%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU658^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:36:00 AM UTC 2026
% Result : Theorem 21.48s 4.33s
% Output : Refutation 21.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 11 unt; 0 typ; 5 def)
% Number of atoms : 3018 ( 822 equ; 0 cnn)
% Maximal formula atoms : 176 ( 55 avg)
% Number of connectives : 1780 ( 71 ~; 57 |; 558 &; 378 @)
% ( 8 <=>; 708 =>; 0 <=; 0 <~>)
% Maximal formula depth : 183 ( 28 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 330 ( 327 usr; 189 con; 0-4 aty)
% Number of variables : 125 ( 0 ^; 85 !; 40 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_203,type,
ksnd: $i > $i ).
thf(func_def_219,type,
sP1: $o > $i > $i > $i > $o ).
thf(func_def_221,type,
sP3: $i > $i > $o ).
thf(func_def_222,type,
sP4: $i > $o ).
thf(func_def_223,type,
sP5: $i > $i > $o ).
thf(func_def_224,type,
sP6: $i > $i > $o ).
thf(func_def_226,type,
sK8: $i > $o ).
thf(func_def_236,type,
sK18: $i > $o ).
thf(func_def_237,type,
sK19: ( $i > $o ) > $i > $i > $i ).
thf(func_def_242,type,
sK24: $i > $i ).
thf(func_def_245,type,
sK27: $i > $o ).
thf(func_def_248,type,
sK30: $i > $o ).
thf(func_def_252,type,
sK34: $i > $i ).
thf(func_def_254,type,
sK36: $i > $i ).
thf(func_def_255,type,
sK37: ( $i > $o ) > $i ).
thf(func_def_256,type,
sK38: $i > $o ).
thf(func_def_264,type,
sK46: $i > $o ).
thf(func_def_266,type,
sK48: $i > $o ).
thf(func_def_268,type,
sK50: ( $i > $o ) > $i > $i ).
thf(func_def_314,type,
sK96: $i > $o ).
thf(func_def_325,type,
sK107: $i > $i > $i > $i ).
thf(func_def_326,type,
sK108: $i > $i > $i > $i ).
thf(func_def_334,type,
sK116: $i > $o ).
thf(func_def_337,type,
sK119: $i > $o ).
thf(func_def_339,type,
sK121: ( $i > $o ) > $i > $i ).
thf(func_def_343,type,
sK125: $i > $o ).
thf(func_def_350,type,
sK132: $i > $i ).
thf(func_def_351,type,
sK133: $i > $o ).
thf(func_def_353,type,
sK135: $i > ( $i > $o ) > $i ).
thf(func_def_356,type,
sK138: $i > $o ).
thf(func_def_359,type,
sK141: $i > ( $i > $o ) > $i ).
thf(func_def_365,type,
sK147: $i > $i > $i ).
thf(func_def_368,type,
sK150: $i > $i > $i ).
thf(func_def_384,type,
sK166: $o > $i > $i > $i ).
thf(func_def_402,type,
sK184: $i > $o ).
thf(func_def_407,type,
sK189: $i > $o ).
thf(func_def_408,type,
sK190: $i > $o ).
thf(func_def_409,type,
sK191: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_410,type,
sK192: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_413,type,
sK195: $i > $o ).
thf(func_def_425,type,
sK207: $i > ( $i > $o ) > $i ).
thf(func_def_426,type,
sK208: $i > $o ).
thf(func_def_433,type,
sK215: $i > $i ).
thf(func_def_440,type,
sK222: $i > $o ).
thf(func_def_442,type,
sK224: ( $i > $o ) > $i > $i ).
thf(func_def_444,type,
sK226: $i > $i ).
thf(func_def_453,type,
sK235: $i > $o ).
thf(func_def_461,type,
sK243: $i > $o ).
thf(func_def_464,type,
sK246: $i > ( $i > $o ) > $i ).
thf(func_def_465,type,
sK247: $i > ( $i > $o ) > $i ).
thf(func_def_472,type,
sK254: $i > $i > $i ).
thf(func_def_493,type,
sK275: $i > $i > $i ).
thf(func_def_511,type,
sK293: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_512,type,
sK294: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_513,type,
sK295: $i > $o ).
thf(func_def_514,type,
sK296: $i > $o ).
thf(func_def_515,type,
sK297: $i > ( $i > $o ) > $i ).
thf(func_def_516,type,
sK298: $i > $o ).
thf(func_def_541,type,
sK323: $i > $i > $i ).
thf(func_def_552,type,
sK334: $i > $i > $i ).
thf(func_def_555,type,
sK337: $i > $o ).
thf(func_def_557,type,
sK339: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_558,type,
sK340: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_559,type,
sK341: $i > $o ).
thf(func_def_560,type,
sK342: $i > $o ).
thf(func_def_567,type,
sK349: $i > $i > $o ).
thf(func_def_569,type,
sK351: $i > $i ).
thf(func_def_570,type,
sK352: $i > $i ).
thf(func_def_571,type,
sK353: $i > ( $i > $i > $o ) > $i ).
thf(func_def_572,type,
sK354: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_573,type,
sK355: $i > ( $i > $i > $o ) > $i ).
thf(func_def_586,type,
sK368: $i > $i > $i ).
thf(func_def_596,type,
sK378: $i > $o ).
thf(func_def_597,type,
sK379: $i > $i ).
thf(func_def_598,type,
sK380: ( $i > $o ) > $i ).
thf(func_def_603,type,
sK385: $i > $i > $i ).
thf(func_def_621,type,
sK403: $i > $i > $i ).
thf(func_def_622,type,
sK404: $i > $i > $i ).
thf(func_def_637,type,
sK419: ( $i > $o ) > $i ).
thf(func_def_638,type,
sK420: $i > $o ).
thf(func_def_639,type,
sK421: $i > $i ).
thf(func_def_646,type,
sK428: $i > $o ).
thf(func_def_649,type,
sK431: $i > ( $i > $o ) > $i ).
thf(func_def_653,type,
sK435: $i > $o ).
thf(func_def_656,type,
sK438: $i > ( $i > $o ) > $i ).
thf(func_def_659,type,
sK441: $i > $o ).
thf(func_def_661,type,
sK443: ( $i > $o ) > $i ).
thf(func_def_662,type,
sK444: ( $i > $o ) > $i ).
thf(func_def_665,type,
sK447: $i > $i > $i ).
thf(func_def_666,type,
sK448: $i > $i > $i ).
thf(func_def_667,type,
sK449: $i > $i > $i ).
thf(func_def_668,type,
sK450: $i > $i > $i ).
thf(func_def_669,type,
sK451: $i > $i > $i > $i ).
thf(func_def_670,type,
sK452: $i > $i ).
thf(func_def_671,type,
sK453: $i > $i ).
thf(func_def_672,type,
sK454: $i > $i ).
thf(func_def_673,type,
sK455: $i > $i ).
thf(func_def_674,type,
sK456: $i > $i > $i ).
thf(func_def_675,type,
sK457: $i > $i > $i > $i ).
thf(func_def_676,type,
sK458: $i > $i > $i > $i ).
thf(func_def_677,type,
sK459: $i > $i > $i ).
thf(func_def_678,type,
sK460: $i > $i > $i ).
thf(func_def_680,type,
sK462: $i > $i ).
thf(func_def_681,type,
sK463: $i > $i ).
thf(func_def_682,type,
sK464: $i > $i ).
thf(func_def_683,type,
sK465: $i > $i > $i ).
thf(func_def_687,type,
sK469: $i > $o ).
thf(func_def_694,type,
sK476: $i > $i ).
thf(func_def_697,type,
sK479: $i > $o ).
thf(func_def_699,type,
sK481: ( $i > $o ) > $i > $i ).
thf(func_def_700,type,
sK482: ( $i > $o ) > $i > $i ).
thf(func_def_705,type,
ph487:
!>[X0: $tType] : X0 ).
thf(f16821,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3931,f4977,f5343,f5626,f6236,f16820]) ).
thf(f16820,plain,
( ~ spl486_308
| ~ spl486_533
| ~ spl486_609 ),
inference(avatar_contradiction_clause,[status(thm)],[f16819]) ).
thf(f16819,plain,
( $false
| ~ spl486_308
| ~ spl486_533
| ~ spl486_609 ),
inference(subsumption_resolution,[status(thm)],[f16818,f1775]) ).
thf(f1775,plain,
( $true
!= ( in @ ( ksnd @ sK80 ) @ sK81 ) ),
inference(cnf_transformation,[status(thm)],[f893]) ).
thf(f893,plain,
( ( powersetsubset = $true )
& ( symdiffIneg1 = $true )
& ( powersetAx = $true )
& ( notsubsetI = $true )
& ( cartprodmempair1 = $true )
& ( upairequniteq = $true )
& ( omega__Cong = $true )
& ( setextAx = $true )
& ( notdexE = $true )
& ( emptysetE = $true )
& ( noeltsimpempty = $true )
& ( subsetE = $true )
& ( sepSubset = $true )
& ( cartprodmempair = $true )
& ( eqimpsubset1 = $true )
& ( emptyinunitempty = $true )
& ( setadjoinAx = $true )
& ( binintersectSubset1 = $true )
& ( dsetconstrI = $true )
& ( emptysetimpfalse = $true )
& ( binintersectEL = $true )
& ( exu__Cong = $true )
& ( exuI3 = $true )
& ( setadjoinE = $true )
& ( setukpairinjL2 = $true )
& ( descr__Cong = $true )
& ( binunionRsub = $true )
& ( subPowSU = $true )
& ( setoftrueEq = $true )
& ( singletoninpowunion = $true )
& ( prop2set2propI = $true )
& ( ksndsingleton = $true )
& ( setunionsingleton = $true )
& ( exuI1 = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( emptyE1 = $true )
& ( setunionI = $true )
& ( setunionE2 = $true )
& ( setukpairIL = $true )
& ( setextsub = $true )
& ( subsetRefl = $true )
& ( bs114d = $true )
& ( foundationAx = $true )
& ( symdiffI2 = $true )
& ( setadjoinSub = $true )
& ( kpairsurjEq = $true )
& ( theprop = $true )
& ( setadjoin__Cong = $true )
& ( binintersectSubset4 = $true )
& ( upairinpowunion = $true )
& ( notinemptyset = $true )
& ( setukpairinjR2 = $true )
& ( nonemptyI1 = $true )
& ( setunion__Cong = $true )
& ( setminusEL = $true )
& ( powersetI = $true )
& ( quantDeMorgan4 = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR12 = $true )
& ( kpairp = $true )
& ( setminusI = $true )
& ( upairset2IR = $true )
& ( setminusLsub = $true )
& ( ( in @ sK80 @ ( cartprod @ sK82 @ sK81 ) )
= $true )
& ( $true
!= ( in @ ( ksnd @ sK80 ) @ sK81 ) )
& ( emptyInPowerset = $true )
& ( sepInPowerset = $true )
& ( omegaSAx = $true )
& ( setminusSubset2 = $true )
& ( subset2powerset = $true )
& ( upairsetIL = $true )
& ( kfstsingleton = $true )
& ( binintersectRsub = $true )
& ( descrp = $true )
& ( dsetconstr__Cong = $true )
& ( singletonsuniq = $true )
& ( exuEu = $true )
& ( setukpairinjR1 = $true )
& ( ex1I2 = $true )
& ( setminusIRneg = $true )
& ( ex1I = $true )
& ( setbeta = $true )
& ( emptyinPowerset = $true )
& ( exuE3u = $true )
& ( upairsetE = $true )
& ( setminusELneg = $true )
& ( setminusER = $true )
& ( setadjoinOr = $true )
& ( kfstpairEq = $true )
& ( setext = $true )
& ( ksndpairEq = $true )
& ( setminusERneg = $true )
& ( binintersectER = $true )
& ( ubforcartprodlem1 = $true )
& ( binintersectSubset3 = $true )
& ( in__Cong = $true )
& ( exuE3e = $true )
& ( kpairiskpair = $true )
& ( singletonsswitch = $true )
& ( binunionIR = $true )
& ( setunionE = $true )
& ( setunionsingleton2 = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( wellorderingAx = $true )
& ( binunionE = $true )
& ( subsetTrans = $true )
& ( setminusSubset1 = $true )
& ( omega0Ax = $true )
& ( subsetE2 = $true )
& ( eqimpsubset2 = $true )
& ( cartprodpairin = $true )
& ( singletonprop = $true )
& ( quantDeMorgan3 = $true )
& ( ex1E1 = $true )
& ( setukpairinjL1 = $true )
& ( vacuousDall = $true )
& ( powersetI1 = $true )
& ( binunionEcases = $true )
& ( cartprodfstin = $true )
& ( setadjoinIL = $true )
& ( setadjoinIR = $true )
& ( setukpairinjL = $true )
& ( binintersectLsub = $true )
& ( nonemptyE1 = $true )
& ( quantDeMorgan2 = $true )
& ( binintersectSubset2 = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrEL = $true )
& ( setukpairIR = $true )
& ( uniqinunit = $true )
& ( emptysetsubset = $true )
& ( powerset__Cong = $true )
& ( powersetE = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( subsetI1 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( nonemptyImpWitness = $true )
& ( ubforcartprodlem2 = $true )
& ( upairsetIR = $true )
& ( upairsubunion = $true )
& ( quantDeMorgan1 = $true )
& ( notequalI2 = $true )
& ( subsetI2 = $true )
& ( emptysetAx = $true )
& ( disjointsetsI1 = $true )
& ( notdallE = $true )
& ( binunionIL = $true )
& ( prop2setI = $true )
& ( binintersectSubset5 = $true )
& ( exuE2 = $true )
& ( inCongP = $true )
& ( binintersectI = $true )
& ( setadjoinSub2 = $true )
& ( secondinupair = $true )
& ( setminusILneg = $true )
& ( setukpairinjR = $true )
& ( binunionLsub = $true )
& ( notequalI1 = $true )
& ( powersetE1 = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( exuI2 = $true )
& ( upairset2E = $true )
& ( emptyset__Cong = $true )
& ( replAx = $true )
& ( ubforcartprodlem3 = $true )
& ( nonemptyI = $true )
& ( setukpairinjR11 = $true )
& ( eqinunit = $true )
& ( emptyI = $true )
& ( symdiffIneg2 = $true )
& ( inPowerset = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK80,sK81,sK82])],[f604,f892]) ).
thf(f892,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) )
& ( $true
!= ( in @ ( ksnd @ X0 ) @ X1 ) ) )
=> ( ( ( in @ sK80 @ ( cartprod @ sK82 @ sK81 ) )
= $true )
& ( $true
!= ( in @ ( ksnd @ sK80 ) @ sK81 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f604,plain,
( ( powersetsubset = $true )
& ( symdiffIneg1 = $true )
& ( powersetAx = $true )
& ( notsubsetI = $true )
& ( cartprodmempair1 = $true )
& ( upairequniteq = $true )
& ( omega__Cong = $true )
& ( setextAx = $true )
& ( notdexE = $true )
& ( emptysetE = $true )
& ( noeltsimpempty = $true )
& ( subsetE = $true )
& ( sepSubset = $true )
& ( cartprodmempair = $true )
& ( eqimpsubset1 = $true )
& ( emptyinunitempty = $true )
& ( setadjoinAx = $true )
& ( binintersectSubset1 = $true )
& ( dsetconstrI = $true )
& ( emptysetimpfalse = $true )
& ( binintersectEL = $true )
& ( exu__Cong = $true )
& ( exuI3 = $true )
& ( setadjoinE = $true )
& ( setukpairinjL2 = $true )
& ( descr__Cong = $true )
& ( binunionRsub = $true )
& ( subPowSU = $true )
& ( setoftrueEq = $true )
& ( singletoninpowunion = $true )
& ( prop2set2propI = $true )
& ( ksndsingleton = $true )
& ( setunionsingleton = $true )
& ( exuI1 = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( emptyE1 = $true )
& ( setunionI = $true )
& ( setunionE2 = $true )
& ( setukpairIL = $true )
& ( setextsub = $true )
& ( subsetRefl = $true )
& ( bs114d = $true )
& ( foundationAx = $true )
& ( symdiffI2 = $true )
& ( setadjoinSub = $true )
& ( kpairsurjEq = $true )
& ( theprop = $true )
& ( setadjoin__Cong = $true )
& ( binintersectSubset4 = $true )
& ( upairinpowunion = $true )
& ( notinemptyset = $true )
& ( setukpairinjR2 = $true )
& ( nonemptyI1 = $true )
& ( setunion__Cong = $true )
& ( setminusEL = $true )
& ( powersetI = $true )
& ( quantDeMorgan4 = $true )
& ( setunionsingleton1 = $true )
& ( setukpairinjR12 = $true )
& ( kpairp = $true )
& ( setminusI = $true )
& ( upairset2IR = $true )
& ( setminusLsub = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) )
& ( $true
!= ( in @ ( ksnd @ X0 ) @ X1 ) ) )
& ( emptyInPowerset = $true )
& ( sepInPowerset = $true )
& ( omegaSAx = $true )
& ( setminusSubset2 = $true )
& ( subset2powerset = $true )
& ( upairsetIL = $true )
& ( kfstsingleton = $true )
& ( binintersectRsub = $true )
& ( descrp = $true )
& ( dsetconstr__Cong = $true )
& ( singletonsuniq = $true )
& ( exuEu = $true )
& ( setukpairinjR1 = $true )
& ( ex1I2 = $true )
& ( setminusIRneg = $true )
& ( ex1I = $true )
& ( setbeta = $true )
& ( emptyinPowerset = $true )
& ( exuE3u = $true )
& ( upairsetE = $true )
& ( setminusELneg = $true )
& ( setminusER = $true )
& ( setadjoinOr = $true )
& ( kfstpairEq = $true )
& ( setext = $true )
& ( ksndpairEq = $true )
& ( setminusERneg = $true )
& ( binintersectER = $true )
& ( ubforcartprodlem1 = $true )
& ( binintersectSubset3 = $true )
& ( in__Cong = $true )
& ( exuE3e = $true )
& ( kpairiskpair = $true )
& ( singletonsswitch = $true )
& ( binunionIR = $true )
& ( setunionE = $true )
& ( setunionsingleton2 = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( wellorderingAx = $true )
& ( binunionE = $true )
& ( subsetTrans = $true )
& ( setminusSubset1 = $true )
& ( omega0Ax = $true )
& ( subsetE2 = $true )
& ( eqimpsubset2 = $true )
& ( cartprodpairin = $true )
& ( singletonprop = $true )
& ( quantDeMorgan3 = $true )
& ( ex1E1 = $true )
& ( setukpairinjL1 = $true )
& ( vacuousDall = $true )
& ( powersetI1 = $true )
& ( binunionEcases = $true )
& ( cartprodfstin = $true )
& ( setadjoinIL = $true )
& ( setadjoinIR = $true )
& ( setukpairinjL = $true )
& ( binintersectLsub = $true )
& ( nonemptyE1 = $true )
& ( quantDeMorgan2 = $true )
& ( binintersectSubset2 = $true )
& ( subsetemptysetimpeq = $true )
& ( dsetconstrEL = $true )
& ( setukpairIR = $true )
& ( uniqinunit = $true )
& ( emptysetsubset = $true )
& ( powerset__Cong = $true )
& ( powersetE = $true )
& ( setunionAx = $true )
& ( prop2setE = $true )
& ( subsetI1 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( nonemptyImpWitness = $true )
& ( ubforcartprodlem2 = $true )
& ( upairsetIR = $true )
& ( upairsubunion = $true )
& ( quantDeMorgan1 = $true )
& ( notequalI2 = $true )
& ( subsetI2 = $true )
& ( emptysetAx = $true )
& ( disjointsetsI1 = $true )
& ( notdallE = $true )
& ( binunionIL = $true )
& ( prop2setI = $true )
& ( binintersectSubset5 = $true )
& ( exuE2 = $true )
& ( inCongP = $true )
& ( binintersectI = $true )
& ( setadjoinSub2 = $true )
& ( secondinupair = $true )
& ( setminusILneg = $true )
& ( setukpairinjR = $true )
& ( binunionLsub = $true )
& ( notequalI1 = $true )
& ( powersetE1 = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( exuI2 = $true )
& ( upairset2E = $true )
& ( emptyset__Cong = $true )
& ( replAx = $true )
& ( ubforcartprodlem3 = $true )
& ( nonemptyI = $true )
& ( setukpairinjR11 = $true )
& ( eqinunit = $true )
& ( emptyI = $true )
& ( symdiffIneg2 = $true )
& ( inPowerset = $true ) ),
inference(flattening,[status(thm)],[f603]) ).
thf(f603,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) )
& ( $true
!= ( in @ ( ksnd @ X0 ) @ X1 ) ) )
& ( kpairsurjEq = $true )
& ( ksndpairEq = $true )
& ( ksndsingleton = $true )
& ( setukpairinjR = $true )
& ( setukpairinjR2 = $true )
& ( upairequniteq = $true )
& ( setukpairinjR1 = $true )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f429]) ).
thf(f429,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ( ( setukpairinjR1 = $true )
=> ( ( upairequniteq = $true )
=> ( ( setukpairinjR2 = $true )
=> ( ( setukpairinjR = $true )
=> ( ( ksndsingleton = $true )
=> ( ( ksndpairEq = $true )
=> ( ( kpairsurjEq = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) )
=> ( $true
= ( in @ ( ksnd @ X0 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f428]) ).
thf(f428,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( cartprod @ X2 @ X1 ) )
=> ( in @ ( ksnd @ X0 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f180]) ).
thf(f180,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ! [X10: $i,X4: $i,X3: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( ksnd @ X10 ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f179]) ).
thf(f179,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ! [X10: $i,X4: $i,X3: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( ksnd @ X10 ) @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PjEOTGotWI/DTF2THF_13158.p',cartprodsndin) ).
thf(f16818,plain,
( ( $true
= ( in @ ( ksnd @ sK80 ) @ sK81 ) )
| ~ spl486_308
| ~ spl486_533
| ~ spl486_609 ),
inference(backward_demodulation,[status(thm)],[f10878,f16800]) ).
thf(f16800,plain,
( ( ( sK108 @ sK82 @ sK81 @ sK80 )
= ( ksnd @ sK80 ) )
| ~ spl486_533
| ~ spl486_609 ),
inference(superposition,[status(thm)],[f5342,f11948]) ).
thf(f11948,plain,
( ( sK80
= ( kpair @ ( sK107 @ sK82 @ sK81 @ sK80 ) @ ( sK108 @ sK82 @ sK81 @ sK80 ) ) )
| ~ spl486_533 ),
inference(trivial_inequality_removal,[status(thm)],[f11931]) ).
thf(f11931,plain,
( ( $true != $true )
| ( sK80
= ( kpair @ ( sK107 @ sK82 @ sK81 @ sK80 ) @ ( sK108 @ sK82 @ sK81 @ sK80 ) ) )
| ~ spl486_533 ),
inference(superposition,[status(thm)],[f4976,f1776]) ).
thf(f1776,plain,
( ( in @ sK80 @ ( cartprod @ sK82 @ sK81 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f893]) ).
thf(f4976,plain,
( ! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) )
| ( ( kpair @ ( sK107 @ X7 @ X6 @ X5 ) @ ( sK108 @ X7 @ X6 @ X5 ) )
= X5 ) )
| ~ spl486_533 ),
inference(avatar_component_clause,[status(thm)],[f4975]) ).
thf(f4975,definition,
( spl486_533
<=> ! [X6: $i,X5: $i,X7: $i] :
( ( $true
!= ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) )
| ( ( kpair @ ( sK107 @ X7 @ X6 @ X5 ) @ ( sK108 @ X7 @ X6 @ X5 ) )
= X5 ) ) ),
introduced(definition,[new_symbols(naming,[spl486_533])],[avatar_definition]) ).
thf(f5342,plain,
( ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 )
| ~ spl486_609 ),
inference(avatar_component_clause,[status(thm)],[f5341]) ).
thf(f5341,definition,
( spl486_609
<=> ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 ) ),
introduced(definition,[new_symbols(naming,[spl486_609])],[avatar_definition]) ).
thf(f10878,plain,
( ( ( in @ ( sK108 @ sK82 @ sK81 @ sK80 ) @ sK81 )
= $true )
| ~ spl486_308 ),
inference(trivial_inequality_removal,[status(thm)],[f10857]) ).
thf(f10857,plain,
( ( ( in @ ( sK108 @ sK82 @ sK81 @ sK80 ) @ sK81 )
= $true )
| ( $true != $true )
| ~ spl486_308 ),
inference(superposition,[status(thm)],[f3930,f1776]) ).
thf(f3930,plain,
( ! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) )
| ( ( in @ ( sK108 @ X7 @ X6 @ X5 ) @ X6 )
= $true ) )
| ~ spl486_308 ),
inference(avatar_component_clause,[status(thm)],[f3929]) ).
thf(f3929,definition,
( spl486_308
<=> ! [X6: $i,X5: $i,X7: $i] :
( ( ( in @ ( sK108 @ X7 @ X6 @ X5 ) @ X6 )
= $true )
| ( $true
!= ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl486_308])],[avatar_definition]) ).
thf(f6236,plain,
spl486_604,
inference(avatar_split_clause,[status(thm)],[f1749,f5317]) ).
thf(f5317,definition,
( spl486_604
<=> ( ksndpairEq = $true ) ),
introduced(definition,[new_symbols(naming,[spl486_604])],[avatar_definition]) ).
thf(f1749,plain,
ksndpairEq = $true,
inference(cnf_transformation,[status(thm)],[f893]) ).
thf(f5626,plain,
spl486_168,
inference(avatar_split_clause,[status(thm)],[f1836,f3293]) ).
thf(f3293,definition,
( spl486_168
<=> ( cartprodmempair1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl486_168])],[avatar_definition]) ).
thf(f1836,plain,
cartprodmempair1 = $true,
inference(cnf_transformation,[status(thm)],[f893]) ).
thf(f5343,plain,
( spl486_609
| ~ spl486_604 ),
inference(avatar_split_clause,[status(thm)],[f2286,f5317,f5341]) ).
thf(f2286,plain,
! [X2: $i,X3: $i] :
( ( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 )
| ( ksndpairEq != $true ) ),
inference(cnf_transformation,[status(thm)],[f1432]) ).
thf(f1432,plain,
( ( ( ksndpairEq = $true )
| ( ( ksnd @ ( kpair @ sK411 @ sK412 ) )
!= sK412 ) )
& ( ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 )
| ( ksndpairEq != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK411,sK412])],[f1430,f1431]) ).
thf(f1431,plain,
( ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 )
=> ( ( ksnd @ ( kpair @ sK411 @ sK412 ) )
!= sK412 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1430,plain,
( ( ( ksndpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 ) )
& ( ! [X2: $i,X3: $i] :
( ( ksnd @ ( kpair @ X2 @ X3 ) )
= X3 )
| ( ksndpairEq != $true ) ) ),
inference(rectify,[status(thm)],[f1429]) ).
thf(f1429,plain,
( ( ( ksndpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
!= X1 ) )
& ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 )
| ( ksndpairEq != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f211]) ).
thf(f211,plain,
( ( ksndpairEq = $true )
<=> ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ),
inference(fool_elimination,[status(thm)],[f210]) ).
thf(f210,plain,
( ksndpairEq
= ( ! [X0: $i,X1: $i] :
( ( ksnd @ ( kpair @ X0 @ X1 ) )
= X1 ) ) ),
inference(rectify,[status(thm)],[f177]) ).
thf(f177,axiom,
( ksndpairEq
= ( ! [X1: $i,X2: $i] :
( ( ksnd @ ( kpair @ X1 @ X2 ) )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PjEOTGotWI/DTF2THF_13158.p',ksndpairEq) ).
thf(f4977,plain,
( spl486_533
| ~ spl486_168 ),
inference(avatar_split_clause,[status(thm)],[f1866,f3293,f4975]) ).
thf(f1866,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( $true
!= ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) )
| ( cartprodmempair1 != $true )
| ( ( kpair @ ( sK107 @ X7 @ X6 @ X5 ) @ ( sK108 @ X7 @ X6 @ X5 ) )
= X5 ) ),
inference(cnf_transformation,[status(thm)],[f929]) ).
thf(f929,plain,
( ( ( cartprodmempair1 = $true )
| ( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK105 ) )
| ( sK104
!= ( kpair @ X3 @ X4 ) ) )
| ( $true
!= ( in @ X3 @ sK106 ) ) )
& ( ( in @ sK104 @ ( cartprod @ sK106 @ sK105 ) )
= $true ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( ( ( in @ ( sK108 @ X7 @ X6 @ X5 ) @ X6 )
= $true )
& ( ( kpair @ ( sK107 @ X7 @ X6 @ X5 ) @ ( sK108 @ X7 @ X6 @ X5 ) )
= X5 )
& ( $true
= ( in @ ( sK107 @ X7 @ X6 @ X5 ) @ X7 ) ) )
| ( $true
!= ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) ) )
| ( cartprodmempair1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK104,sK105,sK106,sK107,sK108])],[f925,f928,f927,f926]) ).
thf(f926,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( kpair @ X3 @ X4 )
!= X0 ) )
| ( $true
!= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) ) )
=> ( ! [X3: $i] :
( ! [X4: $i] :
( ( $true
!= ( in @ X4 @ sK105 ) )
| ( sK104
!= ( kpair @ X3 @ X4 ) ) )
| ( $true
!= ( in @ X3 @ sK106 ) ) )
& ( ( in @ sK104 @ ( cartprod @ sK106 @ sK105 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f927,plain,
! [X5: $i,X6: $i,X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ X6 ) )
& ( ( kpair @ X8 @ X9 )
= X5 ) )
& ( $true
= ( in @ X8 @ X7 ) ) )
=> ( ? [X9: $i] :
( ( $true
= ( in @ X9 @ X6 ) )
& ( ( kpair @ ( sK107 @ X7 @ X6 @ X5 ) @ X9 )
= X5 ) )
& ( $true
= ( in @ ( sK107 @ X7 @ X6 @ X5 ) @ X7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f928,plain,
! [X5: $i,X6: $i,X7: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ X6 ) )
& ( ( kpair @ ( sK107 @ X7 @ X6 @ X5 ) @ X9 )
= X5 ) )
=> ( ( ( in @ ( sK108 @ X7 @ X6 @ X5 ) @ X6 )
= $true )
& ( ( kpair @ ( sK107 @ X7 @ X6 @ X5 ) @ ( sK108 @ X7 @ X6 @ X5 ) )
= X5 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f925,plain,
( ( ( cartprodmempair1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( kpair @ X3 @ X4 )
!= X0 ) )
| ( $true
!= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( $true
= ( in @ X9 @ X6 ) )
& ( ( kpair @ X8 @ X9 )
= X5 ) )
& ( $true
= ( in @ X8 @ X7 ) ) )
| ( $true
!= ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) ) )
| ( cartprodmempair1 != $true ) ) ),
inference(rectify,[status(thm)],[f924]) ).
thf(f924,plain,
( ( ( cartprodmempair1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( in @ X4 @ X1 )
!= $true )
| ( ( kpair @ X3 @ X4 )
!= X0 ) )
| ( $true
!= ( in @ X3 @ X2 ) ) )
& ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( ( kpair @ X3 @ X4 )
= X0 ) )
& ( $true
= ( in @ X3 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) ) )
| ( cartprodmempair1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f598]) ).
thf(f598,plain,
( ( cartprodmempair1 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( ( kpair @ X3 @ X4 )
= X0 ) )
& ( $true
= ( in @ X3 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f521]) ).
thf(f521,plain,
( ( cartprodmempair1 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X2 @ X1 ) ) )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( ( in @ X4 @ X1 )
= $true )
& ( ( kpair @ X3 @ X4 )
= X0 ) )
& ( $true
= ( in @ X3 @ X2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f520]) ).
thf(f520,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( cartprod @ X2 @ X1 ) )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( in @ X4 @ X1 )
& ( ( kpair @ X3 @ X4 )
= X0 ) )
& ( in @ X3 @ X2 ) ) )
= cartprodmempair1 ),
inference(rectify,[status(thm)],[f150]) ).
thf(f150,axiom,
! [X10: $i,X4: $i,X3: $i] :
( ( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ? [X1: $i] :
( ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( ( kpair @ X1 @ X2 )
= X10 ) )
& ( in @ X1 @ X3 ) ) )
= cartprodmempair1 ),
file('/export/starexec/sandbox2/tmp/tmp.PjEOTGotWI/DTF2THF_13158.p',cartprodmempair1) ).
thf(f3931,plain,
( ~ spl486_168
| spl486_308 ),
inference(avatar_split_clause,[status(thm)],[f1867,f3929,f3293]) ).
thf(f1867,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( ( in @ ( sK108 @ X7 @ X6 @ X5 ) @ X6 )
= $true )
| ( $true
!= ( in @ X5 @ ( cartprod @ X7 @ X6 ) ) )
| ( cartprodmempair1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f929]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU658^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n022.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:29:36 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SEU658^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : Ordered Pairs - Properties of Pairs
% 0.28/0.46 % Version : Especial.
% 0.28/0.46 % English : (! A:i.! B:i.! u:i.in u (cartprod A B) -> in (ksnd u) B)
% 0.28/0.46
% 0.28/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.46 % Source : [Bro08]
% 0.28/0.46 % Names : ZFC160g [Bro08]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % 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, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.57 v6.1.0, 0.86 v6.0.0, 0.71 v5.5.0, 0.83 v5.4.0, 0.80 v5.2.0, 1.00 v3.7.0
% 0.28/0.46 % Syntax : Number of formulae : 384 ( 178 unt; 205 typ; 178 def)
% 0.28/0.46 % Number of atoms : 946 ( 267 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 176 ( 5 avg)
% 0.28/0.46 % Number of connectives : 1657 ( 47 ~; 7 |; 35 &;1136 @)
% 0.28/0.46 % ( 14 <=>; 418 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 182 ( 2 avg)
% 0.28/0.46 % Number of types : 2 ( 0 usr)
% 0.28/0.46 % Number of type conns : 84 ( 84 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 208 ( 205 usr; 178 con; 0-2 aty)
% 0.28/0.46 % Number of variables : 518 ( 40 ^; 442 !; 36 ?; 518 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : http://mathgate.info/detsetitem.php?id=214
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(in_type,type,
% 0.28/0.46 in: $i > $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu_type,type,
% 0.28/0.46 exu: ( $i > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(exu,definition,
% 0.28/0.46 ( exu
% 0.28/0.46 = ( ^ [Xphi: $i > $o] :
% 0.28/0.46 ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setextAx_type,type,
% 0.28/0.46 setextAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setextAx,definition,
% 0.28/0.46 ( setextAx
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 <=> ( in @ Xx @ B ) )
% 0.28/0.46 => ( A = B ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyset_type,type,
% 0.28/0.46 emptyset: $i ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetAx_type,type,
% 0.28/0.46 emptysetAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetAx,definition,
% 0.28/0.46 ( emptysetAx
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoin_type,type,
% 0.28/0.46 setadjoin: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinAx_type,type,
% 0.28/0.46 setadjoinAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinAx,definition,
% 0.28/0.46 ( setadjoinAx
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 <=> ( ( Xy = Xx )
% 0.28/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powerset_type,type,
% 0.28/0.46 powerset: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(powersetAx_type,type,
% 0.28/0.46 powersetAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetAx,definition,
% 0.28/0.46 ( powersetAx
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.46 <=> ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunion_type,type,
% 0.28/0.46 setunion: $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(setunionAx_type,type,
% 0.28/0.46 setunionAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionAx,definition,
% 0.28/0.46 ( setunionAx
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.46 <=> ? [B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omega_type,type,
% 0.28/0.46 omega: $i ).
