%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU646^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 09:35:55 AM UTC 2026
% Result : Theorem 33.23s 6.16s
% Output : Refutation 33.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 54 ( 11 unt; 0 typ; 5 def)
% Number of atoms : 2838 ( 774 equ; 0 cnn)
% Maximal formula atoms : 164 ( 52 avg)
% Number of connectives : 1696 ( 71 ~; 57 |; 522 &; 378 @)
% ( 8 <=>; 660 =>; 0 <=; 0 <~>)
% Maximal formula depth : 171 ( 26 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 317 ( 314 usr; 177 con; 0-4 aty)
% Number of variables : 125 ( 0 ^; 85 !; 40 ?; 125 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_177,type,
singleton: $i > $o ).
thf(func_def_179,type,
ex1: $i > ( $i > $o ) > $o ).
thf(func_def_184,type,
atmost1p: $i > $o ).
thf(func_def_185,type,
atleast2p: $i > $o ).
thf(func_def_186,type,
atmost2p: $i > $o ).
thf(func_def_187,type,
upairsetp: $i > $o ).
thf(func_def_191,type,
kfst: $i > $i ).
thf(func_def_205,type,
sP0: $i > $i > $o ).
thf(func_def_206,type,
sP1: $i > $o ).
thf(func_def_207,type,
sP2: $i > $i > $o ).
thf(func_def_208,type,
sP3: $i > $i > $o ).
thf(func_def_209,type,
sP4: $i > $o > $i > $i > $o ).
thf(func_def_219,type,
sK14: $i > $i ).
thf(func_def_220,type,
sK15: $i > $i > $i ).
thf(func_def_236,type,
sK31: $i > $i > $i ).
thf(func_def_237,type,
sK32: $i > $i > $i ).
thf(func_def_238,type,
sK33: $i > $i > $i ).
thf(func_def_239,type,
sK34: $i > $i > $i ).
thf(func_def_240,type,
sK35: $i > $i > $i ).
thf(func_def_241,type,
sK36: $i > $i > $i > $i ).
thf(func_def_242,type,
sK37: $i > $i ).
thf(func_def_243,type,
sK38: $i > $i ).
thf(func_def_244,type,
sK39: $i > $i ).
thf(func_def_245,type,
sK40: $i > $i ).
thf(func_def_246,type,
sK41: $i > $i > $i ).
thf(func_def_247,type,
sK42: $i > $i > $i > $i ).
thf(func_def_248,type,
sK43: $i > $i > $i > $i ).
thf(func_def_249,type,
sK44: $i > $i > $i ).
thf(func_def_250,type,
sK45: $i > $i > $i ).
thf(func_def_252,type,
sK47: $i > $i ).
thf(func_def_253,type,
sK48: $i > $i ).
thf(func_def_254,type,
sK49: $i > $i ).
thf(func_def_283,type,
sK78: $i > $o ).
thf(func_def_297,type,
sK92: $i > $o ).
thf(func_def_303,type,
sK98: $i > $o ).
thf(func_def_305,type,
sK100: ( $i > $o ) > $i ).
thf(func_def_306,type,
sK101: ( $i > $o ) > $i ).
thf(func_def_308,type,
sK103: $i > $o ).
thf(func_def_318,type,
sK113: $i > $i ).
thf(func_def_327,type,
sK122: $i > $o ).
thf(func_def_328,type,
sK123: $i > $o ).
thf(func_def_329,type,
sK124: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_330,type,
sK125: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_342,type,
sK137: $i > $o ).
thf(func_def_343,type,
sK138: $i > $o ).
thf(func_def_345,type,
sK140: $i > ( $i > $o ) > $i ).
thf(func_def_348,type,
sK143: $i > $o ).
thf(func_def_356,type,
sK151: $i > $o ).
thf(func_def_359,type,
sK154: $i > ( $i > $o ) > $i ).
thf(func_def_360,type,
sK155: $i > ( $i > $o ) > $i ).
thf(func_def_361,type,
sK156: $i > $i > $i ).
thf(func_def_366,type,
sK161: $i > $i ).
thf(func_def_371,type,
sK166: $i > $i ).
thf(func_def_377,type,
sK172: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_378,type,
sK173: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_379,type,
sK174: $i > $o ).
thf(func_def_380,type,
sK175: $i > $o ).
thf(func_def_381,type,
sK176: $i > $o ).
thf(func_def_384,type,
sK179: ( $i > $o ) > $i > $i ).
thf(func_def_386,type,
sK181: $i > $o ).
thf(func_def_387,type,
sK182: $i > $i > $i ).
thf(func_def_390,type,
sK185: $i > ( $i > $o ) > $i ).
thf(func_def_391,type,
sK186: $i > $o ).
thf(func_def_397,type,
sK192: $i > $i > $i ).
thf(func_def_404,type,
sK199: $i > $i ).
thf(func_def_406,type,
sK201: $i > $i ).
thf(func_def_408,type,
sK203: $i > $i > $i ).
thf(func_def_409,type,
sK204: $i > $i > $i ).
thf(func_def_412,type,
sK207: $i > ( $i > $o ) > $i ).
thf(func_def_413,type,
sK208: $i > $o ).
thf(func_def_427,type,
sK222: ( $i > $o ) > $i ).
thf(func_def_428,type,
sK223: $i > $o ).
thf(func_def_429,type,
sK224: $i > $i ).
thf(func_def_430,type,
sK225: $i > $i > $o ).
thf(func_def_432,type,
sK227: $i > $i ).
thf(func_def_433,type,
sK228: $i > $i ).
thf(func_def_434,type,
sK229: $i > ( $i > $i > $o ) > $i ).
thf(func_def_435,type,
sK230: $i > ( $i > $i > $o ) > $i ).
thf(func_def_436,type,
sK231: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_447,type,
sK242: $i > $o ).
thf(func_def_457,type,
sK252: $i > ( $i > $o ) > $i ).
thf(func_def_458,type,
sK253: $i > $o ).
thf(func_def_466,type,
sK261: $i > $o ).
thf(func_def_467,type,
sK262: $i > $i ).
thf(func_def_468,type,
sK263: ( $i > $o ) > $i ).
thf(func_def_475,type,
sK270: $i > $o ).
thf(func_def_477,type,
sK272: ( $i > $o ) > $i > $i ).
thf(func_def_478,type,
sK273: ( $i > $o ) > $i > $i ).
thf(func_def_481,type,
sK276: $i > $i > $i ).
thf(func_def_489,type,
sK284: $i > $o ).
thf(func_def_492,type,
sK287: $i > ( $i > $o ) > $i ).
thf(func_def_496,type,
sK291: $i > $o ).
thf(func_def_499,type,
sK294: $i > $i > ( $i > $o ) > $i ).
thf(func_def_516,type,
sK311: $i > $o ).
thf(func_def_517,type,
sK312: $i > $o ).
thf(func_def_518,type,
sK313: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_519,type,
sK314: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_520,type,
sK315: $i > $o ).
thf(func_def_526,type,
sK321: $i > $i > $i > $i ).
thf(func_def_527,type,
sK322: $i > $i > $i > $i ).
thf(func_def_553,type,
sK348: $i > $o ).
thf(func_def_556,type,
sK351: $i > $i > $i ).
thf(func_def_563,type,
sK358: $i > ( $i > $o ) > $i ).
thf(func_def_564,type,
sK359: $i > $o ).
thf(func_def_578,type,
sK373: $i > $o ).
thf(func_def_585,type,
sK380: $i > ( $i > $o ) > $i ).
thf(func_def_586,type,
sK381: $i > $o ).
thf(func_def_603,type,
sK398: $o > $i > $i > $i ).
thf(func_def_606,type,
sK401: $i > $i > $i ).
thf(func_def_609,type,
sK404: $i > $o ).
thf(func_def_616,type,
sK411: $i > $i ).
thf(func_def_638,type,
sK433: $i > $i > $i ).
thf(func_def_643,type,
sK438: ( $i > $o ) > $i ).
thf(func_def_644,type,
sK439: $i > $o ).
thf(func_def_645,type,
sK440: ( $i > $o ) > $i > $i ).
thf(func_def_647,type,
sK442: $i > $o ).
thf(func_def_649,type,
sK444: $i > $o ).
thf(func_def_658,type,
ph453:
!>[X0: $tType] : X0 ).
thf(f16757,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f3073,f3082,f3792,f5120,f5410,f16756]) ).
thf(f16756,plain,
( ~ spl452_148
| ~ spl452_150
| ~ spl452_587 ),
inference(avatar_contradiction_clause,[status(thm)],[f16755]) ).
thf(f16755,plain,
( $false
| ~ spl452_148
| ~ spl452_150
| ~ spl452_587 ),
inference(subsumption_resolution,[status(thm)],[f16754,f2070]) ).
thf(f2070,plain,
( $true
!= ( in @ ( kfst @ sK386 ) @ sK385 ) ),
inference(cnf_transformation,[status(thm)],[f1355]) ).
thf(f1355,plain,
( ( emptyinunitempty = $true )
& ( setunionsingleton2 = $true )
& ( upairsetIL = $true )
& ( uniqinunit = $true )
& ( notequalI2 = $true )
& ( subsetTrans = $true )
& ( symdiffI1 = $true )
& ( binintersectSubset2 = $true )
& ( exuI2 = $true )
& ( bs114d = $true )
& ( exuI1 = $true )
& ( setadjoinOr = $true )
& ( setoftrueEq = $true )
& ( dsetconstr__Cong = $true )
& ( sepInPowerset = $true )
& ( vacuousDall = $true )
& ( sepSubset = $true )
& ( setukpairIR = $true )
& ( binunionIL = $true )
& ( quantDeMorgan4 = $true )
& ( descr__Cong = $true )
& ( emptysetE = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinSub = $true )
& ( setextsub = $true )
& ( ubforcartprodlem2 = $true )
& ( setunionsingleton = $true )
& ( omega0Ax = $true )
& ( powersetE = $true )
& ( subsetE2 = $true )
& ( ex1I2 = $true )
& ( setunionAx = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( setminusSubset1 = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( omega__Cong = $true )
& ( singletonsuniq = $true )
& ( binintersectSubset5 = $true )
& ( binintersectER = $true )
& ( descrp = $true )
& ( setadjoinIR = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( nonemptyI1 = $true )
& ( setadjoinIL = $true )
& ( nonemptyI = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan2 = $true )
& ( singletonprop = $true )
& ( setukpairinjL1 = $true )
& ( theprop = $true )
& ( ex1E1 = $true )
& ( in__Cong = $true )
& ( setadjoin__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( prop2setI = $true )
& ( setadjoinAx = $true )
& ( subsetI1 = $true )
& ( exuI3 = $true )
& ( singletonsswitch = $true )
& ( symdiffI2 = $true )
& ( exu__Cong = $true )
& ( symdiffIneg2 = $true )
& ( omegaIndAx = $true )
& ( wellorderingAx = $true )
& ( upairsubunion = $true )
& ( subPowSU = $true )
& ( subsetE = $true )
& ( singletoninpowunion = $true )
& ( subsetRefl = $true )
& ( setminusLsub = $true )
& ( omegaSAx = $true )
& ( binintersectLsub = $true )
& ( setextAx = $true )
& ( eqimpsubset1 = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( kpairp = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset1 = $true )
& ( binintersectEL = $true )
& ( exuE2 = $true )
& ( binintersectRsub = $true )
& ( setunionE = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrI = $true )
& ( setunionI = $true )
& ( symdiffE = $true )
& ( subset2powerset = $true )
& ( replAx = $true )
& ( emptyset__Cong = $true )
& ( emptyE1 = $true )
& ( eqimpsubset2 = $true )
& ( setminusIRneg = $true )
& ( setukpairIL = $true )
& ( emptyinPowerset = $true )
& ( $true
!= ( in @ ( kfst @ sK386 ) @ sK385 ) )
& ( ( in @ sK386 @ ( cartprod @ sK385 @ sK384 ) )
= $true )
& ( exuEu = $true )
& ( notinemptyset = $true )
& ( kfstsingleton = $true )
& ( setminusI = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( kpairiskpair = $true )
& ( setminusERneg = $true )
& ( binunionE = $true )
& ( binintersectSubset4 = $true )
& ( prop2set2propI = $true )
& ( powerset__Cong = $true )
& ( notsubsetI = $true )
& ( singletoninpowerset = $true )
& ( powersetI = $true )
& ( setunionE2 = $true )
& ( upairinpowunion = $true )
& ( setunionsingleton1 = $true )
& ( notdexE = $true )
& ( emptyI = $true )
& ( powersetsubset = $true )
& ( cartprodmempair1 = $true )
& ( emptysetimpfalse = $true )
& ( kfstpairEq = $true )
& ( upairset2IR = $true )
& ( upairsetE = $true )
& ( ex1I = $true )
& ( quantDeMorgan1 = $true )
& ( binunionRsub = $true )
& ( binintersectI = $true )
& ( powersetAx = $true )
& ( binunionIR = $true )
& ( dsetconstrEL = $true )
& ( ubforcartprodlem3 = $true )
& ( setminusER = $true )
& ( symdiffIneg1 = $true )
& ( emptysetsubset = $true )
& ( setadjoinSub2 = $true )
& ( subsetI2 = $true )
& ( setadjoinE = $true )
& ( upairset2E = $true )
& ( ubforcartprodlem1 = $true )
& ( setbeta = $true )
& ( singletonsubset = $true )
& ( setminusILneg = $true )
& ( setminusEL = $true )
& ( upairsetIR = $true )
& ( subsetemptysetimpeq = $true )
& ( cartprodmempair = $true )
& ( exuE1 = $true )
& ( inCongP = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( binunionLsub = $true )
& ( inPowerset = $true )
& ( notequalI1 = $true )
& ( setminusELneg = $true )
& ( cartprodpairin = $true )
& ( disjointsetsI1 = $true )
& ( binunionEcases = $true )
& ( exuE3u = $true )
& ( secondinupair = $true )
& ( setext = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK384,sK385,sK386])],[f573,f1354]) ).
thf(f1354,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( kfst @ X2 ) @ X1 ) )
& ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
= $true ) )
=> ( ( $true
!= ( in @ ( kfst @ sK386 ) @ sK385 ) )
& ( ( in @ sK386 @ ( cartprod @ sK385 @ sK384 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f573,plain,
( ( emptyinunitempty = $true )
& ( setunionsingleton2 = $true )
& ( upairsetIL = $true )
& ( uniqinunit = $true )
& ( notequalI2 = $true )
& ( subsetTrans = $true )
& ( symdiffI1 = $true )
& ( binintersectSubset2 = $true )
& ( exuI2 = $true )
& ( bs114d = $true )
& ( exuI1 = $true )
& ( setadjoinOr = $true )
& ( setoftrueEq = $true )
& ( dsetconstr__Cong = $true )
& ( sepInPowerset = $true )
& ( vacuousDall = $true )
& ( sepSubset = $true )
& ( setukpairIR = $true )
& ( binunionIL = $true )
& ( quantDeMorgan4 = $true )
& ( descr__Cong = $true )
& ( emptysetE = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinSub = $true )
& ( setextsub = $true )
& ( ubforcartprodlem2 = $true )
& ( setunionsingleton = $true )
& ( omega0Ax = $true )
& ( powersetE = $true )
& ( subsetE2 = $true )
& ( ex1I2 = $true )
& ( setunionAx = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( setminusSubset1 = $true )
& ( nonemptyE1 = $true )
& ( noeltsimpempty = $true )
& ( omega__Cong = $true )
& ( singletonsuniq = $true )
& ( binintersectSubset5 = $true )
& ( binintersectER = $true )
& ( descrp = $true )
& ( setadjoinIR = $true )
& ( foundationAx = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( nonemptyI1 = $true )
& ( setadjoinIL = $true )
& ( nonemptyI = $true )
& ( setunion__Cong = $true )
& ( quantDeMorgan2 = $true )
& ( singletonprop = $true )
& ( setukpairinjL1 = $true )
& ( theprop = $true )
& ( ex1E1 = $true )
& ( in__Cong = $true )
& ( setadjoin__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( prop2setI = $true )
& ( setadjoinAx = $true )
& ( subsetI1 = $true )
& ( exuI3 = $true )
& ( singletonsswitch = $true )
& ( symdiffI2 = $true )
& ( exu__Cong = $true )
& ( symdiffIneg2 = $true )
& ( omegaIndAx = $true )
& ( wellorderingAx = $true )
& ( upairsubunion = $true )
& ( subPowSU = $true )
& ( subsetE = $true )
& ( singletoninpowunion = $true )
& ( subsetRefl = $true )
& ( setminusLsub = $true )
& ( omegaSAx = $true )
& ( binintersectLsub = $true )
& ( setextAx = $true )
& ( eqimpsubset1 = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( kpairp = $true )
& ( setminusSubset2 = $true )
& ( binintersectSubset1 = $true )
& ( binintersectEL = $true )
& ( exuE2 = $true )
& ( binintersectRsub = $true )
& ( setunionE = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrI = $true )
& ( setunionI = $true )
& ( symdiffE = $true )
& ( subset2powerset = $true )
& ( replAx = $true )
& ( emptyset__Cong = $true )
& ( emptyE1 = $true )
& ( eqimpsubset2 = $true )
& ( setminusIRneg = $true )
& ( setukpairIL = $true )
& ( emptyinPowerset = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( kfst @ X2 ) @ X1 ) )
& ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
= $true ) )
& ( exuEu = $true )
& ( notinemptyset = $true )
& ( kfstsingleton = $true )
& ( setminusI = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( kpairiskpair = $true )
& ( setminusERneg = $true )
& ( binunionE = $true )
& ( binintersectSubset4 = $true )
& ( prop2set2propI = $true )
& ( powerset__Cong = $true )
& ( notsubsetI = $true )
& ( singletoninpowerset = $true )
& ( powersetI = $true )
& ( setunionE2 = $true )
& ( upairinpowunion = $true )
& ( setunionsingleton1 = $true )
& ( notdexE = $true )
& ( emptyI = $true )
& ( powersetsubset = $true )
& ( cartprodmempair1 = $true )
& ( emptysetimpfalse = $true )
& ( kfstpairEq = $true )
& ( upairset2IR = $true )
& ( upairsetE = $true )
& ( ex1I = $true )
& ( quantDeMorgan1 = $true )
& ( binunionRsub = $true )
& ( binintersectI = $true )
& ( powersetAx = $true )
& ( binunionIR = $true )
& ( dsetconstrEL = $true )
& ( ubforcartprodlem3 = $true )
& ( setminusER = $true )
& ( symdiffIneg1 = $true )
& ( emptysetsubset = $true )
& ( setadjoinSub2 = $true )
& ( subsetI2 = $true )
& ( setadjoinE = $true )
& ( upairset2E = $true )
& ( ubforcartprodlem1 = $true )
& ( setbeta = $true )
& ( singletonsubset = $true )
& ( setminusILneg = $true )
& ( setminusEL = $true )
& ( upairsetIR = $true )
& ( subsetemptysetimpeq = $true )
& ( cartprodmempair = $true )
& ( exuE1 = $true )
& ( inCongP = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( binunionLsub = $true )
& ( inPowerset = $true )
& ( notequalI1 = $true )
& ( setminusELneg = $true )
& ( cartprodpairin = $true )
& ( disjointsetsI1 = $true )
& ( binunionEcases = $true )
& ( exuE3u = $true )
& ( secondinupair = $true )
& ( setext = $true ) ),
inference(flattening,[status(thm)],[f572]) ).
thf(f572,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ ( kfst @ X2 ) @ X1 ) )
& ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
= $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)],[f379]) ).
thf(f379,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
= $true )
=> ( $true
= ( in @ ( kfst @ X2 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f378]) ).
thf(f378,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( cartprod @ X1 @ X0 ) )
=> ( in @ ( kfst @ X2 ) @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f170]) ).
thf(f170,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
=> ! [X4: $i,X3: $i,X10: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( kfst @ X10 ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f169]) ).
thf(f169,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
=> ! [X4: $i,X3: $i,X10: $i] :
( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ( in @ ( kfst @ X10 ) @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BWMLOxAvmL/DTF2THF_6029.p',cartprodfstin) ).
thf(f16754,plain,
( ( $true
= ( in @ ( kfst @ sK386 ) @ sK385 ) )
| ~ spl452_148
| ~ spl452_150
| ~ spl452_587 ),
inference(backward_demodulation,[status(thm)],[f10216,f16752]) ).
thf(f16752,plain,
( ( ( sK321 @ sK384 @ sK385 @ sK386 )
= ( kfst @ sK386 ) )
| ~ spl452_148
| ~ spl452_587 ),
inference(superposition,[status(thm)],[f3072,f10830]) ).
thf(f10830,plain,
( ( sK386
= ( kpair @ ( sK321 @ sK384 @ sK385 @ sK386 ) @ ( sK322 @ sK384 @ sK385 @ sK386 ) ) )
| ~ spl452_587 ),
inference(trivial_inequality_removal,[status(thm)],[f10811]) ).
thf(f10811,plain,
( ( $true != $true )
| ( sK386
= ( kpair @ ( sK321 @ sK384 @ sK385 @ sK386 ) @ ( sK322 @ sK384 @ sK385 @ sK386 ) ) )
| ~ spl452_587 ),
inference(superposition,[status(thm)],[f5119,f2069]) ).
thf(f2069,plain,
( ( in @ sK386 @ ( cartprod @ sK385 @ sK384 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f1355]) ).
thf(f5119,plain,
( ! [X6: $i,X7: $i,X5: $i] :
( ( ( in @ X5 @ ( cartprod @ X6 @ X7 ) )
!= $true )
| ( ( kpair @ ( sK321 @ X7 @ X6 @ X5 ) @ ( sK322 @ X7 @ X6 @ X5 ) )
= X5 ) )
| ~ spl452_587 ),
inference(avatar_component_clause,[status(thm)],[f5118]) ).
thf(f5118,definition,
( spl452_587
<=> ! [X6: $i,X5: $i,X7: $i] :
( ( ( kpair @ ( sK321 @ X7 @ X6 @ X5 ) @ ( sK322 @ X7 @ X6 @ X5 ) )
= X5 )
| ( ( in @ X5 @ ( cartprod @ X6 @ X7 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl452_587])],[avatar_definition]) ).
thf(f3072,plain,
( ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 )
| ~ spl452_148 ),
inference(avatar_component_clause,[status(thm)],[f3071]) ).
thf(f3071,definition,
( spl452_148
<=> ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 ) ),
introduced(definition,[new_symbols(naming,[spl452_148])],[avatar_definition]) ).
thf(f10216,plain,
( ( ( in @ ( sK321 @ sK384 @ sK385 @ sK386 ) @ sK385 )
= $true )
| ~ spl452_150 ),
inference(trivial_inequality_removal,[status(thm)],[f10195]) ).
thf(f10195,plain,
( ( $true != $true )
| ( ( in @ ( sK321 @ sK384 @ sK385 @ sK386 ) @ sK385 )
= $true )
| ~ spl452_150 ),
inference(superposition,[status(thm)],[f3081,f2069]) ).
