%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU651^1 : 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 : n001.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 09:35:57 AM UTC 2026
% Result : Theorem 2.47s 1.85s
% Output : Refutation 2.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 11
% Syntax : Number of formulae : 73 ( 24 unt; 0 typ; 1 def)
% Number of atoms : 3192 ( 849 equ; 0 cnn)
% Maximal formula atoms : 170 ( 43 avg)
% Number of connectives : 2097 ( 80 ~; 52 |; 533 &; 736 @)
% ( 8 <=>; 688 =>; 0 <=; 0 <~>)
% Maximal formula depth : 175 ( 20 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 322 ( 319 usr; 182 con; 0-4 aty)
% Number of variables : 105 ( 0 ^; 72 !; 33 ?; 105 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_210,type,
sP0: $i > $o > $i > $i > $o ).
thf(func_def_213,type,
sP3: $i > $i > $o ).
thf(func_def_214,type,
sP4: $i > $o ).
thf(func_def_215,type,
sP5: $i > $i > $o ).
thf(func_def_216,type,
sP6: $i > $i > $o ).
thf(func_def_222,type,
sK12: $i > $i > $i ).
thf(func_def_223,type,
sK13: $i > $i ).
thf(func_def_234,type,
sK24: $i > $o ).
thf(func_def_248,type,
sK38: $i > $i > $i ).
thf(func_def_252,type,
sK42: $i > $o ).
thf(func_def_255,type,
sK45: $i > ( $i > $o ) > $i ).
thf(func_def_256,type,
sK46: $i > $i > $i > $i ).
thf(func_def_257,type,
sK47: $i > $i > $i > $i ).
thf(func_def_271,type,
sK61: $i > $o ).
thf(func_def_294,type,
sK84: $i > $o ).
thf(func_def_296,type,
sK86: ( $i > $o ) > $i ).
thf(func_def_297,type,
sK87: ( $i > $o ) > $i ).
thf(func_def_303,type,
sK93: $i > $o ).
thf(func_def_306,type,
sK96: $i > $i > $i ).
thf(func_def_307,type,
sK97: $i > $i > $i ).
thf(func_def_323,type,
sK113: $i > $o ).
thf(func_def_336,type,
sK126: $i > $o ).
thf(func_def_341,type,
sK131: $i > $i > $o ).
thf(func_def_342,type,
sK132: $i > $i ).
thf(func_def_343,type,
sK133: $i > $i ).
thf(func_def_344,type,
sK134: ( $i > $i > $o ) > $i > $i ).
thf(func_def_345,type,
sK135: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_346,type,
sK136: ( $i > $i > $o ) > $i > $i ).
thf(func_def_355,type,
sK145: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_356,type,
sK146: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_357,type,
sK147: $i > $o ).
thf(func_def_358,type,
sK148: $i > $o ).
thf(func_def_359,type,
sK149: $i > ( $i > $o ) > $i ).
thf(func_def_360,type,
sK150: $i > $o ).
thf(func_def_366,type,
sK156: $i > $o ).
thf(func_def_375,type,
sK165: $i > $o ).
thf(func_def_377,type,
sK167: ( $i > $o ) > $i > $i ).
thf(func_def_378,type,
sK168: ( $i > $o ) > $i > $i ).
thf(func_def_386,type,
sK176: $i > $i > $i ).
thf(func_def_387,type,
sK177: $i > $i > $i ).
thf(func_def_388,type,
sK178: $i > $i > $i ).
thf(func_def_389,type,
sK179: $i > $i > $i ).
thf(func_def_390,type,
sK180: $i > $i > $i > $i ).
thf(func_def_391,type,
sK181: $i > $i ).
thf(func_def_392,type,
sK182: $i > $i ).
thf(func_def_393,type,
sK183: $i > $i ).
thf(func_def_394,type,
sK184: $i > $i ).
thf(func_def_395,type,
sK185: $i > $i > $i > $i ).
thf(func_def_396,type,
sK186: $i > $i > $i > $i ).
thf(func_def_397,type,
sK187: $i > $i > $i ).
thf(func_def_398,type,
sK188: $i > $i > $i ).
thf(func_def_399,type,
sK189: $i > $i > $i ).
thf(func_def_401,type,
sK191: $i > $i ).
thf(func_def_402,type,
sK192: $i > $i ).
thf(func_def_403,type,
sK193: $i > $i ).
thf(func_def_404,type,
sK194: $i > $i > $i ).
thf(func_def_406,type,
sK196: $i > $i ).
thf(func_def_411,type,
sK201: $i > $o ).
thf(func_def_412,type,
sK202: $i > $o ).
thf(func_def_413,type,
sK203: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_414,type,
sK204: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_421,type,
sK211: $i > $o ).
thf(func_def_424,type,
sK214: ( $i > $o ) > $i > $i ).
thf(func_def_426,type,
sK216: $i > $o ).
thf(func_def_429,type,
sK219: $i > $o ).
thf(func_def_433,type,
sK223: $i > $i ).
thf(func_def_440,type,
sK230: $i > $i > $i ).
thf(func_def_450,type,
sK240: $i > ( $i > $o ) > $i ).
thf(func_def_451,type,
sK241: $i > $o ).
thf(func_def_472,type,
sK262: ( $i > $o ) > $i ).
thf(func_def_473,type,
sK263: $i > $o ).
thf(func_def_474,type,
sK264: $i > $i ).
thf(func_def_485,type,
sK275: $i > ( $i > $o ) > $i > $i ).
thf(func_def_487,type,
sK277: $i > $o ).
thf(func_def_491,type,
sK281: $i > $o ).
thf(func_def_493,type,
sK283: $i > ( $i > $o ) > $i ).
thf(func_def_498,type,
sK288: $i > $o ).
thf(func_def_507,type,
sK297: $i > $i ).
thf(func_def_508,type,
sK298: $i > $i ).
thf(func_def_511,type,
sK301: $i > $i ).
thf(func_def_524,type,
sK314: $i > $i > $i ).
thf(func_def_525,type,
sK315: $i > $i > $i ).
thf(func_def_544,type,
sK334: $o > $i > $i > $i ).
thf(func_def_558,type,
sK348: $i > $i > $i ).
thf(func_def_572,type,
sK362: ( $i > $o ) > $i > $i ).
thf(func_def_574,type,
sK364: $i > $o ).
thf(func_def_576,type,
sK366: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_577,type,
sK367: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_578,type,
sK368: $i > $o ).
thf(func_def_579,type,
sK369: $i > $o ).
thf(func_def_580,type,
sK370: ( $i > $o ) > $i ).
thf(func_def_581,type,
sK371: $i > $o ).
thf(func_def_582,type,
sK372: $i > $i ).
thf(func_def_585,type,
sK375: $i > ( $i > $o ) > $i ).
thf(func_def_586,type,
sK376: $i > $o ).
thf(func_def_592,type,
sK382: ( $i > $o ) > $i > $i ).
thf(func_def_594,type,
sK384: $i > $o ).
thf(func_def_615,type,
sK405: $i > $o ).
thf(func_def_617,type,
sK407: ( $i > $o ) > $i > $i ).
thf(func_def_618,type,
sK408: ( $i > $o ) > $i > $i ).
thf(func_def_626,type,
sK416: $i > $o ).
thf(func_def_638,type,
sK428: $i > $i ).
thf(func_def_639,type,
sK429: $i > $o ).
thf(func_def_642,type,
sK432: ( $i > $o ) > $i ).
thf(func_def_643,type,
sK433: $i > $o ).
thf(func_def_654,type,
sK444: $i > $o ).
thf(func_def_659,type,
sK449: $i > $i > $i ).
thf(func_def_672,type,
sK462: $i > $o ).
thf(func_def_674,type,
sK464: $i > ( $i > $o ) > $i ).
thf(func_def_675,type,
sK465: $i > $i > $i ).
thf(func_def_679,type,
ph469:
!>[X0: $tType] : X0 ).
thf(f5670,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f5555,f5656]) ).
thf(f5656,plain,
~ spl468_81,
inference(avatar_contradiction_clause,[status(thm)],[f5655]) ).
thf(f5655,plain,
( $false
| ~ spl468_81 ),
inference(trivial_inequality_removal,[status(thm)],[f5610]) ).
thf(f5610,plain,
( ( sK350 != sK350 )
| ~ spl468_81 ),
inference(superposition,[status(thm)],[f2449,f5539]) ).
thf(f5539,plain,
( ( sK351 = sK350 )
| ~ spl468_81 ),
inference(avatar_component_clause,[status(thm)],[f5537]) ).
thf(f5537,definition,
( spl468_81
<=> ( sK351 = sK350 ) ),
introduced(definition,[new_symbols(naming,[spl468_81])],[avatar_definition]) ).
thf(f2449,plain,
sK351 != sK350,
inference(superposition,[status(thm)],[f2150,f2149]) ).
thf(f2149,plain,
sK352 = sK351,
inference(cnf_transformation,[status(thm)],[f1328]) ).
thf(f1328,plain,
( ( omegaSAx = $true )
& ( binunionEcases = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( subset2powerset = $true )
& ( ex1I2 = $true )
& ( in__Cong = $true )
& ( setukpairinjL = $true )
& ( upairset2E = $true )
& ( cartprodmempair = $true )
& ( binunionE = $true )
& ( binintersectI = $true )
& ( setminusSubset1 = $true )
& ( prop2setI = $true )
& ( singletonsubset = $true )
& ( descrp = $true )
& ( setukpairIL = $true )
& ( notinemptyset = $true )
& ( symdiffIneg1 = $true )
& ( setadjoinAx = $true )
& ( powersetAx = $true )
& ( setbeta = $true )
& ( secondinupair = $true )
& ( binintersectSubset3 = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrER = $true )
& ( emptysetE = $true )
& ( sK352 != sK350 )
& ( sK352 = sK351 )
& ( ( setadjoin @ ( setadjoin @ sK353 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK353 @ ( setadjoin @ sK350 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK351 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK351 @ ( setadjoin @ sK352 @ emptyset ) ) @ emptyset ) ) )
& ( notdexE = $true )
& ( setukpairinjR11 = $true )
& ( dsetconstr__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( theprop = $true )
& ( setadjoinOr = $true )
& ( binunionIL = $true )
& ( exuE2 = $true )
& ( subsetemptysetimpeq = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan4 = $true )
& ( subsetI2 = $true )
& ( notdallE = $true )
& ( disjointsetsI1 = $true )
& ( binunionLsub = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinIR = $true )
& ( sepInPowerset = $true )
& ( setukpairinjL1 = $true )
& ( subsetRefl = $true )
& ( eqimpsubset2 = $true )
& ( notequalI2 = $true )
& ( subPowSU = $true )
& ( notinsingleton = $true )
& ( setunionI = $true )
& ( binintersectSubset5 = $true )
& ( emptysetimpfalse = $true )
& ( notequalI1 = $true )
& ( exuI1 = $true )
& ( setminusIRneg = $true )
& ( upairsetE = $true )
& ( binintersectSubset2 = $true )
& ( binintersectER = $true )
& ( upairinpowunion = $true )
& ( exuE3u = $true )
& ( eqinunit = $true )
& ( inCongP = $true )
& ( setextAx = $true )
& ( singletonprop = $true )
& ( notsubsetI = $true )
& ( dsetconstrI = $true )
& ( cartprodmempair1 = $true )
& ( inPowerset = $true )
& ( binintersectEL = $true )
& ( binintersectLsub = $true )
& ( powersetsubset = $true )
& ( noeltsimpempty = $true )
& ( symdiffI2 = $true )
& ( kfstpairEq = $true )
& ( emptysetsubset = $true )
& ( exuI3 = $true )
& ( setminusERneg = $true )
& ( setadjoinSub2 = $true )
& ( emptyinunitempty = $true )
& ( exuI2 = $true )
& ( foundationAx = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( singletoninpowerset = $true )
& ( powersetE = $true )
& ( setminusER = $true )
& ( powersetI1 = $true )
& ( nonemptyI = $true )
& ( setminusLsub = $true )
& ( singletonsswitch = $true )
& ( nonemptyImpWitness = $true )
& ( descr__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( prop2set2propI = $true )
& ( kpairiskpair = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset1 = $true )
& ( binintersectRsub = $true )
& ( replAx = $true )
& ( eqimpsubset1 = $true )
& ( setadjoin__Cong = $true )
& ( uniqinunit = $true )
& ( setunionsingleton = $true )
& ( vacuousDall = $true )
& ( setadjoinIL = $true )
& ( symdiffIneg2 = $true )
& ( emptyE1 = $true )
& ( setukpairIR = $true )
& ( singletonsuniq = $true )
& ( emptysetAx = $true )
& ( setadjoinE = $true )
& ( setunionE2 = $true )
& ( ubforcartprodlem2 = $true )
& ( setadjoinSub = $true )
& ( upairsetIL = $true )
& ( kfstsingleton = $true )
& ( exuE3e = $true )
& ( symdiffI1 = $true )
& ( singletoninpowunion = $true )
& ( ubforcartprodlem1 = $true )
& ( ex1E1 = $true )
& ( cartprodfstin = $true )
& ( quantDeMorgan2 = $true )
& ( sepSubset = $true )
& ( cartprodpairin = $true )
& ( symdiffE = $true )
& ( setextsub = $true )
& ( ex1I = $true )
& ( binunionRsub = $true )
& ( emptyset__Cong = $true )
& ( upairset2IR = $true )
& ( subsetI1 = $true )
& ( setminusEL = $true )
& ( powersetE1 = $true )
& ( emptyI = $true )
& ( setminusI = $true )
& ( omega0Ax = $true )
& ( subsetTrans = $true )
& ( setminusILneg = $true )
& ( setunion__Cong = $true )
& ( upairsetIR = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrEL = $true )
& ( setunionE = $true )
& ( subsetE2 = $true )
& ( setminusELneg = $true )
& ( kpairp = $true )
& ( wellorderingAx = $true )
& ( setunionAx = $true )
& ( exu__Cong = $true )
& ( setext = $true )
& ( powerset__Cong = $true )
& ( ubforcartprodlem3 = $true )
& ( emptyInPowerset = $true )
& ( bs114d = $true )
& ( binintersectSubset4 = $true )
& ( omegaIndAx = $true )
& ( omega__Cong = $true )
& ( exuE1 = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjL2 = $true )
& ( binunionIR = $true )
& ( subsetE = $true )
& ( upairsubunion = $true )
& ( exuEu = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK350,sK351,sK352,sK353])],[f607,f1327]) ).
thf(f1327,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X2 )
& ( X1 = X2 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( sK352 != sK350 )
& ( sK352 = sK351 )
& ( ( setadjoin @ ( setadjoin @ sK353 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK353 @ ( setadjoin @ sK350 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK351 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK351 @ ( setadjoin @ sK352 @ emptyset ) ) @ emptyset ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f607,plain,
( ( omegaSAx = $true )
& ( binunionEcases = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( subset2powerset = $true )
& ( ex1I2 = $true )
& ( in__Cong = $true )
& ( setukpairinjL = $true )
& ( upairset2E = $true )
& ( cartprodmempair = $true )
& ( binunionE = $true )
& ( binintersectI = $true )
& ( setminusSubset1 = $true )
& ( prop2setI = $true )
& ( singletonsubset = $true )
& ( descrp = $true )
& ( setukpairIL = $true )
& ( notinemptyset = $true )
& ( symdiffIneg1 = $true )
& ( setadjoinAx = $true )
& ( powersetAx = $true )
& ( setbeta = $true )
& ( secondinupair = $true )
& ( binintersectSubset3 = $true )
& ( emptyinPowerset = $true )
& ( dsetconstrER = $true )
& ( emptysetE = $true )
& ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X2 )
& ( X1 = X2 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
& ( notdexE = $true )
& ( setukpairinjR11 = $true )
& ( dsetconstr__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( theprop = $true )
& ( setadjoinOr = $true )
& ( binunionIL = $true )
& ( exuE2 = $true )
& ( subsetemptysetimpeq = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan4 = $true )
& ( subsetI2 = $true )
& ( notdallE = $true )
& ( disjointsetsI1 = $true )
& ( binunionLsub = $true )
& ( setukpairinjR12 = $true )
& ( setadjoinIR = $true )
& ( sepInPowerset = $true )
& ( setukpairinjL1 = $true )
& ( subsetRefl = $true )
& ( eqimpsubset2 = $true )
& ( notequalI2 = $true )
& ( subPowSU = $true )
& ( notinsingleton = $true )
& ( setunionI = $true )
& ( binintersectSubset5 = $true )
& ( emptysetimpfalse = $true )
& ( notequalI1 = $true )
& ( exuI1 = $true )
& ( setminusIRneg = $true )
& ( upairsetE = $true )
& ( binintersectSubset2 = $true )
& ( binintersectER = $true )
& ( upairinpowunion = $true )
& ( exuE3u = $true )
& ( eqinunit = $true )
& ( inCongP = $true )
& ( setextAx = $true )
& ( singletonprop = $true )
& ( notsubsetI = $true )
& ( dsetconstrI = $true )
& ( cartprodmempair1 = $true )
& ( inPowerset = $true )
& ( binintersectEL = $true )
& ( binintersectLsub = $true )
& ( powersetsubset = $true )
& ( noeltsimpempty = $true )
& ( symdiffI2 = $true )
& ( kfstpairEq = $true )
& ( emptysetsubset = $true )
& ( exuI3 = $true )
& ( setminusERneg = $true )
& ( setadjoinSub2 = $true )
& ( emptyinunitempty = $true )
& ( exuI2 = $true )
& ( foundationAx = $true )
& ( powersetI = $true )
& ( prop2setE = $true )
& ( singletoninpowerset = $true )
& ( powersetE = $true )
& ( setminusER = $true )
& ( powersetI1 = $true )
& ( nonemptyI = $true )
& ( setminusLsub = $true )
& ( singletonsswitch = $true )
& ( nonemptyImpWitness = $true )
& ( descr__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( prop2set2propI = $true )
& ( kpairiskpair = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset1 = $true )
& ( binintersectRsub = $true )
& ( replAx = $true )
& ( eqimpsubset1 = $true )
& ( setadjoin__Cong = $true )
& ( uniqinunit = $true )
& ( setunionsingleton = $true )
& ( vacuousDall = $true )
& ( setadjoinIL = $true )
& ( symdiffIneg2 = $true )
& ( emptyE1 = $true )
& ( setukpairIR = $true )
& ( singletonsuniq = $true )
& ( emptysetAx = $true )
& ( setadjoinE = $true )
& ( setunionE2 = $true )
& ( ubforcartprodlem2 = $true )
& ( setadjoinSub = $true )
& ( upairsetIL = $true )
& ( kfstsingleton = $true )
& ( exuE3e = $true )
& ( symdiffI1 = $true )
& ( singletoninpowunion = $true )
& ( ubforcartprodlem1 = $true )
& ( ex1E1 = $true )
& ( cartprodfstin = $true )
& ( quantDeMorgan2 = $true )
& ( sepSubset = $true )
& ( cartprodpairin = $true )
& ( symdiffE = $true )
& ( setextsub = $true )
& ( ex1I = $true )
& ( binunionRsub = $true )
& ( emptyset__Cong = $true )
& ( upairset2IR = $true )
& ( subsetI1 = $true )
& ( setminusEL = $true )
& ( powersetE1 = $true )
& ( emptyI = $true )
& ( setminusI = $true )
& ( omega0Ax = $true )
& ( subsetTrans = $true )
& ( setminusILneg = $true )
& ( setunion__Cong = $true )
& ( upairsetIR = $true )
& ( nonemptyI1 = $true )
& ( dsetconstrEL = $true )
& ( setunionE = $true )
& ( subsetE2 = $true )
& ( setminusELneg = $true )
& ( kpairp = $true )
& ( wellorderingAx = $true )
& ( setunionAx = $true )
& ( exu__Cong = $true )
& ( setext = $true )
& ( powerset__Cong = $true )
& ( ubforcartprodlem3 = $true )
& ( emptyInPowerset = $true )
& ( bs114d = $true )
& ( binintersectSubset4 = $true )
& ( omegaIndAx = $true )
& ( omega__Cong = $true )
& ( exuE1 = $true )
& ( nonemptyE1 = $true )
& ( setukpairinjL2 = $true )
& ( binunionIR = $true )
& ( subsetE = $true )
& ( upairsubunion = $true )
& ( exuEu = $true ) ),
inference(flattening,[status(thm)],[f606]) ).
thf(f606,plain,
( ? [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X0 != X2 )
& ( X1 = X2 )
& ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) ) )
& ( setukpairinjR12 = $true )
& ( setukpairinjR11 = $true )
& ( setukpairinjL = $true )
& ( setukpairinjL2 = $true )
& ( cartprodfstin = $true )
& ( kfstpairEq = $true )
& ( theprop = $true )
& ( kfstsingleton = $true )
& ( setukpairinjL1 = $true )
& ( singletonsuniq = $true )
& ( ex1I2 = $true )
& ( ex1I = $true )
& ( ex1E1 = $true )
& ( singletonprop = $true )
& ( setunionsingleton = $true )
& ( setunionsingleton2 = $true )
& ( setunionsingleton1 = $true )
& ( setunionE2 = $true )
& ( cartprodmempair = $true )
& ( cartprodmempair1 = $true )
& ( cartprodpairin = $true )
& ( ubforcartprodlem3 = $true )
& ( ubforcartprodlem2 = $true )
& ( ubforcartprodlem1 = $true )
& ( upairinpowunion = $true )
& ( upairsubunion = $true )
& ( upairset2E = $true )
& ( singletoninpowunion = $true )
& ( singletoninpowerset = $true )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $true )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f497]) ).
thf(f497,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ( ( singletoninpowerset = $true )
=> ( ( singletoninpowunion = $true )
=> ( ( upairset2E = $true )
=> ( ( upairsubunion = $true )
=> ( ( upairinpowunion = $true )
=> ( ( ubforcartprodlem1 = $true )
=> ( ( ubforcartprodlem2 = $true )
=> ( ( ubforcartprodlem3 = $true )
=> ( ( cartprodpairin = $true )
=> ( ( cartprodmempair1 = $true )
=> ( ( cartprodmempair = $true )
=> ( ( setunionE2 = $true )
=> ( ( setunionsingleton1 = $true )
=> ( ( setunionsingleton2 = $true )
=> ( ( setunionsingleton = $true )
=> ( ( singletonprop = $true )
=> ( ( ex1E1 = $true )
=> ( ( ex1I = $true )
=> ( ( ex1I2 = $true )
=> ( ( singletonsuniq = $true )
=> ( ( setukpairinjL1 = $true )
=> ( ( kfstsingleton = $true )
=> ( ( theprop = $true )
=> ( ( kfstpairEq = $true )
=> ( ( cartprodfstin = $true )
=> ( ( setukpairinjL2 = $true )
=> ( ( setukpairinjL = $true )
=> ( ( setukpairinjR11 = $true )
=> ( ( setukpairinjR12 = $true )
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1 = X2 )
=> ( X0 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f496]) ).
thf(f496,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X3 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X3 @ ( setadjoin @ X0 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X1 = X2 )
=> ( X0 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f175]) ).
thf(f175,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ! [X2: $i,X8: $i,X10: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X8 = X10 )
=> ( X2 = X10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f174]) ).
thf(f174,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ( setukpairinjL2
=> ( setukpairinjL
=> ( setukpairinjR11
=> ( setukpairinjR12
=> ! [X2: $i,X8: $i,X10: $i,X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X8 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X8 @ ( setadjoin @ X10 @ emptyset ) ) @ emptyset ) ) )
=> ( ( X8 = X10 )
=> ( X2 = X10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2THF_26106.p',setukpairinjR1) ).
thf(f2150,plain,
sK352 != sK350,
inference(cnf_transformation,[status(thm)],[f1328]) ).
thf(f5555,plain,
spl468_81,
inference(avatar_split_clause,[status(thm)],[f5554,f5537]) ).
thf(f5554,plain,
sK351 = sK350,
inference(trivial_inequality_removal,[status(thm)],[f5553]) ).
thf(f5553,plain,
( ( sK351 = sK350 )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f5529,f2124]) ).
thf(f2124,plain,
notinsingleton = $true,
inference(cnf_transformation,[status(thm)],[f1328]) ).
thf(f5529,plain,
( ( notinsingleton != $true )
| ( sK351 = sK350 ) ),
inference(trivial_inequality_removal,[status(thm)],[f5522]) ).
thf(f5522,plain,
( ( sK351 = sK350 )
| ( notinsingleton != $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1595,f5245]) ).
thf(f5245,plain,
( ( in @ sK350 @ ( setadjoin @ sK351 @ emptyset ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f5244]) ).
thf(f5244,plain,
( ( ( in @ sK350 @ ( setadjoin @ sK351 @ emptyset ) )
= $true )
| ( $true != $true ) ),
inference(forward_demodulation,[status(thm)],[f5241,f2070]) ).
thf(f2070,plain,
setunionsingleton = $true,
inference(cnf_transformation,[status(thm)],[f1328]) ).
thf(f5241,plain,
( ( setunionsingleton != $true )
| ( ( in @ sK350 @ ( setadjoin @ sK351 @ emptyset ) )
= $true ) ),
inference(superposition,[status(thm)],[f2580,f2007]) ).
thf(f2007,plain,
! [X0: $i] :
( ( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) ),
inference(cnf_transformation,[status(thm)],[f1326]) ).
thf(f1326,plain,
( ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) )
& ( ( setunionsingleton = $true )
| ( sK349
!= ( setunion @ ( setadjoin @ sK349 @ emptyset ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK349])],[f1324,f1325]) ).
thf(f1325,plain,
( ? [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
!= X1 )
=> ( sK349
!= ( setunion @ ( setadjoin @ sK349 @ emptyset ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1324,plain,
( ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) )
& ( ( setunionsingleton = $true )
| ? [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
!= X1 ) ) ),
inference(rectify,[status(thm)],[f1323]) ).
thf(f1323,plain,
( ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
| ( setunionsingleton != $true ) )
& ( ( setunionsingleton = $true )
| ? [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
!= X0 ) ) ),
inference(nnf_transformation,[status(thm)],[f361]) ).
thf(f361,plain,
( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 )
<=> ( setunionsingleton = $true ) ),
inference(fool_elimination,[status(thm)],[f360]) ).
thf(f360,plain,
( setunionsingleton
= ( ! [X0: $i] :
( ( setunion @ ( setadjoin @ X0 @ emptyset ) )
= X0 ) ) ),
inference(rectify,[status(thm)],[f157]) ).
thf(f157,axiom,
( setunionsingleton
= ( ! [X1: $i] :
( ( setunion @ ( setadjoin @ X1 @ emptyset ) )
= X1 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2THF_26106.p',setunionsingleton) ).
thf(f2580,plain,
( $true
= ( in @ sK350 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK351 @ emptyset ) @ emptyset ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f2579]) ).
thf(f2579,plain,
( ( $true != $true )
| ( $true
= ( in @ sK350 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK351 @ emptyset ) @ emptyset ) ) ) ) ),
inference(forward_demodulation,[status(thm)],[f2574,f2132]) ).
thf(f2132,plain,
setukpairinjR12 = $true,
inference(cnf_transformation,[status(thm)],[f1328]) ).
thf(f2574,plain,
( ( $true
= ( in @ sK350 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK351 @ emptyset ) @ emptyset ) ) ) )
| ( setukpairinjR12 != $true ) ),
inference(superposition,[status(thm)],[f2556,f2365]) ).
thf(f2365,plain,
! [X1: $i] :
( ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) )
| ( setukpairinjR12 != $true ) ),
inference(equality_resolution,[status(thm)],[f2310]) ).
thf(f2310,plain,
! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) )
| ( setukpairinjR12 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1484]) ).
thf(f1484,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) )
| ( setukpairinjR12 != $true ) )
& ( ( setukpairinjR12 = $true )
| ( ( sK451 = sK450 )
& ( ( setadjoin @ ( setadjoin @ sK450 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ sK450 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK450 @ ( setadjoin @ sK451 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK450,sK451])],[f1482,f1483]) ).
thf(f1483,plain,
( ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
=> ( ( sK451 = sK450 )
& ( ( setadjoin @ ( setadjoin @ sK450 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ sK450 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK450 @ ( setadjoin @ sK451 @ emptyset ) ) @ emptyset ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1482,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) )
| ( setukpairinjR12 != $true ) )
& ( ( setukpairinjR12 = $true )
| ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ emptyset )
!= ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) ) ) ),
inference(rectify,[status(thm)],[f1481]) ).
thf(f1481,plain,
( ( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) )
| ( setukpairinjR12 != $true ) )
& ( ( setukpairinjR12 = $true )
| ? [X0: $i,X1: $i] :
( ( X0 = X1 )
& ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f581]) ).
thf(f581,plain,
( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
| ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) )
<=> ( setukpairinjR12 = $true ) ),
inference(ennf_transformation,[status(thm)],[f319]) ).
thf(f319,plain,
( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) )
<=> ( setukpairinjR12 = $true ) ),
inference(fool_elimination,[status(thm)],[f318]) ).
thf(f318,plain,
( setukpairinjR12
= ( ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ emptyset ) ) ) ) ),
inference(rectify,[status(thm)],[f173]) ).
thf(f173,axiom,
( setukpairinjR12
= ( ! [X1: $i,X2: $i] :
( ( X1 = X2 )
=> ( ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2THF_26106.p',setukpairinjR12) ).
thf(f2556,plain,
( ( in @ sK350 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK351 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK351 @ ( setadjoin @ sK351 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f2555]) ).
thf(f2555,plain,
( ( $true != $true )
| ( ( in @ sK350 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK351 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK351 @ ( setadjoin @ sK351 @ emptyset ) ) @ emptyset ) ) ) )
= $true ) ),
inference(forward_demodulation,[status(thm)],[f2451,f2065]) ).
thf(f2065,plain,
setukpairIR = $true,
inference(cnf_transformation,[status(thm)],[f1328]) ).
thf(f2451,plain,
( ( setukpairIR != $true )
| ( ( in @ sK350 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK351 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK351 @ ( setadjoin @ sK351 @ emptyset ) ) @ emptyset ) ) ) )
= $true ) ),
inference(superposition,[status(thm)],[f1699,f2450]) ).
thf(f2450,plain,
( ( setadjoin @ ( setadjoin @ sK351 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK351 @ ( setadjoin @ sK351 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK353 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK353 @ ( setadjoin @ sK350 @ emptyset ) ) @ emptyset ) ) ),
inference(forward_demodulation,[status(thm)],[f2148,f2149]) ).
thf(f2148,plain,
( ( setadjoin @ ( setadjoin @ sK353 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK353 @ ( setadjoin @ sK350 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK351 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK351 @ ( setadjoin @ sK352 @ emptyset ) ) @ emptyset ) ) ),
inference(cnf_transformation,[status(thm)],[f1328]) ).
thf(f1699,plain,
! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( setukpairIR != $true ) ),
inference(cnf_transformation,[status(thm)],[f975]) ).
thf(f975,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( setukpairIR != $true ) )
& ( ( setukpairIR = $true )
| ( ( in @ sK138 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK137 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK137 @ ( setadjoin @ sK138 @ emptyset ) ) @ emptyset ) ) ) )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK137,sK138])],[f973,f974]) ).
thf(f974,plain,
( ? [X2: $i,X3: $i] :
( ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
!= $true )
=> ( ( in @ sK138 @ ( setunion @ ( setadjoin @ ( setadjoin @ sK137 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK137 @ ( setadjoin @ sK138 @ emptyset ) ) @ emptyset ) ) ) )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f973,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( setukpairIR != $true ) )
& ( ( setukpairIR = $true )
| ? [X2: $i,X3: $i] :
( ( in @ X3 @ ( setunion @ ( setadjoin @ ( setadjoin @ X2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) @ emptyset ) ) ) )
!= $true ) ) ),
inference(rectify,[status(thm)],[f972]) ).
thf(f972,plain,
( ( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ( setukpairIR != $true ) )
& ( ( setukpairIR = $true )
| ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f327]) ).
thf(f327,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) ) )
<=> ( setukpairIR = $true ) ),
inference(fool_elimination,[status(thm)],[f326]) ).
thf(f326,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ ( setadjoin @ ( setadjoin @ X0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) @ emptyset ) ) ) )
= setukpairIR ),
inference(rectify,[status(thm)],[f138]) ).
thf(f138,axiom,
! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setunion @ ( setadjoin @ ( setadjoin @ X1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) @ emptyset ) ) ) )
= setukpairIR ),
file('/export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2THF_26106.p',setukpairIR) ).
thf(f1595,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( notinsingleton != $true )
| ( X0 = X1 ) ),
inference(cnf_transformation,[status(thm)],[f847]) ).
thf(f847,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( notinsingleton != $true ) )
& ( ( notinsingleton = $true )
| ( ( $true
= ( in @ sK67 @ ( setadjoin @ sK68 @ emptyset ) ) )
& ( sK67 != sK68 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f845,f846]) ).
thf(f846,plain,
( ? [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
& ( X2 != X3 ) )
=> ( ( $true
= ( in @ sK67 @ ( setadjoin @ sK68 @ emptyset ) ) )
& ( sK67 != sK68 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f845,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( notinsingleton != $true ) )
& ( ( notinsingleton = $true )
| ? [X2: $i,X3: $i] :
( ( ( in @ X2 @ ( setadjoin @ X3 @ emptyset ) )
= $true )
& ( X2 != X3 ) ) ) ),
inference(rectify,[status(thm)],[f844]) ).
thf(f844,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
| ( notinsingleton != $true ) )
& ( ( notinsingleton = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) ) ) ),
inference(nnf_transformation,[status(thm)],[f680]) ).
thf(f680,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
| ( X0 = X1 ) )
<=> ( notinsingleton = $true ) ),
inference(ennf_transformation,[status(thm)],[f553]) ).
thf(f553,plain,
( ( notinsingleton = $true )
<=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) ) ),
inference(flattening,[status(thm)],[f489]) ).
thf(f489,plain,
( ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true ) )
<=> ( notinsingleton = $true ) ),
inference(fool_elimination,[status(thm)],[f488]) ).
thf(f488,plain,
! [X0: $i,X1: $i] :
( ( ( X0 != X1 )
=> ~ ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= notinsingleton ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,axiom,
! [X2: $i,X1: $i] :
( ( ( X1 != X2 )
=> ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) )
= notinsingleton ),
file('/export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2THF_26106.p',notinsingleton) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU651^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.31 % Computer : n001.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue Feb 24 12:30:05 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.43 ---- Original DTF file ---
% 0.15/0.43 thf(spec,logic,$$dhol).