% 0.28/0.46
% 0.28/0.46 thf(omega0Ax_type,type,
% 0.28/0.46 omega0Ax: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omega0Ax,definition,
% 0.28/0.46 ( omega0Ax
% 0.28/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omegaSAx_type,type,
% 0.28/0.46 omegaSAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omegaSAx,definition,
% 0.28/0.46 ( omegaSAx
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ omega )
% 0.28/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(omegaIndAx_type,type,
% 0.28/0.46 omegaIndAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(omegaIndAx,definition,
% 0.28/0.46 ( omegaIndAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( ( in @ emptyset @ A )
% 0.28/0.46 & ! [Xx: $i] :
% 0.28/0.46 ( ( ( in @ Xx @ omega )
% 0.28/0.46 & ( in @ Xx @ A ) )
% 0.28/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ omega )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(replAx_type,type,
% 0.28/0.46 replAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(replAx,definition,
% 0.28/0.46 ( replAx
% 0.28/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( exu
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.46 => ? [B: $i] :
% 0.28/0.46 ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 <=> ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(foundationAx_type,type,
% 0.28/0.46 foundationAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(foundationAx,definition,
% 0.28/0.46 ( foundationAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.46 => ? [B: $i] :
% 0.28/0.46 ( ( in @ B @ A )
% 0.28/0.46 & ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(wellorderingAx_type,type,
% 0.28/0.46 wellorderingAx: $o ).
% 0.28/0.46
% 0.28/0.46 thf(wellorderingAx,definition,
% 0.28/0.46 ( wellorderingAx
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ? [B: $i] :
% 0.28/0.46 ( ! [C: $i] :
% 0.28/0.46 ( ( in @ C @ B )
% 0.28/0.46 => ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ A ) ) )
% 0.28/0.46 & ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( ( in @ Xx @ A )
% 0.28/0.46 & ( in @ Xy @ A ) )
% 0.28/0.46 => ( ! [C: $i] :
% 0.28/0.46 ( ( in @ C @ B )
% 0.28/0.46 => ( ( in @ Xx @ C )
% 0.28/0.46 <=> ( in @ Xy @ C ) ) )
% 0.28/0.46 => ( Xx = Xy ) ) )
% 0.28/0.46 & ! [C: $i,D: $i] :
% 0.28/0.46 ( ( ( in @ C @ B )
% 0.28/0.46 & ( in @ D @ B ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ D ) )
% 0.28/0.46 | ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ D )
% 0.28/0.46 => ( in @ Xx @ C ) ) ) )
% 0.28/0.46 & ! [C: $i] :
% 0.28/0.46 ( ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ C )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.46 => ? [D: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ D @ B )
% 0.28/0.46 & ( in @ Xx @ C )
% 0.28/0.46 & ~ ? [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ D )
% 0.28/0.46 & ( in @ Xy @ C ) )
% 0.28/0.46 & ! [E: $i] :
% 0.28/0.46 ( ( in @ E @ B )
% 0.28/0.46 => ( ! [Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ E )
% 0.28/0.46 => ( in @ Xy @ D ) )
% 0.28/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(descr_type,type,
% 0.28/0.46 descr: ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(descrp_type,type,
% 0.28/0.46 descrp: $o ).
% 0.28/0.46
% 0.28/0.46 thf(descrp,definition,
% 0.28/0.46 ( descrp
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ( Xphi
% 0.28/0.46 @ ( descr
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstr_type,type,
% 0.28/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI_type,type,
% 0.28/0.46 dsetconstrI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrI,definition,
% 0.28/0.46 ( dsetconstrI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL_type,type,
% 0.28/0.46 dsetconstrEL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrEL,definition,
% 0.28/0.46 ( dsetconstrEL
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER_type,type,
% 0.28/0.46 dsetconstrER: $o ).
% 0.28/0.46
% 0.28/0.46 thf(dsetconstrER,definition,
% 0.28/0.46 ( dsetconstrER
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1_type,type,
% 0.28/0.46 exuE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE1,definition,
% 0.28/0.46 ( exuE1
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( Xphi @ Xx )
% 0.28/0.46 & ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(prop2set_type,type,
% 0.28/0.46 prop2set: $o > $i ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setE_type,type,
% 0.28/0.46 prop2setE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(prop2setE,definition,
% 0.28/0.46 ( prop2setE
% 0.28/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.46 => Xphi ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetE_type,type,
% 0.28/0.46 emptysetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetE,definition,
% 0.28/0.46 ( emptysetE
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetimpfalse_type,type,
% 0.28/0.46 emptysetimpfalse: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptysetimpfalse,definition,
% 0.28/0.46 ( emptysetimpfalse
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => $false ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notinemptyset_type,type,
% 0.28/0.46 notinemptyset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notinemptyset,definition,
% 0.28/0.46 ( notinemptyset
% 0.28/0.46 = ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3e_type,type,
% 0.28/0.46 exuE3e: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE3e,definition,
% 0.28/0.46 ( exuE3e
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setext_type,type,
% 0.28/0.46 setext: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setext,definition,
% 0.28/0.46 ( setext
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ B ) )
% 0.28/0.46 => ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 => ( A = B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyI_type,type,
% 0.28/0.46 emptyI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyI,definition,
% 0.28/0.46 ( emptyI
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ A )
% 0.28/0.46 => ( A = emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(noeltsimpempty_type,type,
% 0.28/0.46 noeltsimpempty: $o ).
% 0.28/0.46
% 0.28/0.46 thf(noeltsimpempty,definition,
% 0.28/0.46 ( noeltsimpempty
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ~ ( in @ Xx @ A )
% 0.28/0.46 => ( A = emptyset ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setbeta_type,type,
% 0.28/0.46 setbeta: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setbeta,definition,
% 0.28/0.46 ( setbeta
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( in @ Xx
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonempty_type,type,
% 0.28/0.46 nonempty: $i > $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonempty,definition,
% 0.28/0.46 ( nonempty
% 0.28/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyE1_type,type,
% 0.28/0.46 nonemptyE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyE1,definition,
% 0.28/0.46 ( nonemptyE1
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( nonempty @ A )
% 0.28/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI_type,type,
% 0.28/0.46 nonemptyI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI,definition,
% 0.28/0.46 ( nonemptyI
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( ( Xphi @ Xx )
% 0.28/0.46 => ( nonempty
% 0.28/0.46 @ ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI1_type,type,
% 0.28/0.46 nonemptyI1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyI1,definition,
% 0.28/0.46 ( nonemptyI1
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIL_type,type,
% 0.28/0.46 setadjoinIL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIL,definition,
% 0.28/0.46 ( setadjoinIL
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinunitempty_type,type,
% 0.28/0.46 emptyinunitempty: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinunitempty,definition,
% 0.28/0.46 ( emptyinunitempty
% 0.28/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIR_type,type,
% 0.28/0.46 setadjoinIR: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinIR,definition,
% 0.28/0.46 ( setadjoinIR
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ A )
% 0.28/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinE_type,type,
% 0.28/0.46 setadjoinE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinE,definition,
% 0.28/0.46 ( setadjoinE
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 => ! [Xphi: $o] :
% 0.28/0.46 ( ( ( Xy = Xx )
% 0.28/0.46 => Xphi )
% 0.28/0.46 => ( ( ( in @ Xy @ A )
% 0.28/0.46 => Xphi )
% 0.28/0.46 => Xphi ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinOr_type,type,
% 0.28/0.46 setadjoinOr: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setadjoinOr,definition,
% 0.28/0.46 ( setadjoinOr
% 0.28/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.46 => ( ( Xy = Xx )
% 0.28/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setoftrueEq_type,type,
% 0.28/0.46 setoftrueEq: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setoftrueEq,definition,
% 0.28/0.46 ( setoftrueEq
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : $true )
% 0.28/0.46 = A ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powersetI_type,type,
% 0.28/0.46 powersetI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetI,definition,
% 0.28/0.46 ( powersetI
% 0.28/0.46 = ( ! [A: $i,B: $i] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) )
% 0.28/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinPowerset_type,type,
% 0.28/0.46 emptyinPowerset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyinPowerset,definition,
% 0.28/0.46 ( emptyinPowerset
% 0.28/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyInPowerset_type,type,
% 0.28/0.46 emptyInPowerset: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyInPowerset,definition,
% 0.28/0.46 ( emptyInPowerset
% 0.28/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(powersetE_type,type,
% 0.28/0.46 powersetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(powersetE,definition,
% 0.28/0.46 ( powersetE
% 0.28/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.46 => ( ( in @ Xx @ B )
% 0.28/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunionI_type,type,
% 0.28/0.46 setunionI: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionI,definition,
% 0.28/0.46 ( setunionI
% 0.28/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( ( in @ B @ A )
% 0.28/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(setunionE_type,type,
% 0.28/0.46 setunionE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(setunionE,definition,
% 0.28/0.46 ( setunionE
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.46 => ! [Xphi: $o] :
% 0.28/0.46 ( ! [B: $i] :
% 0.28/0.46 ( ( in @ Xx @ B )
% 0.28/0.46 => ( ( in @ B @ A )
% 0.28/0.46 => Xphi ) )
% 0.28/0.46 => Xphi ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subPowSU_type,type,
% 0.28/0.46 subPowSU: $o ).
% 0.28/0.46
% 0.28/0.46 thf(subPowSU,definition,
% 0.28/0.46 ( subPowSU
% 0.28/0.46 = ( ! [A: $i,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(exuE2_type,type,
% 0.28/0.46 exuE2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(exuE2,definition,
% 0.28/0.46 ( exuE2
% 0.28/0.46 = ( ! [Xphi: $i > $o] :
% 0.28/0.46 ( ( exu
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ! [Xy: $i] :
% 0.28/0.46 ( ( Xphi @ Xy )
% 0.28/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyImpWitness_type,type,
% 0.28/0.46 nonemptyImpWitness: $o ).
% 0.28/0.46
% 0.28/0.46 thf(nonemptyImpWitness,definition,
% 0.28/0.46 ( nonemptyImpWitness
% 0.28/0.46 = ( ! [A: $i] :
% 0.28/0.46 ( ( nonempty @ A )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & $true ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(uniqinunit_type,type,
% 0.28/0.46 uniqinunit: $o ).
% 0.28/0.46
% 0.28/0.46 thf(uniqinunit,definition,
% 0.28/0.46 ( uniqinunit
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(notinsingleton_type,type,
% 0.28/0.46 notinsingleton: $o ).
% 0.28/0.46
% 0.28/0.46 thf(notinsingleton,definition,
% 0.28/0.46 ( notinsingleton
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx != Xy )
% 0.28/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(eqinunit_type,type,
% 0.28/0.46 eqinunit: $o ).
% 0.28/0.46
% 0.28/0.46 thf(eqinunit,definition,
% 0.28/0.46 ( eqinunit
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( Xx = Xy )
% 0.28/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(singletonsswitch_type,type,
% 0.28/0.46 singletonsswitch: $o ).
% 0.28/0.46
% 0.28/0.46 thf(singletonsswitch,definition,
% 0.28/0.46 ( singletonsswitch
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetE_type,type,
% 0.28/0.46 upairsetE: $o ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetE,definition,
% 0.28/0.46 ( upairsetE
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.46 => ( ( Xz = Xx )
% 0.28/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIL_type,type,
% 0.28/0.46 upairsetIL: $o ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIL,definition,
% 0.28/0.46 ( upairsetIL
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIR_type,type,
% 0.28/0.46 upairsetIR: $o ).
% 0.28/0.46
% 0.28/0.46 thf(upairsetIR,definition,
% 0.28/0.46 ( upairsetIR
% 0.28/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(emptyE1_type,type,
% 0.28/0.46 emptyE1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(emptyE1,definition,
% 0.28/0.46 ( emptyE1
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) )
% 0.28/0.46 => ( ( ( dsetconstr @ A
% 0.28/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.46 = emptyset )
% 0.28/0.46 => $false ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(vacuousDall_type,type,
% 0.28/0.46 vacuousDall: $o ).
% 0.28/0.46
% 0.28/0.46 thf(vacuousDall,definition,
% 0.28/0.46 ( vacuousDall
% 0.28/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ emptyset )
% 0.28/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan1_type,type,
% 0.28/0.46 quantDeMorgan1: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan1,definition,
% 0.28/0.46 ( quantDeMorgan1
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ~ ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ( Xphi @ Xx ) )
% 0.28/0.46 => ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan2_type,type,
% 0.28/0.46 quantDeMorgan2: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan2,definition,
% 0.28/0.46 ( quantDeMorgan2
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ! [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 => ~ ( Xphi @ Xx ) )
% 0.28/0.46 => ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan3_type,type,
% 0.28/0.46 quantDeMorgan3: $o ).
% 0.28/0.46
% 0.28/0.46 thf(quantDeMorgan3,definition,
% 0.28/0.46 ( quantDeMorgan3
% 0.28/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.46 ( ~ ? [Xx: $i] :
% 0.28/0.46 ( ( in @ Xx @ A )
% 0.28/0.46 & ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan4_type,type,
% 0.28/0.47 quantDeMorgan4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan4,definition,
% 0.28/0.47 ( quantDeMorgan4
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) )
% 0.28/0.47 => ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setI_type,type,
% 0.28/0.47 prop2setI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setI,definition,
% 0.28/0.47 ( prop2setI
% 0.28/0.47 = ( ! [Xphi: $o] :
% 0.28/0.47 ( Xphi
% 0.28/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(set2prop_type,type,
% 0.28/0.47 set2prop: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set2propI_type,type,
% 0.28/0.47 prop2set2propI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set2propI,definition,
% 0.28/0.47 ( prop2set2propI
% 0.28/0.47 = ( ! [Xphi: $o] :
% 0.28/0.47 ( Xphi
% 0.28/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notdexE_type,type,
% 0.28/0.47 notdexE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notdexE,definition,
% 0.28/0.47 ( notdexE
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notdallE_type,type,
% 0.28/0.47 notdallE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notdallE,definition,
% 0.28/0.47 ( notdallE
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI1_type,type,
% 0.28/0.47 exuI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI1,definition,
% 0.28/0.47 ( exuI1
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI3_type,type,
% 0.28/0.47 exuI3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI3,definition,
% 0.28/0.47 ( exuI3
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.28/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI2_type,type,
% 0.28/0.47 exuI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI2,definition,
% 0.28/0.47 ( exuI2
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 <=> ( Xy = Xx ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inCongP_type,type,
% 0.28/0.47 inCongP: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inCongP,definition,
% 0.28/0.47 ( inCongP
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong_type,type,
% 0.28/0.47 in__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong,definition,
% 0.28/0.47 ( in__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3u_type,type,
% 0.28/0.47 exuE3u: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3u,definition,
% 0.28/0.47 ( exuE3u
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exu__Cong_type,type,
% 0.28/0.47 exu__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu__Cong,definition,
% 0.28/0.47 ( exu__Cong
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 <=> ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset__Cong_type,type,
% 0.28/0.47 emptyset__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset__Cong,definition,
% 0.28/0.47 ( emptyset__Cong
% 0.28/0.47 = ( emptyset = emptyset ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin__Cong_type,type,
% 0.28/0.47 setadjoin__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin__Cong,definition,
% 0.28/0.47 ( setadjoin__Cong
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ! [Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( Xz = Xu )
% 0.28/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powerset__Cong_type,type,
% 0.28/0.47 powerset__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powerset__Cong,definition,
% 0.28/0.47 ( powerset__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( powerset @ A )
% 0.28/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunion__Cong_type,type,
% 0.28/0.47 setunion__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunion__Cong,definition,
% 0.28/0.47 ( setunion__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( setunion @ A )
% 0.28/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omega__Cong_type,type,
% 0.28/0.47 omega__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omega__Cong,definition,
% 0.28/0.47 ( omega__Cong
% 0.28/0.47 = ( omega = omega ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuEu_type,type,
% 0.28/0.47 exuEu: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuEu,definition,
% 0.28/0.47 ( exuEu
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(descr__Cong_type,type,
% 0.28/0.47 descr__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(descr__Cong,definition,
% 0.28/0.47 ( descr__Cong
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.28/0.47 => ( ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr__Cong_type,type,
% 0.28/0.47 dsetconstr__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr__Cong,definition,
% 0.28/0.47 ( dsetconstr__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.28/0.47 => ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = ( dsetconstr @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subset_type,type,
% 0.28/0.47 subset: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(disjoint_type,type,
% 0.28/0.47 disjoint: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setsmeet_type,type,
% 0.28/0.47 setsmeet: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI1_type,type,
% 0.28/0.47 subsetI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI1,definition,
% 0.28/0.47 ( subsetI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset2_type,type,
% 0.28/0.47 eqimpsubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset2,definition,
% 0.28/0.47 ( eqimpsubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset1_type,type,
% 0.28/0.47 eqimpsubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset1,definition,
% 0.28/0.47 ( eqimpsubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI2_type,type,
% 0.28/0.47 subsetI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI2,definition,
% 0.28/0.47 ( subsetI2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetsubset_type,type,
% 0.28/0.47 emptysetsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetsubset,definition,
% 0.28/0.47 ( emptysetsubset
% 0.28/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE_type,type,
% 0.28/0.47 subsetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE,definition,
% 0.28/0.47 ( subsetE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE2_type,type,
% 0.28/0.47 subsetE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE2,definition,
% 0.28/0.47 ( subsetE2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notsubsetI_type,type,
% 0.28/0.47 notsubsetI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notsubsetI,definition,
% 0.28/0.47 ( notsubsetI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI1_type,type,
% 0.28/0.47 notequalI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI1,definition,
% 0.28/0.47 ( notequalI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ~ ( subset @ A @ B )
% 0.28/0.47 => ( A != B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI2_type,type,
% 0.28/0.47 notequalI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI2,definition,
% 0.28/0.47 ( notequalI2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( A != B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetRefl_type,type,
% 0.28/0.47 subsetRefl: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetRefl,definition,
% 0.28/0.47 ( subsetRefl
% 0.28/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTrans_type,type,
% 0.28/0.47 subsetTrans: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTrans,definition,
% 0.28/0.47 ( subsetTrans
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( subset @ B @ C )
% 0.28/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub_type,type,
% 0.28/0.47 setadjoinSub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub,definition,
% 0.28/0.47 ( setadjoinSub
% 0.28/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub2_type,type,
% 0.28/0.47 setadjoinSub2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub2,definition,
% 0.28/0.47 ( setadjoinSub2
% 0.28/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subset2powerset_type,type,
% 0.28/0.47 subset2powerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subset2powerset,definition,
% 0.28/0.47 ( subset2powerset
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setextsub_type,type,
% 0.28/0.47 setextsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setextsub,definition,
% 0.28/0.47 ( setextsub
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( subset @ B @ A )
% 0.28/0.47 => ( A = B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetemptysetimpeq_type,type,
% 0.28/0.47 subsetemptysetimpeq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetemptysetimpeq,definition,
% 0.28/0.47 ( subsetemptysetimpeq
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( subset @ A @ emptyset )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI1_type,type,
% 0.28/0.47 powersetI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI1,definition,
% 0.28/0.47 ( powersetI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ B @ A )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE1_type,type,
% 0.28/0.47 powersetE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE1,definition,
% 0.28/0.47 ( powersetE1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inPowerset_type,type,
% 0.28/0.47 inPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inPowerset,definition,
% 0.28/0.47 ( inPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetsubset_type,type,
% 0.28/0.47 powersetsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetsubset,definition,
% 0.28/0.47 ( powersetsubset
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sepInPowerset_type,type,
% 0.28/0.47 sepInPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(sepInPowerset,definition,
% 0.28/0.47 ( sepInPowerset
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( in
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sepSubset_type,type,
% 0.28/0.47 sepSubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(sepSubset,definition,
% 0.28/0.47 ( sepSubset
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( subset
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunion_type,type,
% 0.28/0.47 binunion: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIL_type,type,
% 0.28/0.47 binunionIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIL,definition,
% 0.28/0.47 ( binunionIL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2IR_type,type,
% 0.28/0.47 upairset2IR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2IR,definition,
% 0.28/0.47 ( upairset2IR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIR_type,type,
% 0.28/0.47 binunionIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIR,definition,
% 0.28/0.47 ( binunionIR
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionEcases_type,type,
% 0.28/0.47 binunionEcases: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionEcases,definition,
% 0.28/0.47 ( binunionEcases
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.28/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.47 => ( ( ( in @ Xx @ A )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xx @ B )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionE_type,type,
% 0.28/0.47 binunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionE,definition,
% 0.28/0.47 ( binunionE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionLsub_type,type,
% 0.28/0.47 binunionLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionLsub,definition,
% 0.28/0.47 ( binunionLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionRsub_type,type,
% 0.28/0.47 binunionRsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionRsub,definition,
% 0.28/0.47 ( binunionRsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersect_type,type,
% 0.28/0.47 binintersect: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectI_type,type,
% 0.28/0.47 binintersectI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectI,definition,
% 0.28/0.47 ( binintersectI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset5_type,type,
% 0.28/0.47 binintersectSubset5: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset5,definition,
% 0.28/0.47 ( binintersectSubset5
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( subset @ C @ A )
% 0.28/0.47 => ( ( subset @ C @ B )
% 0.28/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectEL_type,type,
% 0.28/0.47 binintersectEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectEL,definition,
% 0.28/0.47 ( binintersectEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectLsub_type,type,
% 0.28/0.47 binintersectLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectLsub,definition,
% 0.28/0.47 ( binintersectLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset2_type,type,
% 0.28/0.47 binintersectSubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset2,definition,
% 0.28/0.47 ( binintersectSubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset3_type,type,
% 0.28/0.47 binintersectSubset3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset3,definition,
% 0.28/0.47 ( binintersectSubset3
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( binintersect @ A @ B )
% 0.28/0.47 = B )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectER_type,type,
% 0.28/0.47 binintersectER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectER,definition,
% 0.28/0.47 ( binintersectER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(disjointsetsI1_type,type,
% 0.28/0.47 disjointsetsI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(disjointsetsI1,definition,
% 0.28/0.47 ( disjointsetsI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( in @ Xx @ B ) )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectRsub_type,type,
% 0.28/0.47 binintersectRsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectRsub,definition,
% 0.28/0.47 ( binintersectRsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset4_type,type,
% 0.28/0.47 binintersectSubset4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset4,definition,
% 0.28/0.47 ( binintersectSubset4
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ B @ A )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset1_type,type,
% 0.28/0.47 binintersectSubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset1,definition,
% 0.28/0.47 ( binintersectSubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( binintersect @ A @ B )
% 0.28/0.47 = A )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(bs114d_type,type,
% 0.28/0.47 bs114d: $o ).
% 0.28/0.47
% 0.28/0.47 thf(bs114d,definition,
% 0.28/0.47 ( bs114d
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.28/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(regular_type,type,
% 0.28/0.47 regular: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminus_type,type,
% 0.28/0.47 setminus: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setminusI_type,type,
% 0.28/0.47 setminusI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusI,definition,
% 0.28/0.47 ( setminusI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusEL_type,type,
% 0.28/0.47 setminusEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusEL,definition,
% 0.28/0.47 ( setminusEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusER_type,type,
% 0.28/0.47 setminusER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusER,definition,
% 0.28/0.47 ( setminusER
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset2_type,type,
% 0.28/0.47 setminusSubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset2,definition,
% 0.28/0.47 ( setminusSubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( setminus @ A @ B )
% 0.28/0.47 = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusERneg_type,type,
% 0.28/0.47 setminusERneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusERneg,definition,
% 0.28/0.47 ( setminusERneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusELneg_type,type,
% 0.28/0.47 setminusELneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusELneg,definition,
% 0.28/0.47 ( setminusELneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusILneg_type,type,
% 0.28/0.47 setminusILneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusILneg,definition,
% 0.28/0.47 ( setminusILneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusIRneg_type,type,
% 0.28/0.47 setminusIRneg: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusIRneg,definition,
% 0.28/0.47 ( setminusIRneg
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusLsub_type,type,
% 0.28/0.47 setminusLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusLsub,definition,
% 0.28/0.47 ( setminusLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset1_type,type,
% 0.28/0.47 setminusSubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setminusSubset1,definition,
% 0.28/0.47 ( setminusSubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( setminus @ A @ B )
% 0.28/0.47 = emptyset )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiff_type,type,
% 0.28/0.47 symdiff: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffE_type,type,
% 0.28/0.47 symdiffE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffE,definition,
% 0.28/0.47 ( symdiffE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => ( ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI1_type,type,
% 0.28/0.47 symdiffI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI1,definition,
% 0.28/0.47 ( symdiffI1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI2_type,type,
% 0.28/0.47 symdiffI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffI2,definition,
% 0.28/0.47 ( symdiffI2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg1_type,type,
% 0.28/0.47 symdiffIneg1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg1,definition,
% 0.28/0.47 ( symdiffIneg1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg2_type,type,
% 0.28/0.47 symdiffIneg2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(symdiffIneg2,definition,
% 0.28/0.47 ( symdiffIneg2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ~ ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(iskpair_type,type,
% 0.28/0.47 iskpair: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(secondinupair_type,type,
% 0.28/0.47 secondinupair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(secondinupair,definition,
% 0.28/0.47 ( secondinupair
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIL_type,type,
% 0.28/0.47 setukpairIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIL,definition,
% 0.28/0.47 ( setukpairIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIR_type,type,
% 0.28/0.47 setukpairIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairIR,definition,
% 0.28/0.47 ( setukpairIR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpairiskpair_type,type,
% 0.28/0.47 kpairiskpair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairiskpair,definition,
% 0.28/0.47 ( kpairiskpair
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpair_type,type,
% 0.28/0.47 kpair: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(kpairp_type,type,
% 0.28/0.47 kpairp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairp,definition,
% 0.28/0.47 ( kpairp
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprod_type,type,
% 0.28/0.47 cartprod: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsubset_type,type,
% 0.28/0.47 singletonsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsubset,definition,
% 0.28/0.47 ( singletonsubset
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowerset_type,type,
% 0.28/0.47 singletoninpowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowerset,definition,
% 0.28/0.47 ( singletoninpowerset
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowunion_type,type,
% 0.28/0.47 singletoninpowunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletoninpowunion,definition,
% 0.28/0.47 ( singletoninpowunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2E_type,type,
% 0.28/0.47 upairset2E: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2E,definition,
% 0.28/0.47 ( upairset2E
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xx )
% 0.28/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsubunion_type,type,
% 0.28/0.47 upairsubunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsubunion,definition,
% 0.28/0.47 ( upairsubunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairinpowunion_type,type,
% 0.28/0.47 upairinpowunion: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairinpowunion,definition,
% 0.28/0.47 ( upairinpowunion
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem1_type,type,
% 0.28/0.47 ubforcartprodlem1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem1,definition,
% 0.28/0.47 ( ubforcartprodlem1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem2_type,type,
% 0.28/0.47 ubforcartprodlem2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem2,definition,
% 0.28/0.47 ( ubforcartprodlem2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem3_type,type,
% 0.28/0.47 ubforcartprodlem3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ubforcartprodlem3,definition,
% 0.28/0.47 ( ubforcartprodlem3
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairin_type,type,
% 0.28/0.47 cartprodpairin: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodpairin,definition,
% 0.28/0.47 ( cartprodpairin
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair1_type,type,
% 0.28/0.47 cartprodmempair1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair1,definition,
% 0.28/0.47 ( cartprodmempair1
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 & ( Xu
% 0.28/0.47 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair_type,type,
% 0.28/0.47 cartprodmempair: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodmempair,definition,
% 0.28/0.47 ( cartprodmempair
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( iskpair @ Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE2_type,type,
% 0.28/0.47 setunionE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE2,definition,
% 0.28/0.47 ( setunionE2
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 => ? [X: $i] :
% 0.28/0.47 ( ( in @ X @ A )
% 0.28/0.47 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton1_type,type,
% 0.28/0.47 setunionsingleton1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton1,definition,
% 0.28/0.47 ( setunionsingleton1
% 0.28/0.47 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton2_type,type,
% 0.28/0.47 setunionsingleton2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton2,definition,
% 0.28/0.47 ( setunionsingleton2
% 0.28/0.47 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton_type,type,
% 0.28/0.47 setunionsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionsingleton,definition,
% 0.28/0.47 ( setunionsingleton
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.28/0.47 = Xx ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singleton_type,type,
% 0.28/0.47 singleton: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(singleton,definition,
% 0.28/0.47 ( singleton
% 0.28/0.47 = ( ^ [A: $i] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( A
% 0.28/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletonprop_type,type,
% 0.28/0.47 singletonprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonprop,definition,
% 0.28/0.47 ( singletonprop
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) )
% 0.28/0.47 => ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1_type,type,
% 0.28/0.47 ex1: $i > ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1,definition,
% 0.28/0.47 ( ex1
% 0.28/0.47 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( singleton
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E1_type,type,
% 0.28/0.47 ex1E1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1E1,definition,
% 0.28/0.47 ( ex1E1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ( ex1 @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I_type,type,
% 0.28/0.47 ex1I: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I,definition,
% 0.28/0.47 ( ex1I
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xy = Xx ) ) )
% 0.28/0.47 => ( ex1 @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I2_type,type,
% 0.28/0.47 ex1I2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ex1I2,definition,
% 0.28/0.47 ( ex1I2
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) )
% 0.28/0.47 => ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( ex1 @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsuniq_type,type,
% 0.28/0.47 singletonsuniq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsuniq,definition,
% 0.28/0.47 ( singletonsuniq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ( setadjoin @ Xx @ emptyset )
% 0.28/0.47 = ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(atmost1p_type,type,
% 0.28/0.47 atmost1p: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(atleast2p_type,type,
% 0.28/0.47 atleast2p: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(atmost2p_type,type,
% 0.28/0.47 atmost2p: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetp_type,type,
% 0.28/0.47 upairsetp: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL1_type,type,
% 0.28/0.47 setukpairinjL1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL1,definition,
% 0.28/0.47 ( setukpairinjL1
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kfstsingleton_type,type,
% 0.28/0.47 kfstsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kfstsingleton,definition,
% 0.28/0.47 ( kfstsingleton
% 0.28/0.47 = ( ! [Xu: $i] :
% 0.28/0.47 ( ( iskpair @ Xu )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.28/0.47 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(theprop_type,type,
% 0.28/0.47 theprop: $o ).