thf(f3081,plain,
( ! [X6: $i,X7: $i,X5: $i] :
( ( ( in @ X5 @ ( cartprod @ X6 @ X7 ) )
!= $true )
| ( ( in @ ( sK321 @ X7 @ X6 @ X5 ) @ X6 )
= $true ) )
| ~ spl452_150 ),
inference(avatar_component_clause,[status(thm)],[f3080]) ).
thf(f3080,definition,
( spl452_150
<=> ! [X6: $i,X5: $i,X7: $i] :
( ( ( in @ ( sK321 @ X7 @ X6 @ X5 ) @ X6 )
= $true )
| ( ( in @ X5 @ ( cartprod @ X6 @ X7 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl452_150])],[avatar_definition]) ).
thf(f5410,plain,
spl452_6,
inference(avatar_split_clause,[status(thm)],[f2045,f2447]) ).
thf(f2447,definition,
( spl452_6
<=> ( kfstpairEq = $true ) ),
introduced(definition,[new_symbols(naming,[spl452_6])],[avatar_definition]) ).
thf(f2045,plain,
kfstpairEq = $true,
inference(cnf_transformation,[status(thm)],[f1355]) ).
thf(f5120,plain,
( ~ spl452_42
| spl452_587 ),
inference(avatar_split_clause,[status(thm)],[f1925,f5118,f2604]) ).
thf(f2604,definition,
( spl452_42
<=> ( cartprodmempair1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl452_42])],[avatar_definition]) ).
thf(f1925,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( ( kpair @ ( sK321 @ X7 @ X6 @ X5 ) @ ( sK322 @ X7 @ X6 @ X5 ) )
= X5 )
| ( ( in @ X5 @ ( cartprod @ X6 @ X7 ) )
!= $true )
| ( cartprodmempair1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1258]) ).
thf(f1258,plain,
( ( ( cartprodmempair1 = $true )
| ( ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= sK318 )
| ( ( in @ X4 @ sK320 )
!= $true ) )
| ( $true
!= ( in @ X3 @ sK319 ) ) )
& ( ( in @ sK318 @ ( cartprod @ sK319 @ sK320 ) )
= $true ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ( ( ( kpair @ ( sK321 @ X7 @ X6 @ X5 ) @ ( sK322 @ X7 @ X6 @ X5 ) )
= X5 )
& ( $true
= ( in @ ( sK322 @ X7 @ X6 @ X5 ) @ X7 ) )
& ( ( in @ ( sK321 @ X7 @ X6 @ X5 ) @ X6 )
= $true ) )
| ( ( in @ X5 @ ( cartprod @ X6 @ X7 ) )
!= $true ) )
| ( cartprodmempair1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK318,sK319,sK320,sK321,sK322])],[f1254,f1257,f1256,f1255]) ).
thf(f1255,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= X0 )
| ( ( in @ X4 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
& ( $true
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) )
=> ( ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= sK318 )
| ( ( in @ X4 @ sK320 )
!= $true ) )
| ( $true
!= ( in @ X3 @ sK319 ) ) )
& ( ( in @ sK318 @ ( cartprod @ sK319 @ sK320 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1256,plain,
! [X5: $i,X6: $i,X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( ( kpair @ X8 @ X9 )
= X5 )
& ( $true
= ( in @ X9 @ X7 ) ) )
& ( $true
= ( in @ X8 @ X6 ) ) )
=> ( ? [X9: $i] :
( ( ( kpair @ ( sK321 @ X7 @ X6 @ X5 ) @ X9 )
= X5 )
& ( $true
= ( in @ X9 @ X7 ) ) )
& ( ( in @ ( sK321 @ X7 @ X6 @ X5 ) @ X6 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1257,plain,
! [X5: $i,X6: $i,X7: $i] :
( ? [X9: $i] :
( ( ( kpair @ ( sK321 @ X7 @ X6 @ X5 ) @ X9 )
= X5 )
& ( $true
= ( in @ X9 @ X7 ) ) )
=> ( ( ( kpair @ ( sK321 @ X7 @ X6 @ X5 ) @ ( sK322 @ X7 @ X6 @ X5 ) )
= X5 )
& ( $true
= ( in @ ( sK322 @ X7 @ X6 @ X5 ) @ X7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f1254,plain,
( ( ( cartprodmempair1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= X0 )
| ( ( in @ X4 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
& ( $true
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ) )
& ( ! [X5: $i,X6: $i,X7: $i] :
( ? [X8: $i] :
( ? [X9: $i] :
( ( ( kpair @ X8 @ X9 )
= X5 )
& ( $true
= ( in @ X9 @ X7 ) ) )
& ( $true
= ( in @ X8 @ X6 ) ) )
| ( ( in @ X5 @ ( cartprod @ X6 @ X7 ) )
!= $true ) )
| ( cartprodmempair1 != $true ) ) ),
inference(rectify,[status(thm)],[f1253]) ).
thf(f1253,plain,
( ( ( cartprodmempair1 = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ! [X3: $i] :
( ! [X4: $i] :
( ( ( kpair @ X3 @ X4 )
!= X0 )
| ( ( in @ X4 @ X2 )
!= $true ) )
| ( $true
!= ( in @ X3 @ X1 ) ) )
& ( $true
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ) )
& ( ! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( kpair @ X3 @ X4 )
= X0 )
& ( ( in @ X4 @ X2 )
= $true ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) )
| ( cartprodmempair1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f668]) ).
thf(f668,plain,
( ( cartprodmempair1 = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ? [X3: $i] :
( ? [X4: $i] :
( ( ( kpair @ X3 @ X4 )
= X0 )
& ( ( in @ X4 @ X2 )
= $true ) )
& ( $true
= ( in @ X3 @ X1 ) ) )
| ( $true
!= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f214]) ).
thf(f214,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( cartprod @ X1 @ X2 ) ) )
=> ? [X3: $i] :
( ? [X4: $i] :
( ( ( kpair @ X3 @ X4 )
= X0 )
& ( ( in @ X4 @ X2 )
= $true ) )
& ( $true
= ( in @ X3 @ X1 ) ) ) )
<=> ( cartprodmempair1 = $true ) ),
inference(fool_elimination,[status(thm)],[f213]) ).
thf(f213,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( cartprod @ X1 @ X2 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X1 )
& ? [X4: $i] :
( ( in @ X4 @ X2 )
& ( ( kpair @ X3 @ X4 )
= X0 ) ) ) )
= cartprodmempair1 ),
inference(rectify,[status(thm)],[f152]) ).
thf(f152,axiom,
! [X10: $i,X3: $i,X4: $i] :
( ( ( in @ X10 @ ( cartprod @ X3 @ X4 ) )
=> ? [X1: $i] :
( ( in @ X1 @ X3 )
& ? [X2: $i] :
( ( in @ X2 @ X4 )
& ( ( kpair @ X1 @ X2 )
= X10 ) ) ) )
= cartprodmempair1 ),
file('/export/starexec/sandbox/tmp/tmp.BWMLOxAvmL/DTF2THF_6029.p',cartprodmempair1) ).
thf(f3792,plain,
spl452_42,
inference(avatar_split_clause,[status(thm)],[f2047,f2604]) ).
thf(f2047,plain,
cartprodmempair1 = $true,
inference(cnf_transformation,[status(thm)],[f1355]) ).
thf(f3082,plain,
( ~ spl452_42
| spl452_150 ),
inference(avatar_split_clause,[status(thm)],[f1923,f3080,f2604]) ).
thf(f1923,plain,
! [X6: $i,X7: $i,X5: $i] :
( ( ( in @ ( sK321 @ X7 @ X6 @ X5 ) @ X6 )
= $true )
| ( ( in @ X5 @ ( cartprod @ X6 @ X7 ) )
!= $true )
| ( cartprodmempair1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f1258]) ).
thf(f3073,plain,
( spl452_148
| ~ spl452_6 ),
inference(avatar_split_clause,[status(thm)],[f1707,f2447,f3071]) ).
thf(f1707,plain,
! [X2: $i,X3: $i] :
( ( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 )
| ( kfstpairEq != $true ) ),
inference(cnf_transformation,[status(thm)],[f999]) ).
thf(f999,plain,
( ( ( kfstpairEq = $true )
| ( sK163
!= ( kfst @ ( kpair @ sK163 @ sK164 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 )
| ( kfstpairEq != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK163,sK164])],[f997,f998]) ).
thf(f998,plain,
( ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
!= X0 )
=> ( sK163
!= ( kfst @ ( kpair @ sK163 @ sK164 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f997,plain,
( ( ( kfstpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
!= X0 ) )
& ( ! [X2: $i,X3: $i] :
( ( kfst @ ( kpair @ X2 @ X3 ) )
= X2 )
| ( kfstpairEq != $true ) ) ),
inference(rectify,[status(thm)],[f996]) ).
thf(f996,plain,
( ( ( kfstpairEq = $true )
| ? [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
!= X0 ) )
& ( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 )
| ( kfstpairEq != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f222]) ).
thf(f222,plain,
( ( kfstpairEq = $true )
<=> ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ),
inference(fool_elimination,[status(thm)],[f221]) ).
thf(f221,plain,
( kfstpairEq
= ( ! [X0: $i,X1: $i] :
( ( kfst @ ( kpair @ X0 @ X1 ) )
= X0 ) ) ),
inference(rectify,[status(thm)],[f168]) ).
thf(f168,axiom,
( kfstpairEq
= ( ! [X1: $i,X2: $i] :
( ( kfst @ ( kpair @ X1 @ X2 ) )
= X1 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.BWMLOxAvmL/DTF2THF_6029.p',kfstpairEq) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU646^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n010.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:29:33 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.49 ---- Original DTF file ---
% 0.30/0.49 thf(spec,logic,$$dhol).
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 % File : SEU646^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.49 % Domain : Set Theory
% 0.30/0.49 % Problem : Ordered Pairs - Properties of Pairs
% 0.30/0.49 % Version : Especial.
% 0.30/0.49 % English : (! A:i.! B:i.! u:i.in u (cartprod A B) -> in (kfst u) A)
% 0.30/0.49
% 0.30/0.49 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.49 % Source : [Bro08]
% 0.30/0.49 % Names : ZFC148g [Bro08]
% 0.30/0.49
% 0.30/0.49 % Status : Theorem
% 0.30/0.49 % Rating : 0.33 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.57 v7.4.0, 0.44 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.57 v6.4.0, 0.67 v6.3.0, 0.80 v6.2.0, 0.57 v6.1.0, 0.86 v6.0.0, 0.57 v5.5.0, 0.67 v5.4.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.30/0.49 % Syntax : Number of formulae : 361 ( 168 unt; 192 typ; 168 def)
% 0.30/0.49 % Number of atoms : 891 ( 238 equ; 0 cnn)
% 0.30/0.49 % Maximal formula atoms : 164 ( 5 avg)
% 0.30/0.49 % Number of connectives : 1544 ( 47 ~; 7 |; 37 &;1045 @)
% 0.30/0.49 % ( 14 <=>; 394 =>; 0 <=; 0 <~>)
% 0.30/0.49 % Maximal formula depth : 170 ( 2 avg)
% 0.30/0.49 % Number of types : 2 ( 0 usr)
% 0.30/0.49 % Number of type conns : 83 ( 83 >; 0 *; 0 +; 0 <<)
% 0.30/0.49 % Number of symbols : 195 ( 192 usr; 166 con; 0-2 aty)
% 0.30/0.49 % Number of variables : 488 ( 42 ^; 408 !; 38 ?; 488 :)
% 0.30/0.49 % SPC : TH0_THM_EQU_NAR
% 0.30/0.49
% 0.30/0.49 % Comments : http://mathgate.info/detsetitem.php?id=203
% 0.30/0.49 %------------------------------------------------------------------------------
% 0.30/0.49 thf(in_type,type,
% 0.30/0.49 in: $i > $i > $o ).
% 0.30/0.49
% 0.30/0.49 thf(exu_type,type,
% 0.30/0.49 exu: ( $i > $o ) > $o ).
% 0.30/0.49
% 0.30/0.49 thf(exu,definition,
% 0.30/0.49 ( exu
% 0.30/0.49 = ( ^ [Xphi: $i > $o] :
% 0.30/0.49 ? [Xx: $i] :
% 0.30/0.49 ( ( Xphi @ Xx )
% 0.30/0.49 & ! [Xy: $i] :
% 0.30/0.49 ( ( Xphi @ Xy )
% 0.30/0.49 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setextAx_type,type,
% 0.30/0.49 setextAx: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setextAx,definition,
% 0.30/0.49 ( setextAx
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 <=> ( in @ Xx @ B ) )
% 0.30/0.49 => ( A = B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(emptyset_type,type,
% 0.30/0.49 emptyset: $i ).
% 0.30/0.49
% 0.30/0.49 thf(emptysetAx_type,type,
% 0.30/0.49 emptysetAx: $o ).
% 0.30/0.49
% 0.30/0.49 thf(emptysetAx,definition,
% 0.30/0.49 ( emptysetAx
% 0.30/0.49 = ( ! [Xx: $i] :
% 0.30/0.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoin_type,type,
% 0.30/0.49 setadjoin: $i > $i > $i ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinAx_type,type,
% 0.30/0.49 setadjoinAx: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinAx,definition,
% 0.30/0.49 ( setadjoinAx
% 0.30/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.49 <=> ( ( Xy = Xx )
% 0.30/0.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(powerset_type,type,
% 0.30/0.49 powerset: $i > $i ).
% 0.30/0.49
% 0.30/0.49 thf(powersetAx_type,type,
% 0.30/0.49 powersetAx: $o ).
% 0.30/0.49
% 0.30/0.49 thf(powersetAx,definition,
% 0.30/0.49 ( powersetAx
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.49 <=> ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ B )
% 0.30/0.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setunion_type,type,
% 0.30/0.49 setunion: $i > $i ).
% 0.30/0.49
% 0.30/0.49 thf(setunionAx_type,type,
% 0.30/0.49 setunionAx: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setunionAx,definition,
% 0.30/0.49 ( setunionAx
% 0.30/0.49 = ( ! [A: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.49 <=> ? [B: $i] :
% 0.30/0.49 ( ( in @ Xx @ B )
% 0.30/0.49 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(omega_type,type,
% 0.30/0.49 omega: $i ).
% 0.30/0.49
% 0.30/0.49 thf(omega0Ax_type,type,
% 0.30/0.49 omega0Ax: $o ).
% 0.30/0.49
% 0.30/0.49 thf(omega0Ax,definition,
% 0.30/0.49 ( omega0Ax
% 0.30/0.49 = ( in @ emptyset @ omega ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(omegaSAx_type,type,
% 0.30/0.49 omegaSAx: $o ).
% 0.30/0.49
% 0.30/0.49 thf(omegaSAx,definition,
% 0.30/0.49 ( omegaSAx
% 0.30/0.49 = ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ omega )
% 0.30/0.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(omegaIndAx_type,type,
% 0.30/0.49 omegaIndAx: $o ).
% 0.30/0.49
% 0.30/0.49 thf(omegaIndAx,definition,
% 0.30/0.49 ( omegaIndAx
% 0.30/0.49 = ( ! [A: $i] :
% 0.30/0.49 ( ( ( in @ emptyset @ A )
% 0.30/0.49 & ! [Xx: $i] :
% 0.30/0.49 ( ( ( in @ Xx @ omega )
% 0.30/0.49 & ( in @ Xx @ A ) )
% 0.30/0.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/0.49 => ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ omega )
% 0.30/0.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(replAx_type,type,
% 0.30/0.49 replAx: $o ).
% 0.30/0.49
% 0.30/0.49 thf(replAx,definition,
% 0.30/0.49 ( replAx
% 0.30/0.49 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( exu
% 0.30/0.49 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.49 => ? [B: $i] :
% 0.30/0.49 ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ B )
% 0.30/0.49 <=> ? [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ A )
% 0.30/0.49 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(foundationAx_type,type,
% 0.30/0.49 foundationAx: $o ).
% 0.30/0.49
% 0.30/0.49 thf(foundationAx,definition,
% 0.30/0.49 ( foundationAx
% 0.30/0.49 = ( ! [A: $i] :
% 0.30/0.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.49 => ? [B: $i] :
% 0.30/0.49 ( ( in @ B @ A )
% 0.30/0.49 & ~ ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ B )
% 0.30/0.49 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(wellorderingAx_type,type,
% 0.30/0.49 wellorderingAx: $o ).
% 0.30/0.49
% 0.30/0.49 thf(wellorderingAx,definition,
% 0.30/0.49 ( wellorderingAx
% 0.30/0.49 = ( ! [A: $i] :
% 0.30/0.49 ? [B: $i] :
% 0.30/0.49 ( ! [C: $i] :
% 0.30/0.49 ( ( in @ C @ B )
% 0.30/0.49 => ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ C )
% 0.30/0.49 => ( in @ Xx @ A ) ) )
% 0.30/0.49 & ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( ( in @ Xx @ A )
% 0.30/0.49 & ( in @ Xy @ A ) )
% 0.30/0.49 => ( ! [C: $i] :
% 0.30/0.49 ( ( in @ C @ B )
% 0.30/0.49 => ( ( in @ Xx @ C )
% 0.30/0.49 <=> ( in @ Xy @ C ) ) )
% 0.30/0.49 => ( Xx = Xy ) ) )
% 0.30/0.49 & ! [C: $i,D: $i] :
% 0.30/0.49 ( ( ( in @ C @ B )
% 0.30/0.49 & ( in @ D @ B ) )
% 0.30/0.49 => ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ C )
% 0.30/0.49 => ( in @ Xx @ D ) )
% 0.30/0.49 | ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ D )
% 0.30/0.49 => ( in @ Xx @ C ) ) ) )
% 0.30/0.49 & ! [C: $i] :
% 0.30/0.49 ( ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ C )
% 0.30/0.49 => ( in @ Xx @ A ) )
% 0.30/0.49 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/0.49 => ? [D: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ D @ B )
% 0.30/0.49 & ( in @ Xx @ C )
% 0.30/0.49 & ~ ? [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ D )
% 0.30/0.49 & ( in @ Xy @ C ) )
% 0.30/0.49 & ! [E: $i] :
% 0.30/0.49 ( ( in @ E @ B )
% 0.30/0.49 => ( ! [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ E )
% 0.30/0.49 => ( in @ Xy @ D ) )
% 0.30/0.49 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(descr_type,type,
% 0.30/0.49 descr: ( $i > $o ) > $i ).
% 0.30/0.49
% 0.30/0.49 thf(descrp_type,type,
% 0.30/0.49 descrp: $o ).
% 0.30/0.49
% 0.30/0.49 thf(descrp,definition,
% 0.30/0.49 ( descrp
% 0.30/0.49 = ( ! [Xphi: $i > $o] :
% 0.30/0.49 ( ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 => ( Xphi
% 0.30/0.49 @ ( descr
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(dsetconstr_type,type,
% 0.30/0.49 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.49
% 0.30/0.49 thf(dsetconstrI_type,type,
% 0.30/0.49 dsetconstrI: $o ).
% 0.30/0.49
% 0.30/0.49 thf(dsetconstrI,definition,
% 0.30/0.49 ( dsetconstrI
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( ( Xphi @ Xx )
% 0.30/0.49 => ( in @ Xx
% 0.30/0.49 @ ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(dsetconstrEL_type,type,
% 0.30/0.49 dsetconstrEL: $o ).
% 0.30/0.49
% 0.30/0.49 thf(dsetconstrEL,definition,
% 0.30/0.49 ( dsetconstrEL
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx
% 0.30/0.49 @ ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.49 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(dsetconstrER_type,type,
% 0.30/0.49 dsetconstrER: $o ).
% 0.30/0.49
% 0.30/0.49 thf(dsetconstrER,definition,
% 0.30/0.49 ( dsetconstrER
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx
% 0.30/0.49 @ ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.49 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(exuE1_type,type,
% 0.30/0.49 exuE1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(exuE1,definition,
% 0.30/0.49 ( exuE1
% 0.30/0.49 = ( ! [Xphi: $i > $o] :
% 0.30/0.49 ( ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 => ? [Xx: $i] :
% 0.30/0.49 ( ( Xphi @ Xx )
% 0.30/0.49 & ! [Xy: $i] :
% 0.30/0.49 ( ( Xphi @ Xy )
% 0.30/0.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(prop2set_type,type,
% 0.30/0.49 prop2set: $o > $i ).
% 0.30/0.49
% 0.30/0.49 thf(prop2setE_type,type,
% 0.30/0.49 prop2setE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(prop2setE,definition,
% 0.30/0.49 ( prop2setE
% 0.30/0.49 = ( ! [Xphi: $o,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.30/0.49 => Xphi ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(emptysetE_type,type,
% 0.30/0.49 emptysetE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(emptysetE,definition,
% 0.30/0.49 ( emptysetE
% 0.30/0.49 = ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ emptyset )
% 0.30/0.49 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(emptysetimpfalse_type,type,
% 0.30/0.49 emptysetimpfalse: $o ).
% 0.30/0.49
% 0.30/0.49 thf(emptysetimpfalse,definition,
% 0.30/0.49 ( emptysetimpfalse
% 0.30/0.49 = ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ emptyset )
% 0.30/0.49 => $false ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(notinemptyset_type,type,
% 0.30/0.49 notinemptyset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(notinemptyset,definition,
% 0.30/0.49 ( notinemptyset
% 0.30/0.49 = ( ! [Xx: $i] :
% 0.30/0.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(exuE3e_type,type,
% 0.30/0.49 exuE3e: $o ).
% 0.30/0.49
% 0.30/0.49 thf(exuE3e,definition,
% 0.30/0.49 ( exuE3e
% 0.30/0.49 = ( ! [Xphi: $i > $o] :
% 0.30/0.49 ( ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setext_type,type,
% 0.30/0.49 setext: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setext,definition,
% 0.30/0.49 ( setext
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( in @ Xx @ B ) )
% 0.30/0.49 => ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ B )
% 0.30/0.49 => ( in @ Xx @ A ) )
% 0.30/0.49 => ( A = B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(emptyI_type,type,
% 0.30/0.49 emptyI: $o ).
% 0.30/0.49
% 0.30/0.49 thf(emptyI,definition,
% 0.30/0.49 ( emptyI
% 0.30/0.49 = ( ! [A: $i] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ~ ( in @ Xx @ A )
% 0.30/0.49 => ( A = emptyset ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(noeltsimpempty_type,type,
% 0.30/0.49 noeltsimpempty: $o ).
% 0.30/0.49
% 0.30/0.49 thf(noeltsimpempty,definition,
% 0.30/0.49 ( noeltsimpempty
% 0.30/0.49 = ( ! [A: $i] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ~ ( in @ Xx @ A )
% 0.30/0.49 => ( A = emptyset ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setbeta_type,type,
% 0.30/0.49 setbeta: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setbeta,definition,
% 0.30/0.49 ( setbeta
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( ( in @ Xx
% 0.30/0.49 @ ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.49 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(nonempty_type,type,
% 0.30/0.49 nonempty: $i > $o ).
% 0.30/0.49
% 0.30/0.49 thf(nonempty,definition,
% 0.30/0.49 ( nonempty
% 0.30/0.49 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(nonemptyE1_type,type,
% 0.30/0.49 nonemptyE1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(nonemptyE1,definition,
% 0.30/0.49 ( nonemptyE1
% 0.30/0.49 = ( ! [A: $i] :
% 0.30/0.49 ( ( nonempty @ A )
% 0.30/0.49 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(nonemptyI_type,type,
% 0.30/0.49 nonemptyI: $o ).