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 % File : SEU651^1 : TPTP v9.2.1. Released v3.7.0.
% 0.15/0.43 % Domain : Set Theory
% 0.15/0.43 % Problem : Ordered Pairs - Properties of Pairs
% 0.15/0.43 % Version : Especial.
% 0.15/0.43 % English : (! x:i.! y:i.! z:i.! u:i.setadjoin (setadjoin x emptyset)
% 0.15/0.43 % (setadjoin (setadjoin x (setadjoin y emptyset)) emptyset) =
% 0.15/0.43 % setadjoin (setadjoin z emptyset) (setadjoin (setadjoin z
% 0.15/0.43 % (setadjoin u emptyset)) emptyset) -> z = u -> y = u)
% 0.15/0.43
% 0.15/0.43 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.15/0.43 % Source : [Bro08]
% 0.15/0.43 % Names : ZFC153g [Bro08]
% 0.15/0.43
% 0.15/0.43 % Status : Theorem
% 0.15/0.43 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.27 v7.5.0, 0.29 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v5.2.0, 1.00 v5.0.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.15/0.43 % Syntax : Number of formulae : 371 ( 173 unt; 197 typ; 173 def)
% 0.15/0.43 % Number of atoms : 917 ( 254 equ; 0 cnn)
% 0.15/0.43 % Maximal formula atoms : 170 ( 5 avg)
% 0.15/0.43 % Number of connectives : 1619 ( 47 ~; 7 |; 37 &;1109 @)
% 0.15/0.43 % ( 14 <=>; 405 =>; 0 <=; 0 <~>)
% 0.15/0.43 % Maximal formula depth : 174 ( 2 avg)
% 0.15/0.43 % Number of types : 2 ( 0 usr)
% 0.15/0.43 % Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% 0.15/0.43 % Number of symbols : 200 ( 197 usr; 171 con; 0-2 aty)
% 0.15/0.43 % Number of variables : 504 ( 42 ^; 424 !; 38 ?; 504 :)
% 0.15/0.43 % SPC : TH0_THM_EQU_NAR
% 0.15/0.43
% 0.15/0.43 % Comments : http://mathgate.info/detsetitem.php?id=207
% 0.15/0.43 %------------------------------------------------------------------------------
% 0.15/0.43 thf(in_type,type,
% 0.15/0.43 in: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(exu_type,type,
% 0.15/0.43 exu: ( $i > $o ) > $o ).
% 0.15/0.43
% 0.15/0.43 thf(exu,definition,
% 0.15/0.43 ( exu
% 0.15/0.43 = ( ^ [Xphi: $i > $o] :
% 0.15/0.43 ? [Xx: $i] :
% 0.15/0.43 ( ( Xphi @ Xx )
% 0.15/0.43 & ! [Xy: $i] :
% 0.15/0.43 ( ( Xphi @ Xy )
% 0.15/0.43 => ( Xx = Xy ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setextAx_type,type,
% 0.15/0.43 setextAx: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setextAx,definition,
% 0.15/0.43 ( setextAx
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 <=> ( in @ Xx @ B ) )
% 0.15/0.43 => ( A = B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(emptyset_type,type,
% 0.15/0.43 emptyset: $i ).
% 0.15/0.43
% 0.15/0.43 thf(emptysetAx_type,type,
% 0.15/0.43 emptysetAx: $o ).
% 0.15/0.43
% 0.15/0.43 thf(emptysetAx,definition,
% 0.15/0.43 ( emptysetAx
% 0.15/0.43 = ( ! [Xx: $i] :
% 0.15/0.43 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoin_type,type,
% 0.15/0.43 setadjoin: $i > $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinAx_type,type,
% 0.15/0.43 setadjoinAx: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinAx,definition,
% 0.15/0.43 ( setadjoinAx
% 0.15/0.43 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.15/0.43 <=> ( ( Xy = Xx )
% 0.15/0.43 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powerset_type,type,
% 0.15/0.43 powerset: $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(powersetAx_type,type,
% 0.15/0.43 powersetAx: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powersetAx,definition,
% 0.15/0.43 ( powersetAx
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( in @ B @ ( powerset @ A ) )
% 0.15/0.43 <=> ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setunion_type,type,
% 0.15/0.43 setunion: $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(setunionAx_type,type,
% 0.15/0.43 setunionAx: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setunionAx,definition,
% 0.15/0.43 ( setunionAx
% 0.15/0.43 = ( ! [A: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( setunion @ A ) )
% 0.15/0.43 <=> ? [B: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 & ( in @ B @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(omega_type,type,
% 0.15/0.43 omega: $i ).
% 0.15/0.43
% 0.15/0.43 thf(omega0Ax_type,type,
% 0.15/0.43 omega0Ax: $o ).
% 0.15/0.43
% 0.15/0.43 thf(omega0Ax,definition,
% 0.15/0.43 ( omega0Ax
% 0.15/0.43 = ( in @ emptyset @ omega ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(omegaSAx_type,type,
% 0.15/0.43 omegaSAx: $o ).
% 0.15/0.43
% 0.15/0.43 thf(omegaSAx,definition,
% 0.15/0.43 ( omegaSAx
% 0.15/0.43 = ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ omega )
% 0.15/0.43 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(omegaIndAx_type,type,
% 0.15/0.43 omegaIndAx: $o ).
% 0.15/0.43
% 0.15/0.43 thf(omegaIndAx,definition,
% 0.15/0.43 ( omegaIndAx
% 0.15/0.43 = ( ! [A: $i] :
% 0.15/0.43 ( ( ( in @ emptyset @ A )
% 0.15/0.43 & ! [Xx: $i] :
% 0.15/0.43 ( ( ( in @ Xx @ omega )
% 0.15/0.43 & ( in @ Xx @ A ) )
% 0.15/0.43 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ omega )
% 0.15/0.43 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(replAx_type,type,
% 0.15/0.43 replAx: $o ).
% 0.15/0.43
% 0.15/0.43 thf(replAx,definition,
% 0.15/0.43 ( replAx
% 0.15/0.43 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( exu
% 0.15/0.43 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.15/0.43 => ? [B: $i] :
% 0.15/0.43 ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 <=> ? [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(foundationAx_type,type,
% 0.15/0.43 foundationAx: $o ).
% 0.15/0.43
% 0.15/0.43 thf(foundationAx,definition,
% 0.15/0.43 ( foundationAx
% 0.15/0.43 = ( ! [A: $i] :
% 0.15/0.43 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.15/0.43 => ? [B: $i] :
% 0.15/0.43 ( ( in @ B @ A )
% 0.15/0.43 & ~ ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(wellorderingAx_type,type,
% 0.15/0.43 wellorderingAx: $o ).
% 0.15/0.43
% 0.15/0.43 thf(wellorderingAx,definition,
% 0.15/0.43 ( wellorderingAx
% 0.15/0.43 = ( ! [A: $i] :
% 0.15/0.43 ? [B: $i] :
% 0.15/0.43 ( ! [C: $i] :
% 0.15/0.43 ( ( in @ C @ B )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ C )
% 0.15/0.43 => ( in @ Xx @ A ) ) )
% 0.15/0.43 & ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( ( in @ Xx @ A )
% 0.15/0.43 & ( in @ Xy @ A ) )
% 0.15/0.43 => ( ! [C: $i] :
% 0.15/0.43 ( ( in @ C @ B )
% 0.15/0.43 => ( ( in @ Xx @ C )
% 0.15/0.43 <=> ( in @ Xy @ C ) ) )
% 0.15/0.43 => ( Xx = Xy ) ) )
% 0.15/0.43 & ! [C: $i,D: $i] :
% 0.15/0.43 ( ( ( in @ C @ B )
% 0.15/0.43 & ( in @ D @ B ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ C )
% 0.15/0.43 => ( in @ Xx @ D ) )
% 0.15/0.43 | ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ D )
% 0.15/0.43 => ( in @ Xx @ C ) ) ) )
% 0.15/0.43 & ! [C: $i] :
% 0.15/0.43 ( ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ C )
% 0.15/0.43 => ( in @ Xx @ A ) )
% 0.15/0.43 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.15/0.43 => ? [D: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ D @ B )
% 0.15/0.43 & ( in @ Xx @ C )
% 0.15/0.43 & ~ ? [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ D )
% 0.15/0.43 & ( in @ Xy @ C ) )
% 0.15/0.43 & ! [E: $i] :
% 0.15/0.43 ( ( in @ E @ B )
% 0.15/0.43 => ( ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ E )
% 0.15/0.43 => ( in @ Xy @ D ) )
% 0.15/0.43 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(descr_type,type,
% 0.15/0.43 descr: ( $i > $o ) > $i ).
% 0.15/0.43
% 0.15/0.43 thf(descrp_type,type,
% 0.15/0.43 descrp: $o ).
% 0.15/0.43
% 0.15/0.43 thf(descrp,definition,
% 0.15/0.43 ( descrp
% 0.15/0.43 = ( ! [Xphi: $i > $o] :
% 0.15/0.43 ( ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 => ( Xphi
% 0.15/0.43 @ ( descr
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(dsetconstr_type,type,
% 0.15/0.43 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.15/0.43
% 0.15/0.43 thf(dsetconstrI_type,type,
% 0.15/0.43 dsetconstrI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(dsetconstrI,definition,
% 0.15/0.43 ( dsetconstrI
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( Xphi @ Xx )
% 0.15/0.43 => ( in @ Xx
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(dsetconstrEL_type,type,
% 0.15/0.43 dsetconstrEL: $o ).
% 0.15/0.43
% 0.15/0.43 thf(dsetconstrEL,definition,
% 0.15/0.43 ( dsetconstrEL
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.15/0.43 => ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(dsetconstrER_type,type,
% 0.15/0.43 dsetconstrER: $o ).
% 0.15/0.43
% 0.15/0.43 thf(dsetconstrER,definition,
% 0.15/0.43 ( dsetconstrER
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.15/0.43 => ( Xphi @ Xx ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(exuE1_type,type,
% 0.15/0.43 exuE1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(exuE1,definition,
% 0.15/0.43 ( exuE1
% 0.15/0.43 = ( ! [Xphi: $i > $o] :
% 0.15/0.43 ( ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 => ? [Xx: $i] :
% 0.15/0.43 ( ( Xphi @ Xx )
% 0.15/0.43 & ! [Xy: $i] :
% 0.15/0.43 ( ( Xphi @ Xy )
% 0.15/0.43 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(prop2set_type,type,
% 0.15/0.43 prop2set: $o > $i ).
% 0.15/0.43
% 0.15/0.43 thf(prop2setE_type,type,
% 0.15/0.43 prop2setE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(prop2setE,definition,
% 0.15/0.43 ( prop2setE
% 0.15/0.43 = ( ! [Xphi: $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.15/0.43 => Xphi ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(emptysetE_type,type,
% 0.15/0.43 emptysetE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(emptysetE,definition,
% 0.15/0.43 ( emptysetE
% 0.15/0.43 = ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ emptyset )
% 0.15/0.43 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(emptysetimpfalse_type,type,
% 0.15/0.43 emptysetimpfalse: $o ).
% 0.15/0.43
% 0.15/0.43 thf(emptysetimpfalse,definition,
% 0.15/0.43 ( emptysetimpfalse
% 0.15/0.43 = ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ emptyset )
% 0.15/0.43 => $false ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(notinemptyset_type,type,
% 0.15/0.43 notinemptyset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(notinemptyset,definition,
% 0.15/0.43 ( notinemptyset
% 0.15/0.43 = ( ! [Xx: $i] :
% 0.15/0.43 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(exuE3e_type,type,
% 0.15/0.43 exuE3e: $o ).
% 0.15/0.43
% 0.15/0.43 thf(exuE3e,definition,
% 0.15/0.43 ( exuE3e
% 0.15/0.43 = ( ! [Xphi: $i > $o] :
% 0.15/0.43 ( ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setext_type,type,
% 0.15/0.43 setext: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setext,definition,
% 0.15/0.43 ( setext
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ Xx @ B ) )
% 0.15/0.43 => ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ A ) )
% 0.15/0.43 => ( A = B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(emptyI_type,type,
% 0.15/0.43 emptyI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(emptyI,definition,
% 0.15/0.43 ( emptyI
% 0.15/0.43 = ( ! [A: $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ~ ( in @ Xx @ A )
% 0.15/0.43 => ( A = emptyset ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(noeltsimpempty_type,type,
% 0.15/0.43 noeltsimpempty: $o ).
% 0.15/0.43
% 0.15/0.43 thf(noeltsimpempty,definition,
% 0.15/0.43 ( noeltsimpempty
% 0.15/0.43 = ( ! [A: $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ~ ( in @ Xx @ A )
% 0.15/0.43 => ( A = emptyset ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setbeta_type,type,
% 0.15/0.43 setbeta: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setbeta,definition,
% 0.15/0.43 ( setbeta
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.15/0.43 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(nonempty_type,type,
% 0.15/0.43 nonempty: $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(nonempty,definition,
% 0.15/0.43 ( nonempty
% 0.15/0.43 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(nonemptyE1_type,type,
% 0.15/0.43 nonemptyE1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(nonemptyE1,definition,
% 0.15/0.43 ( nonemptyE1
% 0.15/0.43 = ( ! [A: $i] :
% 0.15/0.43 ( ( nonempty @ A )
% 0.15/0.43 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(nonemptyI_type,type,
% 0.15/0.43 nonemptyI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(nonemptyI,definition,
% 0.15/0.43 ( nonemptyI
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( Xphi @ Xx )
% 0.15/0.43 => ( nonempty
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(nonemptyI1_type,type,
% 0.15/0.43 nonemptyI1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(nonemptyI1,definition,
% 0.15/0.43 ( nonemptyI1
% 0.15/0.43 = ( ! [A: $i] :
% 0.15/0.43 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.15/0.43 => ( nonempty @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinIL_type,type,
% 0.15/0.43 setadjoinIL: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinIL,definition,
% 0.15/0.43 ( setadjoinIL
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(emptyinunitempty_type,type,
% 0.15/0.43 emptyinunitempty: $o ).
% 0.15/0.43
% 0.15/0.43 thf(emptyinunitempty,definition,
% 0.15/0.43 ( emptyinunitempty
% 0.15/0.43 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinIR_type,type,
% 0.15/0.43 setadjoinIR: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinIR,definition,
% 0.15/0.43 ( setadjoinIR
% 0.15/0.43 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ A )
% 0.15/0.43 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinE_type,type,
% 0.15/0.43 setadjoinE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinE,definition,
% 0.15/0.43 ( setadjoinE
% 0.15/0.43 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.15/0.43 => ! [Xphi: $o] :
% 0.15/0.43 ( ( ( Xy = Xx )
% 0.15/0.43 => Xphi )
% 0.15/0.43 => ( ( ( in @ Xy @ A )
% 0.15/0.43 => Xphi )
% 0.15/0.43 => Xphi ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinOr_type,type,
% 0.15/0.43 setadjoinOr: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinOr,definition,
% 0.15/0.43 ( setadjoinOr
% 0.15/0.43 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.15/0.43 => ( ( Xy = Xx )
% 0.15/0.43 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setoftrueEq_type,type,
% 0.15/0.43 setoftrueEq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setoftrueEq,definition,
% 0.15/0.43 ( setoftrueEq
% 0.15/0.43 = ( ! [A: $i] :
% 0.15/0.43 ( ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xx: $i] : $true )
% 0.15/0.43 = A ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powersetI_type,type,
% 0.15/0.43 powersetI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powersetI,definition,
% 0.15/0.43 ( powersetI
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ A ) )
% 0.15/0.43 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(emptyinPowerset_type,type,
% 0.15/0.43 emptyinPowerset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(emptyinPowerset,definition,
% 0.15/0.43 ( emptyinPowerset
% 0.15/0.43 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(emptyInPowerset_type,type,
% 0.15/0.43 emptyInPowerset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(emptyInPowerset,definition,
% 0.15/0.43 ( emptyInPowerset
% 0.15/0.43 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powersetE_type,type,
% 0.15/0.43 powersetE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powersetE,definition,
% 0.15/0.43 ( powersetE
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ B @ ( powerset @ A ) )
% 0.15/0.43 => ( ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setunionI_type,type,
% 0.15/0.43 setunionI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setunionI,definition,
% 0.15/0.43 ( setunionI
% 0.15/0.43 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 => ( ( in @ B @ A )
% 0.15/0.43 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setunionE_type,type,
% 0.15/0.43 setunionE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setunionE,definition,
% 0.15/0.43 ( setunionE
% 0.15/0.43 = ( ! [A: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( setunion @ A ) )
% 0.15/0.43 => ! [Xphi: $o] :
% 0.15/0.43 ( ! [B: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 => ( ( in @ B @ A )
% 0.15/0.43 => Xphi ) )
% 0.15/0.43 => Xphi ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subPowSU_type,type,
% 0.15/0.43 subPowSU: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subPowSU,definition,
% 0.15/0.43 ( subPowSU
% 0.15/0.43 = ( ! [A: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(exuE2_type,type,
% 0.15/0.43 exuE2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(exuE2,definition,
% 0.15/0.43 ( exuE2
% 0.15/0.43 = ( ! [Xphi: $i > $o] :
% 0.15/0.43 ( ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 => ? [Xx: $i] :
% 0.15/0.43 ! [Xy: $i] :
% 0.15/0.43 ( ( Xphi @ Xy )
% 0.15/0.43 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(nonemptyImpWitness_type,type,
% 0.15/0.43 nonemptyImpWitness: $o ).
% 0.15/0.43
% 0.15/0.43 thf(nonemptyImpWitness,definition,
% 0.15/0.43 ( nonemptyImpWitness
% 0.15/0.43 = ( ! [A: $i] :
% 0.15/0.43 ( ( nonempty @ A )
% 0.15/0.43 => ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & $true ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(uniqinunit_type,type,
% 0.15/0.43 uniqinunit: $o ).
% 0.15/0.43
% 0.15/0.43 thf(uniqinunit,definition,
% 0.15/0.43 ( uniqinunit
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.15/0.43 => ( Xx = Xy ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(notinsingleton_type,type,
% 0.15/0.43 notinsingleton: $o ).
% 0.15/0.43
% 0.15/0.43 thf(notinsingleton,definition,
% 0.15/0.43 ( notinsingleton
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xx != Xy )
% 0.15/0.43 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(eqinunit_type,type,
% 0.15/0.43 eqinunit: $o ).
% 0.15/0.43
% 0.15/0.43 thf(eqinunit,definition,
% 0.15/0.43 ( eqinunit
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xx = Xy )
% 0.15/0.43 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(singletonsswitch_type,type,
% 0.15/0.43 singletonsswitch: $o ).
% 0.15/0.43
% 0.15/0.43 thf(singletonsswitch,definition,
% 0.15/0.43 ( singletonsswitch
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.15/0.43 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(upairsetE_type,type,
% 0.15/0.43 upairsetE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(upairsetE,definition,
% 0.15/0.43 ( upairsetE
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.15/0.43 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.15/0.43 => ( ( Xz = Xx )
% 0.15/0.43 | ( Xz = Xy ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(upairsetIL_type,type,
% 0.15/0.43 upairsetIL: $o ).
% 0.15/0.43
% 0.15/0.43 thf(upairsetIL,definition,
% 0.15/0.43 ( upairsetIL
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(upairsetIR_type,type,
% 0.15/0.43 upairsetIR: $o ).
% 0.15/0.43
% 0.15/0.43 thf(upairsetIR,definition,
% 0.15/0.43 ( upairsetIR
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(emptyE1_type,type,
% 0.15/0.43 emptyE1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(emptyE1,definition,
% 0.15/0.43 ( emptyE1
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ( Xphi @ Xx ) )
% 0.15/0.43 => ( ( ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 = emptyset )
% 0.15/0.43 => $false ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(vacuousDall_type,type,
% 0.15/0.43 vacuousDall: $o ).
% 0.15/0.43
% 0.15/0.43 thf(vacuousDall,definition,
% 0.15/0.43 ( vacuousDall
% 0.15/0.43 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ emptyset )
% 0.15/0.43 => ( Xphi @ Xx ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(quantDeMorgan1_type,type,
% 0.15/0.43 quantDeMorgan1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(quantDeMorgan1,definition,
% 0.15/0.43 ( quantDeMorgan1
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ~ ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( Xphi @ Xx ) )
% 0.15/0.43 => ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(quantDeMorgan2_type,type,
% 0.15/0.43 quantDeMorgan2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(quantDeMorgan2,definition,
% 0.15/0.43 ( quantDeMorgan2
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ~ ( Xphi @ Xx ) )
% 0.15/0.43 => ~ ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(quantDeMorgan3_type,type,
% 0.15/0.43 quantDeMorgan3: $o ).
% 0.15/0.43
% 0.15/0.43 thf(quantDeMorgan3,definition,
% 0.15/0.43 ( quantDeMorgan3
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ~ ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ( Xphi @ Xx ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(quantDeMorgan4_type,type,
% 0.15/0.43 quantDeMorgan4: $o ).
% 0.15/0.43
% 0.15/0.43 thf(quantDeMorgan4,definition,
% 0.15/0.43 ( quantDeMorgan4
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ~ ( Xphi @ Xx ) )
% 0.15/0.43 => ~ ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(prop2setI_type,type,
% 0.15/0.43 prop2setI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(prop2setI,definition,
% 0.15/0.43 ( prop2setI
% 0.15/0.43 = ( ! [Xphi: $o] :
% 0.15/0.43 ( Xphi
% 0.15/0.43 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(set2prop_type,type,
% 0.15/0.43 set2prop: $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(prop2set2propI_type,type,
% 0.15/0.43 prop2set2propI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(prop2set2propI,definition,
% 0.15/0.43 ( prop2set2propI
% 0.15/0.43 = ( ! [Xphi: $o] :
% 0.15/0.43 ( Xphi
% 0.15/0.43 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(notdexE_type,type,
% 0.15/0.43 notdexE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(notdexE,definition,
% 0.15/0.43 ( notdexE
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ~ ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ( Xphi @ Xx ) )
% 0.15/0.43 => ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(notdallE_type,type,
% 0.15/0.43 notdallE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(notdallE,definition,
% 0.15/0.43 ( notdallE
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( ~ ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( Xphi @ Xx ) )
% 0.15/0.43 => ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(exuI1_type,type,
% 0.15/0.43 exuI1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(exuI1,definition,
% 0.15/0.43 ( exuI1
% 0.15/0.43 = ( ! [Xphi: $i > $o] :
% 0.15/0.43 ( ? [Xx: $i] :
% 0.15/0.43 ( ( Xphi @ Xx )
% 0.15/0.43 & ! [Xy: $i] :
% 0.15/0.43 ( ( Xphi @ Xy )
% 0.15/0.43 => ( Xx = Xy ) ) )
% 0.15/0.43 => ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(exuI3_type,type,
% 0.15/0.43 exuI3: $o ).
% 0.15/0.43
% 0.15/0.43 thf(exuI3,definition,
% 0.15/0.43 ( exuI3
% 0.15/0.43 = ( ! [Xphi: $i > $o] :
% 0.15/0.43 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.15/0.43 => ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xphi @ Xx )
% 0.15/0.43 => ( ( Xphi @ Xy )
% 0.15/0.43 => ( Xx = Xy ) ) )
% 0.15/0.43 => ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(exuI2_type,type,
% 0.15/0.43 exuI2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(exuI2,definition,
% 0.15/0.43 ( exuI2
% 0.15/0.43 = ( ! [Xphi: $i > $o] :
% 0.15/0.43 ( ? [Xx: $i] :
% 0.15/0.43 ! [Xy: $i] :
% 0.15/0.43 ( ( Xphi @ Xy )
% 0.15/0.43 <=> ( Xy = Xx ) )
% 0.15/0.43 => ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(inCongP_type,type,
% 0.15/0.43 inCongP: $o ).
% 0.15/0.43
% 0.15/0.43 thf(inCongP,definition,
% 0.15/0.43 ( inCongP
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( A = B )
% 0.15/0.43 => ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xx = Xy )
% 0.15/0.43 => ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(in__Cong_type,type,
% 0.15/0.43 in__Cong: $o ).
% 0.15/0.43
% 0.15/0.43 thf(in__Cong,definition,
% 0.15/0.43 ( in__Cong
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( A = B )
% 0.15/0.43 => ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xx = Xy )
% 0.15/0.43 => ( ( in @ Xx @ A )
% 0.15/0.43 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(exuE3u_type,type,
% 0.15/0.43 exuE3u: $o ).
% 0.15/0.43
% 0.15/0.43 thf(exuE3u,definition,
% 0.15/0.43 ( exuE3u
% 0.15/0.43 = ( ! [Xphi: $i > $o] :
% 0.15/0.43 ( ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 => ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xphi @ Xx )
% 0.15/0.43 => ( ( Xphi @ Xy )
% 0.15/0.43 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(exu__Cong_type,type,
% 0.15/0.43 exu__Cong: $o ).
% 0.15/0.43
% 0.15/0.43 thf(exu__Cong,definition,
% 0.15/0.43 ( exu__Cong
% 0.15/0.43 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.15/0.43 ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xx = Xy )
% 0.15/0.43 => ( ( Xphi @ Xx )
% 0.15/0.43 <=> ( Xpsi @ Xy ) ) )
% 0.15/0.43 => ( ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 <=> ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(emptyset__Cong_type,type,
% 0.15/0.43 emptyset__Cong: $o ).
% 0.15/0.43
% 0.15/0.43 thf(emptyset__Cong,definition,
% 0.15/0.43 ( emptyset__Cong
% 0.15/0.43 = ( emptyset = emptyset ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoin__Cong_type,type,
% 0.15/0.43 setadjoin__Cong: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoin__Cong,definition,
% 0.15/0.43 ( setadjoin__Cong
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xx = Xy )
% 0.15/0.43 => ! [Xz: $i,Xu: $i] :
% 0.15/0.43 ( ( Xz = Xu )
% 0.15/0.43 => ( ( setadjoin @ Xx @ Xz )
% 0.15/0.43 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powerset__Cong_type,type,
% 0.15/0.43 powerset__Cong: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powerset__Cong,definition,
% 0.15/0.43 ( powerset__Cong
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( A = B )
% 0.15/0.43 => ( ( powerset @ A )
% 0.15/0.43 = ( powerset @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setunion__Cong_type,type,
% 0.15/0.43 setunion__Cong: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setunion__Cong,definition,
% 0.15/0.43 ( setunion__Cong
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( A = B )
% 0.15/0.43 => ( ( setunion @ A )
% 0.15/0.43 = ( setunion @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(omega__Cong_type,type,
% 0.15/0.43 omega__Cong: $o ).
