%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU593^1 : 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 : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:28 AM UTC 2026
% Result : Theorem 15.74s 3.64s
% Output : Refutation 15.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 18
% Syntax : Number of formulae : 83 ( 19 unt; 0 typ; 8 def)
% Number of atoms : 2330 ( 649 equ; 0 cnn)
% Maximal formula atoms : 111 ( 28 avg)
% Number of connectives : 1439 ( 130 ~; 103 |; 369 &; 358 @)
% ( 18 <=>; 461 =>; 0 <=; 0 <~>)
% Maximal formula depth : 116 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 242 ( 239 usr; 130 con; 0-4 aty)
% Number of variables : 137 ( 0 ^; 104 !; 33 ?; 137 :)
% 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_140,type,
sP1: $i > $i > $o ).
thf(func_def_141,type,
sP2: $i > $o ).
thf(func_def_142,type,
sP3: $i > $i > $o ).
thf(func_def_143,type,
sP4: $i > $i > $o ).
thf(func_def_147,type,
sK8: $i > $o ).
thf(func_def_148,type,
sK9: $i > $i ).
thf(func_def_149,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_151,type,
sK12: $i > $o ).
thf(func_def_153,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_154,type,
sK15: $i > $o ).
thf(func_def_155,type,
sK16: $i > $o ).
thf(func_def_156,type,
sK17: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_157,type,
sK18: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_163,type,
sK24: $o > $i > $i > $i ).
thf(func_def_166,type,
sK27: $i > $o ).
thf(func_def_168,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_173,type,
sK34: $i > $i ).
thf(func_def_191,type,
sK52: $i > $o ).
thf(func_def_193,type,
sK54: $i > $o ).
thf(func_def_195,type,
sK56: $i > ( $i > $o ) > $i ).
thf(func_def_196,type,
sK57: $i > $o ).
thf(func_def_198,type,
sK59: $i > ( $i > $o ) > $i ).
thf(func_def_199,type,
sK60: $i > ( $i > $o ) > $i ).
thf(func_def_200,type,
sK61: $i > $o ).
thf(func_def_207,type,
sK68: $i > $o ).
thf(func_def_209,type,
sK70: $i > $o ).
thf(func_def_219,type,
sK80: $i > $i > $i ).
thf(func_def_223,type,
sK84: $i > $o ).
thf(func_def_229,type,
sK90: $i > $o ).
thf(func_def_232,type,
sK93: $i > $i ).
thf(func_def_241,type,
sK102: $i > $i > $o ).
thf(func_def_242,type,
sK103: $i > $i ).
thf(func_def_243,type,
sK104: $i > $i ).
thf(func_def_244,type,
sK105: ( $i > $i > $o ) > $i > $i ).
thf(func_def_245,type,
sK106: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_246,type,
sK107: ( $i > $i > $o ) > $i > $i ).
thf(func_def_247,type,
sK108: $i > $o ).
thf(func_def_258,type,
sK119: $i > $i ).
thf(func_def_260,type,
sK121: $i > $o ).
thf(func_def_262,type,
sK123: ( $i > $o ) > $i ).
thf(func_def_263,type,
sK124: ( $i > $o ) > $i ).
thf(func_def_280,type,
sK141: $i > $i ).
thf(func_def_288,type,
sK149: $i > $o ).
thf(func_def_292,type,
sK153: $i > $o ).
thf(func_def_294,type,
sK155: $i > $o ).
thf(func_def_295,type,
sK156: $i > $o ).
thf(func_def_296,type,
sK157: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_297,type,
sK158: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_314,type,
sK175: $i > $i > $i ).
thf(func_def_315,type,
sK176: $i > $i > $i ).
thf(func_def_322,type,
sK183: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_323,type,
sK184: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_326,type,
sK187: $i > $o ).
thf(func_def_327,type,
sK188: $i > $o ).
thf(func_def_328,type,
sK189: $i > $o ).
thf(func_def_333,type,
sK194: $i > $o ).
thf(func_def_334,type,
sK195: $i > $i > $i ).
thf(func_def_340,type,
sK201: $i > $i ).
thf(func_def_341,type,
sK202: $i > $i > $i ).
thf(func_def_349,type,
sK210: $i > $i > $i ).
thf(func_def_359,type,
sK220: $i > $o ).
thf(func_def_365,type,
sK226: $i > ( $i > $o ) > $i ).
thf(func_def_366,type,
sK227: $i > $o ).
thf(func_def_369,type,
sK230: ( $i > $o ) > $i ).
thf(func_def_370,type,
sK231: $i > $o ).
thf(func_def_371,type,
sK232: $i > $i ).
thf(func_def_378,type,
sK239: $i > $i > $i ).
thf(func_def_382,type,
sK243: $i > $i > $i ).
thf(func_def_387,type,
sK248: $i > ( $i > $o ) > $i ).
thf(func_def_388,type,
sK249: $i > $o ).
thf(func_def_391,type,
sK252: ( $i > $o ) > $i ).
thf(func_def_392,type,
sK253: $i > $o ).
thf(func_def_393,type,
sK254: $i > $i ).
thf(func_def_395,type,
sK256: $i > $i ).
thf(func_def_397,type,
sK258: $i > $i > $i ).
thf(func_def_398,type,
sK259: $i > $i > $i ).
thf(func_def_399,type,
sK260: $i > $i > $i ).
thf(func_def_400,type,
sK261: $i > $i > $i ).
thf(func_def_401,type,
sK262: $i > $i > $i > $i ).
thf(func_def_402,type,
sK263: $i > $i ).
thf(func_def_403,type,
sK264: $i > $i ).
thf(func_def_404,type,
sK265: $i > $i ).
thf(func_def_405,type,
sK266: $i > $i ).
thf(func_def_406,type,
sK267: $i > $i > $i ).
thf(func_def_407,type,
sK268: $i > $i > $i > $i ).
thf(func_def_408,type,
sK269: $i > $i > $i > $i ).
thf(func_def_409,type,
sK270: $i > $i > $i ).
thf(func_def_410,type,
sK271: $i > $i > $i ).
thf(func_def_411,type,
sK272: $i > $i ).
thf(func_def_412,type,
sK273: $i > $i > $i ).
thf(func_def_414,type,
sK275: $i > $i ).
thf(func_def_415,type,
sK276: $i > $i ).
thf(func_def_431,type,
sK292: ( $i > $o ) > $i > $i ).
thf(func_def_433,type,
sK294: $i > $o ).
thf(func_def_439,type,
sK300: $i > $o ).
thf(func_def_442,type,
ph303:
!>[X0: $tType] : X0 ).
thf(f7871,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1983,f3011,f3461,f3606,f3694,f3845,f4018,f4019,f7870]) ).
thf(f7870,plain,
( ~ spl302_71
| ~ spl302_183
| ~ spl302_299
| ~ spl302_438 ),
inference(avatar_contradiction_clause,[status(thm)],[f7869]) ).
thf(f7869,plain,
( $false
| ~ spl302_71
| ~ spl302_183
| ~ spl302_299
| ~ spl302_438 ),
inference(subsumption_resolution,[status(thm)],[f7868,f3693]) ).
thf(f3693,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ~ spl302_438 ),
inference(avatar_component_clause,[status(thm)],[f3692]) ).
thf(f3692,definition,
( spl302_438
<=> ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl302_438])],[avatar_definition]) ).
thf(f7868,plain,
( ( ( subset @ ( binintersect @ sK88 @ sK87 ) @ sK88 )
!= $true )
| ~ spl302_71
| ~ spl302_183
| ~ spl302_299 ),
inference(subsumption_resolution,[status(thm)],[f7865,f1188]) ).
thf(f1188,plain,
( ( binintersect @ sK88 @ sK87 )
!= sK88 ),
inference(cnf_transformation,[status(thm)],[f627]) ).
thf(f627,plain,
( ( prop2setE = $true )
& ( omegaSAx = $true )
& ( setunionE = $true )
& ( omegaIndAx = $true )
& ( emptyinPowerset = $true )
& ( notequalI1 = $true )
& ( setunionAx = $true )
& ( eqimpsubset2 = $true )
& ( nonemptyI1 = $true )
& ( emptyInPowerset = $true )
& ( sepInPowerset = $true )
& ( powersetI1 = $true )
& ( emptyinunitempty = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( emptyI = $true )
& ( sepSubset = $true )
& ( quantDeMorgan4 = $true )
& ( emptyE1 = $true )
& ( setadjoin__Cong = $true )
& ( setunionI = $true )
& ( dsetconstrI = $true )
& ( inCongP = $true )
& ( vacuousDall = $true )
& ( upairset2IR = $true )
& ( emptyset__Cong = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( exu__Cong = $true )
& ( binunionEcases = $true )
& ( ( binintersect @ sK88 @ sK87 )
!= sK88 )
& ( ( subset @ sK88 @ sK87 )
= $true )
& ( subsetRefl = $true )
& ( binunionE = $true )
& ( subsetTrans = $true )
& ( binunionIL = $true )
& ( setadjoinSub2 = $true )
& ( exuE1 = $true )
& ( notequalI2 = $true )
& ( emptysetAx = $true )
& ( powersetE = $true )
& ( omega__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( dsetconstrER = $true )
& ( setextsub = $true )
& ( quantDeMorgan2 = $true )
& ( binintersectLsub = $true )
& ( noeltsimpempty = $true )
& ( foundationAx = $true )
& ( prop2setI = $true )
& ( subset2powerset = $true )
& ( exuEu = $true )
& ( exuI2 = $true )
& ( binintersectEL = $true )
& ( descr__Cong = $true )
& ( replAx = $true )
& ( setadjoinAx = $true )
& ( subsetI1 = $true )
& ( eqinunit = $true )
& ( prop2set2propI = $true )
& ( omega0Ax = $true )
& ( setadjoinIL = $true )
& ( setadjoinOr = $true )
& ( in__Cong = $true )
& ( binunionLsub = $true )
& ( setadjoinSub = $true )
& ( upairsetE = $true )
& ( upairsetIR = $true )
& ( nonemptyI = $true )
& ( singletonsswitch = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( dsetconstr__Cong = $true )
& ( binunionIR = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinE = $true )
& ( powersetI = $true )
& ( emptysetsubset = $true )
& ( setbeta = $true )
& ( upairsetIL = $true )
& ( exuE3u = $true )
& ( nonemptyE1 = $true )
& ( inPowerset = $true )
& ( subPowSU = $true )
& ( subsetE2 = $true )
& ( notsubsetI = $true )
& ( setoftrueEq = $true )
& ( exuI3 = $true )
& ( binunionRsub = $true )
& ( eqimpsubset1 = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( subsetI2 = $true )
& ( exuE2 = $true )
& ( setadjoinIR = $true )
& ( setext = $true )
& ( notdexE = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( notinsingleton = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( dsetconstrEL = $true )
& ( uniqinunit = $true )
& ( wellorderingAx = $true )
& ( emptysetE = $true )
& ( subsetemptysetimpeq = $true )
& ( subsetE = $true )
& ( nonemptyImpWitness = $true )
& ( powersetsubset = $true )
& ( powerset__Cong = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK87,sK88])],[f449,f626]) ).
thf(f626,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
!= X1 )
& ( $true
= ( subset @ X1 @ X0 ) ) )
=> ( ( ( binintersect @ sK88 @ sK87 )
!= sK88 )
& ( ( subset @ sK88 @ sK87 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f449,plain,
( ( prop2setE = $true )
& ( omegaSAx = $true )
& ( setunionE = $true )
& ( omegaIndAx = $true )
& ( emptyinPowerset = $true )
& ( notequalI1 = $true )
& ( setunionAx = $true )
& ( eqimpsubset2 = $true )
& ( nonemptyI1 = $true )
& ( emptyInPowerset = $true )
& ( sepInPowerset = $true )
& ( powersetI1 = $true )
& ( emptyinunitempty = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( emptyI = $true )
& ( sepSubset = $true )
& ( quantDeMorgan4 = $true )
& ( emptyE1 = $true )
& ( setadjoin__Cong = $true )
& ( setunionI = $true )
& ( dsetconstrI = $true )
& ( inCongP = $true )
& ( vacuousDall = $true )
& ( upairset2IR = $true )
& ( emptyset__Cong = $true )
& ( powersetE1 = $true )
& ( powersetAx = $true )
& ( exu__Cong = $true )
& ( binunionEcases = $true )
& ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
!= X1 )
& ( $true
= ( subset @ X1 @ X0 ) ) )
& ( subsetRefl = $true )
& ( binunionE = $true )
& ( subsetTrans = $true )
& ( binunionIL = $true )
& ( setadjoinSub2 = $true )
& ( exuE1 = $true )
& ( notequalI2 = $true )
& ( emptysetAx = $true )
& ( powersetE = $true )
& ( omega__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( dsetconstrER = $true )
& ( setextsub = $true )
& ( quantDeMorgan2 = $true )
& ( binintersectLsub = $true )
& ( noeltsimpempty = $true )
& ( foundationAx = $true )
& ( prop2setI = $true )
& ( subset2powerset = $true )
& ( exuEu = $true )
& ( exuI2 = $true )
& ( binintersectEL = $true )
& ( descr__Cong = $true )
& ( replAx = $true )
& ( setadjoinAx = $true )
& ( subsetI1 = $true )
& ( eqinunit = $true )
& ( prop2set2propI = $true )
& ( omega0Ax = $true )
& ( setadjoinIL = $true )
& ( setadjoinOr = $true )
& ( in__Cong = $true )
& ( binunionLsub = $true )
& ( setadjoinSub = $true )
& ( upairsetE = $true )
& ( upairsetIR = $true )
& ( nonemptyI = $true )
& ( singletonsswitch = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( dsetconstr__Cong = $true )
& ( binunionIR = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinE = $true )
& ( powersetI = $true )
& ( emptysetsubset = $true )
& ( setbeta = $true )
& ( upairsetIL = $true )
& ( exuE3u = $true )
& ( nonemptyE1 = $true )
& ( inPowerset = $true )
& ( subPowSU = $true )
& ( subsetE2 = $true )
& ( notsubsetI = $true )
& ( setoftrueEq = $true )
& ( exuI3 = $true )
& ( binunionRsub = $true )
& ( eqimpsubset1 = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( subsetI2 = $true )
& ( exuE2 = $true )
& ( setadjoinIR = $true )
& ( setext = $true )
& ( notdexE = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( notinsingleton = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( dsetconstrEL = $true )
& ( uniqinunit = $true )
& ( wellorderingAx = $true )
& ( emptysetE = $true )
& ( subsetemptysetimpeq = $true )
& ( subsetE = $true )
& ( nonemptyImpWitness = $true )
& ( powersetsubset = $true )
& ( powerset__Cong = $true ) ),
inference(flattening,[status(thm)],[f448]) ).
thf(f448,plain,
( ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
!= X1 )
& ( $true
= ( subset @ X1 @ X0 ) ) )
& ( 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)],[f216]) ).
thf(f216,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 )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
=> ( ( binintersect @ X1 @ X0 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f215]) ).
thf(f215,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
=> ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( ( binintersect @ X1 @ X0 )
= X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f114]) ).
thf(f114,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
=> ! [X4: $i,X3: $i] :
( ( subset @ X3 @ X4 )
=> ( ( binintersect @ X3 @ X4 )
= X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f113]) ).
thf(f113,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
=> ! [X4: $i,X3: $i] :
( ( subset @ X3 @ X4 )
=> ( ( binintersect @ X3 @ X4 )
= X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2THF_25342.p',binintersectSubset2) ).
thf(f7865,plain,
( ( ( binintersect @ sK88 @ sK87 )
= sK88 )
| ( ( subset @ ( binintersect @ sK88 @ sK87 ) @ sK88 )
!= $true )
| ~ spl302_71
| ~ spl302_183
| ~ spl302_299 ),
inference(trivial_inequality_removal,[status(thm)],[f7847]) ).
thf(f7847,plain,
( ( ( binintersect @ sK88 @ sK87 )
= sK88 )
| ( $true != $true )
| ( ( subset @ ( binintersect @ sK88 @ sK87 ) @ sK88 )
!= $true )
| ~ spl302_71
| ~ spl302_183
| ~ spl302_299 ),
inference(superposition,[status(thm)],[f1978,f7841]) ).
thf(f7841,plain,
( ( ( subset @ sK88 @ ( binintersect @ sK88 @ sK87 ) )
= $true )
| ~ spl302_183
| ~ spl302_299 ),
inference(trivial_inequality_removal,[status(thm)],[f7821]) ).
thf(f7821,plain,
( ( $true != $true )
| ( ( subset @ sK88 @ ( binintersect @ sK88 @ sK87 ) )
= $true )
| ~ spl302_183
| ~ spl302_299 ),
inference(superposition,[status(thm)],[f6801,f2469]) ).
thf(f2469,plain,
( ! [X1: $i] :
( ( subset @ X1 @ X1 )
= $true )
| ~ spl302_183 ),
inference(avatar_component_clause,[status(thm)],[f2468]) ).
thf(f2468,definition,
( spl302_183
<=> ! [X1: $i] :
( ( subset @ X1 @ X1 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl302_183])],[avatar_definition]) ).
thf(f6801,plain,
( ! [X0: $i] :
( ( $true
!= ( subset @ sK88 @ X0 ) )
| ( ( subset @ sK88 @ ( binintersect @ X0 @ sK87 ) )
= $true ) )
| ~ spl302_299 ),
inference(trivial_inequality_removal,[status(thm)],[f6786]) ).
thf(f6786,plain,
( ! [X0: $i] :
( ( $true
!= ( subset @ sK88 @ X0 ) )
| ( $true != $true )
| ( ( subset @ sK88 @ ( binintersect @ X0 @ sK87 ) )
= $true ) )
| ~ spl302_299 ),
inference(superposition,[status(thm)],[f3010,f1187]) ).
thf(f1187,plain,
( ( subset @ sK88 @ sK87 )
= $true ),
inference(cnf_transformation,[status(thm)],[f627]) ).
thf(f3010,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X4 )
!= $true )
| ( ( subset @ X5 @ ( binintersect @ X3 @ X4 ) )
= $true )
| ( ( subset @ X5 @ X3 )
!= $true ) )
| ~ spl302_299 ),
inference(avatar_component_clause,[status(thm)],[f3009]) ).
thf(f3009,definition,
( spl302_299
<=> ! [X4: $i,X5: $i,X3: $i] :
( ( ( subset @ X5 @ X3 )
!= $true )
| ( ( subset @ X5 @ X4 )
!= $true )
| ( ( subset @ X5 @ ( binintersect @ X3 @ X4 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl302_299])],[avatar_definition]) ).
thf(f1978,plain,
( ! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X3 @ X2 ) )
| ( X2 = X3 )
| ( ( subset @ X2 @ X3 )
!= $true ) )
| ~ spl302_71 ),
inference(avatar_component_clause,[status(thm)],[f1977]) ).
thf(f1977,definition,
( spl302_71
<=> ! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( $true
!= ( subset @ X3 @ X2 ) )
| ( X2 = X3 ) ) ),
introduced(definition,[new_symbols(naming,[spl302_71])],[avatar_definition]) ).
thf(f4019,plain,
spl302_72,
inference(avatar_split_clause,[status(thm)],[f1174,f1980]) ).
thf(f1980,definition,
( spl302_72
<=> ( setextsub = $true ) ),
introduced(definition,[new_symbols(naming,[spl302_72])],[avatar_definition]) ).
thf(f1174,plain,
setextsub = $true,
inference(cnf_transformation,[status(thm)],[f627]) ).
thf(f4018,plain,
spl302_386,
inference(avatar_split_clause,[status(thm)],[f1172,f3439]) ).
thf(f3439,definition,
( spl302_386
<=> ( binintersectLsub = $true ) ),
introduced(definition,[new_symbols(naming,[spl302_386])],[avatar_definition]) ).
thf(f1172,plain,
binintersectLsub = $true,
inference(cnf_transformation,[status(thm)],[f627]) ).
thf(f3845,plain,
spl302_193,
inference(avatar_split_clause,[status(thm)],[f1213,f2511]) ).
thf(f2511,definition,
( spl302_193
<=> ( notequalI1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl302_193])],[avatar_definition]) ).
thf(f1213,plain,
notequalI1 = $true,
inference(cnf_transformation,[status(thm)],[f627]) ).
thf(f3694,plain,
( ~ spl302_386
| spl302_438 ),
inference(avatar_split_clause,[status(thm)],[f1439,f3692,f3439]) ).
thf(f1439,plain,
! [X0: $i,X1: $i] :
( ( binintersectLsub != $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f883]) ).
thf(f883,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ( ( subset @ ( binintersect @ sK233 @ sK234 ) @ sK233 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK233,sK234])],[f881,f882]) ).
thf(f882,plain,
( ? [X2: $i,X3: $i] :
( $true
!= ( subset @ ( binintersect @ X2 @ X3 ) @ X2 ) )
=> ( ( subset @ ( binintersect @ sK233 @ sK234 ) @ sK233 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f881,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( subset @ ( binintersect @ X2 @ X3 ) @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f880]) ).
thf(f880,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f265]) ).
thf(f265,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
<=> ( binintersectLsub = $true ) ),
inference(fool_elimination,[status(thm)],[f264]) ).
thf(f264,plain,
! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= binintersectLsub ),
inference(rectify,[status(thm)],[f112]) ).
thf(f112,axiom,
! [X3: $i,X4: $i] :
( ( subset @ ( binintersect @ X3 @ X4 ) @ X3 )
= binintersectLsub ),
file('/export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2THF_25342.p',binintersectLsub) ).
thf(f3606,plain,
spl302_226,
inference(avatar_split_clause,[status(thm)],[f1205,f2661]) ).
thf(f2661,definition,
( spl302_226
<=> ( binintersectSubset5 = $true ) ),
introduced(definition,[new_symbols(naming,[spl302_226])],[avatar_definition]) ).
thf(f1205,plain,
binintersectSubset5 = $true,
inference(cnf_transformation,[status(thm)],[f627]) ).
thf(f3461,plain,
( ~ spl302_193
| spl302_183 ),
inference(avatar_split_clause,[status(thm)],[f1551,f2468,f2511]) ).
thf(f1551,plain,
! [X1: $i] :
( ( notequalI1 != $true )
| ( ( subset @ X1 @ X1 )
= $true ) ),
inference(equality_resolution,[status(thm)],[f1045]) ).
thf(f1045,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( X0 != X1 )
| ( notequalI1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f547]) ).
thf(f547,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( X0 != X1 ) )
| ( notequalI1 != $true ) )
& ( ( notequalI1 = $true )
| ( ( ( subset @ sK39 @ sK40 )
!= $true )
& ( sK40 = sK39 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40])],[f545,f546]) ).
thf(f546,plain,
( ? [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
& ( X2 = X3 ) )
=> ( ( ( subset @ sK39 @ sK40 )
!= $true )
& ( sK40 = sK39 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f545,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( X0 != X1 ) )
| ( notequalI1 != $true ) )
& ( ( notequalI1 = $true )
| ? [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
& ( X2 = X3 ) ) ) ),
inference(rectify,[status(thm)],[f544]) ).
thf(f544,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( X0 != X1 ) )
| ( notequalI1 != $true ) )
& ( ( notequalI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( X0 = X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f445]) ).
thf(f445,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
| ( X0 != X1 ) )
<=> ( notequalI1 = $true ) ),
inference(ennf_transformation,[status(thm)],[f342]) ).
thf(f342,plain,
( ( notequalI1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
=> ( X0 != X1 ) ) ),
inference(flattening,[status(thm)],[f173]) ).
thf(f173,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
=> ( X0 != X1 ) )
<=> ( notequalI1 = $true ) ),
inference(fool_elimination,[status(thm)],[f172]) ).
thf(f172,plain,
! [X0: $i,X1: $i] :
( ( ~ ( subset @ X0 @ X1 )
=> ( X0 != X1 ) )
= notequalI1 ),
inference(rectify,[status(thm)],[f86]) ).
thf(f86,axiom,
! [X3: $i,X4: $i] :
( ( ~ ( subset @ X3 @ X4 )
=> ( X3 != X4 ) )
= notequalI1 ),
file('/export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2THF_25342.p',notequalI1) ).
thf(f3011,plain,
( ~ spl302_226
| spl302_299 ),
inference(avatar_split_clause,[status(thm)],[f1424,f3009,f2661]) ).
thf(f1424,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X3 )
!= $true )
| ( ( subset @ X5 @ ( binintersect @ X3 @ X4 ) )
= $true )
| ( binintersectSubset5 != $true )
| ( ( subset @ X5 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f867]) ).
thf(f867,plain,
( ( ( binintersectSubset5 = $true )
| ( ( ( subset @ sK225 @ sK224 )
= $true )
& ( ( subset @ sK225 @ ( binintersect @ sK223 @ sK224 ) )
!= $true )
& ( ( subset @ sK225 @ sK223 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X4 )
!= $true )
| ( ( subset @ X5 @ ( binintersect @ X3 @ X4 ) )
= $true )
| ( ( subset @ X5 @ X3 )
!= $true ) )
| ( binintersectSubset5 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK223,sK224,sK225])],[f865,f866]) ).
thf(f866,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
& ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( subset @ X2 @ X0 )
= $true ) )
=> ( ( ( subset @ sK225 @ sK224 )
= $true )
& ( ( subset @ sK225 @ ( binintersect @ sK223 @ sK224 ) )
!= $true )
& ( ( subset @ sK225 @ sK223 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f865,plain,
( ( ( binintersectSubset5 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
& ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( subset @ X2 @ X0 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X4 )
!= $true )
| ( ( subset @ X5 @ ( binintersect @ X3 @ X4 ) )
= $true )
| ( ( subset @ X5 @ X3 )
!= $true ) )
| ( binintersectSubset5 != $true ) ) ),
inference(rectify,[status(thm)],[f864]) ).
thf(f864,plain,
( ( ( binintersectSubset5 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X2 @ X1 ) )
& ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
!= $true )
& ( ( subset @ X2 @ X0 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X2 @ X1 ) )
| ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( subset @ X2 @ X0 )
!= $true ) )
| ( binintersectSubset5 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f434]) ).
thf(f434,plain,
( ( binintersectSubset5 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( subset @ X2 @ X1 ) )
| ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( ( subset @ X2 @ X0 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f433]) ).
thf(f433,plain,
( ( binintersectSubset5 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true )
| ( $true
!= ( subset @ X2 @ X1 ) )
| ( ( subset @ X2 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f255]) ).
thf(f255,plain,
( ( binintersectSubset5 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
= $true )
=> ( ( $true
= ( subset @ X2 @ X1 ) )
=> ( ( subset @ X2 @ ( binintersect @ X0 @ X1 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f254]) ).
thf(f254,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X2 @ X0 )
=> ( ( subset @ X2 @ X1 )
=> ( subset @ X2 @ ( binintersect @ X0 @ X1 ) ) ) )
= binintersectSubset5 ),
inference(rectify,[status(thm)],[f110]) ).
thf(f110,axiom,
! [X3: $i,X4: $i,X5: $i] :
( ( ( subset @ X5 @ X3 )
=> ( ( subset @ X5 @ X4 )
=> ( subset @ X5 @ ( binintersect @ X3 @ X4 ) ) ) )
= binintersectSubset5 ),
file('/export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2THF_25342.p',binintersectSubset5) ).
thf(f1983,plain,
( spl302_71
| ~ spl302_72 ),
inference(avatar_split_clause,[status(thm)],[f1087,f1980,f1977]) ).
thf(f1087,plain,
! [X2: $i,X3: $i] :
( ( ( subset @ X2 @ X3 )
!= $true )
| ( X2 = X3 )
| ( setextsub != $true )
| ( $true
!= ( subset @ X3 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f607]) ).
thf(f607,plain,
( ( ( setextsub = $true )
| ( ( sK74 != sK75 )
& ( ( subset @ sK74 @ sK75 )
= $true )
& ( $true
= ( subset @ sK75 @ sK74 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( $true
!= ( subset @ X3 @ X2 ) ) )
| ( setextsub != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK74,sK75])],[f605,f606]) ).
thf(f606,plain,
( ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( subset @ X0 @ X1 )
= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) )
=> ( ( sK74 != sK75 )
& ( ( subset @ sK74 @ sK75 )
= $true )
& ( $true
= ( subset @ sK75 @ sK74 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f605,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( subset @ X0 @ X1 )
= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( ( subset @ X2 @ X3 )
!= $true )
| ( $true
!= ( subset @ X3 @ X2 ) ) )
| ( setextsub != $true ) ) ),
inference(rectify,[status(thm)],[f604]) ).
thf(f604,plain,
( ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( X0 != X1 )
& ( ( subset @ X0 @ X1 )
= $true )
& ( $true
= ( subset @ X1 @ X0 ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) )
| ( setextsub != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f472]) ).
thf(f472,plain,
( ( setextsub = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( $true
!= ( subset @ X1 @ X0 ) ) ) ),
inference(flattening,[status(thm)],[f471]) ).
thf(f471,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ( $true
!= ( subset @ X1 @ X0 ) )
| ( ( subset @ X0 @ X1 )
!= $true ) )
<=> ( setextsub = $true ) ),
inference(ennf_transformation,[status(thm)],[f227]) ).
thf(f227,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( $true
= ( subset @ X1 @ X0 ) )
=> ( X0 = X1 ) ) )
<=> ( setextsub = $true ) ),
inference(fool_elimination,[status(thm)],[f226]) ).
thf(f226,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) )
= setextsub ),
inference(rectify,[status(thm)],[f93]) ).
thf(f93,axiom,
! [X3: $i,X4: $i] :
( ( ( subset @ X3 @ X4 )
=> ( ( subset @ X4 @ X3 )
=> ( X3 = X4 ) ) )
= setextsub ),
file('/export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2THF_25342.p',setextsub) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU593^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n023.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:28:34 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SEU593^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English : (! A:i.! B:i.subset A B -> binintersect A B = A)
% 0.31/0.46
% 0.31/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.46 % Source : [Bro08]
% 0.31/0.46 % Names : ZFC095g [Bro08]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.43 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.86 v6.0.0, 0.57 v5.5.0, 0.50 v5.4.0, 0.60 v5.0.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.31/0.46 % Syntax : Number of formulae : 239 ( 112 unt; 126 typ; 112 def)
% 0.31/0.46 % Number of atoms : 597 ( 162 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 111 ( 5 avg)
% 0.31/0.46 % Number of connectives : 940 ( 29 ~; 6 |; 27 &; 597 @)
% 0.31/0.46 % ( 14 <=>; 267 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 115 ( 2 avg)
% 0.31/0.46 % Number of types : 2 ( 0 usr)
% 0.31/0.46 % Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 129 ( 126 usr; 113 con; 0-2 aty)
% 0.31/0.46 % Number of variables : 329 ( 33 ^; 268 !; 28 ?; 329 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : http://mathgate.info/detsetitem.php?id=363
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(in_type,type,
% 0.31/0.46 in: $i > $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(exu_type,type,
% 0.31/0.46 exu: ( $i > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(exu,definition,
% 0.31/0.46 ( exu
% 0.31/0.46 = ( ^ [Xphi: $i > $o] :
% 0.31/0.46 ? [Xx: $i] :
% 0.31/0.46 ( ( Xphi @ Xx )
% 0.31/0.46 & ! [Xy: $i] :
% 0.31/0.46 ( ( Xphi @ Xy )
% 0.31/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setextAx_type,type,
% 0.31/0.46 setextAx: $o ).