% 0.28/0.47
% 0.28/0.47 thf(theprop,definition,
% 0.28/0.47 ( theprop
% 0.28/0.47 = ( ! [X: $i] :
% 0.28/0.47 ( ( singleton @ X )
% 0.28/0.47 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kfst_type,type,
% 0.28/0.47 kfst: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(kfstpairEq_type,type,
% 0.28/0.47 kfstpairEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kfstpairEq,definition,
% 0.28/0.47 ( kfstpairEq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xx ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodfstin_type,type,
% 0.28/0.47 cartprodfstin: $o ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodfstin,definition,
% 0.28/0.47 ( cartprodfstin
% 0.28/0.47 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL2_type,type,
% 0.28/0.47 setukpairinjL2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL2,definition,
% 0.28/0.47 ( setukpairinjL2
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL_type,type,
% 0.28/0.47 setukpairinjL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjL,definition,
% 0.28/0.47 ( setukpairinjL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.28/0.47 = ( kpair @ Xz @ Xu ) )
% 0.28/0.47 => ( Xx = Xz ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR11_type,type,
% 0.28/0.47 setukpairinjR11: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR11,definition,
% 0.28/0.47 ( setukpairinjR11
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR12_type,type,
% 0.28/0.47 setukpairinjR12: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR12,definition,
% 0.28/0.47 ( setukpairinjR12
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR1_type,type,
% 0.28/0.47 setukpairinjR1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR1,definition,
% 0.28/0.47 ( setukpairinjR1
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xu )
% 0.28/0.47 => ( Xy = Xu ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairequniteq_type,type,
% 0.28/0.47 upairequniteq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairequniteq,definition,
% 0.28/0.47 ( upairequniteq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ Xz @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR2_type,type,
% 0.28/0.47 setukpairinjR2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR2,definition,
% 0.28/0.47 ( setukpairinjR2
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.28/0.47 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.28/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR_type,type,
% 0.28/0.47 setukpairinjR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setukpairinjR,definition,
% 0.28/0.47 ( setukpairinjR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( ( kpair @ Xx @ Xy )
% 0.28/0.47 = ( kpair @ Xz @ Xu ) )
% 0.28/0.47 => ( Xy = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ksndsingleton_type,type,
% 0.28/0.47 ksndsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ksndsingleton,definition,
% 0.28/0.47 ( ksndsingleton
% 0.28/0.47 = ( ! [Xu: $i] :
% 0.28/0.47 ( ( iskpair @ Xu )
% 0.28/0.47 => ( singleton
% 0.28/0.47 @ ( dsetconstr @ ( setunion @ Xu )
% 0.28/0.47 @ ^ [Xx: $i] :
% 0.28/0.47 ( Xu
% 0.28/0.47 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(ksnd_type,type,
% 0.28/0.47 ksnd: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(ksndpairEq_type,type,
% 0.28/0.47 ksndpairEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(ksndpairEq,definition,
% 0.28/0.47 ( ksndpairEq
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 0.28/0.47 = Xy ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(kpairsurjEq_type,type,
% 0.28/0.47 kpairsurjEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(kpairsurjEq,definition,
% 0.28/0.47 ( kpairsurjEq
% 0.28/0.47 = ( ! [Xu: $i] :
% 0.28/0.47 ( ( iskpair @ Xu )
% 0.28/0.47 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 0.28/0.47 = Xu ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(cartprodsndin,conjecture,
% 0.28/0.47 ( setextAx
% 0.28/0.47 => ( emptysetAx
% 0.28/0.47 => ( setadjoinAx
% 0.28/0.47 => ( powersetAx
% 0.28/0.47 => ( setunionAx
% 0.28/0.47 => ( omega0Ax
% 0.28/0.47 => ( omegaSAx
% 0.28/0.47 => ( omegaIndAx
% 0.28/0.47 => ( replAx
% 0.28/0.47 => ( foundationAx
% 0.28/0.47 => ( wellorderingAx
% 0.28/0.47 => ( descrp
% 0.28/0.47 => ( dsetconstrI
% 0.28/0.47 => ( dsetconstrEL
% 0.28/0.47 => ( dsetconstrER
% 0.28/0.47 => ( exuE1
% 0.28/0.47 => ( prop2setE
% 0.28/0.47 => ( emptysetE
% 0.28/0.47 => ( emptysetimpfalse
% 0.28/0.47 => ( notinemptyset
% 0.28/0.47 => ( exuE3e
% 0.28/0.47 => ( setext
% 0.28/0.47 => ( emptyI
% 0.28/0.47 => ( noeltsimpempty
% 0.28/0.47 => ( setbeta
% 0.28/0.47 => ( nonemptyE1
% 0.28/0.47 => ( nonemptyI
% 0.28/0.47 => ( nonemptyI1
% 0.28/0.47 => ( setadjoinIL
% 0.28/0.47 => ( emptyinunitempty
% 0.28/0.47 => ( setadjoinIR
% 0.28/0.47 => ( setadjoinE
% 0.28/0.47 => ( setadjoinOr
% 0.28/0.47 => ( setoftrueEq
% 0.28/0.47 => ( powersetI
% 0.28/0.47 => ( emptyinPowerset
% 0.28/0.47 => ( emptyInPowerset
% 0.28/0.47 => ( powersetE
% 0.28/0.47 => ( setunionI
% 0.28/0.47 => ( setunionE
% 0.28/0.47 => ( subPowSU
% 0.28/0.47 => ( exuE2
% 0.28/0.47 => ( nonemptyImpWitness
% 0.28/0.47 => ( uniqinunit
% 0.28/0.47 => ( notinsingleton
% 0.28/0.47 => ( eqinunit
% 0.28/0.47 => ( singletonsswitch
% 0.28/0.47 => ( upairsetE
% 0.28/0.47 => ( upairsetIL
% 0.28/0.47 => ( upairsetIR
% 0.28/0.47 => ( emptyE1
% 0.28/0.47 => ( vacuousDall
% 0.28/0.47 => ( quantDeMorgan1
% 0.28/0.47 => ( quantDeMorgan2
% 0.28/0.47 => ( quantDeMorgan3
% 0.28/0.47 => ( quantDeMorgan4
% 0.28/0.47 => ( prop2setI
% 0.28/0.47 => ( prop2set2propI
% 0.28/0.47 => ( notdexE
% 0.28/0.47 => ( notdallE
% 0.28/0.47 => ( exuI1
% 0.28/0.47 => ( exuI3
% 0.28/0.47 => ( exuI2
% 0.28/0.47 => ( inCongP
% 0.28/0.47 => ( in__Cong
% 0.28/0.47 => ( exuE3u
% 0.28/0.47 => ( exu__Cong
% 0.28/0.47 => ( emptyset__Cong
% 0.28/0.47 => ( setadjoin__Cong
% 0.28/0.47 => ( powerset__Cong
% 0.28/0.47 => ( setunion__Cong
% 0.28/0.47 => ( omega__Cong
% 0.28/0.47 => ( exuEu
% 0.28/0.47 => ( descr__Cong
% 0.28/0.47 => ( dsetconstr__Cong
% 0.28/0.47 => ( subsetI1
% 0.28/0.47 => ( eqimpsubset2
% 0.28/0.47 => ( eqimpsubset1
% 0.28/0.47 => ( subsetI2
% 0.28/0.47 => ( emptysetsubset
% 0.28/0.47 => ( subsetE
% 0.28/0.47 => ( subsetE2
% 0.28/0.47 => ( notsubsetI
% 0.28/0.47 => ( notequalI1
% 0.28/0.47 => ( notequalI2
% 0.28/0.47 => ( subsetRefl
% 0.28/0.47 => ( subsetTrans
% 0.28/0.47 => ( setadjoinSub
% 0.28/0.47 => ( setadjoinSub2
% 0.28/0.47 => ( subset2powerset
% 0.28/0.47 => ( setextsub
% 0.28/0.47 => ( subsetemptysetimpeq
% 0.28/0.47 => ( powersetI1
% 0.28/0.47 => ( powersetE1
% 0.28/0.47 => ( inPowerset
% 0.28/0.47 => ( powersetsubset
% 0.28/0.47 => ( sepInPowerset
% 0.28/0.47 => ( sepSubset
% 0.28/0.47 => ( binunionIL
% 0.28/0.47 => ( upairset2IR
% 0.28/0.47 => ( binunionIR
% 0.28/0.47 => ( binunionEcases
% 0.28/0.47 => ( binunionE
% 0.28/0.47 => ( binunionLsub
% 0.28/0.47 => ( binunionRsub
% 0.28/0.47 => ( binintersectI
% 0.28/0.47 => ( binintersectSubset5
% 0.28/0.47 => ( binintersectEL
% 0.28/0.47 => ( binintersectLsub
% 0.28/0.47 => ( binintersectSubset2
% 0.28/0.47 => ( binintersectSubset3
% 0.28/0.47 => ( binintersectER
% 0.28/0.47 => ( disjointsetsI1
% 0.28/0.47 => ( binintersectRsub
% 0.28/0.47 => ( binintersectSubset4
% 0.28/0.47 => ( binintersectSubset1
% 0.28/0.47 => ( bs114d
% 0.28/0.47 => ( setminusI
% 0.28/0.47 => ( setminusEL
% 0.28/0.47 => ( setminusER
% 0.28/0.47 => ( setminusSubset2
% 0.28/0.47 => ( setminusERneg
% 0.28/0.47 => ( setminusELneg
% 0.28/0.47 => ( setminusILneg
% 0.28/0.47 => ( setminusIRneg
% 0.28/0.47 => ( setminusLsub
% 0.28/0.47 => ( setminusSubset1
% 0.28/0.47 => ( symdiffE
% 0.28/0.47 => ( symdiffI1
% 0.28/0.47 => ( symdiffI2
% 0.28/0.47 => ( symdiffIneg1
% 0.28/0.47 => ( symdiffIneg2
% 0.28/0.47 => ( secondinupair
% 0.28/0.47 => ( setukpairIL
% 0.28/0.47 => ( setukpairIR
% 0.28/0.47 => ( kpairiskpair
% 0.28/0.47 => ( kpairp
% 0.28/0.47 => ( singletonsubset
% 0.28/0.47 => ( singletoninpowerset
% 0.28/0.47 => ( singletoninpowunion
% 0.28/0.47 => ( upairset2E
% 0.28/0.47 => ( upairsubunion
% 0.28/0.47 => ( upairinpowunion
% 0.28/0.47 => ( ubforcartprodlem1
% 0.28/0.47 => ( ubforcartprodlem2
% 0.28/0.47 => ( ubforcartprodlem3
% 0.28/0.47 => ( cartprodpairin
% 0.28/0.47 => ( cartprodmempair1
% 0.28/0.47 => ( cartprodmempair
% 0.28/0.47 => ( setunionE2
% 0.28/0.47 => ( setunionsingleton1
% 0.28/0.47 => ( setunionsingleton2
% 0.28/0.47 => ( setunionsingleton
% 0.28/0.47 => ( singletonprop
% 0.28/0.47 => ( ex1E1
% 0.28/0.47 => ( ex1I
% 0.28/0.47 => ( ex1I2
% 0.28/0.47 => ( singletonsuniq
% 0.28/0.47 => ( setukpairinjL1
% 0.28/0.47 => ( kfstsingleton
% 0.28/0.47 => ( theprop
% 0.28/0.47 => ( kfstpairEq
% 0.28/0.47 => ( cartprodfstin
% 0.28/0.47 => ( setukpairinjL2
% 0.28/0.47 => ( setukpairinjL
% 0.28/0.47 => ( setukpairinjR11
% 0.28/0.47 => ( setukpairinjR12
% 0.28/0.47 => ( setukpairinjR1
% 0.28/0.47 => ( upairequniteq
% 0.28/0.47 => ( setukpairinjR2
% 0.28/0.47 => ( setukpairinjR
% 0.28/0.47 => ( ksndsingleton
% 0.28/0.47 => ( ksndpairEq
% 0.28/0.47 => ( kpairsurjEq
% 0.28/0.47 => ! [A: $i,B: $i,Xu: $i] :
% 0.28/0.47 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.28/0.47 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.33/1.48 ---- Embedded in THF ---
% 2.33/1.48 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.33/1.48 %%% Generated on Tue Feb 24 12:29:37 EST 2026
% 2.33/1.48 %%% using '$$dhol' embedding, version 1.3.0.
% 2.33/1.48 %%% Logic specification used:
% 2.33/1.48 %%% thf(spec, logic, $$dhol).
% 2.33/1.48
% 2.33/1.48 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.PjEOTGotWI/DTF2DTF13158.p
% See solution above
% 2.33/1.48 ------------------------
% 2.57/1.52 ---- Cleaned THF ---
% 2.57/1.52 thf(in_type,type,
% 2.57/1.52 in: $i > $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(exu_type,type,
% 2.57/1.52 exu: ( $i > $o ) > $o ).
% 2.57/1.52
% 2.57/1.52 thf(exu,definition,
% 2.57/1.52 ( exu
% 2.57/1.52 = ( ^ [Xphi: $i > $o] :
% 2.57/1.52 ? [Xx: $i] :
% 2.57/1.52 ( ( Xphi @ Xx )
% 2.57/1.52 & ! [Xy: $i] :
% 2.57/1.52 ( ( Xphi @ Xy )
% 2.57/1.52 => ( Xx = Xy ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setextAx_type,type,
% 2.57/1.52 setextAx: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setextAx,definition,
% 2.57/1.52 ( setextAx
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 <=> ( in @ Xx @ B ) )
% 2.57/1.52 => ( A = B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(emptyset_type,type,
% 2.57/1.52 emptyset: $i ).
% 2.57/1.52
% 2.57/1.52 thf(emptysetAx_type,type,
% 2.57/1.52 emptysetAx: $o ).
% 2.57/1.52
% 2.57/1.52 thf(emptysetAx,definition,
% 2.57/1.52 ( emptysetAx
% 2.57/1.52 = ( ! [Xx: $i] :
% 2.57/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoin_type,type,
% 2.57/1.52 setadjoin: $i > $i > $i ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinAx_type,type,
% 2.57/1.52 setadjoinAx: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinAx,definition,
% 2.57/1.52 ( setadjoinAx
% 2.57/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.57/1.52 <=> ( ( Xy = Xx )
% 2.57/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(powerset_type,type,
% 2.57/1.52 powerset: $i > $i ).
% 2.57/1.52
% 2.57/1.52 thf(powersetAx_type,type,
% 2.57/1.52 powersetAx: $o ).
% 2.57/1.52
% 2.57/1.52 thf(powersetAx,definition,
% 2.57/1.52 ( powersetAx
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.57/1.52 <=> ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ B )
% 2.57/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setunion_type,type,
% 2.57/1.52 setunion: $i > $i ).
% 2.57/1.52
% 2.57/1.52 thf(setunionAx_type,type,
% 2.57/1.52 setunionAx: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setunionAx,definition,
% 2.57/1.52 ( setunionAx
% 2.57/1.52 = ( ! [A: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.57/1.52 <=> ? [B: $i] :
% 2.57/1.52 ( ( in @ Xx @ B )
% 2.57/1.52 & ( in @ B @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(omega_type,type,
% 2.57/1.52 omega: $i ).
% 2.57/1.52
% 2.57/1.52 thf(omega0Ax_type,type,
% 2.57/1.52 omega0Ax: $o ).
% 2.57/1.52
% 2.57/1.52 thf(omega0Ax,definition,
% 2.57/1.52 ( omega0Ax
% 2.57/1.52 = ( in @ emptyset @ omega ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(omegaSAx_type,type,
% 2.57/1.52 omegaSAx: $o ).
% 2.57/1.52
% 2.57/1.52 thf(omegaSAx,definition,
% 2.57/1.52 ( omegaSAx
% 2.57/1.52 = ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ omega )
% 2.57/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(omegaIndAx_type,type,
% 2.57/1.52 omegaIndAx: $o ).
% 2.57/1.52
% 2.57/1.52 thf(omegaIndAx,definition,
% 2.57/1.52 ( omegaIndAx
% 2.57/1.52 = ( ! [A: $i] :
% 2.57/1.52 ( ( ( in @ emptyset @ A )
% 2.57/1.52 & ! [Xx: $i] :
% 2.57/1.52 ( ( ( in @ Xx @ omega )
% 2.57/1.52 & ( in @ Xx @ A ) )
% 2.57/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.57/1.52 => ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ omega )
% 2.57/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(replAx_type,type,
% 2.57/1.52 replAx: $o ).
% 2.57/1.52
% 2.57/1.52 thf(replAx,definition,
% 2.57/1.52 ( replAx
% 2.57/1.52 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( exu
% 2.57/1.52 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.57/1.52 => ? [B: $i] :
% 2.57/1.52 ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ B )
% 2.57/1.52 <=> ? [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ A )
% 2.57/1.52 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(foundationAx_type,type,
% 2.57/1.52 foundationAx: $o ).
% 2.57/1.52
% 2.57/1.52 thf(foundationAx,definition,
% 2.57/1.52 ( foundationAx
% 2.57/1.52 = ( ! [A: $i] :
% 2.57/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.57/1.52 => ? [B: $i] :
% 2.57/1.52 ( ( in @ B @ A )
% 2.57/1.52 & ~ ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ B )
% 2.57/1.52 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(wellorderingAx_type,type,
% 2.57/1.52 wellorderingAx: $o ).
% 2.57/1.52
% 2.57/1.52 thf(wellorderingAx,definition,
% 2.57/1.52 ( wellorderingAx
% 2.57/1.52 = ( ! [A: $i] :
% 2.57/1.52 ? [B: $i] :
% 2.57/1.52 ( ! [C: $i] :
% 2.57/1.52 ( ( in @ C @ B )
% 2.57/1.52 => ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ C )
% 2.57/1.52 => ( in @ Xx @ A ) ) )
% 2.57/1.52 & ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( ( in @ Xx @ A )
% 2.57/1.52 & ( in @ Xy @ A ) )
% 2.57/1.52 => ( ! [C: $i] :
% 2.57/1.52 ( ( in @ C @ B )
% 2.57/1.52 => ( ( in @ Xx @ C )
% 2.57/1.52 <=> ( in @ Xy @ C ) ) )
% 2.57/1.52 => ( Xx = Xy ) ) )
% 2.57/1.52 & ! [C: $i,D: $i] :
% 2.57/1.52 ( ( ( in @ C @ B )
% 2.57/1.52 & ( in @ D @ B ) )
% 2.57/1.52 => ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ C )
% 2.57/1.52 => ( in @ Xx @ D ) )
% 2.57/1.52 | ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ D )
% 2.57/1.52 => ( in @ Xx @ C ) ) ) )
% 2.57/1.52 & ! [C: $i] :
% 2.57/1.52 ( ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ C )
% 2.57/1.52 => ( in @ Xx @ A ) )
% 2.57/1.52 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.57/1.52 => ? [D: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ D @ B )
% 2.57/1.52 & ( in @ Xx @ C )
% 2.57/1.52 & ~ ? [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ D )
% 2.57/1.52 & ( in @ Xy @ C ) )
% 2.57/1.52 & ! [E: $i] :
% 2.57/1.52 ( ( in @ E @ B )
% 2.57/1.52 => ( ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ E )
% 2.57/1.52 => ( in @ Xy @ D ) )
% 2.57/1.52 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(descr_type,type,
% 2.57/1.52 descr: ( $i > $o ) > $i ).
% 2.57/1.52
% 2.57/1.52 thf(descrp_type,type,
% 2.57/1.52 descrp: $o ).
% 2.57/1.52
% 2.57/1.52 thf(descrp,definition,
% 2.57/1.52 ( descrp
% 2.57/1.52 = ( ! [Xphi: $i > $o] :
% 2.57/1.52 ( ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 => ( Xphi
% 2.57/1.52 @ ( descr
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(dsetconstr_type,type,
% 2.57/1.52 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.57/1.52
% 2.57/1.52 thf(dsetconstrI_type,type,
% 2.57/1.52 dsetconstrI: $o ).
% 2.57/1.52
% 2.57/1.52 thf(dsetconstrI,definition,
% 2.57/1.52 ( dsetconstrI
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( ( Xphi @ Xx )
% 2.57/1.52 => ( in @ Xx
% 2.57/1.52 @ ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(dsetconstrEL_type,type,
% 2.57/1.52 dsetconstrEL: $o ).
% 2.57/1.52
% 2.57/1.52 thf(dsetconstrEL,definition,
% 2.57/1.52 ( dsetconstrEL
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx
% 2.57/1.52 @ ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.57/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(dsetconstrER_type,type,
% 2.57/1.52 dsetconstrER: $o ).
% 2.57/1.52
% 2.57/1.52 thf(dsetconstrER,definition,
% 2.57/1.52 ( dsetconstrER
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx
% 2.57/1.52 @ ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.57/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(exuE1_type,type,
% 2.57/1.52 exuE1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(exuE1,definition,
% 2.57/1.52 ( exuE1
% 2.57/1.52 = ( ! [Xphi: $i > $o] :
% 2.57/1.52 ( ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 => ? [Xx: $i] :
% 2.57/1.52 ( ( Xphi @ Xx )
% 2.57/1.52 & ! [Xy: $i] :
% 2.57/1.52 ( ( Xphi @ Xy )
% 2.57/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(prop2set_type,type,
% 2.57/1.52 prop2set: $o > $i ).
% 2.57/1.52
% 2.57/1.52 thf(prop2setE_type,type,
% 2.57/1.52 prop2setE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(prop2setE,definition,
% 2.57/1.52 ( prop2setE
% 2.57/1.52 = ( ! [Xphi: $o,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.57/1.52 => Xphi ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(emptysetE_type,type,
% 2.57/1.52 emptysetE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(emptysetE,definition,
% 2.57/1.52 ( emptysetE
% 2.57/1.52 = ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ emptyset )
% 2.57/1.52 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(emptysetimpfalse_type,type,
% 2.57/1.52 emptysetimpfalse: $o ).
% 2.57/1.52
% 2.57/1.52 thf(emptysetimpfalse,definition,
% 2.57/1.52 ( emptysetimpfalse
% 2.57/1.52 = ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ emptyset )
% 2.57/1.52 => $false ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(notinemptyset_type,type,
% 2.57/1.52 notinemptyset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(notinemptyset,definition,
% 2.57/1.52 ( notinemptyset
% 2.57/1.52 = ( ! [Xx: $i] :
% 2.57/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(exuE3e_type,type,
% 2.57/1.52 exuE3e: $o ).
% 2.57/1.52
% 2.57/1.52 thf(exuE3e,definition,
% 2.57/1.52 ( exuE3e
% 2.57/1.52 = ( ! [Xphi: $i > $o] :
% 2.57/1.52 ( ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setext_type,type,
% 2.57/1.52 setext: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setext,definition,
% 2.57/1.52 ( setext
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( in @ Xx @ B ) )
% 2.57/1.52 => ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ B )
% 2.57/1.52 => ( in @ Xx @ A ) )
% 2.57/1.52 => ( A = B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(emptyI_type,type,
% 2.57/1.52 emptyI: $o ).
% 2.57/1.52
% 2.57/1.52 thf(emptyI,definition,
% 2.57/1.52 ( emptyI
% 2.57/1.52 = ( ! [A: $i] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ~ ( in @ Xx @ A )
% 2.57/1.52 => ( A = emptyset ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(noeltsimpempty_type,type,
% 2.57/1.52 noeltsimpempty: $o ).
% 2.57/1.52
% 2.57/1.52 thf(noeltsimpempty,definition,
% 2.57/1.52 ( noeltsimpempty
% 2.57/1.52 = ( ! [A: $i] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ~ ( in @ Xx @ A )
% 2.57/1.52 => ( A = emptyset ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setbeta_type,type,
% 2.57/1.52 setbeta: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setbeta,definition,
% 2.57/1.52 ( setbeta
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( ( in @ Xx
% 2.57/1.52 @ ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.57/1.52 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(nonempty_type,type,
% 2.57/1.52 nonempty: $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(nonempty,definition,
% 2.57/1.52 ( nonempty
% 2.57/1.52 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(nonemptyE1_type,type,
% 2.57/1.52 nonemptyE1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(nonemptyE1,definition,
% 2.57/1.52 ( nonemptyE1
% 2.57/1.52 = ( ! [A: $i] :
% 2.57/1.52 ( ( nonempty @ A )
% 2.57/1.52 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(nonemptyI_type,type,
% 2.57/1.52 nonemptyI: $o ).
% 2.57/1.52
% 2.57/1.52 thf(nonemptyI,definition,
% 2.57/1.52 ( nonemptyI
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( ( Xphi @ Xx )
% 2.57/1.52 => ( nonempty
% 2.57/1.52 @ ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(nonemptyI1_type,type,
% 2.57/1.52 nonemptyI1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(nonemptyI1,definition,
% 2.57/1.52 ( nonemptyI1
% 2.57/1.52 = ( ! [A: $i] :
% 2.57/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.57/1.52 => ( nonempty @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinIL_type,type,
% 2.57/1.52 setadjoinIL: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinIL,definition,
% 2.57/1.52 ( setadjoinIL
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(emptyinunitempty_type,type,
% 2.57/1.52 emptyinunitempty: $o ).
% 2.57/1.52
% 2.57/1.52 thf(emptyinunitempty,definition,
% 2.57/1.52 ( emptyinunitempty
% 2.57/1.52 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinIR_type,type,
% 2.57/1.52 setadjoinIR: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinIR,definition,
% 2.57/1.52 ( setadjoinIR
% 2.57/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ A )
% 2.57/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinE_type,type,
% 2.57/1.52 setadjoinE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinE,definition,
% 2.57/1.52 ( setadjoinE
% 2.57/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.57/1.52 => ! [Xphi: $o] :
% 2.57/1.52 ( ( ( Xy = Xx )
% 2.57/1.52 => Xphi )
% 2.57/1.52 => ( ( ( in @ Xy @ A )
% 2.57/1.52 => Xphi )
% 2.57/1.52 => Xphi ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinOr_type,type,
% 2.57/1.52 setadjoinOr: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinOr,definition,
% 2.57/1.52 ( setadjoinOr
% 2.57/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.57/1.52 => ( ( Xy = Xx )
% 2.57/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setoftrueEq_type,type,
% 2.57/1.52 setoftrueEq: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setoftrueEq,definition,
% 2.57/1.52 ( setoftrueEq
% 2.57/1.52 = ( ! [A: $i] :
% 2.57/1.52 ( ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xx: $i] : $true )
% 2.57/1.52 = A ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(powersetI_type,type,
% 2.57/1.52 powersetI: $o ).
% 2.57/1.52
% 2.57/1.52 thf(powersetI,definition,
% 2.57/1.52 ( powersetI
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ B )
% 2.57/1.52 => ( in @ Xx @ A ) )
% 2.57/1.52 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(emptyinPowerset_type,type,
% 2.57/1.52 emptyinPowerset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(emptyinPowerset,definition,
% 2.57/1.52 ( emptyinPowerset
% 2.57/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(emptyInPowerset_type,type,
% 2.57/1.52 emptyInPowerset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(emptyInPowerset,definition,
% 2.57/1.52 ( emptyInPowerset
% 2.57/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(powersetE_type,type,
% 2.57/1.52 powersetE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(powersetE,definition,
% 2.57/1.52 ( powersetE
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.57/1.52 => ( ( in @ Xx @ B )
% 2.57/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setunionI_type,type,
% 2.57/1.52 setunionI: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setunionI,definition,
% 2.57/1.52 ( setunionI
% 2.57/1.52 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.57/1.52 ( ( in @ Xx @ B )
% 2.57/1.52 => ( ( in @ B @ A )
% 2.57/1.52 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setunionE_type,type,
% 2.57/1.52 setunionE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setunionE,definition,
% 2.57/1.52 ( setunionE
% 2.57/1.52 = ( ! [A: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.57/1.52 => ! [Xphi: $o] :
% 2.57/1.52 ( ! [B: $i] :
% 2.57/1.52 ( ( in @ Xx @ B )
% 2.57/1.52 => ( ( in @ B @ A )
% 2.57/1.52 => Xphi ) )
% 2.57/1.52 => Xphi ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(subPowSU_type,type,
% 2.57/1.52 subPowSU: $o ).
% 2.57/1.52
% 2.57/1.52 thf(subPowSU,definition,
% 2.57/1.52 ( subPowSU
% 2.57/1.52 = ( ! [A: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(exuE2_type,type,
% 2.57/1.52 exuE2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(exuE2,definition,
% 2.57/1.52 ( exuE2
% 2.57/1.52 = ( ! [Xphi: $i > $o] :
% 2.57/1.52 ( ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 => ? [Xx: $i] :
% 2.57/1.52 ! [Xy: $i] :
% 2.57/1.52 ( ( Xphi @ Xy )
% 2.57/1.52 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(nonemptyImpWitness_type,type,
% 2.57/1.52 nonemptyImpWitness: $o ).
% 2.57/1.52
% 2.57/1.52 thf(nonemptyImpWitness,definition,
% 2.57/1.52 ( nonemptyImpWitness
% 2.57/1.52 = ( ! [A: $i] :
% 2.57/1.52 ( ( nonempty @ A )
% 2.57/1.52 => ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & $true ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(uniqinunit_type,type,
% 2.57/1.52 uniqinunit: $o ).
% 2.57/1.52
% 2.57/1.52 thf(uniqinunit,definition,
% 2.57/1.52 ( uniqinunit
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.57/1.52 => ( Xx = Xy ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(notinsingleton_type,type,
% 2.57/1.52 notinsingleton: $o ).
% 2.57/1.52
% 2.57/1.52 thf(notinsingleton,definition,
% 2.57/1.52 ( notinsingleton
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( Xx != Xy )
% 2.57/1.52 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(eqinunit_type,type,
% 2.57/1.52 eqinunit: $o ).
% 2.57/1.52
% 2.57/1.52 thf(eqinunit,definition,
% 2.57/1.52 ( eqinunit
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( Xx = Xy )
% 2.57/1.52 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(singletonsswitch_type,type,
% 2.57/1.52 singletonsswitch: $o ).
% 2.57/1.52
% 2.57/1.52 thf(singletonsswitch,definition,
% 2.57/1.52 ( singletonsswitch
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.57/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(upairsetE_type,type,
% 2.57/1.52 upairsetE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(upairsetE,definition,
% 2.57/1.52 ( upairsetE
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.57/1.52 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.57/1.52 => ( ( Xz = Xx )
% 2.57/1.52 | ( Xz = Xy ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(upairsetIL_type,type,
% 2.57/1.52 upairsetIL: $o ).
% 2.57/1.52
% 2.57/1.52 thf(upairsetIL,definition,
% 2.57/1.52 ( upairsetIL
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(upairsetIR_type,type,
% 2.57/1.52 upairsetIR: $o ).
% 2.57/1.52
% 2.57/1.52 thf(upairsetIR,definition,
% 2.57/1.52 ( upairsetIR
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(emptyE1_type,type,
% 2.57/1.52 emptyE1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(emptyE1,definition,
% 2.57/1.52 ( emptyE1
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ( Xphi @ Xx ) )
% 2.57/1.52 => ( ( ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 = emptyset )
% 2.57/1.52 => $false ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(vacuousDall_type,type,
% 2.57/1.52 vacuousDall: $o ).
% 2.57/1.52
% 2.57/1.52 thf(vacuousDall,definition,
% 2.57/1.52 ( vacuousDall
% 2.57/1.52 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ emptyset )
% 2.57/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(quantDeMorgan1_type,type,
% 2.57/1.52 quantDeMorgan1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(quantDeMorgan1,definition,
% 2.57/1.52 ( quantDeMorgan1
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( ~ ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( Xphi @ Xx ) )
% 2.57/1.52 => ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(quantDeMorgan2_type,type,
% 2.57/1.52 quantDeMorgan2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(quantDeMorgan2,definition,
% 2.57/1.52 ( quantDeMorgan2
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ~ ( Xphi @ Xx ) )
% 2.57/1.52 => ~ ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(quantDeMorgan3_type,type,
% 2.57/1.52 quantDeMorgan3: $o ).
% 2.57/1.52
% 2.57/1.52 thf(quantDeMorgan3,definition,
% 2.57/1.52 ( quantDeMorgan3
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( ~ ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ( Xphi @ Xx ) )
% 2.57/1.52 => ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(quantDeMorgan4_type,type,
% 2.57/1.52 quantDeMorgan4: $o ).
% 2.57/1.52
% 2.57/1.52 thf(quantDeMorgan4,definition,
% 2.57/1.52 ( quantDeMorgan4
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ~ ( Xphi @ Xx ) )
% 2.57/1.52 => ~ ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(prop2setI_type,type,
% 2.57/1.52 prop2setI: $o ).
% 2.57/1.52
% 2.57/1.52 thf(prop2setI,definition,
% 2.57/1.52 ( prop2setI
% 2.57/1.52 = ( ! [Xphi: $o] :
% 2.57/1.52 ( Xphi
% 2.57/1.52 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(set2prop_type,type,
% 2.57/1.52 set2prop: $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(prop2set2propI_type,type,
% 2.57/1.52 prop2set2propI: $o ).
% 2.57/1.52
% 2.57/1.52 thf(prop2set2propI,definition,
% 2.57/1.52 ( prop2set2propI
% 2.57/1.52 = ( ! [Xphi: $o] :
% 2.57/1.52 ( Xphi
% 2.57/1.52 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(notdexE_type,type,
% 2.57/1.52 notdexE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(notdexE,definition,
% 2.57/1.52 ( notdexE
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( ~ ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ( Xphi @ Xx ) )
% 2.57/1.52 => ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(notdallE_type,type,
% 2.57/1.52 notdallE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(notdallE,definition,
% 2.57/1.52 ( notdallE
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( ~ ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( Xphi @ Xx ) )
% 2.57/1.52 => ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(exuI1_type,type,
% 2.57/1.52 exuI1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(exuI1,definition,
% 2.57/1.52 ( exuI1
% 2.57/1.52 = ( ! [Xphi: $i > $o] :
% 2.57/1.52 ( ? [Xx: $i] :
% 2.57/1.52 ( ( Xphi @ Xx )
% 2.57/1.52 & ! [Xy: $i] :
% 2.57/1.52 ( ( Xphi @ Xy )
% 2.57/1.52 => ( Xx = Xy ) ) )
% 2.57/1.52 => ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(exuI3_type,type,
% 2.57/1.52 exuI3: $o ).
% 2.57/1.52
% 2.57/1.52 thf(exuI3,definition,
% 2.57/1.52 ( exuI3
% 2.57/1.52 = ( ! [Xphi: $i > $o] :
% 2.57/1.52 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.57/1.52 => ( ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( Xphi @ Xx )
% 2.57/1.52 => ( ( Xphi @ Xy )
% 2.57/1.52 => ( Xx = Xy ) ) )
% 2.57/1.52 => ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(exuI2_type,type,
% 2.57/1.52 exuI2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(exuI2,definition,
% 2.57/1.52 ( exuI2
% 2.57/1.52 = ( ! [Xphi: $i > $o] :
% 2.57/1.52 ( ? [Xx: $i] :
% 2.57/1.52 ! [Xy: $i] :
% 2.57/1.52 ( ( Xphi @ Xy )
% 2.57/1.52 <=> ( Xy = Xx ) )
% 2.57/1.52 => ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(inCongP_type,type,
% 2.57/1.52 inCongP: $o ).
% 2.57/1.52
% 2.57/1.52 thf(inCongP,definition,
% 2.57/1.52 ( inCongP
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( A = B )
% 2.57/1.52 => ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( Xx = Xy )
% 2.57/1.52 => ( ( in @ Xx @ A )
% 2.57/1.52 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(in__Cong_type,type,
% 2.57/1.52 in__Cong: $o ).
% 2.57/1.52
% 2.57/1.52 thf(in__Cong,definition,
% 2.57/1.52 ( in__Cong
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( A = B )
% 2.57/1.52 => ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( Xx = Xy )
% 2.57/1.52 => ( ( in @ Xx @ A )
% 2.57/1.52 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(exuE3u_type,type,
% 2.57/1.52 exuE3u: $o ).
% 2.57/1.52
% 2.57/1.52 thf(exuE3u,definition,
% 2.57/1.52 ( exuE3u
% 2.57/1.52 = ( ! [Xphi: $i > $o] :
% 2.57/1.52 ( ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 => ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( Xphi @ Xx )
% 2.57/1.52 => ( ( Xphi @ Xy )
% 2.57/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(exu__Cong_type,type,
% 2.57/1.52 exu__Cong: $o ).
% 2.57/1.52
% 2.57/1.52 thf(exu__Cong,definition,
% 2.57/1.52 ( exu__Cong
% 2.57/1.52 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.57/1.52 ( ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( Xx = Xy )
% 2.57/1.52 => ( ( Xphi @ Xx )
% 2.57/1.52 <=> ( Xpsi @ Xy ) ) )
% 2.57/1.52 => ( ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 <=> ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(emptyset__Cong_type,type,
% 2.57/1.52 emptyset__Cong: $o ).