% 0.15/0.43
% 0.15/0.43 thf(omega__Cong,definition,
% 0.15/0.43 ( omega__Cong
% 0.15/0.43 = ( omega = omega ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(exuEu_type,type,
% 0.15/0.43 exuEu: $o ).
% 0.15/0.43
% 0.15/0.43 thf(exuEu,definition,
% 0.15/0.43 ( exuEu
% 0.15/0.43 = ( ! [Xphi: $i > $o] :
% 0.15/0.43 ( ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 => ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xphi @ Xx )
% 0.15/0.43 => ( ( Xphi @ Xy )
% 0.15/0.43 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(descr__Cong_type,type,
% 0.15/0.43 descr__Cong: $o ).
% 0.15/0.43
% 0.15/0.43 thf(descr__Cong,definition,
% 0.15/0.43 ( descr__Cong
% 0.15/0.43 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.15/0.43 ( ! [Xx: $i,Xy: $i] :
% 0.15/0.43 ( ( Xx = Xy )
% 0.15/0.43 => ( ( Xphi @ Xx )
% 0.15/0.43 <=> ( Xpsi @ Xy ) ) )
% 0.15/0.43 => ( ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 => ( ( exu
% 0.15/0.43 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.15/0.43 => ( ( descr
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 = ( descr
% 0.15/0.43 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(dsetconstr__Cong_type,type,
% 0.15/0.43 dsetconstr__Cong: $o ).
% 0.15/0.43
% 0.15/0.43 thf(dsetconstr__Cong,definition,
% 0.15/0.43 ( dsetconstr__Cong
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( A = B )
% 0.15/0.43 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ! [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ B )
% 0.15/0.43 => ( ( Xx = Xy )
% 0.15/0.43 => ( ( Xphi @ Xx )
% 0.15/0.43 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.15/0.43 => ( ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 = ( dsetconstr @ B
% 0.15/0.43 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subset_type,type,
% 0.15/0.43 subset: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(disjoint_type,type,
% 0.15/0.43 disjoint: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(setsmeet_type,type,
% 0.15/0.43 setsmeet: $i > $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(subsetI1_type,type,
% 0.15/0.43 subsetI1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subsetI1,definition,
% 0.15/0.43 ( subsetI1
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ Xx @ B ) )
% 0.15/0.43 => ( subset @ A @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(eqimpsubset2_type,type,
% 0.15/0.43 eqimpsubset2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(eqimpsubset2,definition,
% 0.15/0.43 ( eqimpsubset2
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( A = B )
% 0.15/0.43 => ( subset @ B @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(eqimpsubset1_type,type,
% 0.15/0.43 eqimpsubset1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(eqimpsubset1,definition,
% 0.15/0.43 ( eqimpsubset1
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( A = B )
% 0.15/0.43 => ( subset @ A @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subsetI2_type,type,
% 0.15/0.43 subsetI2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subsetI2,definition,
% 0.15/0.43 ( subsetI2
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ! [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ Xx @ B ) )
% 0.15/0.43 => ( subset @ A @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(emptysetsubset_type,type,
% 0.15/0.43 emptysetsubset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(emptysetsubset,definition,
% 0.15/0.43 ( emptysetsubset
% 0.15/0.43 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subsetE_type,type,
% 0.15/0.43 subsetE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subsetE,definition,
% 0.15/0.43 ( subsetE
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( subset @ A @ B )
% 0.15/0.43 => ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subsetE2_type,type,
% 0.15/0.43 subsetE2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subsetE2,definition,
% 0.15/0.43 ( subsetE2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( subset @ A @ B )
% 0.15/0.43 => ( ~ ( in @ Xx @ B )
% 0.15/0.43 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(notsubsetI_type,type,
% 0.15/0.43 notsubsetI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(notsubsetI,definition,
% 0.15/0.43 ( notsubsetI
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ B )
% 0.15/0.43 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(notequalI1_type,type,
% 0.15/0.43 notequalI1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(notequalI1,definition,
% 0.15/0.43 ( notequalI1
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ~ ( subset @ A @ B )
% 0.15/0.43 => ( A != B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(notequalI2_type,type,
% 0.15/0.43 notequalI2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(notequalI2,definition,
% 0.15/0.43 ( notequalI2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ B )
% 0.15/0.43 => ( A != B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subsetRefl_type,type,
% 0.15/0.43 subsetRefl: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subsetRefl,definition,
% 0.15/0.43 ( subsetRefl
% 0.15/0.43 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subsetTrans_type,type,
% 0.15/0.43 subsetTrans: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subsetTrans,definition,
% 0.15/0.43 ( subsetTrans
% 0.15/0.43 = ( ! [A: $i,B: $i,C: $i] :
% 0.15/0.43 ( ( subset @ A @ B )
% 0.15/0.43 => ( ( subset @ B @ C )
% 0.15/0.43 => ( subset @ A @ C ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinSub_type,type,
% 0.15/0.43 setadjoinSub: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinSub,definition,
% 0.15/0.43 ( setadjoinSub
% 0.15/0.43 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinSub2_type,type,
% 0.15/0.43 setadjoinSub2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setadjoinSub2,definition,
% 0.15/0.43 ( setadjoinSub2
% 0.15/0.43 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.15/0.43 ( ( subset @ A @ B )
% 0.15/0.43 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subset2powerset_type,type,
% 0.15/0.43 subset2powerset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subset2powerset,definition,
% 0.15/0.43 ( subset2powerset
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( subset @ A @ B )
% 0.15/0.43 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setextsub_type,type,
% 0.15/0.43 setextsub: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setextsub,definition,
% 0.15/0.43 ( setextsub
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( subset @ A @ B )
% 0.15/0.43 => ( ( subset @ B @ A )
% 0.15/0.43 => ( A = B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(subsetemptysetimpeq_type,type,
% 0.15/0.43 subsetemptysetimpeq: $o ).
% 0.15/0.43
% 0.15/0.43 thf(subsetemptysetimpeq,definition,
% 0.15/0.43 ( subsetemptysetimpeq
% 0.15/0.43 = ( ! [A: $i] :
% 0.15/0.43 ( ( subset @ A @ emptyset )
% 0.15/0.43 => ( A = emptyset ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powersetI1_type,type,
% 0.15/0.43 powersetI1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powersetI1,definition,
% 0.15/0.43 ( powersetI1
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( subset @ B @ A )
% 0.15/0.43 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powersetE1_type,type,
% 0.15/0.43 powersetE1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powersetE1,definition,
% 0.15/0.43 ( powersetE1
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( in @ B @ ( powerset @ A ) )
% 0.15/0.43 => ( subset @ B @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(inPowerset_type,type,
% 0.15/0.43 inPowerset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(inPowerset,definition,
% 0.15/0.43 ( inPowerset
% 0.15/0.43 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(powersetsubset_type,type,
% 0.15/0.43 powersetsubset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(powersetsubset,definition,
% 0.15/0.43 ( powersetsubset
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( subset @ A @ B )
% 0.15/0.43 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(sepInPowerset_type,type,
% 0.15/0.43 sepInPowerset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(sepInPowerset,definition,
% 0.15/0.43 ( sepInPowerset
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( in
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 @ ( powerset @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(sepSubset_type,type,
% 0.15/0.43 sepSubset: $o ).
% 0.15/0.43
% 0.15/0.43 thf(sepSubset,definition,
% 0.15/0.43 ( sepSubset
% 0.15/0.43 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.43 ( subset
% 0.15/0.43 @ ( dsetconstr @ A
% 0.15/0.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.43 @ A ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunion_type,type,
% 0.15/0.43 binunion: $i > $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(binunionIL_type,type,
% 0.15/0.43 binunionIL: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionIL,definition,
% 0.15/0.43 ( binunionIL
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(upairset2IR_type,type,
% 0.15/0.43 upairset2IR: $o ).
% 0.15/0.43
% 0.15/0.43 thf(upairset2IR,definition,
% 0.15/0.43 ( upairset2IR
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunionIR_type,type,
% 0.15/0.43 binunionIR: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionIR,definition,
% 0.15/0.43 ( binunionIR
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunionEcases_type,type,
% 0.15/0.43 binunionEcases: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionEcases,definition,
% 0.15/0.43 ( binunionEcases
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.15/0.43 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.15/0.43 => ( ( ( in @ Xx @ A )
% 0.15/0.43 => Xphi )
% 0.15/0.43 => ( ( ( in @ Xx @ B )
% 0.15/0.43 => Xphi )
% 0.15/0.43 => Xphi ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunionE_type,type,
% 0.15/0.43 binunionE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionE,definition,
% 0.15/0.43 ( binunionE
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.15/0.43 => ( ( in @ Xx @ A )
% 0.15/0.43 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunionLsub_type,type,
% 0.15/0.43 binunionLsub: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionLsub,definition,
% 0.15/0.43 ( binunionLsub
% 0.15/0.43 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binunionRsub_type,type,
% 0.15/0.43 binunionRsub: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binunionRsub,definition,
% 0.15/0.43 ( binunionRsub
% 0.15/0.43 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersect_type,type,
% 0.15/0.43 binintersect: $i > $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectI_type,type,
% 0.15/0.43 binintersectI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectI,definition,
% 0.15/0.43 ( binintersectI
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectSubset5_type,type,
% 0.15/0.43 binintersectSubset5: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectSubset5,definition,
% 0.15/0.43 ( binintersectSubset5
% 0.15/0.43 = ( ! [A: $i,B: $i,C: $i] :
% 0.15/0.43 ( ( subset @ C @ A )
% 0.15/0.43 => ( ( subset @ C @ B )
% 0.15/0.43 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectEL_type,type,
% 0.15/0.43 binintersectEL: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectEL,definition,
% 0.15/0.43 ( binintersectEL
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.15/0.43 => ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectLsub_type,type,
% 0.15/0.43 binintersectLsub: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectLsub,definition,
% 0.15/0.43 ( binintersectLsub
% 0.15/0.43 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectSubset2_type,type,
% 0.15/0.43 binintersectSubset2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectSubset2,definition,
% 0.15/0.43 ( binintersectSubset2
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( subset @ A @ B )
% 0.15/0.43 => ( ( binintersect @ A @ B )
% 0.15/0.43 = A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectSubset3_type,type,
% 0.15/0.43 binintersectSubset3: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectSubset3,definition,
% 0.15/0.43 ( binintersectSubset3
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( ( binintersect @ A @ B )
% 0.15/0.43 = B )
% 0.15/0.43 => ( subset @ B @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectER_type,type,
% 0.15/0.43 binintersectER: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectER,definition,
% 0.15/0.43 ( binintersectER
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.15/0.43 => ( in @ Xx @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(disjointsetsI1_type,type,
% 0.15/0.43 disjointsetsI1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(disjointsetsI1,definition,
% 0.15/0.43 ( disjointsetsI1
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ~ ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 & ( in @ Xx @ B ) )
% 0.15/0.43 => ( ( binintersect @ A @ B )
% 0.15/0.43 = emptyset ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectRsub_type,type,
% 0.15/0.43 binintersectRsub: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectRsub,definition,
% 0.15/0.43 ( binintersectRsub
% 0.15/0.43 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectSubset4_type,type,
% 0.15/0.43 binintersectSubset4: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectSubset4,definition,
% 0.15/0.43 ( binintersectSubset4
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( subset @ B @ A )
% 0.15/0.43 => ( ( binintersect @ A @ B )
% 0.15/0.43 = B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectSubset1_type,type,
% 0.15/0.43 binintersectSubset1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(binintersectSubset1,definition,
% 0.15/0.43 ( binintersectSubset1
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( ( binintersect @ A @ B )
% 0.15/0.43 = A )
% 0.15/0.43 => ( subset @ A @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(bs114d_type,type,
% 0.15/0.43 bs114d: $o ).
% 0.15/0.43
% 0.15/0.43 thf(bs114d,definition,
% 0.15/0.43 ( bs114d
% 0.15/0.43 = ( ! [A: $i,B: $i,C: $i] :
% 0.15/0.43 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.15/0.43 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(regular_type,type,
% 0.15/0.43 regular: $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminus_type,type,
% 0.15/0.43 setminus: $i > $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(setminusI_type,type,
% 0.15/0.43 setminusI: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusI,definition,
% 0.15/0.43 ( setminusI
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setminusEL_type,type,
% 0.15/0.43 setminusEL: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusEL,definition,
% 0.15/0.43 ( setminusEL
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.15/0.43 => ( in @ Xx @ A ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setminusER_type,type,
% 0.15/0.43 setminusER: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusER,definition,
% 0.15/0.43 ( setminusER
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.15/0.43 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setminusSubset2_type,type,
% 0.15/0.43 setminusSubset2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusSubset2,definition,
% 0.15/0.43 ( setminusSubset2
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( subset @ A @ B )
% 0.15/0.43 => ( ( setminus @ A @ B )
% 0.15/0.43 = emptyset ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setminusERneg_type,type,
% 0.15/0.43 setminusERneg: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusERneg,definition,
% 0.15/0.43 ( setminusERneg
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.15/0.43 => ( ( in @ Xx @ A )
% 0.15/0.43 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setminusELneg_type,type,
% 0.15/0.43 setminusELneg: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusELneg,definition,
% 0.15/0.43 ( setminusELneg
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.15/0.43 => ( ~ ( in @ Xx @ B )
% 0.15/0.43 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setminusILneg_type,type,
% 0.15/0.43 setminusILneg: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusILneg,definition,
% 0.15/0.43 ( setminusILneg
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ~ ( in @ Xx @ A )
% 0.15/0.43 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setminusIRneg_type,type,
% 0.15/0.43 setminusIRneg: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusIRneg,definition,
% 0.15/0.43 ( setminusIRneg
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ B )
% 0.15/0.43 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setminusLsub_type,type,
% 0.15/0.43 setminusLsub: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusLsub,definition,
% 0.15/0.43 ( setminusLsub
% 0.15/0.43 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setminusSubset1_type,type,
% 0.15/0.43 setminusSubset1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setminusSubset1,definition,
% 0.15/0.43 ( setminusSubset1
% 0.15/0.43 = ( ! [A: $i,B: $i] :
% 0.15/0.43 ( ( ( setminus @ A @ B )
% 0.15/0.43 = emptyset )
% 0.15/0.43 => ( subset @ A @ B ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(symdiff_type,type,
% 0.15/0.43 symdiff: $i > $i > $i ).
% 0.15/0.43
% 0.15/0.43 thf(symdiffE_type,type,
% 0.15/0.43 symdiffE: $o ).
% 0.15/0.43
% 0.15/0.43 thf(symdiffE,definition,
% 0.15/0.43 ( symdiffE
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.15/0.43 => ! [Xphi: $o] :
% 0.15/0.43 ( ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ B )
% 0.15/0.43 => Xphi ) )
% 0.15/0.43 => ( ( ~ ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ B )
% 0.15/0.43 => Xphi ) )
% 0.15/0.43 => Xphi ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(symdiffI1_type,type,
% 0.15/0.43 symdiffI1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(symdiffI1,definition,
% 0.15/0.43 ( symdiffI1
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(symdiffI2_type,type,
% 0.15/0.43 symdiffI2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(symdiffI2,definition,
% 0.15/0.43 ( symdiffI2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ~ ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ B )
% 0.15/0.43 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(symdiffIneg1_type,type,
% 0.15/0.43 symdiffIneg1: $o ).
% 0.15/0.43
% 0.15/0.43 thf(symdiffIneg1,definition,
% 0.15/0.43 ( symdiffIneg1
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ A )
% 0.15/0.43 => ( ( in @ Xx @ B )
% 0.15/0.43 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(symdiffIneg2_type,type,
% 0.15/0.43 symdiffIneg2: $o ).
% 0.15/0.43
% 0.15/0.43 thf(symdiffIneg2,definition,
% 0.15/0.43 ( symdiffIneg2
% 0.15/0.43 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.43 ( ~ ( in @ Xx @ A )
% 0.15/0.43 => ( ~ ( in @ Xx @ B )
% 0.15/0.43 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(iskpair_type,type,
% 0.15/0.43 iskpair: $i > $o ).
% 0.15/0.43
% 0.15/0.43 thf(iskpair,definition,
% 0.15/0.43 ( iskpair
% 0.15/0.43 = ( ^ [A: $i] :
% 0.15/0.43 ? [Xx: $i] :
% 0.15/0.43 ( ( in @ Xx @ ( setunion @ A ) )
% 0.15/0.43 & ? [Xy: $i] :
% 0.15/0.43 ( ( in @ Xy @ ( setunion @ A ) )
% 0.15/0.43 & ( A
% 0.15/0.43 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(secondinupair_type,type,
% 0.15/0.43 secondinupair: $o ).
% 0.15/0.43
% 0.15/0.43 thf(secondinupair,definition,
% 0.15/0.43 ( secondinupair
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairIL_type,type,
% 0.15/0.43 setukpairIL: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairIL,definition,
% 0.15/0.43 ( setukpairIL
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairIR_type,type,
% 0.15/0.43 setukpairIR: $o ).
% 0.15/0.43
% 0.15/0.43 thf(setukpairIR,definition,
% 0.15/0.43 ( setukpairIR
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.15/0.43
% 0.15/0.43 thf(kpairiskpair_type,type,
% 0.15/0.43 kpairiskpair: $o ).
% 0.15/0.43
% 0.15/0.43 thf(kpairiskpair,definition,
% 0.15/0.43 ( kpairiskpair
% 0.15/0.43 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(kpair_type,type,
% 0.15/0.44 kpair: $i > $i > $i ).
% 0.15/0.44
% 0.15/0.44 thf(kpair,definition,
% 0.15/0.44 ( kpair
% 0.15/0.44 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(kpairp_type,type,
% 0.15/0.44 kpairp: $o ).
% 0.15/0.44
% 0.15/0.44 thf(kpairp,definition,
% 0.15/0.44 ( kpairp
% 0.15/0.44 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(cartprod_type,type,
% 0.15/0.44 cartprod: $i > $i > $i ).
% 0.15/0.44
% 0.15/0.44 thf(singletonsubset_type,type,
% 0.15/0.44 singletonsubset: $o ).
% 0.15/0.44
% 0.15/0.44 thf(singletonsubset,definition,
% 0.15/0.44 ( singletonsubset
% 0.15/0.44 = ( ! [A: $i,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(singletoninpowerset_type,type,
% 0.15/0.44 singletoninpowerset: $o ).
% 0.15/0.44
% 0.15/0.44 thf(singletoninpowerset,definition,
% 0.15/0.44 ( singletoninpowerset
% 0.15/0.44 = ( ! [A: $i,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(singletoninpowunion_type,type,
% 0.15/0.44 singletoninpowunion: $o ).
% 0.15/0.44
% 0.15/0.44 thf(singletoninpowunion,definition,
% 0.15/0.44 ( singletoninpowunion
% 0.15/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(upairset2E_type,type,
% 0.15/0.44 upairset2E: $o ).
% 0.15/0.44
% 0.15/0.44 thf(upairset2E,definition,
% 0.15/0.44 ( upairset2E
% 0.15/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.15/0.44 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.15/0.44 => ( ( Xz = Xx )
% 0.15/0.44 | ( Xz = Xy ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(upairsubunion_type,type,
% 0.15/0.44 upairsubunion: $o ).
% 0.15/0.44
% 0.15/0.44 thf(upairsubunion,definition,
% 0.15/0.44 ( upairsubunion
% 0.15/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ! [Xy: $i] :
% 0.15/0.44 ( ( in @ Xy @ B )
% 0.15/0.44 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(upairinpowunion_type,type,
% 0.15/0.44 upairinpowunion: $o ).
% 0.15/0.44
% 0.15/0.44 thf(upairinpowunion,definition,
% 0.15/0.44 ( upairinpowunion
% 0.15/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ! [Xy: $i] :
% 0.15/0.44 ( ( in @ Xy @ B )
% 0.15/0.44 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(ubforcartprodlem1_type,type,
% 0.15/0.44 ubforcartprodlem1: $o ).
% 0.15/0.44
% 0.15/0.44 thf(ubforcartprodlem1,definition,
% 0.15/0.44 ( ubforcartprodlem1
% 0.15/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ! [Xy: $i] :
% 0.15/0.44 ( ( in @ Xy @ B )
% 0.15/0.44 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(ubforcartprodlem2_type,type,
% 0.15/0.44 ubforcartprodlem2: $o ).
% 0.15/0.44
% 0.15/0.44 thf(ubforcartprodlem2,definition,
% 0.15/0.44 ( ubforcartprodlem2
% 0.15/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ! [Xy: $i] :
% 0.15/0.44 ( ( in @ Xy @ B )
% 0.15/0.44 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(ubforcartprodlem3_type,type,
% 0.15/0.44 ubforcartprodlem3: $o ).
% 0.15/0.44
% 0.15/0.44 thf(ubforcartprodlem3,definition,
% 0.15/0.44 ( ubforcartprodlem3
% 0.15/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ! [Xy: $i] :
% 0.15/0.44 ( ( in @ Xy @ B )
% 0.15/0.44 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(cartprodpairin_type,type,
% 0.15/0.44 cartprodpairin: $o ).
% 0.15/0.44
% 0.15/0.44 thf(cartprodpairin,definition,
% 0.15/0.44 ( cartprodpairin
% 0.15/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ! [Xy: $i] :
% 0.15/0.44 ( ( in @ Xy @ B )
% 0.15/0.44 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(cartprodmempair1_type,type,
% 0.15/0.44 cartprodmempair1: $o ).
% 0.15/0.44
% 0.15/0.44 thf(cartprodmempair1,definition,
% 0.15/0.44 ( cartprodmempair1
% 0.15/0.44 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.15/0.44 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.15/0.44 => ? [Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 & ? [Xy: $i] :
% 0.15/0.44 ( ( in @ Xy @ B )
% 0.15/0.44 & ( Xu
% 0.15/0.44 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(cartprodmempair_type,type,
% 0.15/0.44 cartprodmempair: $o ).
% 0.15/0.44
% 0.15/0.44 thf(cartprodmempair,definition,
% 0.15/0.44 ( cartprodmempair
% 0.15/0.44 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.15/0.44 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.15/0.44 => ( iskpair @ Xu ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(setunionE2_type,type,
% 0.15/0.44 setunionE2: $o ).
% 0.15/0.44
% 0.15/0.44 thf(setunionE2,definition,
% 0.15/0.44 ( setunionE2
% 0.15/0.44 = ( ! [A: $i,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.15/0.44 => ? [X: $i] :
% 0.15/0.44 ( ( in @ X @ A )
% 0.15/0.44 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(setunionsingleton1_type,type,
% 0.15/0.44 setunionsingleton1: $o ).
% 0.15/0.44
% 0.15/0.44 thf(setunionsingleton1,definition,
% 0.15/0.44 ( setunionsingleton1
% 0.15/0.44 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(setunionsingleton2_type,type,
% 0.15/0.44 setunionsingleton2: $o ).
% 0.15/0.44
% 0.15/0.44 thf(setunionsingleton2,definition,
% 0.15/0.44 ( setunionsingleton2
% 0.15/0.44 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(setunionsingleton_type,type,
% 0.15/0.44 setunionsingleton: $o ).
% 0.15/0.44
% 0.15/0.44 thf(setunionsingleton,definition,
% 0.15/0.44 ( setunionsingleton
% 0.15/0.44 = ( ! [Xx: $i] :
% 0.15/0.44 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.15/0.44 = Xx ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(singleton_type,type,
% 0.15/0.44 singleton: $i > $o ).
% 0.15/0.44
% 0.15/0.44 thf(singleton,definition,
% 0.15/0.44 ( singleton
% 0.15/0.44 = ( ^ [A: $i] :
% 0.15/0.44 ? [Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 & ( A
% 0.15/0.44 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(singletonprop_type,type,
% 0.15/0.44 singletonprop: $o ).
% 0.15/0.44
% 0.15/0.44 thf(singletonprop,definition,
% 0.15/0.44 ( singletonprop
% 0.15/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.44 ( ! [Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ! [Xy: $i] :
% 0.15/0.44 ( ( in @ Xy @ A )
% 0.15/0.44 => ( ( Xphi @ Xx )
% 0.15/0.44 => ( ( Xphi @ Xy )
% 0.15/0.44 => ( Xx = Xy ) ) ) ) )
% 0.15/0.44 => ( ? [Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 & ( Xphi @ Xx ) )
% 0.15/0.44 => ( singleton
% 0.15/0.44 @ ( dsetconstr @ A
% 0.15/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(ex1_type,type,
% 0.15/0.44 ex1: $i > ( $i > $o ) > $o ).
% 0.15/0.44
% 0.15/0.44 thf(ex1,definition,
% 0.15/0.44 ( ex1
% 0.15/0.44 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.15/0.44 ( singleton
% 0.15/0.44 @ ( dsetconstr @ A
% 0.15/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(ex1E1_type,type,
% 0.15/0.44 ex1E1: $o ).
% 0.15/0.44
% 0.15/0.44 thf(ex1E1,definition,
% 0.15/0.44 ( ex1E1
% 0.15/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.44 ( ( ex1 @ A
% 0.15/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.15/0.44 => ? [Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(ex1I_type,type,
% 0.15/0.44 ex1I: $o ).
% 0.15/0.44
% 0.15/0.44 thf(ex1I,definition,
% 0.15/0.44 ( ex1I
% 0.15/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ( ( Xphi @ Xx )
% 0.15/0.44 => ( ! [Xy: $i] :
% 0.15/0.44 ( ( in @ Xy @ A )
% 0.15/0.44 => ( ( Xphi @ Xy )
% 0.15/0.44 => ( Xy = Xx ) ) )
% 0.15/0.44 => ( ex1 @ A
% 0.15/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(ex1I2_type,type,
% 0.15/0.44 ex1I2: $o ).
% 0.15/0.44
% 0.15/0.44 thf(ex1I2,definition,
% 0.15/0.44 ( ex1I2
% 0.15/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.15/0.44 ( ! [Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 => ! [Xy: $i] :
% 0.15/0.44 ( ( in @ Xy @ A )
% 0.15/0.44 => ( ( Xphi @ Xx )
% 0.15/0.44 => ( ( Xphi @ Xy )
% 0.15/0.44 => ( Xx = Xy ) ) ) ) )
% 0.15/0.44 => ( ? [Xx: $i] :
% 0.15/0.44 ( ( in @ Xx @ A )
% 0.15/0.44 & ( Xphi @ Xx ) )
% 0.15/0.44 => ( ex1 @ A
% 0.15/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(singletonsuniq_type,type,
% 0.15/0.44 singletonsuniq: $o ).
% 0.15/0.44
% 0.15/0.44 thf(singletonsuniq,definition,
% 0.15/0.44 ( singletonsuniq
% 0.15/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.44 ( ( ( setadjoin @ Xx @ emptyset )
% 0.15/0.44 = ( setadjoin @ Xy @ emptyset ) )
% 0.15/0.44 => ( Xx = Xy ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(atmost1p_type,type,
% 0.15/0.44 atmost1p: $i > $o ).
% 0.15/0.44
% 0.15/0.44 thf(atleast2p_type,type,
% 0.15/0.44 atleast2p: $i > $o ).
% 0.15/0.44
% 0.15/0.44 thf(atmost2p_type,type,
% 0.15/0.44 atmost2p: $i > $o ).
% 0.15/0.44
% 0.15/0.44 thf(upairsetp_type,type,
% 0.15/0.44 upairsetp: $i > $o ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjL1_type,type,
% 0.15/0.44 setukpairinjL1: $o ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjL1,definition,
% 0.15/0.44 ( setukpairinjL1
% 0.15/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.15/0.44 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.15/0.44 => ( Xx = Xz ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(kfstsingleton_type,type,
% 0.15/0.44 kfstsingleton: $o ).
% 0.15/0.44
% 0.15/0.44 thf(kfstsingleton,definition,
% 0.15/0.44 ( kfstsingleton
% 0.15/0.44 = ( ! [Xu: $i] :
% 0.15/0.44 ( ( iskpair @ Xu )
% 0.15/0.44 => ( singleton
% 0.15/0.44 @ ( dsetconstr @ ( setunion @ Xu )
% 0.15/0.44 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(theprop_type,type,
% 0.15/0.44 theprop: $o ).
% 0.15/0.44
% 0.15/0.44 thf(theprop,definition,
% 0.15/0.44 ( theprop
% 0.15/0.44 = ( ! [X: $i] :
% 0.15/0.44 ( ( singleton @ X )
% 0.15/0.44 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(kfst_type,type,
% 0.15/0.44 kfst: $i > $i ).
% 0.15/0.44
% 0.15/0.44 thf(kfstpairEq_type,type,
% 0.15/0.44 kfstpairEq: $o ).
% 0.15/0.44
% 0.15/0.44 thf(kfstpairEq,definition,
% 0.15/0.44 ( kfstpairEq
% 0.15/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.44 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.15/0.44 = Xx ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(cartprodfstin_type,type,
% 0.15/0.44 cartprodfstin: $o ).