% 0.31/0.46
% 0.31/0.46 thf(setextAx,definition,
% 0.31/0.46 ( setextAx
% 0.31/0.46 = ( ! [A: $i,B: $i] :
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 <=> ( in @ Xx @ B ) )
% 0.31/0.46 => ( A = B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(emptyset_type,type,
% 0.31/0.46 emptyset: $i ).
% 0.31/0.46
% 0.31/0.46 thf(emptysetAx_type,type,
% 0.31/0.46 emptysetAx: $o ).
% 0.31/0.46
% 0.31/0.46 thf(emptysetAx,definition,
% 0.31/0.46 ( emptysetAx
% 0.31/0.46 = ( ! [Xx: $i] :
% 0.31/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setadjoin_type,type,
% 0.31/0.46 setadjoin: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(setadjoinAx_type,type,
% 0.31/0.46 setadjoinAx: $o ).
% 0.31/0.46
% 0.31/0.46 thf(setadjoinAx,definition,
% 0.31/0.46 ( setadjoinAx
% 0.31/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.46 <=> ( ( Xy = Xx )
% 0.31/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(powerset_type,type,
% 0.31/0.46 powerset: $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(powersetAx_type,type,
% 0.31/0.46 powersetAx: $o ).
% 0.31/0.46
% 0.31/0.46 thf(powersetAx,definition,
% 0.31/0.46 ( powersetAx
% 0.31/0.46 = ( ! [A: $i,B: $i] :
% 0.31/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.46 <=> ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ B )
% 0.31/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setunion_type,type,
% 0.31/0.46 setunion: $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(setunionAx_type,type,
% 0.31/0.46 setunionAx: $o ).
% 0.31/0.46
% 0.31/0.46 thf(setunionAx,definition,
% 0.31/0.46 ( setunionAx
% 0.31/0.46 = ( ! [A: $i,Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.46 <=> ? [B: $i] :
% 0.31/0.46 ( ( in @ Xx @ B )
% 0.31/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(omega_type,type,
% 0.31/0.46 omega: $i ).
% 0.31/0.46
% 0.31/0.46 thf(omega0Ax_type,type,
% 0.31/0.46 omega0Ax: $o ).
% 0.31/0.46
% 0.31/0.46 thf(omega0Ax,definition,
% 0.31/0.46 ( omega0Ax
% 0.31/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(omegaSAx_type,type,
% 0.31/0.46 omegaSAx: $o ).
% 0.31/0.46
% 0.31/0.46 thf(omegaSAx,definition,
% 0.31/0.46 ( omegaSAx
% 0.31/0.46 = ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ omega )
% 0.31/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(omegaIndAx_type,type,
% 0.31/0.46 omegaIndAx: $o ).
% 0.31/0.46
% 0.31/0.46 thf(omegaIndAx,definition,
% 0.31/0.46 ( omegaIndAx
% 0.31/0.46 = ( ! [A: $i] :
% 0.31/0.46 ( ( ( in @ emptyset @ A )
% 0.31/0.46 & ! [Xx: $i] :
% 0.31/0.46 ( ( ( in @ Xx @ omega )
% 0.31/0.46 & ( in @ Xx @ A ) )
% 0.31/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.31/0.46 => ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ omega )
% 0.31/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(replAx_type,type,
% 0.31/0.46 replAx: $o ).
% 0.31/0.46
% 0.31/0.46 thf(replAx,definition,
% 0.31/0.46 ( replAx
% 0.31/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( exu
% 0.31/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.31/0.46 => ? [B: $i] :
% 0.31/0.46 ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ B )
% 0.31/0.46 <=> ? [Xy: $i] :
% 0.31/0.46 ( ( in @ Xy @ A )
% 0.31/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(foundationAx_type,type,
% 0.31/0.46 foundationAx: $o ).
% 0.31/0.46
% 0.31/0.46 thf(foundationAx,definition,
% 0.31/0.46 ( foundationAx
% 0.31/0.46 = ( ! [A: $i] :
% 0.31/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.46 => ? [B: $i] :
% 0.31/0.46 ( ( in @ B @ A )
% 0.31/0.46 & ~ ? [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ B )
% 0.31/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(wellorderingAx_type,type,
% 0.31/0.46 wellorderingAx: $o ).
% 0.31/0.46
% 0.31/0.46 thf(wellorderingAx,definition,
% 0.31/0.46 ( wellorderingAx
% 0.31/0.46 = ( ! [A: $i] :
% 0.31/0.46 ? [B: $i] :
% 0.31/0.46 ( ! [C: $i] :
% 0.31/0.46 ( ( in @ C @ B )
% 0.31/0.46 => ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ C )
% 0.31/0.46 => ( in @ Xx @ A ) ) )
% 0.31/0.46 & ! [Xx: $i,Xy: $i] :
% 0.31/0.46 ( ( ( in @ Xx @ A )
% 0.31/0.46 & ( in @ Xy @ A ) )
% 0.31/0.46 => ( ! [C: $i] :
% 0.31/0.46 ( ( in @ C @ B )
% 0.31/0.46 => ( ( in @ Xx @ C )
% 0.31/0.46 <=> ( in @ Xy @ C ) ) )
% 0.31/0.46 => ( Xx = Xy ) ) )
% 0.31/0.46 & ! [C: $i,D: $i] :
% 0.31/0.46 ( ( ( in @ C @ B )
% 0.31/0.46 & ( in @ D @ B ) )
% 0.31/0.46 => ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ C )
% 0.31/0.46 => ( in @ Xx @ D ) )
% 0.31/0.46 | ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ D )
% 0.31/0.46 => ( in @ Xx @ C ) ) ) )
% 0.31/0.46 & ! [C: $i] :
% 0.31/0.46 ( ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ C )
% 0.31/0.46 => ( in @ Xx @ A ) )
% 0.31/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.31/0.46 => ? [D: $i,Xx: $i] :
% 0.31/0.46 ( ( in @ D @ B )
% 0.31/0.46 & ( in @ Xx @ C )
% 0.31/0.46 & ~ ? [Xy: $i] :
% 0.31/0.46 ( ( in @ Xy @ D )
% 0.31/0.46 & ( in @ Xy @ C ) )
% 0.31/0.46 & ! [E: $i] :
% 0.31/0.46 ( ( in @ E @ B )
% 0.31/0.46 => ( ! [Xy: $i] :
% 0.31/0.46 ( ( in @ Xy @ E )
% 0.31/0.46 => ( in @ Xy @ D ) )
% 0.31/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(descr_type,type,
% 0.31/0.46 descr: ( $i > $o ) > $i ).
% 0.31/0.46
% 0.31/0.46 thf(descrp_type,type,
% 0.31/0.46 descrp: $o ).
% 0.31/0.46
% 0.31/0.46 thf(descrp,definition,
% 0.31/0.46 ( descrp
% 0.31/0.46 = ( ! [Xphi: $i > $o] :
% 0.31/0.46 ( ( exu
% 0.31/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.46 => ( Xphi
% 0.31/0.46 @ ( descr
% 0.31/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(dsetconstr_type,type,
% 0.31/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.46
% 0.31/0.46 thf(dsetconstrI_type,type,
% 0.31/0.46 dsetconstrI: $o ).
% 0.31/0.46
% 0.31/0.46 thf(dsetconstrI,definition,
% 0.31/0.46 ( dsetconstrI
% 0.31/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( ( Xphi @ Xx )
% 0.31/0.46 => ( in @ Xx
% 0.31/0.46 @ ( dsetconstr @ A
% 0.31/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(dsetconstrEL_type,type,
% 0.31/0.46 dsetconstrEL: $o ).
% 0.31/0.46
% 0.31/0.46 thf(dsetconstrEL,definition,
% 0.31/0.46 ( dsetconstrEL
% 0.31/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.46 ( ( in @ Xx
% 0.31/0.46 @ ( dsetconstr @ A
% 0.31/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(dsetconstrER_type,type,
% 0.31/0.46 dsetconstrER: $o ).
% 0.31/0.46
% 0.31/0.46 thf(dsetconstrER,definition,
% 0.31/0.46 ( dsetconstrER
% 0.31/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.46 ( ( in @ Xx
% 0.31/0.46 @ ( dsetconstr @ A
% 0.31/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(exuE1_type,type,
% 0.31/0.46 exuE1: $o ).
% 0.31/0.46
% 0.31/0.46 thf(exuE1,definition,
% 0.31/0.46 ( exuE1
% 0.31/0.46 = ( ! [Xphi: $i > $o] :
% 0.31/0.46 ( ( exu
% 0.31/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.46 => ? [Xx: $i] :
% 0.31/0.46 ( ( Xphi @ Xx )
% 0.31/0.46 & ! [Xy: $i] :
% 0.31/0.46 ( ( Xphi @ Xy )
% 0.31/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(prop2set_type,type,
% 0.31/0.46 prop2set: $o > $i ).
% 0.31/0.46
% 0.31/0.46 thf(prop2setE_type,type,
% 0.31/0.46 prop2setE: $o ).
% 0.31/0.46
% 0.31/0.46 thf(prop2setE,definition,
% 0.31/0.46 ( prop2setE
% 0.31/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.31/0.46 => Xphi ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(emptysetE_type,type,
% 0.31/0.46 emptysetE: $o ).
% 0.31/0.46
% 0.31/0.46 thf(emptysetE,definition,
% 0.31/0.46 ( emptysetE
% 0.31/0.46 = ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ emptyset )
% 0.31/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(emptysetimpfalse_type,type,
% 0.31/0.46 emptysetimpfalse: $o ).
% 0.31/0.46
% 0.31/0.46 thf(emptysetimpfalse,definition,
% 0.31/0.46 ( emptysetimpfalse
% 0.31/0.46 = ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ emptyset )
% 0.31/0.46 => $false ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(notinemptyset_type,type,
% 0.31/0.46 notinemptyset: $o ).
% 0.31/0.46
% 0.31/0.46 thf(notinemptyset,definition,
% 0.31/0.46 ( notinemptyset
% 0.31/0.46 = ( ! [Xx: $i] :
% 0.31/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(exuE3e_type,type,
% 0.31/0.46 exuE3e: $o ).
% 0.31/0.46
% 0.31/0.46 thf(exuE3e,definition,
% 0.31/0.46 ( exuE3e
% 0.31/0.46 = ( ! [Xphi: $i > $o] :
% 0.31/0.46 ( ( exu
% 0.31/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setext_type,type,
% 0.31/0.46 setext: $o ).
% 0.31/0.46
% 0.31/0.46 thf(setext,definition,
% 0.31/0.46 ( setext
% 0.31/0.46 = ( ! [A: $i,B: $i] :
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( in @ Xx @ B ) )
% 0.31/0.46 => ( ! [Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ B )
% 0.31/0.46 => ( in @ Xx @ A ) )
% 0.31/0.46 => ( A = B ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(emptyI_type,type,
% 0.31/0.46 emptyI: $o ).
% 0.31/0.46
% 0.31/0.46 thf(emptyI,definition,
% 0.31/0.46 ( emptyI
% 0.31/0.46 = ( ! [A: $i] :
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ~ ( in @ Xx @ A )
% 0.31/0.46 => ( A = emptyset ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(noeltsimpempty_type,type,
% 0.31/0.46 noeltsimpempty: $o ).
% 0.31/0.46
% 0.31/0.46 thf(noeltsimpempty,definition,
% 0.31/0.46 ( noeltsimpempty
% 0.31/0.46 = ( ! [A: $i] :
% 0.31/0.46 ( ! [Xx: $i] :
% 0.31/0.46 ~ ( in @ Xx @ A )
% 0.31/0.46 => ( A = emptyset ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(setbeta_type,type,
% 0.31/0.46 setbeta: $o ).
% 0.31/0.46
% 0.31/0.46 thf(setbeta,definition,
% 0.31/0.46 ( setbeta
% 0.31/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.46 ( ( in @ Xx @ A )
% 0.31/0.46 => ( ( in @ Xx
% 0.31/0.46 @ ( dsetconstr @ A
% 0.31/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(nonempty_type,type,
% 0.31/0.46 nonempty: $i > $o ).
% 0.31/0.46
% 0.31/0.46 thf(nonempty,definition,
% 0.31/0.46 ( nonempty
% 0.31/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(nonemptyE1_type,type,
% 0.31/0.46 nonemptyE1: $o ).
% 0.31/0.46
% 0.31/0.46 thf(nonemptyE1,definition,
% 0.31/0.47 ( nonemptyE1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( nonempty @ A )
% 0.31/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI_type,type,
% 0.31/0.47 nonemptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI,definition,
% 0.31/0.47 ( nonemptyI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( nonempty
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1_type,type,
% 0.31/0.47 nonemptyI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1,definition,
% 0.31/0.47 ( nonemptyI1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL_type,type,
% 0.31/0.47 setadjoinIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL,definition,
% 0.31/0.47 ( setadjoinIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty_type,type,
% 0.31/0.47 emptyinunitempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty,definition,
% 0.31/0.47 ( emptyinunitempty
% 0.31/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR_type,type,
% 0.31/0.47 setadjoinIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR,definition,
% 0.31/0.47 ( setadjoinIR
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE_type,type,
% 0.31/0.47 setadjoinE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE,definition,
% 0.31/0.47 ( setadjoinE
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ! [Xphi: $o] :
% 0.31/0.47 ( ( ( Xy = Xx )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => ( ( ( in @ Xy @ A )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr_type,type,
% 0.31/0.47 setadjoinOr: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr,definition,
% 0.31/0.47 ( setadjoinOr
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setoftrueEq_type,type,
% 0.31/0.47 setoftrueEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setoftrueEq,definition,
% 0.31/0.47 ( setoftrueEq
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : $true )
% 0.31/0.47 = A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI_type,type,
% 0.31/0.47 powersetI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI,definition,
% 0.31/0.47 ( powersetI
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinPowerset_type,type,
% 0.31/0.47 emptyinPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinPowerset,definition,
% 0.31/0.47 ( emptyinPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyInPowerset_type,type,
% 0.31/0.47 emptyInPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyInPowerset,definition,
% 0.31/0.47 ( emptyInPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE_type,type,
% 0.31/0.47 powersetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE,definition,
% 0.31/0.47 ( powersetE
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 => ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunionI_type,type,
% 0.31/0.47 setunionI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionI,definition,
% 0.31/0.47 ( setunionI
% 0.31/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( ( in @ B @ A )
% 0.31/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunionE_type,type,
% 0.31/0.47 setunionE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionE,definition,
% 0.31/0.47 ( setunionE
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.47 => ! [Xphi: $o] :
% 0.31/0.47 ( ! [B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( ( in @ B @ A )
% 0.31/0.47 => Xphi ) )
% 0.31/0.47 => Xphi ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subPowSU_type,type,
% 0.31/0.47 subPowSU: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subPowSU,definition,
% 0.31/0.47 ( subPowSU
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE2_type,type,
% 0.31/0.47 exuE2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE2,definition,
% 0.31/0.47 ( exuE2
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyImpWitness_type,type,
% 0.31/0.47 nonemptyImpWitness: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyImpWitness,definition,
% 0.31/0.47 ( nonemptyImpWitness
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( nonempty @ A )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & $true ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(uniqinunit_type,type,
% 0.31/0.47 uniqinunit: $o ).
% 0.31/0.47
% 0.31/0.47 thf(uniqinunit,definition,
% 0.31/0.47 ( uniqinunit
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notinsingleton_type,type,
% 0.31/0.47 notinsingleton: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notinsingleton,definition,
% 0.31/0.47 ( notinsingleton
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx != Xy )
% 0.31/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqinunit_type,type,
% 0.31/0.47 eqinunit: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqinunit,definition,
% 0.31/0.47 ( eqinunit
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(singletonsswitch_type,type,
% 0.31/0.47 singletonsswitch: $o ).
% 0.31/0.47
% 0.31/0.47 thf(singletonsswitch,definition,
% 0.31/0.47 ( singletonsswitch
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetE_type,type,
% 0.31/0.47 upairsetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetE,definition,
% 0.31/0.47 ( upairsetE
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.31/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.31/0.47 => ( ( Xz = Xx )
% 0.31/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIL_type,type,
% 0.31/0.47 upairsetIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIL,definition,
% 0.31/0.47 ( upairsetIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIR_type,type,
% 0.31/0.47 upairsetIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIR,definition,
% 0.31/0.47 ( upairsetIR
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyE1_type,type,
% 0.31/0.47 emptyE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyE1,definition,
% 0.31/0.47 ( emptyE1
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ( ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = emptyset )
% 0.31/0.47 => $false ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(vacuousDall_type,type,
% 0.31/0.47 vacuousDall: $o ).
% 0.31/0.47
% 0.31/0.47 thf(vacuousDall,definition,
% 0.31/0.47 ( vacuousDall
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan1_type,type,
% 0.31/0.47 quantDeMorgan1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan1,definition,
% 0.31/0.47 ( quantDeMorgan1
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan2_type,type,
% 0.31/0.47 quantDeMorgan2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan2,definition,
% 0.31/0.47 ( quantDeMorgan2
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) )
% 0.31/0.47 => ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan3_type,type,
% 0.31/0.47 quantDeMorgan3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan3,definition,
% 0.31/0.47 ( quantDeMorgan3
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan4_type,type,
% 0.31/0.47 quantDeMorgan4: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan4,definition,
% 0.31/0.47 ( quantDeMorgan4
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) )
% 0.31/0.47 => ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setI_type,type,
% 0.31/0.47 prop2setI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setI,definition,
% 0.31/0.47 ( prop2setI
% 0.31/0.47 = ( ! [Xphi: $o] :
% 0.31/0.47 ( Xphi
% 0.31/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(set2prop_type,type,
% 0.31/0.47 set2prop: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set2propI_type,type,
% 0.31/0.47 prop2set2propI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set2propI,definition,
% 0.31/0.47 ( prop2set2propI
% 0.31/0.47 = ( ! [Xphi: $o] :
% 0.31/0.47 ( Xphi
% 0.31/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notdexE_type,type,
% 0.31/0.47 notdexE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notdexE,definition,
% 0.31/0.47 ( notdexE
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notdallE_type,type,
% 0.31/0.47 notdallE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notdallE,definition,
% 0.31/0.47 ( notdallE
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI1_type,type,
% 0.31/0.47 exuI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI1,definition,
% 0.31/0.47 ( exuI1
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI3_type,type,
% 0.31/0.47 exuI3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI3,definition,
% 0.31/0.47 ( exuI3
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.31/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI2_type,type,
% 0.31/0.47 exuI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI2,definition,
% 0.31/0.47 ( exuI2
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 <=> ( Xy = Xx ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inCongP_type,type,
% 0.31/0.47 inCongP: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inCongP,definition,
% 0.31/0.47 ( inCongP
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(in__Cong_type,type,
% 0.31/0.47 in__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(in__Cong,definition,
% 0.31/0.47 ( in__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3u_type,type,
% 0.31/0.47 exuE3u: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3u,definition,
% 0.31/0.47 ( exuE3u
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exu__Cong_type,type,
% 0.31/0.47 exu__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu__Cong,definition,
% 0.31/0.47 ( exu__Cong
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 <=> ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset__Cong_type,type,
% 0.31/0.47 emptyset__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset__Cong,definition,
% 0.31/0.47 ( emptyset__Cong
% 0.31/0.47 = ( emptyset = emptyset ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin__Cong_type,type,
% 0.31/0.47 setadjoin__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin__Cong,definition,
% 0.31/0.47 ( setadjoin__Cong
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ! [Xz: $i,Xu: $i] :
% 0.31/0.47 ( ( Xz = Xu )
% 0.31/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.31/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powerset__Cong_type,type,
% 0.31/0.47 powerset__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powerset__Cong,definition,
% 0.31/0.47 ( powerset__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( powerset @ A )
% 0.31/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunion__Cong_type,type,
% 0.31/0.47 setunion__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunion__Cong,definition,
% 0.31/0.47 ( setunion__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( setunion @ A )
% 0.31/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omega__Cong_type,type,
% 0.31/0.47 omega__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omega__Cong,definition,
% 0.31/0.47 ( omega__Cong
% 0.31/0.47 = ( omega = omega ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuEu_type,type,
% 0.31/0.47 exuEu: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuEu,definition,
% 0.31/0.47 ( exuEu
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(descr__Cong_type,type,
% 0.31/0.47 descr__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(descr__Cong,definition,
% 0.31/0.47 ( descr__Cong
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.31/0.47 => ( ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr__Cong_type,type,
% 0.31/0.47 dsetconstr__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr__Cong,definition,
% 0.31/0.47 ( dsetconstr__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.31/0.47 => ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = ( dsetconstr @ B
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subset_type,type,
% 0.31/0.47 subset: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(disjoint_type,type,
% 0.31/0.47 disjoint: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(setsmeet_type,type,
% 0.31/0.47 setsmeet: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI1_type,type,
% 0.31/0.47 subsetI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI1,definition,
% 0.31/0.47 ( subsetI1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset2_type,type,
% 0.31/0.47 eqimpsubset2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset2,definition,
% 0.31/0.47 ( eqimpsubset2
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset1_type,type,
% 0.31/0.47 eqimpsubset1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset1,definition,
% 0.31/0.47 ( eqimpsubset1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI2_type,type,
% 0.31/0.47 subsetI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI2,definition,
% 0.31/0.47 ( subsetI2
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetsubset_type,type,
% 0.31/0.47 emptysetsubset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetsubset,definition,
% 0.31/0.47 ( emptysetsubset
% 0.31/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE_type,type,
% 0.31/0.47 subsetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE,definition,
% 0.31/0.47 ( subsetE
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE2_type,type,
% 0.31/0.47 subsetE2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE2,definition,
% 0.31/0.47 ( subsetE2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notsubsetI_type,type,
% 0.31/0.47 notsubsetI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notsubsetI,definition,
% 0.31/0.47 ( notsubsetI
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI1_type,type,
% 0.31/0.47 notequalI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI1,definition,
% 0.31/0.47 ( notequalI1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ~ ( subset @ A @ B )
% 0.31/0.47 => ( A != B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI2_type,type,
% 0.31/0.47 notequalI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI2,definition,
% 0.31/0.47 ( notequalI2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ( A != B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetRefl_type,type,
% 0.31/0.47 subsetRefl: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetRefl,definition,
% 0.31/0.47 ( subsetRefl
% 0.31/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetTrans_type,type,
% 0.31/0.47 subsetTrans: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetTrans,definition,
% 0.31/0.47 ( subsetTrans
% 0.31/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ( subset @ B @ C )
% 0.31/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub_type,type,
% 0.31/0.47 setadjoinSub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub,definition,
% 0.31/0.47 ( setadjoinSub
% 0.31/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub2_type,type,
% 0.31/0.47 setadjoinSub2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub2,definition,
% 0.31/0.47 ( setadjoinSub2
% 0.31/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subset2powerset_type,type,
% 0.31/0.47 subset2powerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subset2powerset,definition,
% 0.31/0.47 ( subset2powerset
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setextsub_type,type,
% 0.31/0.47 setextsub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setextsub,definition,
% 0.31/0.47 ( setextsub
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ( subset @ B @ A )
% 0.31/0.47 => ( A = B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetemptysetimpeq_type,type,
% 0.31/0.47 subsetemptysetimpeq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetemptysetimpeq,definition,
% 0.31/0.47 ( subsetemptysetimpeq
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( subset @ A @ emptyset )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI1_type,type,
% 0.31/0.47 powersetI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI1,definition,
% 0.31/0.47 ( powersetI1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( subset @ B @ A )
% 0.31/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE1_type,type,
% 0.31/0.47 powersetE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE1,definition,
% 0.31/0.47 ( powersetE1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inPowerset_type,type,
% 0.31/0.47 inPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inPowerset,definition,
% 0.31/0.47 ( inPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetsubset_type,type,
% 0.31/0.47 powersetsubset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetsubset,definition,
% 0.31/0.47 ( powersetsubset
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sepInPowerset_type,type,
% 0.31/0.47 sepInPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(sepInPowerset,definition,
% 0.31/0.47 ( sepInPowerset
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( in
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sepSubset_type,type,
% 0.31/0.47 sepSubset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(sepSubset,definition,
% 0.31/0.47 ( sepSubset
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( subset
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunion_type,type,
% 0.31/0.47 binunion: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(binunionIL_type,type,
% 0.31/0.47 binunionIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionIL,definition,
% 0.31/0.47 ( binunionIL
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairset2IR_type,type,
% 0.31/0.47 upairset2IR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairset2IR,definition,
% 0.31/0.47 ( upairset2IR
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionIR_type,type,
% 0.31/0.47 binunionIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionIR,definition,
% 0.31/0.47 ( binunionIR
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionEcases_type,type,
% 0.31/0.47 binunionEcases: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionEcases,definition,
% 0.31/0.47 ( binunionEcases
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.31/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.31/0.47 => ( ( ( in @ Xx @ A )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => ( ( ( in @ Xx @ B )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionE_type,type,
% 0.31/0.47 binunionE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionE,definition,
% 0.31/0.47 ( binunionE
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionLsub_type,type,
% 0.31/0.47 binunionLsub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionLsub,definition,
% 0.31/0.47 ( binunionLsub
% 0.31/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionRsub_type,type,
% 0.31/0.47 binunionRsub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionRsub,definition,
% 0.31/0.47 ( binunionRsub
% 0.31/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersect_type,type,
% 0.31/0.47 binintersect: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(binintersect,definition,
% 0.31/0.47 ( binintersect
% 0.31/0.47 = ( ^ [A: $i,B: $i] :
% 0.31/0.47 ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectI_type,type,
% 0.31/0.47 binintersectI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectI,definition,
% 0.31/0.47 ( binintersectI
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectSubset5_type,type,
% 0.31/0.47 binintersectSubset5: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectSubset5,definition,
% 0.31/0.47 ( binintersectSubset5
% 0.31/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/0.47 ( ( subset @ C @ A )
% 0.31/0.47 => ( ( subset @ C @ B )
% 0.31/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectEL_type,type,
% 0.31/0.47 binintersectEL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectEL,definition,
% 0.31/0.47 ( binintersectEL
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectLsub_type,type,
% 0.31/0.47 binintersectLsub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectLsub,definition,
% 0.31/0.47 ( binintersectLsub
% 0.31/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectSubset2,conjecture,
% 0.31/0.47 ( setextAx
% 0.31/0.47 => ( emptysetAx
% 0.31/0.47 => ( setadjoinAx
% 0.31/0.47 => ( powersetAx
% 0.31/0.47 => ( setunionAx
% 0.31/0.47 => ( omega0Ax
% 0.31/0.47 => ( omegaSAx
% 0.31/0.47 => ( omegaIndAx
% 0.31/0.47 => ( replAx
% 0.31/0.47 => ( foundationAx
% 0.31/0.47 => ( wellorderingAx
% 0.31/0.47 => ( descrp
% 0.31/0.47 => ( dsetconstrI
% 0.31/0.47 => ( dsetconstrEL
% 0.31/0.47 => ( dsetconstrER
% 0.31/0.47 => ( exuE1
% 0.31/0.47 => ( prop2setE
% 0.31/0.47 => ( emptysetE
% 0.31/0.47 => ( emptysetimpfalse
% 0.31/0.47 => ( notinemptyset
% 0.31/0.47 => ( exuE3e
% 0.31/0.47 => ( setext
% 0.31/0.47 => ( emptyI
% 0.31/0.47 => ( noeltsimpempty
% 0.31/0.47 => ( setbeta
% 0.31/0.47 => ( nonemptyE1
% 0.31/0.47 => ( nonemptyI
% 0.31/0.47 => ( nonemptyI1
% 0.31/0.47 => ( setadjoinIL
% 0.31/0.47 => ( emptyinunitempty
% 0.31/0.47 => ( setadjoinIR
% 0.31/0.47 => ( setadjoinE
% 0.31/0.47 => ( setadjoinOr
% 0.31/0.47 => ( setoftrueEq
% 0.31/0.47 => ( powersetI
% 0.31/0.47 => ( emptyinPowerset
% 0.31/0.47 => ( emptyInPowerset
% 0.31/0.47 => ( powersetE
% 0.31/0.47 => ( setunionI
% 0.31/0.47 => ( setunionE
% 0.31/0.47 => ( subPowSU
% 0.31/0.47 => ( exuE2
% 0.31/0.47 => ( nonemptyImpWitness
% 0.31/0.47 => ( uniqinunit
% 0.31/0.47 => ( notinsingleton
% 0.31/0.47 => ( eqinunit
% 0.31/0.47 => ( singletonsswitch
% 0.31/0.47 => ( upairsetE
% 0.31/0.47 => ( upairsetIL
% 0.31/0.47 => ( upairsetIR
% 0.31/0.47 => ( emptyE1
% 0.31/0.47 => ( vacuousDall
% 0.31/0.47 => ( quantDeMorgan1
% 0.31/0.47 => ( quantDeMorgan2
% 0.31/0.47 => ( quantDeMorgan3
% 0.31/0.47 => ( quantDeMorgan4
% 0.31/0.47 => ( prop2setI
% 0.31/0.47 => ( prop2set2propI
% 0.31/0.47 => ( notdexE
% 0.31/0.47 => ( notdallE
% 0.31/0.47 => ( exuI1
% 0.31/0.47 => ( exuI3
% 0.31/0.47 => ( exuI2
% 0.31/0.47 => ( inCongP
% 0.31/0.47 => ( in__Cong
% 0.31/0.47 => ( exuE3u
% 0.31/0.47 => ( exu__Cong
% 0.31/0.47 => ( emptyset__Cong
% 0.31/0.47 => ( setadjoin__Cong
% 0.31/0.47 => ( powerset__Cong
% 0.31/0.47 => ( setunion__Cong
% 0.31/0.47 => ( omega__Cong
% 0.31/0.47 => ( exuEu
% 0.31/0.47 => ( descr__Cong
% 0.31/0.47 => ( dsetconstr__Cong
% 0.31/0.47 => ( subsetI1
% 0.31/0.47 => ( eqimpsubset2
% 0.31/0.47 => ( eqimpsubset1
% 0.31/0.47 => ( subsetI2
% 0.31/0.47 => ( emptysetsubset
% 0.31/0.47 => ( subsetE
% 0.31/0.47 => ( subsetE2
% 0.31/0.47 => ( notsubsetI
% 0.31/0.47 => ( notequalI1
% 0.31/0.47 => ( notequalI2
% 0.31/0.47 => ( subsetRefl
% 0.31/0.47 => ( subsetTrans
% 0.31/0.47 => ( setadjoinSub
% 0.31/0.47 => ( setadjoinSub2
% 0.31/0.47 => ( subset2powerset
% 0.31/0.47 => ( setextsub
% 0.31/0.47 => ( subsetemptysetimpeq
% 0.31/0.47 => ( powersetI1
% 0.31/0.47 => ( powersetE1
% 0.31/0.47 => ( inPowerset
% 0.31/0.47 => ( powersetsubset
% 0.31/0.47 => ( sepInPowerset
% 0.31/0.47 => ( sepSubset
% 0.31/0.47 => ( binunionIL
% 0.31/0.47 => ( upairset2IR
% 0.31/0.47 => ( binunionIR
% 0.31/0.47 => ( binunionEcases
% 0.31/0.47 => ( binunionE
% 0.31/0.47 => ( binunionLsub
% 0.31/0.47 => ( binunionRsub
% 0.31/0.47 => ( binintersectI
% 0.31/0.47 => ( binintersectSubset5
% 0.31/0.47 => ( binintersectEL
% 0.31/0.47 => ( binintersectLsub
% 0.31/0.47 => ! [A: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ( binintersect @ A @ B )
% 0.31/0.47 = A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 2.54/1.50 ---- Embedded in THF ---
% 2.54/1.50 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.54/1.50 %%% Generated on Tue Feb 24 12:28:35 EST 2026
% 2.54/1.50 %%% using '$$dhol' embedding, version 1.3.0.