% 0.30/0.49
% 0.30/0.49 thf(nonemptyI,definition,
% 0.30/0.49 ( nonemptyI
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( ( Xphi @ Xx )
% 0.30/0.49 => ( nonempty
% 0.30/0.49 @ ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(nonemptyI1_type,type,
% 0.30/0.49 nonemptyI1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(nonemptyI1,definition,
% 0.30/0.49 ( nonemptyI1
% 0.30/0.49 = ( ! [A: $i] :
% 0.30/0.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.49 => ( nonempty @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinIL_type,type,
% 0.30/0.49 setadjoinIL: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinIL,definition,
% 0.30/0.49 ( setadjoinIL
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(emptyinunitempty_type,type,
% 0.30/0.49 emptyinunitempty: $o ).
% 0.30/0.49
% 0.30/0.49 thf(emptyinunitempty,definition,
% 0.30/0.49 ( emptyinunitempty
% 0.30/0.49 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinIR_type,type,
% 0.30/0.49 setadjoinIR: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinIR,definition,
% 0.30/0.49 ( setadjoinIR
% 0.30/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ A )
% 0.30/0.49 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinE_type,type,
% 0.30/0.49 setadjoinE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinE,definition,
% 0.30/0.49 ( setadjoinE
% 0.30/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.49 => ! [Xphi: $o] :
% 0.30/0.49 ( ( ( Xy = Xx )
% 0.30/0.49 => Xphi )
% 0.30/0.49 => ( ( ( in @ Xy @ A )
% 0.30/0.49 => Xphi )
% 0.30/0.49 => Xphi ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinOr_type,type,
% 0.30/0.49 setadjoinOr: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinOr,definition,
% 0.30/0.49 ( setadjoinOr
% 0.30/0.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.49 => ( ( Xy = Xx )
% 0.30/0.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setoftrueEq_type,type,
% 0.30/0.49 setoftrueEq: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setoftrueEq,definition,
% 0.30/0.49 ( setoftrueEq
% 0.30/0.49 = ( ! [A: $i] :
% 0.30/0.49 ( ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xx: $i] : $true )
% 0.30/0.49 = A ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(powersetI_type,type,
% 0.30/0.49 powersetI: $o ).
% 0.30/0.49
% 0.30/0.49 thf(powersetI,definition,
% 0.30/0.49 ( powersetI
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ B )
% 0.30/0.49 => ( in @ Xx @ A ) )
% 0.30/0.49 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(emptyinPowerset_type,type,
% 0.30/0.49 emptyinPowerset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(emptyinPowerset,definition,
% 0.30/0.49 ( emptyinPowerset
% 0.30/0.49 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(emptyInPowerset_type,type,
% 0.30/0.49 emptyInPowerset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(emptyInPowerset,definition,
% 0.30/0.49 ( emptyInPowerset
% 0.30/0.49 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(powersetE_type,type,
% 0.30/0.49 powersetE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(powersetE,definition,
% 0.30/0.49 ( powersetE
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.49 => ( ( in @ Xx @ B )
% 0.30/0.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setunionI_type,type,
% 0.30/0.49 setunionI: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setunionI,definition,
% 0.30/0.49 ( setunionI
% 0.30/0.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.49 ( ( in @ Xx @ B )
% 0.30/0.49 => ( ( in @ B @ A )
% 0.30/0.49 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setunionE_type,type,
% 0.30/0.49 setunionE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setunionE,definition,
% 0.30/0.49 ( setunionE
% 0.30/0.49 = ( ! [A: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.49 => ! [Xphi: $o] :
% 0.30/0.49 ( ! [B: $i] :
% 0.30/0.49 ( ( in @ Xx @ B )
% 0.30/0.49 => ( ( in @ B @ A )
% 0.30/0.49 => Xphi ) )
% 0.30/0.49 => Xphi ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(subPowSU_type,type,
% 0.30/0.49 subPowSU: $o ).
% 0.30/0.49
% 0.30/0.49 thf(subPowSU,definition,
% 0.30/0.49 ( subPowSU
% 0.30/0.49 = ( ! [A: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(exuE2_type,type,
% 0.30/0.49 exuE2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(exuE2,definition,
% 0.30/0.49 ( exuE2
% 0.30/0.49 = ( ! [Xphi: $i > $o] :
% 0.30/0.49 ( ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 => ? [Xx: $i] :
% 0.30/0.49 ! [Xy: $i] :
% 0.30/0.49 ( ( Xphi @ Xy )
% 0.30/0.49 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(nonemptyImpWitness_type,type,
% 0.30/0.49 nonemptyImpWitness: $o ).
% 0.30/0.49
% 0.30/0.49 thf(nonemptyImpWitness,definition,
% 0.30/0.49 ( nonemptyImpWitness
% 0.30/0.49 = ( ! [A: $i] :
% 0.30/0.49 ( ( nonempty @ A )
% 0.30/0.49 => ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & $true ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(uniqinunit_type,type,
% 0.30/0.49 uniqinunit: $o ).
% 0.30/0.49
% 0.30/0.49 thf(uniqinunit,definition,
% 0.30/0.49 ( uniqinunit
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.49 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(notinsingleton_type,type,
% 0.30/0.49 notinsingleton: $o ).
% 0.30/0.49
% 0.30/0.49 thf(notinsingleton,definition,
% 0.30/0.49 ( notinsingleton
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( Xx != Xy )
% 0.30/0.49 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(eqinunit_type,type,
% 0.30/0.49 eqinunit: $o ).
% 0.30/0.49
% 0.30/0.49 thf(eqinunit,definition,
% 0.30/0.49 ( eqinunit
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( Xx = Xy )
% 0.30/0.49 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(singletonsswitch_type,type,
% 0.30/0.49 singletonsswitch: $o ).
% 0.30/0.49
% 0.30/0.49 thf(singletonsswitch,definition,
% 0.30/0.49 ( singletonsswitch
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.49 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(upairsetE_type,type,
% 0.30/0.49 upairsetE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(upairsetE,definition,
% 0.30/0.49 ( upairsetE
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.49 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.49 => ( ( Xz = Xx )
% 0.30/0.49 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(upairsetIL_type,type,
% 0.30/0.49 upairsetIL: $o ).
% 0.30/0.49
% 0.30/0.49 thf(upairsetIL,definition,
% 0.30/0.49 ( upairsetIL
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(upairsetIR_type,type,
% 0.30/0.49 upairsetIR: $o ).
% 0.30/0.49
% 0.30/0.49 thf(upairsetIR,definition,
% 0.30/0.49 ( upairsetIR
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(emptyE1_type,type,
% 0.30/0.49 emptyE1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(emptyE1,definition,
% 0.30/0.49 ( emptyE1
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ( Xphi @ Xx ) )
% 0.30/0.49 => ( ( ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 = emptyset )
% 0.30/0.49 => $false ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(vacuousDall_type,type,
% 0.30/0.49 vacuousDall: $o ).
% 0.30/0.49
% 0.30/0.49 thf(vacuousDall,definition,
% 0.30/0.49 ( vacuousDall
% 0.30/0.49 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ emptyset )
% 0.30/0.49 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(quantDeMorgan1_type,type,
% 0.30/0.49 quantDeMorgan1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(quantDeMorgan1,definition,
% 0.30/0.49 ( quantDeMorgan1
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( ~ ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( Xphi @ Xx ) )
% 0.30/0.49 => ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(quantDeMorgan2_type,type,
% 0.30/0.49 quantDeMorgan2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(quantDeMorgan2,definition,
% 0.30/0.49 ( quantDeMorgan2
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ~ ( Xphi @ Xx ) )
% 0.30/0.49 => ~ ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(quantDeMorgan3_type,type,
% 0.30/0.49 quantDeMorgan3: $o ).
% 0.30/0.49
% 0.30/0.49 thf(quantDeMorgan3,definition,
% 0.30/0.49 ( quantDeMorgan3
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( ~ ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ( Xphi @ Xx ) )
% 0.30/0.49 => ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(quantDeMorgan4_type,type,
% 0.30/0.49 quantDeMorgan4: $o ).
% 0.30/0.49
% 0.30/0.49 thf(quantDeMorgan4,definition,
% 0.30/0.49 ( quantDeMorgan4
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ~ ( Xphi @ Xx ) )
% 0.30/0.49 => ~ ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(prop2setI_type,type,
% 0.30/0.49 prop2setI: $o ).
% 0.30/0.49
% 0.30/0.49 thf(prop2setI,definition,
% 0.30/0.49 ( prop2setI
% 0.30/0.49 = ( ! [Xphi: $o] :
% 0.30/0.49 ( Xphi
% 0.30/0.49 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(set2prop_type,type,
% 0.30/0.49 set2prop: $i > $o ).
% 0.30/0.49
% 0.30/0.49 thf(prop2set2propI_type,type,
% 0.30/0.49 prop2set2propI: $o ).
% 0.30/0.49
% 0.30/0.49 thf(prop2set2propI,definition,
% 0.30/0.49 ( prop2set2propI
% 0.30/0.49 = ( ! [Xphi: $o] :
% 0.30/0.49 ( Xphi
% 0.30/0.49 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(notdexE_type,type,
% 0.30/0.49 notdexE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(notdexE,definition,
% 0.30/0.49 ( notdexE
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( ~ ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ( Xphi @ Xx ) )
% 0.30/0.49 => ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(notdallE_type,type,
% 0.30/0.49 notdallE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(notdallE,definition,
% 0.30/0.49 ( notdallE
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( ~ ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( Xphi @ Xx ) )
% 0.30/0.49 => ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(exuI1_type,type,
% 0.30/0.49 exuI1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(exuI1,definition,
% 0.30/0.49 ( exuI1
% 0.30/0.49 = ( ! [Xphi: $i > $o] :
% 0.30/0.49 ( ? [Xx: $i] :
% 0.30/0.49 ( ( Xphi @ Xx )
% 0.30/0.49 & ! [Xy: $i] :
% 0.30/0.49 ( ( Xphi @ Xy )
% 0.30/0.49 => ( Xx = Xy ) ) )
% 0.30/0.49 => ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(exuI3_type,type,
% 0.30/0.49 exuI3: $o ).
% 0.30/0.49
% 0.30/0.49 thf(exuI3,definition,
% 0.30/0.49 ( exuI3
% 0.30/0.49 = ( ! [Xphi: $i > $o] :
% 0.30/0.49 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.30/0.49 => ( ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( Xphi @ Xx )
% 0.30/0.49 => ( ( Xphi @ Xy )
% 0.30/0.49 => ( Xx = Xy ) ) )
% 0.30/0.49 => ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(exuI2_type,type,
% 0.30/0.49 exuI2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(exuI2,definition,
% 0.30/0.49 ( exuI2
% 0.30/0.49 = ( ! [Xphi: $i > $o] :
% 0.30/0.49 ( ? [Xx: $i] :
% 0.30/0.49 ! [Xy: $i] :
% 0.30/0.49 ( ( Xphi @ Xy )
% 0.30/0.49 <=> ( Xy = Xx ) )
% 0.30/0.49 => ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(inCongP_type,type,
% 0.30/0.49 inCongP: $o ).
% 0.30/0.49
% 0.30/0.49 thf(inCongP,definition,
% 0.30/0.49 ( inCongP
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( A = B )
% 0.30/0.49 => ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( Xx = Xy )
% 0.30/0.49 => ( ( in @ Xx @ A )
% 0.30/0.49 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(in__Cong_type,type,
% 0.30/0.49 in__Cong: $o ).
% 0.30/0.49
% 0.30/0.49 thf(in__Cong,definition,
% 0.30/0.49 ( in__Cong
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( A = B )
% 0.30/0.49 => ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( Xx = Xy )
% 0.30/0.49 => ( ( in @ Xx @ A )
% 0.30/0.49 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(exuE3u_type,type,
% 0.30/0.49 exuE3u: $o ).
% 0.30/0.49
% 0.30/0.49 thf(exuE3u,definition,
% 0.30/0.49 ( exuE3u
% 0.30/0.49 = ( ! [Xphi: $i > $o] :
% 0.30/0.49 ( ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 => ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( Xphi @ Xx )
% 0.30/0.49 => ( ( Xphi @ Xy )
% 0.30/0.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(exu__Cong_type,type,
% 0.30/0.49 exu__Cong: $o ).
% 0.30/0.49
% 0.30/0.49 thf(exu__Cong,definition,
% 0.30/0.49 ( exu__Cong
% 0.30/0.49 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.49 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( Xx = Xy )
% 0.30/0.49 => ( ( Xphi @ Xx )
% 0.30/0.49 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.49 => ( ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 <=> ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(emptyset__Cong_type,type,
% 0.30/0.49 emptyset__Cong: $o ).
% 0.30/0.49
% 0.30/0.49 thf(emptyset__Cong,definition,
% 0.30/0.49 ( emptyset__Cong
% 0.30/0.49 = ( emptyset = emptyset ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoin__Cong_type,type,
% 0.30/0.49 setadjoin__Cong: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoin__Cong,definition,
% 0.30/0.49 ( setadjoin__Cong
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( Xx = Xy )
% 0.30/0.49 => ! [Xz: $i,Xu: $i] :
% 0.30/0.49 ( ( Xz = Xu )
% 0.30/0.49 => ( ( setadjoin @ Xx @ Xz )
% 0.30/0.49 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(powerset__Cong_type,type,
% 0.30/0.49 powerset__Cong: $o ).
% 0.30/0.49
% 0.30/0.49 thf(powerset__Cong,definition,
% 0.30/0.49 ( powerset__Cong
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( A = B )
% 0.30/0.49 => ( ( powerset @ A )
% 0.30/0.49 = ( powerset @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setunion__Cong_type,type,
% 0.30/0.49 setunion__Cong: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setunion__Cong,definition,
% 0.30/0.49 ( setunion__Cong
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( A = B )
% 0.30/0.49 => ( ( setunion @ A )
% 0.30/0.49 = ( setunion @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(omega__Cong_type,type,
% 0.30/0.49 omega__Cong: $o ).
% 0.30/0.49
% 0.30/0.49 thf(omega__Cong,definition,
% 0.30/0.49 ( omega__Cong
% 0.30/0.49 = ( omega = omega ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(exuEu_type,type,
% 0.30/0.49 exuEu: $o ).
% 0.30/0.49
% 0.30/0.49 thf(exuEu,definition,
% 0.30/0.49 ( exuEu
% 0.30/0.49 = ( ! [Xphi: $i > $o] :
% 0.30/0.49 ( ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 => ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( Xphi @ Xx )
% 0.30/0.49 => ( ( Xphi @ Xy )
% 0.30/0.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(descr__Cong_type,type,
% 0.30/0.49 descr__Cong: $o ).
% 0.30/0.49
% 0.30/0.49 thf(descr__Cong,definition,
% 0.30/0.49 ( descr__Cong
% 0.30/0.49 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.49 ( ! [Xx: $i,Xy: $i] :
% 0.30/0.49 ( ( Xx = Xy )
% 0.30/0.49 => ( ( Xphi @ Xx )
% 0.30/0.49 <=> ( Xpsi @ Xy ) ) )
% 0.30/0.49 => ( ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 => ( ( exu
% 0.30/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.30/0.49 => ( ( descr
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 = ( descr
% 0.30/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(dsetconstr__Cong_type,type,
% 0.30/0.49 dsetconstr__Cong: $o ).
% 0.30/0.49
% 0.30/0.49 thf(dsetconstr__Cong,definition,
% 0.30/0.49 ( dsetconstr__Cong
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( A = B )
% 0.30/0.49 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ! [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ B )
% 0.30/0.49 => ( ( Xx = Xy )
% 0.30/0.49 => ( ( Xphi @ Xx )
% 0.30/0.49 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.30/0.49 => ( ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 = ( dsetconstr @ B
% 0.30/0.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(subset_type,type,
% 0.30/0.49 subset: $i > $i > $o ).
% 0.30/0.49
% 0.30/0.49 thf(disjoint_type,type,
% 0.30/0.49 disjoint: $i > $i > $o ).
% 0.30/0.49
% 0.30/0.49 thf(setsmeet_type,type,
% 0.30/0.49 setsmeet: $i > $i > $o ).
% 0.30/0.49
% 0.30/0.49 thf(subsetI1_type,type,
% 0.30/0.49 subsetI1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(subsetI1,definition,
% 0.30/0.49 ( subsetI1
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( in @ Xx @ B ) )
% 0.30/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(eqimpsubset2_type,type,
% 0.30/0.49 eqimpsubset2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(eqimpsubset2,definition,
% 0.30/0.49 ( eqimpsubset2
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( A = B )
% 0.30/0.49 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(eqimpsubset1_type,type,
% 0.30/0.49 eqimpsubset1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(eqimpsubset1,definition,
% 0.30/0.49 ( eqimpsubset1
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( A = B )
% 0.30/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(subsetI2_type,type,
% 0.30/0.49 subsetI2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(subsetI2,definition,
% 0.30/0.49 ( subsetI2
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( in @ Xx @ B ) )
% 0.30/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(emptysetsubset_type,type,
% 0.30/0.49 emptysetsubset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(emptysetsubset,definition,
% 0.30/0.49 ( emptysetsubset
% 0.30/0.49 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(subsetE_type,type,
% 0.30/0.49 subsetE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(subsetE,definition,
% 0.30/0.49 ( subsetE
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( subset @ A @ B )
% 0.30/0.49 => ( ( in @ Xx @ A )
% 0.30/0.49 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(subsetE2_type,type,
% 0.30/0.49 subsetE2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(subsetE2,definition,
% 0.30/0.49 ( subsetE2
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( subset @ A @ B )
% 0.30/0.49 => ( ~ ( in @ Xx @ B )
% 0.30/0.49 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(notsubsetI_type,type,
% 0.30/0.49 notsubsetI: $o ).
% 0.30/0.49
% 0.30/0.49 thf(notsubsetI,definition,
% 0.30/0.49 ( notsubsetI
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( ~ ( in @ Xx @ B )
% 0.30/0.49 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(notequalI1_type,type,
% 0.30/0.49 notequalI1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(notequalI1,definition,
% 0.30/0.49 ( notequalI1
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ~ ( subset @ A @ B )
% 0.30/0.49 => ( A != B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(notequalI2_type,type,
% 0.30/0.49 notequalI2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(notequalI2,definition,
% 0.30/0.49 ( notequalI2
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( ~ ( in @ Xx @ B )
% 0.30/0.49 => ( A != B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(subsetRefl_type,type,
% 0.30/0.49 subsetRefl: $o ).
% 0.30/0.49
% 0.30/0.49 thf(subsetRefl,definition,
% 0.30/0.49 ( subsetRefl
% 0.30/0.49 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(subsetTrans_type,type,
% 0.30/0.49 subsetTrans: $o ).
% 0.30/0.49
% 0.30/0.49 thf(subsetTrans,definition,
% 0.30/0.49 ( subsetTrans
% 0.30/0.49 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.49 ( ( subset @ A @ B )
% 0.30/0.49 => ( ( subset @ B @ C )
% 0.30/0.49 => ( subset @ A @ C ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinSub_type,type,
% 0.30/0.49 setadjoinSub: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinSub,definition,
% 0.30/0.49 ( setadjoinSub
% 0.30/0.49 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinSub2_type,type,
% 0.30/0.49 setadjoinSub2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setadjoinSub2,definition,
% 0.30/0.49 ( setadjoinSub2
% 0.30/0.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.49 ( ( subset @ A @ B )
% 0.30/0.49 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(subset2powerset_type,type,
% 0.30/0.49 subset2powerset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(subset2powerset,definition,
% 0.30/0.49 ( subset2powerset
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( subset @ A @ B )
% 0.30/0.49 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setextsub_type,type,
% 0.30/0.49 setextsub: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setextsub,definition,
% 0.30/0.49 ( setextsub
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( subset @ A @ B )
% 0.30/0.49 => ( ( subset @ B @ A )
% 0.30/0.49 => ( A = B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(subsetemptysetimpeq_type,type,
% 0.30/0.49 subsetemptysetimpeq: $o ).
% 0.30/0.49
% 0.30/0.49 thf(subsetemptysetimpeq,definition,
% 0.30/0.49 ( subsetemptysetimpeq
% 0.30/0.49 = ( ! [A: $i] :
% 0.30/0.49 ( ( subset @ A @ emptyset )
% 0.30/0.49 => ( A = emptyset ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(powersetI1_type,type,
% 0.30/0.49 powersetI1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(powersetI1,definition,
% 0.30/0.49 ( powersetI1
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( subset @ B @ A )
% 0.30/0.49 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(powersetE1_type,type,
% 0.30/0.49 powersetE1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(powersetE1,definition,
% 0.30/0.49 ( powersetE1
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.49 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(inPowerset_type,type,
% 0.30/0.49 inPowerset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(inPowerset,definition,
% 0.30/0.49 ( inPowerset
% 0.30/0.49 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(powersetsubset_type,type,
% 0.30/0.49 powersetsubset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(powersetsubset,definition,
% 0.30/0.49 ( powersetsubset
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( subset @ A @ B )
% 0.30/0.49 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(sepInPowerset_type,type,
% 0.30/0.49 sepInPowerset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(sepInPowerset,definition,
% 0.30/0.49 ( sepInPowerset
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( in
% 0.30/0.49 @ ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 @ ( powerset @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(sepSubset_type,type,
% 0.30/0.49 sepSubset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(sepSubset,definition,
% 0.30/0.49 ( sepSubset
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( subset
% 0.30/0.49 @ ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.49 @ A ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binunion_type,type,
% 0.30/0.49 binunion: $i > $i > $i ).
% 0.30/0.49
% 0.30/0.49 thf(binunionIL_type,type,
% 0.30/0.49 binunionIL: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binunionIL,definition,
% 0.30/0.49 ( binunionIL
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(upairset2IR_type,type,
% 0.30/0.49 upairset2IR: $o ).