% 0.15/0.44
% 0.15/0.44 thf(cartprodfstin,definition,
% 0.15/0.44 ( cartprodfstin
% 0.15/0.44 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.15/0.44 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.15/0.44 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjL2_type,type,
% 0.15/0.44 setukpairinjL2: $o ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjL2,definition,
% 0.15/0.44 ( setukpairinjL2
% 0.15/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.15/0.44 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.15/0.44 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.15/0.44 => ( Xx = Xz ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjL_type,type,
% 0.15/0.44 setukpairinjL: $o ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjL,definition,
% 0.15/0.44 ( setukpairinjL
% 0.15/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.15/0.44 ( ( ( kpair @ Xx @ Xy )
% 0.15/0.44 = ( kpair @ Xz @ Xu ) )
% 0.15/0.44 => ( Xx = Xz ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjR11_type,type,
% 0.15/0.44 setukpairinjR11: $o ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjR11,definition,
% 0.15/0.44 ( setukpairinjR11
% 0.15/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.44 ( ( Xx = Xy )
% 0.15/0.44 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.15/0.44 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjR12_type,type,
% 0.15/0.44 setukpairinjR12: $o ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjR12,definition,
% 0.15/0.44 ( setukpairinjR12
% 0.15/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.15/0.44 ( ( Xx = Xy )
% 0.15/0.44 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.15/0.44 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 thf(setukpairinjR1,conjecture,
% 0.15/0.44 ( setextAx
% 0.15/0.44 => ( emptysetAx
% 0.15/0.44 => ( setadjoinAx
% 0.15/0.44 => ( powersetAx
% 0.15/0.44 => ( setunionAx
% 0.15/0.44 => ( omega0Ax
% 0.15/0.44 => ( omegaSAx
% 0.15/0.44 => ( omegaIndAx
% 0.15/0.44 => ( replAx
% 0.15/0.44 => ( foundationAx
% 0.15/0.44 => ( wellorderingAx
% 0.15/0.44 => ( descrp
% 0.15/0.44 => ( dsetconstrI
% 0.15/0.44 => ( dsetconstrEL
% 0.15/0.44 => ( dsetconstrER
% 0.15/0.44 => ( exuE1
% 0.15/0.44 => ( prop2setE
% 0.15/0.44 => ( emptysetE
% 0.15/0.44 => ( emptysetimpfalse
% 0.15/0.44 => ( notinemptyset
% 0.15/0.44 => ( exuE3e
% 0.15/0.44 => ( setext
% 0.15/0.44 => ( emptyI
% 0.15/0.44 => ( noeltsimpempty
% 0.15/0.44 => ( setbeta
% 0.15/0.44 => ( nonemptyE1
% 0.15/0.44 => ( nonemptyI
% 0.15/0.44 => ( nonemptyI1
% 0.15/0.44 => ( setadjoinIL
% 0.15/0.44 => ( emptyinunitempty
% 0.15/0.44 => ( setadjoinIR
% 0.15/0.44 => ( setadjoinE
% 0.15/0.44 => ( setadjoinOr
% 0.15/0.44 => ( setoftrueEq
% 0.15/0.44 => ( powersetI
% 0.15/0.44 => ( emptyinPowerset
% 0.15/0.44 => ( emptyInPowerset
% 0.15/0.44 => ( powersetE
% 0.15/0.44 => ( setunionI
% 0.15/0.44 => ( setunionE
% 0.15/0.44 => ( subPowSU
% 0.15/0.44 => ( exuE2
% 0.15/0.44 => ( nonemptyImpWitness
% 0.15/0.44 => ( uniqinunit
% 0.15/0.44 => ( notinsingleton
% 0.15/0.44 => ( eqinunit
% 0.15/0.44 => ( singletonsswitch
% 0.15/0.44 => ( upairsetE
% 0.15/0.44 => ( upairsetIL
% 0.15/0.44 => ( upairsetIR
% 0.15/0.44 => ( emptyE1
% 0.15/0.44 => ( vacuousDall
% 0.15/0.44 => ( quantDeMorgan1
% 0.15/0.44 => ( quantDeMorgan2
% 0.15/0.44 => ( quantDeMorgan3
% 0.15/0.44 => ( quantDeMorgan4
% 0.15/0.44 => ( prop2setI
% 0.15/0.44 => ( prop2set2propI
% 0.15/0.44 => ( notdexE
% 0.15/0.44 => ( notdallE
% 0.15/0.44 => ( exuI1
% 0.15/0.44 => ( exuI3
% 0.15/0.44 => ( exuI2
% 0.15/0.44 => ( inCongP
% 0.15/0.44 => ( in__Cong
% 0.15/0.44 => ( exuE3u
% 0.15/0.44 => ( exu__Cong
% 0.15/0.44 => ( emptyset__Cong
% 0.15/0.44 => ( setadjoin__Cong
% 0.15/0.44 => ( powerset__Cong
% 0.15/0.44 => ( setunion__Cong
% 0.15/0.44 => ( omega__Cong
% 0.15/0.44 => ( exuEu
% 0.15/0.44 => ( descr__Cong
% 0.15/0.44 => ( dsetconstr__Cong
% 0.15/0.44 => ( subsetI1
% 0.15/0.44 => ( eqimpsubset2
% 0.15/0.44 => ( eqimpsubset1
% 0.15/0.44 => ( subsetI2
% 0.15/0.44 => ( emptysetsubset
% 0.15/0.44 => ( subsetE
% 0.15/0.44 => ( subsetE2
% 0.15/0.44 => ( notsubsetI
% 0.15/0.44 => ( notequalI1
% 0.15/0.44 => ( notequalI2
% 0.15/0.44 => ( subsetRefl
% 0.15/0.44 => ( subsetTrans
% 0.15/0.44 => ( setadjoinSub
% 0.15/0.44 => ( setadjoinSub2
% 0.15/0.44 => ( subset2powerset
% 0.15/0.44 => ( setextsub
% 0.15/0.44 => ( subsetemptysetimpeq
% 0.15/0.44 => ( powersetI1
% 0.15/0.44 => ( powersetE1
% 0.15/0.44 => ( inPowerset
% 0.15/0.44 => ( powersetsubset
% 0.15/0.44 => ( sepInPowerset
% 0.15/0.44 => ( sepSubset
% 0.15/0.44 => ( binunionIL
% 0.15/0.44 => ( upairset2IR
% 0.15/0.44 => ( binunionIR
% 0.15/0.44 => ( binunionEcases
% 0.15/0.44 => ( binunionE
% 0.15/0.44 => ( binunionLsub
% 0.15/0.44 => ( binunionRsub
% 0.15/0.44 => ( binintersectI
% 0.15/0.44 => ( binintersectSubset5
% 0.15/0.44 => ( binintersectEL
% 0.15/0.44 => ( binintersectLsub
% 0.15/0.44 => ( binintersectSubset2
% 0.15/0.44 => ( binintersectSubset3
% 0.15/0.44 => ( binintersectER
% 0.15/0.44 => ( disjointsetsI1
% 0.15/0.44 => ( binintersectRsub
% 0.15/0.44 => ( binintersectSubset4
% 0.15/0.44 => ( binintersectSubset1
% 0.15/0.44 => ( bs114d
% 0.15/0.44 => ( setminusI
% 0.15/0.44 => ( setminusEL
% 0.15/0.44 => ( setminusER
% 0.15/0.44 => ( setminusSubset2
% 0.15/0.44 => ( setminusERneg
% 0.15/0.44 => ( setminusELneg
% 0.15/0.44 => ( setminusILneg
% 0.15/0.44 => ( setminusIRneg
% 0.15/0.44 => ( setminusLsub
% 0.15/0.44 => ( setminusSubset1
% 0.15/0.44 => ( symdiffE
% 0.15/0.44 => ( symdiffI1
% 0.15/0.44 => ( symdiffI2
% 0.15/0.44 => ( symdiffIneg1
% 0.15/0.44 => ( symdiffIneg2
% 0.15/0.44 => ( secondinupair
% 0.15/0.44 => ( setukpairIL
% 0.15/0.44 => ( setukpairIR
% 0.15/0.44 => ( kpairiskpair
% 0.15/0.44 => ( kpairp
% 0.15/0.44 => ( singletonsubset
% 0.15/0.44 => ( singletoninpowerset
% 0.15/0.44 => ( singletoninpowunion
% 0.15/0.44 => ( upairset2E
% 0.15/0.44 => ( upairsubunion
% 0.15/0.44 => ( upairinpowunion
% 0.15/0.44 => ( ubforcartprodlem1
% 0.15/0.44 => ( ubforcartprodlem2
% 0.15/0.44 => ( ubforcartprodlem3
% 0.15/0.44 => ( cartprodpairin
% 0.15/0.44 => ( cartprodmempair1
% 0.15/0.44 => ( cartprodmempair
% 0.15/0.44 => ( setunionE2
% 0.15/0.44 => ( setunionsingleton1
% 0.15/0.44 => ( setunionsingleton2
% 0.15/0.44 => ( setunionsingleton
% 0.15/0.44 => ( singletonprop
% 0.15/0.44 => ( ex1E1
% 0.15/0.44 => ( ex1I
% 0.15/0.44 => ( ex1I2
% 0.15/0.44 => ( singletonsuniq
% 0.15/0.44 => ( setukpairinjL1
% 0.15/0.44 => ( kfstsingleton
% 0.15/0.44 => ( theprop
% 0.15/0.44 => ( kfstpairEq
% 0.15/0.44 => ( cartprodfstin
% 0.15/0.44 => ( setukpairinjL2
% 0.15/0.44 => ( setukpairinjL
% 0.15/0.44 => ( setukpairinjR11
% 0.15/0.44 => ( setukpairinjR12
% 0.15/0.44 => ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 0.15/0.44 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 0.15/0.44 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 0.15/0.44 => ( ( Xz = Xu )
% 0.15/0.44 => ( Xy = Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.15/0.44
% 0.15/0.44 %------------------------------------------------------------------------------
% 0.15/0.44 ------------------------
% 2.35/1.34 ---- Embedded in THF ---
% 2.35/1.34 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.35/1.34 %%% Generated on Tue Feb 24 12:30:06 EST 2026
% 2.35/1.34 %%% using '$$dhol' embedding, version 1.3.0.
% 2.35/1.34 %%% Logic specification used:
% 2.35/1.34 %%% thf(spec, logic, $$dhol).
% 2.35/1.34
% 2.35/1.34 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2DTF26106.p
% See solution above
% 2.35/1.34 ------------------------
% 2.35/1.37 ---- Cleaned THF ---
% 2.35/1.37 thf(in_type,type,
% 2.35/1.37 in: $i > $i > $o ).
% 2.35/1.37
% 2.35/1.37 thf(exu_type,type,
% 2.35/1.37 exu: ( $i > $o ) > $o ).
% 2.35/1.37
% 2.35/1.37 thf(exu,definition,
% 2.35/1.37 ( exu
% 2.35/1.37 = ( ^ [Xphi: $i > $o] :
% 2.35/1.37 ? [Xx: $i] :
% 2.35/1.37 ( ( Xphi @ Xx )
% 2.35/1.37 & ! [Xy: $i] :
% 2.35/1.37 ( ( Xphi @ Xy )
% 2.35/1.37 => ( Xx = Xy ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setextAx_type,type,
% 2.35/1.37 setextAx: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setextAx,definition,
% 2.35/1.37 ( setextAx
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 <=> ( in @ Xx @ B ) )
% 2.35/1.37 => ( A = B ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(emptyset_type,type,
% 2.35/1.37 emptyset: $i ).
% 2.35/1.37
% 2.35/1.37 thf(emptysetAx_type,type,
% 2.35/1.37 emptysetAx: $o ).
% 2.35/1.37
% 2.35/1.37 thf(emptysetAx,definition,
% 2.35/1.37 ( emptysetAx
% 2.35/1.37 = ( ! [Xx: $i] :
% 2.35/1.37 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoin_type,type,
% 2.35/1.37 setadjoin: $i > $i > $i ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinAx_type,type,
% 2.35/1.37 setadjoinAx: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinAx,definition,
% 2.35/1.37 ( setadjoinAx
% 2.35/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.35/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.35/1.37 <=> ( ( Xy = Xx )
% 2.35/1.37 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(powerset_type,type,
% 2.35/1.37 powerset: $i > $i ).
% 2.35/1.37
% 2.35/1.37 thf(powersetAx_type,type,
% 2.35/1.37 powersetAx: $o ).
% 2.35/1.37
% 2.35/1.37 thf(powersetAx,definition,
% 2.35/1.37 ( powersetAx
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( in @ B @ ( powerset @ A ) )
% 2.35/1.37 <=> ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ B )
% 2.35/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setunion_type,type,
% 2.35/1.37 setunion: $i > $i ).
% 2.35/1.37
% 2.35/1.37 thf(setunionAx_type,type,
% 2.35/1.37 setunionAx: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setunionAx,definition,
% 2.35/1.37 ( setunionAx
% 2.35/1.37 = ( ! [A: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ ( setunion @ A ) )
% 2.35/1.37 <=> ? [B: $i] :
% 2.35/1.37 ( ( in @ Xx @ B )
% 2.35/1.37 & ( in @ B @ A ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(omega_type,type,
% 2.35/1.37 omega: $i ).
% 2.35/1.37
% 2.35/1.37 thf(omega0Ax_type,type,
% 2.35/1.37 omega0Ax: $o ).
% 2.35/1.37
% 2.35/1.37 thf(omega0Ax,definition,
% 2.35/1.37 ( omega0Ax
% 2.35/1.37 = ( in @ emptyset @ omega ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(omegaSAx_type,type,
% 2.35/1.37 omegaSAx: $o ).
% 2.35/1.37
% 2.35/1.37 thf(omegaSAx,definition,
% 2.35/1.37 ( omegaSAx
% 2.35/1.37 = ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ omega )
% 2.35/1.37 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(omegaIndAx_type,type,
% 2.35/1.37 omegaIndAx: $o ).
% 2.35/1.37
% 2.35/1.37 thf(omegaIndAx,definition,
% 2.35/1.37 ( omegaIndAx
% 2.35/1.37 = ( ! [A: $i] :
% 2.35/1.37 ( ( ( in @ emptyset @ A )
% 2.35/1.37 & ! [Xx: $i] :
% 2.35/1.37 ( ( ( in @ Xx @ omega )
% 2.35/1.37 & ( in @ Xx @ A ) )
% 2.35/1.37 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.35/1.37 => ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ omega )
% 2.35/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(replAx_type,type,
% 2.35/1.37 replAx: $o ).
% 2.35/1.37
% 2.35/1.37 thf(replAx,definition,
% 2.35/1.37 ( replAx
% 2.35/1.37 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.35/1.37 ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( exu
% 2.35/1.37 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.35/1.37 => ? [B: $i] :
% 2.35/1.37 ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ B )
% 2.35/1.37 <=> ? [Xy: $i] :
% 2.35/1.37 ( ( in @ Xy @ A )
% 2.35/1.37 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(foundationAx_type,type,
% 2.35/1.37 foundationAx: $o ).
% 2.35/1.37
% 2.35/1.37 thf(foundationAx,definition,
% 2.35/1.37 ( foundationAx
% 2.35/1.37 = ( ! [A: $i] :
% 2.35/1.37 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.35/1.37 => ? [B: $i] :
% 2.35/1.37 ( ( in @ B @ A )
% 2.35/1.37 & ~ ? [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ B )
% 2.35/1.37 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(wellorderingAx_type,type,
% 2.35/1.37 wellorderingAx: $o ).
% 2.35/1.37
% 2.35/1.37 thf(wellorderingAx,definition,
% 2.35/1.37 ( wellorderingAx
% 2.35/1.37 = ( ! [A: $i] :
% 2.35/1.37 ? [B: $i] :
% 2.35/1.37 ( ! [C: $i] :
% 2.35/1.37 ( ( in @ C @ B )
% 2.35/1.37 => ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ C )
% 2.35/1.37 => ( in @ Xx @ A ) ) )
% 2.35/1.37 & ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( ( in @ Xx @ A )
% 2.35/1.37 & ( in @ Xy @ A ) )
% 2.35/1.37 => ( ! [C: $i] :
% 2.35/1.37 ( ( in @ C @ B )
% 2.35/1.37 => ( ( in @ Xx @ C )
% 2.35/1.37 <=> ( in @ Xy @ C ) ) )
% 2.35/1.37 => ( Xx = Xy ) ) )
% 2.35/1.37 & ! [C: $i,D: $i] :
% 2.35/1.37 ( ( ( in @ C @ B )
% 2.35/1.37 & ( in @ D @ B ) )
% 2.35/1.37 => ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ C )
% 2.35/1.37 => ( in @ Xx @ D ) )
% 2.35/1.37 | ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ D )
% 2.35/1.37 => ( in @ Xx @ C ) ) ) )
% 2.35/1.37 & ! [C: $i] :
% 2.35/1.37 ( ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ C )
% 2.35/1.37 => ( in @ Xx @ A ) )
% 2.35/1.37 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.35/1.37 => ? [D: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ D @ B )
% 2.35/1.37 & ( in @ Xx @ C )
% 2.35/1.37 & ~ ? [Xy: $i] :
% 2.35/1.37 ( ( in @ Xy @ D )
% 2.35/1.37 & ( in @ Xy @ C ) )
% 2.35/1.37 & ! [E: $i] :
% 2.35/1.37 ( ( in @ E @ B )
% 2.35/1.37 => ( ! [Xy: $i] :
% 2.35/1.37 ( ( in @ Xy @ E )
% 2.35/1.37 => ( in @ Xy @ D ) )
% 2.35/1.37 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(descr_type,type,
% 2.35/1.37 descr: ( $i > $o ) > $i ).
% 2.35/1.37
% 2.35/1.37 thf(descrp_type,type,
% 2.35/1.37 descrp: $o ).
% 2.35/1.37
% 2.35/1.37 thf(descrp,definition,
% 2.35/1.37 ( descrp
% 2.35/1.37 = ( ! [Xphi: $i > $o] :
% 2.35/1.37 ( ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 => ( Xphi
% 2.35/1.37 @ ( descr
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(dsetconstr_type,type,
% 2.35/1.37 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.35/1.37
% 2.35/1.37 thf(dsetconstrI_type,type,
% 2.35/1.37 dsetconstrI: $o ).
% 2.35/1.37
% 2.35/1.37 thf(dsetconstrI,definition,
% 2.35/1.37 ( dsetconstrI
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( ( Xphi @ Xx )
% 2.35/1.37 => ( in @ Xx
% 2.35/1.37 @ ( dsetconstr @ A
% 2.35/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(dsetconstrEL_type,type,
% 2.35/1.37 dsetconstrEL: $o ).
% 2.35/1.37
% 2.35/1.37 thf(dsetconstrEL,definition,
% 2.35/1.37 ( dsetconstrEL
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx
% 2.35/1.37 @ ( dsetconstr @ A
% 2.35/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.35/1.37 => ( in @ Xx @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(dsetconstrER_type,type,
% 2.35/1.37 dsetconstrER: $o ).
% 2.35/1.37
% 2.35/1.37 thf(dsetconstrER,definition,
% 2.35/1.37 ( dsetconstrER
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx
% 2.35/1.37 @ ( dsetconstr @ A
% 2.35/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.35/1.37 => ( Xphi @ Xx ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(exuE1_type,type,
% 2.35/1.37 exuE1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(exuE1,definition,
% 2.35/1.37 ( exuE1
% 2.35/1.37 = ( ! [Xphi: $i > $o] :
% 2.35/1.37 ( ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 => ? [Xx: $i] :
% 2.35/1.37 ( ( Xphi @ Xx )
% 2.35/1.37 & ! [Xy: $i] :
% 2.35/1.37 ( ( Xphi @ Xy )
% 2.35/1.37 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(prop2set_type,type,
% 2.35/1.37 prop2set: $o > $i ).
% 2.35/1.37
% 2.35/1.37 thf(prop2setE_type,type,
% 2.35/1.37 prop2setE: $o ).
% 2.35/1.37
% 2.35/1.37 thf(prop2setE,definition,
% 2.35/1.37 ( prop2setE
% 2.35/1.37 = ( ! [Xphi: $o,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.35/1.37 => Xphi ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(emptysetE_type,type,
% 2.35/1.37 emptysetE: $o ).
% 2.35/1.37
% 2.35/1.37 thf(emptysetE,definition,
% 2.35/1.37 ( emptysetE
% 2.35/1.37 = ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ emptyset )
% 2.35/1.37 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(emptysetimpfalse_type,type,
% 2.35/1.37 emptysetimpfalse: $o ).
% 2.35/1.37
% 2.35/1.37 thf(emptysetimpfalse,definition,
% 2.35/1.37 ( emptysetimpfalse
% 2.35/1.37 = ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ emptyset )
% 2.35/1.37 => $false ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(notinemptyset_type,type,
% 2.35/1.37 notinemptyset: $o ).
% 2.35/1.37
% 2.35/1.37 thf(notinemptyset,definition,
% 2.35/1.37 ( notinemptyset
% 2.35/1.37 = ( ! [Xx: $i] :
% 2.35/1.37 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(exuE3e_type,type,
% 2.35/1.37 exuE3e: $o ).
% 2.35/1.37
% 2.35/1.37 thf(exuE3e,definition,
% 2.35/1.37 ( exuE3e
% 2.35/1.37 = ( ! [Xphi: $i > $o] :
% 2.35/1.37 ( ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setext_type,type,
% 2.35/1.37 setext: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setext,definition,
% 2.35/1.37 ( setext
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( in @ Xx @ B ) )
% 2.35/1.37 => ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ B )
% 2.35/1.37 => ( in @ Xx @ A ) )
% 2.35/1.37 => ( A = B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(emptyI_type,type,
% 2.35/1.37 emptyI: $o ).
% 2.35/1.37
% 2.35/1.37 thf(emptyI,definition,
% 2.35/1.37 ( emptyI
% 2.35/1.37 = ( ! [A: $i] :
% 2.35/1.37 ( ! [Xx: $i] :
% 2.35/1.37 ~ ( in @ Xx @ A )
% 2.35/1.37 => ( A = emptyset ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(noeltsimpempty_type,type,
% 2.35/1.37 noeltsimpempty: $o ).
% 2.35/1.37
% 2.35/1.37 thf(noeltsimpempty,definition,
% 2.35/1.37 ( noeltsimpempty
% 2.35/1.37 = ( ! [A: $i] :
% 2.35/1.37 ( ! [Xx: $i] :
% 2.35/1.37 ~ ( in @ Xx @ A )
% 2.35/1.37 => ( A = emptyset ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setbeta_type,type,
% 2.35/1.37 setbeta: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setbeta,definition,
% 2.35/1.37 ( setbeta
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( ( in @ Xx
% 2.35/1.37 @ ( dsetconstr @ A
% 2.35/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.35/1.37 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(nonempty_type,type,
% 2.35/1.37 nonempty: $i > $o ).
% 2.35/1.37
% 2.35/1.37 thf(nonempty,definition,
% 2.35/1.37 ( nonempty
% 2.35/1.37 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(nonemptyE1_type,type,
% 2.35/1.37 nonemptyE1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(nonemptyE1,definition,
% 2.35/1.37 ( nonemptyE1
% 2.35/1.37 = ( ! [A: $i] :
% 2.35/1.37 ( ( nonempty @ A )
% 2.35/1.37 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(nonemptyI_type,type,
% 2.35/1.37 nonemptyI: $o ).
% 2.35/1.37
% 2.35/1.37 thf(nonemptyI,definition,
% 2.35/1.37 ( nonemptyI
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( ( Xphi @ Xx )
% 2.35/1.37 => ( nonempty
% 2.35/1.37 @ ( dsetconstr @ A
% 2.35/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(nonemptyI1_type,type,
% 2.35/1.37 nonemptyI1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(nonemptyI1,definition,
% 2.35/1.37 ( nonemptyI1
% 2.35/1.37 = ( ! [A: $i] :
% 2.35/1.37 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.35/1.37 => ( nonempty @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinIL_type,type,
% 2.35/1.37 setadjoinIL: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinIL,definition,
% 2.35/1.37 ( setadjoinIL
% 2.35/1.37 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(emptyinunitempty_type,type,
% 2.35/1.37 emptyinunitempty: $o ).
% 2.35/1.37
% 2.35/1.37 thf(emptyinunitempty,definition,
% 2.35/1.37 ( emptyinunitempty
% 2.35/1.37 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinIR_type,type,
% 2.35/1.37 setadjoinIR: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinIR,definition,
% 2.35/1.37 ( setadjoinIR
% 2.35/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.35/1.37 ( ( in @ Xy @ A )
% 2.35/1.37 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinE_type,type,
% 2.35/1.37 setadjoinE: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinE,definition,
% 2.35/1.37 ( setadjoinE
% 2.35/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.35/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.35/1.37 => ! [Xphi: $o] :
% 2.35/1.37 ( ( ( Xy = Xx )
% 2.35/1.37 => Xphi )
% 2.35/1.37 => ( ( ( in @ Xy @ A )
% 2.35/1.37 => Xphi )
% 2.35/1.37 => Xphi ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinOr_type,type,
% 2.35/1.37 setadjoinOr: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinOr,definition,
% 2.35/1.37 ( setadjoinOr
% 2.35/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.35/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.35/1.37 => ( ( Xy = Xx )
% 2.35/1.37 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setoftrueEq_type,type,
% 2.35/1.37 setoftrueEq: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setoftrueEq,definition,
% 2.35/1.37 ( setoftrueEq
% 2.35/1.37 = ( ! [A: $i] :
% 2.35/1.37 ( ( dsetconstr @ A
% 2.35/1.37 @ ^ [Xx: $i] : $true )
% 2.35/1.37 = A ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(powersetI_type,type,
% 2.35/1.37 powersetI: $o ).
% 2.35/1.37
% 2.35/1.37 thf(powersetI,definition,
% 2.35/1.37 ( powersetI
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ B )
% 2.35/1.37 => ( in @ Xx @ A ) )
% 2.35/1.37 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(emptyinPowerset_type,type,
% 2.35/1.37 emptyinPowerset: $o ).
% 2.35/1.37
% 2.35/1.37 thf(emptyinPowerset,definition,
% 2.35/1.37 ( emptyinPowerset
% 2.35/1.37 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(emptyInPowerset_type,type,
% 2.35/1.37 emptyInPowerset: $o ).
% 2.35/1.37
% 2.35/1.37 thf(emptyInPowerset,definition,
% 2.35/1.37 ( emptyInPowerset
% 2.35/1.37 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(powersetE_type,type,
% 2.35/1.37 powersetE: $o ).
% 2.35/1.37
% 2.35/1.37 thf(powersetE,definition,
% 2.35/1.37 ( powersetE
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ B @ ( powerset @ A ) )
% 2.35/1.37 => ( ( in @ Xx @ B )
% 2.35/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setunionI_type,type,
% 2.35/1.37 setunionI: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setunionI,definition,
% 2.35/1.37 ( setunionI
% 2.35/1.37 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.35/1.37 ( ( in @ Xx @ B )
% 2.35/1.37 => ( ( in @ B @ A )
% 2.35/1.37 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setunionE_type,type,
% 2.35/1.37 setunionE: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setunionE,definition,
% 2.35/1.37 ( setunionE
% 2.35/1.37 = ( ! [A: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ ( setunion @ A ) )
% 2.35/1.37 => ! [Xphi: $o] :
% 2.35/1.37 ( ! [B: $i] :
% 2.35/1.37 ( ( in @ Xx @ B )
% 2.35/1.37 => ( ( in @ B @ A )
% 2.35/1.37 => Xphi ) )
% 2.35/1.37 => Xphi ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(subPowSU_type,type,
% 2.35/1.37 subPowSU: $o ).
% 2.35/1.37
% 2.35/1.37 thf(subPowSU,definition,
% 2.35/1.37 ( subPowSU
% 2.35/1.37 = ( ! [A: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(exuE2_type,type,
% 2.35/1.37 exuE2: $o ).
% 2.35/1.37
% 2.35/1.37 thf(exuE2,definition,
% 2.35/1.37 ( exuE2
% 2.35/1.37 = ( ! [Xphi: $i > $o] :
% 2.35/1.37 ( ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 => ? [Xx: $i] :
% 2.35/1.37 ! [Xy: $i] :
% 2.35/1.37 ( ( Xphi @ Xy )
% 2.35/1.37 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(nonemptyImpWitness_type,type,
% 2.35/1.37 nonemptyImpWitness: $o ).
% 2.35/1.37
% 2.35/1.37 thf(nonemptyImpWitness,definition,
% 2.35/1.37 ( nonemptyImpWitness
% 2.35/1.37 = ( ! [A: $i] :
% 2.35/1.37 ( ( nonempty @ A )
% 2.35/1.37 => ? [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 & $true ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(uniqinunit_type,type,
% 2.35/1.37 uniqinunit: $o ).
% 2.35/1.37
% 2.35/1.37 thf(uniqinunit,definition,
% 2.35/1.37 ( uniqinunit
% 2.35/1.37 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.35/1.37 => ( Xx = Xy ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(notinsingleton_type,type,
% 2.35/1.37 notinsingleton: $o ).
% 2.35/1.37
% 2.35/1.37 thf(notinsingleton,definition,
% 2.35/1.37 ( notinsingleton
% 2.35/1.37 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( Xx != Xy )
% 2.35/1.37 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(eqinunit_type,type,
% 2.35/1.37 eqinunit: $o ).
% 2.35/1.37
% 2.35/1.37 thf(eqinunit,definition,
% 2.35/1.37 ( eqinunit
% 2.35/1.37 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( Xx = Xy )
% 2.35/1.37 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(singletonsswitch_type,type,
% 2.35/1.37 singletonsswitch: $o ).
% 2.35/1.37
% 2.35/1.37 thf(singletonsswitch,definition,
% 2.35/1.37 ( singletonsswitch
% 2.35/1.37 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.35/1.37 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(upairsetE_type,type,
% 2.35/1.37 upairsetE: $o ).
% 2.35/1.37
% 2.35/1.37 thf(upairsetE,definition,
% 2.35/1.37 ( upairsetE
% 2.35/1.37 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.35/1.37 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.35/1.37 => ( ( Xz = Xx )
% 2.35/1.37 | ( Xz = Xy ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(upairsetIL_type,type,
% 2.35/1.37 upairsetIL: $o ).
% 2.35/1.37
% 2.35/1.37 thf(upairsetIL,definition,
% 2.35/1.37 ( upairsetIL
% 2.35/1.37 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(upairsetIR_type,type,
% 2.35/1.37 upairsetIR: $o ).
% 2.35/1.37
% 2.35/1.37 thf(upairsetIR,definition,
% 2.35/1.37 ( upairsetIR
% 2.35/1.37 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(emptyE1_type,type,
% 2.35/1.37 emptyE1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(emptyE1,definition,
% 2.35/1.37 ( emptyE1
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.37 ( ? [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 & ( Xphi @ Xx ) )
% 2.35/1.37 => ( ( ( dsetconstr @ A
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 = emptyset )
% 2.35/1.37 => $false ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(vacuousDall_type,type,
% 2.35/1.37 vacuousDall: $o ).
% 2.35/1.37
% 2.35/1.37 thf(vacuousDall,definition,
% 2.35/1.37 ( vacuousDall
% 2.35/1.37 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ emptyset )
% 2.35/1.37 => ( Xphi @ Xx ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(quantDeMorgan1_type,type,
% 2.35/1.37 quantDeMorgan1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(quantDeMorgan1,definition,
% 2.35/1.37 ( quantDeMorgan1
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.37 ( ~ ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( Xphi @ Xx ) )
% 2.35/1.37 => ? [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(quantDeMorgan2_type,type,
% 2.35/1.37 quantDeMorgan2: $o ).
% 2.35/1.37
% 2.35/1.37 thf(quantDeMorgan2,definition,
% 2.35/1.37 ( quantDeMorgan2
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.37 ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ~ ( Xphi @ Xx ) )
% 2.35/1.37 => ~ ? [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(quantDeMorgan3_type,type,
% 2.35/1.37 quantDeMorgan3: $o ).
% 2.35/1.37
% 2.35/1.37 thf(quantDeMorgan3,definition,
% 2.35/1.37 ( quantDeMorgan3
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.37 ( ~ ? [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 & ( Xphi @ Xx ) )
% 2.35/1.37 => ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(quantDeMorgan4_type,type,
% 2.35/1.37 quantDeMorgan4: $o ).