% 2.57/1.52
% 2.57/1.52 thf(emptyset__Cong,definition,
% 2.57/1.52 ( emptyset__Cong
% 2.57/1.52 = ( emptyset = emptyset ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoin__Cong_type,type,
% 2.57/1.52 setadjoin__Cong: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoin__Cong,definition,
% 2.57/1.52 ( setadjoin__Cong
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( Xx = Xy )
% 2.57/1.52 => ! [Xz: $i,Xu: $i] :
% 2.57/1.52 ( ( Xz = Xu )
% 2.57/1.52 => ( ( setadjoin @ Xx @ Xz )
% 2.57/1.52 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(powerset__Cong_type,type,
% 2.57/1.52 powerset__Cong: $o ).
% 2.57/1.52
% 2.57/1.52 thf(powerset__Cong,definition,
% 2.57/1.52 ( powerset__Cong
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( A = B )
% 2.57/1.52 => ( ( powerset @ A )
% 2.57/1.52 = ( powerset @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setunion__Cong_type,type,
% 2.57/1.52 setunion__Cong: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setunion__Cong,definition,
% 2.57/1.52 ( setunion__Cong
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( A = B )
% 2.57/1.52 => ( ( setunion @ A )
% 2.57/1.52 = ( setunion @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(omega__Cong_type,type,
% 2.57/1.52 omega__Cong: $o ).
% 2.57/1.52
% 2.57/1.52 thf(omega__Cong,definition,
% 2.57/1.52 ( omega__Cong
% 2.57/1.52 = ( omega = omega ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(exuEu_type,type,
% 2.57/1.52 exuEu: $o ).
% 2.57/1.52
% 2.57/1.52 thf(exuEu,definition,
% 2.57/1.52 ( exuEu
% 2.57/1.52 = ( ! [Xphi: $i > $o] :
% 2.57/1.52 ( ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 => ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( Xphi @ Xx )
% 2.57/1.52 => ( ( Xphi @ Xy )
% 2.57/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(descr__Cong_type,type,
% 2.57/1.52 descr__Cong: $o ).
% 2.57/1.52
% 2.57/1.52 thf(descr__Cong,definition,
% 2.57/1.52 ( descr__Cong
% 2.57/1.52 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.57/1.52 ( ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( Xx = Xy )
% 2.57/1.52 => ( ( Xphi @ Xx )
% 2.57/1.52 <=> ( Xpsi @ Xy ) ) )
% 2.57/1.52 => ( ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 => ( ( exu
% 2.57/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.57/1.52 => ( ( descr
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 = ( descr
% 2.57/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(dsetconstr__Cong_type,type,
% 2.57/1.52 dsetconstr__Cong: $o ).
% 2.57/1.52
% 2.57/1.52 thf(dsetconstr__Cong,definition,
% 2.57/1.52 ( dsetconstr__Cong
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( A = B )
% 2.57/1.52 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ B )
% 2.57/1.52 => ( ( Xx = Xy )
% 2.57/1.52 => ( ( Xphi @ Xx )
% 2.57/1.52 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.57/1.52 => ( ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 = ( dsetconstr @ B
% 2.57/1.52 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(subset_type,type,
% 2.57/1.52 subset: $i > $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(disjoint_type,type,
% 2.57/1.52 disjoint: $i > $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(setsmeet_type,type,
% 2.57/1.52 setsmeet: $i > $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(subsetI1_type,type,
% 2.57/1.52 subsetI1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(subsetI1,definition,
% 2.57/1.52 ( subsetI1
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( in @ Xx @ B ) )
% 2.57/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(eqimpsubset2_type,type,
% 2.57/1.52 eqimpsubset2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(eqimpsubset2,definition,
% 2.57/1.52 ( eqimpsubset2
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( A = B )
% 2.57/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(eqimpsubset1_type,type,
% 2.57/1.52 eqimpsubset1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(eqimpsubset1,definition,
% 2.57/1.52 ( eqimpsubset1
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( A = B )
% 2.57/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(subsetI2_type,type,
% 2.57/1.52 subsetI2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(subsetI2,definition,
% 2.57/1.52 ( subsetI2
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( in @ Xx @ B ) )
% 2.57/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(emptysetsubset_type,type,
% 2.57/1.52 emptysetsubset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(emptysetsubset,definition,
% 2.57/1.52 ( emptysetsubset
% 2.57/1.52 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(subsetE_type,type,
% 2.57/1.52 subsetE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(subsetE,definition,
% 2.57/1.52 ( subsetE
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( subset @ A @ B )
% 2.57/1.52 => ( ( in @ Xx @ A )
% 2.57/1.52 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(subsetE2_type,type,
% 2.57/1.52 subsetE2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(subsetE2,definition,
% 2.57/1.52 ( subsetE2
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( subset @ A @ B )
% 2.57/1.52 => ( ~ ( in @ Xx @ B )
% 2.57/1.52 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(notsubsetI_type,type,
% 2.57/1.52 notsubsetI: $o ).
% 2.57/1.52
% 2.57/1.52 thf(notsubsetI,definition,
% 2.57/1.52 ( notsubsetI
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( ~ ( in @ Xx @ B )
% 2.57/1.52 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(notequalI1_type,type,
% 2.57/1.52 notequalI1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(notequalI1,definition,
% 2.57/1.52 ( notequalI1
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ~ ( subset @ A @ B )
% 2.57/1.52 => ( A != B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(notequalI2_type,type,
% 2.57/1.52 notequalI2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(notequalI2,definition,
% 2.57/1.52 ( notequalI2
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( ~ ( in @ Xx @ B )
% 2.57/1.52 => ( A != B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(subsetRefl_type,type,
% 2.57/1.52 subsetRefl: $o ).
% 2.57/1.52
% 2.57/1.52 thf(subsetRefl,definition,
% 2.57/1.52 ( subsetRefl
% 2.57/1.52 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(subsetTrans_type,type,
% 2.57/1.52 subsetTrans: $o ).
% 2.57/1.52
% 2.57/1.52 thf(subsetTrans,definition,
% 2.57/1.52 ( subsetTrans
% 2.57/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.57/1.52 ( ( subset @ A @ B )
% 2.57/1.52 => ( ( subset @ B @ C )
% 2.57/1.52 => ( subset @ A @ C ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinSub_type,type,
% 2.57/1.52 setadjoinSub: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinSub,definition,
% 2.57/1.52 ( setadjoinSub
% 2.57/1.52 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinSub2_type,type,
% 2.57/1.52 setadjoinSub2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setadjoinSub2,definition,
% 2.57/1.52 ( setadjoinSub2
% 2.57/1.52 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.57/1.52 ( ( subset @ A @ B )
% 2.57/1.52 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(subset2powerset_type,type,
% 2.57/1.52 subset2powerset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(subset2powerset,definition,
% 2.57/1.52 ( subset2powerset
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( subset @ A @ B )
% 2.57/1.52 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setextsub_type,type,
% 2.57/1.52 setextsub: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setextsub,definition,
% 2.57/1.52 ( setextsub
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( subset @ A @ B )
% 2.57/1.52 => ( ( subset @ B @ A )
% 2.57/1.52 => ( A = B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(subsetemptysetimpeq_type,type,
% 2.57/1.52 subsetemptysetimpeq: $o ).
% 2.57/1.52
% 2.57/1.52 thf(subsetemptysetimpeq,definition,
% 2.57/1.52 ( subsetemptysetimpeq
% 2.57/1.52 = ( ! [A: $i] :
% 2.57/1.52 ( ( subset @ A @ emptyset )
% 2.57/1.52 => ( A = emptyset ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(powersetI1_type,type,
% 2.57/1.52 powersetI1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(powersetI1,definition,
% 2.57/1.52 ( powersetI1
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( subset @ B @ A )
% 2.57/1.52 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(powersetE1_type,type,
% 2.57/1.52 powersetE1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(powersetE1,definition,
% 2.57/1.52 ( powersetE1
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.57/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(inPowerset_type,type,
% 2.57/1.52 inPowerset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(inPowerset,definition,
% 2.57/1.52 ( inPowerset
% 2.57/1.52 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(powersetsubset_type,type,
% 2.57/1.52 powersetsubset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(powersetsubset,definition,
% 2.57/1.52 ( powersetsubset
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( subset @ A @ B )
% 2.57/1.52 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(sepInPowerset_type,type,
% 2.57/1.52 sepInPowerset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(sepInPowerset,definition,
% 2.57/1.52 ( sepInPowerset
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( in
% 2.57/1.52 @ ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 @ ( powerset @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(sepSubset_type,type,
% 2.57/1.52 sepSubset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(sepSubset,definition,
% 2.57/1.52 ( sepSubset
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( subset
% 2.57/1.52 @ ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 @ A ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binunion_type,type,
% 2.57/1.52 binunion: $i > $i > $i ).
% 2.57/1.52
% 2.57/1.52 thf(binunionIL_type,type,
% 2.57/1.52 binunionIL: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binunionIL,definition,
% 2.57/1.52 ( binunionIL
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(upairset2IR_type,type,
% 2.57/1.52 upairset2IR: $o ).
% 2.57/1.52
% 2.57/1.52 thf(upairset2IR,definition,
% 2.57/1.52 ( upairset2IR
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binunionIR_type,type,
% 2.57/1.52 binunionIR: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binunionIR,definition,
% 2.57/1.52 ( binunionIR
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ B )
% 2.57/1.52 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binunionEcases_type,type,
% 2.57/1.52 binunionEcases: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binunionEcases,definition,
% 2.57/1.52 ( binunionEcases
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.57/1.52 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.57/1.52 => ( ( ( in @ Xx @ A )
% 2.57/1.52 => Xphi )
% 2.57/1.52 => ( ( ( in @ Xx @ B )
% 2.57/1.52 => Xphi )
% 2.57/1.52 => Xphi ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binunionE_type,type,
% 2.57/1.52 binunionE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binunionE,definition,
% 2.57/1.52 ( binunionE
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.57/1.52 => ( ( in @ Xx @ A )
% 2.57/1.52 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binunionLsub_type,type,
% 2.57/1.52 binunionLsub: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binunionLsub,definition,
% 2.57/1.52 ( binunionLsub
% 2.57/1.52 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binunionRsub_type,type,
% 2.57/1.52 binunionRsub: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binunionRsub,definition,
% 2.57/1.52 ( binunionRsub
% 2.57/1.52 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binintersect_type,type,
% 2.57/1.52 binintersect: $i > $i > $i ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectI_type,type,
% 2.57/1.52 binintersectI: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectI,definition,
% 2.57/1.52 ( binintersectI
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( ( in @ Xx @ B )
% 2.57/1.52 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectSubset5_type,type,
% 2.57/1.52 binintersectSubset5: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectSubset5,definition,
% 2.57/1.52 ( binintersectSubset5
% 2.57/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.57/1.52 ( ( subset @ C @ A )
% 2.57/1.52 => ( ( subset @ C @ B )
% 2.57/1.52 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectEL_type,type,
% 2.57/1.52 binintersectEL: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectEL,definition,
% 2.57/1.52 ( binintersectEL
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.57/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectLsub_type,type,
% 2.57/1.52 binintersectLsub: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectLsub,definition,
% 2.57/1.52 ( binintersectLsub
% 2.57/1.52 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectSubset2_type,type,
% 2.57/1.52 binintersectSubset2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectSubset2,definition,
% 2.57/1.52 ( binintersectSubset2
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( subset @ A @ B )
% 2.57/1.52 => ( ( binintersect @ A @ B )
% 2.57/1.52 = A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectSubset3_type,type,
% 2.57/1.52 binintersectSubset3: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectSubset3,definition,
% 2.57/1.52 ( binintersectSubset3
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( ( binintersect @ A @ B )
% 2.57/1.52 = B )
% 2.57/1.52 => ( subset @ B @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectER_type,type,
% 2.57/1.52 binintersectER: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectER,definition,
% 2.57/1.52 ( binintersectER
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.57/1.52 => ( in @ Xx @ B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(disjointsetsI1_type,type,
% 2.57/1.52 disjointsetsI1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(disjointsetsI1,definition,
% 2.57/1.52 ( disjointsetsI1
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ~ ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ( in @ Xx @ B ) )
% 2.57/1.52 => ( ( binintersect @ A @ B )
% 2.57/1.52 = emptyset ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectRsub_type,type,
% 2.57/1.52 binintersectRsub: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectRsub,definition,
% 2.57/1.52 ( binintersectRsub
% 2.57/1.52 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectSubset4_type,type,
% 2.57/1.52 binintersectSubset4: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectSubset4,definition,
% 2.57/1.52 ( binintersectSubset4
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( subset @ B @ A )
% 2.57/1.52 => ( ( binintersect @ A @ B )
% 2.57/1.52 = B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectSubset1_type,type,
% 2.57/1.52 binintersectSubset1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(binintersectSubset1,definition,
% 2.57/1.52 ( binintersectSubset1
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( ( binintersect @ A @ B )
% 2.57/1.52 = A )
% 2.57/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(bs114d_type,type,
% 2.57/1.52 bs114d: $o ).
% 2.57/1.52
% 2.57/1.52 thf(bs114d,definition,
% 2.57/1.52 ( bs114d
% 2.57/1.52 = ( ! [A: $i,B: $i,C: $i] :
% 2.57/1.52 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.57/1.52 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(regular_type,type,
% 2.57/1.52 regular: $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminus_type,type,
% 2.57/1.52 setminus: $i > $i > $i ).
% 2.57/1.52
% 2.57/1.52 thf(setminusI_type,type,
% 2.57/1.52 setminusI: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminusI,definition,
% 2.57/1.52 ( setminusI
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( ~ ( in @ Xx @ B )
% 2.57/1.52 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setminusEL_type,type,
% 2.57/1.52 setminusEL: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminusEL,definition,
% 2.57/1.52 ( setminusEL
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.57/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setminusER_type,type,
% 2.57/1.52 setminusER: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminusER,definition,
% 2.57/1.52 ( setminusER
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.57/1.52 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setminusSubset2_type,type,
% 2.57/1.52 setminusSubset2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminusSubset2,definition,
% 2.57/1.52 ( setminusSubset2
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( subset @ A @ B )
% 2.57/1.52 => ( ( setminus @ A @ B )
% 2.57/1.52 = emptyset ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setminusERneg_type,type,
% 2.57/1.52 setminusERneg: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminusERneg,definition,
% 2.57/1.52 ( setminusERneg
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.57/1.52 => ( ( in @ Xx @ A )
% 2.57/1.52 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setminusELneg_type,type,
% 2.57/1.52 setminusELneg: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminusELneg,definition,
% 2.57/1.52 ( setminusELneg
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.57/1.52 => ( ~ ( in @ Xx @ B )
% 2.57/1.52 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setminusILneg_type,type,
% 2.57/1.52 setminusILneg: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminusILneg,definition,
% 2.57/1.52 ( setminusILneg
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ~ ( in @ Xx @ A )
% 2.57/1.52 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setminusIRneg_type,type,
% 2.57/1.52 setminusIRneg: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminusIRneg,definition,
% 2.57/1.52 ( setminusIRneg
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ B )
% 2.57/1.52 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setminusLsub_type,type,
% 2.57/1.52 setminusLsub: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminusLsub,definition,
% 2.57/1.52 ( setminusLsub
% 2.57/1.52 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setminusSubset1_type,type,
% 2.57/1.52 setminusSubset1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setminusSubset1,definition,
% 2.57/1.52 ( setminusSubset1
% 2.57/1.52 = ( ! [A: $i,B: $i] :
% 2.57/1.52 ( ( ( setminus @ A @ B )
% 2.57/1.52 = emptyset )
% 2.57/1.52 => ( subset @ A @ B ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(symdiff_type,type,
% 2.57/1.52 symdiff: $i > $i > $i ).
% 2.57/1.52
% 2.57/1.52 thf(symdiffE_type,type,
% 2.57/1.52 symdiffE: $o ).
% 2.57/1.52
% 2.57/1.52 thf(symdiffE,definition,
% 2.57/1.52 ( symdiffE
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.57/1.52 => ! [Xphi: $o] :
% 2.57/1.52 ( ( ( in @ Xx @ A )
% 2.57/1.52 => ( ~ ( in @ Xx @ B )
% 2.57/1.52 => Xphi ) )
% 2.57/1.52 => ( ( ~ ( in @ Xx @ A )
% 2.57/1.52 => ( ( in @ Xx @ B )
% 2.57/1.52 => Xphi ) )
% 2.57/1.52 => Xphi ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(symdiffI1_type,type,
% 2.57/1.52 symdiffI1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(symdiffI1,definition,
% 2.57/1.52 ( symdiffI1
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( ~ ( in @ Xx @ B )
% 2.57/1.52 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(symdiffI2_type,type,
% 2.57/1.52 symdiffI2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(symdiffI2,definition,
% 2.57/1.52 ( symdiffI2
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ~ ( in @ Xx @ A )
% 2.57/1.52 => ( ( in @ Xx @ B )
% 2.57/1.52 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(symdiffIneg1_type,type,
% 2.57/1.52 symdiffIneg1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(symdiffIneg1,definition,
% 2.57/1.52 ( symdiffIneg1
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( ( in @ Xx @ B )
% 2.57/1.52 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(symdiffIneg2_type,type,
% 2.57/1.52 symdiffIneg2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(symdiffIneg2,definition,
% 2.57/1.52 ( symdiffIneg2
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ~ ( in @ Xx @ A )
% 2.57/1.52 => ( ~ ( in @ Xx @ B )
% 2.57/1.52 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(iskpair_type,type,
% 2.57/1.52 iskpair: $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(secondinupair_type,type,
% 2.57/1.52 secondinupair: $o ).
% 2.57/1.52
% 2.57/1.52 thf(secondinupair,definition,
% 2.57/1.52 ( secondinupair
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setukpairIL_type,type,
% 2.57/1.52 setukpairIL: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setukpairIL,definition,
% 2.57/1.52 ( setukpairIL
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setukpairIR_type,type,
% 2.57/1.52 setukpairIR: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setukpairIR,definition,
% 2.57/1.52 ( setukpairIR
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(kpairiskpair_type,type,
% 2.57/1.52 kpairiskpair: $o ).
% 2.57/1.52
% 2.57/1.52 thf(kpairiskpair,definition,
% 2.57/1.52 ( kpairiskpair
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(kpair_type,type,
% 2.57/1.52 kpair: $i > $i > $i ).
% 2.57/1.52
% 2.57/1.52 thf(kpairp_type,type,
% 2.57/1.52 kpairp: $o ).
% 2.57/1.52
% 2.57/1.52 thf(kpairp,definition,
% 2.57/1.52 ( kpairp
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(cartprod_type,type,
% 2.57/1.52 cartprod: $i > $i > $i ).
% 2.57/1.52
% 2.57/1.52 thf(singletonsubset_type,type,
% 2.57/1.52 singletonsubset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(singletonsubset,definition,
% 2.57/1.52 ( singletonsubset
% 2.57/1.52 = ( ! [A: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(singletoninpowerset_type,type,
% 2.57/1.52 singletoninpowerset: $o ).
% 2.57/1.52
% 2.57/1.52 thf(singletoninpowerset,definition,
% 2.57/1.52 ( singletoninpowerset
% 2.57/1.52 = ( ! [A: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(singletoninpowunion_type,type,
% 2.57/1.52 singletoninpowunion: $o ).
% 2.57/1.52
% 2.57/1.52 thf(singletoninpowunion,definition,
% 2.57/1.52 ( singletoninpowunion
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(upairset2E_type,type,
% 2.57/1.52 upairset2E: $o ).
% 2.57/1.52
% 2.57/1.52 thf(upairset2E,definition,
% 2.57/1.52 ( upairset2E
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.57/1.52 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.57/1.52 => ( ( Xz = Xx )
% 2.57/1.52 | ( Xz = Xy ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(upairsubunion_type,type,
% 2.57/1.52 upairsubunion: $o ).
% 2.57/1.52
% 2.57/1.52 thf(upairsubunion,definition,
% 2.57/1.52 ( upairsubunion
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ B )
% 2.57/1.52 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(upairinpowunion_type,type,
% 2.57/1.52 upairinpowunion: $o ).
% 2.57/1.52
% 2.57/1.52 thf(upairinpowunion,definition,
% 2.57/1.52 ( upairinpowunion
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ B )
% 2.57/1.52 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(ubforcartprodlem1_type,type,
% 2.57/1.52 ubforcartprodlem1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(ubforcartprodlem1,definition,
% 2.57/1.52 ( ubforcartprodlem1
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ B )
% 2.57/1.52 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(ubforcartprodlem2_type,type,
% 2.57/1.52 ubforcartprodlem2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(ubforcartprodlem2,definition,
% 2.57/1.52 ( ubforcartprodlem2
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ B )
% 2.57/1.52 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(ubforcartprodlem3_type,type,
% 2.57/1.52 ubforcartprodlem3: $o ).
% 2.57/1.52
% 2.57/1.52 thf(ubforcartprodlem3,definition,
% 2.57/1.52 ( ubforcartprodlem3
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ B )
% 2.57/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(cartprodpairin_type,type,
% 2.57/1.52 cartprodpairin: $o ).
% 2.57/1.52
% 2.57/1.52 thf(cartprodpairin,definition,
% 2.57/1.52 ( cartprodpairin
% 2.57/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ B )
% 2.57/1.52 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(cartprodmempair1_type,type,
% 2.57/1.52 cartprodmempair1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(cartprodmempair1,definition,
% 2.57/1.52 ( cartprodmempair1
% 2.57/1.52 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.57/1.52 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.57/1.52 => ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ? [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ B )
% 2.57/1.52 & ( Xu
% 2.57/1.52 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(cartprodmempair_type,type,
% 2.57/1.52 cartprodmempair: $o ).
% 2.57/1.52
% 2.57/1.52 thf(cartprodmempair,definition,
% 2.57/1.52 ( cartprodmempair
% 2.57/1.52 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.57/1.52 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.57/1.52 => ( iskpair @ Xu ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setunionE2_type,type,
% 2.57/1.52 setunionE2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setunionE2,definition,
% 2.57/1.52 ( setunionE2
% 2.57/1.52 = ( ! [A: $i,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.57/1.52 => ? [X: $i] :
% 2.57/1.52 ( ( in @ X @ A )
% 2.57/1.52 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setunionsingleton1_type,type,
% 2.57/1.52 setunionsingleton1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setunionsingleton1,definition,
% 2.57/1.52 ( setunionsingleton1
% 2.57/1.52 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setunionsingleton2_type,type,
% 2.57/1.52 setunionsingleton2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setunionsingleton2,definition,
% 2.57/1.52 ( setunionsingleton2
% 2.57/1.52 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setunionsingleton_type,type,
% 2.57/1.52 setunionsingleton: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setunionsingleton,definition,
% 2.57/1.52 ( setunionsingleton
% 2.57/1.52 = ( ! [Xx: $i] :
% 2.57/1.52 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.57/1.52 = Xx ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(singleton_type,type,
% 2.57/1.52 singleton: $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(singleton,definition,
% 2.57/1.52 ( singleton
% 2.57/1.52 = ( ^ [A: $i] :
% 2.57/1.52 ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ( A
% 2.57/1.52 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(singletonprop_type,type,
% 2.57/1.52 singletonprop: $o ).
% 2.57/1.52
% 2.57/1.52 thf(singletonprop,definition,
% 2.57/1.52 ( singletonprop
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ A )
% 2.57/1.52 => ( ( Xphi @ Xx )
% 2.57/1.52 => ( ( Xphi @ Xy )
% 2.57/1.52 => ( Xx = Xy ) ) ) ) )
% 2.57/1.52 => ( ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ( Xphi @ Xx ) )
% 2.57/1.52 => ( singleton
% 2.57/1.52 @ ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(ex1_type,type,
% 2.57/1.52 ex1: $i > ( $i > $o ) > $o ).
% 2.57/1.52
% 2.57/1.52 thf(ex1,definition,
% 2.57/1.52 ( ex1
% 2.57/1.52 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( singleton
% 2.57/1.52 @ ( dsetconstr @ A
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(ex1E1_type,type,
% 2.57/1.52 ex1E1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(ex1E1,definition,
% 2.57/1.52 ( ex1E1
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( ( ex1 @ A
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.52 => ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(ex1I_type,type,
% 2.57/1.52 ex1I: $o ).
% 2.57/1.52
% 2.57/1.52 thf(ex1I,definition,
% 2.57/1.52 ( ex1I
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ( ( Xphi @ Xx )
% 2.57/1.52 => ( ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ A )
% 2.57/1.52 => ( ( Xphi @ Xy )
% 2.57/1.52 => ( Xy = Xx ) ) )
% 2.57/1.52 => ( ex1 @ A
% 2.57/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(ex1I2_type,type,
% 2.57/1.52 ex1I2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(ex1I2,definition,
% 2.57/1.52 ( ex1I2
% 2.57/1.52 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.52 ( ! [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 => ! [Xy: $i] :
% 2.57/1.52 ( ( in @ Xy @ A )
% 2.57/1.52 => ( ( Xphi @ Xx )
% 2.57/1.52 => ( ( Xphi @ Xy )
% 2.57/1.52 => ( Xx = Xy ) ) ) ) )
% 2.57/1.52 => ( ? [Xx: $i] :
% 2.57/1.52 ( ( in @ Xx @ A )
% 2.57/1.52 & ( Xphi @ Xx ) )
% 2.57/1.52 => ( ex1 @ A
% 2.57/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(singletonsuniq_type,type,
% 2.57/1.52 singletonsuniq: $o ).
% 2.57/1.52
% 2.57/1.52 thf(singletonsuniq,definition,
% 2.57/1.52 ( singletonsuniq
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( ( setadjoin @ Xx @ emptyset )
% 2.57/1.52 = ( setadjoin @ Xy @ emptyset ) )
% 2.57/1.52 => ( Xx = Xy ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(atmost1p_type,type,
% 2.57/1.52 atmost1p: $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(atleast2p_type,type,
% 2.57/1.52 atleast2p: $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(atmost2p_type,type,
% 2.57/1.52 atmost2p: $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(upairsetp_type,type,
% 2.57/1.52 upairsetp: $i > $o ).
% 2.57/1.52
% 2.57/1.52 thf(setukpairinjL1_type,type,
% 2.57/1.52 setukpairinjL1: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setukpairinjL1,definition,
% 2.57/1.52 ( setukpairinjL1
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.57/1.52 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.57/1.52 => ( Xx = Xz ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(kfstsingleton_type,type,
% 2.57/1.52 kfstsingleton: $o ).
% 2.57/1.52
% 2.57/1.52 thf(kfstsingleton,definition,
% 2.57/1.52 ( kfstsingleton
% 2.57/1.52 = ( ! [Xu: $i] :
% 2.57/1.52 ( ( iskpair @ Xu )
% 2.57/1.52 => ( singleton
% 2.57/1.52 @ ( dsetconstr @ ( setunion @ Xu )
% 2.57/1.52 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(theprop_type,type,
% 2.57/1.52 theprop: $o ).
% 2.57/1.52
% 2.57/1.52 thf(theprop,definition,
% 2.57/1.52 ( theprop
% 2.57/1.52 = ( ! [X: $i] :
% 2.57/1.52 ( ( singleton @ X )
% 2.57/1.52 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(kfst_type,type,
% 2.57/1.52 kfst: $i > $i ).
% 2.57/1.52
% 2.57/1.52 thf(kfstpairEq_type,type,
% 2.57/1.52 kfstpairEq: $o ).
% 2.57/1.52
% 2.57/1.52 thf(kfstpairEq,definition,
% 2.57/1.52 ( kfstpairEq
% 2.57/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.52 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.57/1.52 = Xx ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(cartprodfstin_type,type,
% 2.57/1.52 cartprodfstin: $o ).
% 2.57/1.52
% 2.57/1.52 thf(cartprodfstin,definition,
% 2.57/1.52 ( cartprodfstin
% 2.57/1.52 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.57/1.52 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.57/1.52 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.57/1.52
% 2.57/1.52 thf(setukpairinjL2_type,type,
% 2.57/1.52 setukpairinjL2: $o ).
% 2.57/1.52
% 2.57/1.52 thf(setukpairinjL2,definition,
% 2.57/1.52 ( setukpairinjL2
% 2.57/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.57/1.53 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.57/1.53 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.57/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjL_type,type,
% 2.57/1.53 setukpairinjL: $o ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjL,definition,
% 2.57/1.53 ( setukpairinjL
% 2.57/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.57/1.53 ( ( ( kpair @ Xx @ Xy )
% 2.57/1.53 = ( kpair @ Xz @ Xu ) )
% 2.57/1.53 => ( Xx = Xz ) ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjR11_type,type,
% 2.57/1.53 setukpairinjR11: $o ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjR11,definition,
% 2.57/1.53 ( setukpairinjR11
% 2.57/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.53 ( ( Xx = Xy )
% 2.57/1.53 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.57/1.53 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjR12_type,type,
% 2.57/1.53 setukpairinjR12: $o ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjR12,definition,
% 2.57/1.53 ( setukpairinjR12
% 2.57/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.53 ( ( Xx = Xy )
% 2.57/1.53 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.57/1.53 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjR1_type,type,
% 2.57/1.53 setukpairinjR1: $o ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjR1,definition,
% 2.57/1.53 ( setukpairinjR1
% 2.57/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.57/1.53 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.57/1.53 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.57/1.53 => ( ( Xz = Xu )
% 2.57/1.53 => ( Xy = Xu ) ) ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(upairequniteq_type,type,
% 2.57/1.53 upairequniteq: $o ).
% 2.57/1.53
% 2.57/1.53 thf(upairequniteq,definition,
% 2.57/1.53 ( upairequniteq
% 2.57/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.57/1.53 ( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.57/1.53 = ( setadjoin @ Xz @ emptyset ) )
% 2.57/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjR2_type,type,
% 2.57/1.53 setukpairinjR2: $o ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjR2,definition,
% 2.57/1.53 ( setukpairinjR2
% 2.57/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.57/1.53 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.57/1.53 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.57/1.53 => ( Xy = Xu ) ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjR_type,type,
% 2.57/1.53 setukpairinjR: $o ).
% 2.57/1.53
% 2.57/1.53 thf(setukpairinjR,definition,
% 2.57/1.53 ( setukpairinjR
% 2.57/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.57/1.53 ( ( ( kpair @ Xx @ Xy )
% 2.57/1.53 = ( kpair @ Xz @ Xu ) )
% 2.57/1.53 => ( Xy = Xu ) ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(ksndsingleton_type,type,
% 2.57/1.53 ksndsingleton: $o ).
% 2.57/1.53
% 2.57/1.53 thf(ksndsingleton,definition,
% 2.57/1.53 ( ksndsingleton
% 2.57/1.53 = ( ! [Xu: $i] :
% 2.57/1.53 ( ( iskpair @ Xu )
% 2.57/1.53 => ( singleton
% 2.57/1.53 @ ( dsetconstr @ ( setunion @ Xu )
% 2.57/1.53 @ ^ [Xx: $i] :
% 2.57/1.53 ( Xu
% 2.57/1.53 = ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(ksnd_type,type,
% 2.57/1.53 ksnd: $i > $i ).
% 2.57/1.53
% 2.57/1.53 thf(ksndpairEq_type,type,
% 2.57/1.53 ksndpairEq: $o ).
% 2.57/1.53
% 2.57/1.53 thf(ksndpairEq,definition,
% 2.57/1.53 ( ksndpairEq
% 2.57/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.53 ( ( ksnd @ ( kpair @ Xx @ Xy ) )
% 2.57/1.53 = Xy ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(kpairsurjEq_type,type,
% 2.57/1.53 kpairsurjEq: $o ).
% 2.57/1.53
% 2.57/1.53 thf(kpairsurjEq,definition,
% 2.57/1.53 ( kpairsurjEq
% 2.57/1.53 = ( ! [Xu: $i] :
% 2.57/1.53 ( ( iskpair @ Xu )
% 2.57/1.53 => ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
% 2.57/1.53 = Xu ) ) ) ) ).