% 2.54/1.50 %%% Logic specification used:
% 2.54/1.50 %%% thf(spec, logic, $$dhol).
% 2.54/1.50
% 2.54/1.50 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2DTF25342.p
% See solution above
% 2.54/1.51 ------------------------
% 2.54/1.53 ---- Cleaned THF ---
% 2.54/1.53 thf(in_type,type,
% 2.54/1.53 in: $i > $i > $o ).
% 2.54/1.53
% 2.54/1.53 thf(exu_type,type,
% 2.54/1.53 exu: ( $i > $o ) > $o ).
% 2.54/1.53
% 2.54/1.53 thf(exu,definition,
% 2.54/1.53 ( exu
% 2.54/1.53 = ( ^ [Xphi: $i > $o] :
% 2.54/1.53 ? [Xx: $i] :
% 2.54/1.53 ( ( Xphi @ Xx )
% 2.54/1.53 & ! [Xy: $i] :
% 2.54/1.53 ( ( Xphi @ Xy )
% 2.54/1.53 => ( Xx = Xy ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setextAx_type,type,
% 2.54/1.53 setextAx: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setextAx,definition,
% 2.54/1.53 ( setextAx
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 <=> ( in @ Xx @ B ) )
% 2.54/1.53 => ( A = B ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(emptyset_type,type,
% 2.54/1.53 emptyset: $i ).
% 2.54/1.53
% 2.54/1.53 thf(emptysetAx_type,type,
% 2.54/1.53 emptysetAx: $o ).
% 2.54/1.53
% 2.54/1.53 thf(emptysetAx,definition,
% 2.54/1.53 ( emptysetAx
% 2.54/1.53 = ( ! [Xx: $i] :
% 2.54/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoin_type,type,
% 2.54/1.53 setadjoin: $i > $i > $i ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinAx_type,type,
% 2.54/1.53 setadjoinAx: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinAx,definition,
% 2.54/1.53 ( setadjoinAx
% 2.54/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.54/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.54/1.53 <=> ( ( Xy = Xx )
% 2.54/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(powerset_type,type,
% 2.54/1.53 powerset: $i > $i ).
% 2.54/1.53
% 2.54/1.53 thf(powersetAx_type,type,
% 2.54/1.53 powersetAx: $o ).
% 2.54/1.53
% 2.54/1.53 thf(powersetAx,definition,
% 2.54/1.53 ( powersetAx
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.54/1.53 <=> ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ B )
% 2.54/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setunion_type,type,
% 2.54/1.53 setunion: $i > $i ).
% 2.54/1.53
% 2.54/1.53 thf(setunionAx_type,type,
% 2.54/1.53 setunionAx: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setunionAx,definition,
% 2.54/1.53 ( setunionAx
% 2.54/1.53 = ( ! [A: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.54/1.53 <=> ? [B: $i] :
% 2.54/1.53 ( ( in @ Xx @ B )
% 2.54/1.53 & ( in @ B @ A ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(omega_type,type,
% 2.54/1.53 omega: $i ).
% 2.54/1.53
% 2.54/1.53 thf(omega0Ax_type,type,
% 2.54/1.53 omega0Ax: $o ).
% 2.54/1.53
% 2.54/1.53 thf(omega0Ax,definition,
% 2.54/1.53 ( omega0Ax
% 2.54/1.53 = ( in @ emptyset @ omega ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(omegaSAx_type,type,
% 2.54/1.53 omegaSAx: $o ).
% 2.54/1.53
% 2.54/1.53 thf(omegaSAx,definition,
% 2.54/1.53 ( omegaSAx
% 2.54/1.53 = ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ omega )
% 2.54/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(omegaIndAx_type,type,
% 2.54/1.53 omegaIndAx: $o ).
% 2.54/1.53
% 2.54/1.53 thf(omegaIndAx,definition,
% 2.54/1.53 ( omegaIndAx
% 2.54/1.53 = ( ! [A: $i] :
% 2.54/1.53 ( ( ( in @ emptyset @ A )
% 2.54/1.53 & ! [Xx: $i] :
% 2.54/1.53 ( ( ( in @ Xx @ omega )
% 2.54/1.53 & ( in @ Xx @ A ) )
% 2.54/1.53 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.54/1.53 => ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ omega )
% 2.54/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(replAx_type,type,
% 2.54/1.53 replAx: $o ).
% 2.54/1.53
% 2.54/1.53 thf(replAx,definition,
% 2.54/1.53 ( replAx
% 2.54/1.53 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.54/1.53 ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( exu
% 2.54/1.53 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.54/1.53 => ? [B: $i] :
% 2.54/1.53 ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ B )
% 2.54/1.53 <=> ? [Xy: $i] :
% 2.54/1.53 ( ( in @ Xy @ A )
% 2.54/1.53 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(foundationAx_type,type,
% 2.54/1.53 foundationAx: $o ).
% 2.54/1.53
% 2.54/1.53 thf(foundationAx,definition,
% 2.54/1.53 ( foundationAx
% 2.54/1.53 = ( ! [A: $i] :
% 2.54/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.54/1.53 => ? [B: $i] :
% 2.54/1.53 ( ( in @ B @ A )
% 2.54/1.53 & ~ ? [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ B )
% 2.54/1.53 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(wellorderingAx_type,type,
% 2.54/1.53 wellorderingAx: $o ).
% 2.54/1.53
% 2.54/1.53 thf(wellorderingAx,definition,
% 2.54/1.53 ( wellorderingAx
% 2.54/1.53 = ( ! [A: $i] :
% 2.54/1.53 ? [B: $i] :
% 2.54/1.53 ( ! [C: $i] :
% 2.54/1.53 ( ( in @ C @ B )
% 2.54/1.53 => ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ C )
% 2.54/1.53 => ( in @ Xx @ A ) ) )
% 2.54/1.53 & ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( ( in @ Xx @ A )
% 2.54/1.53 & ( in @ Xy @ A ) )
% 2.54/1.53 => ( ! [C: $i] :
% 2.54/1.53 ( ( in @ C @ B )
% 2.54/1.53 => ( ( in @ Xx @ C )
% 2.54/1.53 <=> ( in @ Xy @ C ) ) )
% 2.54/1.53 => ( Xx = Xy ) ) )
% 2.54/1.53 & ! [C: $i,D: $i] :
% 2.54/1.53 ( ( ( in @ C @ B )
% 2.54/1.53 & ( in @ D @ B ) )
% 2.54/1.53 => ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ C )
% 2.54/1.53 => ( in @ Xx @ D ) )
% 2.54/1.53 | ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ D )
% 2.54/1.53 => ( in @ Xx @ C ) ) ) )
% 2.54/1.53 & ! [C: $i] :
% 2.54/1.53 ( ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ C )
% 2.54/1.53 => ( in @ Xx @ A ) )
% 2.54/1.53 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.54/1.53 => ? [D: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ D @ B )
% 2.54/1.53 & ( in @ Xx @ C )
% 2.54/1.53 & ~ ? [Xy: $i] :
% 2.54/1.53 ( ( in @ Xy @ D )
% 2.54/1.53 & ( in @ Xy @ C ) )
% 2.54/1.53 & ! [E: $i] :
% 2.54/1.53 ( ( in @ E @ B )
% 2.54/1.53 => ( ! [Xy: $i] :
% 2.54/1.53 ( ( in @ Xy @ E )
% 2.54/1.53 => ( in @ Xy @ D ) )
% 2.54/1.53 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(descr_type,type,
% 2.54/1.53 descr: ( $i > $o ) > $i ).
% 2.54/1.53
% 2.54/1.53 thf(descrp_type,type,
% 2.54/1.53 descrp: $o ).
% 2.54/1.53
% 2.54/1.53 thf(descrp,definition,
% 2.54/1.53 ( descrp
% 2.54/1.53 = ( ! [Xphi: $i > $o] :
% 2.54/1.53 ( ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 => ( Xphi
% 2.54/1.53 @ ( descr
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(dsetconstr_type,type,
% 2.54/1.53 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.54/1.53
% 2.54/1.53 thf(dsetconstrI_type,type,
% 2.54/1.53 dsetconstrI: $o ).
% 2.54/1.53
% 2.54/1.53 thf(dsetconstrI,definition,
% 2.54/1.53 ( dsetconstrI
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( ( Xphi @ Xx )
% 2.54/1.53 => ( in @ Xx
% 2.54/1.53 @ ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(dsetconstrEL_type,type,
% 2.54/1.53 dsetconstrEL: $o ).
% 2.54/1.53
% 2.54/1.53 thf(dsetconstrEL,definition,
% 2.54/1.53 ( dsetconstrEL
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx
% 2.54/1.53 @ ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.54/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(dsetconstrER_type,type,
% 2.54/1.53 dsetconstrER: $o ).
% 2.54/1.53
% 2.54/1.53 thf(dsetconstrER,definition,
% 2.54/1.53 ( dsetconstrER
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx
% 2.54/1.53 @ ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.54/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(exuE1_type,type,
% 2.54/1.53 exuE1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(exuE1,definition,
% 2.54/1.53 ( exuE1
% 2.54/1.53 = ( ! [Xphi: $i > $o] :
% 2.54/1.53 ( ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 => ? [Xx: $i] :
% 2.54/1.53 ( ( Xphi @ Xx )
% 2.54/1.53 & ! [Xy: $i] :
% 2.54/1.53 ( ( Xphi @ Xy )
% 2.54/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(prop2set_type,type,
% 2.54/1.53 prop2set: $o > $i ).
% 2.54/1.53
% 2.54/1.53 thf(prop2setE_type,type,
% 2.54/1.53 prop2setE: $o ).
% 2.54/1.53
% 2.54/1.53 thf(prop2setE,definition,
% 2.54/1.53 ( prop2setE
% 2.54/1.53 = ( ! [Xphi: $o,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.54/1.53 => Xphi ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(emptysetE_type,type,
% 2.54/1.53 emptysetE: $o ).
% 2.54/1.53
% 2.54/1.53 thf(emptysetE,definition,
% 2.54/1.53 ( emptysetE
% 2.54/1.53 = ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ emptyset )
% 2.54/1.53 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(emptysetimpfalse_type,type,
% 2.54/1.53 emptysetimpfalse: $o ).
% 2.54/1.53
% 2.54/1.53 thf(emptysetimpfalse,definition,
% 2.54/1.53 ( emptysetimpfalse
% 2.54/1.53 = ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ emptyset )
% 2.54/1.53 => $false ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(notinemptyset_type,type,
% 2.54/1.53 notinemptyset: $o ).
% 2.54/1.53
% 2.54/1.53 thf(notinemptyset,definition,
% 2.54/1.53 ( notinemptyset
% 2.54/1.53 = ( ! [Xx: $i] :
% 2.54/1.53 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(exuE3e_type,type,
% 2.54/1.53 exuE3e: $o ).
% 2.54/1.53
% 2.54/1.53 thf(exuE3e,definition,
% 2.54/1.53 ( exuE3e
% 2.54/1.53 = ( ! [Xphi: $i > $o] :
% 2.54/1.53 ( ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setext_type,type,
% 2.54/1.53 setext: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setext,definition,
% 2.54/1.53 ( setext
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( in @ Xx @ B ) )
% 2.54/1.53 => ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ B )
% 2.54/1.53 => ( in @ Xx @ A ) )
% 2.54/1.53 => ( A = B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(emptyI_type,type,
% 2.54/1.53 emptyI: $o ).
% 2.54/1.53
% 2.54/1.53 thf(emptyI,definition,
% 2.54/1.53 ( emptyI
% 2.54/1.53 = ( ! [A: $i] :
% 2.54/1.53 ( ! [Xx: $i] :
% 2.54/1.53 ~ ( in @ Xx @ A )
% 2.54/1.53 => ( A = emptyset ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(noeltsimpempty_type,type,
% 2.54/1.53 noeltsimpempty: $o ).
% 2.54/1.53
% 2.54/1.53 thf(noeltsimpempty,definition,
% 2.54/1.53 ( noeltsimpempty
% 2.54/1.53 = ( ! [A: $i] :
% 2.54/1.53 ( ! [Xx: $i] :
% 2.54/1.53 ~ ( in @ Xx @ A )
% 2.54/1.53 => ( A = emptyset ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setbeta_type,type,
% 2.54/1.53 setbeta: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setbeta,definition,
% 2.54/1.53 ( setbeta
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( ( in @ Xx
% 2.54/1.53 @ ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.54/1.53 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(nonempty_type,type,
% 2.54/1.53 nonempty: $i > $o ).
% 2.54/1.53
% 2.54/1.53 thf(nonempty,definition,
% 2.54/1.53 ( nonempty
% 2.54/1.53 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(nonemptyE1_type,type,
% 2.54/1.53 nonemptyE1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(nonemptyE1,definition,
% 2.54/1.53 ( nonemptyE1
% 2.54/1.53 = ( ! [A: $i] :
% 2.54/1.53 ( ( nonempty @ A )
% 2.54/1.53 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(nonemptyI_type,type,
% 2.54/1.53 nonemptyI: $o ).
% 2.54/1.53
% 2.54/1.53 thf(nonemptyI,definition,
% 2.54/1.53 ( nonemptyI
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( ( Xphi @ Xx )
% 2.54/1.53 => ( nonempty
% 2.54/1.53 @ ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(nonemptyI1_type,type,
% 2.54/1.53 nonemptyI1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(nonemptyI1,definition,
% 2.54/1.53 ( nonemptyI1
% 2.54/1.53 = ( ! [A: $i] :
% 2.54/1.53 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.54/1.53 => ( nonempty @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinIL_type,type,
% 2.54/1.53 setadjoinIL: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinIL,definition,
% 2.54/1.53 ( setadjoinIL
% 2.54/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(emptyinunitempty_type,type,
% 2.54/1.53 emptyinunitempty: $o ).
% 2.54/1.53
% 2.54/1.53 thf(emptyinunitempty,definition,
% 2.54/1.53 ( emptyinunitempty
% 2.54/1.53 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinIR_type,type,
% 2.54/1.53 setadjoinIR: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinIR,definition,
% 2.54/1.53 ( setadjoinIR
% 2.54/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.54/1.53 ( ( in @ Xy @ A )
% 2.54/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinE_type,type,
% 2.54/1.53 setadjoinE: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinE,definition,
% 2.54/1.53 ( setadjoinE
% 2.54/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.54/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.54/1.53 => ! [Xphi: $o] :
% 2.54/1.53 ( ( ( Xy = Xx )
% 2.54/1.53 => Xphi )
% 2.54/1.53 => ( ( ( in @ Xy @ A )
% 2.54/1.53 => Xphi )
% 2.54/1.53 => Xphi ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinOr_type,type,
% 2.54/1.53 setadjoinOr: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinOr,definition,
% 2.54/1.53 ( setadjoinOr
% 2.54/1.53 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.54/1.53 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.54/1.53 => ( ( Xy = Xx )
% 2.54/1.53 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setoftrueEq_type,type,
% 2.54/1.53 setoftrueEq: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setoftrueEq,definition,
% 2.54/1.53 ( setoftrueEq
% 2.54/1.53 = ( ! [A: $i] :
% 2.54/1.53 ( ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xx: $i] : $true )
% 2.54/1.53 = A ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(powersetI_type,type,
% 2.54/1.53 powersetI: $o ).
% 2.54/1.53
% 2.54/1.53 thf(powersetI,definition,
% 2.54/1.53 ( powersetI
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ B )
% 2.54/1.53 => ( in @ Xx @ A ) )
% 2.54/1.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(emptyinPowerset_type,type,
% 2.54/1.53 emptyinPowerset: $o ).
% 2.54/1.53
% 2.54/1.53 thf(emptyinPowerset,definition,
% 2.54/1.53 ( emptyinPowerset
% 2.54/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(emptyInPowerset_type,type,
% 2.54/1.53 emptyInPowerset: $o ).
% 2.54/1.53
% 2.54/1.53 thf(emptyInPowerset,definition,
% 2.54/1.53 ( emptyInPowerset
% 2.54/1.53 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(powersetE_type,type,
% 2.54/1.53 powersetE: $o ).
% 2.54/1.53
% 2.54/1.53 thf(powersetE,definition,
% 2.54/1.53 ( powersetE
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.54/1.53 => ( ( in @ Xx @ B )
% 2.54/1.53 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setunionI_type,type,
% 2.54/1.53 setunionI: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setunionI,definition,
% 2.54/1.53 ( setunionI
% 2.54/1.53 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.54/1.53 ( ( in @ Xx @ B )
% 2.54/1.53 => ( ( in @ B @ A )
% 2.54/1.53 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setunionE_type,type,
% 2.54/1.53 setunionE: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setunionE,definition,
% 2.54/1.53 ( setunionE
% 2.54/1.53 = ( ! [A: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ ( setunion @ A ) )
% 2.54/1.53 => ! [Xphi: $o] :
% 2.54/1.53 ( ! [B: $i] :
% 2.54/1.53 ( ( in @ Xx @ B )
% 2.54/1.53 => ( ( in @ B @ A )
% 2.54/1.53 => Xphi ) )
% 2.54/1.53 => Xphi ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(subPowSU_type,type,
% 2.54/1.53 subPowSU: $o ).
% 2.54/1.53
% 2.54/1.53 thf(subPowSU,definition,
% 2.54/1.53 ( subPowSU
% 2.54/1.53 = ( ! [A: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(exuE2_type,type,
% 2.54/1.53 exuE2: $o ).
% 2.54/1.53
% 2.54/1.53 thf(exuE2,definition,
% 2.54/1.53 ( exuE2
% 2.54/1.53 = ( ! [Xphi: $i > $o] :
% 2.54/1.53 ( ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 => ? [Xx: $i] :
% 2.54/1.53 ! [Xy: $i] :
% 2.54/1.53 ( ( Xphi @ Xy )
% 2.54/1.53 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(nonemptyImpWitness_type,type,
% 2.54/1.53 nonemptyImpWitness: $o ).
% 2.54/1.53
% 2.54/1.53 thf(nonemptyImpWitness,definition,
% 2.54/1.53 ( nonemptyImpWitness
% 2.54/1.53 = ( ! [A: $i] :
% 2.54/1.53 ( ( nonempty @ A )
% 2.54/1.53 => ? [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 & $true ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(uniqinunit_type,type,
% 2.54/1.53 uniqinunit: $o ).
% 2.54/1.53
% 2.54/1.53 thf(uniqinunit,definition,
% 2.54/1.53 ( uniqinunit
% 2.54/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.54/1.53 => ( Xx = Xy ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(notinsingleton_type,type,
% 2.54/1.53 notinsingleton: $o ).
% 2.54/1.53
% 2.54/1.53 thf(notinsingleton,definition,
% 2.54/1.53 ( notinsingleton
% 2.54/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( Xx != Xy )
% 2.54/1.53 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(eqinunit_type,type,
% 2.54/1.53 eqinunit: $o ).
% 2.54/1.53
% 2.54/1.53 thf(eqinunit,definition,
% 2.54/1.53 ( eqinunit
% 2.54/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( Xx = Xy )
% 2.54/1.53 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(singletonsswitch_type,type,
% 2.54/1.53 singletonsswitch: $o ).
% 2.54/1.53
% 2.54/1.53 thf(singletonsswitch,definition,
% 2.54/1.53 ( singletonsswitch
% 2.54/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.54/1.53 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(upairsetE_type,type,
% 2.54/1.53 upairsetE: $o ).
% 2.54/1.53
% 2.54/1.53 thf(upairsetE,definition,
% 2.54/1.53 ( upairsetE
% 2.54/1.53 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.54/1.53 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.54/1.53 => ( ( Xz = Xx )
% 2.54/1.53 | ( Xz = Xy ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(upairsetIL_type,type,
% 2.54/1.53 upairsetIL: $o ).
% 2.54/1.53
% 2.54/1.53 thf(upairsetIL,definition,
% 2.54/1.53 ( upairsetIL
% 2.54/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(upairsetIR_type,type,
% 2.54/1.53 upairsetIR: $o ).
% 2.54/1.53
% 2.54/1.53 thf(upairsetIR,definition,
% 2.54/1.53 ( upairsetIR
% 2.54/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(emptyE1_type,type,
% 2.54/1.53 emptyE1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(emptyE1,definition,
% 2.54/1.53 ( emptyE1
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.53 ( ? [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 & ( Xphi @ Xx ) )
% 2.54/1.53 => ( ( ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 = emptyset )
% 2.54/1.53 => $false ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(vacuousDall_type,type,
% 2.54/1.53 vacuousDall: $o ).
% 2.54/1.53
% 2.54/1.53 thf(vacuousDall,definition,
% 2.54/1.53 ( vacuousDall
% 2.54/1.53 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ emptyset )
% 2.54/1.53 => ( Xphi @ Xx ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(quantDeMorgan1_type,type,
% 2.54/1.53 quantDeMorgan1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(quantDeMorgan1,definition,
% 2.54/1.53 ( quantDeMorgan1
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.53 ( ~ ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( Xphi @ Xx ) )
% 2.54/1.53 => ? [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(quantDeMorgan2_type,type,
% 2.54/1.53 quantDeMorgan2: $o ).
% 2.54/1.53
% 2.54/1.53 thf(quantDeMorgan2,definition,
% 2.54/1.53 ( quantDeMorgan2
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.53 ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ~ ( Xphi @ Xx ) )
% 2.54/1.53 => ~ ? [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(quantDeMorgan3_type,type,
% 2.54/1.53 quantDeMorgan3: $o ).
% 2.54/1.53
% 2.54/1.53 thf(quantDeMorgan3,definition,
% 2.54/1.53 ( quantDeMorgan3
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.53 ( ~ ? [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 & ( Xphi @ Xx ) )
% 2.54/1.53 => ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(quantDeMorgan4_type,type,
% 2.54/1.53 quantDeMorgan4: $o ).
% 2.54/1.53
% 2.54/1.53 thf(quantDeMorgan4,definition,
% 2.54/1.53 ( quantDeMorgan4
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.53 ( ? [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 & ~ ( Xphi @ Xx ) )
% 2.54/1.53 => ~ ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(prop2setI_type,type,
% 2.54/1.53 prop2setI: $o ).
% 2.54/1.53
% 2.54/1.53 thf(prop2setI,definition,
% 2.54/1.53 ( prop2setI
% 2.54/1.53 = ( ! [Xphi: $o] :
% 2.54/1.53 ( Xphi
% 2.54/1.53 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(set2prop_type,type,
% 2.54/1.53 set2prop: $i > $o ).
% 2.54/1.53
% 2.54/1.53 thf(prop2set2propI_type,type,
% 2.54/1.53 prop2set2propI: $o ).
% 2.54/1.53
% 2.54/1.53 thf(prop2set2propI,definition,
% 2.54/1.53 ( prop2set2propI
% 2.54/1.53 = ( ! [Xphi: $o] :
% 2.54/1.53 ( Xphi
% 2.54/1.53 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(notdexE_type,type,
% 2.54/1.53 notdexE: $o ).