% 0.30/0.49
% 0.30/0.49 thf(upairset2IR,definition,
% 0.30/0.49 ( upairset2IR
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binunionIR_type,type,
% 0.30/0.49 binunionIR: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binunionIR,definition,
% 0.30/0.49 ( binunionIR
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ B )
% 0.30/0.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binunionEcases_type,type,
% 0.30/0.49 binunionEcases: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binunionEcases,definition,
% 0.30/0.49 ( binunionEcases
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.30/0.49 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/0.49 => ( ( ( in @ Xx @ A )
% 0.30/0.49 => Xphi )
% 0.30/0.49 => ( ( ( in @ Xx @ B )
% 0.30/0.49 => Xphi )
% 0.30/0.49 => Xphi ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binunionE_type,type,
% 0.30/0.49 binunionE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binunionE,definition,
% 0.30/0.49 ( binunionE
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.30/0.49 => ( ( in @ Xx @ A )
% 0.30/0.49 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binunionLsub_type,type,
% 0.30/0.49 binunionLsub: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binunionLsub,definition,
% 0.30/0.49 ( binunionLsub
% 0.30/0.49 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binunionRsub_type,type,
% 0.30/0.49 binunionRsub: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binunionRsub,definition,
% 0.30/0.49 ( binunionRsub
% 0.30/0.49 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binintersect_type,type,
% 0.30/0.49 binintersect: $i > $i > $i ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectI_type,type,
% 0.30/0.49 binintersectI: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectI,definition,
% 0.30/0.49 ( binintersectI
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( ( in @ Xx @ B )
% 0.30/0.49 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectSubset5_type,type,
% 0.30/0.49 binintersectSubset5: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectSubset5,definition,
% 0.30/0.49 ( binintersectSubset5
% 0.30/0.49 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.49 ( ( subset @ C @ A )
% 0.30/0.49 => ( ( subset @ C @ B )
% 0.30/0.49 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectEL_type,type,
% 0.30/0.49 binintersectEL: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectEL,definition,
% 0.30/0.49 ( binintersectEL
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.49 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectLsub_type,type,
% 0.30/0.49 binintersectLsub: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectLsub,definition,
% 0.30/0.49 ( binintersectLsub
% 0.30/0.49 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectSubset2_type,type,
% 0.30/0.49 binintersectSubset2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectSubset2,definition,
% 0.30/0.49 ( binintersectSubset2
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( subset @ A @ B )
% 0.30/0.49 => ( ( binintersect @ A @ B )
% 0.30/0.49 = A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectSubset3_type,type,
% 0.30/0.49 binintersectSubset3: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectSubset3,definition,
% 0.30/0.49 ( binintersectSubset3
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( ( binintersect @ A @ B )
% 0.30/0.49 = B )
% 0.30/0.49 => ( subset @ B @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectER_type,type,
% 0.30/0.49 binintersectER: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectER,definition,
% 0.30/0.49 ( binintersectER
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.30/0.49 => ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(disjointsetsI1_type,type,
% 0.30/0.49 disjointsetsI1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(disjointsetsI1,definition,
% 0.30/0.49 ( disjointsetsI1
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ~ ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ( in @ Xx @ B ) )
% 0.30/0.49 => ( ( binintersect @ A @ B )
% 0.30/0.49 = emptyset ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectRsub_type,type,
% 0.30/0.49 binintersectRsub: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectRsub,definition,
% 0.30/0.49 ( binintersectRsub
% 0.30/0.49 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectSubset4_type,type,
% 0.30/0.49 binintersectSubset4: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectSubset4,definition,
% 0.30/0.49 ( binintersectSubset4
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( subset @ B @ A )
% 0.30/0.49 => ( ( binintersect @ A @ B )
% 0.30/0.49 = B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectSubset1_type,type,
% 0.30/0.49 binintersectSubset1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(binintersectSubset1,definition,
% 0.30/0.49 ( binintersectSubset1
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( ( binintersect @ A @ B )
% 0.30/0.49 = A )
% 0.30/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(bs114d_type,type,
% 0.30/0.49 bs114d: $o ).
% 0.30/0.49
% 0.30/0.49 thf(bs114d,definition,
% 0.30/0.49 ( bs114d
% 0.30/0.49 = ( ! [A: $i,B: $i,C: $i] :
% 0.30/0.49 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.30/0.49 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(regular_type,type,
% 0.30/0.49 regular: $i > $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminus_type,type,
% 0.30/0.49 setminus: $i > $i > $i ).
% 0.30/0.49
% 0.30/0.49 thf(setminusI_type,type,
% 0.30/0.49 setminusI: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminusI,definition,
% 0.30/0.49 ( setminusI
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( ~ ( in @ Xx @ B )
% 0.30/0.49 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setminusEL_type,type,
% 0.30/0.49 setminusEL: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminusEL,definition,
% 0.30/0.49 ( setminusEL
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.49 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setminusER_type,type,
% 0.30/0.49 setminusER: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminusER,definition,
% 0.30/0.49 ( setminusER
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.49 => ~ ( in @ Xx @ B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setminusSubset2_type,type,
% 0.30/0.49 setminusSubset2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminusSubset2,definition,
% 0.30/0.49 ( setminusSubset2
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( subset @ A @ B )
% 0.30/0.49 => ( ( setminus @ A @ B )
% 0.30/0.49 = emptyset ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setminusERneg_type,type,
% 0.30/0.49 setminusERneg: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminusERneg,definition,
% 0.30/0.49 ( setminusERneg
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.49 => ( ( in @ Xx @ A )
% 0.30/0.49 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setminusELneg_type,type,
% 0.30/0.49 setminusELneg: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminusELneg,definition,
% 0.30/0.49 ( setminusELneg
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 0.30/0.49 => ( ~ ( in @ Xx @ B )
% 0.30/0.49 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setminusILneg_type,type,
% 0.30/0.49 setminusILneg: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminusILneg,definition,
% 0.30/0.49 ( setminusILneg
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ~ ( in @ Xx @ A )
% 0.30/0.49 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setminusIRneg_type,type,
% 0.30/0.49 setminusIRneg: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminusIRneg,definition,
% 0.30/0.49 ( setminusIRneg
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ B )
% 0.30/0.49 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setminusLsub_type,type,
% 0.30/0.49 setminusLsub: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminusLsub,definition,
% 0.30/0.49 ( setminusLsub
% 0.30/0.49 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setminusSubset1_type,type,
% 0.30/0.49 setminusSubset1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setminusSubset1,definition,
% 0.30/0.49 ( setminusSubset1
% 0.30/0.49 = ( ! [A: $i,B: $i] :
% 0.30/0.49 ( ( ( setminus @ A @ B )
% 0.30/0.49 = emptyset )
% 0.30/0.49 => ( subset @ A @ B ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(symdiff_type,type,
% 0.30/0.49 symdiff: $i > $i > $i ).
% 0.30/0.49
% 0.30/0.49 thf(symdiffE_type,type,
% 0.30/0.49 symdiffE: $o ).
% 0.30/0.49
% 0.30/0.49 thf(symdiffE,definition,
% 0.30/0.49 ( symdiffE
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 0.30/0.49 => ! [Xphi: $o] :
% 0.30/0.49 ( ( ( in @ Xx @ A )
% 0.30/0.49 => ( ~ ( in @ Xx @ B )
% 0.30/0.49 => Xphi ) )
% 0.30/0.49 => ( ( ~ ( in @ Xx @ A )
% 0.30/0.49 => ( ( in @ Xx @ B )
% 0.30/0.49 => Xphi ) )
% 0.30/0.49 => Xphi ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(symdiffI1_type,type,
% 0.30/0.49 symdiffI1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(symdiffI1,definition,
% 0.30/0.49 ( symdiffI1
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( ~ ( in @ Xx @ B )
% 0.30/0.49 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(symdiffI2_type,type,
% 0.30/0.49 symdiffI2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(symdiffI2,definition,
% 0.30/0.49 ( symdiffI2
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ~ ( in @ Xx @ A )
% 0.30/0.49 => ( ( in @ Xx @ B )
% 0.30/0.49 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(symdiffIneg1_type,type,
% 0.30/0.49 symdiffIneg1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(symdiffIneg1,definition,
% 0.30/0.49 ( symdiffIneg1
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( ( in @ Xx @ B )
% 0.30/0.49 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(symdiffIneg2_type,type,
% 0.30/0.49 symdiffIneg2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(symdiffIneg2,definition,
% 0.30/0.49 ( symdiffIneg2
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ~ ( in @ Xx @ A )
% 0.30/0.49 => ( ~ ( in @ Xx @ B )
% 0.30/0.49 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(iskpair_type,type,
% 0.30/0.49 iskpair: $i > $o ).
% 0.30/0.49
% 0.30/0.49 thf(iskpair,definition,
% 0.30/0.49 ( iskpair
% 0.30/0.49 = ( ^ [A: $i] :
% 0.30/0.49 ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.49 & ? [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ ( setunion @ A ) )
% 0.30/0.49 & ( A
% 0.30/0.49 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(secondinupair_type,type,
% 0.30/0.49 secondinupair: $o ).
% 0.30/0.49
% 0.30/0.49 thf(secondinupair,definition,
% 0.30/0.49 ( secondinupair
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setukpairIL_type,type,
% 0.30/0.49 setukpairIL: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setukpairIL,definition,
% 0.30/0.49 ( setukpairIL
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setukpairIR_type,type,
% 0.30/0.49 setukpairIR: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setukpairIR,definition,
% 0.30/0.49 ( setukpairIR
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(kpairiskpair_type,type,
% 0.30/0.49 kpairiskpair: $o ).
% 0.30/0.49
% 0.30/0.49 thf(kpairiskpair,definition,
% 0.30/0.49 ( kpairiskpair
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(kpair_type,type,
% 0.30/0.49 kpair: $i > $i > $i ).
% 0.30/0.49
% 0.30/0.49 thf(kpair,definition,
% 0.30/0.49 ( kpair
% 0.30/0.49 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(kpairp_type,type,
% 0.30/0.49 kpairp: $o ).
% 0.30/0.49
% 0.30/0.49 thf(kpairp,definition,
% 0.30/0.49 ( kpairp
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(cartprod_type,type,
% 0.30/0.49 cartprod: $i > $i > $i ).
% 0.30/0.49
% 0.30/0.49 thf(singletonsubset_type,type,
% 0.30/0.49 singletonsubset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(singletonsubset,definition,
% 0.30/0.49 ( singletonsubset
% 0.30/0.49 = ( ! [A: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(singletoninpowerset_type,type,
% 0.30/0.49 singletoninpowerset: $o ).
% 0.30/0.49
% 0.30/0.49 thf(singletoninpowerset,definition,
% 0.30/0.49 ( singletoninpowerset
% 0.30/0.49 = ( ! [A: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(singletoninpowunion_type,type,
% 0.30/0.49 singletoninpowunion: $o ).
% 0.30/0.49
% 0.30/0.49 thf(singletoninpowunion,definition,
% 0.30/0.49 ( singletoninpowunion
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(upairset2E_type,type,
% 0.30/0.49 upairset2E: $o ).
% 0.30/0.49
% 0.30/0.49 thf(upairset2E,definition,
% 0.30/0.49 ( upairset2E
% 0.30/0.49 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.49 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.49 => ( ( Xz = Xx )
% 0.30/0.49 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(upairsubunion_type,type,
% 0.30/0.49 upairsubunion: $o ).
% 0.30/0.49
% 0.30/0.49 thf(upairsubunion,definition,
% 0.30/0.49 ( upairsubunion
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ! [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ B )
% 0.30/0.49 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(upairinpowunion_type,type,
% 0.30/0.49 upairinpowunion: $o ).
% 0.30/0.49
% 0.30/0.49 thf(upairinpowunion,definition,
% 0.30/0.49 ( upairinpowunion
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ! [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ B )
% 0.30/0.49 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(ubforcartprodlem1_type,type,
% 0.30/0.49 ubforcartprodlem1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(ubforcartprodlem1,definition,
% 0.30/0.49 ( ubforcartprodlem1
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ! [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ B )
% 0.30/0.49 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(ubforcartprodlem2_type,type,
% 0.30/0.49 ubforcartprodlem2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(ubforcartprodlem2,definition,
% 0.30/0.49 ( ubforcartprodlem2
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ! [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ B )
% 0.30/0.49 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(ubforcartprodlem3_type,type,
% 0.30/0.49 ubforcartprodlem3: $o ).
% 0.30/0.49
% 0.30/0.49 thf(ubforcartprodlem3,definition,
% 0.30/0.49 ( ubforcartprodlem3
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ! [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ B )
% 0.30/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(cartprodpairin_type,type,
% 0.30/0.49 cartprodpairin: $o ).
% 0.30/0.49
% 0.30/0.49 thf(cartprodpairin,definition,
% 0.30/0.49 ( cartprodpairin
% 0.30/0.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ! [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ B )
% 0.30/0.49 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(cartprodmempair1_type,type,
% 0.30/0.49 cartprodmempair1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(cartprodmempair1,definition,
% 0.30/0.49 ( cartprodmempair1
% 0.30/0.49 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.49 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.49 => ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ? [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ B )
% 0.30/0.49 & ( Xu
% 0.30/0.49 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(cartprodmempair_type,type,
% 0.30/0.49 cartprodmempair: $o ).
% 0.30/0.49
% 0.30/0.49 thf(cartprodmempair,definition,
% 0.30/0.49 ( cartprodmempair
% 0.30/0.49 = ( ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.49 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.49 => ( iskpair @ Xu ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setunionE2_type,type,
% 0.30/0.49 setunionE2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setunionE2,definition,
% 0.30/0.49 ( setunionE2
% 0.30/0.49 = ( ! [A: $i,Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.49 => ? [X: $i] :
% 0.30/0.49 ( ( in @ X @ A )
% 0.30/0.49 & ( in @ Xx @ X ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setunionsingleton1_type,type,
% 0.30/0.49 setunionsingleton1: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setunionsingleton1,definition,
% 0.30/0.49 ( setunionsingleton1
% 0.30/0.49 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setunionsingleton2_type,type,
% 0.30/0.49 setunionsingleton2: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setunionsingleton2,definition,
% 0.30/0.49 ( setunionsingleton2
% 0.30/0.49 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(setunionsingleton_type,type,
% 0.30/0.49 setunionsingleton: $o ).
% 0.30/0.49
% 0.30/0.49 thf(setunionsingleton,definition,
% 0.30/0.49 ( setunionsingleton
% 0.30/0.49 = ( ! [Xx: $i] :
% 0.30/0.49 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 0.30/0.49 = Xx ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(singleton_type,type,
% 0.30/0.49 singleton: $i > $o ).
% 0.30/0.49
% 0.30/0.49 thf(singleton,definition,
% 0.30/0.49 ( singleton
% 0.30/0.49 = ( ^ [A: $i] :
% 0.30/0.49 ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ( A
% 0.30/0.49 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(singletonprop_type,type,
% 0.30/0.49 singletonprop: $o ).
% 0.30/0.49
% 0.30/0.49 thf(singletonprop,definition,
% 0.30/0.49 ( singletonprop
% 0.30/0.49 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( ! [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 => ! [Xy: $i] :
% 0.30/0.49 ( ( in @ Xy @ A )
% 0.30/0.49 => ( ( Xphi @ Xx )
% 0.30/0.49 => ( ( Xphi @ Xy )
% 0.30/0.49 => ( Xx = Xy ) ) ) ) )
% 0.30/0.49 => ( ? [Xx: $i] :
% 0.30/0.49 ( ( in @ Xx @ A )
% 0.30/0.49 & ( Xphi @ Xx ) )
% 0.30/0.49 => ( singleton
% 0.30/0.49 @ ( dsetconstr @ A
% 0.30/0.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.49
% 0.30/0.49 thf(ex1_type,type,
% 0.30/0.49 ex1: $i > ( $i > $o ) > $o ).
% 0.30/0.49
% 0.30/0.49 thf(ex1,definition,
% 0.30/0.49 ( ex1
% 0.30/0.49 = ( ^ [A: $i,Xphi: $i > $o] :
% 0.30/0.49 ( singleton
% 0.30/0.49 @ ( dsetconstr @ A
% 0.30/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(ex1E1_type,type,
% 0.30/0.50 ex1E1: $o ).
% 0.30/0.50
% 0.30/0.50 thf(ex1E1,definition,
% 0.30/0.50 ( ex1E1
% 0.30/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.50 ( ( ex1 @ A
% 0.30/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.50 => ? [Xx: $i] :
% 0.30/0.50 ( ( in @ Xx @ A )
% 0.30/0.50 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(ex1I_type,type,
% 0.30/0.50 ex1I: $o ).
% 0.30/0.50
% 0.30/0.50 thf(ex1I,definition,
% 0.30/0.50 ( ex1I
% 0.30/0.50 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.50 ( ( in @ Xx @ A )
% 0.30/0.50 => ( ( Xphi @ Xx )
% 0.30/0.50 => ( ! [Xy: $i] :
% 0.30/0.50 ( ( in @ Xy @ A )
% 0.30/0.50 => ( ( Xphi @ Xy )
% 0.30/0.50 => ( Xy = Xx ) ) )
% 0.30/0.50 => ( ex1 @ A
% 0.30/0.50 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(ex1I2_type,type,
% 0.30/0.50 ex1I2: $o ).
% 0.30/0.50
% 0.30/0.50 thf(ex1I2,definition,
% 0.30/0.50 ( ex1I2
% 0.30/0.50 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.50 ( ! [Xx: $i] :
% 0.30/0.50 ( ( in @ Xx @ A )
% 0.30/0.50 => ! [Xy: $i] :
% 0.30/0.50 ( ( in @ Xy @ A )
% 0.30/0.50 => ( ( Xphi @ Xx )
% 0.30/0.50 => ( ( Xphi @ Xy )
% 0.30/0.50 => ( Xx = Xy ) ) ) ) )
% 0.30/0.50 => ( ? [Xx: $i] :
% 0.30/0.50 ( ( in @ Xx @ A )
% 0.30/0.50 & ( Xphi @ Xx ) )
% 0.30/0.50 => ( ex1 @ A
% 0.30/0.50 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(singletonsuniq_type,type,
% 0.30/0.50 singletonsuniq: $o ).
% 0.30/0.50
% 0.30/0.50 thf(singletonsuniq,definition,
% 0.30/0.50 ( singletonsuniq
% 0.30/0.50 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.50 ( ( ( setadjoin @ Xx @ emptyset )
% 0.30/0.50 = ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.50 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(atmost1p_type,type,
% 0.30/0.50 atmost1p: $i > $o ).
% 0.30/0.50
% 0.30/0.50 thf(atleast2p_type,type,
% 0.30/0.50 atleast2p: $i > $o ).
% 0.30/0.50
% 0.30/0.50 thf(atmost2p_type,type,
% 0.30/0.50 atmost2p: $i > $o ).
% 0.30/0.50
% 0.30/0.50 thf(upairsetp_type,type,
% 0.30/0.50 upairsetp: $i > $o ).
% 0.30/0.50
% 0.30/0.50 thf(setukpairinjL1_type,type,
% 0.30/0.50 setukpairinjL1: $o ).
% 0.30/0.50
% 0.30/0.50 thf(setukpairinjL1,definition,
% 0.30/0.50 ( setukpairinjL1
% 0.30/0.50 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.50 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 0.30/0.50 => ( Xx = Xz ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(kfstsingleton_type,type,
% 0.30/0.50 kfstsingleton: $o ).
% 0.30/0.50
% 0.30/0.50 thf(kfstsingleton,definition,
% 0.30/0.50 ( kfstsingleton
% 0.30/0.50 = ( ! [Xu: $i] :
% 0.30/0.50 ( ( iskpair @ Xu )
% 0.30/0.50 => ( singleton
% 0.30/0.50 @ ( dsetconstr @ ( setunion @ Xu )
% 0.30/0.50 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(theprop_type,type,
% 0.30/0.50 theprop: $o ).
% 0.30/0.50
% 0.30/0.50 thf(theprop,definition,
% 0.30/0.50 ( theprop
% 0.30/0.50 = ( ! [X: $i] :
% 0.30/0.50 ( ( singleton @ X )
% 0.30/0.50 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(kfst_type,type,
% 0.30/0.50 kfst: $i > $i ).
% 0.30/0.50
% 0.30/0.50 thf(kfstpairEq_type,type,
% 0.30/0.50 kfstpairEq: $o ).
% 0.30/0.50
% 0.30/0.50 thf(kfstpairEq,definition,
% 0.30/0.50 ( kfstpairEq
% 0.30/0.50 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.50 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 0.30/0.50 = Xx ) ) ) ).