% 2.57/1.53
% 2.57/1.53 thf(cartprodsndin,conjecture,
% 2.57/1.53 ( setextAx
% 2.57/1.53 => ( emptysetAx
% 2.57/1.53 => ( setadjoinAx
% 2.57/1.53 => ( powersetAx
% 2.57/1.53 => ( setunionAx
% 2.57/1.53 => ( omega0Ax
% 2.57/1.53 => ( omegaSAx
% 2.57/1.53 => ( omegaIndAx
% 2.57/1.53 => ( replAx
% 2.57/1.53 => ( foundationAx
% 2.57/1.53 => ( wellorderingAx
% 2.57/1.53 => ( descrp
% 2.57/1.53 => ( dsetconstrI
% 2.57/1.53 => ( dsetconstrEL
% 2.57/1.53 => ( dsetconstrER
% 2.57/1.53 => ( exuE1
% 2.57/1.53 => ( prop2setE
% 2.57/1.53 => ( emptysetE
% 2.57/1.53 => ( emptysetimpfalse
% 2.57/1.53 => ( notinemptyset
% 2.57/1.53 => ( exuE3e
% 2.57/1.53 => ( setext
% 2.57/1.53 => ( emptyI
% 2.57/1.53 => ( noeltsimpempty
% 2.57/1.53 => ( setbeta
% 2.57/1.53 => ( nonemptyE1
% 2.57/1.53 => ( nonemptyI
% 2.57/1.53 => ( nonemptyI1
% 2.57/1.53 => ( setadjoinIL
% 2.57/1.53 => ( emptyinunitempty
% 2.57/1.53 => ( setadjoinIR
% 2.57/1.53 => ( setadjoinE
% 2.57/1.53 => ( setadjoinOr
% 2.57/1.53 => ( setoftrueEq
% 2.57/1.53 => ( powersetI
% 2.57/1.53 => ( emptyinPowerset
% 2.57/1.53 => ( emptyInPowerset
% 2.57/1.53 => ( powersetE
% 2.57/1.53 => ( setunionI
% 2.57/1.53 => ( setunionE
% 2.57/1.53 => ( subPowSU
% 2.57/1.53 => ( exuE2
% 2.57/1.53 => ( nonemptyImpWitness
% 2.57/1.53 => ( uniqinunit
% 2.57/1.53 => ( notinsingleton
% 2.57/1.53 => ( eqinunit
% 2.57/1.53 => ( singletonsswitch
% 2.57/1.53 => ( upairsetE
% 2.57/1.53 => ( upairsetIL
% 2.57/1.53 => ( upairsetIR
% 2.57/1.53 => ( emptyE1
% 2.57/1.53 => ( vacuousDall
% 2.57/1.53 => ( quantDeMorgan1
% 2.57/1.53 => ( quantDeMorgan2
% 2.57/1.53 => ( quantDeMorgan3
% 2.57/1.53 => ( quantDeMorgan4
% 2.57/1.53 => ( prop2setI
% 2.57/1.53 => ( prop2set2propI
% 2.57/1.53 => ( notdexE
% 2.57/1.53 => ( notdallE
% 2.57/1.53 => ( exuI1
% 2.57/1.53 => ( exuI3
% 2.57/1.53 => ( exuI2
% 2.57/1.53 => ( inCongP
% 2.57/1.53 => ( in__Cong
% 2.57/1.53 => ( exuE3u
% 2.57/1.53 => ( exu__Cong
% 2.57/1.53 => ( emptyset__Cong
% 2.57/1.53 => ( setadjoin__Cong
% 2.57/1.53 => ( powerset__Cong
% 2.57/1.53 => ( setunion__Cong
% 2.57/1.53 => ( omega__Cong
% 2.57/1.53 => ( exuEu
% 2.57/1.53 => ( descr__Cong
% 2.57/1.53 => ( dsetconstr__Cong
% 2.57/1.53 => ( subsetI1
% 2.57/1.53 => ( eqimpsubset2
% 2.57/1.53 => ( eqimpsubset1
% 2.57/1.53 => ( subsetI2
% 2.57/1.53 => ( emptysetsubset
% 2.57/1.53 => ( subsetE
% 2.57/1.53 => ( subsetE2
% 2.57/1.53 => ( notsubsetI
% 2.57/1.53 => ( notequalI1
% 2.57/1.53 => ( notequalI2
% 2.57/1.53 => ( subsetRefl
% 2.57/1.53 => ( subsetTrans
% 2.57/1.53 => ( setadjoinSub
% 2.57/1.53 => ( setadjoinSub2
% 2.57/1.53 => ( subset2powerset
% 2.57/1.53 => ( setextsub
% 2.57/1.53 => ( subsetemptysetimpeq
% 2.57/1.53 => ( powersetI1
% 2.57/1.53 => ( powersetE1
% 2.57/1.53 => ( inPowerset
% 2.57/1.53 => ( powersetsubset
% 2.57/1.53 => ( sepInPowerset
% 2.57/1.53 => ( sepSubset
% 2.57/1.53 => ( binunionIL
% 2.57/1.53 => ( upairset2IR
% 2.57/1.53 => ( binunionIR
% 2.57/1.53 => ( binunionEcases
% 2.57/1.53 => ( binunionE
% 2.57/1.53 => ( binunionLsub
% 2.57/1.53 => ( binunionRsub
% 2.57/1.53 => ( binintersectI
% 2.57/1.53 => ( binintersectSubset5
% 2.57/1.53 => ( binintersectEL
% 2.57/1.53 => ( binintersectLsub
% 2.57/1.53 => ( binintersectSubset2
% 2.57/1.53 => ( binintersectSubset3
% 2.57/1.53 => ( binintersectER
% 2.57/1.53 => ( disjointsetsI1
% 2.57/1.53 => ( binintersectRsub
% 2.57/1.53 => ( binintersectSubset4
% 2.57/1.53 => ( binintersectSubset1
% 2.57/1.53 => ( bs114d
% 2.57/1.53 => ( setminusI
% 2.57/1.53 => ( setminusEL
% 2.57/1.53 => ( setminusER
% 2.57/1.53 => ( setminusSubset2
% 2.57/1.53 => ( setminusERneg
% 2.57/1.53 => ( setminusELneg
% 2.57/1.53 => ( setminusILneg
% 2.57/1.53 => ( setminusIRneg
% 2.57/1.53 => ( setminusLsub
% 2.57/1.53 => ( setminusSubset1
% 2.57/1.53 => ( symdiffE
% 2.57/1.53 => ( symdiffI1
% 2.57/1.53 => ( symdiffI2
% 2.57/1.53 => ( symdiffIneg1
% 2.57/1.53 => ( symdiffIneg2
% 2.57/1.53 => ( secondinupair
% 2.57/1.53 => ( setukpairIL
% 2.57/1.53 => ( setukpairIR
% 2.57/1.53 => ( kpairiskpair
% 2.57/1.53 => ( kpairp
% 2.57/1.53 => ( singletonsubset
% 2.57/1.53 => ( singletoninpowerset
% 2.57/1.53 => ( singletoninpowunion
% 2.57/1.53 => ( upairset2E
% 2.57/1.53 => ( upairsubunion
% 2.57/1.53 => ( upairinpowunion
% 2.57/1.53 => ( ubforcartprodlem1
% 2.57/1.53 => ( ubforcartprodlem2
% 2.57/1.53 => ( ubforcartprodlem3
% 2.57/1.53 => ( cartprodpairin
% 2.57/1.53 => ( cartprodmempair1
% 2.57/1.53 => ( cartprodmempair
% 2.57/1.53 => ( setunionE2
% 2.57/1.53 => ( setunionsingleton1
% 2.57/1.53 => ( setunionsingleton2
% 2.57/1.53 => ( setunionsingleton
% 2.57/1.53 => ( singletonprop
% 2.57/1.53 => ( ex1E1
% 2.57/1.53 => ( ex1I
% 2.57/1.53 => ( ex1I2
% 2.57/1.53 => ( singletonsuniq
% 2.57/1.53 => ( setukpairinjL1
% 2.57/1.53 => ( kfstsingleton
% 2.57/1.53 => ( theprop
% 2.57/1.53 => ( kfstpairEq
% 2.57/1.53 => ( cartprodfstin
% 2.57/1.53 => ( setukpairinjL2
% 2.57/1.53 => ( setukpairinjL
% 2.57/1.53 => ( setukpairinjR11
% 2.57/1.53 => ( setukpairinjR12
% 2.57/1.53 => ( setukpairinjR1
% 2.57/1.53 => ( upairequniteq
% 2.57/1.53 => ( setukpairinjR2
% 2.57/1.53 => ( setukpairinjR
% 2.57/1.53 => ( ksndsingleton
% 2.57/1.53 => ( ksndpairEq
% 2.57/1.53 => ( kpairsurjEq
% 2.57/1.53 => ! [A: $i,B: $i,Xu: $i] :
% 2.57/1.53 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.57/1.53 => ( in @ ( ksnd @ Xu ) @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.53 ------------------------
% 2.57/1.55 % (13433)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_13158 for (2999ds/27Mi)
% 2.57/1.55 % (13434)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/2Mi)
% 2.57/1.55 % (13434)Instruction limit reached!
% 2.57/1.55 % (13434)------------------------------
% 2.57/1.55 % (13434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.55 % (13434)Termination reason: Unknown
% 2.57/1.55 % (13434)Termination phase: shuffling
% 2.57/1.55
% 2.57/1.55 % (13434)Memory used [KB]: 1279
% 2.57/1.55 % (13434)Time elapsed: 0.002 s
% 2.57/1.55 % (13434)Instructions burned: 3 (million)
% 2.57/1.55 % (13434)------------------------------
% 2.57/1.55 % (13434)------------------------------
% 2.57/1.56 % (13431)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/183Mi)
% 2.57/1.56 % (13432)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_13158 for (2999ds/4Mi)
% 2.57/1.56 % (13435)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_13158 for (2999ds/2Mi)
% 2.57/1.56 % (13436)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_13158 for (2999ds/275Mi)
% 2.57/1.56 % (13437)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/18Mi)
% 2.57/1.56 % (13433)Instruction limit reached!
% 2.57/1.56 % (13433)------------------------------
% 2.57/1.56 % (13433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.56 % (13433)Termination reason: Unknown
% 2.57/1.56 % (13433)Termination phase: Property scanning
% 2.57/1.56
% 2.57/1.56 % (13433)Memory used [KB]: 1918
% 2.57/1.56 % (13433)Time elapsed: 0.010 s
% 2.57/1.56 % (13433)Instructions burned: 30 (million)
% 2.57/1.56 % (13433)------------------------------
% 2.57/1.56 % (13433)------------------------------
% 2.57/1.56 % (13435)Instruction limit reached!
% 2.57/1.56 % (13435)------------------------------
% 2.57/1.56 % (13435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.56 % (13435)Termination reason: Unknown
% 2.57/1.56 % (13435)Termination phase: shuffling
% 2.57/1.56
% 2.57/1.56 % (13435)Memory used [KB]: 1279
% 2.57/1.56 % (13435)Time elapsed: 0.004 s
% 2.57/1.56 % (13435)Instructions burned: 3 (million)
% 2.57/1.56 % (13435)------------------------------
% 2.57/1.56 % (13435)------------------------------
% 2.57/1.56 % (13432)Instruction limit reached!
% 2.57/1.56 % (13432)------------------------------
% 2.57/1.56 % (13432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.56 % (13432)Termination reason: Unknown
% 2.57/1.56 % (13432)Termination phase: shuffling
% 2.57/1.56
% 2.57/1.56 % (13432)Memory used [KB]: 1407
% 2.57/1.56 % (13432)Time elapsed: 0.005 s
% 2.57/1.56 % (13432)Instructions burned: 5 (million)
% 2.57/1.56 % (13432)------------------------------
% 2.57/1.56 % (13432)------------------------------
% 2.57/1.56 % (13438)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/3Mi)
% 2.57/1.56 % (13438)Instruction limit reached!
% 2.57/1.56 % (13438)------------------------------
% 2.57/1.56 % (13438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.56 % (13438)Termination reason: Unknown
% 2.57/1.56 % (13438)Termination phase: shuffling
% 2.57/1.56
% 2.57/1.56 % (13438)Memory used [KB]: 1407
% 2.57/1.56 % (13438)Time elapsed: 0.003 s
% 2.57/1.56 % (13438)Instructions burned: 4 (million)
% 2.57/1.56 % (13438)------------------------------
% 2.57/1.56 % (13438)------------------------------
% 2.57/1.57 % (13437)Instruction limit reached!
% 2.57/1.57 % (13437)------------------------------
% 2.57/1.57 % (13437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.57 % (13437)Termination reason: Unknown
% 2.57/1.57 % (13437)Termination phase: Property scanning
% 2.57/1.57
% 2.57/1.57 % (13437)Memory used [KB]: 1663
% 2.57/1.57 % (13437)Time elapsed: 0.013 s
% 2.57/1.57 % (13437)Instructions burned: 18 (million)
% 2.57/1.57 % (13437)------------------------------
% 2.57/1.57 % (13437)------------------------------
% 2.57/1.57 % (13439)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_13158 for (2999ds/37Mi)
% 2.57/1.57 % (13442)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_13158 for (2999ds/1041Mi)
% 2.57/1.58 % (13440)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_13158 for (2999ds/15Mi)
% 2.57/1.58 % (13441)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_13158 for (2999ds/3Mi)
% 2.57/1.58 % (13439)Instruction limit reached!
% 2.57/1.58 % (13439)------------------------------
% 2.57/1.58 % (13439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.58 % (13439)Termination reason: Unknown
% 2.57/1.58 % (13439)Termination phase: Property scanning
% 2.57/1.58
% 2.57/1.58 % (13439)Memory used [KB]: 1791
% 2.57/1.58 % (13439)Time elapsed: 0.011 s
% 2.57/1.58 % (13439)Instructions burned: 37 (million)
% 2.57/1.58 % (13439)------------------------------
% 2.57/1.58 % (13439)------------------------------
% 2.57/1.58 % (13441)Instruction limit reached!
% 2.57/1.58 % (13441)------------------------------
% 2.57/1.58 % (13441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.58 % (13441)Termination reason: Unknown
% 2.57/1.58 % (13441)Termination phase: shuffling
% 2.57/1.58
% 2.57/1.58 % (13441)Memory used [KB]: 1279
% 2.57/1.58 % (13441)Time elapsed: 0.004 s
% 2.57/1.58 % (13441)Instructions burned: 4 (million)
% 2.57/1.58 % (13441)------------------------------
% 2.57/1.58 % (13441)------------------------------
% 2.57/1.59 % (13440)Instruction limit reached!
% 2.57/1.59 % (13440)------------------------------
% 2.57/1.59 % (13440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.59 % (13440)Termination reason: Unknown
% 2.57/1.59 % (13440)Termination phase: shuffling
% 2.57/1.59
% 2.57/1.59 % (13440)Memory used [KB]: 1663
% 2.57/1.59 % (13440)Time elapsed: 0.011 s
% 2.57/1.59 % (13440)Instructions burned: 15 (million)
% 2.57/1.59 % (13440)------------------------------
% 2.57/1.59 % (13440)------------------------------
% 2.57/1.59 % (13443)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/7Mi)
% 2.57/1.59 % (13444)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/16Mi)
% 2.57/1.59 % (13443)Instruction limit reached!
% 2.57/1.59 % (13443)------------------------------
% 2.57/1.59 % (13443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.59 % (13443)Termination reason: Unknown
% 2.57/1.59 % (13443)Termination phase: shuffling
% 2.57/1.59
% 2.57/1.59 % (13443)Memory used [KB]: 1407
% 2.57/1.59 % (13443)Time elapsed: 0.006 s
% 2.57/1.59 % (13443)Instructions burned: 8 (million)
% 2.57/1.59 % (13443)------------------------------
% 2.57/1.59 % (13443)------------------------------
% 2.57/1.60 % (13444)Instruction limit reached!
% 2.57/1.60 % (13444)------------------------------
% 2.57/1.60 % (13444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.57/1.60 % (13444)Termination reason: Unknown
% 2.57/1.60 % (13444)Termination phase: shuffling
% 2.57/1.60
% 2.57/1.60 % (13444)Memory used [KB]: 1663
% 2.57/1.60 % (13444)Time elapsed: 0.007 s
% 2.57/1.60 % (13444)Instructions burned: 18 (million)
% 2.57/1.60 % (13444)------------------------------
% 2.57/1.60 % (13444)------------------------------
% 2.60/1.60 % (13445)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_13158 for (2999ds/3Mi)
% 2.60/1.60 % (13445)Instruction limit reached!
% 2.60/1.60 % (13445)------------------------------
% 2.60/1.60 % (13445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.60 % (13445)Termination reason: Unknown
% 2.60/1.60 % (13445)Termination phase: shuffling
% 2.60/1.60
% 2.60/1.60 % (13445)Memory used [KB]: 1279
% 2.60/1.60 % (13445)Time elapsed: 0.004 s
% 2.60/1.60 % (13445)Instructions burned: 4 (million)
% 2.60/1.60 % (13445)------------------------------
% 2.60/1.60 % (13445)------------------------------
% 2.60/1.60 % (13446)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_13158 for (2999ds/3Mi)
% 2.60/1.61 % (13448)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/3Mi)
% 2.60/1.61 % (13446)Instruction limit reached!
% 2.60/1.61 % (13446)------------------------------
% 2.60/1.61 % (13446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.61 % (13446)Termination reason: Unknown
% 2.60/1.61 % (13446)Termination phase: shuffling
% 2.60/1.61
% 2.60/1.61 % (13446)Memory used [KB]: 1407
% 2.60/1.61 % (13446)Time elapsed: 0.004 s
% 2.60/1.61 % (13446)Instructions burned: 4 (million)
% 2.60/1.61 % (13446)------------------------------
% 2.60/1.61 % (13446)------------------------------
% 2.60/1.61 % (13448)Instruction limit reached!
% 2.60/1.61 % (13448)------------------------------
% 2.60/1.61 % (13448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.61 % (13448)Termination reason: Unknown
% 2.60/1.61 % (13448)Termination phase: shuffling
% 2.60/1.61
% 2.60/1.61 % (13448)Memory used [KB]: 1407
% 2.60/1.61 % (13448)Time elapsed: 0.003 s
% 2.60/1.61 % (13448)Instructions burned: 4 (million)
% 2.60/1.61 % (13448)------------------------------
% 2.60/1.61 % (13448)------------------------------
% 2.60/1.61 % (13447)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/7Mi)
% 2.60/1.61 % (13447)Instruction limit reached!
% 2.60/1.61 % (13447)------------------------------
% 2.60/1.61 % (13447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.61 % (13447)Termination reason: Unknown
% 2.60/1.61 % (13447)Termination phase: shuffling
% 2.60/1.61
% 2.60/1.61 % (13447)Memory used [KB]: 1407
% 2.60/1.61 % (13447)Time elapsed: 0.006 s
% 2.60/1.61 % (13447)Instructions burned: 8 (million)
% 2.60/1.61 % (13447)------------------------------
% 2.60/1.61 % (13447)------------------------------
% 2.60/1.62 % (13451)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/710Mi)
% 2.60/1.62 % (13449)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/4Mi)
% 2.60/1.62 % (13449)Instruction limit reached!
% 2.60/1.62 % (13449)------------------------------
% 2.60/1.62 % (13449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.62 % (13449)Termination reason: Unknown
% 2.60/1.62 % (13449)Termination phase: shuffling
% 2.60/1.62
% 2.60/1.62 % (13449)Memory used [KB]: 1279
% 2.60/1.62 % (13449)Time elapsed: 0.004 s
% 2.60/1.62 % (13449)Instructions burned: 4 (million)
% 2.60/1.62 % (13449)------------------------------
% 2.60/1.62 % (13449)------------------------------
% 2.60/1.62 % (13450)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/18Mi)
% 2.60/1.63 % (13452)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/6Mi)
% 2.60/1.63 % (13452)Instruction limit reached!
% 2.60/1.63 % (13452)------------------------------
% 2.60/1.63 % (13452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.63 % (13452)Termination reason: Unknown
% 2.60/1.63 % (13452)Termination phase: shuffling
% 2.60/1.63
% 2.60/1.63 % (13452)Memory used [KB]: 1407
% 2.60/1.63 % (13452)Time elapsed: 0.005 s
% 2.60/1.63 % (13452)Instructions burned: 6 (million)
% 2.60/1.63 % (13452)------------------------------
% 2.60/1.63 % (13452)------------------------------
% 2.60/1.63 % (13450)Instruction limit reached!
% 2.60/1.63 % (13450)------------------------------
% 2.60/1.63 % (13450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.63 % (13450)Termination reason: Unknown
% 2.60/1.63 % (13450)Termination phase: shuffling
% 2.60/1.63
% 2.60/1.63 % (13450)Memory used [KB]: 1663
% 2.60/1.63 % (13450)Time elapsed: 0.012 s
% 2.60/1.63 % (13450)Instructions burned: 19 (million)
% 2.60/1.63 % (13450)------------------------------
% 2.60/1.63 % (13450)------------------------------
% 2.60/1.64 % (13453)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_13158 for (2999ds/902Mi)
% 2.60/1.65 % (13455)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13158 for (2999ds/5Mi)
% 2.60/1.65 % (13454)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_13158 for (2999ds/21Mi)
% 2.60/1.65 % (13431)Instruction limit reached!
% 2.60/1.65 % (13431)------------------------------
% 2.60/1.65 % (13431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.65 % (13431)Termination reason: Unknown
% 2.60/1.65 % (13431)Termination phase: Saturation
% 2.60/1.65
% 2.60/1.65 % (13431)Memory used [KB]: 7419
% 2.60/1.65 % (13431)Time elapsed: 0.095 s
% 2.60/1.65 % (13431)Instructions burned: 184 (million)
% 2.60/1.65 % (13431)------------------------------
% 2.60/1.65 % (13431)------------------------------
% 2.60/1.65 % (13455)Instruction limit reached!
% 2.60/1.65 % (13455)------------------------------
% 2.60/1.65 % (13455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.65 % (13455)Termination reason: Unknown
% 2.60/1.65 % (13455)Termination phase: shuffling
% 2.60/1.65
% 2.60/1.65 % (13455)Memory used [KB]: 1407
% 2.60/1.65 % (13455)Time elapsed: 0.005 s
% 2.60/1.65 % (13455)Instructions burned: 7 (million)
% 2.60/1.65 % (13455)------------------------------
% 2.60/1.65 % (13455)------------------------------
% 2.60/1.66 % (13436)Instruction limit reached!
% 2.60/1.66 % (13436)------------------------------
% 2.60/1.66 % (13436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.66 % (13436)Termination reason: Unknown
% 2.60/1.66 % (13436)Termination phase: Saturation
% 2.60/1.66
% 2.60/1.66 % (13436)Memory used [KB]: 8187
% 2.60/1.66 % (13436)Time elapsed: 0.104 s
% 2.60/1.66 % (13436)Instructions burned: 276 (million)
% 2.60/1.66 % (13436)------------------------------
% 2.60/1.66 % (13436)------------------------------
% 2.60/1.66 % (13454)Instruction limit reached!
% 2.60/1.66 % (13454)------------------------------
% 2.60/1.66 % (13454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.66 % (13454)Termination reason: Unknown
% 2.60/1.66 % (13454)Termination phase: shuffling
% 2.60/1.66
% 2.60/1.66 % (13454)Memory used [KB]: 1791
% 2.60/1.66 % (13454)Time elapsed: 0.013 s
% 2.60/1.66 % (13454)Instructions burned: 21 (million)
% 2.60/1.66 % (13454)------------------------------
% 2.60/1.66 % (13454)------------------------------
% 2.60/1.66 % (13457)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13158 for (2998ds/377Mi)
% 2.60/1.67 % (13456)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_13158 for (2998ds/6Mi)
% 2.60/1.67 % (13458)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_13158 for (2998ds/779Mi)
% 2.60/1.67 % (13456)Instruction limit reached!
% 2.60/1.67 % (13456)------------------------------
% 2.60/1.67 % (13456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.67 % (13456)Termination reason: Unknown
% 2.60/1.67 % (13456)Termination phase: shuffling
% 2.60/1.67
% 2.60/1.67 % (13456)Memory used [KB]: 1407
% 2.60/1.67 % (13456)Time elapsed: 0.004 s
% 2.60/1.67 % (13456)Instructions burned: 7 (million)
% 2.60/1.67 % (13456)------------------------------
% 2.60/1.67 % (13456)------------------------------
% 2.60/1.68 % (13459)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_13158 for (2998ds/19Mi)
% 2.60/1.68 % (13460)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13158 for (2998ds/879Mi)
% 2.60/1.68 % (13459)Instruction limit reached!
% 2.60/1.68 % (13459)------------------------------
% 2.60/1.68 % (13459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.68 % (13459)Termination reason: Unknown
% 2.60/1.68 % (13459)Termination phase: shuffling
% 2.60/1.68
% 2.60/1.68 % (13459)Memory used [KB]: 1791
% 2.60/1.68 % (13459)Time elapsed: 0.008 s
% 2.60/1.68 % (13459)Instructions burned: 22 (million)
% 2.60/1.68 % (13459)------------------------------
% 2.60/1.68 % (13459)------------------------------
% 2.60/1.69 % (13461)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13158 for (2998ds/17Mi)
% 2.60/1.70 % (13461)Instruction limit reached!
% 2.60/1.70 % (13461)------------------------------
% 2.60/1.70 % (13461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.70 % (13461)Termination reason: Unknown
% 2.60/1.70 % (13461)Termination phase: shuffling
% 2.60/1.70
% 2.60/1.70 % (13461)Memory used [KB]: 1663
% 2.60/1.70 % (13461)Time elapsed: 0.007 s
% 2.60/1.70 % (13461)Instructions burned: 17 (million)
% 2.60/1.70 % (13461)------------------------------
% 2.60/1.70 % (13461)------------------------------
% 2.60/1.71 % (13462)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13158 for (2998ds/3Mi)
% 2.60/1.71 % (13462)Instruction limit reached!
% 2.60/1.71 % (13462)------------------------------
% 2.60/1.71 % (13462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.71 % (13462)Termination reason: Unknown
% 2.60/1.71 % (13462)Termination phase: shuffling
% 2.60/1.71
% 2.60/1.71 % (13462)Memory used [KB]: 1407
% 2.60/1.71 % (13462)Time elapsed: 0.003 s
% 2.60/1.71 % (13462)Instructions burned: 4 (million)
% 2.60/1.71 % (13462)------------------------------
% 2.60/1.71 % (13462)------------------------------
% 2.60/1.72 % (13463)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13158 for (2998ds/30Mi)
% 2.60/1.73 % (13463)Instruction limit reached!
% 2.60/1.73 % (13463)------------------------------
% 2.60/1.73 % (13463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.73 % (13463)Termination reason: Unknown
% 2.60/1.73 % (13463)Termination phase: Property scanning
% 2.60/1.73
% 2.60/1.73 % (13463)Memory used [KB]: 1791
% 2.60/1.73 % (13463)Time elapsed: 0.011 s
% 2.60/1.73 % (13463)Instructions burned: 32 (million)
% 2.60/1.73 % (13463)------------------------------
% 2.60/1.73 % (13463)------------------------------
% 2.60/1.74 % (13464)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13158 for (2997ds/127Mi)
% 2.60/1.77 % (13464)Instruction limit reached!
% 2.60/1.77 % (13464)------------------------------
% 2.60/1.77 % (13464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.77 % (13464)Termination reason: Unknown
% 2.60/1.77 % (13464)Termination phase: Saturation
% 2.60/1.77
% 2.60/1.77 % (13464)Memory used [KB]: 6908
% 2.60/1.77 % (13464)Time elapsed: 0.037 s
% 2.60/1.77 % (13464)Instructions burned: 129 (million)
% 2.60/1.77 % (13464)------------------------------
% 2.60/1.77 % (13464)------------------------------
% 2.60/1.78 % (13457)Instruction limit reached!
% 2.60/1.78 % (13457)------------------------------
% 2.60/1.78 % (13457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.78 % (13457)Termination reason: Unknown
% 2.60/1.78 % (13457)Termination phase: Saturation
% 2.60/1.78
% 2.60/1.78 % (13457)Memory used [KB]: 8059
% 2.60/1.78 % (13457)Time elapsed: 0.121 s
% 2.60/1.78 % (13457)Instructions burned: 379 (million)
% 2.60/1.78 % (13457)------------------------------
% 2.60/1.78 % (13457)------------------------------
% 2.60/1.78 % (13465)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13158 for (2997ds/100Mi)
% 2.60/1.79 % (13466)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_13158 for (2997ds/3Mi)
% 2.60/1.80 % (13466)Instruction limit reached!
% 2.60/1.80 % (13466)------------------------------
% 2.60/1.80 % (13466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.80 % (13466)Termination reason: Unknown
% 2.60/1.80 % (13466)Termination phase: shuffling
% 2.60/1.80
% 2.60/1.80 % (13466)Memory used [KB]: 1279
% 2.60/1.80 % (13466)Time elapsed: 0.002 s
% 2.60/1.80 % (13466)Instructions burned: 4 (million)
% 2.60/1.80 % (13466)------------------------------
% 2.60/1.80 % (13466)------------------------------
% 2.60/1.81 % (13467)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_13158 for (2997ds/20Mi)
% 2.60/1.81 % (13465)Instruction limit reached!
% 2.60/1.81 % (13465)------------------------------
% 2.60/1.81 % (13465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.81 % (13465)Termination reason: Unknown
% 2.60/1.81 % (13465)Termination phase: Saturation
% 2.60/1.81
% 2.60/1.81 % (13465)Memory used [KB]: 6652
% 2.60/1.81 % (13465)Time elapsed: 0.029 s
% 2.60/1.81 % (13465)Instructions burned: 101 (million)
% 2.60/1.81 % (13465)------------------------------
% 2.60/1.81 % (13465)------------------------------
% 2.60/1.81 % (13467)Instruction limit reached!
% 2.60/1.81 % (13467)------------------------------
% 2.60/1.81 % (13467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.81 % (13467)Termination reason: Unknown
% 2.60/1.81 % (13467)Termination phase: Property scanning
% 2.60/1.81
% 2.60/1.81 % (13467)Memory used [KB]: 1663
% 2.60/1.81 % (13467)Time elapsed: 0.009 s
% 2.60/1.81 % (13467)Instructions burned: 23 (million)
% 2.60/1.81 % (13467)------------------------------
% 2.60/1.81 % (13467)------------------------------
% 2.60/1.82 % (13468)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_13158 for (2997ds/86Mi)
% 2.60/1.82 % (13469)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_13158 for (2997ds/107Mi)
% 2.60/1.83 % (13442)Instruction limit reached!
% 2.60/1.83 % (13442)------------------------------
% 2.60/1.83 % (13442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.83 % (13442)Termination reason: Unknown
% 2.60/1.83 % (13442)Termination phase: Saturation
% 2.60/1.83
% 2.60/1.83 % (13442)Memory used [KB]: 10490
% 2.60/1.83 % (13442)Time elapsed: 0.262 s
% 2.60/1.83 % (13442)Instructions burned: 1044 (million)
% 2.60/1.83 % (13442)------------------------------
% 2.60/1.83 % (13442)------------------------------
% 2.60/1.84 % (13451)Instruction limit reached!
% 2.60/1.84 % (13451)------------------------------
% 2.60/1.84 % (13451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.84 % (13451)Termination reason: Unknown
% 2.60/1.84 % (13451)Termination phase: Saturation
% 2.60/1.84
% 2.60/1.84 % (13451)Memory used [KB]: 9338
% 2.60/1.84 % (13451)Time elapsed: 0.227 s
% 2.60/1.84 % (13451)Instructions burned: 710 (million)
% 2.60/1.84 % (13451)------------------------------
% 2.60/1.84 % (13451)------------------------------
% 2.60/1.84 % (13470)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_13158 for (2996ds/39Mi)
% 2.60/1.85 % (13468)Instruction limit reached!
% 2.60/1.85 % (13468)------------------------------
% 2.60/1.85 % (13468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.85 % (13468)Termination reason: Unknown
% 2.60/1.85 % (13468)Termination phase: Saturation
% 2.60/1.85
% 2.60/1.85 % (13468)Memory used [KB]: 6652
% 2.60/1.85 % (13468)Time elapsed: 0.026 s
% 2.60/1.85 % (13468)Instructions burned: 88 (million)
% 2.60/1.85 % (13468)------------------------------
% 2.60/1.85 % (13468)------------------------------
% 2.60/1.85 % (13471)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_13158 for (2996ds/448Mi)
% 2.60/1.85 % (13469)Instruction limit reached!
% 2.60/1.85 % (13469)------------------------------
% 2.60/1.85 % (13469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.85 % (13469)Termination reason: Unknown
% 2.60/1.85 % (13469)Termination phase: Saturation
% 2.60/1.85
% 2.60/1.85 % (13469)Memory used [KB]: 6780
% 2.60/1.85 % (13469)Time elapsed: 0.031 s
% 2.60/1.85 % (13469)Instructions burned: 107 (million)
% 2.60/1.85 % (13469)------------------------------
% 2.60/1.85 % (13469)------------------------------
% 2.60/1.85 % (13470)Instruction limit reached!
% 2.60/1.85 % (13470)------------------------------
% 2.60/1.85 % (13470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.85 % (13470)Termination reason: Unknown
% 2.60/1.85 % (13470)Termination phase: Property scanning
% 2.60/1.85
% 2.60/1.85 % (13470)Memory used [KB]: 1918
% 2.60/1.85 % (13470)Time elapsed: 0.012 s
% 2.60/1.85 % (13470)Instructions burned: 42 (million)
% 2.60/1.85 % (13470)------------------------------
% 2.60/1.85 % (13470)------------------------------
% 2.60/1.86 % (13458)Instruction limit reached!
% 2.60/1.86 % (13458)------------------------------
% 2.60/1.86 % (13458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.86 % (13458)Termination reason: Unknown
% 2.60/1.86 % (13458)Termination phase: Saturation
% 2.60/1.86
% 2.60/1.86 % (13458)Memory used [KB]: 6908
% 2.60/1.86 % (13458)Time elapsed: 0.188 s
% 2.60/1.86 % (13458)Instructions burned: 781 (million)
% 2.60/1.86 % (13458)------------------------------
% 2.60/1.86 % (13458)------------------------------
% 2.60/1.86 % (13472)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_13158 for (2996ds/46Mi)
% 2.60/1.86 % (13473)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_13158 for (2996ds/98Mi)
% 2.60/1.86 % (13474)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_13158 for (2996ds/507Mi)
% 2.60/1.87 % (13475)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_13158 for (2996ds/149Mi)
% 2.60/1.87 % (13472)Instruction limit reached!
% 2.60/1.87 % (13472)------------------------------
% 2.60/1.87 % (13472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.87 % (13472)Termination reason: Unknown
% 2.60/1.87 % (13472)Termination phase: SInE selection
% 2.60/1.87
% 2.60/1.87 % (13472)Memory used [KB]: 1918
% 2.60/1.87 % (13472)Time elapsed: 0.014 s
% 2.60/1.87 % (13472)Instructions burned: 47 (million)
% 2.60/1.87 % (13472)------------------------------
% 2.60/1.87 % (13472)------------------------------
% 2.60/1.88 % (13476)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_13158 for (2996ds/39Mi)
% 2.60/1.89 % (13473)Instruction limit reached!
% 2.60/1.89 % (13473)------------------------------
% 2.60/1.89 % (13473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.89 % (13473)Termination reason: Unknown
% 2.60/1.89 % (13473)Termination phase: Saturation
% 2.60/1.89
% 2.60/1.89 % (13473)Memory used [KB]: 2174
% 2.60/1.89 % (13473)Time elapsed: 0.029 s
% 2.60/1.89 % (13473)Instructions burned: 100 (million)
% 2.60/1.89 % (13473)------------------------------
% 2.60/1.89 % (13473)------------------------------
% 2.60/1.89 % (13476)Instruction limit reached!
% 2.60/1.89 % (13476)------------------------------
% 2.60/1.89 % (13476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.89 % (13476)Termination reason: Unknown
% 2.60/1.89 % (13476)Termination phase: Property scanning
% 2.60/1.89
% 2.60/1.89 % (13476)Memory used [KB]: 1918
% 2.60/1.89 % (13476)Time elapsed: 0.013 s
% 2.60/1.89 % (13476)Instructions burned: 39 (million)
% 2.60/1.89 % (13476)------------------------------
% 2.60/1.89 % (13476)------------------------------
% 2.60/1.90 % (13477)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_13158 for (2996ds/6Mi)
% 2.60/1.90 % (13478)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_13158 for (2996ds/1087Mi)
% 2.60/1.90 % (13477)Instruction limit reached!