% 2.54/1.53
% 2.54/1.53 thf(notdexE,definition,
% 2.54/1.53 ( notdexE
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.53 ( ~ ? [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 & ( Xphi @ Xx ) )
% 2.54/1.53 => ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(notdallE_type,type,
% 2.54/1.53 notdallE: $o ).
% 2.54/1.53
% 2.54/1.53 thf(notdallE,definition,
% 2.54/1.53 ( notdallE
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.53 ( ~ ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( Xphi @ Xx ) )
% 2.54/1.53 => ? [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(exuI1_type,type,
% 2.54/1.53 exuI1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(exuI1,definition,
% 2.54/1.53 ( exuI1
% 2.54/1.53 = ( ! [Xphi: $i > $o] :
% 2.54/1.53 ( ? [Xx: $i] :
% 2.54/1.53 ( ( Xphi @ Xx )
% 2.54/1.53 & ! [Xy: $i] :
% 2.54/1.53 ( ( Xphi @ Xy )
% 2.54/1.53 => ( Xx = Xy ) ) )
% 2.54/1.53 => ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(exuI3_type,type,
% 2.54/1.53 exuI3: $o ).
% 2.54/1.53
% 2.54/1.53 thf(exuI3,definition,
% 2.54/1.53 ( exuI3
% 2.54/1.53 = ( ! [Xphi: $i > $o] :
% 2.54/1.53 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.54/1.53 => ( ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( Xphi @ Xx )
% 2.54/1.53 => ( ( Xphi @ Xy )
% 2.54/1.53 => ( Xx = Xy ) ) )
% 2.54/1.53 => ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(exuI2_type,type,
% 2.54/1.53 exuI2: $o ).
% 2.54/1.53
% 2.54/1.53 thf(exuI2,definition,
% 2.54/1.53 ( exuI2
% 2.54/1.53 = ( ! [Xphi: $i > $o] :
% 2.54/1.53 ( ? [Xx: $i] :
% 2.54/1.53 ! [Xy: $i] :
% 2.54/1.53 ( ( Xphi @ Xy )
% 2.54/1.53 <=> ( Xy = Xx ) )
% 2.54/1.53 => ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(inCongP_type,type,
% 2.54/1.53 inCongP: $o ).
% 2.54/1.53
% 2.54/1.53 thf(inCongP,definition,
% 2.54/1.53 ( inCongP
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( A = B )
% 2.54/1.53 => ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( Xx = Xy )
% 2.54/1.53 => ( ( in @ Xx @ A )
% 2.54/1.53 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(in__Cong_type,type,
% 2.54/1.53 in__Cong: $o ).
% 2.54/1.53
% 2.54/1.53 thf(in__Cong,definition,
% 2.54/1.53 ( in__Cong
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( A = B )
% 2.54/1.53 => ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( Xx = Xy )
% 2.54/1.53 => ( ( in @ Xx @ A )
% 2.54/1.53 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(exuE3u_type,type,
% 2.54/1.53 exuE3u: $o ).
% 2.54/1.53
% 2.54/1.53 thf(exuE3u,definition,
% 2.54/1.53 ( exuE3u
% 2.54/1.53 = ( ! [Xphi: $i > $o] :
% 2.54/1.53 ( ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 => ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( Xphi @ Xx )
% 2.54/1.53 => ( ( Xphi @ Xy )
% 2.54/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(exu__Cong_type,type,
% 2.54/1.53 exu__Cong: $o ).
% 2.54/1.53
% 2.54/1.53 thf(exu__Cong,definition,
% 2.54/1.53 ( exu__Cong
% 2.54/1.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.54/1.53 ( ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( Xx = Xy )
% 2.54/1.53 => ( ( Xphi @ Xx )
% 2.54/1.53 <=> ( Xpsi @ Xy ) ) )
% 2.54/1.53 => ( ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 <=> ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(emptyset__Cong_type,type,
% 2.54/1.53 emptyset__Cong: $o ).
% 2.54/1.53
% 2.54/1.53 thf(emptyset__Cong,definition,
% 2.54/1.53 ( emptyset__Cong
% 2.54/1.53 = ( emptyset = emptyset ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoin__Cong_type,type,
% 2.54/1.53 setadjoin__Cong: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoin__Cong,definition,
% 2.54/1.53 ( setadjoin__Cong
% 2.54/1.53 = ( ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( Xx = Xy )
% 2.54/1.53 => ! [Xz: $i,Xu: $i] :
% 2.54/1.53 ( ( Xz = Xu )
% 2.54/1.53 => ( ( setadjoin @ Xx @ Xz )
% 2.54/1.53 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(powerset__Cong_type,type,
% 2.54/1.53 powerset__Cong: $o ).
% 2.54/1.53
% 2.54/1.53 thf(powerset__Cong,definition,
% 2.54/1.53 ( powerset__Cong
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( A = B )
% 2.54/1.53 => ( ( powerset @ A )
% 2.54/1.53 = ( powerset @ B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setunion__Cong_type,type,
% 2.54/1.53 setunion__Cong: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setunion__Cong,definition,
% 2.54/1.53 ( setunion__Cong
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( A = B )
% 2.54/1.53 => ( ( setunion @ A )
% 2.54/1.53 = ( setunion @ B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(omega__Cong_type,type,
% 2.54/1.53 omega__Cong: $o ).
% 2.54/1.53
% 2.54/1.53 thf(omega__Cong,definition,
% 2.54/1.53 ( omega__Cong
% 2.54/1.53 = ( omega = omega ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(exuEu_type,type,
% 2.54/1.53 exuEu: $o ).
% 2.54/1.53
% 2.54/1.53 thf(exuEu,definition,
% 2.54/1.53 ( exuEu
% 2.54/1.53 = ( ! [Xphi: $i > $o] :
% 2.54/1.53 ( ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 => ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( Xphi @ Xx )
% 2.54/1.53 => ( ( Xphi @ Xy )
% 2.54/1.53 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(descr__Cong_type,type,
% 2.54/1.53 descr__Cong: $o ).
% 2.54/1.53
% 2.54/1.53 thf(descr__Cong,definition,
% 2.54/1.53 ( descr__Cong
% 2.54/1.53 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.54/1.53 ( ! [Xx: $i,Xy: $i] :
% 2.54/1.53 ( ( Xx = Xy )
% 2.54/1.53 => ( ( Xphi @ Xx )
% 2.54/1.53 <=> ( Xpsi @ Xy ) ) )
% 2.54/1.53 => ( ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 => ( ( exu
% 2.54/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.54/1.53 => ( ( descr
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 = ( descr
% 2.54/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(dsetconstr__Cong_type,type,
% 2.54/1.53 dsetconstr__Cong: $o ).
% 2.54/1.53
% 2.54/1.53 thf(dsetconstr__Cong,definition,
% 2.54/1.53 ( dsetconstr__Cong
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( A = B )
% 2.54/1.53 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.54/1.53 ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ! [Xy: $i] :
% 2.54/1.53 ( ( in @ Xy @ B )
% 2.54/1.53 => ( ( Xx = Xy )
% 2.54/1.53 => ( ( Xphi @ Xx )
% 2.54/1.53 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.54/1.53 => ( ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 = ( dsetconstr @ B
% 2.54/1.53 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(subset_type,type,
% 2.54/1.53 subset: $i > $i > $o ).
% 2.54/1.53
% 2.54/1.53 thf(disjoint_type,type,
% 2.54/1.53 disjoint: $i > $i > $o ).
% 2.54/1.53
% 2.54/1.53 thf(setsmeet_type,type,
% 2.54/1.53 setsmeet: $i > $i > $o ).
% 2.54/1.53
% 2.54/1.53 thf(subsetI1_type,type,
% 2.54/1.53 subsetI1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(subsetI1,definition,
% 2.54/1.53 ( subsetI1
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( in @ Xx @ B ) )
% 2.54/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(eqimpsubset2_type,type,
% 2.54/1.53 eqimpsubset2: $o ).
% 2.54/1.53
% 2.54/1.53 thf(eqimpsubset2,definition,
% 2.54/1.53 ( eqimpsubset2
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( A = B )
% 2.54/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(eqimpsubset1_type,type,
% 2.54/1.53 eqimpsubset1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(eqimpsubset1,definition,
% 2.54/1.53 ( eqimpsubset1
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( A = B )
% 2.54/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(subsetI2_type,type,
% 2.54/1.53 subsetI2: $o ).
% 2.54/1.53
% 2.54/1.53 thf(subsetI2,definition,
% 2.54/1.53 ( subsetI2
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ! [Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( in @ Xx @ B ) )
% 2.54/1.53 => ( subset @ A @ B ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(emptysetsubset_type,type,
% 2.54/1.53 emptysetsubset: $o ).
% 2.54/1.53
% 2.54/1.53 thf(emptysetsubset,definition,
% 2.54/1.53 ( emptysetsubset
% 2.54/1.53 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(subsetE_type,type,
% 2.54/1.53 subsetE: $o ).
% 2.54/1.53
% 2.54/1.53 thf(subsetE,definition,
% 2.54/1.53 ( subsetE
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.53 ( ( subset @ A @ B )
% 2.54/1.53 => ( ( in @ Xx @ A )
% 2.54/1.53 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(subsetE2_type,type,
% 2.54/1.53 subsetE2: $o ).
% 2.54/1.53
% 2.54/1.53 thf(subsetE2,definition,
% 2.54/1.53 ( subsetE2
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.53 ( ( subset @ A @ B )
% 2.54/1.53 => ( ~ ( in @ Xx @ B )
% 2.54/1.53 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(notsubsetI_type,type,
% 2.54/1.53 notsubsetI: $o ).
% 2.54/1.53
% 2.54/1.53 thf(notsubsetI,definition,
% 2.54/1.53 ( notsubsetI
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( ~ ( in @ Xx @ B )
% 2.54/1.53 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(notequalI1_type,type,
% 2.54/1.53 notequalI1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(notequalI1,definition,
% 2.54/1.53 ( notequalI1
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ~ ( subset @ A @ B )
% 2.54/1.53 => ( A != B ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(notequalI2_type,type,
% 2.54/1.53 notequalI2: $o ).
% 2.54/1.53
% 2.54/1.53 thf(notequalI2,definition,
% 2.54/1.53 ( notequalI2
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( ~ ( in @ Xx @ B )
% 2.54/1.53 => ( A != B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(subsetRefl_type,type,
% 2.54/1.53 subsetRefl: $o ).
% 2.54/1.53
% 2.54/1.53 thf(subsetRefl,definition,
% 2.54/1.53 ( subsetRefl
% 2.54/1.53 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(subsetTrans_type,type,
% 2.54/1.53 subsetTrans: $o ).
% 2.54/1.53
% 2.54/1.53 thf(subsetTrans,definition,
% 2.54/1.53 ( subsetTrans
% 2.54/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.54/1.53 ( ( subset @ A @ B )
% 2.54/1.53 => ( ( subset @ B @ C )
% 2.54/1.53 => ( subset @ A @ C ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinSub_type,type,
% 2.54/1.53 setadjoinSub: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinSub,definition,
% 2.54/1.53 ( setadjoinSub
% 2.54/1.53 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinSub2_type,type,
% 2.54/1.53 setadjoinSub2: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setadjoinSub2,definition,
% 2.54/1.53 ( setadjoinSub2
% 2.54/1.53 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.54/1.53 ( ( subset @ A @ B )
% 2.54/1.53 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(subset2powerset_type,type,
% 2.54/1.53 subset2powerset: $o ).
% 2.54/1.53
% 2.54/1.53 thf(subset2powerset,definition,
% 2.54/1.53 ( subset2powerset
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( subset @ A @ B )
% 2.54/1.53 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(setextsub_type,type,
% 2.54/1.53 setextsub: $o ).
% 2.54/1.53
% 2.54/1.53 thf(setextsub,definition,
% 2.54/1.53 ( setextsub
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( subset @ A @ B )
% 2.54/1.53 => ( ( subset @ B @ A )
% 2.54/1.53 => ( A = B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(subsetemptysetimpeq_type,type,
% 2.54/1.53 subsetemptysetimpeq: $o ).
% 2.54/1.53
% 2.54/1.53 thf(subsetemptysetimpeq,definition,
% 2.54/1.53 ( subsetemptysetimpeq
% 2.54/1.53 = ( ! [A: $i] :
% 2.54/1.53 ( ( subset @ A @ emptyset )
% 2.54/1.53 => ( A = emptyset ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(powersetI1_type,type,
% 2.54/1.53 powersetI1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(powersetI1,definition,
% 2.54/1.53 ( powersetI1
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( subset @ B @ A )
% 2.54/1.53 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(powersetE1_type,type,
% 2.54/1.53 powersetE1: $o ).
% 2.54/1.53
% 2.54/1.53 thf(powersetE1,definition,
% 2.54/1.53 ( powersetE1
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( in @ B @ ( powerset @ A ) )
% 2.54/1.53 => ( subset @ B @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(inPowerset_type,type,
% 2.54/1.53 inPowerset: $o ).
% 2.54/1.53
% 2.54/1.53 thf(inPowerset,definition,
% 2.54/1.53 ( inPowerset
% 2.54/1.53 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(powersetsubset_type,type,
% 2.54/1.53 powersetsubset: $o ).
% 2.54/1.53
% 2.54/1.53 thf(powersetsubset,definition,
% 2.54/1.53 ( powersetsubset
% 2.54/1.53 = ( ! [A: $i,B: $i] :
% 2.54/1.53 ( ( subset @ A @ B )
% 2.54/1.53 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(sepInPowerset_type,type,
% 2.54/1.53 sepInPowerset: $o ).
% 2.54/1.53
% 2.54/1.53 thf(sepInPowerset,definition,
% 2.54/1.53 ( sepInPowerset
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.53 ( in
% 2.54/1.53 @ ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 @ ( powerset @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(sepSubset_type,type,
% 2.54/1.53 sepSubset: $o ).
% 2.54/1.53
% 2.54/1.53 thf(sepSubset,definition,
% 2.54/1.53 ( sepSubset
% 2.54/1.53 = ( ! [A: $i,Xphi: $i > $o] :
% 2.54/1.53 ( subset
% 2.54/1.53 @ ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.54/1.53 @ A ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binunion_type,type,
% 2.54/1.53 binunion: $i > $i > $i ).
% 2.54/1.53
% 2.54/1.53 thf(binunionIL_type,type,
% 2.54/1.53 binunionIL: $o ).
% 2.54/1.53
% 2.54/1.53 thf(binunionIL,definition,
% 2.54/1.53 ( binunionIL
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(upairset2IR_type,type,
% 2.54/1.53 upairset2IR: $o ).
% 2.54/1.53
% 2.54/1.53 thf(upairset2IR,definition,
% 2.54/1.53 ( upairset2IR
% 2.54/1.53 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binunionIR_type,type,
% 2.54/1.53 binunionIR: $o ).
% 2.54/1.53
% 2.54/1.53 thf(binunionIR,definition,
% 2.54/1.53 ( binunionIR
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ B )
% 2.54/1.53 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binunionEcases_type,type,
% 2.54/1.53 binunionEcases: $o ).
% 2.54/1.53
% 2.54/1.53 thf(binunionEcases,definition,
% 2.54/1.53 ( binunionEcases
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.54/1.53 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.54/1.53 => ( ( ( in @ Xx @ A )
% 2.54/1.53 => Xphi )
% 2.54/1.53 => ( ( ( in @ Xx @ B )
% 2.54/1.53 => Xphi )
% 2.54/1.53 => Xphi ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binunionE_type,type,
% 2.54/1.53 binunionE: $o ).
% 2.54/1.53
% 2.54/1.53 thf(binunionE,definition,
% 2.54/1.53 ( binunionE
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.54/1.53 => ( ( in @ Xx @ A )
% 2.54/1.53 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binunionLsub_type,type,
% 2.54/1.53 binunionLsub: $o ).
% 2.54/1.53
% 2.54/1.53 thf(binunionLsub,definition,
% 2.54/1.53 ( binunionLsub
% 2.54/1.53 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binunionRsub_type,type,
% 2.54/1.53 binunionRsub: $o ).
% 2.54/1.53
% 2.54/1.53 thf(binunionRsub,definition,
% 2.54/1.53 ( binunionRsub
% 2.54/1.53 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binintersect_type,type,
% 2.54/1.53 binintersect: $i > $i > $i ).
% 2.54/1.53
% 2.54/1.53 thf(binintersect,definition,
% 2.54/1.53 ( binintersect
% 2.54/1.53 = ( ^ [A: $i,B: $i] :
% 2.54/1.53 ( dsetconstr @ A
% 2.54/1.53 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binintersectI_type,type,
% 2.54/1.53 binintersectI: $o ).
% 2.54/1.53
% 2.54/1.53 thf(binintersectI,definition,
% 2.54/1.53 ( binintersectI
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ A )
% 2.54/1.53 => ( ( in @ Xx @ B )
% 2.54/1.53 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binintersectSubset5_type,type,
% 2.54/1.53 binintersectSubset5: $o ).
% 2.54/1.53
% 2.54/1.53 thf(binintersectSubset5,definition,
% 2.54/1.53 ( binintersectSubset5
% 2.54/1.53 = ( ! [A: $i,B: $i,C: $i] :
% 2.54/1.53 ( ( subset @ C @ A )
% 2.54/1.53 => ( ( subset @ C @ B )
% 2.54/1.53 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binintersectEL_type,type,
% 2.54/1.53 binintersectEL: $o ).
% 2.54/1.53
% 2.54/1.53 thf(binintersectEL,definition,
% 2.54/1.53 ( binintersectEL
% 2.54/1.53 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.54/1.53 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.54/1.53 => ( in @ Xx @ A ) ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binintersectLsub_type,type,
% 2.54/1.53 binintersectLsub: $o ).
% 2.54/1.53
% 2.54/1.53 thf(binintersectLsub,definition,
% 2.54/1.53 ( binintersectLsub
% 2.54/1.53 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.54/1.53
% 2.54/1.53 thf(binintersectSubset2,conjecture,
% 2.54/1.53 ( setextAx
% 2.54/1.53 => ( emptysetAx
% 2.54/1.53 => ( setadjoinAx
% 2.54/1.53 => ( powersetAx
% 2.54/1.53 => ( setunionAx
% 2.54/1.53 => ( omega0Ax
% 2.54/1.53 => ( omegaSAx
% 2.54/1.53 => ( omegaIndAx
% 2.54/1.53 => ( replAx
% 2.54/1.53 => ( foundationAx
% 2.54/1.53 => ( wellorderingAx
% 2.54/1.53 => ( descrp
% 2.54/1.53 => ( dsetconstrI
% 2.54/1.53 => ( dsetconstrEL
% 2.54/1.53 => ( dsetconstrER
% 2.54/1.53 => ( exuE1
% 2.54/1.53 => ( prop2setE
% 2.54/1.53 => ( emptysetE
% 2.54/1.53 => ( emptysetimpfalse
% 2.54/1.53 => ( notinemptyset
% 2.54/1.53 => ( exuE3e
% 2.54/1.53 => ( setext
% 2.54/1.53 => ( emptyI
% 2.54/1.53 => ( noeltsimpempty
% 2.54/1.53 => ( setbeta
% 2.54/1.53 => ( nonemptyE1
% 2.54/1.53 => ( nonemptyI
% 2.54/1.53 => ( nonemptyI1
% 2.54/1.53 => ( setadjoinIL
% 2.54/1.53 => ( emptyinunitempty
% 2.54/1.53 => ( setadjoinIR
% 2.54/1.53 => ( setadjoinE
% 2.54/1.53 => ( setadjoinOr
% 2.54/1.53 => ( setoftrueEq
% 2.54/1.53 => ( powersetI
% 2.54/1.53 => ( emptyinPowerset
% 2.54/1.53 => ( emptyInPowerset
% 2.54/1.53 => ( powersetE
% 2.54/1.53 => ( setunionI
% 2.54/1.53 => ( setunionE
% 2.54/1.53 => ( subPowSU
% 2.54/1.53 => ( exuE2
% 2.54/1.53 => ( nonemptyImpWitness
% 2.54/1.53 => ( uniqinunit
% 2.54/1.53 => ( notinsingleton
% 2.54/1.53 => ( eqinunit
% 2.54/1.53 => ( singletonsswitch
% 2.54/1.53 => ( upairsetE
% 2.54/1.53 => ( upairsetIL
% 2.54/1.53 => ( upairsetIR
% 2.54/1.53 => ( emptyE1
% 2.54/1.53 => ( vacuousDall
% 2.54/1.53 => ( quantDeMorgan1
% 2.54/1.53 => ( quantDeMorgan2
% 2.54/1.53 => ( quantDeMorgan3
% 2.54/1.53 => ( quantDeMorgan4
% 2.54/1.53 => ( prop2setI
% 2.54/1.53 => ( prop2set2propI
% 2.54/1.53 => ( notdexE
% 2.54/1.53 => ( notdallE
% 2.54/1.53 => ( exuI1
% 2.54/1.53 => ( exuI3
% 2.54/1.53 => ( exuI2
% 2.54/1.53 => ( inCongP
% 2.54/1.53 => ( in__Cong
% 2.54/1.53 => ( exuE3u
% 2.54/1.53 => ( exu__Cong
% 2.54/1.53 => ( emptyset__Cong
% 2.54/1.53 => ( setadjoin__Cong
% 2.54/1.53 => ( powerset__Cong
% 2.54/1.53 => ( setunion__Cong
% 2.54/1.53 => ( omega__Cong
% 2.54/1.53 => ( exuEu
% 2.54/1.53 => ( descr__Cong
% 2.54/1.53 => ( dsetconstr__Cong
% 2.54/1.53 => ( subsetI1
% 2.54/1.53 => ( eqimpsubset2
% 2.54/1.53 => ( eqimpsubset1
% 2.54/1.53 => ( subsetI2
% 2.54/1.53 => ( emptysetsubset
% 2.54/1.53 => ( subsetE
% 2.54/1.53 => ( subsetE2
% 2.54/1.53 => ( notsubsetI
% 2.54/1.53 => ( notequalI1
% 2.54/1.53 => ( notequalI2
% 2.54/1.53 => ( subsetRefl
% 2.54/1.53 => ( subsetTrans
% 2.54/1.53 => ( setadjoinSub
% 2.54/1.53 => ( setadjoinSub2
% 2.54/1.53 => ( subset2powerset
% 2.54/1.53 => ( setextsub
% 2.54/1.53 => ( subsetemptysetimpeq
% 2.54/1.53 => ( powersetI1
% 2.54/1.53 => ( powersetE1
% 2.54/1.53 => ( inPowerset
% 2.54/1.53 => ( powersetsubset
% 2.54/1.53 => ( sepInPowerset
% 2.54/1.53 => ( sepSubset
% 2.54/1.53 => ( binunionIL
% 2.54/1.53 => ( upairset2IR
% 2.54/1.53 => ( binunionIR
% 2.54/1.53 => ( binunionEcases
% 2.54/1.53 => ( binunionE
% 2.54/1.53 => ( binunionLsub
% 2.54/1.53 => ( binunionRsub
% 2.54/1.53 => ( binintersectI
% 2.54/1.53 => ( binintersectSubset5
% 2.54/1.53 => ( binintersectEL
% 2.54/1.53 => ( binintersectLsub
% 2.54/1.53 => ! [A: $i,B: $i] :
% 2.54/1.53 ( ( subset @ A @ B )
% 2.54/1.53 => ( ( binintersect @ A @ B )
% 2.54/1.53 = A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.54/1.53 ------------------------
% 2.54/1.55 % (25526)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/183Mi)
% 2.54/1.55 % (25527)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_25342 for (2999ds/4Mi)
% 2.54/1.55 % (25527)Instruction limit reached!
% 2.54/1.55 % (25527)------------------------------
% 2.54/1.55 % (25527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.55 % (25527)Termination reason: Unknown
% 2.54/1.55 % (25527)Termination phase: shuffling
% 2.54/1.55
% 2.54/1.55 % (25527)Memory used [KB]: 1279
% 2.54/1.55 % (25527)Time elapsed: 0.003 s
% 2.54/1.55 % (25527)Instructions burned: 6 (million)
% 2.54/1.55 % (25527)------------------------------
% 2.54/1.55 % (25527)------------------------------
% 2.54/1.56 % (25529)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/2Mi)
% 2.54/1.56 % (25530)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_25342 for (2999ds/2Mi)
% 2.54/1.56 % (25528)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_25342 for (2999ds/27Mi)
% 2.54/1.56 % (25529)Instruction limit reached!
% 2.54/1.56 % (25529)------------------------------
% 2.54/1.56 % (25529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.56 % (25529)Termination reason: Unknown
% 2.54/1.56 % (25529)Termination phase: shuffling
% 2.54/1.56
% 2.54/1.56 % (25529)Memory used [KB]: 1151
% 2.54/1.56 % (25529)Time elapsed: 0.002 s
% 2.54/1.56 % (25529)Instructions burned: 2 (million)
% 2.54/1.56 % (25529)------------------------------
% 2.54/1.56 % (25529)------------------------------
% 2.54/1.56 % (25530)Instruction limit reached!
% 2.54/1.56 % (25530)------------------------------
% 2.54/1.56 % (25530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.56 % (25530)Termination reason: Unknown
% 2.54/1.56 % (25530)Termination phase: shuffling
% 2.54/1.56
% 2.54/1.56 % (25530)Memory used [KB]: 1151
% 2.54/1.56 % (25530)Time elapsed: 0.003 s
% 2.54/1.56 % (25530)Instructions burned: 3 (million)
% 2.54/1.56 % (25530)------------------------------
% 2.54/1.56 % (25530)------------------------------
% 2.54/1.56 % (25532)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/18Mi)
% 2.54/1.56 % (25531)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_25342 for (2999ds/275Mi)
% 2.54/1.56 % (25534)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/3Mi)
% 2.54/1.56 % (25534)Instruction limit reached!
% 2.54/1.56 % (25534)------------------------------
% 2.54/1.56 % (25534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.56 % (25534)Termination reason: Unknown
% 2.54/1.56 % (25534)Termination phase: shuffling
% 2.54/1.56
% 2.54/1.56 % (25534)Memory used [KB]: 1151
% 2.54/1.56 % (25534)Time elapsed: 0.002 s
% 2.54/1.56 % (25534)Instructions burned: 4 (million)
% 2.54/1.56 % (25534)------------------------------
% 2.54/1.56 % (25534)------------------------------
% 2.54/1.57 % (25532)Instruction limit reached!
% 2.54/1.57 % (25532)------------------------------
% 2.54/1.57 % (25532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (25532)Termination reason: Unknown
% 2.54/1.57 % (25532)Termination phase: Preprocessing 3
% 2.54/1.57
% 2.54/1.57 % (25532)Memory used [KB]: 1535
% 2.54/1.57 % (25532)Time elapsed: 0.012 s
% 2.54/1.57 % (25532)Instructions burned: 19 (million)
% 2.54/1.57 % (25532)------------------------------
% 2.54/1.57 % (25532)------------------------------
% 2.54/1.57 % (25528)Instruction limit reached!
% 2.54/1.57 % (25528)------------------------------
% 2.54/1.57 % (25528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.57 % (25528)Termination reason: Unknown
% 2.54/1.57 % (25528)Termination phase: Property scanning
% 2.54/1.57
% 2.54/1.57 % (25528)Memory used [KB]: 1535
% 2.54/1.57 % (25528)Time elapsed: 0.014 s
% 2.54/1.57 % (25528)Instructions burned: 27 (million)
% 2.54/1.57 % (25528)------------------------------
% 2.54/1.57 % (25528)------------------------------
% 2.54/1.57 % (25536)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_25342 for (2999ds/15Mi)
% 2.54/1.57 % (25538)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_25342 for (2999ds/3Mi)
% 2.54/1.57 % (25538)Instruction limit reached!
% 2.54/1.57 % (25538)------------------------------
% 2.54/1.57 % (25538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.58 % (25538)Termination reason: Unknown
% 2.54/1.58 % (25538)Termination phase: shuffling
% 2.54/1.58
% 2.54/1.58 % (25538)Memory used [KB]: 1151
% 2.54/1.58 % (25538)Time elapsed: 0.002 s
% 2.54/1.58 % (25538)Instructions burned: 4 (million)
% 2.54/1.58 % (25538)------------------------------
% 2.54/1.58 % (25538)------------------------------
% 2.54/1.58 % (25535)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_25342 for (2999ds/37Mi)
% 2.54/1.58 % (25536)Instruction limit reached!