% 2.35/1.37
% 2.35/1.37 thf(quantDeMorgan4,definition,
% 2.35/1.37 ( quantDeMorgan4
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.37 ( ? [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 & ~ ( Xphi @ Xx ) )
% 2.35/1.37 => ~ ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(prop2setI_type,type,
% 2.35/1.37 prop2setI: $o ).
% 2.35/1.37
% 2.35/1.37 thf(prop2setI,definition,
% 2.35/1.37 ( prop2setI
% 2.35/1.37 = ( ! [Xphi: $o] :
% 2.35/1.37 ( Xphi
% 2.35/1.37 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(set2prop_type,type,
% 2.35/1.37 set2prop: $i > $o ).
% 2.35/1.37
% 2.35/1.37 thf(prop2set2propI_type,type,
% 2.35/1.37 prop2set2propI: $o ).
% 2.35/1.37
% 2.35/1.37 thf(prop2set2propI,definition,
% 2.35/1.37 ( prop2set2propI
% 2.35/1.37 = ( ! [Xphi: $o] :
% 2.35/1.37 ( Xphi
% 2.35/1.37 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(notdexE_type,type,
% 2.35/1.37 notdexE: $o ).
% 2.35/1.37
% 2.35/1.37 thf(notdexE,definition,
% 2.35/1.37 ( notdexE
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.37 ( ~ ? [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 & ( Xphi @ Xx ) )
% 2.35/1.37 => ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(notdallE_type,type,
% 2.35/1.37 notdallE: $o ).
% 2.35/1.37
% 2.35/1.37 thf(notdallE,definition,
% 2.35/1.37 ( notdallE
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.37 ( ~ ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( Xphi @ Xx ) )
% 2.35/1.37 => ? [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(exuI1_type,type,
% 2.35/1.37 exuI1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(exuI1,definition,
% 2.35/1.37 ( exuI1
% 2.35/1.37 = ( ! [Xphi: $i > $o] :
% 2.35/1.37 ( ? [Xx: $i] :
% 2.35/1.37 ( ( Xphi @ Xx )
% 2.35/1.37 & ! [Xy: $i] :
% 2.35/1.37 ( ( Xphi @ Xy )
% 2.35/1.37 => ( Xx = Xy ) ) )
% 2.35/1.37 => ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(exuI3_type,type,
% 2.35/1.37 exuI3: $o ).
% 2.35/1.37
% 2.35/1.37 thf(exuI3,definition,
% 2.35/1.37 ( exuI3
% 2.35/1.37 = ( ! [Xphi: $i > $o] :
% 2.35/1.37 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.35/1.37 => ( ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( Xphi @ Xx )
% 2.35/1.37 => ( ( Xphi @ Xy )
% 2.35/1.37 => ( Xx = Xy ) ) )
% 2.35/1.37 => ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(exuI2_type,type,
% 2.35/1.37 exuI2: $o ).
% 2.35/1.37
% 2.35/1.37 thf(exuI2,definition,
% 2.35/1.37 ( exuI2
% 2.35/1.37 = ( ! [Xphi: $i > $o] :
% 2.35/1.37 ( ? [Xx: $i] :
% 2.35/1.37 ! [Xy: $i] :
% 2.35/1.37 ( ( Xphi @ Xy )
% 2.35/1.37 <=> ( Xy = Xx ) )
% 2.35/1.37 => ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(inCongP_type,type,
% 2.35/1.37 inCongP: $o ).
% 2.35/1.37
% 2.35/1.37 thf(inCongP,definition,
% 2.35/1.37 ( inCongP
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( A = B )
% 2.35/1.37 => ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( Xx = Xy )
% 2.35/1.37 => ( ( in @ Xx @ A )
% 2.35/1.37 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(in__Cong_type,type,
% 2.35/1.37 in__Cong: $o ).
% 2.35/1.37
% 2.35/1.37 thf(in__Cong,definition,
% 2.35/1.37 ( in__Cong
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( A = B )
% 2.35/1.37 => ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( Xx = Xy )
% 2.35/1.37 => ( ( in @ Xx @ A )
% 2.35/1.37 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(exuE3u_type,type,
% 2.35/1.37 exuE3u: $o ).
% 2.35/1.37
% 2.35/1.37 thf(exuE3u,definition,
% 2.35/1.37 ( exuE3u
% 2.35/1.37 = ( ! [Xphi: $i > $o] :
% 2.35/1.37 ( ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 => ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( Xphi @ Xx )
% 2.35/1.37 => ( ( Xphi @ Xy )
% 2.35/1.37 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(exu__Cong_type,type,
% 2.35/1.37 exu__Cong: $o ).
% 2.35/1.37
% 2.35/1.37 thf(exu__Cong,definition,
% 2.35/1.37 ( exu__Cong
% 2.35/1.37 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.35/1.37 ( ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( Xx = Xy )
% 2.35/1.37 => ( ( Xphi @ Xx )
% 2.35/1.37 <=> ( Xpsi @ Xy ) ) )
% 2.35/1.37 => ( ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 <=> ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(emptyset__Cong_type,type,
% 2.35/1.37 emptyset__Cong: $o ).
% 2.35/1.37
% 2.35/1.37 thf(emptyset__Cong,definition,
% 2.35/1.37 ( emptyset__Cong
% 2.35/1.37 = ( emptyset = emptyset ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoin__Cong_type,type,
% 2.35/1.37 setadjoin__Cong: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoin__Cong,definition,
% 2.35/1.37 ( setadjoin__Cong
% 2.35/1.37 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( Xx = Xy )
% 2.35/1.37 => ! [Xz: $i,Xu: $i] :
% 2.35/1.37 ( ( Xz = Xu )
% 2.35/1.37 => ( ( setadjoin @ Xx @ Xz )
% 2.35/1.37 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(powerset__Cong_type,type,
% 2.35/1.37 powerset__Cong: $o ).
% 2.35/1.37
% 2.35/1.37 thf(powerset__Cong,definition,
% 2.35/1.37 ( powerset__Cong
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( A = B )
% 2.35/1.37 => ( ( powerset @ A )
% 2.35/1.37 = ( powerset @ B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setunion__Cong_type,type,
% 2.35/1.37 setunion__Cong: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setunion__Cong,definition,
% 2.35/1.37 ( setunion__Cong
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( A = B )
% 2.35/1.37 => ( ( setunion @ A )
% 2.35/1.37 = ( setunion @ B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(omega__Cong_type,type,
% 2.35/1.37 omega__Cong: $o ).
% 2.35/1.37
% 2.35/1.37 thf(omega__Cong,definition,
% 2.35/1.37 ( omega__Cong
% 2.35/1.37 = ( omega = omega ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(exuEu_type,type,
% 2.35/1.37 exuEu: $o ).
% 2.35/1.37
% 2.35/1.37 thf(exuEu,definition,
% 2.35/1.37 ( exuEu
% 2.35/1.37 = ( ! [Xphi: $i > $o] :
% 2.35/1.37 ( ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 => ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( Xphi @ Xx )
% 2.35/1.37 => ( ( Xphi @ Xy )
% 2.35/1.37 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(descr__Cong_type,type,
% 2.35/1.37 descr__Cong: $o ).
% 2.35/1.37
% 2.35/1.37 thf(descr__Cong,definition,
% 2.35/1.37 ( descr__Cong
% 2.35/1.37 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.35/1.37 ( ! [Xx: $i,Xy: $i] :
% 2.35/1.37 ( ( Xx = Xy )
% 2.35/1.37 => ( ( Xphi @ Xx )
% 2.35/1.37 <=> ( Xpsi @ Xy ) ) )
% 2.35/1.37 => ( ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 => ( ( exu
% 2.35/1.37 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.35/1.37 => ( ( descr
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 = ( descr
% 2.35/1.37 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(dsetconstr__Cong_type,type,
% 2.35/1.37 dsetconstr__Cong: $o ).
% 2.35/1.37
% 2.35/1.37 thf(dsetconstr__Cong,definition,
% 2.35/1.37 ( dsetconstr__Cong
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( A = B )
% 2.35/1.37 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.35/1.37 ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ! [Xy: $i] :
% 2.35/1.37 ( ( in @ Xy @ B )
% 2.35/1.37 => ( ( Xx = Xy )
% 2.35/1.37 => ( ( Xphi @ Xx )
% 2.35/1.37 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.35/1.37 => ( ( dsetconstr @ A
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 = ( dsetconstr @ B
% 2.35/1.37 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(subset_type,type,
% 2.35/1.37 subset: $i > $i > $o ).
% 2.35/1.37
% 2.35/1.37 thf(disjoint_type,type,
% 2.35/1.37 disjoint: $i > $i > $o ).
% 2.35/1.37
% 2.35/1.37 thf(setsmeet_type,type,
% 2.35/1.37 setsmeet: $i > $i > $o ).
% 2.35/1.37
% 2.35/1.37 thf(subsetI1_type,type,
% 2.35/1.37 subsetI1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(subsetI1,definition,
% 2.35/1.37 ( subsetI1
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( in @ Xx @ B ) )
% 2.35/1.37 => ( subset @ A @ B ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(eqimpsubset2_type,type,
% 2.35/1.37 eqimpsubset2: $o ).
% 2.35/1.37
% 2.35/1.37 thf(eqimpsubset2,definition,
% 2.35/1.37 ( eqimpsubset2
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( A = B )
% 2.35/1.37 => ( subset @ B @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(eqimpsubset1_type,type,
% 2.35/1.37 eqimpsubset1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(eqimpsubset1,definition,
% 2.35/1.37 ( eqimpsubset1
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( A = B )
% 2.35/1.37 => ( subset @ A @ B ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(subsetI2_type,type,
% 2.35/1.37 subsetI2: $o ).
% 2.35/1.37
% 2.35/1.37 thf(subsetI2,definition,
% 2.35/1.37 ( subsetI2
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ! [Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( in @ Xx @ B ) )
% 2.35/1.37 => ( subset @ A @ B ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(emptysetsubset_type,type,
% 2.35/1.37 emptysetsubset: $o ).
% 2.35/1.37
% 2.35/1.37 thf(emptysetsubset,definition,
% 2.35/1.37 ( emptysetsubset
% 2.35/1.37 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(subsetE_type,type,
% 2.35/1.37 subsetE: $o ).
% 2.35/1.37
% 2.35/1.37 thf(subsetE,definition,
% 2.35/1.37 ( subsetE
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( subset @ A @ B )
% 2.35/1.37 => ( ( in @ Xx @ A )
% 2.35/1.37 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(subsetE2_type,type,
% 2.35/1.37 subsetE2: $o ).
% 2.35/1.37
% 2.35/1.37 thf(subsetE2,definition,
% 2.35/1.37 ( subsetE2
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( subset @ A @ B )
% 2.35/1.37 => ( ~ ( in @ Xx @ B )
% 2.35/1.37 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(notsubsetI_type,type,
% 2.35/1.37 notsubsetI: $o ).
% 2.35/1.37
% 2.35/1.37 thf(notsubsetI,definition,
% 2.35/1.37 ( notsubsetI
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( ~ ( in @ Xx @ B )
% 2.35/1.37 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(notequalI1_type,type,
% 2.35/1.37 notequalI1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(notequalI1,definition,
% 2.35/1.37 ( notequalI1
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ~ ( subset @ A @ B )
% 2.35/1.37 => ( A != B ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(notequalI2_type,type,
% 2.35/1.37 notequalI2: $o ).
% 2.35/1.37
% 2.35/1.37 thf(notequalI2,definition,
% 2.35/1.37 ( notequalI2
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( ~ ( in @ Xx @ B )
% 2.35/1.37 => ( A != B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(subsetRefl_type,type,
% 2.35/1.37 subsetRefl: $o ).
% 2.35/1.37
% 2.35/1.37 thf(subsetRefl,definition,
% 2.35/1.37 ( subsetRefl
% 2.35/1.37 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(subsetTrans_type,type,
% 2.35/1.37 subsetTrans: $o ).
% 2.35/1.37
% 2.35/1.37 thf(subsetTrans,definition,
% 2.35/1.37 ( subsetTrans
% 2.35/1.37 = ( ! [A: $i,B: $i,C: $i] :
% 2.35/1.37 ( ( subset @ A @ B )
% 2.35/1.37 => ( ( subset @ B @ C )
% 2.35/1.37 => ( subset @ A @ C ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinSub_type,type,
% 2.35/1.37 setadjoinSub: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinSub,definition,
% 2.35/1.37 ( setadjoinSub
% 2.35/1.37 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinSub2_type,type,
% 2.35/1.37 setadjoinSub2: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setadjoinSub2,definition,
% 2.35/1.37 ( setadjoinSub2
% 2.35/1.37 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.35/1.37 ( ( subset @ A @ B )
% 2.35/1.37 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(subset2powerset_type,type,
% 2.35/1.37 subset2powerset: $o ).
% 2.35/1.37
% 2.35/1.37 thf(subset2powerset,definition,
% 2.35/1.37 ( subset2powerset
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( subset @ A @ B )
% 2.35/1.37 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(setextsub_type,type,
% 2.35/1.37 setextsub: $o ).
% 2.35/1.37
% 2.35/1.37 thf(setextsub,definition,
% 2.35/1.37 ( setextsub
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( subset @ A @ B )
% 2.35/1.37 => ( ( subset @ B @ A )
% 2.35/1.37 => ( A = B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(subsetemptysetimpeq_type,type,
% 2.35/1.37 subsetemptysetimpeq: $o ).
% 2.35/1.37
% 2.35/1.37 thf(subsetemptysetimpeq,definition,
% 2.35/1.37 ( subsetemptysetimpeq
% 2.35/1.37 = ( ! [A: $i] :
% 2.35/1.37 ( ( subset @ A @ emptyset )
% 2.35/1.37 => ( A = emptyset ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(powersetI1_type,type,
% 2.35/1.37 powersetI1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(powersetI1,definition,
% 2.35/1.37 ( powersetI1
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( subset @ B @ A )
% 2.35/1.37 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(powersetE1_type,type,
% 2.35/1.37 powersetE1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(powersetE1,definition,
% 2.35/1.37 ( powersetE1
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( in @ B @ ( powerset @ A ) )
% 2.35/1.37 => ( subset @ B @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(inPowerset_type,type,
% 2.35/1.37 inPowerset: $o ).
% 2.35/1.37
% 2.35/1.37 thf(inPowerset,definition,
% 2.35/1.37 ( inPowerset
% 2.35/1.37 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(powersetsubset_type,type,
% 2.35/1.37 powersetsubset: $o ).
% 2.35/1.37
% 2.35/1.37 thf(powersetsubset,definition,
% 2.35/1.37 ( powersetsubset
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( subset @ A @ B )
% 2.35/1.37 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(sepInPowerset_type,type,
% 2.35/1.37 sepInPowerset: $o ).
% 2.35/1.37
% 2.35/1.37 thf(sepInPowerset,definition,
% 2.35/1.37 ( sepInPowerset
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.37 ( in
% 2.35/1.37 @ ( dsetconstr @ A
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 @ ( powerset @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(sepSubset_type,type,
% 2.35/1.37 sepSubset: $o ).
% 2.35/1.37
% 2.35/1.37 thf(sepSubset,definition,
% 2.35/1.37 ( sepSubset
% 2.35/1.37 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.37 ( subset
% 2.35/1.37 @ ( dsetconstr @ A
% 2.35/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.37 @ A ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binunion_type,type,
% 2.35/1.37 binunion: $i > $i > $i ).
% 2.35/1.37
% 2.35/1.37 thf(binunionIL_type,type,
% 2.35/1.37 binunionIL: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binunionIL,definition,
% 2.35/1.37 ( binunionIL
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(upairset2IR_type,type,
% 2.35/1.37 upairset2IR: $o ).
% 2.35/1.37
% 2.35/1.37 thf(upairset2IR,definition,
% 2.35/1.37 ( upairset2IR
% 2.35/1.37 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binunionIR_type,type,
% 2.35/1.37 binunionIR: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binunionIR,definition,
% 2.35/1.37 ( binunionIR
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ B )
% 2.35/1.37 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binunionEcases_type,type,
% 2.35/1.37 binunionEcases: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binunionEcases,definition,
% 2.35/1.37 ( binunionEcases
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.35/1.37 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.35/1.37 => ( ( ( in @ Xx @ A )
% 2.35/1.37 => Xphi )
% 2.35/1.37 => ( ( ( in @ Xx @ B )
% 2.35/1.37 => Xphi )
% 2.35/1.37 => Xphi ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binunionE_type,type,
% 2.35/1.37 binunionE: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binunionE,definition,
% 2.35/1.37 ( binunionE
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.35/1.37 => ( ( in @ Xx @ A )
% 2.35/1.37 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binunionLsub_type,type,
% 2.35/1.37 binunionLsub: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binunionLsub,definition,
% 2.35/1.37 ( binunionLsub
% 2.35/1.37 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binunionRsub_type,type,
% 2.35/1.37 binunionRsub: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binunionRsub,definition,
% 2.35/1.37 ( binunionRsub
% 2.35/1.37 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binintersect_type,type,
% 2.35/1.37 binintersect: $i > $i > $i ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectI_type,type,
% 2.35/1.37 binintersectI: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectI,definition,
% 2.35/1.37 ( binintersectI
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ A )
% 2.35/1.37 => ( ( in @ Xx @ B )
% 2.35/1.37 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectSubset5_type,type,
% 2.35/1.37 binintersectSubset5: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectSubset5,definition,
% 2.35/1.37 ( binintersectSubset5
% 2.35/1.37 = ( ! [A: $i,B: $i,C: $i] :
% 2.35/1.37 ( ( subset @ C @ A )
% 2.35/1.37 => ( ( subset @ C @ B )
% 2.35/1.37 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectEL_type,type,
% 2.35/1.37 binintersectEL: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectEL,definition,
% 2.35/1.37 ( binintersectEL
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.35/1.37 => ( in @ Xx @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectLsub_type,type,
% 2.35/1.37 binintersectLsub: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectLsub,definition,
% 2.35/1.37 ( binintersectLsub
% 2.35/1.37 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectSubset2_type,type,
% 2.35/1.37 binintersectSubset2: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectSubset2,definition,
% 2.35/1.37 ( binintersectSubset2
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( subset @ A @ B )
% 2.35/1.37 => ( ( binintersect @ A @ B )
% 2.35/1.37 = A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectSubset3_type,type,
% 2.35/1.37 binintersectSubset3: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectSubset3,definition,
% 2.35/1.37 ( binintersectSubset3
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.37 ( ( ( binintersect @ A @ B )
% 2.35/1.37 = B )
% 2.35/1.37 => ( subset @ B @ A ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectER_type,type,
% 2.35/1.37 binintersectER: $o ).
% 2.35/1.37
% 2.35/1.37 thf(binintersectER,definition,
% 2.35/1.37 ( binintersectER
% 2.35/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.37 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.35/1.37 => ( in @ Xx @ B ) ) ) ) ).
% 2.35/1.37
% 2.35/1.37 thf(disjointsetsI1_type,type,
% 2.35/1.37 disjointsetsI1: $o ).
% 2.35/1.37
% 2.35/1.37 thf(disjointsetsI1,definition,
% 2.35/1.37 ( disjointsetsI1
% 2.35/1.37 = ( ! [A: $i,B: $i] :
% 2.35/1.38 ( ~ ? [Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 & ( in @ Xx @ B ) )
% 2.35/1.38 => ( ( binintersect @ A @ B )
% 2.35/1.38 = emptyset ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(binintersectRsub_type,type,
% 2.35/1.38 binintersectRsub: $o ).
% 2.35/1.38
% 2.35/1.38 thf(binintersectRsub,definition,
% 2.35/1.38 ( binintersectRsub
% 2.35/1.38 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(binintersectSubset4_type,type,
% 2.35/1.38 binintersectSubset4: $o ).
% 2.35/1.38
% 2.35/1.38 thf(binintersectSubset4,definition,
% 2.35/1.38 ( binintersectSubset4
% 2.35/1.38 = ( ! [A: $i,B: $i] :
% 2.35/1.38 ( ( subset @ B @ A )
% 2.35/1.38 => ( ( binintersect @ A @ B )
% 2.35/1.38 = B ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(binintersectSubset1_type,type,
% 2.35/1.38 binintersectSubset1: $o ).
% 2.35/1.38
% 2.35/1.38 thf(binintersectSubset1,definition,
% 2.35/1.38 ( binintersectSubset1
% 2.35/1.38 = ( ! [A: $i,B: $i] :
% 2.35/1.38 ( ( ( binintersect @ A @ B )
% 2.35/1.38 = A )
% 2.35/1.38 => ( subset @ A @ B ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(bs114d_type,type,
% 2.35/1.38 bs114d: $o ).
% 2.35/1.38
% 2.35/1.38 thf(bs114d,definition,
% 2.35/1.38 ( bs114d
% 2.35/1.38 = ( ! [A: $i,B: $i,C: $i] :
% 2.35/1.38 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.35/1.38 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(regular_type,type,
% 2.35/1.38 regular: $i > $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminus_type,type,
% 2.35/1.38 setminus: $i > $i > $i ).
% 2.35/1.38
% 2.35/1.38 thf(setminusI_type,type,
% 2.35/1.38 setminusI: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminusI,definition,
% 2.35/1.38 ( setminusI
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ( ~ ( in @ Xx @ B )
% 2.35/1.38 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setminusEL_type,type,
% 2.35/1.38 setminusEL: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminusEL,definition,
% 2.35/1.38 ( setminusEL
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.35/1.38 => ( in @ Xx @ A ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setminusER_type,type,
% 2.35/1.38 setminusER: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminusER,definition,
% 2.35/1.38 ( setminusER
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.35/1.38 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setminusSubset2_type,type,
% 2.35/1.38 setminusSubset2: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminusSubset2,definition,
% 2.35/1.38 ( setminusSubset2
% 2.35/1.38 = ( ! [A: $i,B: $i] :
% 2.35/1.38 ( ( subset @ A @ B )
% 2.35/1.38 => ( ( setminus @ A @ B )
% 2.35/1.38 = emptyset ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setminusERneg_type,type,
% 2.35/1.38 setminusERneg: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminusERneg,definition,
% 2.35/1.38 ( setminusERneg
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.35/1.38 => ( ( in @ Xx @ A )
% 2.35/1.38 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setminusELneg_type,type,
% 2.35/1.38 setminusELneg: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminusELneg,definition,
% 2.35/1.38 ( setminusELneg
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.35/1.38 => ( ~ ( in @ Xx @ B )
% 2.35/1.38 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setminusILneg_type,type,
% 2.35/1.38 setminusILneg: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminusILneg,definition,
% 2.35/1.38 ( setminusILneg
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ~ ( in @ Xx @ A )
% 2.35/1.38 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setminusIRneg_type,type,
% 2.35/1.38 setminusIRneg: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminusIRneg,definition,
% 2.35/1.38 ( setminusIRneg
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ B )
% 2.35/1.38 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setminusLsub_type,type,
% 2.35/1.38 setminusLsub: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminusLsub,definition,
% 2.35/1.38 ( setminusLsub
% 2.35/1.38 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setminusSubset1_type,type,
% 2.35/1.38 setminusSubset1: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setminusSubset1,definition,
% 2.35/1.38 ( setminusSubset1
% 2.35/1.38 = ( ! [A: $i,B: $i] :
% 2.35/1.38 ( ( ( setminus @ A @ B )
% 2.35/1.38 = emptyset )
% 2.35/1.38 => ( subset @ A @ B ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(symdiff_type,type,
% 2.35/1.38 symdiff: $i > $i > $i ).
% 2.35/1.38
% 2.35/1.38 thf(symdiffE_type,type,
% 2.35/1.38 symdiffE: $o ).
% 2.35/1.38
% 2.35/1.38 thf(symdiffE,definition,
% 2.35/1.38 ( symdiffE
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.35/1.38 => ! [Xphi: $o] :
% 2.35/1.38 ( ( ( in @ Xx @ A )
% 2.35/1.38 => ( ~ ( in @ Xx @ B )
% 2.35/1.38 => Xphi ) )
% 2.35/1.38 => ( ( ~ ( in @ Xx @ A )
% 2.35/1.38 => ( ( in @ Xx @ B )
% 2.35/1.38 => Xphi ) )
% 2.35/1.38 => Xphi ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(symdiffI1_type,type,
% 2.35/1.38 symdiffI1: $o ).
% 2.35/1.38
% 2.35/1.38 thf(symdiffI1,definition,
% 2.35/1.38 ( symdiffI1
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ( ~ ( in @ Xx @ B )
% 2.35/1.38 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(symdiffI2_type,type,
% 2.35/1.38 symdiffI2: $o ).
% 2.35/1.38
% 2.35/1.38 thf(symdiffI2,definition,
% 2.35/1.38 ( symdiffI2
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ~ ( in @ Xx @ A )
% 2.35/1.38 => ( ( in @ Xx @ B )
% 2.35/1.38 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(symdiffIneg1_type,type,
% 2.35/1.38 symdiffIneg1: $o ).
% 2.35/1.38
% 2.35/1.38 thf(symdiffIneg1,definition,
% 2.35/1.38 ( symdiffIneg1
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ( ( in @ Xx @ B )
% 2.35/1.38 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(symdiffIneg2_type,type,
% 2.35/1.38 symdiffIneg2: $o ).
% 2.35/1.38
% 2.35/1.38 thf(symdiffIneg2,definition,
% 2.35/1.38 ( symdiffIneg2
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ~ ( in @ Xx @ A )
% 2.35/1.38 => ( ~ ( in @ Xx @ B )
% 2.35/1.38 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(iskpair_type,type,
% 2.35/1.38 iskpair: $i > $o ).
% 2.35/1.38
% 2.35/1.38 thf(iskpair,definition,
% 2.35/1.38 ( iskpair
% 2.35/1.38 = ( ^ [A: $i] :
% 2.35/1.38 ? [Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ ( setunion @ A ) )
% 2.35/1.38 & ? [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ ( setunion @ A ) )
% 2.35/1.38 & ( A
% 2.35/1.38 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(secondinupair_type,type,
% 2.35/1.38 secondinupair: $o ).
% 2.35/1.38
% 2.35/1.38 thf(secondinupair,definition,
% 2.35/1.38 ( secondinupair
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairIL_type,type,
% 2.35/1.38 setukpairIL: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairIL,definition,
% 2.35/1.38 ( setukpairIL
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairIR_type,type,
% 2.35/1.38 setukpairIR: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairIR,definition,
% 2.35/1.38 ( setukpairIR
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(kpairiskpair_type,type,
% 2.35/1.38 kpairiskpair: $o ).
% 2.35/1.38
% 2.35/1.38 thf(kpairiskpair,definition,
% 2.35/1.38 ( kpairiskpair
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(kpair_type,type,
% 2.35/1.38 kpair: $i > $i > $i ).
% 2.35/1.38
% 2.35/1.38 thf(kpair,definition,
% 2.35/1.38 ( kpair
% 2.35/1.38 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(kpairp_type,type,
% 2.35/1.38 kpairp: $o ).
% 2.35/1.38
% 2.35/1.38 thf(kpairp,definition,
% 2.35/1.38 ( kpairp
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(cartprod_type,type,
% 2.35/1.38 cartprod: $i > $i > $i ).
% 2.35/1.38
% 2.35/1.38 thf(singletonsubset_type,type,
% 2.35/1.38 singletonsubset: $o ).
% 2.35/1.38
% 2.35/1.38 thf(singletonsubset,definition,
% 2.35/1.38 ( singletonsubset
% 2.35/1.38 = ( ! [A: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(singletoninpowerset_type,type,
% 2.35/1.38 singletoninpowerset: $o ).
% 2.35/1.38
% 2.35/1.38 thf(singletoninpowerset,definition,
% 2.35/1.38 ( singletoninpowerset
% 2.35/1.38 = ( ! [A: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(singletoninpowunion_type,type,
% 2.35/1.38 singletoninpowunion: $o ).
% 2.35/1.38
% 2.35/1.38 thf(singletoninpowunion,definition,
% 2.35/1.38 ( singletoninpowunion
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(upairset2E_type,type,
% 2.35/1.38 upairset2E: $o ).
% 2.35/1.38
% 2.35/1.38 thf(upairset2E,definition,
% 2.35/1.38 ( upairset2E
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.35/1.38 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.35/1.38 => ( ( Xz = Xx )
% 2.35/1.38 | ( Xz = Xy ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(upairsubunion_type,type,
% 2.35/1.38 upairsubunion: $o ).
% 2.35/1.38
% 2.35/1.38 thf(upairsubunion,definition,
% 2.35/1.38 ( upairsubunion
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ! [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ B )
% 2.35/1.38 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(upairinpowunion_type,type,
% 2.35/1.38 upairinpowunion: $o ).
% 2.35/1.38
% 2.35/1.38 thf(upairinpowunion,definition,
% 2.35/1.38 ( upairinpowunion
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ! [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ B )
% 2.35/1.38 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(ubforcartprodlem1_type,type,
% 2.35/1.38 ubforcartprodlem1: $o ).
% 2.35/1.38
% 2.35/1.38 thf(ubforcartprodlem1,definition,
% 2.35/1.38 ( ubforcartprodlem1
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ! [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ B )
% 2.35/1.38 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(ubforcartprodlem2_type,type,
% 2.35/1.38 ubforcartprodlem2: $o ).
% 2.35/1.38
% 2.35/1.38 thf(ubforcartprodlem2,definition,
% 2.35/1.38 ( ubforcartprodlem2
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ! [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ B )
% 2.35/1.38 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(ubforcartprodlem3_type,type,
% 2.35/1.38 ubforcartprodlem3: $o ).
% 2.35/1.38
% 2.35/1.38 thf(ubforcartprodlem3,definition,
% 2.35/1.38 ( ubforcartprodlem3
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ! [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ B )
% 2.35/1.38 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(cartprodpairin_type,type,
% 2.35/1.38 cartprodpairin: $o ).
% 2.35/1.38
% 2.35/1.38 thf(cartprodpairin,definition,
% 2.35/1.38 ( cartprodpairin
% 2.35/1.38 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ! [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ B )
% 2.35/1.38 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(cartprodmempair1_type,type,
% 2.35/1.38 cartprodmempair1: $o ).
% 2.35/1.38
% 2.35/1.38 thf(cartprodmempair1,definition,
% 2.35/1.38 ( cartprodmempair1
% 2.35/1.38 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.35/1.38 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.35/1.38 => ? [Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 & ? [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ B )
% 2.35/1.38 & ( Xu
% 2.35/1.38 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(cartprodmempair_type,type,
% 2.35/1.38 cartprodmempair: $o ).