% 2.60/1.90 % (13477)------------------------------
% 2.60/1.90 % (13477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.90 % (13477)Termination reason: Unknown
% 2.60/1.90 % (13477)Termination phase: shuffling
% 2.60/1.90
% 2.60/1.90 % (13477)Memory used [KB]: 1407
% 2.60/1.90 % (13477)Time elapsed: 0.004 s
% 2.60/1.90 % (13477)Instructions burned: 8 (million)
% 2.60/1.90 % (13477)------------------------------
% 2.60/1.90 % (13477)------------------------------
% 2.60/1.91 % (13475)Instruction limit reached!
% 2.60/1.91 % (13475)------------------------------
% 2.60/1.91 % (13475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.91 % (13475)Termination reason: Unknown
% 2.60/1.91 % (13475)Termination phase: Saturation
% 2.60/1.91
% 2.60/1.91 % (13475)Memory used [KB]: 7291
% 2.60/1.91 % (13475)Time elapsed: 0.043 s
% 2.60/1.91 % (13475)Instructions burned: 150 (million)
% 2.60/1.91 % (13475)------------------------------
% 2.60/1.91 % (13475)------------------------------
% 2.60/1.91 % (13479)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_13158 for (2996ds/47Mi)
% 2.60/1.92 % (13480)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_13158 for (2996ds/44Mi)
% 2.60/1.93 % (13479)Instruction limit reached!
% 2.60/1.93 % (13479)------------------------------
% 2.60/1.93 % (13479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.93 % (13479)Termination reason: Unknown
% 2.60/1.93 % (13479)Termination phase: Property scanning
% 2.60/1.93
% 2.60/1.93 % (13479)Memory used [KB]: 1918
% 2.60/1.93 % (13479)Time elapsed: 0.015 s
% 2.60/1.93 % (13479)Instructions burned: 47 (million)
% 2.60/1.93 % (13479)------------------------------
% 2.60/1.93 % (13479)------------------------------
% 2.60/1.93 % (13480)Instruction limit reached!
% 2.60/1.93 % (13480)------------------------------
% 2.60/1.93 % (13480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.93 % (13480)Termination reason: Unknown
% 2.60/1.93 % (13480)Termination phase: SInE selection
% 2.60/1.93
% 2.60/1.93 % (13480)Memory used [KB]: 1918
% 2.60/1.93 % (13480)Time elapsed: 0.013 s
% 2.60/1.93 % (13480)Instructions burned: 46 (million)
% 2.60/1.93 % (13480)------------------------------
% 2.60/1.93 % (13480)------------------------------
% 2.60/1.94 % (13481)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_13158 for (2996ds/432Mi)
% 2.60/1.94 % (13482)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_13158 for (2995ds/62Mi)
% 2.60/1.94 % (13453)Instruction limit reached!
% 2.60/1.94 % (13453)------------------------------
% 2.60/1.94 % (13453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.94 % (13453)Termination reason: Unknown
% 2.60/1.94 % (13453)Termination phase: Saturation
% 2.60/1.94
% 2.60/1.94 % (13453)Memory used [KB]: 10874
% 2.60/1.94 % (13453)Time elapsed: 0.308 s
% 2.60/1.94 % (13453)Instructions burned: 903 (million)
% 2.60/1.94 % (13453)------------------------------
% 2.60/1.94 % (13453)------------------------------
% 2.60/1.95 % (13483)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_13158 for (2995ds/31Mi)
% 2.60/1.95 % (13482)Instruction limit reached!
% 2.60/1.95 % (13482)------------------------------
% 2.60/1.95 % (13482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.95 % (13482)Termination reason: Unknown
% 2.60/1.95 % (13482)Termination phase: Function definition elimination
% 2.60/1.95
% 2.60/1.95 % (13482)Memory used [KB]: 1918
% 2.60/1.95 % (13482)Time elapsed: 0.017 s
% 2.60/1.95 % (13482)Instructions burned: 65 (million)
% 2.60/1.95 % (13482)------------------------------
% 2.60/1.95 % (13482)------------------------------
% 2.60/1.96 % (13471)Instruction limit reached!
% 2.60/1.96 % (13471)------------------------------
% 2.60/1.96 % (13471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.96 % (13471)Termination reason: Unknown
% 2.60/1.96 % (13471)Termination phase: Saturation
% 2.60/1.96
% 2.60/1.96 % (13471)Memory used [KB]: 6780
% 2.60/1.96 % (13471)Time elapsed: 0.109 s
% 2.60/1.96 % (13471)Instructions burned: 451 (million)
% 2.60/1.96 % (13471)------------------------------
% 2.60/1.96 % (13471)------------------------------
% 2.60/1.96 % (13483)Instruction limit reached!
% 2.60/1.96 % (13483)------------------------------
% 2.60/1.96 % (13483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.96 % (13483)Termination reason: Unknown
% 2.60/1.96 % (13483)Termination phase: Property scanning
% 2.60/1.96
% 2.60/1.96 % (13483)Memory used [KB]: 1791
% 2.60/1.96 % (13483)Time elapsed: 0.010 s
% 2.60/1.96 % (13483)Instructions burned: 32 (million)
% 2.60/1.96 % (13483)------------------------------
% 2.60/1.96 % (13483)------------------------------
% 2.60/1.96 % (13484)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_13158 for (2995ds/96Mi)
% 2.60/1.97 % (13485)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_13158 for (2995ds/453Mi)
% 2.60/1.97 % (13486)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_13158 for (2995ds/71Mi)
% 2.60/1.98 % (13460)Instruction limit reached!
% 2.60/1.98 % (13460)------------------------------
% 2.60/1.98 % (13460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.98 % (13460)Termination reason: Unknown
% 2.60/1.98 % (13460)Termination phase: Saturation
% 2.60/1.98
% 2.60/1.98 % (13460)Memory used [KB]: 8443
% 2.60/1.98 % (13460)Time elapsed: 0.320 s
% 2.60/1.98 % (13460)Instructions burned: 881 (million)
% 2.60/1.98 % (13460)------------------------------
% 2.60/1.98 % (13460)------------------------------
% 2.60/1.99 % (13487)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_13158 for (2995ds/83Mi)
% 2.60/1.99 % (13484)Instruction limit reached!
% 2.60/1.99 % (13484)------------------------------
% 2.60/1.99 % (13484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.99 % (13484)Termination reason: Unknown
% 2.60/1.99 % (13484)Termination phase: Saturation
% 2.60/1.99
% 2.60/1.99 % (13484)Memory used [KB]: 6780
% 2.60/1.99 % (13484)Time elapsed: 0.026 s
% 2.60/1.99 % (13484)Instructions burned: 97 (million)
% 2.60/1.99 % (13484)------------------------------
% 2.60/1.99 % (13484)------------------------------
% 2.60/1.99 % (13486)Instruction limit reached!
% 2.60/1.99 % (13486)------------------------------
% 2.60/1.99 % (13486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/1.99 % (13486)Termination reason: Unknown
% 2.60/1.99 % (13486)Termination phase: Property scanning
% 2.60/1.99
% 2.60/1.99 % (13486)Memory used [KB]: 2046
% 2.60/1.99 % (13486)Time elapsed: 0.022 s
% 2.60/1.99 % (13486)Instructions burned: 73 (million)
% 2.60/1.99 % (13486)------------------------------
% 2.60/1.99 % (13486)------------------------------
% 2.60/2.00 % (13488)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_13158 for (2995ds/11Mi)
% 2.60/2.00 % (13488)Instruction limit reached!
% 2.60/2.00 % (13488)------------------------------
% 2.60/2.00 % (13488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.60/2.00 % (13488)Termination reason: Unknown
% 2.60/2.00 % (13488)Termination phase: shuffling
% 2.60/2.00
% 2.60/2.00 % (13488)Memory used [KB]: 1535
% 2.60/2.00 % (13488)Time elapsed: 0.004 s
% 2.60/2.00 % (13488)Instructions burned: 12 (million)
% 2.60/2.00 % (13488)------------------------------
% 2.60/2.00 % (13488)------------------------------
% 2.60/2.00 % (13489)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_13158 for (2995ds/41Mi)
% 2.60/2.01 % (13490)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13158 for (2995ds/6Mi)
% 5.85/2.01 % (13490)Instruction limit reached!
% 5.85/2.01 % (13490)------------------------------
% 5.85/2.01 % (13490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.01 % (13490)Termination reason: Unknown
% 5.85/2.01 % (13490)Termination phase: shuffling
% 5.85/2.01
% 5.85/2.01 % (13490)Memory used [KB]: 1407
% 5.85/2.01 % (13490)Time elapsed: 0.003 s
% 5.85/2.01 % (13490)Instructions burned: 7 (million)
% 5.85/2.01 % (13490)------------------------------
% 5.85/2.01 % (13490)------------------------------
% 5.85/2.01 % (13489)Instruction limit reached!
% 5.85/2.01 % (13489)------------------------------
% 5.85/2.01 % (13489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.01 % (13489)Termination reason: Unknown
% 5.85/2.01 % (13489)Termination phase: Property scanning
% 5.85/2.01
% 5.85/2.01 % (13489)Memory used [KB]: 1791
% 5.85/2.01 % (13489)Time elapsed: 0.012 s
% 5.85/2.01 % (13489)Instructions burned: 41 (million)
% 5.85/2.01 % (13489)------------------------------
% 5.85/2.01 % (13489)------------------------------
% 5.85/2.01 % (13474)Instruction limit reached!
% 5.85/2.01 % (13474)------------------------------
% 5.85/2.01 % (13474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.01 % (13474)Termination reason: Unknown
% 5.85/2.01 % (13474)Termination phase: Saturation
% 5.85/2.01
% 5.85/2.01 % (13474)Memory used [KB]: 7547
% 5.85/2.01 % (13474)Time elapsed: 0.151 s
% 5.85/2.01 % (13474)Instructions burned: 509 (million)
% 5.85/2.01 % (13474)------------------------------
% 5.85/2.01 % (13474)------------------------------
% 5.85/2.02 % (13487)Instruction limit reached!
% 5.85/2.02 % (13487)------------------------------
% 5.85/2.02 % (13487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.02 % (13487)Termination reason: Unknown
% 5.85/2.02 % (13487)Termination phase: Property scanning
% 5.85/2.02
% 5.85/2.02 % (13487)Memory used [KB]: 2046
% 5.85/2.02 % (13487)Time elapsed: 0.036 s
% 5.85/2.02 % (13487)Instructions burned: 85 (million)
% 5.85/2.02 % (13487)------------------------------
% 5.85/2.02 % (13487)------------------------------
% 5.85/2.02 % (13491)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_13158 for (2995ds/150Mi)
% 5.85/2.02 % (13492)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_13158 for (2995ds/343Mi)
% 5.85/2.02 % (13493)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_13158 for (2995ds/109Mi)
% 5.85/2.04 % (13494)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_13158 for (2995ds/253Mi)
% 5.85/2.05 % (13481)Instruction limit reached!
% 5.85/2.05 % (13481)------------------------------
% 5.85/2.05 % (13481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.05 % (13481)Termination reason: Unknown
% 5.85/2.05 % (13481)Termination phase: Saturation
% 5.85/2.05
% 5.85/2.05 % (13481)Memory used [KB]: 3070
% 5.85/2.05 % (13481)Time elapsed: 0.114 s
% 5.85/2.05 % (13481)Instructions burned: 433 (million)
% 5.85/2.05 % (13481)------------------------------
% 5.85/2.05 % (13481)------------------------------
% 5.85/2.05 % (13493)Instruction limit reached!
% 5.85/2.05 % (13493)------------------------------
% 5.85/2.05 % (13493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.05 % (13493)Termination reason: Unknown
% 5.85/2.05 % (13493)Termination phase: Saturation
% 5.85/2.05
% 5.85/2.05 % (13493)Memory used [KB]: 6780
% 5.85/2.05 % (13493)Time elapsed: 0.029 s
% 5.85/2.05 % (13493)Instructions burned: 110 (million)
% 5.85/2.05 % (13493)------------------------------
% 5.85/2.05 % (13493)------------------------------
% 5.85/2.06 % (13495)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_13158 for (2994ds/140Mi)
% 5.85/2.06 % (13496)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_13158 for (2994ds/614Mi)
% 5.85/2.07 % (13491)Instruction limit reached!
% 5.85/2.07 % (13491)------------------------------
% 5.85/2.07 % (13491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.07 % (13491)Termination reason: Unknown
% 5.85/2.07 % (13491)Termination phase: Saturation
% 5.85/2.07
% 5.85/2.07 % (13491)Memory used [KB]: 7931
% 5.85/2.07 % (13491)Time elapsed: 0.045 s
% 5.85/2.07 % (13491)Instructions burned: 151 (million)
% 5.85/2.07 % (13491)------------------------------
% 5.85/2.07 % (13491)------------------------------
% 5.85/2.08 % (13497)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_13158 for (2994ds/202Mi)
% 5.85/2.08 % (13485)Instruction limit reached!
% 5.85/2.08 % (13485)------------------------------
% 5.85/2.08 % (13485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.08 % (13485)Termination reason: Unknown
% 5.85/2.08 % (13485)Termination phase: Saturation
% 5.85/2.08
% 5.85/2.08 % (13485)Memory used [KB]: 6780
% 5.85/2.08 % (13485)Time elapsed: 0.113 s
% 5.85/2.08 % (13485)Instructions burned: 455 (million)
% 5.85/2.08 % (13485)------------------------------
% 5.85/2.08 % (13485)------------------------------
% 5.85/2.09 % (13498)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_13158 for (2994ds/339Mi)
% 5.85/2.10 % (13495)Instruction limit reached!
% 5.85/2.10 % (13495)------------------------------
% 5.85/2.10 % (13495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.85/2.10 % (13495)Termination reason: Unknown
% 5.85/2.10 % (13495)Termination phase: Saturation
% 5.85/2.10
% 5.85/2.10 % (13495)Memory used [KB]: 6780
% 5.85/2.10 % (13495)Time elapsed: 0.039 s
% 5.85/2.10 % (13495)Instructions burned: 141 (million)
% 5.85/2.10 % (13495)------------------------------
% 5.85/2.10 % (13495)------------------------------
% 5.85/2.11 % (13499)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_13158 for (2994ds/283Mi)
% 6.26/2.12 % (13492)Instruction limit reached!
% 6.26/2.12 % (13492)------------------------------
% 6.26/2.12 % (13492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.12 % (13492)Termination reason: Unknown
% 6.26/2.12 % (13492)Termination phase: Saturation
% 6.26/2.12
% 6.26/2.12 % (13492)Memory used [KB]: 7931
% 6.26/2.12 % (13492)Time elapsed: 0.100 s
% 6.26/2.12 % (13492)Instructions burned: 343 (million)
% 6.26/2.12 % (13492)------------------------------
% 6.26/2.12 % (13492)------------------------------
% 6.26/2.13 % (13500)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_13158 for (2994ds/134Mi)
% 6.26/2.13 % (13497)Instruction limit reached!
% 6.26/2.13 % (13497)------------------------------
% 6.26/2.13 % (13497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.13 % (13497)Termination reason: Unknown
% 6.26/2.13 % (13497)Termination phase: Saturation
% 6.26/2.13
% 6.26/2.13 % (13497)Memory used [KB]: 8827
% 6.26/2.13 % (13497)Time elapsed: 0.060 s
% 6.26/2.13 % (13497)Instructions burned: 202 (million)
% 6.26/2.13 % (13497)------------------------------
% 6.26/2.13 % (13497)------------------------------
% 6.26/2.14 % (13501)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_13158 for (2994ds/298Mi)
% 6.26/2.16 % (13494)Instruction limit reached!
% 6.26/2.16 % (13494)------------------------------
% 6.26/2.16 % (13494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.16 % (13494)Termination reason: Unknown
% 6.26/2.16 % (13494)Termination phase: Saturation
% 6.26/2.16
% 6.26/2.16 % (13494)Memory used [KB]: 8315
% 6.26/2.16 % (13494)Time elapsed: 0.143 s
% 6.26/2.16 % (13494)Instructions burned: 255 (million)
% 6.26/2.16 % (13494)------------------------------
% 6.26/2.16 % (13494)------------------------------
% 6.26/2.17 % (13500)Instruction limit reached!
% 6.26/2.17 % (13500)------------------------------
% 6.26/2.17 % (13500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.17 % (13500)Termination reason: Unknown
% 6.26/2.17 % (13500)Termination phase: Saturation
% 6.26/2.17
% 6.26/2.17 % (13500)Memory used [KB]: 7036
% 6.26/2.17 % (13500)Time elapsed: 0.037 s
% 6.26/2.17 % (13500)Instructions burned: 137 (million)
% 6.26/2.17 % (13500)------------------------------
% 6.26/2.17 % (13500)------------------------------
% 6.26/2.17 % (13502)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_13158 for (2993ds/192Mi)
% 6.26/2.18 % (13503)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_13158 for (2993ds/258Mi)
% 6.26/2.18 % (13499)Instruction limit reached!
% 6.26/2.18 % (13499)------------------------------
% 6.26/2.18 % (13499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.18 % (13499)Termination reason: Unknown
% 6.26/2.18 % (13499)Termination phase: Saturation
% 6.26/2.18
% 6.26/2.18 % (13499)Memory used [KB]: 9594
% 6.26/2.18 % (13499)Time elapsed: 0.073 s
% 6.26/2.18 % (13499)Instructions burned: 286 (million)
% 6.26/2.18 % (13499)------------------------------
% 6.26/2.18 % (13499)------------------------------
% 6.26/2.19 % (13504)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_13158 for (2993ds/90Mi)
% 6.26/2.19 % (13498)Instruction limit reached!
% 6.26/2.19 % (13498)------------------------------
% 6.26/2.19 % (13498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.26/2.19 % (13498)Termination reason: Unknown
% 6.26/2.19 % (13498)Termination phase: Saturation
% 6.26/2.19
% 6.26/2.19 % (13498)Memory used [KB]: 7547
% 6.26/2.19 % (13498)Time elapsed: 0.098 s
% 6.26/2.19 % (13498)Instructions burned: 340 (million)
% 6.26/2.19 % (13498)------------------------------
% 6.26/2.19 % (13498)------------------------------
% 6.89/2.20 % (13505)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_13158 for (2993ds/231Mi)
% 6.89/2.21 % (13504)Instruction limit reached!
% 6.89/2.21 % (13504)------------------------------
% 6.89/2.21 % (13504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.21 % (13504)Termination reason: Unknown
% 6.89/2.21 % (13504)Termination phase: Property scanning
% 6.89/2.21
% 6.89/2.21 % (13504)Memory used [KB]: 2558
% 6.89/2.21 % (13504)Time elapsed: 0.025 s
% 6.89/2.21 % (13504)Instructions burned: 94 (million)
% 6.89/2.21 % (13504)------------------------------
% 6.89/2.21 % (13504)------------------------------
% 6.89/2.22 % (13501)Instruction limit reached!
% 6.89/2.22 % (13501)------------------------------
% 6.89/2.22 % (13501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.22 % (13501)Termination reason: Unknown
% 6.89/2.22 % (13501)Termination phase: Saturation
% 6.89/2.22
% 6.89/2.22 % (13501)Memory used [KB]: 6780
% 6.89/2.22 % (13501)Time elapsed: 0.076 s
% 6.89/2.22 % (13501)Instructions burned: 299 (million)
% 6.89/2.22 % (13501)------------------------------
% 6.89/2.22 % (13501)------------------------------
% 6.89/2.22 % (13506)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_13158 for (2993ds/458Mi)
% 6.89/2.22 % (13502)Instruction limit reached!
% 6.89/2.22 % (13502)------------------------------
% 6.89/2.22 % (13502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.22 % (13502)Termination reason: Unknown
% 6.89/2.22 % (13502)Termination phase: Saturation
% 6.89/2.22
% 6.89/2.22 % (13502)Memory used [KB]: 7547
% 6.89/2.22 % (13502)Time elapsed: 0.057 s
% 6.89/2.22 % (13502)Instructions burned: 192 (million)
% 6.89/2.22 % (13502)------------------------------
% 6.89/2.22 % (13502)------------------------------
% 6.89/2.23 % (13507)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_13158 for (2993ds/31Mi)
% 6.89/2.23 % (13508)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_13158 for (2992ds/297Mi)
% 6.89/2.24 % (13507)Instruction limit reached!
% 6.89/2.24 % (13507)------------------------------
% 6.89/2.24 % (13507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.24 % (13507)Termination reason: Unknown
% 6.89/2.24 % (13507)Termination phase: Property scanning
% 6.89/2.24
% 6.89/2.24 % (13507)Memory used [KB]: 1918
% 6.89/2.24 % (13507)Time elapsed: 0.010 s
% 6.89/2.24 % (13507)Instructions burned: 34 (million)
% 6.89/2.24 % (13507)------------------------------
% 6.89/2.24 % (13507)------------------------------
% 6.89/2.25 % (13496)Instruction limit reached!
% 6.89/2.25 % (13496)------------------------------
% 6.89/2.25 % (13496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.25 % (13496)Termination reason: Unknown
% 6.89/2.25 % (13496)Termination phase: Saturation
% 6.89/2.25
% 6.89/2.25 % (13496)Memory used [KB]: 8699
% 6.89/2.25 % (13496)Time elapsed: 0.210 s
% 6.89/2.25 % (13496)Instructions burned: 616 (million)
% 6.89/2.25 % (13496)------------------------------
% 6.89/2.25 % (13496)------------------------------
% 6.89/2.25 % (13509)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_13158 for (2992ds/987Mi)
% 6.89/2.25 % (13503)Instruction limit reached!
% 6.89/2.25 % (13503)------------------------------
% 6.89/2.25 % (13503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.25 % (13503)Termination reason: Unknown
% 6.89/2.25 % (13503)Termination phase: Saturation
% 6.89/2.25
% 6.89/2.25 % (13503)Memory used [KB]: 7675
% 6.89/2.25 % (13503)Time elapsed: 0.073 s
% 6.89/2.25 % (13503)Instructions burned: 258 (million)
% 6.89/2.25 % (13503)------------------------------
% 6.89/2.25 % (13503)------------------------------
% 6.89/2.25 % (13478)Instruction limit reached!
% 6.89/2.25 % (13478)------------------------------
% 6.89/2.25 % (13478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.25 % (13478)Termination reason: Unknown
% 6.89/2.25 % (13478)Termination phase: Saturation
% 6.89/2.25
% 6.89/2.25 % (13478)Memory used [KB]: 10618
% 6.89/2.25 % (13478)Time elapsed: 0.352 s
% 6.89/2.25 % (13478)Instructions burned: 1087 (million)
% 6.89/2.25 % (13478)------------------------------
% 6.89/2.25 % (13478)------------------------------
% 6.89/2.26 % (13510)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_13158 for (2992ds/182Mi)
% 6.89/2.26 % (13511)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_13158 for (2992ds/182Mi)
% 6.89/2.26 % (13512)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_13158 for (2992ds/154Mi)
% 6.89/2.26 % (13505)Instruction limit reached!
% 6.89/2.26 % (13505)------------------------------
% 6.89/2.26 % (13505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.26 % (13505)Termination reason: Unknown
% 6.89/2.26 % (13505)Termination phase: Saturation
% 6.89/2.26
% 6.89/2.26 % (13505)Memory used [KB]: 11129
% 6.89/2.26 % (13505)Time elapsed: 0.066 s
% 6.89/2.26 % (13505)Instructions burned: 234 (million)
% 6.89/2.26 % (13505)------------------------------
% 6.89/2.26 % (13505)------------------------------
% 6.89/2.27 % (13513)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_13158 for (2992ds/79Mi)
% 6.89/2.29 % (13513)Instruction limit reached!
% 6.89/2.29 % (13513)------------------------------
% 6.89/2.29 % (13513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.89/2.29 % (13513)Termination reason: Unknown
% 6.89/2.29 % (13513)Termination phase: Property scanning
% 6.89/2.29
% 6.89/2.29 % (13513)Memory used [KB]: 2046
% 6.89/2.29 % (13513)Time elapsed: 0.021 s
% 6.89/2.29 % (13513)Instructions burned: 80 (million)
% 6.89/2.29 % (13513)------------------------------
% 6.89/2.29 % (13513)------------------------------
% 7.54/2.30 % (13512)Instruction limit reached!
% 7.54/2.30 % (13512)------------------------------
% 7.54/2.30 % (13512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.30 % (13512)Termination reason: Unknown
% 7.54/2.30 % (13512)Termination phase: Saturation
% 7.54/2.30
% 7.54/2.30 % (13512)Memory used [KB]: 6780
% 7.54/2.30 % (13512)Time elapsed: 0.040 s
% 7.54/2.30 % (13512)Instructions burned: 156 (million)
% 7.54/2.30 % (13512)------------------------------
% 7.54/2.30 % (13512)------------------------------
% 7.54/2.30 % (13514)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_13158 for (2992ds/216Mi)
% 7.54/2.31 % (13510)Instruction limit reached!
% 7.54/2.31 % (13510)------------------------------
% 7.54/2.31 % (13510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.31 % (13510)Termination reason: Unknown
% 7.54/2.31 % (13510)Termination phase: Saturation
% 7.54/2.31
% 7.54/2.31 % (13510)Memory used [KB]: 7419
% 7.54/2.31 % (13510)Time elapsed: 0.050 s
% 7.54/2.31 % (13510)Instructions burned: 183 (million)
% 7.54/2.31 % (13510)------------------------------
% 7.54/2.31 % (13510)------------------------------
% 7.54/2.31 % (13515)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_13158 for (2992ds/114Mi)
% 7.54/2.31 % (13511)Instruction limit reached!
% 7.54/2.31 % (13511)------------------------------
% 7.54/2.31 % (13511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.31 % (13511)Termination reason: Unknown
% 7.54/2.31 % (13511)Termination phase: Saturation
% 7.54/2.31
% 7.54/2.31 % (13511)Memory used [KB]: 9978
% 7.54/2.31 % (13511)Time elapsed: 0.054 s
% 7.54/2.31 % (13511)Instructions burned: 183 (million)
% 7.54/2.31 % (13511)------------------------------
% 7.54/2.31 % (13511)------------------------------
% 7.54/2.31 % (13508)Instruction limit reached!
% 7.54/2.31 % (13508)------------------------------
% 7.54/2.31 % (13508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.31 % (13508)Termination reason: Unknown
% 7.54/2.31 % (13508)Termination phase: Saturation
% 7.54/2.31
% 7.54/2.31 % (13508)Memory used [KB]: 9083
% 7.54/2.31 % (13508)Time elapsed: 0.081 s
% 7.54/2.31 % (13508)Instructions burned: 299 (million)
% 7.54/2.31 % (13508)------------------------------
% 7.54/2.31 % (13508)------------------------------
% 7.54/2.31 % (13516)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_13158 for (2992ds/922Mi)
% 7.54/2.32 % (13517)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_13158 for (2992ds/182Mi)
% 7.54/2.32 % (13518)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_13158 for (2992ds/164Mi)
% 7.54/2.34 % (13515)Instruction limit reached!
% 7.54/2.34 % (13515)------------------------------
% 7.54/2.34 % (13515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.34 % (13515)Termination reason: Unknown
% 7.54/2.34 % (13515)Termination phase: Saturation
% 7.54/2.34
% 7.54/2.34 % (13515)Memory used [KB]: 6908
% 7.54/2.34 % (13515)Time elapsed: 0.031 s
% 7.54/2.34 % (13515)Instructions burned: 115 (million)
% 7.54/2.34 % (13515)------------------------------
% 7.54/2.34 % (13515)------------------------------
% 7.54/2.35 % (13519)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_13158 for (2991ds/50Mi)
% 7.54/2.36 % (13506)Instruction limit reached!
% 7.54/2.36 % (13506)------------------------------
% 7.54/2.36 % (13506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.36 % (13506)Termination reason: Unknown
% 7.54/2.36 % (13506)Termination phase: Saturation
% 7.54/2.36
% 7.54/2.36 % (13506)Memory used [KB]: 8059
% 7.54/2.36 % (13506)Time elapsed: 0.136 s
% 7.54/2.36 % (13506)Instructions burned: 460 (million)
% 7.54/2.36 % (13506)------------------------------
% 7.54/2.36 % (13506)------------------------------
% 7.54/2.36 % (13514)Instruction limit reached!
% 7.54/2.36 % (13514)------------------------------
% 7.54/2.36 % (13514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.36 % (13514)Termination reason: Unknown
% 7.54/2.36 % (13514)Termination phase: Saturation
% 7.54/2.36
% 7.54/2.36 % (13514)Memory used [KB]: 6780
% 7.54/2.36 % (13514)Time elapsed: 0.055 s
% 7.54/2.36 % (13514)Instructions burned: 219 (million)
% 7.54/2.36 % (13514)------------------------------
% 7.54/2.36 % (13514)------------------------------
% 7.54/2.36 % (13519)Instruction limit reached!
% 7.54/2.36 % (13519)------------------------------
% 7.54/2.36 % (13519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.36 % (13519)Termination reason: Unknown
% 7.54/2.36 % (13519)Termination phase: Property scanning
% 7.54/2.36
% 7.54/2.36 % (13519)Memory used [KB]: 1918
% 7.54/2.36 % (13519)Time elapsed: 0.014 s
% 7.54/2.36 % (13519)Instructions burned: 52 (million)
% 7.54/2.36 % (13519)------------------------------
% 7.54/2.36 % (13519)------------------------------
% 7.54/2.37 % (13520)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_13158 for (2991ds/368Mi)
% 7.54/2.37 % (13521)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_13158 for (2991ds/1021Mi)
% 7.54/2.37 % (13517)Instruction limit reached!
% 7.54/2.37 % (13517)------------------------------
% 7.54/2.37 % (13517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.37 % (13517)Termination reason: Unknown
% 7.54/2.37 % (13517)Termination phase: Saturation
% 7.54/2.37
% 7.54/2.37 % (13517)Memory used [KB]: 6780
% 7.54/2.37 % (13517)Time elapsed: 0.047 s
% 7.54/2.37 % (13517)Instructions burned: 184 (million)
% 7.54/2.37 % (13517)------------------------------
% 7.54/2.37 % (13517)------------------------------
% 7.54/2.37 % (13518)Instruction limit reached!
% 7.54/2.37 % (13518)------------------------------
% 7.54/2.37 % (13518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.37 % (13518)Termination reason: Unknown
% 7.54/2.37 % (13518)Termination phase: Saturation
% 7.54/2.37
% 7.54/2.37 % (13518)Memory used [KB]: 2430
% 7.54/2.37 % (13518)Time elapsed: 0.048 s
% 7.54/2.37 % (13518)Instructions burned: 165 (million)
% 7.54/2.37 % (13518)------------------------------
% 7.54/2.37 % (13518)------------------------------
% 7.54/2.37 % (13522)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_13158 for (2991ds/267Mi)
% 7.54/2.38 % (13523)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_13158 for (2991ds/204Mi)
% 7.54/2.38 % (13524)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_13158 for (2991ds/26Mi)
% 7.54/2.39 % (13524)Instruction limit reached!
% 7.54/2.39 % (13524)------------------------------
% 7.54/2.39 % (13524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.54/2.39 % (13524)Termination reason: Unknown
% 7.54/2.39 % (13524)Termination phase: Property scanning
% 7.54/2.39
% 7.54/2.39 % (13524)Memory used [KB]: 1791
% 7.54/2.39 % (13524)Time elapsed: 0.010 s
% 7.54/2.39 % (13524)Instructions burned: 29 (million)
% 7.54/2.39 % (13524)------------------------------
% 7.54/2.39 % (13524)------------------------------
% 8.21/2.40 % (13525)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_13158 for (2991ds/53Mi)
% 8.21/2.42 % (13525)Instruction limit reached!
% 8.21/2.42 % (13525)------------------------------
% 8.21/2.42 % (13525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.42 % (13525)Termination reason: Unknown
% 8.21/2.42 % (13525)Termination phase: Property scanning
% 8.21/2.42
% 8.21/2.42 % (13525)Memory used [KB]: 1918
% 8.21/2.42 % (13525)Time elapsed: 0.016 s
% 8.21/2.42 % (13525)Instructions burned: 55 (million)
% 8.21/2.42 % (13525)------------------------------
% 8.21/2.42 % (13525)------------------------------
% 8.21/2.43 % (13526)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_13158 for (2991ds/4436Mi)
% 8.21/2.43 % (13523)Instruction limit reached!
% 8.21/2.43 % (13523)------------------------------
% 8.21/2.43 % (13523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.43 % (13523)Termination reason: Unknown
% 8.21/2.43 % (13523)Termination phase: Saturation
% 8.21/2.43
% 8.21/2.43 % (13523)Memory used [KB]: 7547
% 8.21/2.43 % (13523)Time elapsed: 0.056 s
% 8.21/2.43 % (13523)Instructions burned: 206 (million)
% 8.21/2.43 % (13523)------------------------------
% 8.21/2.43 % (13523)------------------------------
% 8.21/2.44 % (13522)Instruction limit reached!
% 8.21/2.44 % (13522)------------------------------
% 8.21/2.44 % (13522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.44 % (13522)Termination reason: Unknown
% 8.21/2.44 % (13522)Termination phase: Saturation
% 8.21/2.44
% 8.21/2.44 % (13522)Memory used [KB]: 8571
% 8.21/2.44 % (13522)Time elapsed: 0.068 s
% 8.21/2.44 % (13522)Instructions burned: 267 (million)
% 8.21/2.44 % (13522)------------------------------
% 8.21/2.44 % (13522)------------------------------
% 8.21/2.44 % (13527)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_13158 for (2990ds/1539Mi)
% 8.21/2.45 % (13528)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_13158 for (2990ds/408Mi)
% 8.21/2.48 % (13520)Instruction limit reached!
% 8.21/2.48 % (13520)------------------------------
% 8.21/2.48 % (13520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.48 % (13520)Termination reason: Unknown
% 8.21/2.48 % (13520)Termination phase: Saturation
% 8.21/2.48
% 8.21/2.48 % (13520)Memory used [KB]: 8059
% 8.21/2.48 % (13520)Time elapsed: 0.111 s
% 8.21/2.48 % (13520)Instructions burned: 370 (million)
% 8.21/2.48 % (13520)------------------------------
% 8.21/2.48 % (13520)------------------------------
% 8.21/2.49 % (13529)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_13158 for (2990ds/5205Mi)
% 8.21/2.49 % (13509)Instruction limit reached!