% 2.54/1.58 % (25536)------------------------------
% 2.54/1.58 % (25536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.58 % (25536)Termination reason: Unknown
% 2.54/1.58 % (25536)Termination phase: Naming
% 2.54/1.58
% 2.54/1.58 % (25536)Memory used [KB]: 1535
% 2.54/1.58 % (25536)Time elapsed: 0.009 s
% 2.54/1.58 % (25536)Instructions burned: 16 (million)
% 2.54/1.58 % (25536)------------------------------
% 2.54/1.58 % (25536)------------------------------
% 2.54/1.58 % (25539)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_25342 for (2999ds/1041Mi)
% 2.54/1.58 % (25541)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/16Mi)
% 2.54/1.58 % (25540)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/7Mi)
% 2.54/1.59 % (25540)Instruction limit reached!
% 2.54/1.59 % (25540)------------------------------
% 2.54/1.59 % (25540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (25540)Termination reason: Unknown
% 2.54/1.59 % (25540)Termination phase: shuffling
% 2.54/1.59
% 2.54/1.59 % (25540)Memory used [KB]: 1279
% 2.54/1.59 % (25540)Time elapsed: 0.005 s
% 2.54/1.59 % (25540)Instructions burned: 8 (million)
% 2.54/1.59 % (25540)------------------------------
% 2.54/1.59 % (25540)------------------------------
% 2.54/1.59 % (25541)Instruction limit reached!
% 2.54/1.59 % (25541)------------------------------
% 2.54/1.59 % (25541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (25541)Termination reason: Unknown
% 2.54/1.59 % (25541)Termination phase: Property scanning
% 2.54/1.59
% 2.54/1.59 % (25541)Memory used [KB]: 1535
% 2.54/1.59 % (25541)Time elapsed: 0.006 s
% 2.54/1.59 % (25541)Instructions burned: 18 (million)
% 2.54/1.59 % (25541)------------------------------
% 2.54/1.59 % (25541)------------------------------
% 2.54/1.59 % (25535)Instruction limit reached!
% 2.54/1.59 % (25535)------------------------------
% 2.54/1.59 % (25535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.54/1.59 % (25535)Termination reason: Unknown
% 2.54/1.59 % (25535)Termination phase: Function definition elimination
% 2.54/1.59
% 2.54/1.59 % (25535)Memory used [KB]: 1535
% 2.54/1.59 % (25535)Time elapsed: 0.020 s
% 2.54/1.59 % (25535)Instructions burned: 38 (million)
% 2.54/1.59 % (25535)------------------------------
% 2.54/1.59 % (25535)------------------------------
% 2.58/1.60 % (25542)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_25342 for (2999ds/3Mi)
% 2.58/1.60 % (25542)Instruction limit reached!
% 2.58/1.60 % (25542)------------------------------
% 2.58/1.60 % (25542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.60 % (25542)Termination reason: Unknown
% 2.58/1.60 % (25542)Termination phase: shuffling
% 2.58/1.60
% 2.58/1.60 % (25542)Memory used [KB]: 1151
% 2.58/1.60 % (25542)Time elapsed: 0.003 s
% 2.58/1.60 % (25542)Instructions burned: 4 (million)
% 2.58/1.60 % (25542)------------------------------
% 2.58/1.60 % (25542)------------------------------
% 2.58/1.60 % (25543)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_25342 for (2999ds/3Mi)
% 2.58/1.60 % (25543)Instruction limit reached!
% 2.58/1.60 % (25543)------------------------------
% 2.58/1.60 % (25543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.60 % (25543)Termination reason: Unknown
% 2.58/1.60 % (25543)Termination phase: shuffling
% 2.58/1.60
% 2.58/1.60 % (25543)Memory used [KB]: 1151
% 2.58/1.60 % (25543)Time elapsed: 0.002 s
% 2.58/1.60 % (25543)Instructions burned: 4 (million)
% 2.58/1.60 % (25543)------------------------------
% 2.58/1.60 % (25543)------------------------------
% 2.58/1.61 % (25544)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/7Mi)
% 2.58/1.61 % (25544)Instruction limit reached!
% 2.58/1.61 % (25544)------------------------------
% 2.58/1.61 % (25544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (25544)Termination reason: Unknown
% 2.58/1.61 % (25544)Termination phase: shuffling
% 2.58/1.61
% 2.58/1.61 % (25544)Memory used [KB]: 1279
% 2.58/1.61 % (25544)Time elapsed: 0.005 s
% 2.58/1.61 % (25544)Instructions burned: 8 (million)
% 2.58/1.61 % (25544)------------------------------
% 2.58/1.61 % (25544)------------------------------
% 2.58/1.61 % (25547)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/18Mi)
% 2.58/1.61 % (25545)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/3Mi)
% 2.58/1.61 % (25545)Instruction limit reached!
% 2.58/1.61 % (25545)------------------------------
% 2.58/1.61 % (25545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (25545)Termination reason: Unknown
% 2.58/1.61 % (25545)Termination phase: shuffling
% 2.58/1.61
% 2.58/1.61 % (25545)Memory used [KB]: 1151
% 2.58/1.61 % (25545)Time elapsed: 0.003 s
% 2.58/1.61 % (25545)Instructions burned: 3 (million)
% 2.58/1.61 % (25545)------------------------------
% 2.58/1.61 % (25545)------------------------------
% 2.58/1.61 % (25547)Instruction limit reached!
% 2.58/1.61 % (25547)------------------------------
% 2.58/1.61 % (25547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.61 % (25547)Termination reason: Unknown
% 2.58/1.61 % (25547)Termination phase: Property scanning
% 2.58/1.61
% 2.58/1.61 % (25547)Memory used [KB]: 1535
% 2.58/1.61 % (25547)Time elapsed: 0.006 s
% 2.58/1.61 % (25547)Instructions burned: 18 (million)
% 2.58/1.61 % (25547)------------------------------
% 2.58/1.61 % (25547)------------------------------
% 2.58/1.62 % (25546)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/4Mi)
% 2.58/1.62 % (25546)Instruction limit reached!
% 2.58/1.62 % (25546)------------------------------
% 2.58/1.62 % (25546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.62 % (25546)Termination reason: Unknown
% 2.58/1.62 % (25546)Termination phase: shuffling
% 2.58/1.62
% 2.58/1.62 % (25546)Memory used [KB]: 1151
% 2.58/1.62 % (25546)Time elapsed: 0.004 s
% 2.58/1.62 % (25546)Instructions burned: 4 (million)
% 2.58/1.62 % (25546)------------------------------
% 2.58/1.62 % (25546)------------------------------
% 2.58/1.62 % (25548)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/710Mi)
% 2.58/1.63 % (25549)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/6Mi)
% 2.58/1.63 % (25549)Instruction limit reached!
% 2.58/1.63 % (25549)------------------------------
% 2.58/1.63 % (25549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.63 % (25549)Termination reason: Unknown
% 2.58/1.63 % (25549)Termination phase: shuffling
% 2.58/1.63
% 2.58/1.63 % (25549)Memory used [KB]: 1279
% 2.58/1.63 % (25549)Time elapsed: 0.005 s
% 2.58/1.63 % (25549)Instructions burned: 7 (million)
% 2.58/1.63 % (25549)------------------------------
% 2.58/1.63 % (25549)------------------------------
% 2.58/1.64 % (25553)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_25342 for (2999ds/21Mi)
% 2.58/1.64 % (25551)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_25342 for (2999ds/902Mi)
% 2.58/1.64 % (25526)Instruction limit reached!
% 2.58/1.64 % (25526)------------------------------
% 2.58/1.64 % (25526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.64 % (25526)Termination reason: Unknown
% 2.58/1.64 % (25526)Termination phase: Saturation
% 2.58/1.64
% 2.58/1.64 % (25526)Memory used [KB]: 6908
% 2.58/1.64 % (25526)Time elapsed: 0.090 s
% 2.58/1.64 % (25526)Instructions burned: 183 (million)
% 2.58/1.64 % (25526)------------------------------
% 2.58/1.64 % (25526)------------------------------
% 2.58/1.65 % (25553)Instruction limit reached!
% 2.58/1.65 % (25553)------------------------------
% 2.58/1.65 % (25553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.65 % (25553)Termination reason: Unknown
% 2.58/1.65 % (25553)Termination phase: Property scanning
% 2.58/1.65
% 2.58/1.65 % (25553)Memory used [KB]: 1535
% 2.58/1.65 % (25553)Time elapsed: 0.013 s
% 2.58/1.65 % (25553)Instructions burned: 22 (million)
% 2.58/1.65 % (25553)------------------------------
% 2.58/1.65 % (25553)------------------------------
% 2.58/1.65 % (25555)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_25342 for (2999ds/5Mi)
% 2.58/1.65 % (25555)Instruction limit reached!
% 2.58/1.65 % (25555)------------------------------
% 2.58/1.65 % (25555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.65 % (25555)Termination reason: Unknown
% 2.58/1.65 % (25555)Termination phase: shuffling
% 2.58/1.65
% 2.58/1.65 % (25555)Memory used [KB]: 1279
% 2.58/1.65 % (25555)Time elapsed: 0.005 s
% 2.58/1.65 % (25555)Instructions burned: 6 (million)
% 2.58/1.65 % (25555)------------------------------
% 2.58/1.65 % (25555)------------------------------
% 2.58/1.66 % (25556)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_25342 for (2999ds/6Mi)
% 2.58/1.66 % (25556)Instruction limit reached!
% 2.58/1.66 % (25556)------------------------------
% 2.58/1.66 % (25556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.66 % (25556)Termination reason: Unknown
% 2.58/1.66 % (25556)Termination phase: shuffling
% 2.58/1.66
% 2.58/1.66 % (25556)Memory used [KB]: 1279
% 2.58/1.66 % (25556)Time elapsed: 0.004 s
% 2.58/1.66 % (25556)Instructions burned: 6 (million)
% 2.58/1.66 % (25556)------------------------------
% 2.58/1.66 % (25556)------------------------------
% 2.58/1.66 % (25558)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_25342 for (2998ds/377Mi)
% 2.58/1.67 % (25560)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_25342 for (2998ds/779Mi)
% 2.58/1.67 % (25561)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_25342 for (2998ds/19Mi)
% 2.58/1.67 % (25561)Instruction limit reached!
% 2.58/1.67 % (25561)------------------------------
% 2.58/1.67 % (25561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.67 % (25561)Termination reason: Unknown
% 2.58/1.67 % (25561)Termination phase: Property scanning
% 2.58/1.67
% 2.58/1.67 % (25561)Memory used [KB]: 1535
% 2.58/1.67 % (25561)Time elapsed: 0.006 s
% 2.58/1.67 % (25561)Instructions burned: 19 (million)
% 2.58/1.67 % (25561)------------------------------
% 2.58/1.67 % (25561)------------------------------
% 2.58/1.68 % (25531)Instruction limit reached!
% 2.58/1.68 % (25531)------------------------------
% 2.58/1.68 % (25531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.68 % (25531)Termination reason: Unknown
% 2.58/1.68 % (25531)Termination phase: Saturation
% 2.58/1.68
% 2.58/1.68 % (25531)Memory used [KB]: 7675
% 2.58/1.68 % (25531)Time elapsed: 0.113 s
% 2.58/1.68 % (25531)Instructions burned: 277 (million)
% 2.58/1.68 % (25531)------------------------------
% 2.58/1.68 % (25531)------------------------------
% 2.58/1.68 % (25563)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_25342 for (2998ds/879Mi)
% 2.58/1.69 % (25564)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_25342 for (2998ds/17Mi)
% 2.58/1.70 % (25564)Instruction limit reached!
% 2.58/1.70 % (25564)------------------------------
% 2.58/1.70 % (25564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.70 % (25564)Termination reason: Unknown
% 2.58/1.70 % (25564)Termination phase: Property scanning
% 2.58/1.70
% 2.58/1.70 % (25564)Memory used [KB]: 1535
% 2.58/1.70 % (25564)Time elapsed: 0.006 s
% 2.58/1.70 % (25564)Instructions burned: 19 (million)
% 2.58/1.70 % (25564)------------------------------
% 2.58/1.70 % (25564)------------------------------
% 2.58/1.71 % (25565)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25342 for (2998ds/3Mi)
% 2.58/1.71 % (25565)Instruction limit reached!
% 2.58/1.71 % (25565)------------------------------
% 2.58/1.71 % (25565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.71 % (25565)Termination reason: Unknown
% 2.58/1.71 % (25565)Termination phase: shuffling
% 2.58/1.71
% 2.58/1.71 % (25565)Memory used [KB]: 1151
% 2.58/1.71 % (25565)Time elapsed: 0.002 s
% 2.58/1.71 % (25565)Instructions burned: 4 (million)
% 2.58/1.71 % (25565)------------------------------
% 2.58/1.71 % (25565)------------------------------
% 2.58/1.72 % (25566)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_25342 for (2998ds/30Mi)
% 2.58/1.72 % (25566)Instruction limit reached!
% 2.58/1.72 % (25566)------------------------------
% 2.58/1.72 % (25566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.72 % (25566)Termination reason: Unknown
% 2.58/1.72 % (25566)Termination phase: Property scanning
% 2.58/1.72
% 2.58/1.72 % (25566)Memory used [KB]: 1535
% 2.58/1.72 % (25566)Time elapsed: 0.010 s
% 2.58/1.72 % (25566)Instructions burned: 32 (million)
% 2.58/1.72 % (25566)------------------------------
% 2.58/1.72 % (25566)------------------------------
% 2.58/1.73 % (25567)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_25342 for (2998ds/127Mi)
% 2.58/1.77 % (25567)Instruction limit reached!
% 2.58/1.77 % (25567)------------------------------
% 2.58/1.77 % (25567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.77 % (25567)Termination reason: Unknown
% 2.58/1.77 % (25567)Termination phase: Saturation
% 2.58/1.77
% 2.58/1.77 % (25567)Memory used [KB]: 6780
% 2.58/1.77 % (25567)Time elapsed: 0.036 s
% 2.58/1.77 % (25567)Instructions burned: 128 (million)
% 2.58/1.77 % (25567)------------------------------
% 2.58/1.77 % (25567)------------------------------
% 2.58/1.77 % (25558)Instruction limit reached!
% 2.58/1.77 % (25558)------------------------------
% 2.58/1.77 % (25558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.77 % (25558)Termination reason: Unknown
% 2.58/1.77 % (25558)Termination phase: Saturation
% 2.58/1.77
% 2.58/1.77 % (25558)Memory used [KB]: 7164
% 2.58/1.77 % (25558)Time elapsed: 0.115 s
% 2.58/1.77 % (25558)Instructions burned: 377 (million)
% 2.58/1.77 % (25558)------------------------------
% 2.58/1.77 % (25558)------------------------------
% 2.58/1.78 % (25568)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_25342 for (2997ds/100Mi)
% 2.58/1.78 % (25569)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_25342 for (2997ds/3Mi)
% 2.58/1.79 % (25569)Instruction limit reached!
% 2.58/1.79 % (25569)------------------------------
% 2.58/1.79 % (25569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.79 % (25569)Termination reason: Unknown
% 2.58/1.79 % (25569)Termination phase: shuffling
% 2.58/1.79
% 2.58/1.79 % (25569)Memory used [KB]: 1151
% 2.58/1.79 % (25569)Time elapsed: 0.002 s
% 2.58/1.79 % (25569)Instructions burned: 4 (million)
% 2.58/1.79 % (25569)------------------------------
% 2.58/1.79 % (25569)------------------------------
% 2.58/1.80 % (25571)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_25342 for (2997ds/20Mi)
% 2.58/1.80 % (25571)Instruction limit reached!
% 2.58/1.80 % (25571)------------------------------
% 2.58/1.80 % (25571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.80 % (25571)Termination reason: Unknown
% 2.58/1.80 % (25571)Termination phase: Naming
% 2.58/1.80
% 2.58/1.80 % (25571)Memory used [KB]: 1535
% 2.58/1.80 % (25571)Time elapsed: 0.008 s
% 2.58/1.80 % (25571)Instructions burned: 22 (million)
% 2.58/1.80 % (25571)------------------------------
% 2.58/1.80 % (25571)------------------------------
% 2.58/1.81 % (25568)Instruction limit reached!
% 2.58/1.81 % (25568)------------------------------
% 2.58/1.81 % (25568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.81 % (25568)Termination reason: Unknown
% 2.58/1.81 % (25568)Termination phase: Saturation
% 2.58/1.81
% 2.58/1.81 % (25568)Memory used [KB]: 6268
% 2.58/1.81 % (25568)Time elapsed: 0.030 s
% 2.58/1.81 % (25568)Instructions burned: 101 (million)
% 2.58/1.81 % (25568)------------------------------
% 2.58/1.81 % (25568)------------------------------
% 2.58/1.81 % (25578)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_25342 for (2997ds/86Mi)
% 2.58/1.82 % (25582)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_25342 for (2997ds/107Mi)
% 2.58/1.83 % (25578)Instruction limit reached!
% 2.58/1.83 % (25578)------------------------------
% 2.58/1.83 % (25578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.83 % (25578)Termination reason: Unknown
% 2.58/1.83 % (25578)Termination phase: Saturation
% 2.58/1.83
% 2.58/1.83 % (25578)Memory used [KB]: 6396
% 2.58/1.83 % (25578)Time elapsed: 0.024 s
% 2.58/1.83 % (25578)Instructions burned: 88 (million)
% 2.58/1.83 % (25578)------------------------------
% 2.58/1.83 % (25578)------------------------------
% 2.58/1.84 % (25593)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_25342 for (2997ds/39Mi)
% 2.58/1.85 % (25582)Instruction limit reached!
% 2.58/1.85 % (25582)------------------------------
% 2.58/1.85 % (25582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.85 % (25582)Termination reason: Unknown
% 2.58/1.85 % (25582)Termination phase: Saturation
% 2.58/1.85
% 2.58/1.85 % (25582)Memory used [KB]: 6652
% 2.58/1.85 % (25582)Time elapsed: 0.030 s
% 2.58/1.85 % (25582)Instructions burned: 110 (million)
% 2.58/1.85 % (25582)------------------------------
% 2.58/1.85 % (25582)------------------------------
% 2.58/1.85 % (25560)Instruction limit reached!
% 2.58/1.85 % (25560)------------------------------
% 2.58/1.85 % (25560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.85 % (25560)Termination reason: Unknown
% 2.58/1.85 % (25560)Termination phase: Saturation
% 2.58/1.85
% 2.58/1.85 % (25560)Memory used [KB]: 6652
% 2.58/1.85 % (25560)Time elapsed: 0.188 s
% 2.58/1.85 % (25560)Instructions burned: 781 (million)
% 2.58/1.85 % (25560)------------------------------
% 2.58/1.85 % (25560)------------------------------
% 2.58/1.85 % (25593)Instruction limit reached!
% 2.58/1.85 % (25593)------------------------------
% 2.58/1.85 % (25593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.85 % (25593)Termination reason: Unknown
% 2.58/1.85 % (25593)Termination phase: Function definition elimination
% 2.58/1.85
% 2.58/1.85 % (25593)Memory used [KB]: 1663
% 2.58/1.85 % (25593)Time elapsed: 0.011 s
% 2.58/1.85 % (25593)Instructions burned: 40 (million)
% 2.58/1.85 % (25593)------------------------------
% 2.58/1.85 % (25593)------------------------------
% 2.58/1.86 % (25599)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_25342 for (2997ds/448Mi)
% 2.58/1.86 % (25602)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_25342 for (2996ds/46Mi)
% 2.58/1.86 % (25603)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_25342 for (2996ds/98Mi)
% 2.58/1.86 % (25548)Instruction limit reached!
% 2.58/1.86 % (25548)------------------------------
% 2.58/1.86 % (25548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.86 % (25548)Termination reason: Unknown
% 2.58/1.86 % (25548)Termination phase: Saturation
% 2.58/1.86
% 2.58/1.86 % (25548)Memory used [KB]: 8955
% 2.58/1.86 % (25548)Time elapsed: 0.241 s
% 2.58/1.86 % (25548)Instructions burned: 713 (million)
% 2.58/1.86 % (25548)------------------------------
% 2.58/1.86 % (25548)------------------------------
% 2.58/1.87 % (25602)Instruction limit reached!
% 2.58/1.87 % (25602)------------------------------
% 2.58/1.87 % (25602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.87 % (25602)Termination reason: Unknown
% 2.58/1.87 % (25602)Termination phase: Twee Goal Transformation
% 2.58/1.87
% 2.58/1.87 % (25602)Memory used [KB]: 1535
% 2.58/1.87 % (25602)Time elapsed: 0.013 s
% 2.58/1.87 % (25602)Instructions burned: 46 (million)
% 2.58/1.87 % (25602)------------------------------
% 2.58/1.87 % (25602)------------------------------
% 2.58/1.87 % (25611)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_25342 for (2996ds/507Mi)
% 2.58/1.88 % (25617)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_25342 for (2996ds/149Mi)
% 2.58/1.88 % (25539)Instruction limit reached!
% 2.58/1.88 % (25539)------------------------------
% 2.58/1.88 % (25539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.88 % (25539)Termination reason: Unknown
% 2.58/1.88 % (25539)Termination phase: Saturation
% 2.58/1.88
% 2.58/1.88 % (25539)Memory used [KB]: 7931
% 2.58/1.88 % (25539)Time elapsed: 0.301 s
% 2.58/1.88 % (25539)Instructions burned: 1042 (million)
% 2.58/1.88 % (25539)------------------------------
% 2.58/1.88 % (25539)------------------------------
% 2.58/1.89 % (25603)Instruction limit reached!
% 2.58/1.89 % (25603)------------------------------
% 2.58/1.89 % (25603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.89 % (25603)Termination reason: Unknown
% 2.58/1.89 % (25603)Termination phase: Saturation
% 2.58/1.89
% 2.58/1.89 % (25603)Memory used [KB]: 1663
% 2.58/1.89 % (25603)Time elapsed: 0.026 s
% 2.58/1.89 % (25603)Instructions burned: 98 (million)
% 2.58/1.89 % (25603)------------------------------
% 2.58/1.89 % (25603)------------------------------
% 2.58/1.89 % (25619)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_25342 for (2996ds/39Mi)
% 2.58/1.90 % (25622)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_25342 for (2996ds/6Mi)
% 2.58/1.90 % (25622)Instruction limit reached!
% 2.58/1.90 % (25622)------------------------------
% 2.58/1.90 % (25622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.90 % (25622)Termination reason: Unknown
% 2.58/1.90 % (25622)Termination phase: shuffling
% 2.58/1.90
% 2.58/1.90 % (25622)Memory used [KB]: 1279
% 2.58/1.90 % (25622)Time elapsed: 0.003 s
% 2.58/1.90 % (25622)Instructions burned: 8 (million)
% 2.58/1.90 % (25622)------------------------------
% 2.58/1.90 % (25622)------------------------------
% 2.58/1.90 % (25619)Instruction limit reached!
% 2.58/1.90 % (25619)------------------------------
% 2.58/1.90 % (25619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.90 % (25619)Termination reason: Unknown
% 2.58/1.90 % (25619)Termination phase: Property scanning
% 2.58/1.90
% 2.58/1.90 % (25619)Memory used [KB]: 1535
% 2.58/1.90 % (25619)Time elapsed: 0.012 s
% 2.58/1.90 % (25619)Instructions burned: 40 (million)
% 2.58/1.90 % (25619)------------------------------
% 2.58/1.90 % (25619)------------------------------
% 2.58/1.91 % (25627)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_25342 for (2996ds/1087Mi)
% 2.58/1.91 % (25630)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_25342 for (2996ds/47Mi)
% 2.58/1.93 % (25630)Instruction limit reached!
% 2.58/1.93 % (25630)------------------------------
% 2.58/1.93 % (25630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.93 % (25630)Termination reason: Unknown
% 2.58/1.93 % (25630)Termination phase: Property scanning
% 2.58/1.93
% 2.58/1.93 % (25630)Memory used [KB]: 1535
% 2.58/1.93 % (25630)Time elapsed: 0.013 s
% 2.58/1.93 % (25630)Instructions burned: 47 (million)
% 2.58/1.93 % (25630)------------------------------
% 2.58/1.93 % (25630)------------------------------
% 2.58/1.93 % (25551)Instruction limit reached!
% 2.58/1.93 % (25551)------------------------------
% 2.58/1.93 % (25551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.93 % (25551)Termination reason: Unknown
% 2.58/1.93 % (25551)Termination phase: Saturation
% 2.58/1.93
% 2.58/1.93 % (25551)Memory used [KB]: 10618
% 2.58/1.93 % (25551)Time elapsed: 0.315 s
% 2.58/1.93 % (25551)Instructions burned: 904 (million)
% 2.58/1.93 % (25551)------------------------------
% 2.58/1.93 % (25551)------------------------------
% 2.58/1.93 % (25617)Instruction limit reached!
% 2.58/1.93 % (25617)------------------------------
% 2.58/1.93 % (25617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.93 % (25617)Termination reason: Unknown
% 2.58/1.93 % (25617)Termination phase: Saturation
% 2.58/1.93
% 2.58/1.93 % (25617)Memory used [KB]: 6652
% 2.58/1.93 % (25617)Time elapsed: 0.067 s
% 2.58/1.93 % (25617)Instructions burned: 149 (million)
% 2.58/1.93 % (25617)------------------------------
% 2.58/1.93 % (25617)------------------------------
% 2.58/1.93 % (25639)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_25342 for (2996ds/44Mi)
% 2.58/1.94 % (25641)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_25342 for (2996ds/432Mi)
% 2.58/1.94 % (25642)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_25342 for (2996ds/62Mi)
% 2.58/1.95 % (25639)Instruction limit reached!
% 2.58/1.95 % (25639)------------------------------
% 2.58/1.95 % (25639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.95 % (25639)Termination reason: Unknown
% 2.58/1.95 % (25639)Termination phase: Function definition elimination
% 2.58/1.95
% 2.58/1.95 % (25639)Memory used [KB]: 1535
% 2.58/1.95 % (25639)Time elapsed: 0.012 s
% 2.58/1.95 % (25639)Instructions burned: 44 (million)
% 2.58/1.95 % (25639)------------------------------
% 2.58/1.95 % (25639)------------------------------
% 2.58/1.95 % (25642)Instruction limit reached!
% 2.58/1.95 % (25642)------------------------------
% 2.58/1.95 % (25642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.95 % (25642)Termination reason: Unknown
% 2.58/1.95 % (25642)Termination phase: Saturation
% 2.58/1.95
% 2.58/1.95 % (25642)Memory used [KB]: 6140
% 2.58/1.95 % (25642)Time elapsed: 0.017 s
% 2.58/1.95 % (25642)Instructions burned: 63 (million)
% 2.58/1.95 % (25642)------------------------------
% 2.58/1.95 % (25642)------------------------------
% 2.58/1.96 % (25650)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_25342 for (2996ds/31Mi)
% 2.58/1.96 % (25599)Instruction limit reached!
% 2.58/1.96 % (25599)------------------------------
% 2.58/1.96 % (25599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.96 % (25599)Termination reason: Unknown
% 2.58/1.96 % (25599)Termination phase: Saturation
% 2.58/1.96
% 2.58/1.96 % (25599)Memory used [KB]: 6268
% 2.58/1.96 % (25599)Time elapsed: 0.105 s
% 2.58/1.96 % (25599)Instructions burned: 448 (million)
% 2.58/1.96 % (25599)------------------------------
% 2.58/1.96 % (25599)------------------------------
% 2.58/1.96 % (25563)Refutation not found, non-redundant clauses discarded% (25563)------------------------------
% 2.58/1.96 % (25563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.96 % (25563)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.58/1.96
% 2.58/1.96 % (25563)Memory used [KB]: 7419
% 2.58/1.96 % (25563)Time elapsed: 0.278 s
% 2.58/1.96 % (25563)Instructions burned: 877 (million)
% 2.58/1.96 % (25563)------------------------------
% 2.58/1.96 % (25563)------------------------------
% 2.58/1.96 % (25653)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_25342 for (2995ds/96Mi)
% 2.58/1.96 % (25650)Instruction limit reached!
% 2.58/1.96 % (25650)------------------------------
% 2.58/1.96 % (25650)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.96 % (25650)Termination reason: Unknown
% 2.58/1.96 % (25650)Termination phase: Property scanning
% 2.58/1.96
% 2.58/1.96 % (25650)Memory used [KB]: 1535
% 2.58/1.96 % (25650)Time elapsed: 0.010 s
% 2.58/1.96 % (25650)Instructions burned: 33 (million)
% 2.58/1.96 % (25650)------------------------------
% 2.58/1.96 % (25650)------------------------------
% 2.58/1.97 % (25654)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_25342 for (2995ds/453Mi)
% 2.58/1.97 % (25655)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_25342 for (2995ds/71Mi)
% 2.58/1.97 % (25656)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_25342 for (2995ds/83Mi)
% 2.58/1.99 % (25653)Instruction limit reached!