% 2.35/1.38
% 2.35/1.38 thf(cartprodmempair,definition,
% 2.35/1.38 ( cartprodmempair
% 2.35/1.38 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.35/1.38 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.35/1.38 => ( iskpair @ Xu ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setunionE2_type,type,
% 2.35/1.38 setunionE2: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setunionE2,definition,
% 2.35/1.38 ( setunionE2
% 2.35/1.38 = ( ! [A: $i,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ ( setunion @ A ) )
% 2.35/1.38 => ? [X: $i] :
% 2.35/1.38 ( ( in @ X @ A )
% 2.35/1.38 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setunionsingleton1_type,type,
% 2.35/1.38 setunionsingleton1: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setunionsingleton1,definition,
% 2.35/1.38 ( setunionsingleton1
% 2.35/1.38 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setunionsingleton2_type,type,
% 2.35/1.38 setunionsingleton2: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setunionsingleton2,definition,
% 2.35/1.38 ( setunionsingleton2
% 2.35/1.38 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setunionsingleton_type,type,
% 2.35/1.38 setunionsingleton: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setunionsingleton,definition,
% 2.35/1.38 ( setunionsingleton
% 2.35/1.38 = ( ! [Xx: $i] :
% 2.35/1.38 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.35/1.38 = Xx ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(singleton_type,type,
% 2.35/1.38 singleton: $i > $o ).
% 2.35/1.38
% 2.35/1.38 thf(singleton,definition,
% 2.35/1.38 ( singleton
% 2.35/1.38 = ( ^ [A: $i] :
% 2.35/1.38 ? [Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 & ( A
% 2.35/1.38 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(singletonprop_type,type,
% 2.35/1.38 singletonprop: $o ).
% 2.35/1.38
% 2.35/1.38 thf(singletonprop,definition,
% 2.35/1.38 ( singletonprop
% 2.35/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.38 ( ! [Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ! [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ A )
% 2.35/1.38 => ( ( Xphi @ Xx )
% 2.35/1.38 => ( ( Xphi @ Xy )
% 2.35/1.38 => ( Xx = Xy ) ) ) ) )
% 2.35/1.38 => ( ? [Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 & ( Xphi @ Xx ) )
% 2.35/1.38 => ( singleton
% 2.35/1.38 @ ( dsetconstr @ A
% 2.35/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(ex1_type,type,
% 2.35/1.38 ex1: $i > ( $i > $o ) > $o ).
% 2.35/1.38
% 2.35/1.38 thf(ex1,definition,
% 2.35/1.38 ( ex1
% 2.35/1.38 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.35/1.38 ( singleton
% 2.35/1.38 @ ( dsetconstr @ A
% 2.35/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(ex1E1_type,type,
% 2.35/1.38 ex1E1: $o ).
% 2.35/1.38
% 2.35/1.38 thf(ex1E1,definition,
% 2.35/1.38 ( ex1E1
% 2.35/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.38 ( ( ex1 @ A
% 2.35/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.35/1.38 => ? [Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(ex1I_type,type,
% 2.35/1.38 ex1I: $o ).
% 2.35/1.38
% 2.35/1.38 thf(ex1I,definition,
% 2.35/1.38 ( ex1I
% 2.35/1.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ( ( Xphi @ Xx )
% 2.35/1.38 => ( ! [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ A )
% 2.35/1.38 => ( ( Xphi @ Xy )
% 2.35/1.38 => ( Xy = Xx ) ) )
% 2.35/1.38 => ( ex1 @ A
% 2.35/1.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(ex1I2_type,type,
% 2.35/1.38 ex1I2: $o ).
% 2.35/1.38
% 2.35/1.38 thf(ex1I2,definition,
% 2.35/1.38 ( ex1I2
% 2.35/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 2.35/1.38 ( ! [Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 => ! [Xy: $i] :
% 2.35/1.38 ( ( in @ Xy @ A )
% 2.35/1.38 => ( ( Xphi @ Xx )
% 2.35/1.38 => ( ( Xphi @ Xy )
% 2.35/1.38 => ( Xx = Xy ) ) ) ) )
% 2.35/1.38 => ( ? [Xx: $i] :
% 2.35/1.38 ( ( in @ Xx @ A )
% 2.35/1.38 & ( Xphi @ Xx ) )
% 2.35/1.38 => ( ex1 @ A
% 2.35/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(singletonsuniq_type,type,
% 2.35/1.38 singletonsuniq: $o ).
% 2.35/1.38
% 2.35/1.38 thf(singletonsuniq,definition,
% 2.35/1.38 ( singletonsuniq
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.38 ( ( ( setadjoin @ Xx @ emptyset )
% 2.35/1.38 = ( setadjoin @ Xy @ emptyset ) )
% 2.35/1.38 => ( Xx = Xy ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(atmost1p_type,type,
% 2.35/1.38 atmost1p: $i > $o ).
% 2.35/1.38
% 2.35/1.38 thf(atleast2p_type,type,
% 2.35/1.38 atleast2p: $i > $o ).
% 2.35/1.38
% 2.35/1.38 thf(atmost2p_type,type,
% 2.35/1.38 atmost2p: $i > $o ).
% 2.35/1.38
% 2.35/1.38 thf(upairsetp_type,type,
% 2.35/1.38 upairsetp: $i > $o ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjL1_type,type,
% 2.35/1.38 setukpairinjL1: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjL1,definition,
% 2.35/1.38 ( setukpairinjL1
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.35/1.38 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.35/1.38 => ( Xx = Xz ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(kfstsingleton_type,type,
% 2.35/1.38 kfstsingleton: $o ).
% 2.35/1.38
% 2.35/1.38 thf(kfstsingleton,definition,
% 2.35/1.38 ( kfstsingleton
% 2.35/1.38 = ( ! [Xu: $i] :
% 2.35/1.38 ( ( iskpair @ Xu )
% 2.35/1.38 => ( singleton
% 2.35/1.38 @ ( dsetconstr @ ( setunion @ Xu )
% 2.35/1.38 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(theprop_type,type,
% 2.35/1.38 theprop: $o ).
% 2.35/1.38
% 2.35/1.38 thf(theprop,definition,
% 2.35/1.38 ( theprop
% 2.35/1.38 = ( ! [X: $i] :
% 2.35/1.38 ( ( singleton @ X )
% 2.35/1.38 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(kfst_type,type,
% 2.35/1.38 kfst: $i > $i ).
% 2.35/1.38
% 2.35/1.38 thf(kfstpairEq_type,type,
% 2.35/1.38 kfstpairEq: $o ).
% 2.35/1.38
% 2.35/1.38 thf(kfstpairEq,definition,
% 2.35/1.38 ( kfstpairEq
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.38 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.35/1.38 = Xx ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(cartprodfstin_type,type,
% 2.35/1.38 cartprodfstin: $o ).
% 2.35/1.38
% 2.35/1.38 thf(cartprodfstin,definition,
% 2.35/1.38 ( cartprodfstin
% 2.35/1.38 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.35/1.38 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.35/1.38 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjL2_type,type,
% 2.35/1.38 setukpairinjL2: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjL2,definition,
% 2.35/1.38 ( setukpairinjL2
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.35/1.38 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.35/1.38 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.35/1.38 => ( Xx = Xz ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjL_type,type,
% 2.35/1.38 setukpairinjL: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjL,definition,
% 2.35/1.38 ( setukpairinjL
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.35/1.38 ( ( ( kpair @ Xx @ Xy )
% 2.35/1.38 = ( kpair @ Xz @ Xu ) )
% 2.35/1.38 => ( Xx = Xz ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjR11_type,type,
% 2.35/1.38 setukpairinjR11: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjR11,definition,
% 2.35/1.38 ( setukpairinjR11
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.38 ( ( Xx = Xy )
% 2.35/1.38 => ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.35/1.38 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjR12_type,type,
% 2.35/1.38 setukpairinjR12: $o ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjR12,definition,
% 2.35/1.38 ( setukpairinjR12
% 2.35/1.38 = ( ! [Xx: $i,Xy: $i] :
% 2.35/1.38 ( ( Xx = Xy )
% 2.35/1.38 => ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.35/1.38 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ emptyset ) ) ) ) ) ).
% 2.35/1.38
% 2.35/1.38 thf(setukpairinjR1,conjecture,
% 2.35/1.38 ( setextAx
% 2.35/1.38 => ( emptysetAx
% 2.35/1.38 => ( setadjoinAx
% 2.35/1.38 => ( powersetAx
% 2.35/1.38 => ( setunionAx
% 2.35/1.38 => ( omega0Ax
% 2.35/1.38 => ( omegaSAx
% 2.35/1.38 => ( omegaIndAx
% 2.35/1.38 => ( replAx
% 2.35/1.38 => ( foundationAx
% 2.35/1.38 => ( wellorderingAx
% 2.35/1.38 => ( descrp
% 2.35/1.38 => ( dsetconstrI
% 2.35/1.38 => ( dsetconstrEL
% 2.35/1.38 => ( dsetconstrER
% 2.35/1.38 => ( exuE1
% 2.35/1.38 => ( prop2setE
% 2.35/1.38 => ( emptysetE
% 2.35/1.38 => ( emptysetimpfalse
% 2.35/1.38 => ( notinemptyset
% 2.35/1.38 => ( exuE3e
% 2.35/1.38 => ( setext
% 2.35/1.38 => ( emptyI
% 2.35/1.38 => ( noeltsimpempty
% 2.35/1.38 => ( setbeta
% 2.35/1.38 => ( nonemptyE1
% 2.35/1.38 => ( nonemptyI
% 2.35/1.38 => ( nonemptyI1
% 2.35/1.38 => ( setadjoinIL
% 2.35/1.38 => ( emptyinunitempty
% 2.35/1.38 => ( setadjoinIR
% 2.35/1.38 => ( setadjoinE
% 2.35/1.38 => ( setadjoinOr
% 2.35/1.38 => ( setoftrueEq
% 2.35/1.38 => ( powersetI
% 2.35/1.38 => ( emptyinPowerset
% 2.35/1.38 => ( emptyInPowerset
% 2.35/1.38 => ( powersetE
% 2.35/1.38 => ( setunionI
% 2.35/1.38 => ( setunionE
% 2.35/1.38 => ( subPowSU
% 2.35/1.38 => ( exuE2
% 2.35/1.38 => ( nonemptyImpWitness
% 2.35/1.38 => ( uniqinunit
% 2.35/1.38 => ( notinsingleton
% 2.35/1.38 => ( eqinunit
% 2.35/1.38 => ( singletonsswitch
% 2.35/1.38 => ( upairsetE
% 2.35/1.38 => ( upairsetIL
% 2.35/1.38 => ( upairsetIR
% 2.35/1.38 => ( emptyE1
% 2.35/1.38 => ( vacuousDall
% 2.35/1.38 => ( quantDeMorgan1
% 2.35/1.38 => ( quantDeMorgan2
% 2.35/1.38 => ( quantDeMorgan3
% 2.35/1.38 => ( quantDeMorgan4
% 2.35/1.38 => ( prop2setI
% 2.35/1.38 => ( prop2set2propI
% 2.35/1.38 => ( notdexE
% 2.35/1.38 => ( notdallE
% 2.35/1.38 => ( exuI1
% 2.35/1.38 => ( exuI3
% 2.35/1.38 => ( exuI2
% 2.35/1.38 => ( inCongP
% 2.35/1.38 => ( in__Cong
% 2.35/1.38 => ( exuE3u
% 2.35/1.38 => ( exu__Cong
% 2.35/1.38 => ( emptyset__Cong
% 2.35/1.38 => ( setadjoin__Cong
% 2.35/1.38 => ( powerset__Cong
% 2.35/1.38 => ( setunion__Cong
% 2.35/1.38 => ( omega__Cong
% 2.35/1.38 => ( exuEu
% 2.35/1.38 => ( descr__Cong
% 2.35/1.38 => ( dsetconstr__Cong
% 2.35/1.38 => ( subsetI1
% 2.35/1.38 => ( eqimpsubset2
% 2.35/1.38 => ( eqimpsubset1
% 2.35/1.38 => ( subsetI2
% 2.35/1.38 => ( emptysetsubset
% 2.35/1.38 => ( subsetE
% 2.35/1.38 => ( subsetE2
% 2.35/1.38 => ( notsubsetI
% 2.35/1.38 => ( notequalI1
% 2.35/1.38 => ( notequalI2
% 2.35/1.38 => ( subsetRefl
% 2.35/1.38 => ( subsetTrans
% 2.35/1.38 => ( setadjoinSub
% 2.35/1.38 => ( setadjoinSub2
% 2.35/1.38 => ( subset2powerset
% 2.35/1.38 => ( setextsub
% 2.35/1.38 => ( subsetemptysetimpeq
% 2.35/1.38 => ( powersetI1
% 2.35/1.38 => ( powersetE1
% 2.35/1.38 => ( inPowerset
% 2.35/1.38 => ( powersetsubset
% 2.35/1.38 => ( sepInPowerset
% 2.35/1.38 => ( sepSubset
% 2.35/1.38 => ( binunionIL
% 2.35/1.38 => ( upairset2IR
% 2.35/1.38 => ( binunionIR
% 2.35/1.38 => ( binunionEcases
% 2.35/1.38 => ( binunionE
% 2.35/1.38 => ( binunionLsub
% 2.35/1.38 => ( binunionRsub
% 2.35/1.38 => ( binintersectI
% 2.35/1.38 => ( binintersectSubset5
% 2.35/1.38 => ( binintersectEL
% 2.35/1.38 => ( binintersectLsub
% 2.35/1.38 => ( binintersectSubset2
% 2.35/1.38 => ( binintersectSubset3
% 2.35/1.38 => ( binintersectER
% 2.35/1.38 => ( disjointsetsI1
% 2.35/1.38 => ( binintersectRsub
% 2.35/1.38 => ( binintersectSubset4
% 2.35/1.38 => ( binintersectSubset1
% 2.35/1.38 => ( bs114d
% 2.35/1.38 => ( setminusI
% 2.35/1.38 => ( setminusEL
% 2.35/1.38 => ( setminusER
% 2.35/1.38 => ( setminusSubset2
% 2.35/1.38 => ( setminusERneg
% 2.35/1.38 => ( setminusELneg
% 2.35/1.38 => ( setminusILneg
% 2.35/1.38 => ( setminusIRneg
% 2.35/1.38 => ( setminusLsub
% 2.35/1.38 => ( setminusSubset1
% 2.35/1.38 => ( symdiffE
% 2.35/1.38 => ( symdiffI1
% 2.35/1.38 => ( symdiffI2
% 2.35/1.38 => ( symdiffIneg1
% 2.35/1.38 => ( symdiffIneg2
% 2.35/1.38 => ( secondinupair
% 2.35/1.38 => ( setukpairIL
% 2.35/1.38 => ( setukpairIR
% 2.35/1.38 => ( kpairiskpair
% 2.35/1.38 => ( kpairp
% 2.35/1.38 => ( singletonsubset
% 2.35/1.38 => ( singletoninpowerset
% 2.35/1.38 => ( singletoninpowunion
% 2.35/1.38 => ( upairset2E
% 2.35/1.38 => ( upairsubunion
% 2.35/1.38 => ( upairinpowunion
% 2.35/1.38 => ( ubforcartprodlem1
% 2.35/1.38 => ( ubforcartprodlem2
% 2.35/1.38 => ( ubforcartprodlem3
% 2.35/1.38 => ( cartprodpairin
% 2.35/1.38 => ( cartprodmempair1
% 2.35/1.38 => ( cartprodmempair
% 2.35/1.38 => ( setunionE2
% 2.35/1.38 => ( setunionsingleton1
% 2.35/1.38 => ( setunionsingleton2
% 2.35/1.38 => ( setunionsingleton
% 2.35/1.38 => ( singletonprop
% 2.35/1.38 => ( ex1E1
% 2.35/1.38 => ( ex1I
% 2.35/1.38 => ( ex1I2
% 2.35/1.38 => ( singletonsuniq
% 2.35/1.38 => ( setukpairinjL1
% 2.35/1.38 => ( kfstsingleton
% 2.35/1.38 => ( theprop
% 2.35/1.38 => ( kfstpairEq
% 2.35/1.38 => ( cartprodfstin
% 2.35/1.38 => ( setukpairinjL2
% 2.35/1.38 => ( setukpairinjL
% 2.35/1.38 => ( setukpairinjR11
% 2.35/1.38 => ( setukpairinjR12
% 2.35/1.38 => ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
% 2.35/1.38 ( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
% 2.35/1.38 = ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
% 2.35/1.38 => ( ( Xz = Xu )
% 2.35/1.38 => ( Xy = Xu ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.35/1.38 ------------------------
% 2.35/1.39 % (26242)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/183Mi)
% 2.47/1.40 % (26243)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_26106 for (2999ds/4Mi)
% 2.47/1.40 % (26247)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_26106 for (2999ds/275Mi)
% 2.47/1.40 % (26245)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/2Mi)
% 2.47/1.40 % (26244)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_26106 for (2999ds/27Mi)
% 2.47/1.40 % (26248)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/18Mi)
% 2.47/1.40 % (26246)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_26106 for (2999ds/2Mi)
% 2.47/1.40 % (26245)Instruction limit reached!
% 2.47/1.40 % (26245)------------------------------
% 2.47/1.40 % (26245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.40 % (26246)Instruction limit reached!
% 2.47/1.40 % (26246)------------------------------
% 2.47/1.40 % (26246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.40 % (26245)Termination reason: Unknown
% 2.47/1.40 % (26245)Termination phase: shuffling
% 2.47/1.40
% 2.47/1.40 % (26245)Memory used [KB]: 1279
% 2.47/1.40 % (26245)Time elapsed: 0.003 s
% 2.47/1.40 % (26245)Instructions burned: 3 (million)
% 2.47/1.40 % (26245)------------------------------
% 2.47/1.40 % (26245)------------------------------
% 2.47/1.40 % (26246)Termination reason: Unknown
% 2.47/1.40 % (26246)Termination phase: shuffling
% 2.47/1.40
% 2.47/1.40 % (26246)Memory used [KB]: 1279
% 2.47/1.40 % (26246)Time elapsed: 0.002 s
% 2.47/1.40 % (26246)Instructions burned: 2 (million)
% 2.47/1.40 % (26246)------------------------------
% 2.47/1.40 % (26246)------------------------------
% 2.47/1.40 % (26243)Instruction limit reached!
% 2.47/1.40 % (26243)------------------------------
% 2.47/1.40 % (26243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.40 % (26243)Termination reason: Unknown
% 2.47/1.40 % (26243)Termination phase: shuffling
% 2.47/1.40
% 2.47/1.40 % (26243)Memory used [KB]: 1279
% 2.47/1.40 % (26243)Time elapsed: 0.004 s
% 2.47/1.40 % (26243)Instructions burned: 5 (million)
% 2.47/1.40 % (26243)------------------------------
% 2.47/1.40 % (26243)------------------------------
% 2.47/1.41 % (26248)Instruction limit reached!
% 2.47/1.41 % (26248)------------------------------
% 2.47/1.41 % (26248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.41 % (26248)Termination reason: Unknown
% 2.47/1.41 % (26248)Termination phase: Property scanning
% 2.47/1.41
% 2.47/1.41 % (26248)Memory used [KB]: 1535
% 2.47/1.41 % (26248)Time elapsed: 0.011 s
% 2.47/1.41 % (26248)Instructions burned: 19 (million)
% 2.47/1.41 % (26248)------------------------------
% 2.47/1.41 % (26248)------------------------------
% 2.47/1.41 % (26244)Instruction limit reached!
% 2.47/1.41 % (26244)------------------------------
% 2.47/1.41 % (26244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.41 % (26244)Termination reason: Unknown
% 2.47/1.41 % (26244)Termination phase: Property scanning
% 2.47/1.41
% 2.47/1.41 % (26244)Memory used [KB]: 1791
% 2.47/1.41 % (26244)Time elapsed: 0.015 s
% 2.47/1.41 % (26244)Instructions burned: 29 (million)
% 2.47/1.41 % (26244)------------------------------
% 2.47/1.41 % (26244)------------------------------
% 2.47/1.42 % (26250)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_26106 for (2999ds/37Mi)
% 2.47/1.42 % (26249)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/3Mi)
% 2.47/1.42 % (26249)Instruction limit reached!
% 2.47/1.42 % (26249)------------------------------
% 2.47/1.42 % (26249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.42 % (26249)Termination reason: Unknown
% 2.47/1.42 % (26249)Termination phase: shuffling
% 2.47/1.42
% 2.47/1.42 % (26249)Memory used [KB]: 1279
% 2.47/1.42 % (26249)Time elapsed: 0.003 s
% 2.47/1.42 % (26249)Instructions burned: 3 (million)
% 2.47/1.42 % (26249)------------------------------
% 2.47/1.42 % (26249)------------------------------
% 2.47/1.42 % (26251)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_26106 for (2999ds/15Mi)
% 2.47/1.43 % (26253)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_26106 for (2999ds/3Mi)
% 2.47/1.43 % (26251)Instruction limit reached!
% 2.47/1.43 % (26251)------------------------------
% 2.47/1.43 % (26251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.43 % (26251)Termination reason: Unknown
% 2.47/1.43 % (26251)Termination phase: shuffling
% 2.47/1.43
% 2.47/1.43 % (26251)Memory used [KB]: 1535
% 2.47/1.43 % (26251)Time elapsed: 0.009 s
% 2.47/1.43 % (26251)Instructions burned: 15 (million)
% 2.47/1.43 % (26251)------------------------------
% 2.47/1.43 % (26251)------------------------------
% 2.47/1.43 % (26253)Instruction limit reached!
% 2.47/1.43 % (26253)------------------------------
% 2.47/1.43 % (26253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.43 % (26253)Termination reason: Unknown
% 2.47/1.43 % (26253)Termination phase: shuffling
% 2.47/1.43
% 2.47/1.43 % (26253)Memory used [KB]: 1279
% 2.47/1.43 % (26253)Time elapsed: 0.003 s
% 2.47/1.43 % (26253)Instructions burned: 3 (million)
% 2.47/1.43 % (26253)------------------------------
% 2.47/1.43 % (26253)------------------------------
% 2.47/1.43 % (26250)Instruction limit reached!
% 2.47/1.43 % (26250)------------------------------
% 2.47/1.43 % (26250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.43 % (26250)Termination reason: Unknown
% 2.47/1.43 % (26250)Termination phase: Property scanning
% 2.47/1.43
% 2.47/1.43 % (26250)Memory used [KB]: 1791
% 2.47/1.43 % (26250)Time elapsed: 0.018 s
% 2.47/1.43 % (26250)Instructions burned: 38 (million)
% 2.47/1.43 % (26250)------------------------------
% 2.47/1.43 % (26250)------------------------------
% 2.47/1.43 % (26255)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/7Mi)
% 2.47/1.44 % (26255)Instruction limit reached!
% 2.47/1.44 % (26255)------------------------------
% 2.47/1.44 % (26255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.44 % (26255)Termination reason: Unknown
% 2.47/1.44 % (26255)Termination phase: shuffling
% 2.47/1.44
% 2.47/1.44 % (26255)Memory used [KB]: 1407
% 2.47/1.44 % (26255)Time elapsed: 0.005 s
% 2.47/1.44 % (26255)Instructions burned: 8 (million)
% 2.47/1.44 % (26255)------------------------------
% 2.47/1.44 % (26255)------------------------------
% 2.47/1.44 % (26254)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_26106 for (2999ds/1041Mi)
% 2.47/1.44 % (26242)Instruction limit reached!
% 2.47/1.44 % (26242)------------------------------
% 2.47/1.44 % (26242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.44 % (26242)Termination reason: Unknown
% 2.47/1.44 % (26242)Termination phase: Saturation
% 2.47/1.44
% 2.47/1.44 % (26242)Memory used [KB]: 7419
% 2.47/1.44 % (26242)Time elapsed: 0.051 s
% 2.47/1.44 % (26242)Instructions burned: 184 (million)
% 2.47/1.44 % (26242)------------------------------
% 2.47/1.44 % (26242)------------------------------
% 2.47/1.44 % (26257)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_26106 for (2999ds/3Mi)
% 2.47/1.45 % (26256)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/16Mi)
% 2.47/1.45 % (26257)Instruction limit reached!
% 2.47/1.45 % (26257)------------------------------
% 2.47/1.45 % (26257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.45 % (26257)Termination reason: Unknown
% 2.47/1.45 % (26257)Termination phase: shuffling
% 2.47/1.45
% 2.47/1.45 % (26257)Memory used [KB]: 1279
% 2.47/1.45 % (26257)Time elapsed: 0.003 s
% 2.47/1.45 % (26257)Instructions burned: 4 (million)
% 2.47/1.45 % (26257)------------------------------
% 2.47/1.45 % (26257)------------------------------
% 2.47/1.45 % (26258)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_26106 for (2999ds/3Mi)
% 2.47/1.45 % (26260)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/3Mi)
% 2.47/1.45 % (26258)Instruction limit reached!
% 2.47/1.45 % (26258)------------------------------
% 2.47/1.45 % (26258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.45 % (26258)Termination reason: Unknown
% 2.47/1.45 % (26258)Termination phase: shuffling
% 2.47/1.45
% 2.47/1.45 % (26258)Memory used [KB]: 1279
% 2.47/1.45 % (26258)Time elapsed: 0.003 s
% 2.47/1.45 % (26258)Instructions burned: 3 (million)
% 2.47/1.45 % (26258)------------------------------
% 2.47/1.45 % (26258)------------------------------
% 2.47/1.45 % (26260)Instruction limit reached!
% 2.47/1.45 % (26260)------------------------------
% 2.47/1.45 % (26260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.45 % (26260)Termination reason: Unknown
% 2.47/1.45 % (26260)Termination phase: shuffling
% 2.47/1.45
% 2.47/1.45 % (26260)Memory used [KB]: 1279
% 2.47/1.45 % (26260)Time elapsed: 0.002 s
% 2.47/1.45 % (26260)Instructions burned: 3 (million)
% 2.47/1.45 % (26260)------------------------------
% 2.47/1.45 % (26260)------------------------------
% 2.47/1.45 % (26256)Instruction limit reached!
% 2.47/1.45 % (26256)------------------------------
% 2.47/1.45 % (26256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.45 % (26256)Termination reason: Unknown
% 2.47/1.45 % (26256)Termination phase: shuffling
% 2.47/1.45
% 2.47/1.45 % (26256)Memory used [KB]: 1663
% 2.47/1.45 % (26256)Time elapsed: 0.009 s
% 2.47/1.45 % (26256)Instructions burned: 16 (million)
% 2.47/1.45 % (26256)------------------------------
% 2.47/1.45 % (26256)------------------------------
% 2.47/1.46 % (26259)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/7Mi)
% 2.47/1.46 % (26259)Instruction limit reached!
% 2.47/1.46 % (26259)------------------------------
% 2.47/1.46 % (26259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.46 % (26259)Termination reason: Unknown
% 2.47/1.46 % (26259)Termination phase: shuffling
% 2.47/1.46
% 2.47/1.46 % (26259)Memory used [KB]: 1407
% 2.47/1.46 % (26259)Time elapsed: 0.005 s
% 2.47/1.46 % (26259)Instructions burned: 8 (million)
% 2.47/1.46 % (26259)------------------------------
% 2.47/1.46 % (26259)------------------------------
% 2.47/1.46 % (26261)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/4Mi)
% 2.47/1.46 % (26261)Instruction limit reached!
% 2.47/1.46 % (26261)------------------------------
% 2.47/1.46 % (26261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.46 % (26261)Termination reason: Unknown
% 2.47/1.46 % (26261)Termination phase: shuffling
% 2.47/1.46
% 2.47/1.46 % (26261)Memory used [KB]: 1407
% 2.47/1.46 % (26261)Time elapsed: 0.003 s
% 2.47/1.46 % (26261)Instructions burned: 7 (million)
% 2.47/1.46 % (26261)------------------------------
% 2.47/1.46 % (26261)------------------------------
% 2.47/1.47 % (26262)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/18Mi)
% 2.47/1.47 % (26263)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/710Mi)
% 2.47/1.47 % (26264)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/6Mi)
% 2.47/1.47 % (26264)Instruction limit reached!
% 2.47/1.47 % (26264)------------------------------
% 2.47/1.47 % (26264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.47 % (26264)Termination reason: Unknown
% 2.47/1.47 % (26264)Termination phase: shuffling
% 2.47/1.47
% 2.47/1.47 % (26264)Memory used [KB]: 1407
% 2.47/1.47 % (26264)Time elapsed: 0.004 s
% 2.47/1.47 % (26264)Instructions burned: 6 (million)
% 2.47/1.47 % (26264)------------------------------
% 2.47/1.47 % (26264)------------------------------
% 2.47/1.47 % (26266)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_26106 for (2999ds/21Mi)
% 2.47/1.48 % (26262)Instruction limit reached!
% 2.47/1.48 % (26262)------------------------------
% 2.47/1.48 % (26262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.48 % (26262)Termination reason: Unknown
% 2.47/1.48 % (26262)Termination phase: shuffling
% 2.47/1.48
% 2.47/1.48 % (26262)Memory used [KB]: 1663
% 2.47/1.48 % (26262)Time elapsed: 0.010 s
% 2.47/1.48 % (26262)Instructions burned: 19 (million)
% 2.47/1.48 % (26262)------------------------------
% 2.47/1.48 % (26262)------------------------------
% 2.47/1.48 % (26265)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_26106 for (2999ds/902Mi)
% 2.47/1.48 % (26266)Instruction limit reached!
% 2.47/1.48 % (26266)------------------------------
% 2.47/1.48 % (26266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.48 % (26266)Termination reason: Unknown
% 2.47/1.48 % (26266)Termination phase: shuffling
% 2.47/1.48
% 2.47/1.48 % (26266)Memory used [KB]: 1791
% 2.47/1.48 % (26266)Time elapsed: 0.007 s
% 2.47/1.48 % (26266)Instructions burned: 22 (million)
% 2.47/1.48 % (26266)------------------------------
% 2.47/1.48 % (26266)------------------------------
% 2.47/1.49 % (26267)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/5Mi)
% 2.47/1.49 % (26269)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_26106 for (2999ds/377Mi)
% 2.47/1.49 % (26267)Instruction limit reached!
% 2.47/1.49 % (26267)------------------------------
% 2.47/1.49 % (26267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.49 % (26267)Termination reason: Unknown
% 2.47/1.49 % (26267)Termination phase: shuffling
% 2.47/1.49
% 2.47/1.49 % (26267)Memory used [KB]: 1407
% 2.47/1.49 % (26267)Time elapsed: 0.004 s
% 2.47/1.49 % (26267)Instructions burned: 6 (million)
% 2.47/1.49 % (26267)------------------------------
% 2.47/1.49 % (26267)------------------------------
% 2.47/1.49 % (26268)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_26106 for (2999ds/6Mi)
% 2.47/1.50 % (26268)Instruction limit reached!