% 8.21/2.49 % (13509)------------------------------
% 8.21/2.49 % (13509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.21/2.49 % (13509)Termination reason: Unknown
% 8.21/2.49 % (13509)Termination phase: Saturation
% 8.21/2.49
% 8.21/2.49 % (13509)Memory used [KB]: 10490
% 8.21/2.49 % (13509)Time elapsed: 0.243 s
% 8.21/2.49 % (13509)Instructions burned: 989 (million)
% 8.21/2.49 % (13509)------------------------------
% 8.21/2.49 % (13509)------------------------------
% 8.74/2.50 % (13530)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_13158 for (2990ds/1913Mi)
% 8.74/2.58 % (13528)Instruction limit reached!
% 8.74/2.58 % (13528)------------------------------
% 8.74/2.58 % (13528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.74/2.58 % (13528)Termination reason: Unknown
% 8.74/2.58 % (13528)Termination phase: Saturation
% 8.74/2.58
% 8.74/2.58 % (13528)Memory used [KB]: 9338
% 8.74/2.58 % (13528)Time elapsed: 0.128 s
% 8.74/2.58 % (13528)Instructions burned: 410 (million)
% 8.74/2.58 % (13528)------------------------------
% 8.74/2.58 % (13528)------------------------------
% 8.74/2.59 % (13531)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_13158 for (2989ds/4350Mi)
% 8.89/2.60 % (13516)Instruction limit reached!
% 8.89/2.60 % (13516)------------------------------
% 8.89/2.60 % (13516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.60 % (13516)Termination reason: Unknown
% 8.89/2.60 % (13516)Termination phase: Saturation
% 8.89/2.60
% 8.89/2.60 % (13516)Memory used [KB]: 9978
% 8.89/2.60 % (13516)Time elapsed: 0.290 s
% 8.89/2.60 % (13516)Instructions burned: 922 (million)
% 8.89/2.60 % (13516)------------------------------
% 8.89/2.60 % (13516)------------------------------
% 8.89/2.61 % (13532)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_13158 for (2989ds/68Mi)
% 8.89/2.63 % (13532)Instruction limit reached!
% 8.89/2.63 % (13532)------------------------------
% 8.89/2.63 % (13532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.63 % (13532)Termination reason: Unknown
% 8.89/2.63 % (13532)Termination phase: Property scanning
% 8.89/2.63
% 8.89/2.63 % (13532)Memory used [KB]: 2046
% 8.89/2.63 % (13532)Time elapsed: 0.020 s
% 8.89/2.63 % (13532)Instructions burned: 71 (million)
% 8.89/2.63 % (13532)------------------------------
% 8.89/2.63 % (13532)------------------------------
% 8.89/2.64 % (13533)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_13158 for (2989ds/358Mi)
% 8.89/2.69 % (13521)Instruction limit reached!
% 8.89/2.69 % (13521)------------------------------
% 8.89/2.69 % (13521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.89/2.69 % (13521)Termination reason: Unknown
% 8.89/2.69 % (13521)Termination phase: Saturation
% 8.89/2.69
% 8.89/2.69 % (13521)Memory used [KB]: 10106
% 8.89/2.69 % (13521)Time elapsed: 0.322 s
% 8.89/2.69 % (13521)Instructions burned: 1023 (million)
% 8.89/2.69 % (13521)------------------------------
% 8.89/2.69 % (13521)------------------------------
% 8.89/2.70 % (13534)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_13158 for (2988ds/31Mi)
% 9.55/2.70 % (13534)Instruction limit reached!
% 9.55/2.70 % (13534)------------------------------
% 9.55/2.70 % (13534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.70 % (13534)Termination reason: Unknown
% 9.55/2.70 % (13534)Termination phase: Property scanning
% 9.55/2.70
% 9.55/2.70 % (13534)Memory used [KB]: 1918
% 9.55/2.70 % (13534)Time elapsed: 0.010 s
% 9.55/2.70 % (13534)Instructions burned: 33 (million)
% 9.55/2.70 % (13534)------------------------------
% 9.55/2.70 % (13534)------------------------------
% 9.55/2.71 % (13535)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_13158 for (2988ds/279Mi)
% 9.55/2.75 % (13533)Instruction limit reached!
% 9.55/2.75 % (13533)------------------------------
% 9.55/2.75 % (13533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.75 % (13533)Termination reason: Unknown
% 9.55/2.75 % (13533)Termination phase: Saturation
% 9.55/2.75
% 9.55/2.75 % (13533)Memory used [KB]: 7803
% 9.55/2.75 % (13533)Time elapsed: 0.104 s
% 9.55/2.75 % (13533)Instructions burned: 361 (million)
% 9.55/2.75 % (13533)------------------------------
% 9.55/2.75 % (13533)------------------------------
% 9.55/2.76 % (13536)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_13158 for (2987ds/258Mi)
% 9.55/2.78 % (13535)Instruction limit reached!
% 9.55/2.78 % (13535)------------------------------
% 9.55/2.78 % (13535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.78 % (13535)Termination reason: Unknown
% 9.55/2.78 % (13535)Termination phase: Saturation
% 9.55/2.78
% 9.55/2.78 % (13535)Memory used [KB]: 6780
% 9.55/2.78 % (13535)Time elapsed: 0.071 s
% 9.55/2.78 % (13535)Instructions burned: 282 (million)
% 9.55/2.78 % (13535)------------------------------
% 9.55/2.78 % (13535)------------------------------
% 9.55/2.79 % (13537)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_13158 for (2987ds/26Mi)
% 9.75/2.80 % (13537)Instruction limit reached!
% 9.75/2.80 % (13537)------------------------------
% 9.75/2.80 % (13537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.80 % (13537)Termination reason: Unknown
% 9.75/2.80 % (13537)Termination phase: shuffling
% 9.75/2.80
% 9.75/2.80 % (13537)Memory used [KB]: 1791
% 9.75/2.80 % (13537)Time elapsed: 0.008 s
% 9.75/2.80 % (13537)Instructions burned: 26 (million)
% 9.75/2.80 % (13537)------------------------------
% 9.75/2.80 % (13537)------------------------------
% 9.75/2.81 % (13538)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_13158 for (2987ds/995Mi)
% 9.75/2.83 % (13536)Instruction limit reached!
% 9.75/2.83 % (13536)------------------------------
% 9.75/2.83 % (13536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.75/2.83 % (13536)Termination reason: Unknown
% 9.75/2.83 % (13536)Termination phase: Saturation
% 9.75/2.83
% 9.75/2.83 % (13536)Memory used [KB]: 7803
% 9.75/2.83 % (13536)Time elapsed: 0.072 s
% 9.75/2.83 % (13536)Instructions burned: 260 (million)
% 9.75/2.83 % (13536)------------------------------
% 9.75/2.83 % (13536)------------------------------
% 9.75/2.84 % (13539)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_13158 for (2987ds/373Mi)
% 9.86/2.92 % (13527)Instruction limit reached!
% 9.86/2.92 % (13527)------------------------------
% 9.86/2.92 % (13527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.86/2.92 % (13527)Termination reason: Unknown
% 9.86/2.92 % (13527)Termination phase: Saturation
% 9.86/2.92
% 9.86/2.92 % (13527)Memory used [KB]: 9210
% 9.86/2.92 % (13527)Time elapsed: 0.482 s
% 9.86/2.92 % (13527)Instructions burned: 1540 (million)
% 9.86/2.92 % (13527)------------------------------
% 9.86/2.92 % (13527)------------------------------
% 9.86/2.93 % (13540)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_13158 for (2986ds/253Mi)
% 9.86/2.95 % (13539)Instruction limit reached!
% 9.86/2.95 % (13539)------------------------------
% 9.86/2.95 % (13539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.86/2.95 % (13539)Termination reason: Unknown
% 9.86/2.95 % (13539)Termination phase: Saturation
% 9.86/2.95
% 9.86/2.95 % (13539)Memory used [KB]: 7803
% 9.86/2.95 % (13539)Time elapsed: 0.134 s
% 9.86/2.95 % (13539)Instructions burned: 374 (million)
% 9.86/2.95 % (13539)------------------------------
% 9.86/2.95 % (13539)------------------------------
% 9.86/2.96 % (13541)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_13158 for (2985ds/832Mi)
% 9.86/3.00 % (13540)Instruction limit reached!
% 9.86/3.00 % (13540)------------------------------
% 9.86/3.00 % (13540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.86/3.00 % (13540)Termination reason: Unknown
% 9.86/3.00 % (13540)Termination phase: Saturation
% 9.86/3.00
% 9.86/3.00 % (13540)Memory used [KB]: 6908
% 9.86/3.00 % (13540)Time elapsed: 0.065 s
% 9.86/3.00 % (13540)Instructions burned: 255 (million)
% 9.86/3.00 % (13540)------------------------------
% 9.86/3.00 % (13540)------------------------------
% 9.86/3.01 % (13542)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_13158 for (2985ds/668Mi)
% 12.93/3.06 % (13538)Instruction limit reached!
% 12.93/3.06 % (13538)------------------------------
% 12.93/3.06 % (13538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.06 % (13538)Termination reason: Unknown
% 12.93/3.06 % (13538)Termination phase: Saturation
% 12.93/3.06
% 12.93/3.06 % (13538)Memory used [KB]: 9978
% 12.93/3.06 % (13538)Time elapsed: 0.246 s
% 12.93/3.06 % (13538)Instructions burned: 998 (million)
% 12.93/3.06 % (13538)------------------------------
% 12.93/3.06 % (13538)------------------------------
% 12.93/3.07 % (13543)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_13158 for (2984ds/40Mi)
% 12.93/3.08 % (13543)Instruction limit reached!
% 12.93/3.08 % (13543)------------------------------
% 12.93/3.08 % (13543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.08 % (13543)Termination reason: Unknown
% 12.93/3.08 % (13543)Termination phase: Property scanning
% 12.93/3.08
% 12.93/3.08 % (13543)Memory used [KB]: 1918
% 12.93/3.08 % (13543)Time elapsed: 0.012 s
% 12.93/3.08 % (13543)Instructions burned: 42 (million)
% 12.93/3.08 % (13543)------------------------------
% 12.93/3.08 % (13543)------------------------------
% 12.93/3.09 % (13544)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_13158 for (2984ds/294Mi)
% 12.93/3.09 % (13530)Instruction limit reached!
% 12.93/3.09 % (13530)------------------------------
% 12.93/3.09 % (13530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.93/3.09 % (13530)Termination reason: Unknown
% 12.93/3.09 % (13530)Termination phase: Saturation
% 12.93/3.09
% 12.93/3.09 % (13530)Memory used [KB]: 4477
% 12.93/3.09 % (13530)Time elapsed: 0.592 s
% 12.93/3.09 % (13530)Instructions burned: 1913 (million)
% 12.93/3.09 % (13530)------------------------------
% 12.93/3.09 % (13530)------------------------------
% 12.93/3.10 % (13545)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_13158 for (2984ds/187Mi)
% 13.59/3.15 % (13545)Instruction limit reached!
% 13.59/3.15 % (13545)------------------------------
% 13.59/3.15 % (13545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.15 % (13545)Termination reason: Unknown
% 13.59/3.15 % (13545)Termination phase: Saturation
% 13.59/3.15
% 13.59/3.15 % (13545)Memory used [KB]: 7547
% 13.59/3.15 % (13545)Time elapsed: 0.053 s
% 13.59/3.15 % (13545)Instructions burned: 188 (million)
% 13.59/3.15 % (13545)------------------------------
% 13.59/3.15 % (13545)------------------------------
% 13.59/3.16 % (13546)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_13158 for (2983ds/371Mi)
% 13.59/3.16 % (13544)Instruction limit reached!
% 13.59/3.16 % (13544)------------------------------
% 13.59/3.16 % (13544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.16 % (13544)Termination reason: Unknown
% 13.59/3.16 % (13544)Termination phase: Saturation
% 13.59/3.16
% 13.59/3.16 % (13544)Memory used [KB]: 6652
% 13.59/3.16 % (13544)Time elapsed: 0.077 s
% 13.59/3.16 % (13544)Instructions burned: 298 (million)
% 13.59/3.16 % (13544)------------------------------
% 13.59/3.16 % (13544)------------------------------
% 13.59/3.17 % (13547)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_13158 for (2983ds/1827Mi)
% 13.59/3.17 % (13542)Instruction limit reached!
% 13.59/3.17 % (13542)------------------------------
% 13.59/3.17 % (13542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.59/3.17 % (13542)Termination reason: Unknown
% 13.59/3.17 % (13542)Termination phase: Saturation
% 13.59/3.17
% 13.59/3.17 % (13542)Memory used [KB]: 14711
% 13.59/3.17 % (13542)Time elapsed: 0.168 s
% 13.59/3.17 % (13542)Instructions burned: 669 (million)
% 13.59/3.17 % (13542)------------------------------
% 13.59/3.17 % (13542)------------------------------
% 13.59/3.18 % (13548)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_13158 for (2983ds/70Mi)
% 14.07/3.20 % (13548)Instruction limit reached!
% 14.07/3.20 % (13548)------------------------------
% 14.07/3.20 % (13548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.07/3.20 % (13548)Termination reason: Unknown
% 14.07/3.20 % (13548)Termination phase: Property scanning
% 14.07/3.20
% 14.07/3.20 % (13548)Memory used [KB]: 2174
% 14.07/3.20 % (13548)Time elapsed: 0.019 s
% 14.07/3.20 % (13548)Instructions burned: 71 (million)
% 14.07/3.20 % (13548)------------------------------
% 14.07/3.20 % (13548)------------------------------
% 14.07/3.21 % (13549)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_13158 for (2983ds/316Mi)
% 14.07/3.21 % (13541)Instruction limit reached!
% 14.07/3.21 % (13541)------------------------------
% 14.07/3.21 % (13541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.07/3.21 % (13541)Termination reason: Unknown
% 14.07/3.21 % (13541)Termination phase: Saturation
% 14.07/3.21
% 14.07/3.21 % (13541)Memory used [KB]: 9210
% 14.07/3.21 % (13541)Time elapsed: 0.278 s
% 14.07/3.21 % (13541)Instructions burned: 833 (million)
% 14.07/3.21 % (13541)------------------------------
% 14.07/3.21 % (13541)------------------------------
% 14.07/3.22 % (13550)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_13158 for (2983ds/932Mi)
% 14.07/3.27 % (13546)Instruction limit reached!
% 14.07/3.27 % (13546)------------------------------
% 14.07/3.27 % (13546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.07/3.27 % (13546)Termination reason: Unknown
% 14.07/3.27 % (13546)Termination phase: Saturation
% 14.07/3.27
% 14.07/3.27 % (13546)Memory used [KB]: 7931
% 14.07/3.27 % (13546)Time elapsed: 0.110 s
% 14.07/3.27 % (13546)Instructions burned: 372 (million)
% 14.07/3.27 % (13546)------------------------------
% 14.07/3.27 % (13546)------------------------------
% 14.07/3.28 % (13551)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_13158 for (2982ds/4714Mi)
% 14.07/3.29 % (13549)Instruction limit reached!
% 14.07/3.29 % (13549)------------------------------
% 14.07/3.29 % (13549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.07/3.29 % (13549)Termination reason: Unknown
% 14.07/3.29 % (13549)Termination phase: Saturation
% 14.07/3.29
% 14.07/3.29 % (13549)Memory used [KB]: 7419
% 14.07/3.29 % (13549)Time elapsed: 0.083 s
% 14.07/3.29 % (13549)Instructions burned: 316 (million)
% 14.07/3.29 % (13549)------------------------------
% 14.07/3.29 % (13549)------------------------------
% 14.64/3.30 % (13552)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_13158 for (2982ds/8250Mi)
% 14.95/3.46 % (13550)Instruction limit reached!
% 14.95/3.46 % (13550)------------------------------
% 14.95/3.46 % (13550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.95/3.46 % (13550)Termination reason: Unknown
% 14.95/3.46 % (13550)Termination phase: Saturation
% 14.95/3.46
% 14.95/3.46 % (13550)Memory used [KB]: 11129
% 14.95/3.46 % (13550)Time elapsed: 0.235 s
% 14.95/3.46 % (13550)Instructions burned: 933 (million)
% 14.95/3.46 % (13550)------------------------------
% 14.95/3.46 % (13550)------------------------------
% 14.95/3.47 % (13553)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_13158 for (2980ds/770Mi)
% 15.79/3.69 % (13553)Instruction limit reached!
% 15.79/3.69 % (13553)------------------------------
% 15.79/3.69 % (13553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.79/3.69 % (13553)Termination reason: Unknown
% 15.79/3.69 % (13553)Termination phase: Saturation
% 15.79/3.69
% 15.79/3.69 % (13553)Memory used [KB]: 6908
% 15.79/3.69 % (13553)Time elapsed: 0.220 s
% 15.79/3.69 % (13553)Instructions burned: 772 (million)
% 15.79/3.69 % (13553)------------------------------
% 15.79/3.69 % (13553)------------------------------
% 15.79/3.70 % (13554)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_13158 for (2978ds/794Mi)
% 16.32/3.72 % (13547)Instruction limit reached!
% 16.32/3.72 % (13547)------------------------------
% 16.32/3.72 % (13547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.32/3.72 % (13547)Termination reason: Unknown
% 16.32/3.72 % (13547)Termination phase: Saturation
% 16.32/3.72
% 16.32/3.72 % (13547)Memory used [KB]: 16375
% 16.32/3.72 % (13547)Time elapsed: 0.577 s
% 16.32/3.72 % (13547)Instructions burned: 1829 (million)
% 16.32/3.72 % (13547)------------------------------
% 16.32/3.72 % (13547)------------------------------
% 16.32/3.74 % (13555)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_13158 for (2977ds/464Mi)
% 16.32/3.75 % (13529)Instruction limit reached!
% 16.32/3.75 % (13529)------------------------------
% 16.32/3.75 % (13529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.32/3.75 % (13529)Termination reason: Unknown
% 16.32/3.75 % (13529)Termination phase: Saturation
% 16.32/3.75
% 16.32/3.75 % (13529)Memory used [KB]: 10746
% 16.32/3.75 % (13529)Time elapsed: 1.262 s
% 16.32/3.75 % (13529)Instructions burned: 5206 (million)
% 16.32/3.75 % (13529)------------------------------
% 16.32/3.75 % (13529)------------------------------
% 16.32/3.76 % (13556)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_13158 for (2977ds/1376Mi)
% 17.16/3.83 % (13526)Instruction limit reached!
% 17.16/3.83 % (13526)------------------------------
% 17.16/3.83 % (13526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.16/3.83 % (13526)Termination reason: Unknown
% 17.16/3.83 % (13526)Termination phase: Saturation
% 17.16/3.83
% 17.16/3.83 % (13526)Memory used [KB]: 16886
% 17.16/3.83 % (13526)Time elapsed: 1.405 s
% 17.16/3.83 % (13526)Instructions burned: 4438 (million)
% 17.16/3.83 % (13526)------------------------------
% 17.16/3.83 % (13526)------------------------------
% 17.16/3.84 % (13557)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_13158 for (2976ds/906Mi)
% 17.16/3.88 % (13555)Instruction limit reached!
% 17.16/3.88 % (13555)------------------------------
% 17.16/3.88 % (13555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.16/3.88 % (13555)Termination reason: Unknown
% 17.16/3.88 % (13555)Termination phase: Saturation
% 17.16/3.88
% 17.16/3.88 % (13555)Memory used [KB]: 8059
% 17.16/3.88 % (13555)Time elapsed: 0.144 s
% 17.16/3.88 % (13555)Instructions burned: 466 (million)
% 17.16/3.88 % (13555)------------------------------
% 17.16/3.88 % (13555)------------------------------
% 17.16/3.89 % (13558)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_13158 for (2976ds/434Mi)
% 17.45/3.92 % (13531)Instruction limit reached!
% 17.45/3.92 % (13531)------------------------------
% 17.45/3.92 % (13531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.45/3.92 % (13531)Termination reason: Unknown
% 17.45/3.92 % (13531)Termination phase: Saturation
% 17.45/3.92
% 17.45/3.92 % (13531)Memory used [KB]: 11257
% 17.45/3.92 % (13531)Time elapsed: 1.337 s
% 17.45/3.92 % (13531)Instructions burned: 4352 (million)
% 17.45/3.92 % (13531)------------------------------
% 17.45/3.92 % (13531)------------------------------
% 17.45/3.93 % (13559)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_13158 for (2976ds/865Mi)
% 17.45/3.94 % (13554)Instruction limit reached!
% 17.45/3.94 % (13554)------------------------------
% 17.45/3.94 % (13554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.45/3.94 % (13554)Termination reason: Unknown
% 17.45/3.94 % (13554)Termination phase: Saturation
% 17.45/3.94
% 17.45/3.94 % (13554)Memory used [KB]: 4221
% 17.45/3.94 % (13554)Time elapsed: 0.247 s
% 17.45/3.94 % (13554)Instructions burned: 795 (million)
% 17.45/3.94 % (13554)------------------------------
% 17.45/3.94 % (13554)------------------------------
% 17.45/3.95 % (13560)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_13158 for (2975ds/593Mi)
% 17.45/4.01 % (13558)Refutation not found, non-redundant clauses discarded% (13558)------------------------------
% 17.45/4.01 % (13558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.45/4.01 % (13558)Termination reason: Refutation not found, non-redundant clauses discarded
% 17.45/4.01
% 17.45/4.01 % (13558)Memory used [KB]: 9083
% 17.45/4.01 % (13558)Time elapsed: 0.127 s
% 17.45/4.01 % (13558)Instructions burned: 427 (million)
% 17.45/4.01 % (13558)------------------------------
% 17.45/4.01 % (13558)------------------------------
% 19.95/4.02 % (13561)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_13158 for (2975ds/443Mi)
% 19.95/4.10 % (13560)Instruction limit reached!
% 19.95/4.10 % (13560)------------------------------
% 19.95/4.10 % (13560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.95/4.10 % (13560)Termination reason: Unknown
% 19.95/4.10 % (13560)Termination phase: Saturation
% 19.95/4.10
% 19.95/4.10 % (13560)Memory used [KB]: 6908
% 19.95/4.10 % (13560)Time elapsed: 0.145 s
% 19.95/4.10 % (13560)Instructions burned: 595 (million)
% 19.95/4.10 % (13560)------------------------------
% 19.95/4.10 % (13560)------------------------------
% 19.95/4.10 % (13556)Instruction limit reached!
% 19.95/4.10 % (13556)------------------------------
% 19.95/4.10 % (13556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.95/4.10 % (13556)Termination reason: Unknown
% 19.95/4.10 % (13556)Termination phase: Saturation
% 19.95/4.10
% 19.95/4.10 % (13556)Memory used [KB]: 8059
% 19.95/4.10 % (13556)Time elapsed: 0.350 s
% 19.95/4.10 % (13556)Instructions burned: 1378 (million)
% 19.95/4.10 % (13556)------------------------------
% 19.95/4.10 % (13556)------------------------------
% 19.95/4.11 % (13562)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_13158 for (2974ds/594Mi)
% 19.95/4.11 % (13563)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_13158 for (2974ds/327Mi)
% 19.95/4.12 % (13557)Instruction limit reached!
% 19.95/4.12 % (13557)------------------------------
% 19.95/4.12 % (13557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.95/4.12 % (13557)Termination reason: Unknown
% 19.95/4.12 % (13557)Termination phase: Saturation
% 19.95/4.12
% 19.95/4.12 % (13557)Memory used [KB]: 9083
% 19.95/4.12 % (13557)Time elapsed: 0.282 s
% 19.95/4.12 % (13557)Instructions burned: 907 (million)
% 19.95/4.12 % (13557)------------------------------
% 19.95/4.12 % (13557)------------------------------
% 20.54/4.13 % (13564)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_13158 for (2974ds/5411Mi)
% 20.54/4.16 % (13561)Instruction limit reached!
% 20.54/4.16 % (13561)------------------------------
% 20.54/4.16 % (13561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.54/4.16 % (13561)Termination reason: Unknown
% 20.54/4.16 % (13561)Termination phase: Saturation
% 20.54/4.16
% 20.54/4.16 % (13561)Memory used [KB]: 8187
% 20.54/4.16 % (13561)Time elapsed: 0.155 s
% 20.54/4.16 % (13561)Instructions burned: 445 (million)
% 20.54/4.16 % (13561)------------------------------
% 20.54/4.16 % (13561)------------------------------
% 20.54/4.17 % (13565)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_13158 for (2973ds/1762Mi)
% 20.54/4.19 % (13559)Instruction limit reached!
% 20.54/4.19 % (13559)------------------------------
% 20.54/4.19 % (13559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.54/4.19 % (13559)Termination reason: Unknown
% 20.54/4.19 % (13559)Termination phase: Saturation
% 20.54/4.19
% 20.54/4.19 % (13559)Memory used [KB]: 9466
% 20.54/4.19 % (13559)Time elapsed: 0.259 s
% 20.54/4.19 % (13559)Instructions burned: 867 (million)
% 20.54/4.19 % (13559)------------------------------
% 20.54/4.19 % (13559)------------------------------
% 20.92/4.20 % (13566)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_13158 for (2973ds/96Mi)
% 20.92/4.22 % (13563)Instruction limit reached!
% 20.92/4.22 % (13563)------------------------------
% 20.92/4.22 % (13563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.92/4.22 % (13563)Termination reason: Unknown
% 20.92/4.22 % (13563)Termination phase: Saturation
% 20.92/4.22
% 20.92/4.22 % (13563)Memory used [KB]: 9722
% 20.92/4.22 % (13563)Time elapsed: 0.124 s
% 20.92/4.22 % (13563)Instructions burned: 327 (million)
% 20.92/4.22 % (13563)------------------------------
% 20.92/4.22 % (13563)------------------------------
% 20.92/4.22 % (13566)Instruction limit reached!
% 20.92/4.22 % (13566)------------------------------
% 20.92/4.22 % (13566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.92/4.22 % (13566)Termination reason: Unknown
% 20.92/4.22 % (13566)Termination phase: Saturation
% 20.92/4.22
% 20.92/4.22 % (13566)Memory used [KB]: 6652
% 20.92/4.22 % (13566)Time elapsed: 0.026 s
% 20.92/4.22 % (13566)Instructions burned: 97 (million)
% 20.92/4.22 % (13566)------------------------------
% 20.92/4.22 % (13566)------------------------------
% 20.92/4.23 % (13567)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_13158 for (2973ds/503Mi)
% 20.92/4.23 % (13568)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_13158 for (2973ds/90Mi)
% 20.92/4.26 % (13568)Instruction limit reached!
% 20.92/4.26 % (13568)------------------------------
% 20.92/4.26 % (13568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.92/4.26 % (13568)Termination reason: Unknown
% 20.92/4.26 % (13568)Termination phase: Property scanning
% 20.92/4.26
% 20.92/4.26 % (13568)Memory used [KB]: 2430
% 20.92/4.26 % (13568)Time elapsed: 0.025 s
% 20.92/4.26 % (13568)Instructions burned: 93 (million)
% 20.92/4.26 % (13568)------------------------------
% 20.92/4.26 % (13568)------------------------------
% 20.92/4.27 % (13569)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_13158 for (2972ds/593Mi)
% 20.92/4.28 % (13562)Instruction limit reached!
% 20.92/4.28 % (13562)------------------------------
% 20.92/4.28 % (13562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.92/4.28 % (13562)Termination reason: Unknown
% 20.92/4.28 % (13562)Termination phase: Saturation
% 20.92/4.28
% 20.92/4.28 % (13562)Memory used [KB]: 8187
% 20.92/4.28 % (13562)Time elapsed: 0.202 s
% 20.92/4.28 % (13562)Instructions burned: 596 (million)
% 20.92/4.28 % (13562)------------------------------
% 20.92/4.28 % (13562)------------------------------
% 20.92/4.29 % (13570)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_13158 for (2972ds/1512Mi)
% 21.48/4.33 % (13552)First to succeed.
% 21.48/4.33 % (13552)Refutation found. Thanks to Tanya!
% 21.48/4.33 % SZS status Theorem for DTF2THF_13158
% 21.48/4.33 % SZS output start Proof for DTF2THF_13158
% 21.48/4.33 thf(func_def_0, type, in: $i > $i > $o).
% 21.48/4.33 thf(func_def_1, type, exu: ($i > $o) > $o).
% 21.48/4.33 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 21.48/4.33 thf(func_def_8, type, powerset: $i > $i).
% 21.48/4.33 thf(func_def_10, type, setunion: $i > $i).
% 21.48/4.33 thf(func_def_19, type, descr: ($i > $o) > $i).
% 21.48/4.33 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_26, type, prop2set: $o > $i).
% 21.48/4.33 thf(func_def_36, type, nonempty: $i > $o).
% 21.48/4.33 thf(func_def_69, type, set2prop: $i > $o).
% 21.48/4.33 thf(func_def_88, type, subset: $i > $i > $o).
% 21.48/4.33 thf(func_def_89, type, disjoint: $i > $i > $o).
% 21.48/4.33 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 21.48/4.33 thf(func_def_114, type, binunion: $i > $i > $i).
% 21.48/4.33 thf(func_def_122, type, binintersect: $i > $i > $i).
% 21.48/4.33 thf(func_def_135, type, regular: $i > $o).
% 21.48/4.33 thf(func_def_136, type, setminus: $i > $i > $i).
% 21.48/4.33 thf(func_def_147, type, symdiff: $i > $i > $i).
% 21.48/4.33 thf(func_def_153, type, iskpair: $i > $o).
% 21.48/4.33 thf(func_def_158, type, kpair: $i > $i > $i).
% 21.48/4.33 thf(func_def_160, type, cartprod: $i > $i > $i).
% 21.48/4.33 thf(func_def_177, type, singleton: $i > $o).
% 21.48/4.33 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 21.48/4.33 thf(func_def_184, type, atmost1p: $i > $o).
% 21.48/4.33 thf(func_def_185, type, atleast2p: $i > $o).
% 21.48/4.33 thf(func_def_186, type, atmost2p: $i > $o).
% 21.48/4.33 thf(func_def_187, type, upairsetp: $i > $o).
% 21.48/4.33 thf(func_def_191, type, kfst: $i > $i).
% 21.48/4.33 thf(func_def_203, type, ksnd: $i > $i).
% 21.48/4.33 thf(func_def_219, type, sP1: $o > $i > $i > $i > $o).
% 21.48/4.33 thf(func_def_221, type, sP3: $i > $i > $o).
% 21.48/4.33 thf(func_def_222, type, sP4: $i > $o).
% 21.48/4.33 thf(func_def_223, type, sP5: $i > $i > $o).
% 21.48/4.33 thf(func_def_224, type, sP6: $i > $i > $o).
% 21.48/4.33 thf(func_def_226, type, sK8: $i > $o).
% 21.48/4.33 thf(func_def_236, type, sK18: $i > $o).
% 21.48/4.33 thf(func_def_237, type, sK19: ($i > $o) > $i > $i > $i).
% 21.48/4.33 thf(func_def_242, type, sK24: $i > $i).
% 21.48/4.33 thf(func_def_245, type, sK27: $i > $o).
% 21.48/4.33 thf(func_def_248, type, sK30: $i > $o).
% 21.48/4.33 thf(func_def_252, type, sK34: $i > $i).
% 21.48/4.33 thf(func_def_254, type, sK36: $i > $i).
% 21.48/4.33 thf(func_def_255, type, sK37: ($i > $o) > $i).
% 21.48/4.33 thf(func_def_256, type, sK38: $i > $o).
% 21.48/4.33 thf(func_def_264, type, sK46: $i > $o).
% 21.48/4.33 thf(func_def_266, type, sK48: $i > $o).
% 21.48/4.33 thf(func_def_268, type, sK50: ($i > $o) > $i > $i).
% 21.48/4.33 thf(func_def_314, type, sK96: $i > $o).
% 21.48/4.33 thf(func_def_325, type, sK107: $i > $i > $i > $i).
% 21.48/4.33 thf(func_def_326, type, sK108: $i > $i > $i > $i).
% 21.48/4.33 thf(func_def_334, type, sK116: $i > $o).
% 21.48/4.33 thf(func_def_337, type, sK119: $i > $o).
% 21.48/4.33 thf(func_def_339, type, sK121: ($i > $o) > $i > $i).
% 21.48/4.33 thf(func_def_343, type, sK125: $i > $o).
% 21.48/4.33 thf(func_def_350, type, sK132: $i > $i).
% 21.48/4.33 thf(func_def_351, type, sK133: $i > $o).
% 21.48/4.33 thf(func_def_353, type, sK135: $i > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_356, type, sK138: $i > $o).
% 21.48/4.33 thf(func_def_359, type, sK141: $i > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_365, type, sK147: $i > $i > $i).
% 21.48/4.33 thf(func_def_368, type, sK150: $i > $i > $i).
% 21.48/4.33 thf(func_def_384, type, sK166: $o > $i > $i > $i).
% 21.48/4.33 thf(func_def_402, type, sK184: $i > $o).
% 21.48/4.33 thf(func_def_407, type, sK189: $i > $o).
% 21.48/4.33 thf(func_def_408, type, sK190: $i > $o).
% 21.48/4.33 thf(func_def_409, type, sK191: ($i > $o) > ($i > $o) > $i > $i > $i).
% 21.48/4.33 thf(func_def_410, type, sK192: ($i > $o) > ($i > $o) > $i > $i > $i).
% 21.48/4.33 thf(func_def_413, type, sK195: $i > $o).
% 21.48/4.33 thf(func_def_425, type, sK207: $i > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_426, type, sK208: $i > $o).
% 21.48/4.33 thf(func_def_433, type, sK215: $i > $i).
% 21.48/4.33 thf(func_def_440, type, sK222: $i > $o).
% 21.48/4.33 thf(func_def_442, type, sK224: ($i > $o) > $i > $i).
% 21.48/4.33 thf(func_def_444, type, sK226: $i > $i).
% 21.48/4.33 thf(func_def_453, type, sK235: $i > $o).
% 21.48/4.33 thf(func_def_461, type, sK243: $i > $o).
% 21.48/4.33 thf(func_def_464, type, sK246: $i > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_465, type, sK247: $i > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_472, type, sK254: $i > $i > $i).
% 21.48/4.33 thf(func_def_493, type, sK275: $i > $i > $i).