% 2.58/1.99 % (25653)------------------------------
% 2.58/1.99 % (25653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.99 % (25653)Termination reason: Unknown
% 2.58/1.99 % (25653)Termination phase: Saturation
% 2.58/1.99
% 2.58/1.99 % (25653)Memory used [KB]: 6652
% 2.58/1.99 % (25653)Time elapsed: 0.027 s
% 2.58/1.99 % (25653)Instructions burned: 98 (million)
% 2.58/1.99 % (25653)------------------------------
% 2.58/1.99 % (25653)------------------------------
% 2.58/1.99 % (25655)Instruction limit reached!
% 2.58/1.99 % (25655)------------------------------
% 2.58/1.99 % (25655)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/1.99 % (25655)Termination reason: Unknown
% 2.58/1.99 % (25655)Termination phase: Saturation
% 2.58/1.99
% 2.58/1.99 % (25655)Memory used [KB]: 6268
% 2.58/1.99 % (25655)Time elapsed: 0.020 s
% 2.58/1.99 % (25655)Instructions burned: 72 (million)
% 2.58/1.99 % (25655)------------------------------
% 2.58/1.99 % (25655)------------------------------
% 2.58/2.00 % (25656)Instruction limit reached!
% 2.58/2.00 % (25656)------------------------------
% 2.58/2.00 % (25656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/2.00 % (25656)Termination reason: Unknown
% 2.58/2.00 % (25656)Termination phase: Saturation
% 2.58/2.00
% 2.58/2.00 % (25656)Memory used [KB]: 6268
% 2.58/2.00 % (25656)Time elapsed: 0.023 s
% 2.58/2.00 % (25656)Instructions burned: 85 (million)
% 2.58/2.00 % (25656)------------------------------
% 2.58/2.00 % (25656)------------------------------
% 2.58/2.00 % (25672)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_25342 for (2995ds/11Mi)
% 2.58/2.00 % (25673)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_25342 for (2995ds/41Mi)
% 2.58/2.00 % (25672)Instruction limit reached!
% 2.58/2.00 % (25672)------------------------------
% 2.58/2.00 % (25672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/2.00 % (25672)Termination reason: Unknown
% 2.58/2.00 % (25672)Termination phase: shuffling
% 2.58/2.00
% 2.58/2.00 % (25672)Memory used [KB]: 1407
% 2.58/2.00 % (25672)Time elapsed: 0.004 s
% 2.58/2.00 % (25672)Instructions burned: 11 (million)
% 2.58/2.00 % (25672)------------------------------
% 2.58/2.00 % (25672)------------------------------
% 2.58/2.01 % (25680)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_25342 for (2995ds/150Mi)
% 2.58/2.01 % (25673)Instruction limit reached!
% 2.58/2.01 % (25673)------------------------------
% 2.58/2.01 % (25673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.58/2.01 % (25673)Termination reason: Unknown
% 2.58/2.01 % (25673)Termination phase: Property scanning
% 2.58/2.01
% 2.58/2.01 % (25673)Memory used [KB]: 1663
% 2.58/2.01 % (25673)Time elapsed: 0.012 s
% 2.58/2.01 % (25673)Instructions burned: 44 (million)
% 2.58/2.01 % (25673)------------------------------
% 2.58/2.01 % (25673)------------------------------
% 5.78/2.02 % (25679)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25342 for (2995ds/6Mi)
% 5.78/2.02 % (25681)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_25342 for (2995ds/343Mi)
% 5.78/2.02 % (25679)Instruction limit reached!
% 5.78/2.02 % (25679)------------------------------
% 5.78/2.02 % (25679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.02 % (25679)Termination reason: Unknown
% 5.78/2.02 % (25679)Termination phase: shuffling
% 5.78/2.02
% 5.78/2.02 % (25679)Memory used [KB]: 1279
% 5.78/2.02 % (25679)Time elapsed: 0.005 s
% 5.78/2.02 % (25679)Instructions burned: 6 (million)
% 5.78/2.02 % (25679)------------------------------
% 5.78/2.02 % (25679)------------------------------
% 5.78/2.03 % (25611)Instruction limit reached!
% 5.78/2.03 % (25611)------------------------------
% 5.78/2.03 % (25611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.03 % (25611)Termination reason: Unknown
% 5.78/2.03 % (25611)Termination phase: Saturation
% 5.78/2.03
% 5.78/2.03 % (25611)Memory used [KB]: 7036
% 5.78/2.03 % (25611)Time elapsed: 0.175 s
% 5.78/2.03 % (25611)Instructions burned: 509 (million)
% 5.78/2.03 % (25611)------------------------------
% 5.78/2.03 % (25611)------------------------------
% 5.78/2.04 % (25698)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_25342 for (2995ds/253Mi)
% 5.78/2.04 % (25692)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_25342 for (2995ds/109Mi)
% 5.78/2.04 % (25641)Instruction limit reached!
% 5.78/2.04 % (25641)------------------------------
% 5.78/2.04 % (25641)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.04 % (25641)Termination reason: Unknown
% 5.78/2.04 % (25641)Termination phase: Saturation
% 5.78/2.04
% 5.78/2.04 % (25641)Memory used [KB]: 2430
% 5.78/2.04 % (25641)Time elapsed: 0.130 s
% 5.78/2.04 % (25641)Instructions burned: 432 (million)
% 5.78/2.04 % (25641)------------------------------
% 5.78/2.04 % (25641)------------------------------
% 5.78/2.05 % (25708)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_25342 for (2994ds/140Mi)
% 5.78/2.06 % (25680)Instruction limit reached!
% 5.78/2.06 % (25680)------------------------------
% 5.78/2.06 % (25680)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.06 % (25680)Termination reason: Unknown
% 5.78/2.06 % (25680)Termination phase: Saturation
% 5.78/2.06
% 5.78/2.06 % (25680)Memory used [KB]: 7419
% 5.78/2.06 % (25680)Time elapsed: 0.048 s
% 5.78/2.06 % (25680)Instructions burned: 152 (million)
% 5.78/2.06 % (25680)------------------------------
% 5.78/2.06 % (25680)------------------------------
% 5.78/2.07 % (25709)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_25342 for (2994ds/614Mi)
% 5.78/2.08 % (25654)Instruction limit reached!
% 5.78/2.08 % (25654)------------------------------
% 5.78/2.08 % (25654)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.08 % (25654)Termination reason: Unknown
% 5.78/2.08 % (25654)Termination phase: Saturation
% 5.78/2.08
% 5.78/2.08 % (25654)Memory used [KB]: 6268
% 5.78/2.08 % (25654)Time elapsed: 0.112 s
% 5.78/2.08 % (25654)Instructions burned: 453 (million)
% 5.78/2.08 % (25654)------------------------------
% 5.78/2.08 % (25654)------------------------------
% 5.78/2.09 % (25725)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_25342 for (2994ds/202Mi)
% 5.78/2.09 % (25708)Instruction limit reached!
% 5.78/2.09 % (25708)------------------------------
% 5.78/2.09 % (25708)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.09 % (25708)Termination reason: Unknown
% 5.78/2.09 % (25708)Termination phase: Saturation
% 5.78/2.09
% 5.78/2.09 % (25708)Memory used [KB]: 6268
% 5.78/2.09 % (25708)Time elapsed: 0.039 s
% 5.78/2.09 % (25708)Instructions burned: 140 (million)
% 5.78/2.09 % (25708)------------------------------
% 5.78/2.09 % (25708)------------------------------
% 5.78/2.09 % (25692)Instruction limit reached!
% 5.78/2.09 % (25692)------------------------------
% 5.78/2.09 % (25692)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.78/2.09 % (25692)Termination reason: Unknown
% 5.78/2.09 % (25692)Termination phase: Saturation
% 5.78/2.09
% 5.78/2.09 % (25692)Memory used [KB]: 6652
% 5.78/2.09 % (25692)Time elapsed: 0.056 s
% 5.78/2.09 % (25692)Instructions burned: 111 (million)
% 5.78/2.09 % (25692)------------------------------
% 5.78/2.09 % (25692)------------------------------
% 5.78/2.10 % (25728)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_25342 for (2994ds/339Mi)
% 5.78/2.10 % (25730)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_25342 for (2994ds/283Mi)
% 6.22/2.12 % (25698)Instruction limit reached!
% 6.22/2.12 % (25698)------------------------------
% 6.22/2.12 % (25698)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.12 % (25698)Termination reason: Unknown
% 6.22/2.12 % (25698)Termination phase: Saturation
% 6.22/2.12
% 6.22/2.12 % (25698)Memory used [KB]: 7675
% 6.22/2.12 % (25698)Time elapsed: 0.080 s
% 6.22/2.12 % (25698)Instructions burned: 253 (million)
% 6.22/2.12 % (25698)------------------------------
% 6.22/2.12 % (25698)------------------------------
% 6.22/2.12 % (25681)Instruction limit reached!
% 6.22/2.12 % (25681)------------------------------
% 6.22/2.12 % (25681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.12 % (25681)Termination reason: Unknown
% 6.22/2.12 % (25681)Termination phase: Saturation
% 6.22/2.12
% 6.22/2.12 % (25681)Memory used [KB]: 7291
% 6.22/2.12 % (25681)Time elapsed: 0.105 s
% 6.22/2.12 % (25681)Instructions burned: 343 (million)
% 6.22/2.12 % (25681)------------------------------
% 6.22/2.12 % (25681)------------------------------
% 6.22/2.13 % (25743)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_25342 for (2994ds/134Mi)
% 6.22/2.13 % (25745)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_25342 for (2994ds/298Mi)
% 6.22/2.15 % (25725)Instruction limit reached!
% 6.22/2.15 % (25725)------------------------------
% 6.22/2.15 % (25725)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.15 % (25725)Termination reason: Unknown
% 6.22/2.15 % (25725)Termination phase: Saturation
% 6.22/2.15
% 6.22/2.15 % (25725)Memory used [KB]: 7675
% 6.22/2.15 % (25725)Time elapsed: 0.064 s
% 6.22/2.15 % (25725)Instructions burned: 204 (million)
% 6.22/2.15 % (25725)------------------------------
% 6.22/2.15 % (25725)------------------------------
% 6.22/2.16 % (25756)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_25342 for (2993ds/192Mi)
% 6.22/2.16 % (25743)Instruction limit reached!
% 6.22/2.16 % (25743)------------------------------
% 6.22/2.16 % (25743)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.16 % (25743)Termination reason: Unknown
% 6.22/2.16 % (25743)Termination phase: Saturation
% 6.22/2.16
% 6.22/2.16 % (25743)Memory used [KB]: 6908
% 6.22/2.16 % (25743)Time elapsed: 0.040 s
% 6.22/2.16 % (25743)Instructions burned: 136 (million)
% 6.22/2.16 % (25743)------------------------------
% 6.22/2.16 % (25743)------------------------------
% 6.22/2.17 % (25760)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_25342 for (2993ds/258Mi)
% 6.22/2.18 % (25730)Instruction limit reached!
% 6.22/2.18 % (25730)------------------------------
% 6.22/2.18 % (25730)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.22/2.18 % (25730)Termination reason: Unknown
% 6.22/2.18 % (25730)Termination phase: Saturation
% 6.22/2.18
% 6.22/2.18 % (25730)Memory used [KB]: 8059
% 6.22/2.18 % (25730)Time elapsed: 0.077 s
% 6.22/2.18 % (25730)Instructions burned: 285 (million)
% 6.22/2.18 % (25730)------------------------------
% 6.22/2.18 % (25730)------------------------------
% 6.22/2.19 % (25769)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_25342 for (2993ds/90Mi)
% 6.73/2.20 % (25728)Instruction limit reached!
% 6.73/2.20 % (25728)------------------------------
% 6.73/2.20 % (25728)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.20 % (25728)Termination reason: Unknown
% 6.73/2.20 % (25728)Termination phase: Saturation
% 6.73/2.20
% 6.73/2.20 % (25728)Memory used [KB]: 7547
% 6.73/2.20 % (25728)Time elapsed: 0.102 s
% 6.73/2.20 % (25728)Instructions burned: 341 (million)
% 6.73/2.20 % (25728)------------------------------
% 6.73/2.20 % (25728)------------------------------
% 6.73/2.21 % (25745)Instruction limit reached!
% 6.73/2.21 % (25745)------------------------------
% 6.73/2.21 % (25745)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.21 % (25745)Termination reason: Unknown
% 6.73/2.21 % (25745)Termination phase: Saturation
% 6.73/2.21
% 6.73/2.21 % (25745)Memory used [KB]: 6396
% 6.73/2.21 % (25745)Time elapsed: 0.078 s
% 6.73/2.21 % (25745)Instructions burned: 299 (million)
% 6.73/2.21 % (25745)------------------------------
% 6.73/2.21 % (25745)------------------------------
% 6.73/2.21 % (25778)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_25342 for (2993ds/231Mi)
% 6.73/2.22 % (25769)Instruction limit reached!
% 6.73/2.22 % (25769)------------------------------
% 6.73/2.22 % (25769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.22 % (25769)Termination reason: Unknown
% 6.73/2.22 % (25769)Termination phase: Saturation
% 6.73/2.22
% 6.73/2.22 % (25769)Memory used [KB]: 6524
% 6.73/2.22 % (25769)Time elapsed: 0.028 s
% 6.73/2.22 % (25769)Instructions burned: 90 (million)
% 6.73/2.22 % (25769)------------------------------
% 6.73/2.22 % (25769)------------------------------
% 6.73/2.22 % (25756)Instruction limit reached!
% 6.73/2.22 % (25756)------------------------------
% 6.73/2.22 % (25756)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.22 % (25756)Termination reason: Unknown
% 6.73/2.22 % (25756)Termination phase: Saturation
% 6.73/2.22
% 6.73/2.22 % (25756)Memory used [KB]: 7036
% 6.73/2.22 % (25756)Time elapsed: 0.057 s
% 6.73/2.22 % (25756)Instructions burned: 193 (million)
% 6.73/2.22 % (25756)------------------------------
% 6.73/2.22 % (25756)------------------------------
% 6.73/2.22 % (25781)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_25342 for (2993ds/458Mi)
% 6.73/2.23 % (25785)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_25342 for (2993ds/297Mi)
% 6.73/2.23 % (25783)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_25342 for (2993ds/31Mi)
% 6.73/2.24 % (25783)Instruction limit reached!
% 6.73/2.24 % (25783)------------------------------
% 6.73/2.24 % (25783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.24 % (25783)Termination reason: Unknown
% 6.73/2.24 % (25783)Termination phase: Property scanning
% 6.73/2.24
% 6.73/2.24 % (25783)Memory used [KB]: 1535
% 6.73/2.24 % (25783)Time elapsed: 0.011 s
% 6.73/2.24 % (25783)Instructions burned: 33 (million)
% 6.73/2.24 % (25783)------------------------------
% 6.73/2.24 % (25783)------------------------------
% 6.73/2.25 % (25789)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_25342 for (2993ds/987Mi)
% 6.73/2.25 % (25760)Instruction limit reached!
% 6.73/2.25 % (25760)------------------------------
% 6.73/2.25 % (25760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.25 % (25760)Termination reason: Unknown
% 6.73/2.25 % (25760)Termination phase: Saturation
% 6.73/2.25
% 6.73/2.25 % (25760)Memory used [KB]: 7036
% 6.73/2.25 % (25760)Time elapsed: 0.079 s
% 6.73/2.25 % (25760)Instructions burned: 260 (million)
% 6.73/2.25 % (25760)------------------------------
% 6.73/2.25 % (25760)------------------------------
% 6.73/2.25 % (25709)Instruction limit reached!
% 6.73/2.25 % (25709)------------------------------
% 6.73/2.25 % (25709)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.25 % (25709)Termination reason: Unknown
% 6.73/2.25 % (25709)Termination phase: Saturation
% 6.73/2.25
% 6.73/2.25 % (25709)Memory used [KB]: 7931
% 6.73/2.25 % (25709)Time elapsed: 0.189 s
% 6.73/2.25 % (25709)Instructions burned: 614 (million)
% 6.73/2.25 % (25709)------------------------------
% 6.73/2.25 % (25709)------------------------------
% 6.73/2.26 % (25627)Instruction limit reached!
% 6.73/2.26 % (25627)------------------------------
% 6.73/2.26 % (25627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.26 % (25627)Termination reason: Unknown
% 6.73/2.26 % (25627)Termination phase: Saturation
% 6.73/2.26
% 6.73/2.26 % (25627)Memory used [KB]: 9978
% 6.73/2.26 % (25627)Time elapsed: 0.374 s
% 6.73/2.26 % (25627)Instructions burned: 1089 (million)
% 6.73/2.26 % (25627)------------------------------
% 6.73/2.26 % (25627)------------------------------
% 6.73/2.26 % (25796)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_25342 for (2992ds/182Mi)
% 6.73/2.26 % (25797)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_25342 for (2992ds/182Mi)
% 6.73/2.27 % (25800)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_25342 for (2992ds/154Mi)
% 6.73/2.28 % (25778)Instruction limit reached!
% 6.73/2.28 % (25778)------------------------------
% 6.73/2.28 % (25778)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.73/2.28 % (25778)Termination reason: Unknown
% 6.73/2.28 % (25778)Termination phase: Saturation
% 6.73/2.28
% 6.73/2.28 % (25778)Memory used [KB]: 9594
% 6.73/2.28 % (25778)Time elapsed: 0.068 s
% 6.73/2.28 % (25778)Instructions burned: 232 (million)
% 6.73/2.28 % (25778)------------------------------
% 6.73/2.28 % (25778)------------------------------
% 6.73/2.29 % (25807)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_25342 for (2992ds/79Mi)
% 7.47/2.30 % (25785)Instruction limit reached!
% 7.47/2.30 % (25785)------------------------------
% 7.47/2.30 % (25785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.30 % (25785)Termination reason: Unknown
% 7.47/2.30 % (25785)Termination phase: Saturation
% 7.47/2.30
% 7.47/2.30 % (25785)Memory used [KB]: 7547
% 7.47/2.30 % (25785)Time elapsed: 0.074 s
% 7.47/2.30 % (25785)Instructions burned: 299 (million)
% 7.47/2.30 % (25785)------------------------------
% 7.47/2.30 % (25785)------------------------------
% 7.47/2.31 % (25800)Instruction limit reached!
% 7.47/2.31 % (25800)------------------------------
% 7.47/2.31 % (25800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.31 % (25800)Termination reason: Unknown
% 7.47/2.31 % (25800)Termination phase: Saturation
% 7.47/2.31
% 7.47/2.31 % (25800)Memory used [KB]: 6268
% 7.47/2.31 % (25800)Time elapsed: 0.039 s
% 7.47/2.31 % (25800)Instructions burned: 156 (million)
% 7.47/2.31 % (25800)------------------------------
% 7.47/2.31 % (25800)------------------------------
% 7.47/2.31 % (25807)Instruction limit reached!
% 7.47/2.31 % (25807)------------------------------
% 7.47/2.31 % (25807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.31 % (25807)Termination reason: Unknown
% 7.47/2.31 % (25807)Termination phase: Saturation
% 7.47/2.31
% 7.47/2.31 % (25807)Memory used [KB]: 6268
% 7.47/2.31 % (25807)Time elapsed: 0.022 s
% 7.47/2.31 % (25807)Instructions burned: 79 (million)
% 7.47/2.31 % (25807)------------------------------
% 7.47/2.31 % (25807)------------------------------
% 7.47/2.31 % (25814)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_25342 for (2992ds/216Mi)
% 7.47/2.31 % (25796)Instruction limit reached!
% 7.47/2.31 % (25796)------------------------------
% 7.47/2.31 % (25796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.31 % (25796)Termination reason: Unknown
% 7.47/2.31 % (25796)Termination phase: Saturation
% 7.47/2.31
% 7.47/2.31 % (25796)Memory used [KB]: 6908
% 7.47/2.31 % (25796)Time elapsed: 0.054 s
% 7.47/2.31 % (25796)Instructions burned: 182 (million)
% 7.47/2.31 % (25796)------------------------------
% 7.47/2.31 % (25796)------------------------------
% 7.47/2.32 % (25817)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_25342 for (2992ds/114Mi)
% 7.47/2.32 % (25820)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_25342 for (2992ds/922Mi)
% 7.47/2.32 % (25797)Instruction limit reached!
% 7.47/2.32 % (25797)------------------------------
% 7.47/2.32 % (25797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.32 % (25797)Termination reason: Unknown
% 7.47/2.32 % (25797)Termination phase: Saturation
% 7.47/2.32
% 7.47/2.32 % (25797)Memory used [KB]: 8699
% 7.47/2.32 % (25797)Time elapsed: 0.058 s
% 7.47/2.32 % (25797)Instructions burned: 182 (million)
% 7.47/2.32 % (25797)------------------------------
% 7.47/2.32 % (25797)------------------------------
% 7.47/2.32 % (25824)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_25342 for (2992ds/182Mi)
% 7.47/2.33 % (25829)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_25342 for (2992ds/164Mi)
% 7.47/2.35 % (25817)Instruction limit reached!
% 7.47/2.35 % (25817)------------------------------
% 7.47/2.35 % (25817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.35 % (25817)Termination reason: Unknown
% 7.47/2.35 % (25817)Termination phase: Saturation
% 7.47/2.35
% 7.47/2.35 % (25817)Memory used [KB]: 6652
% 7.47/2.35 % (25817)Time elapsed: 0.032 s
% 7.47/2.35 % (25817)Instructions burned: 114 (million)
% 7.47/2.35 % (25817)------------------------------
% 7.47/2.35 % (25817)------------------------------
% 7.47/2.36 % (25846)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_25342 for (2991ds/50Mi)
% 7.47/2.36 % (25781)Instruction limit reached!
% 7.47/2.36 % (25781)------------------------------
% 7.47/2.36 % (25781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.36 % (25781)Termination reason: Unknown
% 7.47/2.36 % (25781)Termination phase: Saturation
% 7.47/2.36
% 7.47/2.36 % (25781)Memory used [KB]: 7419
% 7.47/2.36 % (25781)Time elapsed: 0.143 s
% 7.47/2.36 % (25781)Instructions burned: 460 (million)
% 7.47/2.36 % (25781)------------------------------
% 7.47/2.36 % (25781)------------------------------
% 7.47/2.36 % (25814)Instruction limit reached!
% 7.47/2.36 % (25814)------------------------------
% 7.47/2.36 % (25814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.36 % (25814)Termination reason: Unknown
% 7.47/2.36 % (25814)Termination phase: Saturation
% 7.47/2.36
% 7.47/2.36 % (25814)Memory used [KB]: 6908
% 7.47/2.36 % (25814)Time elapsed: 0.055 s
% 7.47/2.36 % (25814)Instructions burned: 220 (million)
% 7.47/2.36 % (25814)------------------------------
% 7.47/2.36 % (25814)------------------------------
% 7.47/2.37 % (25846)Instruction limit reached!
% 7.47/2.37 % (25846)------------------------------
% 7.47/2.37 % (25846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.37 % (25846)Termination reason: Unknown
% 7.47/2.37 % (25846)Termination phase: Property scanning
% 7.47/2.37
% 7.47/2.37 % (25846)Memory used [KB]: 1663
% 7.47/2.37 % (25846)Time elapsed: 0.014 s
% 7.47/2.37 % (25846)Instructions burned: 52 (million)
% 7.47/2.37 % (25846)------------------------------
% 7.47/2.37 % (25846)------------------------------
% 7.47/2.37 % (25824)Instruction limit reached!
% 7.47/2.37 % (25824)------------------------------
% 7.47/2.37 % (25824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.37 % (25824)Termination reason: Unknown
% 7.47/2.37 % (25824)Termination phase: Saturation
% 7.47/2.37
% 7.47/2.37 % (25824)Memory used [KB]: 6268
% 7.47/2.37 % (25824)Time elapsed: 0.068 s
% 7.47/2.37 % (25824)Instructions burned: 183 (million)
% 7.47/2.37 % (25824)------------------------------
% 7.47/2.37 % (25824)------------------------------
% 7.47/2.37 % (25851)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_25342 for (2991ds/368Mi)
% 7.47/2.37 % (25853)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_25342 for (2991ds/1021Mi)
% 7.47/2.38 % (25829)Instruction limit reached!
% 7.47/2.38 % (25829)------------------------------
% 7.47/2.38 % (25829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.47/2.38 % (25829)Termination reason: Unknown
% 7.47/2.38 % (25829)Termination phase: Saturation
% 7.47/2.38
% 7.47/2.38 % (25829)Memory used [KB]: 2174
% 7.47/2.38 % (25829)Time elapsed: 0.048 s
% 7.47/2.38 % (25829)Instructions burned: 165 (million)
% 7.47/2.38 % (25829)------------------------------
% 7.47/2.38 % (25829)------------------------------
% 7.47/2.38 % (25856)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_25342 for (2991ds/267Mi)
% 7.47/2.38 % (25858)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_25342 for (2991ds/204Mi)
% 7.47/2.40 % (25859)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_25342 for (2991ds/26Mi)
% 8.15/2.41 % (25859)Instruction limit reached!
% 8.15/2.41 % (25859)------------------------------
% 8.15/2.41 % (25859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.41 % (25859)Termination reason: Unknown
% 8.15/2.41 % (25859)Termination phase: Property scanning
% 8.15/2.41
% 8.15/2.41 % (25859)Memory used [KB]: 1535
% 8.15/2.41 % (25859)Time elapsed: 0.016 s
% 8.15/2.41 % (25859)Instructions burned: 27 (million)
% 8.15/2.41 % (25859)------------------------------
% 8.15/2.41 % (25859)------------------------------
% 8.15/2.43 % (25860)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_25342 for (2991ds/53Mi)
% 8.15/2.44 % (25858)Instruction limit reached!
% 8.15/2.44 % (25858)------------------------------
% 8.15/2.44 % (25858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.44 % (25858)Termination reason: Unknown
% 8.15/2.44 % (25858)Termination phase: Saturation
% 8.15/2.44
% 8.15/2.44 % (25858)Memory used [KB]: 6908
% 8.15/2.44 % (25858)Time elapsed: 0.062 s
% 8.15/2.44 % (25858)Instructions burned: 204 (million)
% 8.15/2.44 % (25858)------------------------------
% 8.15/2.44 % (25858)------------------------------
% 8.15/2.44 % (25856)Instruction limit reached!
% 8.15/2.44 % (25856)------------------------------
% 8.15/2.44 % (25856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.44 % (25856)Termination reason: Unknown
% 8.15/2.44 % (25856)Termination phase: Saturation
% 8.15/2.44
% 8.15/2.44 % (25856)Memory used [KB]: 7931
% 8.15/2.44 % (25856)Time elapsed: 0.068 s
% 8.15/2.44 % (25856)Instructions burned: 267 (million)
% 8.15/2.44 % (25856)------------------------------
% 8.15/2.44 % (25856)------------------------------
% 8.15/2.45 % (25860)Instruction limit reached!
% 8.15/2.45 % (25860)------------------------------
% 8.15/2.45 % (25860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.45 % (25860)Termination reason: Unknown
% 8.15/2.45 % (25860)Termination phase: Saturation
% 8.15/2.45
% 8.15/2.45 % (25860)Memory used [KB]: 6140
% 8.15/2.45 % (25860)Time elapsed: 0.022 s
% 8.15/2.45 % (25860)Instructions burned: 53 (million)
% 8.15/2.45 % (25860)------------------------------
% 8.15/2.45 % (25860)------------------------------
% 8.15/2.45 % (25861)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_25342 for (2990ds/4436Mi)
% 8.15/2.45 % (25862)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_25342 for (2990ds/1539Mi)
% 8.15/2.46 % (25863)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_25342 for (2990ds/408Mi)
% 8.15/2.49 % (25851)Instruction limit reached!
% 8.15/2.49 % (25851)------------------------------
% 8.15/2.49 % (25851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.49 % (25851)Termination reason: Unknown
% 8.15/2.49 % (25851)Termination phase: Saturation
% 8.15/2.49
% 8.15/2.49 % (25851)Memory used [KB]: 7419
% 8.15/2.49 % (25851)Time elapsed: 0.116 s
% 8.15/2.49 % (25851)Instructions burned: 369 (million)
% 8.15/2.49 % (25851)------------------------------
% 8.15/2.49 % (25851)------------------------------
% 8.15/2.49 % (25789)Instruction limit reached!
% 8.15/2.49 % (25789)------------------------------
% 8.15/2.49 % (25789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.15/2.49 % (25789)Termination reason: Unknown
% 8.15/2.49 % (25789)Termination phase: Saturation
% 8.15/2.49
% 8.15/2.49 % (25789)Memory used [KB]: 8059
% 8.15/2.49 % (25789)Time elapsed: 0.250 s
% 8.15/2.49 % (25789)Instructions burned: 988 (million)
% 8.15/2.49 % (25789)------------------------------
% 8.15/2.49 % (25789)------------------------------
% 8.15/2.50 % (25864)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_25342 for (2990ds/5205Mi)
% 8.76/2.50 % (25865)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_25342 for (2990ds/1913Mi)
% 8.76/2.59 % (25863)Instruction limit reached!