% 2.47/1.50 % (26268)------------------------------
% 2.47/1.50 % (26268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.50 % (26268)Termination reason: Unknown
% 2.47/1.50 % (26268)Termination phase: shuffling
% 2.47/1.50
% 2.47/1.50 % (26268)Memory used [KB]: 1407
% 2.47/1.50 % (26268)Time elapsed: 0.005 s
% 2.47/1.50 % (26268)Instructions burned: 8 (million)
% 2.47/1.50 % (26268)------------------------------
% 2.47/1.50 % (26268)------------------------------
% 2.47/1.51 % (26270)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_26106 for (2998ds/779Mi)
% 2.47/1.51 % (26271)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_26106 for (2998ds/19Mi)
% 2.47/1.52 % (26271)Instruction limit reached!
% 2.47/1.52 % (26271)------------------------------
% 2.47/1.52 % (26271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.52 % (26271)Termination reason: Unknown
% 2.47/1.52 % (26271)Termination phase: shuffling
% 2.47/1.52
% 2.47/1.52 % (26271)Memory used [KB]: 1663
% 2.47/1.52 % (26271)Time elapsed: 0.010 s
% 2.47/1.52 % (26271)Instructions burned: 19 (million)
% 2.47/1.52 % (26271)------------------------------
% 2.47/1.52 % (26271)------------------------------
% 2.47/1.53 % (26247)Instruction limit reached!
% 2.47/1.53 % (26247)------------------------------
% 2.47/1.53 % (26247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.53 % (26247)Termination reason: Unknown
% 2.47/1.53 % (26247)Termination phase: Saturation
% 2.47/1.53
% 2.47/1.53 % (26247)Memory used [KB]: 8187
% 2.47/1.53 % (26247)Time elapsed: 0.135 s
% 2.47/1.53 % (26247)Instructions burned: 275 (million)
% 2.47/1.53 % (26247)------------------------------
% 2.47/1.53 % (26247)------------------------------
% 2.47/1.54 % (26272)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_26106 for (2998ds/879Mi)
% 2.47/1.55 % (26273)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_26106 for (2998ds/17Mi)
% 2.47/1.56 % (26273)Instruction limit reached!
% 2.47/1.56 % (26273)------------------------------
% 2.47/1.56 % (26273)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.56 % (26273)Termination reason: Unknown
% 2.47/1.56 % (26273)Termination phase: shuffling
% 2.47/1.56
% 2.47/1.56 % (26273)Memory used [KB]: 1663
% 2.47/1.56 % (26273)Time elapsed: 0.010 s
% 2.47/1.56 % (26273)Instructions burned: 18 (million)
% 2.47/1.56 % (26273)------------------------------
% 2.47/1.56 % (26273)------------------------------
% 2.47/1.58 % (26275)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_26106 for (2998ds/3Mi)
% 2.47/1.58 % (26275)Instruction limit reached!
% 2.47/1.58 % (26275)------------------------------
% 2.47/1.58 % (26275)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.58 % (26275)Termination reason: Unknown
% 2.47/1.58 % (26275)Termination phase: shuffling
% 2.47/1.58
% 2.47/1.58 % (26275)Memory used [KB]: 1279
% 2.47/1.58 % (26275)Time elapsed: 0.004 s
% 2.47/1.58 % (26275)Instructions burned: 5 (million)
% 2.47/1.58 % (26275)------------------------------
% 2.47/1.58 % (26275)------------------------------
% 2.47/1.59 % (26276)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_26106 for (2998ds/30Mi)
% 2.47/1.61 % (26276)Instruction limit reached!
% 2.47/1.61 % (26276)------------------------------
% 2.47/1.61 % (26276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.61 % (26276)Termination reason: Unknown
% 2.47/1.61 % (26276)Termination phase: Property scanning
% 2.47/1.61
% 2.47/1.61 % (26276)Memory used [KB]: 1791
% 2.47/1.61 % (26276)Time elapsed: 0.015 s
% 2.47/1.61 % (26276)Instructions burned: 30 (million)
% 2.47/1.61 % (26276)------------------------------
% 2.47/1.61 % (26276)------------------------------
% 2.47/1.62 % (26277)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_26106 for (2997ds/127Mi)
% 2.47/1.64 % (26269)Instruction limit reached!
% 2.47/1.64 % (26269)------------------------------
% 2.47/1.64 % (26269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.64 % (26269)Termination reason: Unknown
% 2.47/1.64 % (26269)Termination phase: Saturation
% 2.47/1.64
% 2.47/1.64 % (26269)Memory used [KB]: 8059
% 2.47/1.64 % (26269)Time elapsed: 0.155 s
% 2.47/1.64 % (26269)Instructions burned: 378 (million)
% 2.47/1.64 % (26269)------------------------------
% 2.47/1.64 % (26269)------------------------------
% 2.47/1.66 % (26279)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_26106 for (2997ds/100Mi)
% 2.47/1.68 % (26277)Instruction limit reached!
% 2.47/1.68 % (26277)------------------------------
% 2.47/1.68 % (26277)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.68 % (26277)Termination reason: Unknown
% 2.47/1.68 % (26277)Termination phase: Saturation
% 2.47/1.68
% 2.47/1.68 % (26277)Memory used [KB]: 6908
% 2.47/1.68 % (26277)Time elapsed: 0.058 s
% 2.47/1.68 % (26277)Instructions burned: 128 (million)
% 2.47/1.68 % (26277)------------------------------
% 2.47/1.68 % (26277)------------------------------
% 2.47/1.70 % (26280)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_26106 for (2996ds/3Mi)
% 2.47/1.70 % (26280)Instruction limit reached!
% 2.47/1.70 % (26280)------------------------------
% 2.47/1.70 % (26280)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.70 % (26280)Termination reason: Unknown
% 2.47/1.70 % (26280)Termination phase: shuffling
% 2.47/1.70
% 2.47/1.70 % (26280)Memory used [KB]: 1279
% 2.47/1.70 % (26280)Time elapsed: 0.003 s
% 2.47/1.70 % (26280)Instructions burned: 3 (million)
% 2.47/1.70 % (26280)------------------------------
% 2.47/1.70 % (26280)------------------------------
% 2.47/1.70 % (26279)Instruction limit reached!
% 2.47/1.70 % (26279)------------------------------
% 2.47/1.70 % (26279)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.70 % (26279)Termination reason: Unknown
% 2.47/1.70 % (26279)Termination phase: Saturation
% 2.47/1.70
% 2.47/1.70 % (26279)Memory used [KB]: 6524
% 2.47/1.70 % (26279)Time elapsed: 0.045 s
% 2.47/1.70 % (26279)Instructions burned: 100 (million)
% 2.47/1.70 % (26279)------------------------------
% 2.47/1.70 % (26279)------------------------------
% 2.47/1.72 % (26281)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_26106 for (2996ds/20Mi)
% 2.47/1.72 % (26282)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_26106 for (2996ds/86Mi)
% 2.47/1.73 % (26281)Instruction limit reached!
% 2.47/1.73 % (26281)------------------------------
% 2.47/1.73 % (26281)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.73 % (26281)Termination reason: Unknown
% 2.47/1.73 % (26281)Termination phase: Property scanning
% 2.47/1.73
% 2.47/1.73 % (26281)Memory used [KB]: 1535
% 2.47/1.73 % (26281)Time elapsed: 0.011 s
% 2.47/1.73 % (26281)Instructions burned: 20 (million)
% 2.47/1.73 % (26281)------------------------------
% 2.47/1.73 % (26281)------------------------------
% 2.47/1.74 % (26283)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_26106 for (2996ds/107Mi)
% 2.47/1.75 % (26270)Instruction limit reached!
% 2.47/1.75 % (26270)------------------------------
% 2.47/1.75 % (26270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.75 % (26270)Termination reason: Unknown
% 2.47/1.75 % (26270)Termination phase: Saturation
% 2.47/1.75
% 2.47/1.75 % (26270)Memory used [KB]: 6780
% 2.47/1.75 % (26270)Time elapsed: 0.244 s
% 2.47/1.75 % (26270)Instructions burned: 781 (million)
% 2.47/1.75 % (26270)------------------------------
% 2.47/1.75 % (26270)------------------------------
% 2.47/1.76 % (26282)Instruction limit reached!
% 2.47/1.76 % (26282)------------------------------
% 2.47/1.76 % (26282)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.76 % (26282)Termination reason: Unknown
% 2.47/1.76 % (26282)Termination phase: Saturation
% 2.47/1.76
% 2.47/1.76 % (26282)Memory used [KB]: 6524
% 2.47/1.76 % (26282)Time elapsed: 0.039 s
% 2.47/1.76 % (26282)Instructions burned: 86 (million)
% 2.47/1.76 % (26282)------------------------------
% 2.47/1.76 % (26282)------------------------------
% 2.47/1.76 % (26254)Instruction limit reached!
% 2.47/1.76 % (26254)------------------------------
% 2.47/1.76 % (26254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.76 % (26254)Termination reason: Unknown
% 2.47/1.76 % (26254)Termination phase: Saturation
% 2.47/1.76
% 2.47/1.76 % (26254)Memory used [KB]: 10106
% 2.47/1.76 % (26254)Time elapsed: 0.321 s
% 2.47/1.76 % (26254)Instructions burned: 1042 (million)
% 2.47/1.76 % (26254)------------------------------
% 2.47/1.76 % (26254)------------------------------
% 2.47/1.77 % (26284)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_26106 for (2996ds/39Mi)
% 2.47/1.77 % (26285)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_26106 for (2996ds/448Mi)
% 2.47/1.77 % (26286)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_26106 for (2996ds/46Mi)
% 2.47/1.78 % (26284)Instruction limit reached!
% 2.47/1.78 % (26284)------------------------------
% 2.47/1.78 % (26284)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.78 % (26284)Termination reason: Unknown
% 2.47/1.78 % (26284)Termination phase: Property scanning
% 2.47/1.78
% 2.47/1.78 % (26284)Memory used [KB]: 1791
% 2.47/1.78 % (26284)Time elapsed: 0.011 s
% 2.47/1.78 % (26284)Instructions burned: 39 (million)
% 2.47/1.78 % (26284)------------------------------
% 2.47/1.78 % (26284)------------------------------
% 2.47/1.79 % (26287)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_26106 for (2995ds/98Mi)
% 2.47/1.79 % (26283)Instruction limit reached!
% 2.47/1.79 % (26283)------------------------------
% 2.47/1.79 % (26283)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.79 % (26283)Termination reason: Unknown
% 2.47/1.79 % (26283)Termination phase: Saturation
% 2.47/1.79
% 2.47/1.79 % (26283)Memory used [KB]: 6780
% 2.47/1.79 % (26283)Time elapsed: 0.049 s
% 2.47/1.79 % (26283)Instructions burned: 108 (million)
% 2.47/1.79 % (26283)------------------------------
% 2.47/1.79 % (26283)------------------------------
% 2.47/1.79 % (26286)Instruction limit reached!
% 2.47/1.79 % (26286)------------------------------
% 2.47/1.79 % (26286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.79 % (26286)Termination reason: Unknown
% 2.47/1.79 % (26286)Termination phase: SInE selection
% 2.47/1.79
% 2.47/1.79 % (26286)Memory used [KB]: 1791
% 2.47/1.79 % (26286)Time elapsed: 0.022 s
% 2.47/1.79 % (26286)Instructions burned: 47 (million)
% 2.47/1.79 % (26286)------------------------------
% 2.47/1.79 % (26286)------------------------------
% 2.47/1.80 % (26289)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_26106 for (2995ds/149Mi)
% 2.47/1.81 % (26288)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_26106 for (2995ds/507Mi)
% 2.47/1.82 % (26287)Instruction limit reached!
% 2.47/1.82 % (26287)------------------------------
% 2.47/1.82 % (26287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.82 % (26287)Termination reason: Unknown
% 2.47/1.82 % (26287)Termination phase: Saturation
% 2.47/1.82
% 2.47/1.82 % (26287)Memory used [KB]: 2174
% 2.47/1.82 % (26287)Time elapsed: 0.038 s
% 2.47/1.82 % (26287)Instructions burned: 100 (million)
% 2.47/1.82 % (26287)------------------------------
% 2.47/1.82 % (26287)------------------------------
% 2.47/1.82 % (26263)Instruction limit reached!
% 2.47/1.82 % (26263)------------------------------
% 2.47/1.82 % (26263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.82 % (26263)Termination reason: Unknown
% 2.47/1.82 % (26263)Termination phase: Saturation
% 2.47/1.82
% 2.47/1.82 % (26263)Memory used [KB]: 9338
% 2.47/1.82 % (26263)Time elapsed: 0.357 s
% 2.47/1.82 % (26263)Instructions burned: 710 (million)
% 2.47/1.82 % (26263)------------------------------
% 2.47/1.82 % (26263)------------------------------
% 2.47/1.84 % (26290)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_26106 for (2995ds/39Mi)
% 2.47/1.84 % (26291)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_26106 for (2995ds/6Mi)
% 2.47/1.84 % (26291)Instruction limit reached!
% 2.47/1.84 % (26291)------------------------------
% 2.47/1.84 % (26291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.84 % (26291)Termination reason: Unknown
% 2.47/1.84 % (26291)Termination phase: shuffling
% 2.47/1.84
% 2.47/1.84 % (26291)Memory used [KB]: 1407
% 2.47/1.84 % (26291)Time elapsed: 0.004 s
% 2.47/1.84 % (26291)Instructions burned: 6 (million)
% 2.47/1.84 % (26291)------------------------------
% 2.47/1.84 % (26291)------------------------------
% 2.47/1.84 % (26289)Instruction limit reached!
% 2.47/1.84 % (26289)------------------------------
% 2.47/1.84 % (26289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.84 % (26289)Termination reason: Unknown
% 2.47/1.84 % (26289)Termination phase: Saturation
% 2.47/1.84
% 2.47/1.84 % (26289)Memory used [KB]: 7164
% 2.47/1.84 % (26289)Time elapsed: 0.043 s
% 2.47/1.84 % (26289)Instructions burned: 151 (million)
% 2.47/1.84 % (26289)------------------------------
% 2.47/1.84 % (26289)------------------------------
% 2.47/1.85 % (26265)First to succeed.
% 2.47/1.85 % (26265)Refutation found. Thanks to Tanya!
% 2.47/1.85 % SZS status Theorem for DTF2THF_26106
% 2.47/1.85 % SZS output start Proof for DTF2THF_26106
% 2.47/1.85 thf(func_def_0, type, in: $i > $i > $o).
% 2.47/1.85 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.47/1.85 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.47/1.85 thf(func_def_8, type, powerset: $i > $i).
% 2.47/1.85 thf(func_def_10, type, setunion: $i > $i).
% 2.47/1.85 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.47/1.85 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_26, type, prop2set: $o > $i).
% 2.47/1.85 thf(func_def_36, type, nonempty: $i > $o).
% 2.47/1.85 thf(func_def_69, type, set2prop: $i > $o).
% 2.47/1.85 thf(func_def_88, type, subset: $i > $i > $o).
% 2.47/1.85 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.47/1.85 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.47/1.85 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.47/1.85 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.47/1.85 thf(func_def_135, type, regular: $i > $o).
% 2.47/1.85 thf(func_def_136, type, setminus: $i > $i > $i).
% 2.47/1.85 thf(func_def_147, type, symdiff: $i > $i > $i).
% 2.47/1.85 thf(func_def_153, type, iskpair: $i > $o).
% 2.47/1.85 thf(func_def_158, type, kpair: $i > $i > $i).
% 2.47/1.85 thf(func_def_160, type, cartprod: $i > $i > $i).
% 2.47/1.85 thf(func_def_177, type, singleton: $i > $o).
% 2.47/1.85 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 2.47/1.85 thf(func_def_184, type, atmost1p: $i > $o).
% 2.47/1.85 thf(func_def_185, type, atleast2p: $i > $o).
% 2.47/1.85 thf(func_def_186, type, atmost2p: $i > $o).
% 2.47/1.85 thf(func_def_187, type, upairsetp: $i > $o).
% 2.47/1.85 thf(func_def_191, type, kfst: $i > $i).
% 2.47/1.85 thf(func_def_210, type, sP0: $i > $o > $i > $i > $o).
% 2.47/1.85 thf(func_def_213, type, sP3: $i > $i > $o).
% 2.47/1.85 thf(func_def_214, type, sP4: $i > $o).
% 2.47/1.85 thf(func_def_215, type, sP5: $i > $i > $o).
% 2.47/1.85 thf(func_def_216, type, sP6: $i > $i > $o).
% 2.47/1.85 thf(func_def_222, type, sK12: $i > $i > $i).
% 2.47/1.85 thf(func_def_223, type, sK13: $i > $i).
% 2.47/1.85 thf(func_def_234, type, sK24: $i > $o).
% 2.47/1.85 thf(func_def_248, type, sK38: $i > $i > $i).
% 2.47/1.85 thf(func_def_252, type, sK42: $i > $o).
% 2.47/1.85 thf(func_def_255, type, sK45: $i > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_256, type, sK46: $i > $i > $i > $i).
% 2.47/1.85 thf(func_def_257, type, sK47: $i > $i > $i > $i).
% 2.47/1.85 thf(func_def_271, type, sK61: $i > $o).
% 2.47/1.85 thf(func_def_294, type, sK84: $i > $o).
% 2.47/1.85 thf(func_def_296, type, sK86: ($i > $o) > $i).
% 2.47/1.85 thf(func_def_297, type, sK87: ($i > $o) > $i).
% 2.47/1.85 thf(func_def_303, type, sK93: $i > $o).
% 2.47/1.85 thf(func_def_306, type, sK96: $i > $i > $i).
% 2.47/1.85 thf(func_def_307, type, sK97: $i > $i > $i).
% 2.47/1.85 thf(func_def_323, type, sK113: $i > $o).
% 2.47/1.85 thf(func_def_336, type, sK126: $i > $o).
% 2.47/1.85 thf(func_def_341, type, sK131: $i > $i > $o).
% 2.47/1.85 thf(func_def_342, type, sK132: $i > $i).
% 2.47/1.85 thf(func_def_343, type, sK133: $i > $i).
% 2.47/1.85 thf(func_def_344, type, sK134: ($i > $i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_345, type, sK135: $i > ($i > $i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_346, type, sK136: ($i > $i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_355, type, sK145: ($i > $o) > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_356, type, sK146: ($i > $o) > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_357, type, sK147: $i > $o).
% 2.47/1.85 thf(func_def_358, type, sK148: $i > $o).
% 2.47/1.85 thf(func_def_359, type, sK149: $i > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_360, type, sK150: $i > $o).
% 2.47/1.85 thf(func_def_366, type, sK156: $i > $o).
% 2.47/1.85 thf(func_def_375, type, sK165: $i > $o).
% 2.47/1.85 thf(func_def_377, type, sK167: ($i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_378, type, sK168: ($i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_386, type, sK176: $i > $i > $i).
% 2.47/1.85 thf(func_def_387, type, sK177: $i > $i > $i).
% 2.47/1.85 thf(func_def_388, type, sK178: $i > $i > $i).
% 2.47/1.85 thf(func_def_389, type, sK179: $i > $i > $i).
% 2.47/1.85 thf(func_def_390, type, sK180: $i > $i > $i > $i).
% 2.47/1.85 thf(func_def_391, type, sK181: $i > $i).
% 2.47/1.85 thf(func_def_392, type, sK182: $i > $i).
% 2.47/1.85 thf(func_def_393, type, sK183: $i > $i).
% 2.47/1.85 thf(func_def_394, type, sK184: $i > $i).
% 2.47/1.85 thf(func_def_395, type, sK185: $i > $i > $i > $i).
% 2.47/1.85 thf(func_def_396, type, sK186: $i > $i > $i > $i).
% 2.47/1.85 thf(func_def_397, type, sK187: $i > $i > $i).
% 2.47/1.85 thf(func_def_398, type, sK188: $i > $i > $i).
% 2.47/1.85 thf(func_def_399, type, sK189: $i > $i > $i).
% 2.47/1.85 thf(func_def_401, type, sK191: $i > $i).
% 2.47/1.85 thf(func_def_402, type, sK192: $i > $i).
% 2.47/1.85 thf(func_def_403, type, sK193: $i > $i).
% 2.47/1.85 thf(func_def_404, type, sK194: $i > $i > $i).
% 2.47/1.85 thf(func_def_406, type, sK196: $i > $i).
% 2.47/1.85 thf(func_def_411, type, sK201: $i > $o).
% 2.47/1.85 thf(func_def_412, type, sK202: $i > $o).
% 2.47/1.85 thf(func_def_413, type, sK203: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.47/1.85 thf(func_def_414, type, sK204: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.47/1.85 thf(func_def_421, type, sK211: $i > $o).
% 2.47/1.85 thf(func_def_424, type, sK214: ($i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_426, type, sK216: $i > $o).
% 2.47/1.85 thf(func_def_429, type, sK219: $i > $o).
% 2.47/1.85 thf(func_def_433, type, sK223: $i > $i).
% 2.47/1.85 thf(func_def_440, type, sK230: $i > $i > $i).
% 2.47/1.85 thf(func_def_450, type, sK240: $i > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_451, type, sK241: $i > $o).
% 2.47/1.85 thf(func_def_472, type, sK262: ($i > $o) > $i).
% 2.47/1.85 thf(func_def_473, type, sK263: $i > $o).
% 2.47/1.85 thf(func_def_474, type, sK264: $i > $i).
% 2.47/1.85 thf(func_def_485, type, sK275: $i > ($i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_487, type, sK277: $i > $o).
% 2.47/1.85 thf(func_def_491, type, sK281: $i > $o).
% 2.47/1.85 thf(func_def_493, type, sK283: $i > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_498, type, sK288: $i > $o).
% 2.47/1.85 thf(func_def_507, type, sK297: $i > $i).
% 2.47/1.85 thf(func_def_508, type, sK298: $i > $i).
% 2.47/1.85 thf(func_def_511, type, sK301: $i > $i).
% 2.47/1.85 thf(func_def_524, type, sK314: $i > $i > $i).
% 2.47/1.85 thf(func_def_525, type, sK315: $i > $i > $i).
% 2.47/1.85 thf(func_def_544, type, sK334: $o > $i > $i > $i).
% 2.47/1.85 thf(func_def_558, type, sK348: $i > $i > $i).
% 2.47/1.85 thf(func_def_572, type, sK362: ($i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_574, type, sK364: $i > $o).
% 2.47/1.85 thf(func_def_576, type, sK366: ($i > $o) > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_577, type, sK367: ($i > $o) > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_578, type, sK368: $i > $o).
% 2.47/1.85 thf(func_def_579, type, sK369: $i > $o).
% 2.47/1.85 thf(func_def_580, type, sK370: ($i > $o) > $i).
% 2.47/1.85 thf(func_def_581, type, sK371: $i > $o).
% 2.47/1.85 thf(func_def_582, type, sK372: $i > $i).
% 2.47/1.85 thf(func_def_585, type, sK375: $i > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_586, type, sK376: $i > $o).
% 2.47/1.85 thf(func_def_592, type, sK382: ($i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_594, type, sK384: $i > $o).
% 2.47/1.85 thf(func_def_615, type, sK405: $i > $o).
% 2.47/1.85 thf(func_def_617, type, sK407: ($i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_618, type, sK408: ($i > $o) > $i > $i).
% 2.47/1.85 thf(func_def_626, type, sK416: $i > $o).
% 2.47/1.85 thf(func_def_638, type, sK428: $i > $i).
% 2.47/1.85 thf(func_def_639, type, sK429: $i > $o).
% 2.47/1.85 thf(func_def_642, type, sK432: ($i > $o) > $i).
% 2.47/1.85 thf(func_def_643, type, sK433: $i > $o).
% 2.47/1.85 thf(func_def_654, type, sK444: $i > $o).
% 2.47/1.85 thf(func_def_659, type, sK449: $i > $i > $i).
% 2.47/1.85 thf(func_def_672, type, sK462: $i > $o).
% 2.47/1.85 thf(func_def_674, type, sK464: $i > ($i > $o) > $i).
% 2.47/1.85 thf(func_def_675, type, sK465: $i > $i > $i).
% 2.47/1.85 thf(func_def_679, type, ph469: !>[X0: $tType]:(X0)).
% 2.47/1.85 thf(f5670,plain,(
% 2.47/1.85 $false),
% 2.47/1.85 inference(avatar_sat_refutation,[status(thm)],[f5555,f5656])).
% 2.47/1.85 thf(f5656,plain,(
% 2.47/1.85 ~spl468_81),
% 2.47/1.85 inference(avatar_contradiction_clause,[status(thm)],[f5655])).
% 2.47/1.85 thf(f5655,plain,(
% 2.47/1.85 $false | ~spl468_81),
% 2.47/1.85 inference(trivial_inequality_removal,[status(thm)],[f5610])).
% 2.47/1.85 thf(f5610,plain,(
% 2.47/1.85 (sK350 != sK350) | ~spl468_81),
% 2.47/1.85 inference(superposition,[status(thm)],[f2449,f5539])).
% 2.47/1.85 thf(f5539,plain,(
% 2.47/1.85 (sK351 = sK350) | ~spl468_81),
% 2.47/1.85 inference(avatar_component_clause,[status(thm)],[f5537])).
% 2.47/1.85 thf(f5537,definition,(
% 2.47/1.85 spl468_81 <=> (sK351 = sK350)),
% 2.47/1.85 introduced(definition,[new_symbols(naming,[spl468_81])],[avatar_definition])).
% 2.47/1.85 thf(f2449,plain,(
% 2.47/1.85 (sK351 != sK350)),
% 2.47/1.85 inference(superposition,[status(thm)],[f2150,f2149])).
% 2.47/1.85 thf(f2149,plain,(
% 2.47/1.85 (sK352 = sK351)),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f1328])).
% 2.47/1.85 thf(f1328,plain,(
% 2.47/1.85 (omegaSAx = $true) & (binunionEcases = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (subset2powerset = $true) & (ex1I2 = $true) & (in__Cong = $true) & (setukpairinjL = $true) & (upairset2E = $true) & (cartprodmempair = $true) & (binunionE = $true) & (binintersectI = $true) & (setminusSubset1 = $true) & (prop2setI = $true) & (singletonsubset = $true) & (descrp = $true) & (setukpairIL = $true) & (notinemptyset = $true) & (symdiffIneg1 = $true) & (setadjoinAx = $true) & (powersetAx = $true) & (setbeta = $true) & (secondinupair = $true) & (binintersectSubset3 = $true) & (emptyinPowerset = $true) & (dsetconstrER = $true) & (emptysetE = $true) & ((sK352 != sK350) & (sK352 = sK351) & ((setadjoin @ (setadjoin @ sK353 @ emptyset) @ (setadjoin @ (setadjoin @ sK353 @ (setadjoin @ sK350 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK351 @ emptyset) @ (setadjoin @ (setadjoin @ sK351 @ (setadjoin @ sK352 @ emptyset)) @ emptyset)))) & (notdexE = $true) & (setukpairinjR11 = $true) & (dsetconstr__Cong = $true) & (quantDeMorgan3 = $true) & (theprop = $true) & (setadjoinOr = $true) & (binunionIL = $true) & (exuE2 = $true) & (subsetemptysetimpeq = $true) & (setoftrueEq = $true) & (quantDeMorgan4 = $true) & (subsetI2 = $true) & (notdallE = $true) & (disjointsetsI1 = $true) & (binunionLsub = $true) & (setukpairinjR12 = $true) & (setadjoinIR = $true) & (sepInPowerset = $true) & (setukpairinjL1 = $true) & (subsetRefl = $true) & (eqimpsubset2 = $true) & (notequalI2 = $true) & (subPowSU = $true) & (notinsingleton = $true) & (setunionI = $true) & (binintersectSubset5 = $true) & (emptysetimpfalse = $true) & (notequalI1 = $true) & (exuI1 = $true) & (setminusIRneg = $true) & (upairsetE = $true) & (binintersectSubset2 = $true) & (binintersectER = $true) & (upairinpowunion = $true) & (exuE3u = $true) & (eqinunit = $true) & (inCongP = $true) & (setextAx = $true) & (singletonprop = $true) & (notsubsetI = $true) & (dsetconstrI = $true) & (cartprodmempair1 = $true) & (inPowerset = $true) & (binintersectEL = $true) & (binintersectLsub = $true) & (powersetsubset = $true) & (noeltsimpempty = $true) & (symdiffI2 = $true) & (kfstpairEq = $true) & (emptysetsubset = $true) & (exuI3 = $true) & (setminusERneg = $true) & (setadjoinSub2 = $true) & (emptyinunitempty = $true) & (exuI2 = $true) & (foundationAx = $true) & (powersetI = $true) & (prop2setE = $true) & (singletoninpowerset = $true) & (powersetE = $true) & (setminusER = $true) & (powersetI1 = $true) & (nonemptyI = $true) & (setminusLsub = $true) & (singletonsswitch = $true) & (nonemptyImpWitness = $true) & (descr__Cong = $true) & (quantDeMorgan1 = $true) & (prop2set2propI = $true) & (kpairiskpair = $true) & (setminusSubset2 = $true) & (binintersectSubset1 = $true) & (binintersectRsub = $true) & (replAx = $true) & (eqimpsubset1 = $true) & (setadjoin__Cong = $true) & (uniqinunit = $true) & (setunionsingleton = $true) & (vacuousDall = $true) & (setadjoinIL = $true) & (symdiffIneg2 = $true) & (emptyE1 = $true) & (setukpairIR = $true) & (singletonsuniq = $true) & (emptysetAx = $true) & (setadjoinE = $true) & (setunionE2 = $true) & (ubforcartprodlem2 = $true) & (setadjoinSub = $true) & (upairsetIL = $true) & (kfstsingleton = $true) & (exuE3e = $true) & (symdiffI1 = $true) & (singletoninpowunion = $true) & (ubforcartprodlem1 = $true) & (ex1E1 = $true) & (cartprodfstin = $true) & (quantDeMorgan2 = $true) & (sepSubset = $true) & (cartprodpairin = $true) & (symdiffE = $true) & (setextsub = $true) & (ex1I = $true) & (binunionRsub = $true) & (emptyset__Cong = $true) & (upairset2IR = $true) & (subsetI1 = $true) & (setminusEL = $true) & (powersetE1 = $true) & (emptyI = $true) & (setminusI = $true) & (omega0Ax = $true) & (subsetTrans = $true) & (setminusILneg = $true) & (setunion__Cong = $true) & (upairsetIR = $true) & (nonemptyI1 = $true) & (dsetconstrEL = $true) & (setunionE = $true) & (subsetE2 = $true) & (setminusELneg = $true) & (kpairp = $true) & (wellorderingAx = $true) & (setunionAx = $true) & (exu__Cong = $true) & (setext = $true) & (powerset__Cong = $true) & (ubforcartprodlem3 = $true) & (emptyInPowerset = $true) & (bs114d = $true) & (binintersectSubset4 = $true) & (omegaIndAx = $true) & (omega__Cong = $true) & (exuE1 = $true) & (nonemptyE1 = $true) & (setukpairinjL2 = $true) & (binunionIR = $true) & (subsetE = $true) & (upairsubunion = $true) & (exuEu = $true)),
% 2.47/1.85 inference(skolemisation,[status(esa),new_symbols(skolem,[sK350,sK351,sK352,sK353])],[f607,f1327])).