% 21.48/4.33 thf(func_def_511, type, sK293: ($i > $o) > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_512, type, sK294: ($i > $o) > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_513, type, sK295: $i > $o).
% 21.48/4.33 thf(func_def_514, type, sK296: $i > $o).
% 21.48/4.33 thf(func_def_515, type, sK297: $i > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_516, type, sK298: $i > $o).
% 21.48/4.33 thf(func_def_541, type, sK323: $i > $i > $i).
% 21.48/4.33 thf(func_def_552, type, sK334: $i > $i > $i).
% 21.48/4.33 thf(func_def_555, type, sK337: $i > $o).
% 21.48/4.33 thf(func_def_557, type, sK339: ($i > $o) > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_558, type, sK340: ($i > $o) > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_559, type, sK341: $i > $o).
% 21.48/4.33 thf(func_def_560, type, sK342: $i > $o).
% 21.48/4.33 thf(func_def_567, type, sK349: $i > $i > $o).
% 21.48/4.33 thf(func_def_569, type, sK351: $i > $i).
% 21.48/4.33 thf(func_def_570, type, sK352: $i > $i).
% 21.48/4.33 thf(func_def_571, type, sK353: $i > ($i > $i > $o) > $i).
% 21.48/4.33 thf(func_def_572, type, sK354: $i > $i > ($i > $i > $o) > $i).
% 21.48/4.33 thf(func_def_573, type, sK355: $i > ($i > $i > $o) > $i).
% 21.48/4.33 thf(func_def_586, type, sK368: $i > $i > $i).
% 21.48/4.33 thf(func_def_596, type, sK378: $i > $o).
% 21.48/4.33 thf(func_def_597, type, sK379: $i > $i).
% 21.48/4.33 thf(func_def_598, type, sK380: ($i > $o) > $i).
% 21.48/4.33 thf(func_def_603, type, sK385: $i > $i > $i).
% 21.48/4.33 thf(func_def_621, type, sK403: $i > $i > $i).
% 21.48/4.33 thf(func_def_622, type, sK404: $i > $i > $i).
% 21.48/4.33 thf(func_def_637, type, sK419: ($i > $o) > $i).
% 21.48/4.33 thf(func_def_638, type, sK420: $i > $o).
% 21.48/4.33 thf(func_def_639, type, sK421: $i > $i).
% 21.48/4.33 thf(func_def_646, type, sK428: $i > $o).
% 21.48/4.33 thf(func_def_649, type, sK431: $i > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_653, type, sK435: $i > $o).
% 21.48/4.33 thf(func_def_656, type, sK438: $i > ($i > $o) > $i).
% 21.48/4.33 thf(func_def_659, type, sK441: $i > $o).
% 21.48/4.33 thf(func_def_661, type, sK443: ($i > $o) > $i).
% 21.48/4.33 thf(func_def_662, type, sK444: ($i > $o) > $i).
% 21.48/4.33 thf(func_def_665, type, sK447: $i > $i > $i).
% 21.48/4.33 thf(func_def_666, type, sK448: $i > $i > $i).
% 21.48/4.33 thf(func_def_667, type, sK449: $i > $i > $i).
% 21.48/4.33 thf(func_def_668, type, sK450: $i > $i > $i).
% 21.48/4.33 thf(func_def_669, type, sK451: $i > $i > $i > $i).
% 21.48/4.33 thf(func_def_670, type, sK452: $i > $i).
% 21.48/4.33 thf(func_def_671, type, sK453: $i > $i).
% 21.48/4.33 thf(func_def_672, type, sK454: $i > $i).
% 21.48/4.33 thf(func_def_673, type, sK455: $i > $i).
% 21.48/4.33 thf(func_def_674, type, sK456: $i > $i > $i).
% 21.48/4.33 thf(func_def_675, type, sK457: $i > $i > $i > $i).
% 21.48/4.33 thf(func_def_676, type, sK458: $i > $i > $i > $i).
% 21.48/4.33 thf(func_def_677, type, sK459: $i > $i > $i).
% 21.48/4.33 thf(func_def_678, type, sK460: $i > $i > $i).
% 21.48/4.33 thf(func_def_680, type, sK462: $i > $i).
% 21.48/4.33 thf(func_def_681, type, sK463: $i > $i).
% 21.48/4.33 thf(func_def_682, type, sK464: $i > $i).
% 21.48/4.33 thf(func_def_683, type, sK465: $i > $i > $i).
% 21.48/4.33 thf(func_def_687, type, sK469: $i > $o).
% 21.48/4.33 thf(func_def_694, type, sK476: $i > $i).
% 21.48/4.33 thf(func_def_697, type, sK479: $i > $o).
% 21.48/4.33 thf(func_def_699, type, sK481: ($i > $o) > $i > $i).
% 21.48/4.33 thf(func_def_700, type, sK482: ($i > $o) > $i > $i).
% 21.48/4.33 thf(func_def_705, type, ph487: !>[X0: $tType]:(X0)).
% 21.48/4.33 thf(f16821,plain,(
% 21.48/4.33 $false),
% 21.48/4.33 inference(avatar_sat_refutation,[status(thm)],[f3931,f4977,f5343,f5626,f6236,f16820])).
% 21.48/4.33 thf(f16820,plain,(
% 21.48/4.33 ~spl486_308 | ~spl486_533 | ~spl486_609),
% 21.48/4.33 inference(avatar_contradiction_clause,[status(thm)],[f16819])).
% 21.48/4.33 thf(f16819,plain,(
% 21.48/4.33 $false | (~spl486_308 | ~spl486_533 | ~spl486_609)),
% 21.48/4.33 inference(subsumption_resolution,[status(thm)],[f16818,f1775])).
% 21.48/4.33 thf(f1775,plain,(
% 21.48/4.33 ($true != (in @ (ksnd @ sK80) @ sK81))),
% 21.48/4.33 inference(cnf_transformation,[status(thm)],[f893])).
% 21.48/4.33 thf(f893,plain,(
% 21.48/4.33 (powersetsubset = $true) & (symdiffIneg1 = $true) & (powersetAx = $true) & (notsubsetI = $true) & (cartprodmempair1 = $true) & (upairequniteq = $true) & (omega__Cong = $true) & (setextAx = $true) & (notdexE = $true) & (emptysetE = $true) & (noeltsimpempty = $true) & (subsetE = $true) & (sepSubset = $true) & (cartprodmempair = $true) & (eqimpsubset1 = $true) & (emptyinunitempty = $true) & (setadjoinAx = $true) & (binintersectSubset1 = $true) & (dsetconstrI = $true) & (emptysetimpfalse = $true) & (binintersectEL = $true) & (exu__Cong = $true) & (exuI3 = $true) & (setadjoinE = $true) & (setukpairinjL2 = $true) & (descr__Cong = $true) & (binunionRsub = $true) & (subPowSU = $true) & (setoftrueEq = $true) & (singletoninpowunion = $true) & (prop2set2propI = $true) & (ksndsingleton = $true) & (setunionsingleton = $true) & (exuI1 = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (emptyE1 = $true) & (setunionI = $true) & (setunionE2 = $true) & (setukpairIL = $true) & (setextsub = $true) & (subsetRefl = $true) & (bs114d = $true) & (foundationAx = $true) & (symdiffI2 = $true) & (setadjoinSub = $true) & (kpairsurjEq = $true) & (theprop = $true) & (setadjoin__Cong = $true) & (binintersectSubset4 = $true) & (upairinpowunion = $true) & (notinemptyset = $true) & (setukpairinjR2 = $true) & (nonemptyI1 = $true) & (setunion__Cong = $true) & (setminusEL = $true) & (powersetI = $true) & (quantDeMorgan4 = $true) & (setunionsingleton1 = $true) & (setukpairinjR12 = $true) & (kpairp = $true) & (setminusI = $true) & (upairset2IR = $true) & (setminusLsub = $true) & (((in @ sK80 @ (cartprod @ sK82 @ sK81)) = $true) & ($true != (in @ (ksnd @ sK80) @ sK81))) & (emptyInPowerset = $true) & (sepInPowerset = $true) & (omegaSAx = $true) & (setminusSubset2 = $true) & (subset2powerset = $true) & (upairsetIL = $true) & (kfstsingleton = $true) & (binintersectRsub = $true) & (descrp = $true) & (dsetconstr__Cong = $true) & (singletonsuniq = $true) & (exuEu = $true) & (setukpairinjR1 = $true) & (ex1I2 = $true) & (setminusIRneg = $true) & (ex1I = $true) & (setbeta = $true) & (emptyinPowerset = $true) & (exuE3u = $true) & (upairsetE = $true) & (setminusELneg = $true) & (setminusER = $true) & (setadjoinOr = $true) & (kfstpairEq = $true) & (setext = $true) & (ksndpairEq = $true) & (setminusERneg = $true) & (binintersectER = $true) & (ubforcartprodlem1 = $true) & (binintersectSubset3 = $true) & (in__Cong = $true) & (exuE3e = $true) & (kpairiskpair = $true) & (singletonsswitch = $true) & (binunionIR = $true) & (setunionE = $true) & (setunionsingleton2 = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (wellorderingAx = $true) & (binunionE = $true) & (subsetTrans = $true) & (setminusSubset1 = $true) & (omega0Ax = $true) & (subsetE2 = $true) & (eqimpsubset2 = $true) & (cartprodpairin = $true) & (singletonprop = $true) & (quantDeMorgan3 = $true) & (ex1E1 = $true) & (setukpairinjL1 = $true) & (vacuousDall = $true) & (powersetI1 = $true) & (binunionEcases = $true) & (cartprodfstin = $true) & (setadjoinIL = $true) & (setadjoinIR = $true) & (setukpairinjL = $true) & (binintersectLsub = $true) & (nonemptyE1 = $true) & (quantDeMorgan2 = $true) & (binintersectSubset2 = $true) & (subsetemptysetimpeq = $true) & (dsetconstrEL = $true) & (setukpairIR = $true) & (uniqinunit = $true) & (emptysetsubset = $true) & (powerset__Cong = $true) & (powersetE = $true) & (setunionAx = $true) & (prop2setE = $true) & (subsetI1 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (nonemptyImpWitness = $true) & (ubforcartprodlem2 = $true) & (upairsetIR = $true) & (upairsubunion = $true) & (quantDeMorgan1 = $true) & (notequalI2 = $true) & (subsetI2 = $true) & (emptysetAx = $true) & (disjointsetsI1 = $true) & (notdallE = $true) & (binunionIL = $true) & (prop2setI = $true) & (binintersectSubset5 = $true) & (exuE2 = $true) & (inCongP = $true) & (binintersectI = $true) & (setadjoinSub2 = $true) & (secondinupair = $true) & (setminusILneg = $true) & (setukpairinjR = $true) & (binunionLsub = $true) & (notequalI1 = $true) & (powersetE1 = $true) & (omegaIndAx = $true) & (notinsingleton = $true) & (exuI2 = $true) & (upairset2E = $true) & (emptyset__Cong = $true) & (replAx = $true) & (ubforcartprodlem3 = $true) & (nonemptyI = $true) & (setukpairinjR11 = $true) & (eqinunit = $true) & (emptyI = $true) & (symdiffIneg2 = $true) & (inPowerset = $true)),
% 21.48/4.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK80,sK81,sK82])],[f604,f892])).
% 21.48/4.33 thf(f892,plain,(
% 21.48/4.33 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X2 @ X1))) & ($true != (in @ (ksnd @ X0) @ X1))) => (((in @ sK80 @ (cartprod @ sK82 @ sK81)) = $true) & ($true != (in @ (ksnd @ sK80) @ sK81)))),
% 21.48/4.33 introduced(definition,[],[choice_axiom])).
% 21.48/4.33 thf(f604,plain,(
% 21.48/4.33 (powersetsubset = $true) & (symdiffIneg1 = $true) & (powersetAx = $true) & (notsubsetI = $true) & (cartprodmempair1 = $true) & (upairequniteq = $true) & (omega__Cong = $true) & (setextAx = $true) & (notdexE = $true) & (emptysetE = $true) & (noeltsimpempty = $true) & (subsetE = $true) & (sepSubset = $true) & (cartprodmempair = $true) & (eqimpsubset1 = $true) & (emptyinunitempty = $true) & (setadjoinAx = $true) & (binintersectSubset1 = $true) & (dsetconstrI = $true) & (emptysetimpfalse = $true) & (binintersectEL = $true) & (exu__Cong = $true) & (exuI3 = $true) & (setadjoinE = $true) & (setukpairinjL2 = $true) & (descr__Cong = $true) & (binunionRsub = $true) & (subPowSU = $true) & (setoftrueEq = $true) & (singletoninpowunion = $true) & (prop2set2propI = $true) & (ksndsingleton = $true) & (setunionsingleton = $true) & (exuI1 = $true) & (singletoninpowerset = $true) & (singletonsubset = $true) & (emptyE1 = $true) & (setunionI = $true) & (setunionE2 = $true) & (setukpairIL = $true) & (setextsub = $true) & (subsetRefl = $true) & (bs114d = $true) & (foundationAx = $true) & (symdiffI2 = $true) & (setadjoinSub = $true) & (kpairsurjEq = $true) & (theprop = $true) & (setadjoin__Cong = $true) & (binintersectSubset4 = $true) & (upairinpowunion = $true) & (notinemptyset = $true) & (setukpairinjR2 = $true) & (nonemptyI1 = $true) & (setunion__Cong = $true) & (setminusEL = $true) & (powersetI = $true) & (quantDeMorgan4 = $true) & (setunionsingleton1 = $true) & (setukpairinjR12 = $true) & (kpairp = $true) & (setminusI = $true) & (upairset2IR = $true) & (setminusLsub = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X2 @ X1))) & ($true != (in @ (ksnd @ X0) @ X1))) & (emptyInPowerset = $true) & (sepInPowerset = $true) & (omegaSAx = $true) & (setminusSubset2 = $true) & (subset2powerset = $true) & (upairsetIL = $true) & (kfstsingleton = $true) & (binintersectRsub = $true) & (descrp = $true) & (dsetconstr__Cong = $true) & (singletonsuniq = $true) & (exuEu = $true) & (setukpairinjR1 = $true) & (ex1I2 = $true) & (setminusIRneg = $true) & (ex1I = $true) & (setbeta = $true) & (emptyinPowerset = $true) & (exuE3u = $true) & (upairsetE = $true) & (setminusELneg = $true) & (setminusER = $true) & (setadjoinOr = $true) & (kfstpairEq = $true) & (setext = $true) & (ksndpairEq = $true) & (setminusERneg = $true) & (binintersectER = $true) & (ubforcartprodlem1 = $true) & (binintersectSubset3 = $true) & (in__Cong = $true) & (exuE3e = $true) & (kpairiskpair = $true) & (singletonsswitch = $true) & (binunionIR = $true) & (setunionE = $true) & (setunionsingleton2 = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (wellorderingAx = $true) & (binunionE = $true) & (subsetTrans = $true) & (setminusSubset1 = $true) & (omega0Ax = $true) & (subsetE2 = $true) & (eqimpsubset2 = $true) & (cartprodpairin = $true) & (singletonprop = $true) & (quantDeMorgan3 = $true) & (ex1E1 = $true) & (setukpairinjL1 = $true) & (vacuousDall = $true) & (powersetI1 = $true) & (binunionEcases = $true) & (cartprodfstin = $true) & (setadjoinIL = $true) & (setadjoinIR = $true) & (setukpairinjL = $true) & (binintersectLsub = $true) & (nonemptyE1 = $true) & (quantDeMorgan2 = $true) & (binintersectSubset2 = $true) & (subsetemptysetimpeq = $true) & (dsetconstrEL = $true) & (setukpairIR = $true) & (uniqinunit = $true) & (emptysetsubset = $true) & (powerset__Cong = $true) & (powersetE = $true) & (setunionAx = $true) & (prop2setE = $true) & (subsetI1 = $true) & (symdiffI1 = $true) & (symdiffE = $true) & (nonemptyImpWitness = $true) & (ubforcartprodlem2 = $true) & (upairsetIR = $true) & (upairsubunion = $true) & (quantDeMorgan1 = $true) & (notequalI2 = $true) & (subsetI2 = $true) & (emptysetAx = $true) & (disjointsetsI1 = $true) & (notdallE = $true) & (binunionIL = $true) & (prop2setI = $true) & (binintersectSubset5 = $true) & (exuE2 = $true) & (inCongP = $true) & (binintersectI = $true) & (setadjoinSub2 = $true) & (secondinupair = $true) & (setminusILneg = $true) & (setukpairinjR = $true) & (binunionLsub = $true) & (notequalI1 = $true) & (powersetE1 = $true) & (omegaIndAx = $true) & (notinsingleton = $true) & (exuI2 = $true) & (upairset2E = $true) & (emptyset__Cong = $true) & (replAx = $true) & (ubforcartprodlem3 = $true) & (nonemptyI = $true) & (setukpairinjR11 = $true) & (eqinunit = $true) & (emptyI = $true) & (symdiffIneg2 = $true) & (inPowerset = $true)),
% 21.48/4.33 inference(flattening,[status(thm)],[f603])).
% 21.48/4.33 thf(f603,plain,(
% 21.48/4.33 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X2 @ X1))) & ($true != (in @ (ksnd @ X0) @ X1))) & (kpairsurjEq = $true)) & (ksndpairEq = $true)) & (ksndsingleton = $true)) & (setukpairinjR = $true)) & (setukpairinjR2 = $true)) & (upairequniteq = $true)) & (setukpairinjR1 = $true)) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 21.48/4.33 inference(ennf_transformation,[status(thm)],[f429])).
% 21.48/4.33 thf(f429,plain,(
% 21.48/4.33 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ((setukpairinjR1 = $true) => ((upairequniteq = $true) => ((setukpairinjR2 = $true) => ((setukpairinjR = $true) => ((ksndsingleton = $true) => ((ksndpairEq = $true) => ((kpairsurjEq = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X2 @ X1))) => ($true = (in @ (ksnd @ X0) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 21.48/4.33 inference(fool_elimination,[status(thm)],[f428])).
% 21.48/4.33 thf(f428,plain,(
% 21.48/4.33 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X2 @ X1)) => (in @ (ksnd @ X0) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 21.48/4.33 inference(rectify,[status(thm)],[f180])).
% 21.48/4.33 thf(f180,negated_conjecture,(
% 21.48/4.33 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => ! [X10 : $i,X4 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (ksnd @ X10) @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 21.48/4.33 inference(negated_conjecture,[status(cth)],[f179])).
% 21.48/4.33 thf(f179,conjecture,(
% 21.48/4.33 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => (setukpairinjR1 => (upairequniteq => (setukpairinjR2 => (setukpairinjR => (ksndsingleton => (ksndpairEq => (kpairsurjEq => ! [X10 : $i,X4 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (ksnd @ X10) @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 21.48/4.33 file('/export/starexec/sandbox2/tmp/tmp.PjEOTGotWI/DTF2THF_13158.p',cartprodsndin)).
% 21.48/4.33 thf(f16818,plain,(
% 21.48/4.33 ($true = (in @ (ksnd @ sK80) @ sK81)) | (~spl486_308 | ~spl486_533 | ~spl486_609)),
% 21.48/4.33 inference(backward_demodulation,[status(thm)],[f10878,f16800])).
% 21.48/4.33 thf(f16800,plain,(
% 21.48/4.33 ((sK108 @ sK82 @ sK81 @ sK80) = (ksnd @ sK80)) | (~spl486_533 | ~spl486_609)),
% 21.48/4.33 inference(superposition,[status(thm)],[f5342,f11948])).
% 21.48/4.33 thf(f11948,plain,(
% 21.48/4.33 (sK80 = (kpair @ (sK107 @ sK82 @ sK81 @ sK80) @ (sK108 @ sK82 @ sK81 @ sK80))) | ~spl486_533),
% 21.48/4.33 inference(trivial_inequality_removal,[status(thm)],[f11931])).
% 21.48/4.33 thf(f11931,plain,(
% 21.48/4.33 ($true != $true) | (sK80 = (kpair @ (sK107 @ sK82 @ sK81 @ sK80) @ (sK108 @ sK82 @ sK81 @ sK80))) | ~spl486_533),
% 21.48/4.33 inference(superposition,[status(thm)],[f4976,f1776])).
% 21.48/4.33 thf(f1776,plain,(
% 21.48/4.33 ((in @ sK80 @ (cartprod @ sK82 @ sK81)) = $true)),
% 21.48/4.33 inference(cnf_transformation,[status(thm)],[f893])).
% 21.48/4.33 thf(f4976,plain,(
% 21.48/4.33 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ((kpair @ (sK107 @ X7 @ X6 @ X5) @ (sK108 @ X7 @ X6 @ X5)) = X5)) ) | ~spl486_533),
% 21.48/4.33 inference(avatar_component_clause,[status(thm)],[f4975])).
% 21.48/4.33 thf(f4975,definition,(
% 21.48/4.33 spl486_533 <=> ! [X6 : $i,X5 : $i,X7 : $i] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ((kpair @ (sK107 @ X7 @ X6 @ X5) @ (sK108 @ X7 @ X6 @ X5)) = X5))),
% 21.48/4.33 introduced(definition,[new_symbols(naming,[spl486_533])],[avatar_definition])).
% 21.48/4.33 thf(f5342,plain,(
% 21.48/4.33 ( ! [X2 : $i,X3 : $i] : (((ksnd @ (kpair @ X2 @ X3)) = X3)) ) | ~spl486_609),
% 21.48/4.33 inference(avatar_component_clause,[status(thm)],[f5341])).
% 21.48/4.33 thf(f5341,definition,(
% 21.48/4.33 spl486_609 <=> ! [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X2 @ X3)) = X3)),
% 21.48/4.33 introduced(definition,[new_symbols(naming,[spl486_609])],[avatar_definition])).
% 21.48/4.33 thf(f10878,plain,(
% 21.48/4.33 ((in @ (sK108 @ sK82 @ sK81 @ sK80) @ sK81) = $true) | ~spl486_308),
% 21.48/4.33 inference(trivial_inequality_removal,[status(thm)],[f10857])).
% 21.48/4.33 thf(f10857,plain,(
% 21.48/4.33 ((in @ (sK108 @ sK82 @ sK81 @ sK80) @ sK81) = $true) | ($true != $true) | ~spl486_308),
% 21.48/4.33 inference(superposition,[status(thm)],[f3930,f1776])).
% 21.48/4.33 thf(f3930,plain,(
% 21.48/4.33 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | ((in @ (sK108 @ X7 @ X6 @ X5) @ X6) = $true)) ) | ~spl486_308),
% 21.48/4.33 inference(avatar_component_clause,[status(thm)],[f3929])).
% 21.48/4.33 thf(f3929,definition,(
% 21.48/4.33 spl486_308 <=> ! [X6 : $i,X5 : $i,X7 : $i] : (((in @ (sK108 @ X7 @ X6 @ X5) @ X6) = $true) | ($true != (in @ X5 @ (cartprod @ X7 @ X6))))),
% 21.48/4.33 introduced(definition,[new_symbols(naming,[spl486_308])],[avatar_definition])).
% 21.48/4.33 thf(f6236,plain,(
% 21.48/4.33 spl486_604),
% 21.48/4.33 inference(avatar_split_clause,[status(thm)],[f1749,f5317])).
% 21.48/4.33 thf(f5317,definition,(
% 21.48/4.33 spl486_604 <=> (ksndpairEq = $true)),
% 21.48/4.33 introduced(definition,[new_symbols(naming,[spl486_604])],[avatar_definition])).
% 21.48/4.33 thf(f1749,plain,(
% 21.48/4.33 (ksndpairEq = $true)),
% 21.48/4.33 inference(cnf_transformation,[status(thm)],[f893])).
% 21.48/4.33 thf(f5626,plain,(
% 21.48/4.33 spl486_168),
% 21.48/4.33 inference(avatar_split_clause,[status(thm)],[f1836,f3293])).
% 21.48/4.33 thf(f3293,definition,(
% 21.48/4.33 spl486_168 <=> (cartprodmempair1 = $true)),
% 21.48/4.33 introduced(definition,[new_symbols(naming,[spl486_168])],[avatar_definition])).
% 21.48/4.33 thf(f1836,plain,(
% 21.48/4.33 (cartprodmempair1 = $true)),
% 21.48/4.33 inference(cnf_transformation,[status(thm)],[f893])).
% 21.48/4.33 thf(f5343,plain,(
% 21.48/4.33 spl486_609 | ~spl486_604),
% 21.48/4.33 inference(avatar_split_clause,[status(thm)],[f2286,f5317,f5341])).
% 21.48/4.33 thf(f2286,plain,(
% 21.48/4.33 ( ! [X2 : $i,X3 : $i] : (((ksnd @ (kpair @ X2 @ X3)) = X3) | (ksndpairEq != $true)) )),
% 21.48/4.33 inference(cnf_transformation,[status(thm)],[f1432])).
% 21.48/4.33 thf(f1432,plain,(
% 21.48/4.33 ((ksndpairEq = $true) | ((ksnd @ (kpair @ sK411 @ sK412)) != sK412)) & (! [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X2 @ X3)) = X3) | (ksndpairEq != $true))),
% 21.48/4.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK411,sK412])],[f1430,f1431])).
% 21.48/4.33 thf(f1431,plain,(
% 21.48/4.33 ? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) != X1) => ((ksnd @ (kpair @ sK411 @ sK412)) != sK412)),
% 21.48/4.33 introduced(definition,[],[choice_axiom])).
% 21.48/4.33 thf(f1430,plain,(
% 21.48/4.33 ((ksndpairEq = $true) | ? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) != X1)) & (! [X2 : $i,X3 : $i] : ((ksnd @ (kpair @ X2 @ X3)) = X3) | (ksndpairEq != $true))),
% 21.48/4.33 inference(rectify,[status(thm)],[f1429])).
% 21.48/4.33 thf(f1429,plain,(
% 21.48/4.33 ((ksndpairEq = $true) | ? [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) != X1)) & (! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1) | (ksndpairEq != $true))),
% 21.48/4.33 inference(nnf_transformation,[status(thm)],[f211])).
% 21.48/4.33 thf(f211,plain,(
% 21.48/4.33 (ksndpairEq = $true) <=> ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1)),
% 21.48/4.33 inference(fool_elimination,[status(thm)],[f210])).
% 21.48/4.33 thf(f210,plain,(
% 21.48/4.33 (ksndpairEq = ! [X0 : $i,X1 : $i] : ((ksnd @ (kpair @ X0 @ X1)) = X1))),
% 21.48/4.33 inference(rectify,[status(thm)],[f177])).
% 21.48/4.33 thf(f177,axiom,(
% 21.48/4.33 (ksndpairEq = ! [X1 : $i,X2 : $i] : ((ksnd @ (kpair @ X1 @ X2)) = X2))),
% 21.48/4.33 file('/export/starexec/sandbox2/tmp/tmp.PjEOTGotWI/DTF2THF_13158.p',ksndpairEq)).
% 21.48/4.33 thf(f4977,plain,(
% 21.48/4.33 spl486_533 | ~spl486_168),
% 21.48/4.33 inference(avatar_split_clause,[status(thm)],[f1866,f3293,f4975])).
% 21.48/4.33 thf(f1866,plain,(
% 21.48/4.33 ( ! [X6 : $i,X7 : $i,X5 : $i] : (($true != (in @ X5 @ (cartprod @ X7 @ X6))) | (cartprodmempair1 != $true) | ((kpair @ (sK107 @ X7 @ X6 @ X5) @ (sK108 @ X7 @ X6 @ X5)) = X5)) )),
% 21.48/4.33 inference(cnf_transformation,[status(thm)],[f929])).
% 21.48/4.33 thf(f929,plain,(
% 21.48/4.33 ((cartprodmempair1 = $true) | (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ sK105)) | (sK104 != (kpair @ X3 @ X4))) | ($true != (in @ X3 @ sK106))) & ((in @ sK104 @ (cartprod @ sK106 @ sK105)) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : (((((in @ (sK108 @ X7 @ X6 @ X5) @ X6) = $true) & ((kpair @ (sK107 @ X7 @ X6 @ X5) @ (sK108 @ X7 @ X6 @ X5)) = X5)) & ($true = (in @ (sK107 @ X7 @ X6 @ X5) @ X7))) | ($true != (in @ X5 @ (cartprod @ X7 @ X6)))) | (cartprodmempair1 != $true))),
% 21.48/4.33 inference(skolemisation,[status(esa),new_symbols(skolem,[sK104,sK105,sK106,sK107,sK108])],[f925,f928,f927,f926])).
% 21.48/4.33 thf(f926,plain,(
% 21.48/4.33 ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X1) != $true) | ((kpair @ X3 @ X4) != X0)) | ($true != (in @ X3 @ X2))) & ($true = (in @ X0 @ (cartprod @ X2 @ X1)))) => (! [X3 : $i] : (! [X4 : $i] : (($true != (in @ X4 @ sK105)) | (sK104 != (kpair @ X3 @ X4))) | ($true != (in @ X3 @ sK106))) & ((in @ sK104 @ (cartprod @ sK106 @ sK105)) = $true))),
% 21.48/4.33 introduced(definition,[],[choice_axiom])).
% 21.48/4.33 thf(f927,plain,(
% 21.48/4.33 ! [X5 : $i,X6 : $i,X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ X6)) & ((kpair @ X8 @ X9) = X5)) & ($true = (in @ X8 @ X7))) => (? [X9 : $i] : (($true = (in @ X9 @ X6)) & ((kpair @ (sK107 @ X7 @ X6 @ X5) @ X9) = X5)) & ($true = (in @ (sK107 @ X7 @ X6 @ X5) @ X7))))),
% 21.48/4.33 introduced(definition,[],[choice_axiom])).
% 21.48/4.33 thf(f928,plain,(
% 21.48/4.33 ! [X5 : $i,X6 : $i,X7 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ X6)) & ((kpair @ (sK107 @ X7 @ X6 @ X5) @ X9) = X5)) => (((in @ (sK108 @ X7 @ X6 @ X5) @ X6) = $true) & ((kpair @ (sK107 @ X7 @ X6 @ X5) @ (sK108 @ X7 @ X6 @ X5)) = X5)))),
% 21.48/4.33 introduced(definition,[],[choice_axiom])).
% 21.48/4.33 thf(f925,plain,(
% 21.48/4.33 ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X1) != $true) | ((kpair @ X3 @ X4) != X0)) | ($true != (in @ X3 @ X2))) & ($true = (in @ X0 @ (cartprod @ X2 @ X1))))) & (! [X5 : $i,X6 : $i,X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : (($true = (in @ X9 @ X6)) & ((kpair @ X8 @ X9) = X5)) & ($true = (in @ X8 @ X7))) | ($true != (in @ X5 @ (cartprod @ X7 @ X6)))) | (cartprodmempair1 != $true))),
% 21.48/4.33 inference(rectify,[status(thm)],[f924])).
% 21.48/4.33 thf(f924,plain,(
% 21.48/4.33 ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((in @ X4 @ X1) != $true) | ((kpair @ X3 @ X4) != X0)) | ($true != (in @ X3 @ X2))) & ($true = (in @ X0 @ (cartprod @ X2 @ X1))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ X1) = $true) & ((kpair @ X3 @ X4) = X0)) & ($true = (in @ X3 @ X2))) | ($true != (in @ X0 @ (cartprod @ X2 @ X1)))) | (cartprodmempair1 != $true))),
% 21.48/4.33 inference(nnf_transformation,[status(thm)],[f598])).
% 21.48/4.33 thf(f598,plain,(
% 21.48/4.33 (cartprodmempair1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ X1) = $true) & ((kpair @ X3 @ X4) = X0)) & ($true = (in @ X3 @ X2))) | ($true != (in @ X0 @ (cartprod @ X2 @ X1))))),
% 21.48/4.33 inference(ennf_transformation,[status(thm)],[f521])).
% 21.48/4.33 thf(f521,plain,(
% 21.48/4.33 (cartprodmempair1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X2 @ X1))) => ? [X3 : $i] : (? [X4 : $i] : (((in @ X4 @ X1) = $true) & ((kpair @ X3 @ X4) = X0)) & ($true = (in @ X3 @ X2))))),
% 21.48/4.33 inference(fool_elimination,[status(thm)],[f520])).
% 21.48/4.33 thf(f520,plain,(
% 21.48/4.33 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X2 @ X1)) => ? [X3 : $i] : (? [X4 : $i] : ((in @ X4 @ X1) & ((kpair @ X3 @ X4) = X0)) & (in @ X3 @ X2))) = cartprodmempair1)),
% 21.48/4.33 inference(rectify,[status(thm)],[f150])).
% 21.48/4.33 thf(f150,axiom,(
% 21.48/4.33 (! [X10 : $i,X4 : $i,X3 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ? [X1 : $i] : (? [X2 : $i] : ((in @ X2 @ X4) & ((kpair @ X1 @ X2) = X10)) & (in @ X1 @ X3))) = cartprodmempair1)),
% 21.48/4.33 file('/export/starexec/sandbox2/tmp/tmp.PjEOTGotWI/DTF2THF_13158.p',cartprodmempair1)).
% 21.48/4.33 thf(f3931,plain,(
% 21.48/4.33 ~spl486_168 | spl486_308),
% 21.48/4.33 inference(avatar_split_clause,[status(thm)],[f1867,f3929,f3293])).
% 21.48/4.33 thf(f1867,plain,(
% 21.48/4.33 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ (sK108 @ X7 @ X6 @ X5) @ X6) = $true) | ($true != (in @ X5 @ (cartprod @ X7 @ X6))) | (cartprodmempair1 != $true)) )),
% 21.48/4.33 inference(cnf_transformation,[status(thm)],[f929])).
% 21.48/4.33 % SZS output end Proof for DTF2THF_13158
% 21.48/4.33 % (13552)------------------------------
% 21.48/4.33 % (13552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.48/4.33 % (13552)Termination reason: Refutation
% 21.48/4.33
% 21.48/4.33 % (13552)Memory used [KB]: 17014
% 21.48/4.33 % (13552)Time elapsed: 1.029 s
% 21.48/4.33 % (13552)Instructions burned: 3181 (million)
% 21.48/4.33 % (13552)------------------------------
% 21.48/4.33 % (13552)------------------------------
% 21.48/4.33 % (13430)Success in time 2.812 s
%------------------------------------------------------------------------------