = (in @ X3 @ X2)))) <=> (cartprodmempair1 = $true)),
% 31.18/5.90 inference(fool_elimination,[status(thm)],[f204])).
% 31.18/5.90 thf(f204,plain,(
% 31.18/5.90 (cartprodmempair1 = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ (cartprod @ X2 @ X0)) => ? [X3 : $i] : ((in @ X3 @ X2) & ? [X4 : $i] : ((in @ X4 @ X0) & ((kpair @ X3 @ X4) = X1)))))),
% 31.18/5.90 inference(rectify,[status(thm)],[f152])).
% 31.18/5.90 thf(f152,axiom,(
% 31.18/5.90 (cartprodmempair1 = ! [X4 : $i,X10 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ? [X1 : $i] : ((in @ X1 @ X3) & ? [X2 : $i] : ((in @ X2 @ X4) & ((kpair @ X1 @ X2) = X10)))))),
% 31.18/5.90 file('/export/starexec/sandbox/tmp/tmp.qvI7ApaoRY/DTF2THF_26806.p',cartprodmempair1)).
% 31.18/5.90 thf(f2936,plain,(
% 31.18/5.90 spl415_170 | ~spl415_171),
% 31.18/5.90 inference(avatar_split_clause,[status(thm)],[f1437,f2933,f2930])).
% 31.18/5.90 thf(f1437,plain,(
% 31.18/5.90 ( ! [X0 : $i,X1 : $i] : ((kpairp != $true) | ($true = (iskpair @ (kpair @ X0 @ X1)))) )),
% 31.18/5.90 inference(cnf_transformation,[status(thm)],[f782])).
% 31.18/5.90 thf(f782,plain,(
% 31.18/5.90 (! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X0 @ X1))) | (kpairp != $true)) & ((kpairp = $true) | ($true != (iskpair @ (kpair @ sK79 @ sK80))))),
% 31.18/5.90 inference(skolemisation,[status(esa),new_symbols(skolem,[sK79,sK80])],[f780,f781])).
% 31.18/5.90 thf(f781,plain,(
% 31.18/5.90 ? [X2 : $i,X3 : $i] : ($true != (iskpair @ (kpair @ X2 @ X3))) => ($true != (iskpair @ (kpair @ sK79 @ sK80)))),
% 31.18/5.90 introduced(definition,[],[choice_axiom])).
% 31.18/5.90 thf(f780,plain,(
% 31.18/5.90 (! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X0 @ X1))) | (kpairp != $true)) & ((kpairp = $true) | ? [X2 : $i,X3 : $i] : ($true != (iskpair @ (kpair @ X2 @ X3))))),
% 31.18/5.90 inference(rectify,[status(thm)],[f779])).
% 31.18/5.90 thf(f779,plain,(
% 31.18/5.90 (! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X0 @ X1))) | (kpairp != $true)) & ((kpairp = $true) | ? [X0 : $i,X1 : $i] : ($true != (iskpair @ (kpair @ X0 @ X1))))),
% 31.18/5.90 inference(nnf_transformation,[status(thm)],[f203])).
% 31.18/5.90 thf(f203,plain,(
% 31.18/5.90 ! [X0 : $i,X1 : $i] : ($true = (iskpair @ (kpair @ X0 @ X1))) <=> (kpairp = $true)),
% 31.18/5.90 inference(fool_elimination,[status(thm)],[f202])).
% 31.18/5.90 thf(f202,plain,(
% 31.18/5.90 (! [X0 : $i,X1 : $i] : (iskpair @ (kpair @ X0 @ X1)) = kpairp)),
% 31.18/5.90 inference(rectify,[status(thm)],[f141])).
% 31.18/5.90 thf(f141,axiom,(
% 31.18/5.90 (! [X1 : $i,X2 : $i] : (iskpair @ (kpair @ X1 @ X2)) = kpairp)),
% 31.18/5.90 file('/export/starexec/sandbox/tmp/tmp.qvI7ApaoRY/DTF2THF_26806.p',kpairp)).
% 31.18/5.90 % SZS output end Proof for DTF2THF_26806
% 31.18/5.90 % (27032)------------------------------
% 31.18/5.90 % (27032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.18/5.90 % (27032)Termination reason: Refutation
% 31.18/5.90
% 31.18/5.90 % (27032)Memory used [KB]: 15607
% 31.18/5.90 % (27032)Time elapsed: 1.617 s
% 31.18/5.90 % (27032)Instructions burned: 3092 (million)
% 31.18/5.90 % (27032)------------------------------
% 31.18/5.90 % (27032)------------------------------
% 31.18/5.90 % (26910)Success in time 4.174 s
%------------------------------------------------------------------------------