% 0.30/0.50
% 0.30/0.50 thf(cartprodfstin,conjecture,
% 0.30/0.50 ( setextAx
% 0.30/0.50 => ( emptysetAx
% 0.30/0.50 => ( setadjoinAx
% 0.30/0.50 => ( powersetAx
% 0.30/0.50 => ( setunionAx
% 0.30/0.50 => ( omega0Ax
% 0.30/0.50 => ( omegaSAx
% 0.30/0.50 => ( omegaIndAx
% 0.30/0.50 => ( replAx
% 0.30/0.50 => ( foundationAx
% 0.30/0.50 => ( wellorderingAx
% 0.30/0.50 => ( descrp
% 0.30/0.50 => ( dsetconstrI
% 0.30/0.50 => ( dsetconstrEL
% 0.30/0.50 => ( dsetconstrER
% 0.30/0.50 => ( exuE1
% 0.30/0.50 => ( prop2setE
% 0.30/0.50 => ( emptysetE
% 0.30/0.50 => ( emptysetimpfalse
% 0.30/0.50 => ( notinemptyset
% 0.30/0.50 => ( exuE3e
% 0.30/0.50 => ( setext
% 0.30/0.50 => ( emptyI
% 0.30/0.50 => ( noeltsimpempty
% 0.30/0.50 => ( setbeta
% 0.30/0.50 => ( nonemptyE1
% 0.30/0.50 => ( nonemptyI
% 0.30/0.50 => ( nonemptyI1
% 0.30/0.50 => ( setadjoinIL
% 0.30/0.50 => ( emptyinunitempty
% 0.30/0.50 => ( setadjoinIR
% 0.30/0.50 => ( setadjoinE
% 0.30/0.50 => ( setadjoinOr
% 0.30/0.50 => ( setoftrueEq
% 0.30/0.50 => ( powersetI
% 0.30/0.50 => ( emptyinPowerset
% 0.30/0.50 => ( emptyInPowerset
% 0.30/0.50 => ( powersetE
% 0.30/0.50 => ( setunionI
% 0.30/0.50 => ( setunionE
% 0.30/0.50 => ( subPowSU
% 0.30/0.50 => ( exuE2
% 0.30/0.50 => ( nonemptyImpWitness
% 0.30/0.50 => ( uniqinunit
% 0.30/0.50 => ( notinsingleton
% 0.30/0.50 => ( eqinunit
% 0.30/0.50 => ( singletonsswitch
% 0.30/0.50 => ( upairsetE
% 0.30/0.50 => ( upairsetIL
% 0.30/0.50 => ( upairsetIR
% 0.30/0.50 => ( emptyE1
% 0.30/0.50 => ( vacuousDall
% 0.30/0.50 => ( quantDeMorgan1
% 0.30/0.50 => ( quantDeMorgan2
% 0.30/0.50 => ( quantDeMorgan3
% 0.30/0.50 => ( quantDeMorgan4
% 0.30/0.50 => ( prop2setI
% 0.30/0.50 => ( prop2set2propI
% 0.30/0.50 => ( notdexE
% 0.30/0.50 => ( notdallE
% 0.30/0.50 => ( exuI1
% 0.30/0.50 => ( exuI3
% 0.30/0.50 => ( exuI2
% 0.30/0.50 => ( inCongP
% 0.30/0.50 => ( in__Cong
% 0.30/0.50 => ( exuE3u
% 0.30/0.50 => ( exu__Cong
% 0.30/0.50 => ( emptyset__Cong
% 0.30/0.50 => ( setadjoin__Cong
% 0.30/0.50 => ( powerset__Cong
% 0.30/0.50 => ( setunion__Cong
% 0.30/0.50 => ( omega__Cong
% 0.30/0.50 => ( exuEu
% 0.30/0.50 => ( descr__Cong
% 0.30/0.50 => ( dsetconstr__Cong
% 0.30/0.50 => ( subsetI1
% 0.30/0.50 => ( eqimpsubset2
% 0.30/0.50 => ( eqimpsubset1
% 0.30/0.50 => ( subsetI2
% 0.30/0.50 => ( emptysetsubset
% 0.30/0.50 => ( subsetE
% 0.30/0.50 => ( subsetE2
% 0.30/0.50 => ( notsubsetI
% 0.30/0.50 => ( notequalI1
% 0.30/0.50 => ( notequalI2
% 0.30/0.50 => ( subsetRefl
% 0.30/0.50 => ( subsetTrans
% 0.30/0.50 => ( setadjoinSub
% 0.30/0.50 => ( setadjoinSub2
% 0.30/0.50 => ( subset2powerset
% 0.30/0.50 => ( setextsub
% 0.30/0.50 => ( subsetemptysetimpeq
% 0.30/0.50 => ( powersetI1
% 0.30/0.50 => ( powersetE1
% 0.30/0.50 => ( inPowerset
% 0.30/0.50 => ( powersetsubset
% 0.30/0.50 => ( sepInPowerset
% 0.30/0.50 => ( sepSubset
% 0.30/0.50 => ( binunionIL
% 0.30/0.50 => ( upairset2IR
% 0.30/0.50 => ( binunionIR
% 0.30/0.50 => ( binunionEcases
% 0.30/0.50 => ( binunionE
% 0.30/0.50 => ( binunionLsub
% 0.30/0.50 => ( binunionRsub
% 0.30/0.50 => ( binintersectI
% 0.30/0.50 => ( binintersectSubset5
% 0.30/0.50 => ( binintersectEL
% 0.30/0.50 => ( binintersectLsub
% 0.30/0.50 => ( binintersectSubset2
% 0.30/0.50 => ( binintersectSubset3
% 0.30/0.50 => ( binintersectER
% 0.30/0.50 => ( disjointsetsI1
% 0.30/0.50 => ( binintersectRsub
% 0.30/0.50 => ( binintersectSubset4
% 0.30/0.50 => ( binintersectSubset1
% 0.30/0.50 => ( bs114d
% 0.30/0.50 => ( setminusI
% 0.30/0.50 => ( setminusEL
% 0.30/0.50 => ( setminusER
% 0.30/0.50 => ( setminusSubset2
% 0.30/0.50 => ( setminusERneg
% 0.30/0.50 => ( setminusELneg
% 0.30/0.50 => ( setminusILneg
% 0.30/0.50 => ( setminusIRneg
% 0.30/0.50 => ( setminusLsub
% 0.30/0.50 => ( setminusSubset1
% 0.30/0.50 => ( symdiffE
% 0.30/0.50 => ( symdiffI1
% 0.30/0.50 => ( symdiffI2
% 0.30/0.50 => ( symdiffIneg1
% 0.30/0.50 => ( symdiffIneg2
% 0.30/0.50 => ( secondinupair
% 0.30/0.50 => ( setukpairIL
% 0.30/0.50 => ( setukpairIR
% 0.30/0.50 => ( kpairiskpair
% 0.30/0.50 => ( kpairp
% 0.30/0.50 => ( singletonsubset
% 0.30/0.50 => ( singletoninpowerset
% 0.30/0.50 => ( singletoninpowunion
% 0.30/0.50 => ( upairset2E
% 0.30/0.50 => ( upairsubunion
% 0.30/0.50 => ( upairinpowunion
% 0.30/0.50 => ( ubforcartprodlem1
% 0.30/0.50 => ( ubforcartprodlem2
% 0.30/0.50 => ( ubforcartprodlem3
% 0.30/0.50 => ( cartprodpairin
% 0.30/0.50 => ( cartprodmempair1
% 0.30/0.50 => ( cartprodmempair
% 0.30/0.50 => ( setunionE2
% 0.30/0.50 => ( setunionsingleton1
% 0.30/0.50 => ( setunionsingleton2
% 0.30/0.50 => ( setunionsingleton
% 0.30/0.50 => ( singletonprop
% 0.30/0.50 => ( ex1E1
% 0.30/0.50 => ( ex1I
% 0.30/0.50 => ( ex1I2
% 0.30/0.50 => ( singletonsuniq
% 0.30/0.50 => ( setukpairinjL1
% 0.30/0.50 => ( kfstsingleton
% 0.30/0.50 => ( theprop
% 0.30/0.50 => ( kfstpairEq
% 0.30/0.50 => ! [A: $i,B: $i,Xu: $i] :
% 0.30/0.50 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 0.30/0.50 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.50
% 0.30/0.50 %------------------------------------------------------------------------------
% 0.30/0.50 ------------------------
% 2.61/1.69 ---- Embedded in THF ---
% 2.61/1.70 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.61/1.70 %%% Generated on Tue Feb 24 12:29:34 EST 2026
% 2.61/1.70 %%% using '$$dhol' embedding, version 1.3.0.
% 2.61/1.70 %%% Logic specification used:
% 2.61/1.70 %%% thf(spec, logic, $$dhol).
% 2.61/1.70
% 2.61/1.70 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.BWMLOxAvmL/DTF2DTF6029.p
% See solution above
% 2.89/1.70 ------------------------
% 2.89/1.73 ---- Cleaned THF ---
% 2.89/1.73 thf(in_type,type,
% 2.89/1.73 in: $i > $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(exu_type,type,
% 2.89/1.73 exu: ( $i > $o ) > $o ).
% 2.89/1.73
% 2.89/1.73 thf(exu,definition,
% 2.89/1.73 ( exu
% 2.89/1.73 = ( ^ [Xphi: $i > $o] :
% 2.89/1.73 ? [Xx: $i] :
% 2.89/1.73 ( ( Xphi @ Xx )
% 2.89/1.73 & ! [Xy: $i] :
% 2.89/1.73 ( ( Xphi @ Xy )
% 2.89/1.73 => ( Xx = Xy ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setextAx_type,type,
% 2.89/1.73 setextAx: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setextAx,definition,
% 2.89/1.73 ( setextAx
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 <=> ( in @ Xx @ B ) )
% 2.89/1.73 => ( A = B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(emptyset_type,type,
% 2.89/1.73 emptyset: $i ).
% 2.89/1.73
% 2.89/1.73 thf(emptysetAx_type,type,
% 2.89/1.73 emptysetAx: $o ).
% 2.89/1.73
% 2.89/1.73 thf(emptysetAx,definition,
% 2.89/1.73 ( emptysetAx
% 2.89/1.73 = ( ! [Xx: $i] :
% 2.89/1.73 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoin_type,type,
% 2.89/1.73 setadjoin: $i > $i > $i ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinAx_type,type,
% 2.89/1.73 setadjoinAx: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinAx,definition,
% 2.89/1.73 ( setadjoinAx
% 2.89/1.73 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.89/1.73 <=> ( ( Xy = Xx )
% 2.89/1.73 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(powerset_type,type,
% 2.89/1.73 powerset: $i > $i ).
% 2.89/1.73
% 2.89/1.73 thf(powersetAx_type,type,
% 2.89/1.73 powersetAx: $o ).
% 2.89/1.73
% 2.89/1.73 thf(powersetAx,definition,
% 2.89/1.73 ( powersetAx
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( in @ B @ ( powerset @ A ) )
% 2.89/1.73 <=> ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ B )
% 2.89/1.73 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setunion_type,type,
% 2.89/1.73 setunion: $i > $i ).
% 2.89/1.73
% 2.89/1.73 thf(setunionAx_type,type,
% 2.89/1.73 setunionAx: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setunionAx,definition,
% 2.89/1.73 ( setunionAx
% 2.89/1.73 = ( ! [A: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( setunion @ A ) )
% 2.89/1.73 <=> ? [B: $i] :
% 2.89/1.73 ( ( in @ Xx @ B )
% 2.89/1.73 & ( in @ B @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(omega_type,type,
% 2.89/1.73 omega: $i ).
% 2.89/1.73
% 2.89/1.73 thf(omega0Ax_type,type,
% 2.89/1.73 omega0Ax: $o ).
% 2.89/1.73
% 2.89/1.73 thf(omega0Ax,definition,
% 2.89/1.73 ( omega0Ax
% 2.89/1.73 = ( in @ emptyset @ omega ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(omegaSAx_type,type,
% 2.89/1.73 omegaSAx: $o ).
% 2.89/1.73
% 2.89/1.73 thf(omegaSAx,definition,
% 2.89/1.73 ( omegaSAx
% 2.89/1.73 = ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ omega )
% 2.89/1.73 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(omegaIndAx_type,type,
% 2.89/1.73 omegaIndAx: $o ).
% 2.89/1.73
% 2.89/1.73 thf(omegaIndAx,definition,
% 2.89/1.73 ( omegaIndAx
% 2.89/1.73 = ( ! [A: $i] :
% 2.89/1.73 ( ( ( in @ emptyset @ A )
% 2.89/1.73 & ! [Xx: $i] :
% 2.89/1.73 ( ( ( in @ Xx @ omega )
% 2.89/1.73 & ( in @ Xx @ A ) )
% 2.89/1.73 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.89/1.73 => ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ omega )
% 2.89/1.73 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(replAx_type,type,
% 2.89/1.73 replAx: $o ).
% 2.89/1.73
% 2.89/1.73 thf(replAx,definition,
% 2.89/1.73 ( replAx
% 2.89/1.73 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( exu
% 2.89/1.73 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.89/1.73 => ? [B: $i] :
% 2.89/1.73 ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ B )
% 2.89/1.73 <=> ? [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ A )
% 2.89/1.73 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(foundationAx_type,type,
% 2.89/1.73 foundationAx: $o ).
% 2.89/1.73
% 2.89/1.73 thf(foundationAx,definition,
% 2.89/1.73 ( foundationAx
% 2.89/1.73 = ( ! [A: $i] :
% 2.89/1.73 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.89/1.73 => ? [B: $i] :
% 2.89/1.73 ( ( in @ B @ A )
% 2.89/1.73 & ~ ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ B )
% 2.89/1.73 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(wellorderingAx_type,type,
% 2.89/1.73 wellorderingAx: $o ).
% 2.89/1.73
% 2.89/1.73 thf(wellorderingAx,definition,
% 2.89/1.73 ( wellorderingAx
% 2.89/1.73 = ( ! [A: $i] :
% 2.89/1.73 ? [B: $i] :
% 2.89/1.73 ( ! [C: $i] :
% 2.89/1.73 ( ( in @ C @ B )
% 2.89/1.73 => ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ C )
% 2.89/1.73 => ( in @ Xx @ A ) ) )
% 2.89/1.73 & ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( ( in @ Xx @ A )
% 2.89/1.73 & ( in @ Xy @ A ) )
% 2.89/1.73 => ( ! [C: $i] :
% 2.89/1.73 ( ( in @ C @ B )
% 2.89/1.73 => ( ( in @ Xx @ C )
% 2.89/1.73 <=> ( in @ Xy @ C ) ) )
% 2.89/1.73 => ( Xx = Xy ) ) )
% 2.89/1.73 & ! [C: $i,D: $i] :
% 2.89/1.73 ( ( ( in @ C @ B )
% 2.89/1.73 & ( in @ D @ B ) )
% 2.89/1.73 => ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ C )
% 2.89/1.73 => ( in @ Xx @ D ) )
% 2.89/1.73 | ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ D )
% 2.89/1.73 => ( in @ Xx @ C ) ) ) )
% 2.89/1.73 & ! [C: $i] :
% 2.89/1.73 ( ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ C )
% 2.89/1.73 => ( in @ Xx @ A ) )
% 2.89/1.73 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.89/1.73 => ? [D: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ D @ B )
% 2.89/1.73 & ( in @ Xx @ C )
% 2.89/1.73 & ~ ? [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ D )
% 2.89/1.73 & ( in @ Xy @ C ) )
% 2.89/1.73 & ! [E: $i] :
% 2.89/1.73 ( ( in @ E @ B )
% 2.89/1.73 => ( ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ E )
% 2.89/1.73 => ( in @ Xy @ D ) )
% 2.89/1.73 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(descr_type,type,
% 2.89/1.73 descr: ( $i > $o ) > $i ).
% 2.89/1.73
% 2.89/1.73 thf(descrp_type,type,
% 2.89/1.73 descrp: $o ).
% 2.89/1.73
% 2.89/1.73 thf(descrp,definition,
% 2.89/1.73 ( descrp
% 2.89/1.73 = ( ! [Xphi: $i > $o] :
% 2.89/1.73 ( ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 => ( Xphi
% 2.89/1.73 @ ( descr
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(dsetconstr_type,type,
% 2.89/1.73 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.89/1.73
% 2.89/1.73 thf(dsetconstrI_type,type,
% 2.89/1.73 dsetconstrI: $o ).
% 2.89/1.73
% 2.89/1.73 thf(dsetconstrI,definition,
% 2.89/1.73 ( dsetconstrI
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( ( Xphi @ Xx )
% 2.89/1.73 => ( in @ Xx
% 2.89/1.73 @ ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(dsetconstrEL_type,type,
% 2.89/1.73 dsetconstrEL: $o ).
% 2.89/1.73
% 2.89/1.73 thf(dsetconstrEL,definition,
% 2.89/1.73 ( dsetconstrEL
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx
% 2.89/1.73 @ ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.89/1.73 => ( in @ Xx @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(dsetconstrER_type,type,
% 2.89/1.73 dsetconstrER: $o ).
% 2.89/1.73
% 2.89/1.73 thf(dsetconstrER,definition,
% 2.89/1.73 ( dsetconstrER
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx
% 2.89/1.73 @ ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.89/1.73 => ( Xphi @ Xx ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(exuE1_type,type,
% 2.89/1.73 exuE1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(exuE1,definition,
% 2.89/1.73 ( exuE1
% 2.89/1.73 = ( ! [Xphi: $i > $o] :
% 2.89/1.73 ( ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 => ? [Xx: $i] :
% 2.89/1.73 ( ( Xphi @ Xx )
% 2.89/1.73 & ! [Xy: $i] :
% 2.89/1.73 ( ( Xphi @ Xy )
% 2.89/1.73 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(prop2set_type,type,
% 2.89/1.73 prop2set: $o > $i ).
% 2.89/1.73
% 2.89/1.73 thf(prop2setE_type,type,
% 2.89/1.73 prop2setE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(prop2setE,definition,
% 2.89/1.73 ( prop2setE
% 2.89/1.73 = ( ! [Xphi: $o,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.89/1.73 => Xphi ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(emptysetE_type,type,
% 2.89/1.73 emptysetE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(emptysetE,definition,
% 2.89/1.73 ( emptysetE
% 2.89/1.73 = ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ emptyset )
% 2.89/1.73 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(emptysetimpfalse_type,type,
% 2.89/1.73 emptysetimpfalse: $o ).
% 2.89/1.73
% 2.89/1.73 thf(emptysetimpfalse,definition,
% 2.89/1.73 ( emptysetimpfalse
% 2.89/1.73 = ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ emptyset )
% 2.89/1.73 => $false ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(notinemptyset_type,type,
% 2.89/1.73 notinemptyset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(notinemptyset,definition,
% 2.89/1.73 ( notinemptyset
% 2.89/1.73 = ( ! [Xx: $i] :
% 2.89/1.73 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(exuE3e_type,type,
% 2.89/1.73 exuE3e: $o ).
% 2.89/1.73
% 2.89/1.73 thf(exuE3e,definition,
% 2.89/1.73 ( exuE3e
% 2.89/1.73 = ( ! [Xphi: $i > $o] :
% 2.89/1.73 ( ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setext_type,type,
% 2.89/1.73 setext: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setext,definition,
% 2.89/1.73 ( setext
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( in @ Xx @ B ) )
% 2.89/1.73 => ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ B )
% 2.89/1.73 => ( in @ Xx @ A ) )
% 2.89/1.73 => ( A = B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(emptyI_type,type,
% 2.89/1.73 emptyI: $o ).
% 2.89/1.73
% 2.89/1.73 thf(emptyI,definition,
% 2.89/1.73 ( emptyI
% 2.89/1.73 = ( ! [A: $i] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ~ ( in @ Xx @ A )
% 2.89/1.73 => ( A = emptyset ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(noeltsimpempty_type,type,
% 2.89/1.73 noeltsimpempty: $o ).
% 2.89/1.73
% 2.89/1.73 thf(noeltsimpempty,definition,
% 2.89/1.73 ( noeltsimpempty
% 2.89/1.73 = ( ! [A: $i] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ~ ( in @ Xx @ A )
% 2.89/1.73 => ( A = emptyset ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setbeta_type,type,
% 2.89/1.73 setbeta: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setbeta,definition,
% 2.89/1.73 ( setbeta
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( ( in @ Xx
% 2.89/1.73 @ ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.89/1.73 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(nonempty_type,type,
% 2.89/1.73 nonempty: $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(nonempty,definition,
% 2.89/1.73 ( nonempty
% 2.89/1.73 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(nonemptyE1_type,type,
% 2.89/1.73 nonemptyE1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(nonemptyE1,definition,
% 2.89/1.73 ( nonemptyE1
% 2.89/1.73 = ( ! [A: $i] :
% 2.89/1.73 ( ( nonempty @ A )
% 2.89/1.73 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(nonemptyI_type,type,
% 2.89/1.73 nonemptyI: $o ).
% 2.89/1.73
% 2.89/1.73 thf(nonemptyI,definition,
% 2.89/1.73 ( nonemptyI
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( ( Xphi @ Xx )
% 2.89/1.73 => ( nonempty
% 2.89/1.73 @ ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(nonemptyI1_type,type,
% 2.89/1.73 nonemptyI1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(nonemptyI1,definition,
% 2.89/1.73 ( nonemptyI1
% 2.89/1.73 = ( ! [A: $i] :
% 2.89/1.73 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.89/1.73 => ( nonempty @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinIL_type,type,
% 2.89/1.73 setadjoinIL: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinIL,definition,
% 2.89/1.73 ( setadjoinIL
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(emptyinunitempty_type,type,
% 2.89/1.73 emptyinunitempty: $o ).
% 2.89/1.73
% 2.89/1.73 thf(emptyinunitempty,definition,
% 2.89/1.73 ( emptyinunitempty
% 2.89/1.73 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinIR_type,type,
% 2.89/1.73 setadjoinIR: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinIR,definition,
% 2.89/1.73 ( setadjoinIR
% 2.89/1.73 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ A )
% 2.89/1.73 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinE_type,type,
% 2.89/1.73 setadjoinE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinE,definition,
% 2.89/1.73 ( setadjoinE
% 2.89/1.73 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.89/1.73 => ! [Xphi: $o] :
% 2.89/1.73 ( ( ( Xy = Xx )
% 2.89/1.73 => Xphi )
% 2.89/1.73 => ( ( ( in @ Xy @ A )
% 2.89/1.73 => Xphi )
% 2.89/1.73 => Xphi ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinOr_type,type,
% 2.89/1.73 setadjoinOr: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinOr,definition,
% 2.89/1.73 ( setadjoinOr
% 2.89/1.73 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.89/1.73 => ( ( Xy = Xx )
% 2.89/1.73 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setoftrueEq_type,type,
% 2.89/1.73 setoftrueEq: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setoftrueEq,definition,
% 2.89/1.73 ( setoftrueEq
% 2.89/1.73 = ( ! [A: $i] :
% 2.89/1.73 ( ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xx: $i] : $true )
% 2.89/1.73 = A ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(powersetI_type,type,
% 2.89/1.73 powersetI: $o ).
% 2.89/1.73
% 2.89/1.73 thf(powersetI,definition,
% 2.89/1.73 ( powersetI
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ B )
% 2.89/1.73 => ( in @ Xx @ A ) )
% 2.89/1.73 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(emptyinPowerset_type,type,
% 2.89/1.73 emptyinPowerset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(emptyinPowerset,definition,
% 2.89/1.73 ( emptyinPowerset
% 2.89/1.73 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(emptyInPowerset_type,type,
% 2.89/1.73 emptyInPowerset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(emptyInPowerset,definition,
% 2.89/1.73 ( emptyInPowerset
% 2.89/1.73 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(powersetE_type,type,
% 2.89/1.73 powersetE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(powersetE,definition,
% 2.89/1.73 ( powersetE
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ B @ ( powerset @ A ) )
% 2.89/1.73 => ( ( in @ Xx @ B )
% 2.89/1.73 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setunionI_type,type,
% 2.89/1.73 setunionI: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setunionI,definition,
% 2.89/1.73 ( setunionI
% 2.89/1.73 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.89/1.73 ( ( in @ Xx @ B )
% 2.89/1.73 => ( ( in @ B @ A )
% 2.89/1.73 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setunionE_type,type,
% 2.89/1.73 setunionE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setunionE,definition,
% 2.89/1.73 ( setunionE
% 2.89/1.73 = ( ! [A: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( setunion @ A ) )
% 2.89/1.73 => ! [Xphi: $o] :
% 2.89/1.73 ( ! [B: $i] :
% 2.89/1.73 ( ( in @ Xx @ B )
% 2.89/1.73 => ( ( in @ B @ A )
% 2.89/1.73 => Xphi ) )
% 2.89/1.73 => Xphi ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(subPowSU_type,type,
% 2.89/1.73 subPowSU: $o ).
% 2.89/1.73
% 2.89/1.73 thf(subPowSU,definition,
% 2.89/1.73 ( subPowSU
% 2.89/1.73 = ( ! [A: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(exuE2_type,type,
% 2.89/1.73 exuE2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(exuE2,definition,
% 2.89/1.73 ( exuE2
% 2.89/1.73 = ( ! [Xphi: $i > $o] :
% 2.89/1.73 ( ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 => ? [Xx: $i] :
% 2.89/1.73 ! [Xy: $i] :
% 2.89/1.73 ( ( Xphi @ Xy )
% 2.89/1.73 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(nonemptyImpWitness_type,type,
% 2.89/1.73 nonemptyImpWitness: $o ).
% 2.89/1.73
% 2.89/1.73 thf(nonemptyImpWitness,definition,
% 2.89/1.73 ( nonemptyImpWitness
% 2.89/1.73 = ( ! [A: $i] :
% 2.89/1.73 ( ( nonempty @ A )
% 2.89/1.73 => ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & $true ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(uniqinunit_type,type,
% 2.89/1.73 uniqinunit: $o ).
% 2.89/1.73
% 2.89/1.73 thf(uniqinunit,definition,
% 2.89/1.73 ( uniqinunit
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.89/1.73 => ( Xx = Xy ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(notinsingleton_type,type,
% 2.89/1.73 notinsingleton: $o ).
% 2.89/1.73
% 2.89/1.73 thf(notinsingleton,definition,
% 2.89/1.73 ( notinsingleton
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( Xx != Xy )
% 2.89/1.73 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(eqinunit_type,type,
% 2.89/1.73 eqinunit: $o ).
% 2.89/1.73
% 2.89/1.73 thf(eqinunit,definition,
% 2.89/1.73 ( eqinunit
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( Xx = Xy )
% 2.89/1.73 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(singletonsswitch_type,type,
% 2.89/1.73 singletonsswitch: $o ).