% 8.76/2.59 % (25863)------------------------------
% 8.76/2.59 % (25863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.76/2.59 % (25863)Termination reason: Unknown
% 8.76/2.59 % (25863)Termination phase: Saturation
% 8.76/2.59
% 8.76/2.59 % (25863)Memory used [KB]: 9083
% 8.76/2.59 % (25863)Time elapsed: 0.131 s
% 8.76/2.59 % (25863)Instructions burned: 408 (million)
% 8.76/2.59 % (25863)------------------------------
% 8.76/2.59 % (25863)------------------------------
% 8.90/2.60 % (25866)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_25342 for (2989ds/4350Mi)
% 8.90/2.61 % (25820)Instruction limit reached!
% 8.90/2.61 % (25820)------------------------------
% 8.90/2.61 % (25820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.61 % (25820)Termination reason: Unknown
% 8.90/2.61 % (25820)Termination phase: Saturation
% 8.90/2.61
% 8.90/2.61 % (25820)Memory used [KB]: 9083
% 8.90/2.61 % (25820)Time elapsed: 0.312 s
% 8.90/2.61 % (25820)Instructions burned: 923 (million)
% 8.90/2.61 % (25820)------------------------------
% 8.90/2.61 % (25820)------------------------------
% 8.90/2.62 % (25867)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_25342 for (2989ds/68Mi)
% 8.90/2.63 % (25867)Instruction limit reached!
% 8.90/2.63 % (25867)------------------------------
% 8.90/2.63 % (25867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.63 % (25867)Termination reason: Unknown
% 8.90/2.63 % (25867)Termination phase: Saturation
% 8.90/2.63
% 8.90/2.63 % (25867)Memory used [KB]: 6268
% 8.90/2.63 % (25867)Time elapsed: 0.019 s
% 8.90/2.63 % (25867)Instructions burned: 69 (million)
% 8.90/2.63 % (25867)------------------------------
% 8.90/2.63 % (25867)------------------------------
% 8.90/2.64 % (25868)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_25342 for (2989ds/358Mi)
% 8.90/2.69 % (25853)Instruction limit reached!
% 8.90/2.69 % (25853)------------------------------
% 8.90/2.69 % (25853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.90/2.69 % (25853)Termination reason: Unknown
% 8.90/2.69 % (25853)Termination phase: Saturation
% 8.90/2.69
% 8.90/2.69 % (25853)Memory used [KB]: 9722
% 8.90/2.69 % (25853)Time elapsed: 0.321 s
% 8.90/2.69 % (25853)Instructions burned: 1021 (million)
% 8.90/2.69 % (25853)------------------------------
% 8.90/2.69 % (25853)------------------------------
% 9.55/2.70 % (25869)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_25342 for (2988ds/31Mi)
% 9.55/2.71 % (25869)Instruction limit reached!
% 9.55/2.71 % (25869)------------------------------
% 9.55/2.71 % (25869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.71 % (25869)Termination reason: Unknown
% 9.55/2.71 % (25869)Termination phase: Property scanning
% 9.55/2.71
% 9.55/2.71 % (25869)Memory used [KB]: 1535
% 9.55/2.71 % (25869)Time elapsed: 0.009 s
% 9.55/2.71 % (25869)Instructions burned: 31 (million)
% 9.55/2.71 % (25869)------------------------------
% 9.55/2.71 % (25869)------------------------------
% 9.55/2.72 % (25870)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_25342 for (2988ds/279Mi)
% 9.55/2.75 % (25868)Instruction limit reached!
% 9.55/2.75 % (25868)------------------------------
% 9.55/2.75 % (25868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.75 % (25868)Termination reason: Unknown
% 9.55/2.75 % (25868)Termination phase: Saturation
% 9.55/2.75
% 9.55/2.75 % (25868)Memory used [KB]: 7164
% 9.55/2.75 % (25868)Time elapsed: 0.109 s
% 9.55/2.75 % (25868)Instructions burned: 358 (million)
% 9.55/2.75 % (25868)------------------------------
% 9.55/2.75 % (25868)------------------------------
% 9.55/2.76 % (25871)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_25342 for (2987ds/258Mi)
% 9.55/2.79 % (25870)Instruction limit reached!
% 9.55/2.79 % (25870)------------------------------
% 9.55/2.79 % (25870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.55/2.79 % (25870)Termination reason: Unknown
% 9.55/2.79 % (25870)Termination phase: Saturation
% 9.55/2.79
% 9.55/2.79 % (25870)Memory used [KB]: 6396
% 9.55/2.79 % (25870)Time elapsed: 0.068 s
% 9.55/2.79 % (25870)Instructions burned: 279 (million)
% 9.55/2.79 % (25870)------------------------------
% 9.55/2.79 % (25870)------------------------------
% 9.76/2.80 % (25872)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_25342 for (2987ds/26Mi)
% 9.76/2.80 % (25872)Instruction limit reached!
% 9.76/2.80 % (25872)------------------------------
% 9.76/2.80 % (25872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.76/2.80 % (25872)Termination reason: Unknown
% 9.76/2.80 % (25872)Termination phase: Naming
% 9.76/2.80
% 9.76/2.80 % (25872)Memory used [KB]: 1535
% 9.76/2.80 % (25872)Time elapsed: 0.008 s
% 9.76/2.80 % (25872)Instructions burned: 27 (million)
% 9.76/2.80 % (25872)------------------------------
% 9.76/2.80 % (25872)------------------------------
% 9.76/2.81 % (25873)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_25342 for (2987ds/995Mi)
% 9.76/2.83 % (25871)Instruction limit reached!
% 9.76/2.83 % (25871)------------------------------
% 9.76/2.83 % (25871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.76/2.83 % (25871)Termination reason: Unknown
% 9.76/2.83 % (25871)Termination phase: Saturation
% 9.76/2.83
% 9.76/2.83 % (25871)Memory used [KB]: 7803
% 9.76/2.83 % (25871)Time elapsed: 0.071 s
% 9.76/2.83 % (25871)Instructions burned: 258 (million)
% 9.76/2.83 % (25871)------------------------------
% 9.76/2.83 % (25871)------------------------------
% 9.76/2.84 % (25874)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_25342 for (2987ds/373Mi)
% 9.87/2.93 % (25862)Instruction limit reached!
% 9.87/2.93 % (25862)------------------------------
% 9.87/2.93 % (25862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.93 % (25862)Termination reason: Unknown
% 9.87/2.93 % (25862)Termination phase: Saturation
% 9.87/2.93
% 9.87/2.94 % (25862)Memory used [KB]: 8699
% 9.87/2.94 % (25862)Time elapsed: 0.482 s
% 9.87/2.94 % (25862)Instructions burned: 1539 (million)
% 9.87/2.94 % (25862)------------------------------
% 9.87/2.94 % (25862)------------------------------
% 9.87/2.95 % (25875)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_25342 for (2986ds/253Mi)
% 9.87/2.96 % (25874)Instruction limit reached!
% 9.87/2.96 % (25874)------------------------------
% 9.87/2.96 % (25874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/2.96 % (25874)Termination reason: Unknown
% 9.87/2.96 % (25874)Termination phase: Saturation
% 9.87/2.96
% 9.87/2.96 % (25874)Memory used [KB]: 7291
% 9.87/2.96 % (25874)Time elapsed: 0.117 s
% 9.87/2.96 % (25874)Instructions burned: 374 (million)
% 9.87/2.96 % (25874)------------------------------
% 9.87/2.96 % (25874)------------------------------
% 9.87/2.97 % (25876)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_25342 for (2985ds/832Mi)
% 9.87/3.01 % (25875)Instruction limit reached!
% 9.87/3.01 % (25875)------------------------------
% 9.87/3.01 % (25875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.87/3.01 % (25875)Termination reason: Unknown
% 9.87/3.01 % (25875)Termination phase: Saturation
% 9.87/3.01
% 9.87/3.01 % (25875)Memory used [KB]: 6268
% 9.87/3.01 % (25875)Time elapsed: 0.063 s
% 9.87/3.01 % (25875)Instructions burned: 253 (million)
% 9.87/3.01 % (25875)------------------------------
% 9.87/3.01 % (25875)------------------------------
% 12.73/3.02 % (25877)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_25342 for (2985ds/668Mi)
% 12.73/3.07 % (25873)Instruction limit reached!
% 12.73/3.07 % (25873)------------------------------
% 12.73/3.07 % (25873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.73/3.07 % (25873)Termination reason: Unknown
% 12.73/3.07 % (25873)Termination phase: Saturation
% 12.73/3.07
% 12.73/3.07 % (25873)Memory used [KB]: 7931
% 12.73/3.07 % (25873)Time elapsed: 0.253 s
% 12.73/3.07 % (25873)Instructions burned: 998 (million)
% 12.73/3.07 % (25873)------------------------------
% 12.73/3.07 % (25873)------------------------------
% 12.73/3.07 % (25865)Instruction limit reached!
% 12.73/3.07 % (25865)------------------------------
% 12.73/3.07 % (25865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.73/3.07 % (25865)Termination reason: Unknown
% 12.73/3.07 % (25865)Termination phase: Saturation
% 12.73/3.07
% 12.73/3.07 % (25865)Memory used [KB]: 3070
% 12.73/3.07 % (25865)Time elapsed: 0.569 s
% 12.73/3.07 % (25865)Instructions burned: 1913 (million)
% 12.73/3.07 % (25865)------------------------------
% 12.73/3.07 % (25865)------------------------------
% 12.73/3.08 % (25878)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_25342 for (2984ds/40Mi)
% 12.73/3.08 % (25879)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_25342 for (2984ds/294Mi)
% 12.73/3.09 % (25878)Instruction limit reached!
% 12.73/3.09 % (25878)------------------------------
% 12.73/3.09 % (25878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.73/3.09 % (25878)Termination reason: Unknown
% 12.73/3.09 % (25878)Termination phase: Property scanning
% 12.73/3.09
% 12.73/3.09 % (25878)Memory used [KB]: 1663
% 12.73/3.09 % (25878)Time elapsed: 0.012 s
% 12.73/3.09 % (25878)Instructions burned: 42 (million)
% 12.73/3.09 % (25878)------------------------------
% 12.73/3.09 % (25878)------------------------------
% 12.73/3.10 % (25880)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_25342 for (2984ds/187Mi)
% 13.37/3.15 % (25880)Instruction limit reached!
% 13.37/3.15 % (25880)------------------------------
% 13.37/3.15 % (25880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/3.15 % (25880)Termination reason: Unknown
% 13.37/3.15 % (25880)Termination phase: Saturation
% 13.37/3.15
% 13.37/3.15 % (25880)Memory used [KB]: 7036
% 13.37/3.15 % (25880)Time elapsed: 0.056 s
% 13.37/3.15 % (25880)Instructions burned: 190 (million)
% 13.37/3.15 % (25880)------------------------------
% 13.37/3.15 % (25880)------------------------------
% 13.37/3.16 % (25879)Instruction limit reached!
% 13.37/3.16 % (25879)------------------------------
% 13.37/3.16 % (25879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/3.16 % (25879)Termination reason: Unknown
% 13.37/3.16 % (25879)Termination phase: Saturation
% 13.37/3.16
% 13.37/3.16 % (25879)Memory used [KB]: 6268
% 13.37/3.16 % (25879)Time elapsed: 0.075 s
% 13.37/3.16 % (25879)Instructions burned: 295 (million)
% 13.37/3.16 % (25879)------------------------------
% 13.37/3.16 % (25879)------------------------------
% 13.37/3.16 % (25881)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_25342 for (2983ds/371Mi)
% 13.37/3.17 % (25882)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_25342 for (2983ds/1827Mi)
% 13.37/3.18 % (25877)Instruction limit reached!
% 13.37/3.18 % (25877)------------------------------
% 13.37/3.18 % (25877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/3.18 % (25877)Termination reason: Unknown
% 13.37/3.18 % (25877)Termination phase: Saturation
% 13.37/3.18
% 13.37/3.18 % (25877)Memory used [KB]: 12409
% 13.37/3.18 % (25877)Time elapsed: 0.164 s
% 13.37/3.18 % (25877)Instructions burned: 670 (million)
% 13.37/3.18 % (25877)------------------------------
% 13.37/3.18 % (25877)------------------------------
% 13.37/3.19 % (25883)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_25342 for (2983ds/70Mi)
% 14.02/3.21 % (25883)Instruction limit reached!
% 14.02/3.21 % (25883)------------------------------
% 14.02/3.21 % (25883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.02/3.21 % (25883)Termination reason: Unknown
% 14.02/3.21 % (25883)Termination phase: Saturation
% 14.02/3.21
% 14.02/3.21 % (25883)Memory used [KB]: 1663
% 14.02/3.21 % (25883)Time elapsed: 0.019 s
% 14.02/3.21 % (25883)Instructions burned: 71 (million)
% 14.02/3.21 % (25883)------------------------------
% 14.02/3.21 % (25883)------------------------------
% 14.02/3.22 % (25885)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_25342 for (2983ds/316Mi)
% 14.02/3.23 % (25876)Instruction limit reached!
% 14.02/3.23 % (25876)------------------------------
% 14.02/3.23 % (25876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.02/3.23 % (25876)Termination reason: Unknown
% 14.02/3.23 % (25876)Termination phase: Saturation
% 14.02/3.23
% 14.02/3.23 % (25876)Memory used [KB]: 8571
% 14.02/3.23 % (25876)Time elapsed: 0.262 s
% 14.02/3.23 % (25876)Instructions burned: 834 (million)
% 14.02/3.23 % (25876)------------------------------
% 14.02/3.23 % (25876)------------------------------
% 14.02/3.24 % (25886)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_25342 for (2983ds/932Mi)
% 14.02/3.27 % (25881)Instruction limit reached!
% 14.02/3.27 % (25881)------------------------------
% 14.02/3.27 % (25881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.02/3.27 % (25881)Termination reason: Unknown
% 14.02/3.27 % (25881)Termination phase: Saturation
% 14.02/3.27
% 14.02/3.27 % (25881)Memory used [KB]: 7164
% 14.02/3.27 % (25881)Time elapsed: 0.110 s
% 14.02/3.27 % (25881)Instructions burned: 371 (million)
% 14.02/3.27 % (25881)------------------------------
% 14.02/3.27 % (25881)------------------------------
% 14.02/3.28 % (25887)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_25342 for (2982ds/4714Mi)
% 14.50/3.30 % (25885)Instruction limit reached!
% 14.50/3.30 % (25885)------------------------------
% 14.50/3.30 % (25885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.50/3.30 % (25885)Termination reason: Unknown
% 14.50/3.30 % (25885)Termination phase: Saturation
% 14.50/3.30
% 14.50/3.30 % (25885)Memory used [KB]: 6780
% 14.50/3.30 % (25885)Time elapsed: 0.079 s
% 14.50/3.30 % (25885)Instructions burned: 316 (million)
% 14.50/3.30 % (25885)------------------------------
% 14.50/3.30 % (25885)------------------------------
% 14.50/3.31 % (25888)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_25342 for (2982ds/8250Mi)
% 14.89/3.46 % (25886)Instruction limit reached!
% 14.89/3.46 % (25886)------------------------------
% 14.89/3.46 % (25886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.89/3.46 % (25886)Termination reason: Unknown
% 14.89/3.46 % (25886)Termination phase: Saturation
% 14.89/3.46
% 14.89/3.46 % (25886)Memory used [KB]: 8571
% 14.89/3.46 % (25886)Time elapsed: 0.228 s
% 14.89/3.46 % (25886)Instructions burned: 932 (million)
% 14.89/3.46 % (25886)------------------------------
% 14.89/3.46 % (25886)------------------------------
% 14.89/3.47 % (25889)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_25342 for (2980ds/770Mi)
% 15.74/3.63 % (25888)First to succeed.
% 15.74/3.64 % (25888)Refutation found. Thanks to Tanya!
% 15.74/3.64 % SZS status Theorem for DTF2THF_25342
% 15.74/3.64 % SZS output start Proof for DTF2THF_25342
% 15.74/3.64 thf(func_def_0, type, in: $i > $i > $o).
% 15.74/3.64 thf(func_def_1, type, exu: ($i > $o) > $o).
% 15.74/3.64 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 15.74/3.64 thf(func_def_8, type, powerset: $i > $i).
% 15.74/3.64 thf(func_def_10, type, setunion: $i > $i).
% 15.74/3.64 thf(func_def_19, type, descr: ($i > $o) > $i).
% 15.74/3.64 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 15.74/3.64 thf(func_def_26, type, prop2set: $o > $i).
% 15.74/3.64 thf(func_def_36, type, nonempty: $i > $o).
% 15.74/3.64 thf(func_def_69, type, set2prop: $i > $o).
% 15.74/3.64 thf(func_def_88, type, subset: $i > $i > $o).
% 15.74/3.64 thf(func_def_89, type, disjoint: $i > $i > $o).
% 15.74/3.64 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 15.74/3.64 thf(func_def_114, type, binunion: $i > $i > $i).
% 15.74/3.64 thf(func_def_122, type, binintersect: $i > $i > $i).
% 15.74/3.64 thf(func_def_140, type, sP1: $i > $i > $o).
% 15.74/3.64 thf(func_def_141, type, sP2: $i > $o).
% 15.74/3.64 thf(func_def_142, type, sP3: $i > $i > $o).
% 15.74/3.64 thf(func_def_143, type, sP4: $i > $i > $o).
% 15.74/3.64 thf(func_def_147, type, sK8: $i > $o).
% 15.74/3.64 thf(func_def_148, type, sK9: $i > $i).
% 15.74/3.64 thf(func_def_149, type, sK10: ($i > $o) > $i).
% 15.74/3.64 thf(func_def_151, type, sK12: $i > $o).
% 15.74/3.64 thf(func_def_153, type, sK14: ($i > $o) > $i > $i).
% 15.74/3.64 thf(func_def_154, type, sK15: $i > $o).
% 15.74/3.64 thf(func_def_155, type, sK16: $i > $o).
% 15.74/3.64 thf(func_def_156, type, sK17: ($i > $o) > ($i > $o) > $i).
% 15.74/3.64 thf(func_def_157, type, sK18: ($i > $o) > ($i > $o) > $i).
% 15.74/3.64 thf(func_def_163, type, sK24: $o > $i > $i > $i).
% 15.74/3.64 thf(func_def_166, type, sK27: $i > $o).
% 15.74/3.64 thf(func_def_168, type, sK29: ($i > $o) > $i > $i).
% 15.74/3.64 thf(func_def_173, type, sK34: $i > $i).
% 15.74/3.64 thf(func_def_191, type, sK52: $i > $o).
% 15.74/3.64 thf(func_def_193, type, sK54: $i > $o).
% 15.74/3.64 thf(func_def_195, type, sK56: $i > ($i > $o) > $i).
% 15.74/3.64 thf(func_def_196, type, sK57: $i > $o).
% 15.74/3.64 thf(func_def_198, type, sK59: $i > ($i > $o) > $i).
% 15.74/3.64 thf(func_def_199, type, sK60: $i > ($i > $o) > $i).
% 15.74/3.64 thf(func_def_200, type, sK61: $i > $o).
% 15.74/3.64 thf(func_def_207, type, sK68: $i > $o).
% 15.74/3.64 thf(func_def_209, type, sK70: $i > $o).
% 15.74/3.64 thf(func_def_219, type, sK80: $i > $i > $i).
% 15.74/3.64 thf(func_def_223, type, sK84: $i > $o).
% 15.74/3.64 thf(func_def_229, type, sK90: $i > $o).
% 15.74/3.64 thf(func_def_232, type, sK93: $i > $i).
% 15.74/3.64 thf(func_def_241, type, sK102: $i > $i > $o).
% 15.74/3.64 thf(func_def_242, type, sK103: $i > $i).
% 15.74/3.64 thf(func_def_243, type, sK104: $i > $i).
% 15.74/3.64 thf(func_def_244, type, sK105: ($i > $i > $o) > $i > $i).
% 15.74/3.64 thf(func_def_245, type, sK106: $i > ($i > $i > $o) > $i > $i).
% 15.74/3.64 thf(func_def_246, type, sK107: ($i > $i > $o) > $i > $i).
% 15.74/3.64 thf(func_def_247, type, sK108: $i > $o).
% 15.74/3.64 thf(func_def_258, type, sK119: $i > $i).
% 15.74/3.64 thf(func_def_260, type, sK121: $i > $o).
% 15.74/3.64 thf(func_def_262, type, sK123: ($i > $o) > $i).
% 15.74/3.64 thf(func_def_263, type, sK124: ($i > $o) > $i).
% 15.74/3.64 thf(func_def_280, type, sK141: $i > $i).
% 15.74/3.64 thf(func_def_288, type, sK149: $i > $o).
% 15.74/3.64 thf(func_def_292, type, sK153: $i > $o).
% 15.74/3.64 thf(func_def_294, type, sK155: $i > $o).
% 15.74/3.64 thf(func_def_295, type, sK156: $i > $o).
% 15.74/3.64 thf(func_def_296, type, sK157: ($i > $o) > ($i > $o) > $i).
% 15.74/3.64 thf(func_def_297, type, sK158: ($i > $o) > ($i > $o) > $i).
% 15.74/3.64 thf(func_def_314, type, sK175: $i > $i > $i).
% 15.74/3.64 thf(func_def_315, type, sK176: $i > $i > $i).
% 15.74/3.64 thf(func_def_322, type, sK183: ($i > $o) > ($i > $o) > $i > $i > $i).
% 15.74/3.64 thf(func_def_323, type, sK184: ($i > $o) > ($i > $o) > $i > $i > $i).
% 15.74/3.64 thf(func_def_326, type, sK187: $i > $o).
% 15.74/3.64 thf(func_def_327, type, sK188: $i > $o).
% 15.74/3.64 thf(func_def_328, type, sK189: $i > $o).
% 15.74/3.64 thf(func_def_333, type, sK194: $i > $o).
% 15.74/3.64 thf(func_def_334, type, sK195: $i > $i > $i).
% 15.74/3.64 thf(func_def_340, type, sK201: $i > $i).
% 15.74/3.64 thf(func_def_341, type, sK202: $i > $i > $i).
% 15.74/3.64 thf(func_def_349, type, sK210: $i > $i > $i).
% 15.74/3.64 thf(func_def_359, type, sK220: $i > $o).
% 15.74/3.64 thf(func_def_365, type, sK226: $i > ($i > $o) > $i).
% 15.74/3.64 thf(func_def_366, type, sK227: $i > $o).
% 15.74/3.64 thf(func_def_369, type, sK230: ($i > $o) > $i).
% 15.74/3.64 thf(func_def_370, type, sK231: $i > $o).
% 15.74/3.64 thf(func_def_371, type, sK232: $i > $i).
% 15.74/3.64 thf(func_def_378, type, sK239: $i > $i > $i).
% 15.74/3.64 thf(func_def_382, type, sK243: $i > $i > $i).
% 15.74/3.64 thf(func_def_387, type, sK248: $i > ($i > $o) > $i).
% 15.74/3.64 thf(func_def_388, type, sK249: $i > $o).
% 15.74/3.64 thf(func_def_391, type, sK252: ($i > $o) > $i).
% 15.74/3.64 thf(func_def_392, type, sK253: $i > $o).
% 15.74/3.64 thf(func_def_393, type, sK254: $i > $i).
% 15.74/3.64 thf(func_def_395, type, sK256: $i > $i).
% 15.74/3.64 thf(func_def_397, type, sK258: $i > $i > $i).
% 15.74/3.64 thf(func_def_398, type, sK259: $i > $i > $i).
% 15.74/3.64 thf(func_def_399, type, sK260: $i > $i > $i).
% 15.74/3.64 thf(func_def_400, type, sK261: $i > $i > $i).
% 15.74/3.64 thf(func_def_401, type, sK262: $i > $i > $i > $i).
% 15.74/3.64 thf(func_def_402, type, sK263: $i > $i).
% 15.74/3.64 thf(func_def_403, type, sK264: $i > $i).
% 15.74/3.64 thf(func_def_404, type, sK265: $i > $i).
% 15.74/3.64 thf(func_def_405, type, sK266: $i > $i).
% 15.74/3.64 thf(func_def_406, type, sK267: $i > $i > $i).
% 15.74/3.64 thf(func_def_407, type, sK268: $i > $i > $i > $i).
% 15.74/3.64 thf(func_def_408, type, sK269: $i > $i > $i > $i).
% 15.74/3.64 thf(func_def_409, type, sK270: $i > $i > $i).
% 15.74/3.64 thf(func_def_410, type, sK271: $i > $i > $i).
% 15.74/3.64 thf(func_def_411, type, sK272: $i > $i).
% 15.74/3.64 thf(func_def_412, type, sK273: $i > $i > $i).
% 15.74/3.64 thf(func_def_414, type, sK275: $i > $i).
% 15.74/3.64 thf(func_def_415, type, sK276: $i > $i).
% 15.74/3.64 thf(func_def_431, type, sK292: ($i > $o) > $i > $i).
% 15.74/3.64 thf(func_def_433, type, sK294: $i > $o).
% 15.74/3.64 thf(func_def_439, type, sK300: $i > $o).
% 15.74/3.64 thf(func_def_442, type, ph303: !>[X0: $tType]:(X0)).
% 15.74/3.64 thf(f7871,plain,(
% 15.74/3.64 $false),
% 15.74/3.64 inference(avatar_sat_refutation,[status(thm)],[f1983,f3011,f3461,f3606,f3694,f3845,f4018,f4019,f7870])).
% 15.74/3.64 thf(f7870,plain,(
% 15.74/3.64 ~spl302_71 | ~spl302_183 | ~spl302_299 | ~spl302_438),
% 15.74/3.64 inference(avatar_contradiction_clause,[status(thm)],[f7869])).
% 15.74/3.64 thf(f7869,plain,(
% 15.74/3.64 $false | (~spl302_71 | ~spl302_183 | ~spl302_299 | ~spl302_438)),
% 15.74/3.64 inference(subsumption_resolution,[status(thm)],[f7868,f3693])).
% 15.74/3.64 thf(f3693,plain,(
% 15.74/3.64 ( ! [X0 : $i,X1 : $i] : (((subset @ (binintersect @ X0 @ X1) @ X0) = $true)) ) | ~spl302_438),
% 15.74/3.64 inference(avatar_component_clause,[status(thm)],[f3692])).
% 15.74/3.64 thf(f3692,definition,(
% 15.74/3.64 spl302_438 <=> ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) = $true)),
% 15.74/3.64 introduced(definition,[new_symbols(naming,[spl302_438])],[avatar_definition])).
% 15.74/3.64 thf(f7868,plain,(
% 15.74/3.64 ((subset @ (binintersect @ sK88 @ sK87) @ sK88) != $true) | (~spl302_71 | ~spl302_183 | ~spl302_299)),
% 15.74/3.64 inference(subsumption_resolution,[status(thm)],[f7865,f1188])).
% 15.74/3.64 thf(f1188,plain,(
% 15.74/3.64 ((binintersect @ sK88 @ sK87) != sK88)),
% 15.74/3.64 inference(cnf_transformation,[status(thm)],[f627])).