% 2.47/1.85 thf(f1327,plain,(
% 2.47/1.85 ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X2) & (X1 = X2) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) => ((sK352 != sK350) & (sK352 = sK351) & ((setadjoin @ (setadjoin @ sK353 @ emptyset) @ (setadjoin @ (setadjoin @ sK353 @ (setadjoin @ sK350 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK351 @ emptyset) @ (setadjoin @ (setadjoin @ sK351 @ (setadjoin @ sK352 @ emptyset)) @ emptyset))))),
% 2.47/1.85 introduced(definition,[],[choice_axiom])).
% 2.47/1.85 thf(f607,plain,(
% 2.47/1.85 (omegaSAx = $true) & (binunionEcases = $true) & (setunionsingleton2 = $true) & (setunionsingleton1 = $true) & (subset2powerset = $true) & (ex1I2 = $true) & (in__Cong = $true) & (setukpairinjL = $true) & (upairset2E = $true) & (cartprodmempair = $true) & (binunionE = $true) & (binintersectI = $true) & (setminusSubset1 = $true) & (prop2setI = $true) & (singletonsubset = $true) & (descrp = $true) & (setukpairIL = $true) & (notinemptyset = $true) & (symdiffIneg1 = $true) & (setadjoinAx = $true) & (powersetAx = $true) & (setbeta = $true) & (secondinupair = $true) & (binintersectSubset3 = $true) & (emptyinPowerset = $true) & (dsetconstrER = $true) & (emptysetE = $true) & ? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : ((X0 != X2) & (X1 = X2) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) & (notdexE = $true) & (setukpairinjR11 = $true) & (dsetconstr__Cong = $true) & (quantDeMorgan3 = $true) & (theprop = $true) & (setadjoinOr = $true) & (binunionIL = $true) & (exuE2 = $true) & (subsetemptysetimpeq = $true) & (setoftrueEq = $true) & (quantDeMorgan4 = $true) & (subsetI2 = $true) & (notdallE = $true) & (disjointsetsI1 = $true) & (binunionLsub = $true) & (setukpairinjR12 = $true) & (setadjoinIR = $true) & (sepInPowerset = $true) & (setukpairinjL1 = $true) & (subsetRefl = $true) & (eqimpsubset2 = $true) & (notequalI2 = $true) & (subPowSU = $true) & (notinsingleton = $true) & (setunionI = $true) & (binintersectSubset5 = $true) & (emptysetimpfalse = $true) & (notequalI1 = $true) & (exuI1 = $true) & (setminusIRneg = $true) & (upairsetE = $true) & (binintersectSubset2 = $true) & (binintersectER = $true) & (upairinpowunion = $true) & (exuE3u = $true) & (eqinunit = $true) & (inCongP = $true) & (setextAx = $true) & (singletonprop = $true) & (notsubsetI = $true) & (dsetconstrI = $true) & (cartprodmempair1 = $true) & (inPowerset = $true) & (binintersectEL = $true) & (binintersectLsub = $true) & (powersetsubset = $true) & (noeltsimpempty = $true) & (symdiffI2 = $true) & (kfstpairEq = $true) & (emptysetsubset = $true) & (exuI3 = $true) & (setminusERneg = $true) & (setadjoinSub2 = $true) & (emptyinunitempty = $true) & (exuI2 = $true) & (foundationAx = $true) & (powersetI = $true) & (prop2setE = $true) & (singletoninpowerset = $true) & (powersetE = $true) & (setminusER = $true) & (powersetI1 = $true) & (nonemptyI = $true) & (setminusLsub = $true) & (singletonsswitch = $true) & (nonemptyImpWitness = $true) & (descr__Cong = $true) & (quantDeMorgan1 = $true) & (prop2set2propI = $true) & (kpairiskpair = $true) & (setminusSubset2 = $true) & (binintersectSubset1 = $true) & (binintersectRsub = $true) & (replAx = $true) & (eqimpsubset1 = $true) & (setadjoin__Cong = $true) & (uniqinunit = $true) & (setunionsingleton = $true) & (vacuousDall = $true) & (setadjoinIL = $true) & (symdiffIneg2 = $true) & (emptyE1 = $true) & (setukpairIR = $true) & (singletonsuniq = $true) & (emptysetAx = $true) & (setadjoinE = $true) & (setunionE2 = $true) & (ubforcartprodlem2 = $true) & (setadjoinSub = $true) & (upairsetIL = $true) & (kfstsingleton = $true) & (exuE3e = $true) & (symdiffI1 = $true) & (singletoninpowunion = $true) & (ubforcartprodlem1 = $true) & (ex1E1 = $true) & (cartprodfstin = $true) & (quantDeMorgan2 = $true) & (sepSubset = $true) & (cartprodpairin = $true) & (symdiffE = $true) & (setextsub = $true) & (ex1I = $true) & (binunionRsub = $true) & (emptyset__Cong = $true) & (upairset2IR = $true) & (subsetI1 = $true) & (setminusEL = $true) & (powersetE1 = $true) & (emptyI = $true) & (setminusI = $true) & (omega0Ax = $true) & (subsetTrans = $true) & (setminusILneg = $true) & (setunion__Cong = $true) & (upairsetIR = $true) & (nonemptyI1 = $true) & (dsetconstrEL = $true) & (setunionE = $true) & (subsetE2 = $true) & (setminusELneg = $true) & (kpairp = $true) & (wellorderingAx = $true) & (setunionAx = $true) & (exu__Cong = $true) & (setext = $true) & (powerset__Cong = $true) & (ubforcartprodlem3 = $true) & (emptyInPowerset = $true) & (bs114d = $true) & (binintersectSubset4 = $true) & (omegaIndAx = $true) & (omega__Cong = $true) & (exuE1 = $true) & (nonemptyE1 = $true) & (setukpairinjL2 = $true) & (binunionIR = $true) & (subsetE = $true) & (upairsubunion = $true) & (exuEu = $true)),
% 2.47/1.85 inference(flattening,[status(thm)],[f606])).
% 2.47/1.85 thf(f606,plain,(
% 2.47/1.85 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((X0 != X2) & (X1 = X2)) & ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X0 @ emptyset)) @ emptyset)))) & (setukpairinjR12 = $true)) & (setukpairinjR11 = $true)) & (setukpairinjL = $true)) & (setukpairinjL2 = $true)) & (cartprodfstin = $true)) & (kfstpairEq = $true)) & (theprop = $true)) & (kfstsingleton = $true)) & (setukpairinjL1 = $true)) & (singletonsuniq = $true)) & (ex1I2 = $true)) & (ex1I = $true)) & (ex1E1 = $true)) & (singletonprop = $true)) & (setunionsingleton = $true)) & (setunionsingleton2 = $true)) & (setunionsingleton1 = $true)) & (setunionE2 = $true)) & (cartprodmempair = $true)) & (cartprodmempair1 = $true)) & (cartprodpairin = $true)) & (ubforcartprodlem3 = $true)) & (ubforcartprodlem2 = $true)) & (ubforcartprodlem1 = $true)) & (upairinpowunion = $true)) & (upairsubunion = $true)) & (upairset2E = $true)) & (singletoninpowunion = $true)) & (singletoninpowerset = $true)) & (singletonsubset = $true)) & (kpairp = $true)) & (kpairiskpair = $true)) & (setukpairIR = $true)) & (setukpairIL = $true)) & (secondinupair = $true)) & (symdiffIneg2 = $true)) & (symdiffIneg1 = $true)) & (symdiffI2 = $true)) & (symdiffI1 = $true)) & (symdiffE = $true)) & (setminusSubset1 = $true)) & (setminusLsub = $true)) & (setminusIRneg = $true)) & (setminusILneg = $true)) & (setminusELneg = $true)) & (setminusERneg = $true)) & (setminusSubset2 = $true)) & (setminusER = $true)) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.47/1.85 inference(ennf_transformation,[status(thm)],[f497])).
% 2.47/1.85 thf(f497,plain,(
% 2.47/1.85 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ((setminusER = $true) => ((setminusSubset2 = $true) => ((setminusERneg = $true) => ((setminusELneg = $true) => ((setminusILneg = $true) => ((setminusIRneg = $true) => ((setminusLsub = $true) => ((setminusSubset1 = $true) => ((symdiffE = $true) => ((symdiffI1 = $true) => ((symdiffI2 = $true) => ((symdiffIneg1 = $true) => ((symdiffIneg2 = $true) => ((secondinupair = $true) => ((setukpairIL = $true) => ((setukpairIR = $true) => ((kpairiskpair = $true) => ((kpairp = $true) => ((singletonsubset = $true) => ((singletoninpowerset = $true) => ((singletoninpowunion = $true) => ((upairset2E = $true) => ((upairsubunion = $true) => ((upairinpowunion = $true) => ((ubforcartprodlem1 = $true) => ((ubforcartprodlem2 = $true) => ((ubforcartprodlem3 = $true) => ((cartprodpairin = $true) => ((cartprodmempair1 = $true) => ((cartprodmempair = $true) => ((setunionE2 = $true) => ((setunionsingleton1 = $true) => ((setunionsingleton2 = $true) => ((setunionsingleton = $true) => ((singletonprop = $true) => ((ex1E1 = $true) => ((ex1I = $true) => ((ex1I2 = $true) => ((singletonsuniq = $true) => ((setukpairinjL1 = $true) => ((kfstsingleton = $true) => ((theprop = $true) => ((kfstpairEq = $true) => ((cartprodfstin = $true) => ((setukpairinjL2 = $true) => ((setukpairinjL = $true) => ((setukpairinjR11 = $true) => ((setukpairinjR12 = $true) => ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => ((X1 = X2) => (X0 = X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.47/1.85 inference(fool_elimination,[status(thm)],[f496])).
% 2.47/1.85 thf(f496,plain,(
% 2.47/1.85 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => ! [X0 : $i,X1 : $i,X2 : $i,X3 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X3 @ emptyset) @ (setadjoin @ (setadjoin @ X3 @ (setadjoin @ X0 @ emptyset)) @ emptyset))) => ((X1 = X2) => (X0 = X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.47/1.85 inference(rectify,[status(thm)],[f175])).
% 2.47/1.85 thf(f175,negated_conjecture,(
% 2.47/1.85 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => ! [X2 : $i,X8 : $i,X10 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => ((X8 = X10) => (X2 = X10))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.47/1.85 inference(negated_conjecture,[status(cth)],[f174])).
% 2.47/1.85 thf(f174,conjecture,(
% 2.47/1.85 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => (setminusER => (setminusSubset2 => (setminusERneg => (setminusELneg => (setminusILneg => (setminusIRneg => (setminusLsub => (setminusSubset1 => (symdiffE => (symdiffI1 => (symdiffI2 => (symdiffIneg1 => (symdiffIneg2 => (secondinupair => (setukpairIL => (setukpairIR => (kpairiskpair => (kpairp => (singletonsubset => (singletoninpowerset => (singletoninpowunion => (upairset2E => (upairsubunion => (upairinpowunion => (ubforcartprodlem1 => (ubforcartprodlem2 => (ubforcartprodlem3 => (cartprodpairin => (cartprodmempair1 => (cartprodmempair => (setunionE2 => (setunionsingleton1 => (setunionsingleton2 => (setunionsingleton => (singletonprop => (ex1E1 => (ex1I => (ex1I2 => (singletonsuniq => (setukpairinjL1 => (kfstsingleton => (theprop => (kfstpairEq => (cartprodfstin => (setukpairinjL2 => (setukpairinjL => (setukpairinjR11 => (setukpairinjR12 => ! [X2 : $i,X8 : $i,X10 : $i,X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X8 @ emptyset) @ (setadjoin @ (setadjoin @ X8 @ (setadjoin @ X10 @ emptyset)) @ emptyset))) => ((X8 = X10) => (X2 = X10)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.47/1.85 file('/export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2THF_26106.p',setukpairinjR1)).
% 2.47/1.85 thf(f2150,plain,(
% 2.47/1.85 (sK352 != sK350)),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f1328])).
% 2.47/1.85 thf(f5555,plain,(
% 2.47/1.85 spl468_81),
% 2.47/1.85 inference(avatar_split_clause,[status(thm)],[f5554,f5537])).
% 2.47/1.85 thf(f5554,plain,(
% 2.47/1.85 (sK351 = sK350)),
% 2.47/1.85 inference(trivial_inequality_removal,[status(thm)],[f5553])).
% 2.47/1.85 thf(f5553,plain,(
% 2.47/1.85 (sK351 = sK350) | ($true != $true)),
% 2.47/1.85 inference(forward_demodulation,[status(thm)],[f5529,f2124])).
% 2.47/1.85 thf(f2124,plain,(
% 2.47/1.85 (notinsingleton = $true)),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f1328])).
% 2.47/1.85 thf(f5529,plain,(
% 2.47/1.85 (notinsingleton != $true) | (sK351 = sK350)),
% 2.47/1.85 inference(trivial_inequality_removal,[status(thm)],[f5522])).
% 2.47/1.85 thf(f5522,plain,(
% 2.47/1.85 (sK351 = sK350) | (notinsingleton != $true) | ($true != $true)),
% 2.47/1.85 inference(superposition,[status(thm)],[f1595,f5245])).
% 2.47/1.85 thf(f5245,plain,(
% 2.47/1.85 ((in @ sK350 @ (setadjoin @ sK351 @ emptyset)) = $true)),
% 2.47/1.85 inference(trivial_inequality_removal,[status(thm)],[f5244])).
% 2.47/1.85 thf(f5244,plain,(
% 2.47/1.85 ((in @ sK350 @ (setadjoin @ sK351 @ emptyset)) = $true) | ($true != $true)),
% 2.47/1.85 inference(forward_demodulation,[status(thm)],[f5241,f2070])).
% 2.47/1.85 thf(f2070,plain,(
% 2.47/1.85 (setunionsingleton = $true)),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f1328])).
% 2.47/1.85 thf(f5241,plain,(
% 2.47/1.85 (setunionsingleton != $true) | ((in @ sK350 @ (setadjoin @ sK351 @ emptyset)) = $true)),
% 2.47/1.85 inference(superposition,[status(thm)],[f2580,f2007])).
% 2.47/1.85 thf(f2007,plain,(
% 2.47/1.85 ( ! [X0 : $i] : (((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) )),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f1326])).
% 2.47/1.85 thf(f1326,plain,(
% 2.47/1.85 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) & ((setunionsingleton = $true) | (sK349 != (setunion @ (setadjoin @ sK349 @ emptyset))))),
% 2.47/1.85 inference(skolemisation,[status(esa),new_symbols(skolem,[sK349])],[f1324,f1325])).
% 2.47/1.85 thf(f1325,plain,(
% 2.47/1.85 ? [X1 : $i] : ((setunion @ (setadjoin @ X1 @ emptyset)) != X1) => (sK349 != (setunion @ (setadjoin @ sK349 @ emptyset)))),
% 2.47/1.85 introduced(definition,[],[choice_axiom])).
% 2.47/1.85 thf(f1324,plain,(
% 2.47/1.85 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) & ((setunionsingleton = $true) | ? [X1 : $i] : ((setunion @ (setadjoin @ X1 @ emptyset)) != X1))),
% 2.47/1.85 inference(rectify,[status(thm)],[f1323])).
% 2.47/1.85 thf(f1323,plain,(
% 2.47/1.85 (! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) | (setunionsingleton != $true)) & ((setunionsingleton = $true) | ? [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) != X0))),
% 2.47/1.85 inference(nnf_transformation,[status(thm)],[f361])).
% 2.47/1.85 thf(f361,plain,(
% 2.47/1.85 ! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0) <=> (setunionsingleton = $true)),
% 2.47/1.85 inference(fool_elimination,[status(thm)],[f360])).
% 2.47/1.85 thf(f360,plain,(
% 2.47/1.85 (setunionsingleton = ! [X0 : $i] : ((setunion @ (setadjoin @ X0 @ emptyset)) = X0))),
% 2.47/1.85 inference(rectify,[status(thm)],[f157])).
% 2.47/1.85 thf(f157,axiom,(
% 2.47/1.85 (setunionsingleton = ! [X1 : $i] : ((setunion @ (setadjoin @ X1 @ emptyset)) = X1))),
% 2.47/1.85 file('/export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2THF_26106.p',setunionsingleton)).
% 2.47/1.85 thf(f2580,plain,(
% 2.47/1.85 ($true = (in @ sK350 @ (setunion @ (setadjoin @ (setadjoin @ sK351 @ emptyset) @ emptyset))))),
% 2.47/1.85 inference(trivial_inequality_removal,[status(thm)],[f2579])).
% 2.47/1.85 thf(f2579,plain,(
% 2.47/1.85 ($true != $true) | ($true = (in @ sK350 @ (setunion @ (setadjoin @ (setadjoin @ sK351 @ emptyset) @ emptyset))))),
% 2.47/1.85 inference(forward_demodulation,[status(thm)],[f2574,f2132])).
% 2.47/1.85 thf(f2132,plain,(
% 2.47/1.85 (setukpairinjR12 = $true)),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f1328])).
% 2.47/1.85 thf(f2574,plain,(
% 2.47/1.85 ($true = (in @ sK350 @ (setunion @ (setadjoin @ (setadjoin @ sK351 @ emptyset) @ emptyset)))) | (setukpairinjR12 != $true)),
% 2.47/1.85 inference(superposition,[status(thm)],[f2556,f2365])).
% 2.47/1.85 thf(f2365,plain,(
% 2.47/1.85 ( ! [X1 : $i] : (((setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X1 @ emptyset)) @ emptyset))) | (setukpairinjR12 != $true)) )),
% 2.47/1.85 inference(equality_resolution,[status(thm)],[f2310])).
% 2.47/1.85 thf(f2310,plain,(
% 2.47/1.85 ( ! [X0 : $i,X1 : $i] : ((X0 != X1) | ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset)) | (setukpairinjR12 != $true)) )),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f1484])).
% 2.47/1.85 thf(f1484,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : ((X0 != X1) | ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))) | (setukpairinjR12 != $true)) & ((setukpairinjR12 = $true) | ((sK451 = sK450) & ((setadjoin @ (setadjoin @ sK450 @ emptyset) @ emptyset) != (setadjoin @ (setadjoin @ sK450 @ emptyset) @ (setadjoin @ (setadjoin @ sK450 @ (setadjoin @ sK451 @ emptyset)) @ emptyset)))))),
% 2.47/1.85 inference(skolemisation,[status(esa),new_symbols(skolem,[sK450,sK451])],[f1482,f1483])).
% 2.47/1.85 thf(f1483,plain,(
% 2.47/1.85 ? [X2 : $i,X3 : $i] : ((X2 = X3) & ((setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset) != (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) => ((sK451 = sK450) & ((setadjoin @ (setadjoin @ sK450 @ emptyset) @ emptyset) != (setadjoin @ (setadjoin @ sK450 @ emptyset) @ (setadjoin @ (setadjoin @ sK450 @ (setadjoin @ sK451 @ emptyset)) @ emptyset))))),
% 2.47/1.85 introduced(definition,[],[choice_axiom])).
% 2.47/1.85 thf(f1482,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : ((X0 != X1) | ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))) | (setukpairinjR12 != $true)) & ((setukpairinjR12 = $true) | ? [X2 : $i,X3 : $i] : ((X2 = X3) & ((setadjoin @ (setadjoin @ X2 @ emptyset) @ emptyset) != (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))))),
% 2.47/1.85 inference(rectify,[status(thm)],[f1481])).
% 2.47/1.85 thf(f1481,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : ((X0 != X1) | ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))) | (setukpairinjR12 != $true)) & ((setukpairinjR12 = $true) | ? [X0 : $i,X1 : $i] : ((X0 = X1) & ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) != (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))))),
% 2.47/1.85 inference(nnf_transformation,[status(thm)],[f581])).
% 2.47/1.85 thf(f581,plain,(
% 2.47/1.85 ! [X0 : $i,X1 : $i] : ((X0 != X1) | ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))) <=> (setukpairinjR12 = $true)),
% 2.47/1.85 inference(ennf_transformation,[status(thm)],[f319])).
% 2.47/1.85 thf(f319,plain,(
% 2.47/1.85 ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))) <=> (setukpairinjR12 = $true)),
% 2.47/1.85 inference(fool_elimination,[status(thm)],[f318])).
% 2.47/1.85 thf(f318,plain,(
% 2.47/1.85 (setukpairinjR12 = ! [X0 : $i,X1 : $i] : ((X0 = X1) => ((setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X0 @ emptyset) @ emptyset))))),
% 2.47/1.85 inference(rectify,[status(thm)],[f173])).
% 2.47/1.85 thf(f173,axiom,(
% 2.47/1.85 (setukpairinjR12 = ! [X1 : $i,X2 : $i] : ((X1 = X2) => ((setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ X1 @ emptyset) @ emptyset))))),
% 2.47/1.85 file('/export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2THF_26106.p',setukpairinjR12)).
% 2.47/1.85 thf(f2556,plain,(
% 2.47/1.85 ((in @ sK350 @ (setunion @ (setadjoin @ (setadjoin @ sK351 @ emptyset) @ (setadjoin @ (setadjoin @ sK351 @ (setadjoin @ sK351 @ emptyset)) @ emptyset)))) = $true)),
% 2.47/1.85 inference(trivial_inequality_removal,[status(thm)],[f2555])).
% 2.47/1.85 thf(f2555,plain,(
% 2.47/1.85 ($true != $true) | ((in @ sK350 @ (setunion @ (setadjoin @ (setadjoin @ sK351 @ emptyset) @ (setadjoin @ (setadjoin @ sK351 @ (setadjoin @ sK351 @ emptyset)) @ emptyset)))) = $true)),
% 2.47/1.85 inference(forward_demodulation,[status(thm)],[f2451,f2065])).
% 2.47/1.85 thf(f2065,plain,(
% 2.47/1.85 (setukpairIR = $true)),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f1328])).
% 2.47/1.85 thf(f2451,plain,(
% 2.47/1.85 (setukpairIR != $true) | ((in @ sK350 @ (setunion @ (setadjoin @ (setadjoin @ sK351 @ emptyset) @ (setadjoin @ (setadjoin @ sK351 @ (setadjoin @ sK351 @ emptyset)) @ emptyset)))) = $true)),
% 2.47/1.85 inference(superposition,[status(thm)],[f1699,f2450])).
% 2.47/1.85 thf(f2450,plain,(
% 2.47/1.85 ((setadjoin @ (setadjoin @ sK351 @ emptyset) @ (setadjoin @ (setadjoin @ sK351 @ (setadjoin @ sK351 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK353 @ emptyset) @ (setadjoin @ (setadjoin @ sK353 @ (setadjoin @ sK350 @ emptyset)) @ emptyset)))),
% 2.47/1.85 inference(forward_demodulation,[status(thm)],[f2148,f2149])).
% 2.47/1.85 thf(f2148,plain,(
% 2.47/1.85 ((setadjoin @ (setadjoin @ sK353 @ emptyset) @ (setadjoin @ (setadjoin @ sK353 @ (setadjoin @ sK350 @ emptyset)) @ emptyset)) = (setadjoin @ (setadjoin @ sK351 @ emptyset) @ (setadjoin @ (setadjoin @ sK351 @ (setadjoin @ sK352 @ emptyset)) @ emptyset)))),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f1328])).
% 2.47/1.85 thf(f1699,plain,(
% 2.47/1.85 ( ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) | (setukpairIR != $true)) )),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f975])).
% 2.47/1.85 thf(f975,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) | (setukpairIR != $true)) & ((setukpairIR = $true) | ((in @ sK138 @ (setunion @ (setadjoin @ (setadjoin @ sK137 @ emptyset) @ (setadjoin @ (setadjoin @ sK137 @ (setadjoin @ sK138 @ emptyset)) @ emptyset)))) != $true))),
% 2.47/1.85 inference(skolemisation,[status(esa),new_symbols(skolem,[sK137,sK138])],[f973,f974])).
% 2.47/1.85 thf(f974,plain,(
% 2.47/1.85 ? [X2 : $i,X3 : $i] : ((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) != $true) => ((in @ sK138 @ (setunion @ (setadjoin @ (setadjoin @ sK137 @ emptyset) @ (setadjoin @ (setadjoin @ sK137 @ (setadjoin @ sK138 @ emptyset)) @ emptyset)))) != $true)),
% 2.47/1.85 introduced(definition,[],[choice_axiom])).
% 2.47/1.85 thf(f973,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) | (setukpairIR != $true)) & ((setukpairIR = $true) | ? [X2 : $i,X3 : $i] : ((in @ X3 @ (setunion @ (setadjoin @ (setadjoin @ X2 @ emptyset) @ (setadjoin @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)) @ emptyset)))) != $true))),
% 2.47/1.85 inference(rectify,[status(thm)],[f972])).
% 2.47/1.85 thf(f972,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) | (setukpairIR != $true)) & ((setukpairIR = $true) | ? [X0 : $i,X1 : $i] : ($true != (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))))),
% 2.47/1.85 inference(nnf_transformation,[status(thm)],[f327])).
% 2.47/1.85 thf(f327,plain,(
% 2.47/1.85 ! [X0 : $i,X1 : $i] : ($true = (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset))))) <=> (setukpairIR = $true)),
% 2.47/1.85 inference(fool_elimination,[status(thm)],[f326])).
% 2.47/1.85 thf(f326,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setunion @ (setadjoin @ (setadjoin @ X0 @ emptyset) @ (setadjoin @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)) @ emptyset)))) = setukpairIR)),
% 2.47/1.85 inference(rectify,[status(thm)],[f138])).
% 2.47/1.85 thf(f138,axiom,(
% 2.47/1.85 (! [X1 : $i,X2 : $i] : (in @ X2 @ (setunion @ (setadjoin @ (setadjoin @ X1 @ emptyset) @ (setadjoin @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)) @ emptyset)))) = setukpairIR)),
% 2.47/1.85 file('/export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2THF_26106.p',setukpairIR)).
% 2.47/1.85 thf(f1595,plain,(
% 2.47/1.85 ( ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (notinsingleton != $true) | (X0 = X1)) )),
% 2.47/1.85 inference(cnf_transformation,[status(thm)],[f847])).
% 2.47/1.85 thf(f847,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) | (notinsingleton != $true)) & ((notinsingleton = $true) | (($true = (in @ sK67 @ (setadjoin @ sK68 @ emptyset))) & (sK67 != sK68)))),
% 2.47/1.85 inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f845,f846])).
% 2.47/1.85 thf(f846,plain,(
% 2.47/1.85 ? [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X3 @ emptyset)) = $true) & (X2 != X3)) => (($true = (in @ sK67 @ (setadjoin @ sK68 @ emptyset))) & (sK67 != sK68))),
% 2.47/1.85 introduced(definition,[],[choice_axiom])).
% 2.47/1.85 thf(f845,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) | (notinsingleton != $true)) & ((notinsingleton = $true) | ? [X2 : $i,X3 : $i] : (((in @ X2 @ (setadjoin @ X3 @ emptyset)) = $true) & (X2 != X3)))),
% 2.47/1.85 inference(rectify,[status(thm)],[f844])).
% 2.47/1.85 thf(f844,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) | (notinsingleton != $true)) & ((notinsingleton = $true) | ? [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true) & (X0 != X1)))),
% 2.47/1.85 inference(nnf_transformation,[status(thm)],[f680])).
% 2.47/1.85 thf(f680,plain,(
% 2.47/1.85 ! [X0 : $i,X1 : $i] : (((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true) | (X0 = X1)) <=> (notinsingleton = $true)),
% 2.47/1.85 inference(ennf_transformation,[status(thm)],[f553])).
% 2.47/1.85 thf(f553,plain,(
% 2.47/1.85 (notinsingleton = $true) <=> ! [X0 : $i,X1 : $i] : ((X0 != X1) => ((in @ X0 @ (setadjoin @ X1 @ emptyset)) != $true))),
% 2.47/1.85 inference(flattening,[status(thm)],[f489])).
% 2.47/1.85 thf(f489,plain,(
% 2.47/1.85 ! [X0 : $i,X1 : $i] : ((X0 != X1) => ~((in @ X0 @ (setadjoin @ X1 @ emptyset)) = $true)) <=> (notinsingleton = $true)),
% 2.47/1.85 inference(fool_elimination,[status(thm)],[f488])).
% 2.47/1.85 thf(f488,plain,(
% 2.47/1.85 (! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X0 @ (setadjoin @ X1 @ emptyset))) = notinsingleton)),
% 2.47/1.85 inference(rectify,[status(thm)],[f47])).
% 2.47/1.85 thf(f47,axiom,(
% 2.47/1.85 (! [X2 : $i,X1 : $i] : ((X1 != X2) => ~(in @ X2 @ (setadjoin @ X1 @ emptyset))) = notinsingleton)),
% 2.47/1.85 file('/export/starexec/sandbox2/tmp/tmp.S6XhyIJwe2/DTF2THF_26106.p',notinsingleton)).
% 2.47/1.85 % SZS output end Proof for DTF2THF_26106
% 2.47/1.85 % (26265)------------------------------
% 2.47/1.85 % (26265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.47/1.85 % (26265)Termination reason: Refutation
% 2.47/1.85
% 2.47/1.85 % (26265)Memory used [KB]: 9210
% 2.47/1.85 % (26265)Time elapsed: 0.375 s
% 2.47/1.85 % (26265)Instructions burned: 849 (million)
% 2.47/1.85 % (26265)------------------------------
% 2.47/1.85 % (26265)------------------------------
% 2.47/1.85 % (26241)Success in time 0.477 s
%------------------------------------------------------------------------------