% 2.89/1.73
% 2.89/1.73 thf(singletonsswitch,definition,
% 2.89/1.73 ( singletonsswitch
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.89/1.73 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(upairsetE_type,type,
% 2.89/1.73 upairsetE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(upairsetE,definition,
% 2.89/1.73 ( upairsetE
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.89/1.73 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.89/1.73 => ( ( Xz = Xx )
% 2.89/1.73 | ( Xz = Xy ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(upairsetIL_type,type,
% 2.89/1.73 upairsetIL: $o ).
% 2.89/1.73
% 2.89/1.73 thf(upairsetIL,definition,
% 2.89/1.73 ( upairsetIL
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(upairsetIR_type,type,
% 2.89/1.73 upairsetIR: $o ).
% 2.89/1.73
% 2.89/1.73 thf(upairsetIR,definition,
% 2.89/1.73 ( upairsetIR
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(emptyE1_type,type,
% 2.89/1.73 emptyE1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(emptyE1,definition,
% 2.89/1.73 ( emptyE1
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ( Xphi @ Xx ) )
% 2.89/1.73 => ( ( ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 = emptyset )
% 2.89/1.73 => $false ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(vacuousDall_type,type,
% 2.89/1.73 vacuousDall: $o ).
% 2.89/1.73
% 2.89/1.73 thf(vacuousDall,definition,
% 2.89/1.73 ( vacuousDall
% 2.89/1.73 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ emptyset )
% 2.89/1.73 => ( Xphi @ Xx ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(quantDeMorgan1_type,type,
% 2.89/1.73 quantDeMorgan1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(quantDeMorgan1,definition,
% 2.89/1.73 ( quantDeMorgan1
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( ~ ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( Xphi @ Xx ) )
% 2.89/1.73 => ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(quantDeMorgan2_type,type,
% 2.89/1.73 quantDeMorgan2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(quantDeMorgan2,definition,
% 2.89/1.73 ( quantDeMorgan2
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ~ ( Xphi @ Xx ) )
% 2.89/1.73 => ~ ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(quantDeMorgan3_type,type,
% 2.89/1.73 quantDeMorgan3: $o ).
% 2.89/1.73
% 2.89/1.73 thf(quantDeMorgan3,definition,
% 2.89/1.73 ( quantDeMorgan3
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( ~ ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ( Xphi @ Xx ) )
% 2.89/1.73 => ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(quantDeMorgan4_type,type,
% 2.89/1.73 quantDeMorgan4: $o ).
% 2.89/1.73
% 2.89/1.73 thf(quantDeMorgan4,definition,
% 2.89/1.73 ( quantDeMorgan4
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ~ ( Xphi @ Xx ) )
% 2.89/1.73 => ~ ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(prop2setI_type,type,
% 2.89/1.73 prop2setI: $o ).
% 2.89/1.73
% 2.89/1.73 thf(prop2setI,definition,
% 2.89/1.73 ( prop2setI
% 2.89/1.73 = ( ! [Xphi: $o] :
% 2.89/1.73 ( Xphi
% 2.89/1.73 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(set2prop_type,type,
% 2.89/1.73 set2prop: $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(prop2set2propI_type,type,
% 2.89/1.73 prop2set2propI: $o ).
% 2.89/1.73
% 2.89/1.73 thf(prop2set2propI,definition,
% 2.89/1.73 ( prop2set2propI
% 2.89/1.73 = ( ! [Xphi: $o] :
% 2.89/1.73 ( Xphi
% 2.89/1.73 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(notdexE_type,type,
% 2.89/1.73 notdexE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(notdexE,definition,
% 2.89/1.73 ( notdexE
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( ~ ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ( Xphi @ Xx ) )
% 2.89/1.73 => ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(notdallE_type,type,
% 2.89/1.73 notdallE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(notdallE,definition,
% 2.89/1.73 ( notdallE
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( ~ ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( Xphi @ Xx ) )
% 2.89/1.73 => ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(exuI1_type,type,
% 2.89/1.73 exuI1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(exuI1,definition,
% 2.89/1.73 ( exuI1
% 2.89/1.73 = ( ! [Xphi: $i > $o] :
% 2.89/1.73 ( ? [Xx: $i] :
% 2.89/1.73 ( ( Xphi @ Xx )
% 2.89/1.73 & ! [Xy: $i] :
% 2.89/1.73 ( ( Xphi @ Xy )
% 2.89/1.73 => ( Xx = Xy ) ) )
% 2.89/1.73 => ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(exuI3_type,type,
% 2.89/1.73 exuI3: $o ).
% 2.89/1.73
% 2.89/1.73 thf(exuI3,definition,
% 2.89/1.73 ( exuI3
% 2.89/1.73 = ( ! [Xphi: $i > $o] :
% 2.89/1.73 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.89/1.73 => ( ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( Xphi @ Xx )
% 2.89/1.73 => ( ( Xphi @ Xy )
% 2.89/1.73 => ( Xx = Xy ) ) )
% 2.89/1.73 => ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(exuI2_type,type,
% 2.89/1.73 exuI2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(exuI2,definition,
% 2.89/1.73 ( exuI2
% 2.89/1.73 = ( ! [Xphi: $i > $o] :
% 2.89/1.73 ( ? [Xx: $i] :
% 2.89/1.73 ! [Xy: $i] :
% 2.89/1.73 ( ( Xphi @ Xy )
% 2.89/1.73 <=> ( Xy = Xx ) )
% 2.89/1.73 => ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(inCongP_type,type,
% 2.89/1.73 inCongP: $o ).
% 2.89/1.73
% 2.89/1.73 thf(inCongP,definition,
% 2.89/1.73 ( inCongP
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( A = B )
% 2.89/1.73 => ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( Xx = Xy )
% 2.89/1.73 => ( ( in @ Xx @ A )
% 2.89/1.73 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(in__Cong_type,type,
% 2.89/1.73 in__Cong: $o ).
% 2.89/1.73
% 2.89/1.73 thf(in__Cong,definition,
% 2.89/1.73 ( in__Cong
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( A = B )
% 2.89/1.73 => ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( Xx = Xy )
% 2.89/1.73 => ( ( in @ Xx @ A )
% 2.89/1.73 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(exuE3u_type,type,
% 2.89/1.73 exuE3u: $o ).
% 2.89/1.73
% 2.89/1.73 thf(exuE3u,definition,
% 2.89/1.73 ( exuE3u
% 2.89/1.73 = ( ! [Xphi: $i > $o] :
% 2.89/1.73 ( ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 => ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( Xphi @ Xx )
% 2.89/1.73 => ( ( Xphi @ Xy )
% 2.89/1.73 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(exu__Cong_type,type,
% 2.89/1.73 exu__Cong: $o ).
% 2.89/1.73
% 2.89/1.73 thf(exu__Cong,definition,
% 2.89/1.73 ( exu__Cong
% 2.89/1.73 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.89/1.73 ( ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( Xx = Xy )
% 2.89/1.73 => ( ( Xphi @ Xx )
% 2.89/1.73 <=> ( Xpsi @ Xy ) ) )
% 2.89/1.73 => ( ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 <=> ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(emptyset__Cong_type,type,
% 2.89/1.73 emptyset__Cong: $o ).
% 2.89/1.73
% 2.89/1.73 thf(emptyset__Cong,definition,
% 2.89/1.73 ( emptyset__Cong
% 2.89/1.73 = ( emptyset = emptyset ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoin__Cong_type,type,
% 2.89/1.73 setadjoin__Cong: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoin__Cong,definition,
% 2.89/1.73 ( setadjoin__Cong
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( Xx = Xy )
% 2.89/1.73 => ! [Xz: $i,Xu: $i] :
% 2.89/1.73 ( ( Xz = Xu )
% 2.89/1.73 => ( ( setadjoin @ Xx @ Xz )
% 2.89/1.73 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(powerset__Cong_type,type,
% 2.89/1.73 powerset__Cong: $o ).
% 2.89/1.73
% 2.89/1.73 thf(powerset__Cong,definition,
% 2.89/1.73 ( powerset__Cong
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( A = B )
% 2.89/1.73 => ( ( powerset @ A )
% 2.89/1.73 = ( powerset @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setunion__Cong_type,type,
% 2.89/1.73 setunion__Cong: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setunion__Cong,definition,
% 2.89/1.73 ( setunion__Cong
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( A = B )
% 2.89/1.73 => ( ( setunion @ A )
% 2.89/1.73 = ( setunion @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(omega__Cong_type,type,
% 2.89/1.73 omega__Cong: $o ).
% 2.89/1.73
% 2.89/1.73 thf(omega__Cong,definition,
% 2.89/1.73 ( omega__Cong
% 2.89/1.73 = ( omega = omega ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(exuEu_type,type,
% 2.89/1.73 exuEu: $o ).
% 2.89/1.73
% 2.89/1.73 thf(exuEu,definition,
% 2.89/1.73 ( exuEu
% 2.89/1.73 = ( ! [Xphi: $i > $o] :
% 2.89/1.73 ( ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 => ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( Xphi @ Xx )
% 2.89/1.73 => ( ( Xphi @ Xy )
% 2.89/1.73 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(descr__Cong_type,type,
% 2.89/1.73 descr__Cong: $o ).
% 2.89/1.73
% 2.89/1.73 thf(descr__Cong,definition,
% 2.89/1.73 ( descr__Cong
% 2.89/1.73 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.89/1.73 ( ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( Xx = Xy )
% 2.89/1.73 => ( ( Xphi @ Xx )
% 2.89/1.73 <=> ( Xpsi @ Xy ) ) )
% 2.89/1.73 => ( ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 => ( ( exu
% 2.89/1.73 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.89/1.73 => ( ( descr
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 = ( descr
% 2.89/1.73 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(dsetconstr__Cong_type,type,
% 2.89/1.73 dsetconstr__Cong: $o ).
% 2.89/1.73
% 2.89/1.73 thf(dsetconstr__Cong,definition,
% 2.89/1.73 ( dsetconstr__Cong
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( A = B )
% 2.89/1.73 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ B )
% 2.89/1.73 => ( ( Xx = Xy )
% 2.89/1.73 => ( ( Xphi @ Xx )
% 2.89/1.73 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.89/1.73 => ( ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 = ( dsetconstr @ B
% 2.89/1.73 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(subset_type,type,
% 2.89/1.73 subset: $i > $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(disjoint_type,type,
% 2.89/1.73 disjoint: $i > $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(setsmeet_type,type,
% 2.89/1.73 setsmeet: $i > $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(subsetI1_type,type,
% 2.89/1.73 subsetI1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(subsetI1,definition,
% 2.89/1.73 ( subsetI1
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( in @ Xx @ B ) )
% 2.89/1.73 => ( subset @ A @ B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(eqimpsubset2_type,type,
% 2.89/1.73 eqimpsubset2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(eqimpsubset2,definition,
% 2.89/1.73 ( eqimpsubset2
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( A = B )
% 2.89/1.73 => ( subset @ B @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(eqimpsubset1_type,type,
% 2.89/1.73 eqimpsubset1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(eqimpsubset1,definition,
% 2.89/1.73 ( eqimpsubset1
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( A = B )
% 2.89/1.73 => ( subset @ A @ B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(subsetI2_type,type,
% 2.89/1.73 subsetI2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(subsetI2,definition,
% 2.89/1.73 ( subsetI2
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( in @ Xx @ B ) )
% 2.89/1.73 => ( subset @ A @ B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(emptysetsubset_type,type,
% 2.89/1.73 emptysetsubset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(emptysetsubset,definition,
% 2.89/1.73 ( emptysetsubset
% 2.89/1.73 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(subsetE_type,type,
% 2.89/1.73 subsetE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(subsetE,definition,
% 2.89/1.73 ( subsetE
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( subset @ A @ B )
% 2.89/1.73 => ( ( in @ Xx @ A )
% 2.89/1.73 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(subsetE2_type,type,
% 2.89/1.73 subsetE2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(subsetE2,definition,
% 2.89/1.73 ( subsetE2
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( subset @ A @ B )
% 2.89/1.73 => ( ~ ( in @ Xx @ B )
% 2.89/1.73 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(notsubsetI_type,type,
% 2.89/1.73 notsubsetI: $o ).
% 2.89/1.73
% 2.89/1.73 thf(notsubsetI,definition,
% 2.89/1.73 ( notsubsetI
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( ~ ( in @ Xx @ B )
% 2.89/1.73 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(notequalI1_type,type,
% 2.89/1.73 notequalI1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(notequalI1,definition,
% 2.89/1.73 ( notequalI1
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ~ ( subset @ A @ B )
% 2.89/1.73 => ( A != B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(notequalI2_type,type,
% 2.89/1.73 notequalI2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(notequalI2,definition,
% 2.89/1.73 ( notequalI2
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( ~ ( in @ Xx @ B )
% 2.89/1.73 => ( A != B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(subsetRefl_type,type,
% 2.89/1.73 subsetRefl: $o ).
% 2.89/1.73
% 2.89/1.73 thf(subsetRefl,definition,
% 2.89/1.73 ( subsetRefl
% 2.89/1.73 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(subsetTrans_type,type,
% 2.89/1.73 subsetTrans: $o ).
% 2.89/1.73
% 2.89/1.73 thf(subsetTrans,definition,
% 2.89/1.73 ( subsetTrans
% 2.89/1.73 = ( ! [A: $i,B: $i,C: $i] :
% 2.89/1.73 ( ( subset @ A @ B )
% 2.89/1.73 => ( ( subset @ B @ C )
% 2.89/1.73 => ( subset @ A @ C ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinSub_type,type,
% 2.89/1.73 setadjoinSub: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinSub,definition,
% 2.89/1.73 ( setadjoinSub
% 2.89/1.73 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinSub2_type,type,
% 2.89/1.73 setadjoinSub2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setadjoinSub2,definition,
% 2.89/1.73 ( setadjoinSub2
% 2.89/1.73 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.89/1.73 ( ( subset @ A @ B )
% 2.89/1.73 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(subset2powerset_type,type,
% 2.89/1.73 subset2powerset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(subset2powerset,definition,
% 2.89/1.73 ( subset2powerset
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( subset @ A @ B )
% 2.89/1.73 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setextsub_type,type,
% 2.89/1.73 setextsub: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setextsub,definition,
% 2.89/1.73 ( setextsub
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( subset @ A @ B )
% 2.89/1.73 => ( ( subset @ B @ A )
% 2.89/1.73 => ( A = B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(subsetemptysetimpeq_type,type,
% 2.89/1.73 subsetemptysetimpeq: $o ).
% 2.89/1.73
% 2.89/1.73 thf(subsetemptysetimpeq,definition,
% 2.89/1.73 ( subsetemptysetimpeq
% 2.89/1.73 = ( ! [A: $i] :
% 2.89/1.73 ( ( subset @ A @ emptyset )
% 2.89/1.73 => ( A = emptyset ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(powersetI1_type,type,
% 2.89/1.73 powersetI1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(powersetI1,definition,
% 2.89/1.73 ( powersetI1
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( subset @ B @ A )
% 2.89/1.73 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(powersetE1_type,type,
% 2.89/1.73 powersetE1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(powersetE1,definition,
% 2.89/1.73 ( powersetE1
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( in @ B @ ( powerset @ A ) )
% 2.89/1.73 => ( subset @ B @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(inPowerset_type,type,
% 2.89/1.73 inPowerset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(inPowerset,definition,
% 2.89/1.73 ( inPowerset
% 2.89/1.73 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(powersetsubset_type,type,
% 2.89/1.73 powersetsubset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(powersetsubset,definition,
% 2.89/1.73 ( powersetsubset
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( subset @ A @ B )
% 2.89/1.73 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(sepInPowerset_type,type,
% 2.89/1.73 sepInPowerset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(sepInPowerset,definition,
% 2.89/1.73 ( sepInPowerset
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( in
% 2.89/1.73 @ ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 @ ( powerset @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(sepSubset_type,type,
% 2.89/1.73 sepSubset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(sepSubset,definition,
% 2.89/1.73 ( sepSubset
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( subset
% 2.89/1.73 @ ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 @ A ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binunion_type,type,
% 2.89/1.73 binunion: $i > $i > $i ).
% 2.89/1.73
% 2.89/1.73 thf(binunionIL_type,type,
% 2.89/1.73 binunionIL: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binunionIL,definition,
% 2.89/1.73 ( binunionIL
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(upairset2IR_type,type,
% 2.89/1.73 upairset2IR: $o ).
% 2.89/1.73
% 2.89/1.73 thf(upairset2IR,definition,
% 2.89/1.73 ( upairset2IR
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binunionIR_type,type,
% 2.89/1.73 binunionIR: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binunionIR,definition,
% 2.89/1.73 ( binunionIR
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ B )
% 2.89/1.73 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binunionEcases_type,type,
% 2.89/1.73 binunionEcases: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binunionEcases,definition,
% 2.89/1.73 ( binunionEcases
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.89/1.73 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.89/1.73 => ( ( ( in @ Xx @ A )
% 2.89/1.73 => Xphi )
% 2.89/1.73 => ( ( ( in @ Xx @ B )
% 2.89/1.73 => Xphi )
% 2.89/1.73 => Xphi ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binunionE_type,type,
% 2.89/1.73 binunionE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binunionE,definition,
% 2.89/1.73 ( binunionE
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.89/1.73 => ( ( in @ Xx @ A )
% 2.89/1.73 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binunionLsub_type,type,
% 2.89/1.73 binunionLsub: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binunionLsub,definition,
% 2.89/1.73 ( binunionLsub
% 2.89/1.73 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binunionRsub_type,type,
% 2.89/1.73 binunionRsub: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binunionRsub,definition,
% 2.89/1.73 ( binunionRsub
% 2.89/1.73 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binintersect_type,type,
% 2.89/1.73 binintersect: $i > $i > $i ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectI_type,type,
% 2.89/1.73 binintersectI: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectI,definition,
% 2.89/1.73 ( binintersectI
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( ( in @ Xx @ B )
% 2.89/1.73 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectSubset5_type,type,
% 2.89/1.73 binintersectSubset5: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectSubset5,definition,
% 2.89/1.73 ( binintersectSubset5
% 2.89/1.73 = ( ! [A: $i,B: $i,C: $i] :
% 2.89/1.73 ( ( subset @ C @ A )
% 2.89/1.73 => ( ( subset @ C @ B )
% 2.89/1.73 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectEL_type,type,
% 2.89/1.73 binintersectEL: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectEL,definition,
% 2.89/1.73 ( binintersectEL
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.89/1.73 => ( in @ Xx @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectLsub_type,type,
% 2.89/1.73 binintersectLsub: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectLsub,definition,
% 2.89/1.73 ( binintersectLsub
% 2.89/1.73 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectSubset2_type,type,
% 2.89/1.73 binintersectSubset2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectSubset2,definition,
% 2.89/1.73 ( binintersectSubset2
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( subset @ A @ B )
% 2.89/1.73 => ( ( binintersect @ A @ B )
% 2.89/1.73 = A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectSubset3_type,type,
% 2.89/1.73 binintersectSubset3: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectSubset3,definition,
% 2.89/1.73 ( binintersectSubset3
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( ( binintersect @ A @ B )
% 2.89/1.73 = B )
% 2.89/1.73 => ( subset @ B @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectER_type,type,
% 2.89/1.73 binintersectER: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectER,definition,
% 2.89/1.73 ( binintersectER
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.89/1.73 => ( in @ Xx @ B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(disjointsetsI1_type,type,
% 2.89/1.73 disjointsetsI1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(disjointsetsI1,definition,
% 2.89/1.73 ( disjointsetsI1
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ~ ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ( in @ Xx @ B ) )
% 2.89/1.73 => ( ( binintersect @ A @ B )
% 2.89/1.73 = emptyset ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectRsub_type,type,
% 2.89/1.73 binintersectRsub: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectRsub,definition,
% 2.89/1.73 ( binintersectRsub
% 2.89/1.73 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectSubset4_type,type,
% 2.89/1.73 binintersectSubset4: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectSubset4,definition,
% 2.89/1.73 ( binintersectSubset4
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( subset @ B @ A )
% 2.89/1.73 => ( ( binintersect @ A @ B )
% 2.89/1.73 = B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectSubset1_type,type,
% 2.89/1.73 binintersectSubset1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(binintersectSubset1,definition,
% 2.89/1.73 ( binintersectSubset1
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( ( binintersect @ A @ B )
% 2.89/1.73 = A )
% 2.89/1.73 => ( subset @ A @ B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(bs114d_type,type,
% 2.89/1.73 bs114d: $o ).
% 2.89/1.73
% 2.89/1.73 thf(bs114d,definition,
% 2.89/1.73 ( bs114d
% 2.89/1.73 = ( ! [A: $i,B: $i,C: $i] :
% 2.89/1.73 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 2.89/1.73 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(regular_type,type,
% 2.89/1.73 regular: $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminus_type,type,
% 2.89/1.73 setminus: $i > $i > $i ).
% 2.89/1.73
% 2.89/1.73 thf(setminusI_type,type,
% 2.89/1.73 setminusI: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminusI,definition,
% 2.89/1.73 ( setminusI
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( ~ ( in @ Xx @ B )
% 2.89/1.73 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setminusEL_type,type,
% 2.89/1.73 setminusEL: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminusEL,definition,
% 2.89/1.73 ( setminusEL
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.89/1.73 => ( in @ Xx @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setminusER_type,type,
% 2.89/1.73 setminusER: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminusER,definition,
% 2.89/1.73 ( setminusER
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 2.89/1.73 => ~ ( in @ Xx @ B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setminusSubset2_type,type,
% 2.89/1.73 setminusSubset2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminusSubset2,definition,
% 2.89/1.73 ( setminusSubset2
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( subset @ A @ B )
% 2.89/1.73 => ( ( setminus @ A @ B )
% 2.89/1.73 = emptyset ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setminusERneg_type,type,
% 2.89/1.73 setminusERneg: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminusERneg,definition,
% 2.89/1.73 ( setminusERneg
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.89/1.73 => ( ( in @ Xx @ A )
% 2.89/1.73 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setminusELneg_type,type,
% 2.89/1.73 setminusELneg: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminusELneg,definition,
% 2.89/1.73 ( setminusELneg
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ~ ( in @ Xx @ ( setminus @ A @ B ) )
% 2.89/1.73 => ( ~ ( in @ Xx @ B )
% 2.89/1.73 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setminusILneg_type,type,
% 2.89/1.73 setminusILneg: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminusILneg,definition,
% 2.89/1.73 ( setminusILneg
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ~ ( in @ Xx @ A )
% 2.89/1.73 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setminusIRneg_type,type,
% 2.89/1.73 setminusIRneg: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminusIRneg,definition,
% 2.89/1.73 ( setminusIRneg
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ B )
% 2.89/1.73 => ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setminusLsub_type,type,
% 2.89/1.73 setminusLsub: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminusLsub,definition,
% 2.89/1.73 ( setminusLsub
% 2.89/1.73 = ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setminusSubset1_type,type,
% 2.89/1.73 setminusSubset1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setminusSubset1,definition,
% 2.89/1.73 ( setminusSubset1
% 2.89/1.73 = ( ! [A: $i,B: $i] :
% 2.89/1.73 ( ( ( setminus @ A @ B )
% 2.89/1.73 = emptyset )
% 2.89/1.73 => ( subset @ A @ B ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(symdiff_type,type,
% 2.89/1.73 symdiff: $i > $i > $i ).