% 15.74/3.64 thf(f627,plain,(
% 15.74/3.64 (prop2setE = $true) & (omegaSAx = $true) & (setunionE = $true) & (omegaIndAx = $true) & (emptyinPowerset = $true) & (notequalI1 = $true) & (setunionAx = $true) & (eqimpsubset2 = $true) & (nonemptyI1 = $true) & (emptyInPowerset = $true) & (sepInPowerset = $true) & (powersetI1 = $true) & (emptyinunitempty = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (emptyI = $true) & (sepSubset = $true) & (quantDeMorgan4 = $true) & (emptyE1 = $true) & (setadjoin__Cong = $true) & (setunionI = $true) & (dsetconstrI = $true) & (inCongP = $true) & (vacuousDall = $true) & (upairset2IR = $true) & (emptyset__Cong = $true) & (powersetE1 = $true) & (powersetAx = $true) & (exu__Cong = $true) & (binunionEcases = $true) & (((binintersect @ sK88 @ sK87) != sK88) & ((subset @ sK88 @ sK87) = $true)) & (subsetRefl = $true) & (binunionE = $true) & (subsetTrans = $true) & (binunionIL = $true) & (setadjoinSub2 = $true) & (exuE1 = $true) & (notequalI2 = $true) & (emptysetAx = $true) & (powersetE = $true) & (omega__Cong = $true) & (quantDeMorgan3 = $true) & (dsetconstrER = $true) & (setextsub = $true) & (quantDeMorgan2 = $true) & (binintersectLsub = $true) & (noeltsimpempty = $true) & (foundationAx = $true) & (prop2setI = $true) & (subset2powerset = $true) & (exuEu = $true) & (exuI2 = $true) & (binintersectEL = $true) & (descr__Cong = $true) & (replAx = $true) & (setadjoinAx = $true) & (subsetI1 = $true) & (eqinunit = $true) & (prop2set2propI = $true) & (omega0Ax = $true) & (setadjoinIL = $true) & (setadjoinOr = $true) & (in__Cong = $true) & (binunionLsub = $true) & (setadjoinSub = $true) & (upairsetE = $true) & (upairsetIR = $true) & (nonemptyI = $true) & (singletonsswitch = $true) & (descrp = $true) & (setextAx = $true) & (dsetconstr__Cong = $true) & (binunionIR = $true) & (emptysetimpfalse = $true) & (setadjoinE = $true) & (powersetI = $true) & (emptysetsubset = $true) & (setbeta = $true) & (upairsetIL = $true) & (exuE3u = $true) & (nonemptyE1 = $true) & (inPowerset = $true) & (subPowSU = $true) & (subsetE2 = $true) & (notsubsetI = $true) & (setoftrueEq = $true) & (exuI3 = $true) & (binunionRsub = $true) & (eqimpsubset1 = $true) & (exuE3e = $true) & (notinemptyset = $true) & (subsetI2 = $true) & (exuE2 = $true) & (setadjoinIR = $true) & (setext = $true) & (notdexE = $true) & (setunion__Cong = $true) & (quantDeMorgan1 = $true) & (notinsingleton = $true) & (exuI1 = $true) & (notdallE = $true) & (dsetconstrEL = $true) & (uniqinunit = $true) & (wellorderingAx = $true) & (emptysetE = $true) & (subsetemptysetimpeq = $true) & (subsetE = $true) & (nonemptyImpWitness = $true) & (powersetsubset = $true) & (powerset__Cong = $true)),
% 15.74/3.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK87,sK88])],[f449,f626])).
% 15.74/3.64 thf(f626,plain,(
% 15.74/3.64 ? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) != X1) & ($true = (subset @ X1 @ X0))) => (((binintersect @ sK88 @ sK87) != sK88) & ((subset @ sK88 @ sK87) = $true))),
% 15.74/3.64 introduced(definition,[],[choice_axiom])).
% 15.74/3.64 thf(f449,plain,(
% 15.74/3.64 (prop2setE = $true) & (omegaSAx = $true) & (setunionE = $true) & (omegaIndAx = $true) & (emptyinPowerset = $true) & (notequalI1 = $true) & (setunionAx = $true) & (eqimpsubset2 = $true) & (nonemptyI1 = $true) & (emptyInPowerset = $true) & (sepInPowerset = $true) & (powersetI1 = $true) & (emptyinunitempty = $true) & (binintersectSubset5 = $true) & (binintersectI = $true) & (emptyI = $true) & (sepSubset = $true) & (quantDeMorgan4 = $true) & (emptyE1 = $true) & (setadjoin__Cong = $true) & (setunionI = $true) & (dsetconstrI = $true) & (inCongP = $true) & (vacuousDall = $true) & (upairset2IR = $true) & (emptyset__Cong = $true) & (powersetE1 = $true) & (powersetAx = $true) & (exu__Cong = $true) & (binunionEcases = $true) & ? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) != X1) & ($true = (subset @ X1 @ X0))) & (subsetRefl = $true) & (binunionE = $true) & (subsetTrans = $true) & (binunionIL = $true) & (setadjoinSub2 = $true) & (exuE1 = $true) & (notequalI2 = $true) & (emptysetAx = $true) & (powersetE = $true) & (omega__Cong = $true) & (quantDeMorgan3 = $true) & (dsetconstrER = $true) & (setextsub = $true) & (quantDeMorgan2 = $true) & (binintersectLsub = $true) & (noeltsimpempty = $true) & (foundationAx = $true) & (prop2setI = $true) & (subset2powerset = $true) & (exuEu = $true) & (exuI2 = $true) & (binintersectEL = $true) & (descr__Cong = $true) & (replAx = $true) & (setadjoinAx = $true) & (subsetI1 = $true) & (eqinunit = $true) & (prop2set2propI = $true) & (omega0Ax = $true) & (setadjoinIL = $true) & (setadjoinOr = $true) & (in__Cong = $true) & (binunionLsub = $true) & (setadjoinSub = $true) & (upairsetE = $true) & (upairsetIR = $true) & (nonemptyI = $true) & (singletonsswitch = $true) & (descrp = $true) & (setextAx = $true) & (dsetconstr__Cong = $true) & (binunionIR = $true) & (emptysetimpfalse = $true) & (setadjoinE = $true) & (powersetI = $true) & (emptysetsubset = $true) & (setbeta = $true) & (upairsetIL = $true) & (exuE3u = $true) & (nonemptyE1 = $true) & (inPowerset = $true) & (subPowSU = $true) & (subsetE2 = $true) & (notsubsetI = $true) & (setoftrueEq = $true) & (exuI3 = $true) & (binunionRsub = $true) & (eqimpsubset1 = $true) & (exuE3e = $true) & (notinemptyset = $true) & (subsetI2 = $true) & (exuE2 = $true) & (setadjoinIR = $true) & (setext = $true) & (notdexE = $true) & (setunion__Cong = $true) & (quantDeMorgan1 = $true) & (notinsingleton = $true) & (exuI1 = $true) & (notdallE = $true) & (dsetconstrEL = $true) & (uniqinunit = $true) & (wellorderingAx = $true) & (emptysetE = $true) & (subsetemptysetimpeq = $true) & (subsetE = $true) & (nonemptyImpWitness = $true) & (powersetsubset = $true) & (powerset__Cong = $true)),
% 15.74/3.64 inference(flattening,[status(thm)],[f448])).
% 15.74/3.64 thf(f448,plain,(
% 15.74/3.64 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (((binintersect @ X1 @ X0) != X1) & ($true = (subset @ X1 @ X0))) & (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)),
% 15.74/3.64 inference(ennf_transformation,[status(thm)],[f216])).
% 15.74/3.64 thf(f216,plain,(
% 15.74/3.64 ~((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) => ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) => ((binintersect @ X1 @ X0) = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.74/3.64 inference(fool_elimination,[status(thm)],[f215])).
% 15.74/3.64 thf(f215,plain,(
% 15.74/3.64 ~(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 => ! [X0 : $i,X1 : $i] : ((subset @ X1 @ X0) => ((binintersect @ X1 @ X0) = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.74/3.64 inference(rectify,[status(thm)],[f114])).
% 15.74/3.64 thf(f114,negated_conjecture,(
% 15.74/3.64 ~(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 => ! [X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((binintersect @ X3 @ X4) = X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.74/3.64 inference(negated_conjecture,[status(cth)],[f113])).
% 15.74/3.64 thf(f113,conjecture,(
% 15.74/3.64 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 => ! [X4 : $i,X3 : $i] : ((subset @ X3 @ X4) => ((binintersect @ X3 @ X4) = X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 15.74/3.64 file('/export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2THF_25342.p',binintersectSubset2)).
% 15.74/3.64 thf(f7865,plain,(
% 15.74/3.64 ((binintersect @ sK88 @ sK87) = sK88) | ((subset @ (binintersect @ sK88 @ sK87) @ sK88) != $true) | (~spl302_71 | ~spl302_183 | ~spl302_299)),
% 15.74/3.64 inference(trivial_inequality_removal,[status(thm)],[f7847])).
% 15.74/3.64 thf(f7847,plain,(
% 15.74/3.64 ((binintersect @ sK88 @ sK87) = sK88) | ($true != $true) | ((subset @ (binintersect @ sK88 @ sK87) @ sK88) != $true) | (~spl302_71 | ~spl302_183 | ~spl302_299)),
% 15.74/3.64 inference(superposition,[status(thm)],[f1978,f7841])).
% 15.74/3.64 thf(f7841,plain,(
% 15.74/3.64 ((subset @ sK88 @ (binintersect @ sK88 @ sK87)) = $true) | (~spl302_183 | ~spl302_299)),
% 15.74/3.64 inference(trivial_inequality_removal,[status(thm)],[f7821])).
% 15.74/3.64 thf(f7821,plain,(
% 15.74/3.64 ($true != $true) | ((subset @ sK88 @ (binintersect @ sK88 @ sK87)) = $true) | (~spl302_183 | ~spl302_299)),
% 15.74/3.64 inference(superposition,[status(thm)],[f6801,f2469])).
% 15.74/3.64 thf(f2469,plain,(
% 15.74/3.64 ( ! [X1 : $i] : (((subset @ X1 @ X1) = $true)) ) | ~spl302_183),
% 15.74/3.64 inference(avatar_component_clause,[status(thm)],[f2468])).
% 15.74/3.64 thf(f2468,definition,(
% 15.74/3.64 spl302_183 <=> ! [X1 : $i] : ((subset @ X1 @ X1) = $true)),
% 15.74/3.64 introduced(definition,[new_symbols(naming,[spl302_183])],[avatar_definition])).
% 15.74/3.64 thf(f6801,plain,(
% 15.74/3.64 ( ! [X0 : $i] : (($true != (subset @ sK88 @ X0)) | ((subset @ sK88 @ (binintersect @ X0 @ sK87)) = $true)) ) | ~spl302_299),
% 15.74/3.64 inference(trivial_inequality_removal,[status(thm)],[f6786])).
% 15.74/3.64 thf(f6786,plain,(
% 15.74/3.64 ( ! [X0 : $i] : (($true != (subset @ sK88 @ X0)) | ($true != $true) | ((subset @ sK88 @ (binintersect @ X0 @ sK87)) = $true)) ) | ~spl302_299),
% 15.74/3.64 inference(superposition,[status(thm)],[f3010,f1187])).
% 15.74/3.64 thf(f1187,plain,(
% 15.74/3.64 ((subset @ sK88 @ sK87) = $true)),
% 15.74/3.64 inference(cnf_transformation,[status(thm)],[f627])).
% 15.74/3.64 thf(f3010,plain,(
% 15.74/3.64 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X4) != $true) | ((subset @ X5 @ (binintersect @ X3 @ X4)) = $true) | ((subset @ X5 @ X3) != $true)) ) | ~spl302_299),
% 15.74/3.64 inference(avatar_component_clause,[status(thm)],[f3009])).
% 15.74/3.64 thf(f3009,definition,(
% 15.74/3.64 spl302_299 <=> ! [X4 : $i,X5 : $i,X3 : $i] : (((subset @ X5 @ X3) != $true) | ((subset @ X5 @ X4) != $true) | ((subset @ X5 @ (binintersect @ X3 @ X4)) = $true))),
% 15.74/3.64 introduced(definition,[new_symbols(naming,[spl302_299])],[avatar_definition])).
% 15.74/3.64 thf(f1978,plain,(
% 15.74/3.64 ( ! [X2 : $i,X3 : $i] : (($true != (subset @ X3 @ X2)) | (X2 = X3) | ((subset @ X2 @ X3) != $true)) ) | ~spl302_71),
% 15.74/3.64 inference(avatar_component_clause,[status(thm)],[f1977])).
% 15.74/3.64 thf(f1977,definition,(
% 15.74/3.64 spl302_71 <=> ! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | ($true != (subset @ X3 @ X2)) | (X2 = X3))),
% 15.74/3.64 introduced(definition,[new_symbols(naming,[spl302_71])],[avatar_definition])).
% 15.74/3.64 thf(f4019,plain,(
% 15.74/3.64 spl302_72),
% 15.74/3.64 inference(avatar_split_clause,[status(thm)],[f1174,f1980])).
% 15.74/3.64 thf(f1980,definition,(
% 15.74/3.64 spl302_72 <=> (setextsub = $true)),
% 15.74/3.64 introduced(definition,[new_symbols(naming,[spl302_72])],[avatar_definition])).
% 15.74/3.64 thf(f1174,plain,(
% 15.74/3.64 (setextsub = $true)),
% 15.74/3.64 inference(cnf_transformation,[status(thm)],[f627])).
% 15.74/3.64 thf(f4018,plain,(
% 15.74/3.64 spl302_386),
% 15.74/3.64 inference(avatar_split_clause,[status(thm)],[f1172,f3439])).
% 15.74/3.64 thf(f3439,definition,(
% 15.74/3.64 spl302_386 <=> (binintersectLsub = $true)),
% 15.74/3.64 introduced(definition,[new_symbols(naming,[spl302_386])],[avatar_definition])).
% 15.74/3.64 thf(f1172,plain,(
% 15.74/3.64 (binintersectLsub = $true)),
% 15.74/3.64 inference(cnf_transformation,[status(thm)],[f627])).
% 15.74/3.64 thf(f3845,plain,(
% 15.74/3.64 spl302_193),
% 15.74/3.64 inference(avatar_split_clause,[status(thm)],[f1213,f2511])).
% 15.74/3.64 thf(f2511,definition,(
% 15.74/3.64 spl302_193 <=> (notequalI1 = $true)),
% 15.74/3.64 introduced(definition,[new_symbols(naming,[spl302_193])],[avatar_definition])).
% 15.74/3.64 thf(f1213,plain,(
% 15.74/3.64 (notequalI1 = $true)),
% 15.74/3.64 inference(cnf_transformation,[status(thm)],[f627])).
% 15.74/3.64 thf(f3694,plain,(
% 15.74/3.64 ~spl302_386 | spl302_438),
% 15.74/3.64 inference(avatar_split_clause,[status(thm)],[f1439,f3692,f3439])).
% 15.74/3.64 thf(f1439,plain,(
% 15.74/3.64 ( ! [X0 : $i,X1 : $i] : ((binintersectLsub != $true) | ((subset @ (binintersect @ X0 @ X1) @ X0) = $true)) )),
% 15.74/3.64 inference(cnf_transformation,[status(thm)],[f883])).
% 15.74/3.64 thf(f883,plain,(
% 15.74/3.64 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ((subset @ (binintersect @ sK233 @ sK234) @ sK233) != $true))),
% 15.74/3.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK233,sK234])],[f881,f882])).
% 15.74/3.64 thf(f882,plain,(
% 15.74/3.64 ? [X2 : $i,X3 : $i] : ($true != (subset @ (binintersect @ X2 @ X3) @ X2)) => ((subset @ (binintersect @ sK233 @ sK234) @ sK233) != $true)),
% 15.74/3.64 introduced(definition,[],[choice_axiom])).
% 15.74/3.64 thf(f881,plain,(
% 15.74/3.64 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ? [X2 : $i,X3 : $i] : ($true != (subset @ (binintersect @ X2 @ X3) @ X2)))),
% 15.74/3.64 inference(rectify,[status(thm)],[f880])).
% 15.74/3.64 thf(f880,plain,(
% 15.74/3.64 (! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) = $true) | (binintersectLsub != $true)) & ((binintersectLsub = $true) | ? [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) != $true))),
% 15.74/3.64 inference(nnf_transformation,[status(thm)],[f265])).
% 15.74/3.64 thf(f265,plain,(
% 15.74/3.64 ! [X0 : $i,X1 : $i] : ((subset @ (binintersect @ X0 @ X1) @ X0) = $true) <=> (binintersectLsub = $true)),
% 15.74/3.64 inference(fool_elimination,[status(thm)],[f264])).
% 15.74/3.64 thf(f264,plain,(
% 15.74/3.64 (! [X0 : $i,X1 : $i] : (subset @ (binintersect @ X0 @ X1) @ X0) = binintersectLsub)),
% 15.74/3.64 inference(rectify,[status(thm)],[f112])).
% 15.74/3.64 thf(f112,axiom,(
% 15.74/3.64 (! [X3 : $i,X4 : $i] : (subset @ (binintersect @ X3 @ X4) @ X3) = binintersectLsub)),
% 15.74/3.64 file('/export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2THF_25342.p',binintersectLsub)).
% 15.74/3.64 thf(f3606,plain,(
% 15.74/3.64 spl302_226),
% 15.74/3.64 inference(avatar_split_clause,[status(thm)],[f1205,f2661])).
% 15.74/3.64 thf(f2661,definition,(
% 15.74/3.64 spl302_226 <=> (binintersectSubset5 = $true)),
% 15.74/3.64 introduced(definition,[new_symbols(naming,[spl302_226])],[avatar_definition])).
% 15.74/3.64 thf(f1205,plain,(
% 15.74/3.64 (binintersectSubset5 = $true)),
% 15.74/3.64 inference(cnf_transformation,[status(thm)],[f627])).
% 15.74/3.64 thf(f3461,plain,(
% 15.74/3.64 ~spl302_193 | spl302_183),
% 15.74/3.64 inference(avatar_split_clause,[status(thm)],[f1551,f2468,f2511])).
% 15.74/3.64 thf(f1551,plain,(
% 15.74/3.64 ( ! [X1 : $i] : ((notequalI1 != $true) | ((subset @ X1 @ X1) = $true)) )),
% 15.74/3.64 inference(equality_resolution,[status(thm)],[f1045])).
% 15.74/3.64 thf(f1045,plain,(
% 15.74/3.64 ( ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (X0 != X1) | (notequalI1 != $true)) )),
% 15.74/3.64 inference(cnf_transformation,[status(thm)],[f547])).
% 15.74/3.64 thf(f547,plain,(
% 15.74/3.64 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (X0 != X1)) | (notequalI1 != $true)) & ((notequalI1 = $true) | (((subset @ sK39 @ sK40) != $true) & (sK40 = sK39)))),
% 15.74/3.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40])],[f545,f546])).
% 15.74/3.64 thf(f546,plain,(
% 15.74/3.64 ? [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) & (X2 = X3)) => (((subset @ sK39 @ sK40) != $true) & (sK40 = sK39))),
% 15.74/3.64 introduced(definition,[],[choice_axiom])).
% 15.74/3.64 thf(f545,plain,(
% 15.74/3.64 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (X0 != X1)) | (notequalI1 != $true)) & ((notequalI1 = $true) | ? [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) & (X2 = X3)))),
% 15.74/3.64 inference(rectify,[status(thm)],[f544])).
% 15.74/3.64 thf(f544,plain,(
% 15.74/3.64 (! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (X0 != X1)) | (notequalI1 != $true)) & ((notequalI1 = $true) | ? [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) & (X0 = X1)))),
% 15.74/3.64 inference(nnf_transformation,[status(thm)],[f445])).
% 15.74/3.64 thf(f445,plain,(
% 15.74/3.64 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) | (X0 != X1)) <=> (notequalI1 = $true)),
% 15.74/3.64 inference(ennf_transformation,[status(thm)],[f342])).
% 15.74/3.64 thf(f342,plain,(
% 15.74/3.64 (notequalI1 = $true) <=> ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) != $true) => (X0 != X1))),
% 15.74/3.64 inference(flattening,[status(thm)],[f173])).
% 15.74/3.64 thf(f173,plain,(
% 15.74/3.64 ! [X0 : $i,X1 : $i] : (~((subset @ X0 @ X1) = $true) => (X0 != X1)) <=> (notequalI1 = $true)),
% 15.74/3.64 inference(fool_elimination,[status(thm)],[f172])).
% 15.74/3.64 thf(f172,plain,(
% 15.74/3.64 (! [X0 : $i,X1 : $i] : (~(subset @ X0 @ X1) => (X0 != X1)) = notequalI1)),
% 15.74/3.64 inference(rectify,[status(thm)],[f86])).
% 15.74/3.64 thf(f86,axiom,(
% 15.74/3.64 (! [X3 : $i,X4 : $i] : (~(subset @ X3 @ X4) => (X3 != X4)) = notequalI1)),
% 15.74/3.64 file('/export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2THF_25342.p',notequalI1)).
% 15.74/3.64 thf(f3011,plain,(
% 15.74/3.64 ~spl302_226 | spl302_299),
% 15.74/3.64 inference(avatar_split_clause,[status(thm)],[f1424,f3009,f2661])).
% 15.74/3.64 thf(f1424,plain,(
% 15.74/3.64 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X3) != $true) | ((subset @ X5 @ (binintersect @ X3 @ X4)) = $true) | (binintersectSubset5 != $true) | ((subset @ X5 @ X4) != $true)) )),
% 15.74/3.64 inference(cnf_transformation,[status(thm)],[f867])).
% 15.74/3.64 thf(f867,plain,(
% 15.74/3.64 ((binintersectSubset5 = $true) | (((subset @ sK225 @ sK224) = $true) & ((subset @ sK225 @ (binintersect @ sK223 @ sK224)) != $true) & ((subset @ sK225 @ sK223) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X4) != $true) | ((subset @ X5 @ (binintersect @ X3 @ X4)) = $true) | ((subset @ X5 @ X3) != $true)) | (binintersectSubset5 != $true))),
% 15.74/3.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK223,sK224,sK225])],[f865,f866])).
% 15.74/3.64 thf(f866,plain,(
% 15.74/3.64 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X2 @ X1)) & ((subset @ X2 @ (binintersect @ X0 @ X1)) != $true) & ((subset @ X2 @ X0) = $true)) => (((subset @ sK225 @ sK224) = $true) & ((subset @ sK225 @ (binintersect @ sK223 @ sK224)) != $true) & ((subset @ sK225 @ sK223) = $true))),
% 15.74/3.64 introduced(definition,[],[choice_axiom])).
% 15.74/3.64 thf(f865,plain,(
% 15.74/3.64 ((binintersectSubset5 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X2 @ X1)) & ((subset @ X2 @ (binintersect @ X0 @ X1)) != $true) & ((subset @ X2 @ X0) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i] : (((subset @ X5 @ X4) != $true) | ((subset @ X5 @ (binintersect @ X3 @ X4)) = $true) | ((subset @ X5 @ X3) != $true)) | (binintersectSubset5 != $true))),
% 15.74/3.64 inference(rectify,[status(thm)],[f864])).
% 15.74/3.64 thf(f864,plain,(
% 15.74/3.64 ((binintersectSubset5 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X2 @ X1)) & ((subset @ X2 @ (binintersect @ X0 @ X1)) != $true) & ((subset @ X2 @ X0) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X2 @ X1)) | ((subset @ X2 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X2 @ X0) != $true)) | (binintersectSubset5 != $true))),
% 15.74/3.64 inference(nnf_transformation,[status(thm)],[f434])).
% 15.74/3.64 thf(f434,plain,(
% 15.74/3.64 (binintersectSubset5 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (subset @ X2 @ X1)) | ((subset @ X2 @ (binintersect @ X0 @ X1)) = $true) | ((subset @ X2 @ X0) != $true))),
% 15.74/3.64 inference(flattening,[status(thm)],[f433])).
% 15.74/3.64 thf(f433,plain,(
% 15.74/3.64 (binintersectSubset5 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((subset @ X2 @ (binintersect @ X0 @ X1)) = $true) | ($true != (subset @ X2 @ X1))) | ((subset @ X2 @ X0) != $true))),
% 15.74/3.64 inference(ennf_transformation,[status(thm)],[f255])).
% 15.74/3.64 thf(f255,plain,(
% 15.74/3.64 (binintersectSubset5 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (((subset @ X2 @ X0) = $true) => (($true = (subset @ X2 @ X1)) => ((subset @ X2 @ (binintersect @ X0 @ X1)) = $true)))),
% 15.74/3.64 inference(fool_elimination,[status(thm)],[f254])).
% 15.74/3.64 thf(f254,plain,(
% 15.74/3.64 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X2 @ X0) => ((subset @ X2 @ X1) => (subset @ X2 @ (binintersect @ X0 @ X1)))) = binintersectSubset5)),
% 15.74/3.64 inference(rectify,[status(thm)],[f110])).
% 15.74/3.64 thf(f110,axiom,(
% 15.74/3.64 (! [X3 : $i,X4 : $i,X5 : $i] : ((subset @ X5 @ X3) => ((subset @ X5 @ X4) => (subset @ X5 @ (binintersect @ X3 @ X4)))) = binintersectSubset5)),
% 15.74/3.64 file('/export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2THF_25342.p',binintersectSubset5)).
% 15.74/3.64 thf(f1983,plain,(
% 15.74/3.64 spl302_71 | ~spl302_72),
% 15.74/3.64 inference(avatar_split_clause,[status(thm)],[f1087,f1980,f1977])).
% 15.74/3.64 thf(f1087,plain,(
% 15.74/3.64 ( ! [X2 : $i,X3 : $i] : (((subset @ X2 @ X3) != $true) | (X2 = X3) | (setextsub != $true) | ($true != (subset @ X3 @ X2))) )),
% 15.74/3.64 inference(cnf_transformation,[status(thm)],[f607])).
% 15.74/3.64 thf(f607,plain,(
% 15.74/3.64 ((setextsub = $true) | ((sK74 != sK75) & ((subset @ sK74 @ sK75) = $true) & ($true = (subset @ sK75 @ sK74)))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ((subset @ X2 @ X3) != $true) | ($true != (subset @ X3 @ X2))) | (setextsub != $true))),
% 15.74/3.64 inference(skolemisation,[status(esa),new_symbols(skolem,[sK74,sK75])],[f605,f606])).
% 15.74/3.64 thf(f606,plain,(
% 15.74/3.64 ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((subset @ X0 @ X1) = $true) & ($true = (subset @ X1 @ X0))) => ((sK74 != sK75) & ((subset @ sK74 @ sK75) = $true) & ($true = (subset @ sK75 @ sK74)))),
% 15.74/3.64 introduced(definition,[],[choice_axiom])).
% 15.74/3.64 thf(f605,plain,(
% 15.74/3.64 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((subset @ X0 @ X1) = $true) & ($true = (subset @ X1 @ X0)))) & (! [X2 : $i,X3 : $i] : ((X2 = X3) | ((subset @ X2 @ X3) != $true) | ($true != (subset @ X3 @ X2))) | (setextsub != $true))),
% 15.74/3.64 inference(rectify,[status(thm)],[f604])).
% 15.74/3.64 thf(f604,plain,(
% 15.74/3.64 ((setextsub = $true) | ? [X0 : $i,X1 : $i] : ((X0 != X1) & ((subset @ X0 @ X1) = $true) & ($true = (subset @ X1 @ X0)))) & (! [X0 : $i,X1 : $i] : ((X0 = X1) | ((subset @ X0 @ X1) != $true) | ($true != (subset @ X1 @ X0))) | (setextsub != $true))),
% 15.74/3.64 inference(nnf_transformation,[status(thm)],[f472])).
% 15.74/3.64 thf(f472,plain,(
% 15.74/3.64 (setextsub = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 = X1) | ((subset @ X0 @ X1) != $true) | ($true != (subset @ X1 @ X0)))),
% 15.74/3.64 inference(flattening,[status(thm)],[f471])).
% 15.74/3.64 thf(f471,plain,(
% 15.74/3.64 ! [X0 : $i,X1 : $i] : (((X0 = X1) | ($true != (subset @ X1 @ X0))) | ((subset @ X0 @ X1) != $true)) <=> (setextsub = $true)),
% 15.74/3.64 inference(ennf_transformation,[status(thm)],[f227])).
% 15.74/3.64 thf(f227,plain,(
% 15.74/3.64 ! [X0 : $i,X1 : $i] : (((subset @ X0 @ X1) = $true) => (($true = (subset @ X1 @ X0)) => (X0 = X1))) <=> (setextsub = $true)),
% 15.74/3.64 inference(fool_elimination,[status(thm)],[f226])).
% 15.74/3.64 thf(f226,plain,(
% 15.74/3.64 (! [X0 : $i,X1 : $i] : ((subset @ X0 @ X1) => ((subset @ X1 @ X0) => (X0 = X1))) = setextsub)),
% 15.74/3.64 inference(rectify,[status(thm)],[f93])).
% 15.74/3.64 thf(f93,axiom,(
% 15.74/3.64 (! [X3 : $i,X4 : $i] : ((subset @ X3 @ X4) => ((subset @ X4 @ X3) => (X3 = X4))) = setextsub)),
% 15.74/3.64 file('/export/starexec/sandbox2/tmp/tmp.LuBVJlPjqs/DTF2THF_25342.p',setextsub)).
% 15.74/3.64 % SZS output end Proof for DTF2THF_25342
% 15.74/3.64 % (25888)------------------------------
% 15.74/3.64 % (25888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.74/3.64 % (25888)Termination reason: Refutation
% 15.74/3.64
% 15.74/3.64 % (25888)Memory used [KB]: 11129
% 15.74/3.64 % (25888)Time elapsed: 0.329 s
% 15.74/3.64 % (25888)Instructions burned: 1000 (million)
% 15.74/3.64 % (25888)------------------------------
% 15.74/3.64 % (25888)------------------------------
% 15.74/3.64 % (25525)Success in time 2.101 s
%------------------------------------------------------------------------------