% 2.89/1.73
% 2.89/1.73 thf(symdiffE_type,type,
% 2.89/1.73 symdiffE: $o ).
% 2.89/1.73
% 2.89/1.73 thf(symdiffE,definition,
% 2.89/1.73 ( symdiffE
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( symdiff @ A @ B ) )
% 2.89/1.73 => ! [Xphi: $o] :
% 2.89/1.73 ( ( ( in @ Xx @ A )
% 2.89/1.73 => ( ~ ( in @ Xx @ B )
% 2.89/1.73 => Xphi ) )
% 2.89/1.73 => ( ( ~ ( in @ Xx @ A )
% 2.89/1.73 => ( ( in @ Xx @ B )
% 2.89/1.73 => Xphi ) )
% 2.89/1.73 => Xphi ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(symdiffI1_type,type,
% 2.89/1.73 symdiffI1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(symdiffI1,definition,
% 2.89/1.73 ( symdiffI1
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( ~ ( in @ Xx @ B )
% 2.89/1.73 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(symdiffI2_type,type,
% 2.89/1.73 symdiffI2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(symdiffI2,definition,
% 2.89/1.73 ( symdiffI2
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ~ ( in @ Xx @ A )
% 2.89/1.73 => ( ( in @ Xx @ B )
% 2.89/1.73 => ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(symdiffIneg1_type,type,
% 2.89/1.73 symdiffIneg1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(symdiffIneg1,definition,
% 2.89/1.73 ( symdiffIneg1
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( ( in @ Xx @ B )
% 2.89/1.73 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(symdiffIneg2_type,type,
% 2.89/1.73 symdiffIneg2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(symdiffIneg2,definition,
% 2.89/1.73 ( symdiffIneg2
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ~ ( in @ Xx @ A )
% 2.89/1.73 => ( ~ ( in @ Xx @ B )
% 2.89/1.73 => ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(iskpair_type,type,
% 2.89/1.73 iskpair: $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(iskpair,definition,
% 2.89/1.73 ( iskpair
% 2.89/1.73 = ( ^ [A: $i] :
% 2.89/1.73 ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( setunion @ A ) )
% 2.89/1.73 & ? [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ ( setunion @ A ) )
% 2.89/1.73 & ( A
% 2.89/1.73 = ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(secondinupair_type,type,
% 2.89/1.73 secondinupair: $o ).
% 2.89/1.73
% 2.89/1.73 thf(secondinupair,definition,
% 2.89/1.73 ( secondinupair
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setukpairIL_type,type,
% 2.89/1.73 setukpairIL: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setukpairIL,definition,
% 2.89/1.73 ( setukpairIL
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setukpairIR_type,type,
% 2.89/1.73 setukpairIR: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setukpairIR,definition,
% 2.89/1.73 ( setukpairIR
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(kpairiskpair_type,type,
% 2.89/1.73 kpairiskpair: $o ).
% 2.89/1.73
% 2.89/1.73 thf(kpairiskpair,definition,
% 2.89/1.73 ( kpairiskpair
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(kpair_type,type,
% 2.89/1.73 kpair: $i > $i > $i ).
% 2.89/1.73
% 2.89/1.73 thf(kpair,definition,
% 2.89/1.73 ( kpair
% 2.89/1.73 = ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(kpairp_type,type,
% 2.89/1.73 kpairp: $o ).
% 2.89/1.73
% 2.89/1.73 thf(kpairp,definition,
% 2.89/1.73 ( kpairp
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(cartprod_type,type,
% 2.89/1.73 cartprod: $i > $i > $i ).
% 2.89/1.73
% 2.89/1.73 thf(singletonsubset_type,type,
% 2.89/1.73 singletonsubset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(singletonsubset,definition,
% 2.89/1.73 ( singletonsubset
% 2.89/1.73 = ( ! [A: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(singletoninpowerset_type,type,
% 2.89/1.73 singletoninpowerset: $o ).
% 2.89/1.73
% 2.89/1.73 thf(singletoninpowerset,definition,
% 2.89/1.73 ( singletoninpowerset
% 2.89/1.73 = ( ! [A: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(singletoninpowunion_type,type,
% 2.89/1.73 singletoninpowunion: $o ).
% 2.89/1.73
% 2.89/1.73 thf(singletoninpowunion,definition,
% 2.89/1.73 ( singletoninpowunion
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(upairset2E_type,type,
% 2.89/1.73 upairset2E: $o ).
% 2.89/1.73
% 2.89/1.73 thf(upairset2E,definition,
% 2.89/1.73 ( upairset2E
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.89/1.73 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.89/1.73 => ( ( Xz = Xx )
% 2.89/1.73 | ( Xz = Xy ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(upairsubunion_type,type,
% 2.89/1.73 upairsubunion: $o ).
% 2.89/1.73
% 2.89/1.73 thf(upairsubunion,definition,
% 2.89/1.73 ( upairsubunion
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ B )
% 2.89/1.73 => ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(upairinpowunion_type,type,
% 2.89/1.73 upairinpowunion: $o ).
% 2.89/1.73
% 2.89/1.73 thf(upairinpowunion,definition,
% 2.89/1.73 ( upairinpowunion
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ B )
% 2.89/1.73 => ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(ubforcartprodlem1_type,type,
% 2.89/1.73 ubforcartprodlem1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(ubforcartprodlem1,definition,
% 2.89/1.73 ( ubforcartprodlem1
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ B )
% 2.89/1.73 => ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(ubforcartprodlem2_type,type,
% 2.89/1.73 ubforcartprodlem2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(ubforcartprodlem2,definition,
% 2.89/1.73 ( ubforcartprodlem2
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ B )
% 2.89/1.73 => ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(ubforcartprodlem3_type,type,
% 2.89/1.73 ubforcartprodlem3: $o ).
% 2.89/1.73
% 2.89/1.73 thf(ubforcartprodlem3,definition,
% 2.89/1.73 ( ubforcartprodlem3
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ B )
% 2.89/1.73 => ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(cartprodpairin_type,type,
% 2.89/1.73 cartprodpairin: $o ).
% 2.89/1.73
% 2.89/1.73 thf(cartprodpairin,definition,
% 2.89/1.73 ( cartprodpairin
% 2.89/1.73 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ B )
% 2.89/1.73 => ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(cartprodmempair1_type,type,
% 2.89/1.73 cartprodmempair1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(cartprodmempair1,definition,
% 2.89/1.73 ( cartprodmempair1
% 2.89/1.73 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.89/1.73 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.89/1.73 => ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ? [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ B )
% 2.89/1.73 & ( Xu
% 2.89/1.73 = ( kpair @ Xx @ Xy ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(cartprodmempair_type,type,
% 2.89/1.73 cartprodmempair: $o ).
% 2.89/1.73
% 2.89/1.73 thf(cartprodmempair,definition,
% 2.89/1.73 ( cartprodmempair
% 2.89/1.73 = ( ! [A: $i,B: $i,Xu: $i] :
% 2.89/1.73 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.89/1.73 => ( iskpair @ Xu ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setunionE2_type,type,
% 2.89/1.73 setunionE2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setunionE2,definition,
% 2.89/1.73 ( setunionE2
% 2.89/1.73 = ( ! [A: $i,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ ( setunion @ A ) )
% 2.89/1.73 => ? [X: $i] :
% 2.89/1.73 ( ( in @ X @ A )
% 2.89/1.73 & ( in @ Xx @ X ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setunionsingleton1_type,type,
% 2.89/1.73 setunionsingleton1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setunionsingleton1,definition,
% 2.89/1.73 ( setunionsingleton1
% 2.89/1.73 = ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setunionsingleton2_type,type,
% 2.89/1.73 setunionsingleton2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setunionsingleton2,definition,
% 2.89/1.73 ( setunionsingleton2
% 2.89/1.73 = ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(setunionsingleton_type,type,
% 2.89/1.73 setunionsingleton: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setunionsingleton,definition,
% 2.89/1.73 ( setunionsingleton
% 2.89/1.73 = ( ! [Xx: $i] :
% 2.89/1.73 ( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
% 2.89/1.73 = Xx ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(singleton_type,type,
% 2.89/1.73 singleton: $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(singleton,definition,
% 2.89/1.73 ( singleton
% 2.89/1.73 = ( ^ [A: $i] :
% 2.89/1.73 ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ( A
% 2.89/1.73 = ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(singletonprop_type,type,
% 2.89/1.73 singletonprop: $o ).
% 2.89/1.73
% 2.89/1.73 thf(singletonprop,definition,
% 2.89/1.73 ( singletonprop
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ A )
% 2.89/1.73 => ( ( Xphi @ Xx )
% 2.89/1.73 => ( ( Xphi @ Xy )
% 2.89/1.73 => ( Xx = Xy ) ) ) ) )
% 2.89/1.73 => ( ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ( Xphi @ Xx ) )
% 2.89/1.73 => ( singleton
% 2.89/1.73 @ ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(ex1_type,type,
% 2.89/1.73 ex1: $i > ( $i > $o ) > $o ).
% 2.89/1.73
% 2.89/1.73 thf(ex1,definition,
% 2.89/1.73 ( ex1
% 2.89/1.73 = ( ^ [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( singleton
% 2.89/1.73 @ ( dsetconstr @ A
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(ex1E1_type,type,
% 2.89/1.73 ex1E1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(ex1E1,definition,
% 2.89/1.73 ( ex1E1
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( ( ex1 @ A
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.89/1.73 => ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(ex1I_type,type,
% 2.89/1.73 ex1I: $o ).
% 2.89/1.73
% 2.89/1.73 thf(ex1I,definition,
% 2.89/1.73 ( ex1I
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ( ( Xphi @ Xx )
% 2.89/1.73 => ( ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ A )
% 2.89/1.73 => ( ( Xphi @ Xy )
% 2.89/1.73 => ( Xy = Xx ) ) )
% 2.89/1.73 => ( ex1 @ A
% 2.89/1.73 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(ex1I2_type,type,
% 2.89/1.73 ex1I2: $o ).
% 2.89/1.73
% 2.89/1.73 thf(ex1I2,definition,
% 2.89/1.73 ( ex1I2
% 2.89/1.73 = ( ! [A: $i,Xphi: $i > $o] :
% 2.89/1.73 ( ! [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 => ! [Xy: $i] :
% 2.89/1.73 ( ( in @ Xy @ A )
% 2.89/1.73 => ( ( Xphi @ Xx )
% 2.89/1.73 => ( ( Xphi @ Xy )
% 2.89/1.73 => ( Xx = Xy ) ) ) ) )
% 2.89/1.73 => ( ? [Xx: $i] :
% 2.89/1.73 ( ( in @ Xx @ A )
% 2.89/1.73 & ( Xphi @ Xx ) )
% 2.89/1.73 => ( ex1 @ A
% 2.89/1.73 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(singletonsuniq_type,type,
% 2.89/1.73 singletonsuniq: $o ).
% 2.89/1.73
% 2.89/1.73 thf(singletonsuniq,definition,
% 2.89/1.73 ( singletonsuniq
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( ( setadjoin @ Xx @ emptyset )
% 2.89/1.73 = ( setadjoin @ Xy @ emptyset ) )
% 2.89/1.73 => ( Xx = Xy ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(atmost1p_type,type,
% 2.89/1.73 atmost1p: $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(atleast2p_type,type,
% 2.89/1.73 atleast2p: $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(atmost2p_type,type,
% 2.89/1.73 atmost2p: $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(upairsetp_type,type,
% 2.89/1.73 upairsetp: $i > $o ).
% 2.89/1.73
% 2.89/1.73 thf(setukpairinjL1_type,type,
% 2.89/1.73 setukpairinjL1: $o ).
% 2.89/1.73
% 2.89/1.73 thf(setukpairinjL1,definition,
% 2.89/1.73 ( setukpairinjL1
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.89/1.73 ( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
% 2.89/1.73 => ( Xx = Xz ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(kfstsingleton_type,type,
% 2.89/1.73 kfstsingleton: $o ).
% 2.89/1.73
% 2.89/1.73 thf(kfstsingleton,definition,
% 2.89/1.73 ( kfstsingleton
% 2.89/1.73 = ( ! [Xu: $i] :
% 2.89/1.73 ( ( iskpair @ Xu )
% 2.89/1.73 => ( singleton
% 2.89/1.73 @ ( dsetconstr @ ( setunion @ Xu )
% 2.89/1.73 @ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(theprop_type,type,
% 2.89/1.73 theprop: $o ).
% 2.89/1.73
% 2.89/1.73 thf(theprop,definition,
% 2.89/1.73 ( theprop
% 2.89/1.73 = ( ! [X: $i] :
% 2.89/1.73 ( ( singleton @ X )
% 2.89/1.73 => ( in @ ( setunion @ X ) @ X ) ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(kfst_type,type,
% 2.89/1.73 kfst: $i > $i ).
% 2.89/1.73
% 2.89/1.73 thf(kfstpairEq_type,type,
% 2.89/1.73 kfstpairEq: $o ).
% 2.89/1.73
% 2.89/1.73 thf(kfstpairEq,definition,
% 2.89/1.73 ( kfstpairEq
% 2.89/1.73 = ( ! [Xx: $i,Xy: $i] :
% 2.89/1.73 ( ( kfst @ ( kpair @ Xx @ Xy ) )
% 2.89/1.73 = Xx ) ) ) ).
% 2.89/1.73
% 2.89/1.73 thf(cartprodfstin,conjecture,
% 2.89/1.73 ( setextAx
% 2.89/1.73 => ( emptysetAx
% 2.89/1.73 => ( setadjoinAx
% 2.89/1.73 => ( powersetAx
% 2.89/1.73 => ( setunionAx
% 2.89/1.73 => ( omega0Ax
% 2.89/1.73 => ( omegaSAx
% 2.89/1.73 => ( omegaIndAx
% 2.89/1.73 => ( replAx
% 2.89/1.73 => ( foundationAx
% 2.89/1.73 => ( wellorderingAx
% 2.89/1.73 => ( descrp
% 2.89/1.73 => ( dsetconstrI
% 2.89/1.73 => ( dsetconstrEL
% 2.89/1.73 => ( dsetconstrER
% 2.89/1.73 => ( exuE1
% 2.89/1.73 => ( prop2setE
% 2.89/1.73 => ( emptysetE
% 2.89/1.73 => ( emptysetimpfalse
% 2.89/1.73 => ( notinemptyset
% 2.89/1.73 => ( exuE3e
% 2.89/1.73 => ( setext
% 2.89/1.73 => ( emptyI
% 2.89/1.73 => ( noeltsimpempty
% 2.89/1.73 => ( setbeta
% 2.89/1.73 => ( nonemptyE1
% 2.89/1.73 => ( nonemptyI
% 2.89/1.73 => ( nonemptyI1
% 2.89/1.73 => ( setadjoinIL
% 2.89/1.73 => ( emptyinunitempty
% 2.89/1.73 => ( setadjoinIR
% 2.89/1.73 => ( setadjoinE
% 2.89/1.73 => ( setadjoinOr
% 2.89/1.73 => ( setoftrueEq
% 2.89/1.73 => ( powersetI
% 2.89/1.73 => ( emptyinPowerset
% 2.89/1.73 => ( emptyInPowerset
% 2.89/1.73 => ( powersetE
% 2.89/1.73 => ( setunionI
% 2.89/1.73 => ( setunionE
% 2.89/1.73 => ( subPowSU
% 2.89/1.73 => ( exuE2
% 2.89/1.73 => ( nonemptyImpWitness
% 2.89/1.73 => ( uniqinunit
% 2.89/1.73 => ( notinsingleton
% 2.89/1.73 => ( eqinunit
% 2.89/1.74 => ( singletonsswitch
% 2.89/1.74 => ( upairsetE
% 2.89/1.74 => ( upairsetIL
% 2.89/1.74 => ( upairsetIR
% 2.89/1.74 => ( emptyE1
% 2.89/1.74 => ( vacuousDall
% 2.89/1.74 => ( quantDeMorgan1
% 2.89/1.74 => ( quantDeMorgan2
% 2.89/1.74 => ( quantDeMorgan3
% 2.89/1.74 => ( quantDeMorgan4
% 2.89/1.74 => ( prop2setI
% 2.89/1.74 => ( prop2set2propI
% 2.89/1.74 => ( notdexE
% 2.89/1.74 => ( notdallE
% 2.89/1.74 => ( exuI1
% 2.89/1.74 => ( exuI3
% 2.89/1.74 => ( exuI2
% 2.89/1.74 => ( inCongP
% 2.89/1.74 => ( in__Cong
% 2.89/1.74 => ( exuE3u
% 2.89/1.74 => ( exu__Cong
% 2.89/1.74 => ( emptyset__Cong
% 2.89/1.74 => ( setadjoin__Cong
% 2.89/1.74 => ( powerset__Cong
% 2.89/1.74 => ( setunion__Cong
% 2.89/1.74 => ( omega__Cong
% 2.89/1.74 => ( exuEu
% 2.89/1.74 => ( descr__Cong
% 2.89/1.74 => ( dsetconstr__Cong
% 2.89/1.74 => ( subsetI1
% 2.89/1.74 => ( eqimpsubset2
% 2.89/1.74 => ( eqimpsubset1
% 2.89/1.74 => ( subsetI2
% 2.89/1.74 => ( emptysetsubset
% 2.89/1.74 => ( subsetE
% 2.89/1.74 => ( subsetE2
% 2.89/1.74 => ( notsubsetI
% 2.89/1.74 => ( notequalI1
% 2.89/1.74 => ( notequalI2
% 2.89/1.74 => ( subsetRefl
% 2.89/1.74 => ( subsetTrans
% 2.89/1.74 => ( setadjoinSub
% 2.89/1.74 => ( setadjoinSub2
% 2.89/1.74 => ( subset2powerset
% 2.89/1.74 => ( setextsub
% 2.89/1.74 => ( subsetemptysetimpeq
% 2.89/1.74 => ( powersetI1
% 2.89/1.74 => ( powersetE1
% 2.89/1.74 => ( inPowerset
% 2.89/1.74 => ( powersetsubset
% 2.89/1.74 => ( sepInPowerset
% 2.89/1.74 => ( sepSubset
% 2.89/1.74 => ( binunionIL
% 2.89/1.74 => ( upairset2IR
% 2.89/1.74 => ( binunionIR
% 2.89/1.74 => ( binunionEcases
% 2.89/1.74 => ( binunionE
% 2.89/1.74 => ( binunionLsub
% 2.89/1.74 => ( binunionRsub
% 2.89/1.74 => ( binintersectI
% 2.89/1.74 => ( binintersectSubset5
% 2.89/1.74 => ( binintersectEL
% 2.89/1.74 => ( binintersectLsub
% 2.89/1.74 => ( binintersectSubset2
% 2.89/1.74 => ( binintersectSubset3
% 2.89/1.74 => ( binintersectER
% 2.89/1.74 => ( disjointsetsI1
% 2.89/1.74 => ( binintersectRsub
% 2.89/1.74 => ( binintersectSubset4
% 2.89/1.74 => ( binintersectSubset1
% 2.89/1.74 => ( bs114d
% 2.89/1.74 => ( setminusI
% 2.89/1.74 => ( setminusEL
% 2.89/1.74 => ( setminusER
% 2.89/1.74 => ( setminusSubset2
% 2.89/1.74 => ( setminusERneg
% 2.89/1.74 => ( setminusELneg
% 2.89/1.74 => ( setminusILneg
% 2.89/1.74 => ( setminusIRneg
% 2.89/1.74 => ( setminusLsub
% 2.89/1.74 => ( setminusSubset1
% 2.89/1.74 => ( symdiffE
% 2.89/1.74 => ( symdiffI1
% 2.89/1.74 => ( symdiffI2
% 2.89/1.74 => ( symdiffIneg1
% 2.89/1.74 => ( symdiffIneg2
% 2.89/1.74 => ( secondinupair
% 2.89/1.74 => ( setukpairIL
% 2.89/1.74 => ( setukpairIR
% 2.89/1.74 => ( kpairiskpair
% 2.89/1.74 => ( kpairp
% 2.89/1.74 => ( singletonsubset
% 2.89/1.74 => ( singletoninpowerset
% 2.89/1.74 => ( singletoninpowunion
% 2.89/1.74 => ( upairset2E
% 2.89/1.74 => ( upairsubunion
% 2.89/1.74 => ( upairinpowunion
% 2.89/1.74 => ( ubforcartprodlem1
% 2.89/1.74 => ( ubforcartprodlem2
% 2.89/1.74 => ( ubforcartprodlem3
% 2.89/1.74 => ( cartprodpairin
% 2.89/1.74 => ( cartprodmempair1
% 2.89/1.74 => ( cartprodmempair
% 2.89/1.74 => ( setunionE2
% 2.89/1.74 => ( setunionsingleton1
% 2.89/1.74 => ( setunionsingleton2
% 2.89/1.74 => ( setunionsingleton
% 2.89/1.74 => ( singletonprop
% 2.89/1.74 => ( ex1E1
% 2.89/1.74 => ( ex1I
% 2.89/1.74 => ( ex1I2
% 2.89/1.74 => ( singletonsuniq
% 2.89/1.74 => ( setukpairinjL1
% 2.89/1.74 => ( kfstsingleton
% 2.89/1.74 => ( theprop
% 2.89/1.74 => ( kfstpairEq
% 2.89/1.74 => ! [A: $i,B: $i,Xu: $i] :
% 2.89/1.74 ( ( in @ Xu @ ( cartprod @ A @ B ) )
% 2.89/1.74 => ( in @ ( kfst @ Xu ) @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.89/1.74 ------------------------
% 2.89/1.76 % (6139)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/183Mi)
% 2.89/1.76 % (6141)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_6029 for (2999ds/27Mi)
% 2.89/1.76 % (6145)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/18Mi)
% 2.89/1.76 % (6140)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_6029 for (2999ds/4Mi)
% 2.89/1.76 % (6143)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_6029 for (2999ds/2Mi)
% 2.89/1.76 % (6144)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_6029 for (2999ds/275Mi)
% 2.89/1.76 % (6142)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/2Mi)
% 2.89/1.76 % (6142)Instruction limit reached!
% 2.89/1.76 % (6142)------------------------------
% 2.89/1.76 % (6142)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.76 % (6142)Termination reason: Unknown
% 2.89/1.76 % (6142)Termination phase: shuffling
% 2.89/1.76
% 2.89/1.76 % (6142)Memory used [KB]: 1279
% 2.89/1.76 % (6142)Time elapsed: 0.003 s
% 2.89/1.76 % (6142)Instructions burned: 2 (million)
% 2.89/1.76 % (6142)------------------------------
% 2.89/1.76 % (6142)------------------------------
% 2.89/1.76 % (6143)Instruction limit reached!
% 2.89/1.76 % (6143)------------------------------
% 2.89/1.76 % (6143)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.76 % (6143)Termination reason: Unknown
% 2.89/1.76 % (6143)Termination phase: shuffling
% 2.89/1.76
% 2.89/1.76 % (6143)Memory used [KB]: 1279
% 2.89/1.76 % (6143)Time elapsed: 0.003 s
% 2.89/1.76 % (6143)Instructions burned: 2 (million)
% 2.89/1.76 % (6143)------------------------------
% 2.89/1.76 % (6143)------------------------------
% 2.89/1.76 % (6140)Instruction limit reached!
% 2.89/1.76 % (6140)------------------------------
% 2.89/1.76 % (6140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.76 % (6140)Termination reason: Unknown
% 2.89/1.76 % (6140)Termination phase: shuffling
% 2.89/1.76
% 2.89/1.76 % (6140)Memory used [KB]: 1279
% 2.89/1.76 % (6140)Time elapsed: 0.004 s
% 2.89/1.76 % (6140)Instructions burned: 4 (million)
% 2.89/1.76 % (6140)------------------------------
% 2.89/1.76 % (6140)------------------------------
% 2.89/1.77 % (6145)Instruction limit reached!
% 2.89/1.77 % (6145)------------------------------
% 2.89/1.77 % (6145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.77 % (6145)Termination reason: Unknown
% 2.89/1.77 % (6145)Termination phase: Property scanning
% 2.89/1.77
% 2.89/1.77 % (6145)Memory used [KB]: 1535
% 2.89/1.77 % (6145)Time elapsed: 0.011 s
% 2.89/1.77 % (6145)Instructions burned: 19 (million)
% 2.89/1.77 % (6145)------------------------------
% 2.89/1.77 % (6145)------------------------------
% 2.89/1.78 % (6141)Instruction limit reached!
% 2.89/1.78 % (6141)------------------------------
% 2.89/1.78 % (6141)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.78 % (6141)Termination reason: Unknown
% 2.89/1.78 % (6141)Termination phase: Property scanning
% 2.89/1.78
% 2.89/1.78 % (6141)Memory used [KB]: 1791
% 2.89/1.78 % (6141)Time elapsed: 0.015 s
% 2.89/1.78 % (6141)Instructions burned: 28 (million)
% 2.89/1.78 % (6141)------------------------------
% 2.89/1.78 % (6141)------------------------------
% 2.89/1.78 % (6146)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/3Mi)
% 2.89/1.78 % (6147)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_6029 for (2999ds/37Mi)
% 2.89/1.78 % (6148)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_6029 for (2999ds/15Mi)
% 2.89/1.78 % (6146)Instruction limit reached!
% 2.89/1.78 % (6146)------------------------------
% 2.89/1.78 % (6146)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.78 % (6146)Termination reason: Unknown
% 2.89/1.78 % (6146)Termination phase: shuffling
% 2.89/1.78
% 2.89/1.78 % (6146)Memory used [KB]: 1279
% 2.89/1.78 % (6146)Time elapsed: 0.003 s
% 2.89/1.78 % (6146)Instructions burned: 3 (million)
% 2.89/1.78 % (6146)------------------------------
% 2.89/1.78 % (6146)------------------------------
% 2.89/1.79 % (6148)Instruction limit reached!
% 2.89/1.79 % (6148)------------------------------
% 2.89/1.79 % (6148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.79 % (6148)Termination reason: Unknown
% 2.89/1.79 % (6148)Termination phase: Property scanning
% 2.89/1.79
% 2.89/1.79 % (6149)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_6029 for (2999ds/3Mi)
% 2.89/1.79 % (6148)Memory used [KB]: 1535
% 2.89/1.79 % (6148)Time elapsed: 0.009 s
% 2.89/1.79 % (6148)Instructions burned: 15 (million)
% 2.89/1.79 % (6148)------------------------------
% 2.89/1.79 % (6148)------------------------------
% 2.89/1.79 % (6149)Instruction limit reached!
% 2.89/1.79 % (6149)------------------------------
% 2.89/1.79 % (6149)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.79 % (6149)Termination reason: Unknown
% 2.89/1.79 % (6149)Termination phase: shuffling
% 2.89/1.79
% 2.89/1.79 % (6149)Memory used [KB]: 1279
% 2.89/1.79 % (6149)Time elapsed: 0.003 s
% 2.89/1.79 % (6149)Instructions burned: 3 (million)
% 2.89/1.79 % (6149)------------------------------
% 2.89/1.79 % (6149)------------------------------
% 2.89/1.79 % (6150)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_6029 for (2999ds/1041Mi)
% 2.89/1.80 % (6147)Instruction limit reached!
% 2.89/1.80 % (6147)------------------------------
% 2.89/1.80 % (6147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.89/1.80 % (6147)Termination reason: Unknown
% 2.89/1.80 % (6147)Termination phase: Property scanning
% 2.89/1.80
% 2.89/1.80 % (6147)Memory used [KB]: 1791
% 2.89/1.80 % (6147)Time elapsed: 0.018 s
% 2.89/1.80 % (6147)Instructions burned: 37 (million)
% 2.89/1.80 % (6147)------------------------------
% 2.89/1.80 % (6147)------------------------------
% 2.92/1.80 % (6151)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/7Mi)
% 2.92/1.80 % (6151)Instruction limit reached!
% 2.92/1.80 % (6151)------------------------------
% 2.92/1.80 % (6151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.80 % (6151)Termination reason: Unknown
% 2.92/1.80 % (6151)Termination phase: shuffling
% 2.92/1.80
% 2.92/1.80 % (6151)Memory used [KB]: 1407
% 2.92/1.80 % (6151)Time elapsed: 0.005 s
% 2.92/1.80 % (6151)Instructions burned: 7 (million)
% 2.92/1.80 % (6151)------------------------------
% 2.92/1.80 % (6151)------------------------------
% 2.92/1.80 % (6152)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/16Mi)
% 2.92/1.81 % (6153)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_6029 for (2999ds/3Mi)
% 2.92/1.81 % (6153)Instruction limit reached!
% 2.92/1.81 % (6153)------------------------------
% 2.92/1.81 % (6153)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.81 % (6153)Termination reason: Unknown
% 2.92/1.81 % (6153)Termination phase: shuffling
% 2.92/1.81
% 2.92/1.81 % (6153)Memory used [KB]: 1279
% 2.92/1.81 % (6153)Time elapsed: 0.003 s
% 2.92/1.81 % (6153)Instructions burned: 3 (million)
% 2.92/1.81 % (6153)------------------------------
% 2.92/1.81 % (6153)------------------------------
% 2.92/1.81 % (6152)Instruction limit reached!
% 2.92/1.81 % (6152)------------------------------
% 2.92/1.81 % (6152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.81 % (6152)Termination reason: Unknown
% 2.92/1.81 % (6152)Termination phase: shuffling
% 2.92/1.81
% 2.92/1.81 % (6152)Memory used [KB]: 1663
% 2.92/1.81 % (6152)Time elapsed: 0.009 s
% 2.92/1.81 % (6152)Instructions burned: 16 (million)
% 2.92/1.81 % (6152)------------------------------
% 2.92/1.81 % (6152)------------------------------
% 2.92/1.81 % (6154)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_6029 for (2999ds/3Mi)
% 2.92/1.81 % (6154)Instruction limit reached!
% 2.92/1.81 % (6154)------------------------------
% 2.92/1.81 % (6154)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.81 % (6154)Termination reason: Unknown
% 2.92/1.81 % (6154)Termination phase: shuffling
% 2.92/1.81
% 2.92/1.81 % (6154)Memory used [KB]: 1279
% 2.92/1.81 % (6154)Time elapsed: 0.003 s
% 2.92/1.81 % (6154)Instructions burned: 3 (million)
% 2.92/1.81 % (6154)------------------------------
% 2.92/1.81 % (6154)------------------------------
% 2.92/1.82 % (6155)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/7Mi)
% 2.92/1.82 % (6155)Instruction limit reached!
% 2.92/1.82 % (6155)------------------------------
% 2.92/1.82 % (6155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.82 % (6155)Termination reason: Unknown
% 2.92/1.82 % (6155)Termination phase: shuffling
% 2.92/1.82
% 2.92/1.82 % (6155)Memory used [KB]: 1407
% 2.92/1.82 % (6155)Time elapsed: 0.005 s
% 2.92/1.82 % (6155)Instructions burned: 8 (million)
% 2.92/1.82 % (6155)------------------------------
% 2.92/1.82 % (6155)------------------------------
% 2.92/1.82 % (6156)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/3Mi)
% 2.92/1.82 % (6156)Instruction limit reached!
% 2.92/1.82 % (6156)------------------------------
% 2.92/1.82 % (6156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.82 % (6156)Termination reason: Unknown
% 2.92/1.82 % (6156)Termination phase: shuffling
% 2.92/1.82
% 2.92/1.82 % (6156)Memory used [KB]: 1279
% 2.92/1.82 % (6156)Time elapsed: 0.003 s
% 2.92/1.82 % (6156)Instructions burned: 3 (million)
% 2.92/1.82 % (6156)------------------------------
% 2.92/1.82 % (6156)------------------------------
% 2.92/1.83 % (6157)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/4Mi)
% 2.92/1.83 % (6158)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/18Mi)
% 2.92/1.83 % (6157)Instruction limit reached!
% 2.92/1.83 % (6157)------------------------------
% 2.92/1.83 % (6157)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.83 % (6157)Termination reason: Unknown
% 2.92/1.83 % (6157)Termination phase: shuffling
% 2.92/1.83
% 2.92/1.83 % (6157)Memory used [KB]: 1407
% 2.92/1.83 % (6157)Time elapsed: 0.004 s
% 2.92/1.83 % (6157)Instructions burned: 5 (million)
% 2.92/1.83 % (6157)------------------------------
% 2.92/1.83 % (6157)------------------------------
% 2.92/1.84 % (6159)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/710Mi)
% 2.92/1.84 % (6158)Instruction limit reached!
% 2.92/1.84 % (6158)------------------------------
% 2.92/1.84 % (6158)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.84 % (6158)Termination reason: Unknown
% 2.92/1.84 % (6158)Termination phase: shuffling
% 2.92/1.84
% 2.92/1.84 % (6158)Memory used [KB]: 1663
% 2.92/1.84 % (6158)Time elapsed: 0.010 s
% 2.92/1.84 % (6158)Instructions burned: 18 (million)
% 2.92/1.84 % (6158)------------------------------
% 2.92/1.84 % (6158)------------------------------
% 2.92/1.84 % (6160)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/6Mi)
% 2.92/1.84 % (6160)Instruction limit reached!
% 2.92/1.84 % (6160)------------------------------
% 2.92/1.84 % (6160)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.84 % (6160)Termination reason: Unknown
% 2.92/1.84 % (6160)Termination phase: shuffling
% 2.92/1.84
% 2.92/1.84 % (6160)Memory used [KB]: 1407
% 2.92/1.84 % (6160)Time elapsed: 0.004 s
% 2.92/1.84 % (6160)Instructions burned: 6 (million)
% 2.92/1.84 % (6160)------------------------------
% 2.92/1.84 % (6160)------------------------------
% 2.92/1.85 % (6139)Instruction limit reached!
% 2.92/1.85 % (6139)------------------------------
% 2.92/1.85 % (6139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.85 % (6139)Termination reason: Unknown
% 2.92/1.85 % (6139)Termination phase: Saturation
% 2.92/1.85
% 2.92/1.85 % (6139)Memory used [KB]: 7419
% 2.92/1.85 % (6139)Time elapsed: 0.085 s
% 2.92/1.85 % (6139)Instructions burned: 183 (million)
% 2.92/1.85 % (6139)------------------------------
% 2.92/1.85 % (6139)------------------------------
% 2.92/1.85 % (6161)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_6029 for (2999ds/902Mi)
% 2.92/1.85 % (6162)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_6029 for (2999ds/21Mi)
% 2.92/1.86 % (6163)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_6029 for (2999ds/5Mi)
% 2.92/1.86 % (6163)Instruction limit reached!
% 2.92/1.86 % (6163)------------------------------
% 2.92/1.86 % (6163)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.86 % (6163)Termination reason: Unknown
% 2.92/1.86 % (6163)Termination phase: shuffling
% 2.92/1.86
% 2.92/1.86 % (6163)Memory used [KB]: 1407
% 2.92/1.86 % (6163)Time elapsed: 0.004 s
% 2.92/1.86 % (6163)Instructions burned: 6 (million)
% 2.92/1.86 % (6163)------------------------------
% 2.92/1.86 % (6163)------------------------------
% 2.92/1.86 % (6164)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_6029 for (2998ds/6Mi)
% 2.92/1.86 % (6162)Instruction limit reached!
% 2.92/1.86 % (6162)------------------------------
% 2.92/1.86 % (6162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.86 % (6162)Termination reason: Unknown
% 2.92/1.86 % (6162)Termination phase: shuffling
% 2.92/1.86
% 2.92/1.86 % (6162)Memory used [KB]: 1791
% 2.92/1.86 % (6162)Time elapsed: 0.012 s
% 2.92/1.86 % (6162)Instructions burned: 22 (million)
% 2.92/1.86 % (6162)------------------------------
% 2.92/1.86 % (6162)------------------------------
% 2.92/1.86 % (6164)Instruction limit reached!
% 2.92/1.86 % (6164)------------------------------
% 2.92/1.86 % (6164)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.86 % (6164)Termination reason: Unknown
% 2.92/1.86 % (6164)Termination phase: shuffling
% 2.92/1.86
% 2.92/1.86 % (6164)Memory used [KB]: 1407
% 2.92/1.86 % (6164)Time elapsed: 0.005 s
% 2.92/1.86 % (6164)Instructions burned: 7 (million)
% 2.92/1.86 % (6164)------------------------------
% 2.92/1.86 % (6164)------------------------------
% 2.92/1.88 % (6165)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_6029 for (2998ds/377Mi)
% 2.92/1.88 % (6166)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_6029 for (2998ds/779Mi)
% 2.92/1.88 % (6167)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_6029 for (2998ds/19Mi)
% 2.92/1.89 % (6167)Instruction limit reached!
% 2.92/1.89 % (6167)------------------------------
% 2.92/1.89 % (6167)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.89 % (6167)Termination reason: Unknown
% 2.92/1.89 % (6167)Termination phase: shuffling
% 2.92/1.89
% 2.92/1.89 % (6167)Memory used [KB]: 1663
% 2.92/1.89 % (6167)Time elapsed: 0.010 s
% 2.92/1.89 % (6167)Instructions burned: 19 (million)
% 2.92/1.89 % (6167)------------------------------
% 2.92/1.89 % (6167)------------------------------
% 2.92/1.90 % (6144)Instruction limit reached!
% 2.92/1.90 % (6144)------------------------------
% 2.92/1.90 % (6144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.90 % (6144)Termination reason: Unknown
% 2.92/1.90 % (6144)Termination phase: Saturation
% 2.92/1.90
% 2.92/1.90 % (6144)Memory used [KB]: 8187
% 2.92/1.90 % (6144)Time elapsed: 0.137 s
% 2.92/1.90 % (6144)Instructions burned: 275 (million)
% 2.92/1.90 % (6144)------------------------------
% 2.92/1.90 % (6144)------------------------------
% 2.92/1.91 % (6168)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_6029 for (2998ds/879Mi)
% 2.92/1.91 % (6169)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_6029 for (2998ds/17Mi)
% 2.92/1.92 % (6169)Instruction limit reached!
% 2.92/1.92 % (6169)------------------------------
% 2.92/1.92 % (6169)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.92 % (6169)Termination reason: Unknown
% 2.92/1.92 % (6169)Termination phase: shuffling
% 2.92/1.92
% 2.92/1.92 % (6169)Memory used [KB]: 1663
% 2.92/1.92 % (6169)Time elapsed: 0.010 s
% 2.92/1.92 % (6169)Instructions burned: 18 (million)
% 2.92/1.92 % (6169)------------------------------
% 2.92/1.92 % (6169)------------------------------
% 2.92/1.94 % (6170)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_6029 for (2998ds/3Mi)
% 2.92/1.94 % (6170)Instruction limit reached!
% 2.92/1.94 % (6170)------------------------------
% 2.92/1.94 % (6170)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.94 % (6170)Termination reason: Unknown
% 2.92/1.94 % (6170)Termination phase: shuffling
% 2.92/1.94
% 2.92/1.94 % (6170)Memory used [KB]: 1279
% 2.92/1.94 % (6170)Time elapsed: 0.003 s
% 2.92/1.94 % (6170)Instructions burned: 3 (million)
% 2.92/1.94 % (6170)------------------------------
% 2.92/1.94 % (6170)------------------------------
% 2.92/1.96 % (6171)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_6029 for (2998ds/30Mi)
% 2.92/1.97 % (6171)Instruction limit reached!
% 2.92/1.97 % (6171)------------------------------
% 2.92/1.97 % (6171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.92/1.97 % (6171)Termination reason: Unknown
% 2.92/1.97 % (6171)Termination phase: Property scanning
% 2.92/1.97
% 2.92/1.97 % (6171)Memory used [KB]: 1791
% 2.92/1.97 % (6171)Time elapsed: 0.016 s
% 2.92/1.97 % (6171)Instructions burned: 31 (million)
% 2.92/1.97 % (6171)------------------------------
% 2.92/1.97 % (6171)------------------------------
% 2.92/1.99 % (6172)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_6029 for (2997ds/127Mi)
% 4.77/2.04 % (6172)Instruction limit reached!
% 4.77/2.04 % (6172)------------------------------
% 4.77/2.04 % (6172)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.04 % (6172)Termination reason: Unknown
% 4.77/2.04 % (6172)Termination phase: Saturation
% 4.77/2.04
% 4.77/2.04 % (6172)Memory used [KB]: 6908
% 4.77/2.04 % (6172)Time elapsed: 0.058 s
% 4.77/2.04 % (6172)Instructions burned: 127 (million)
% 4.77/2.04 % (6172)------------------------------
% 4.77/2.04 % (6172)------------------------------
% 4.77/2.06 % (6165)Instruction limit reached!
% 4.77/2.06 % (6165)------------------------------
% 4.77/2.06 % (6165)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.06 % (6165)Termination reason: Unknown
% 4.77/2.06 % (6165)Termination phase: Saturation
% 4.77/2.06
% 4.77/2.06 % (6165)Memory used [KB]: 7931
% 4.77/2.06 % (6165)Time elapsed: 0.184 s
% 4.77/2.06 % (6165)Instructions burned: 377 (million)
% 4.77/2.06 % (6165)------------------------------
% 4.77/2.06 % (6165)------------------------------
% 4.77/2.06 % (6173)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_6029 for (2996ds/100Mi)
% 4.77/2.08 % (6174)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_6029 for (2996ds/3Mi)
% 4.77/2.08 % (6174)Instruction limit reached!
% 4.77/2.08 % (6174)------------------------------
% 4.77/2.08 % (6174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.08 % (6174)Termination reason: Unknown
% 4.77/2.08 % (6174)Termination phase: shuffling
% 4.77/2.08
% 4.77/2.08 % (6174)Memory used [KB]: 1279
% 4.77/2.08 % (6174)Time elapsed: 0.003 s
% 4.77/2.08 % (6174)Instructions burned: 3 (million)
% 4.77/2.08 % (6174)------------------------------
% 4.77/2.08 % (6174)------------------------------
% 4.77/2.09 % (6175)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_6029 for (2996ds/20Mi)
% 4.77/2.10 % (6175)Instruction limit reached!
% 4.77/2.10 % (6175)------------------------------
% 4.77/2.10 % (6175)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.10 % (6175)Termination reason: Unknown
% 4.77/2.10 % (6175)Termination phase: Property scanning
% 4.77/2.10
% 4.77/2.10 % (6175)Memory used [KB]: 1535
% 4.77/2.10 % (6175)Time elapsed: 0.011 s
% 4.77/2.10 % (6175)Instructions burned: 20 (million)
% 4.77/2.10 % (6175)------------------------------
% 4.77/2.10 % (6175)------------------------------
% 4.77/2.11 % (6173)Instruction limit reached!
% 4.77/2.11 % (6173)------------------------------
% 4.77/2.11 % (6173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.77/2.11 % (6173)Termination reason: Unknown
% 4.77/2.11 % (6173)Termination phase: Saturation
% 4.77/2.11
% 4.77/2.11 % (6173)Memory used [KB]: 6652
% 4.77/2.11 % (6173)Time elapsed: 0.047 s
% 4.77/2.11 % (6173)Instructions burned: 101 (million)
% 4.77/2.11 % (6173)------------------------------
% 4.77/2.11 % (6173)------------------------------
% 4.77/2.12 % (6176)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_6029 for (2996ds/86Mi)
% 4.77/2.12 % (6177)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_6029 for (2996ds/107Mi)
% 5.47/2.16 % (6176)Instruction limit reached!
% 5.47/2.16 % (6176)------------------------------
% 5.47/2.16 % (6176)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.47/2.16 % (6176)Termination reason: Unknown
% 5.47/2.16 % (6176)Termination phase: Saturation
% 5.47/2.16
% 5.47/2.16 % (6176)Memory used [KB]: 6524
% 5.47/2.16 % (6176)Time elapsed: 0.040 s
% 5.47/2.16 % (6176)Instructions burned: 87 (million)
% 5.47/2.16 % (6176)------------------------------
% 5.47/2.16 % (6176)------------------------------
% 5.47/2.16 % (6166)Instruction limit reached!
% 5.47/2.16 % (6166)------------------------------
% 5.47/2.16 % (6166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.47/2.16 % (6166)Termination reason: Unknown
% 5.47/2.16 % (6166)Termination phase: Saturation
% 5.47/2.16
% 5.47/2.16 % (6166)Memory used [KB]: 6780
% 5.47/2.16 % (6166)Time elapsed: 0.282 s
% 5.47/2.16 % (6166)Instructions burned: 780 (million)
% 5.47/2.16 % (6166)------------------------------
% 5.47/2.16 % (6166)------------------------------
% 5.47/2.17 % (6177)Instruction limit reached!
% 5.47/2.17 % (6177)------------------------------
% 5.47/2.17 % (6177)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.47/2.17 % (6177)Termination reason: Unknown
% 5.47/2.17 % (6177)Termination phase: Saturation
% 5.47/2.17
% 5.47/2.17 % (6177)Memory used [KB]: 6780
% 5.47/2.17 % (6177)Time elapsed: 0.050 s
% 5.47/2.17 % (6177)Instructions burned: 108 (million)
% 5.47/2.17 % (6177)------------------------------
% 5.47/2.17 % (6177)------------------------------
% 5.47/2.17 % (6178)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_6029 for (2995ds/39Mi)
% 5.47/2.18 % (6179)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_6029 for (2995ds/448Mi)
% 5.47/2.18 % (6150)Instruction limit reached!
% 5.47/2.18 % (6150)------------------------------
% 5.47/2.18 % (6150)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.47/2.18 % (6150)Termination reason: Unknown
% 5.47/2.18 % (6150)Termination phase: Saturation
% 5.47/2.18
% 5.47/2.18 % (6150)Memory used [KB]: 9850
% 5.47/2.18 % (6150)Time elapsed: 0.388 s
% 5.47/2.18 % (6150)Instructions burned: 1043 (million)
% 5.47/2.18 % (6150)------------------------------
% 5.47/2.18 % (6150)------------------------------
% 5.47/2.19 % (6180)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_6029 for (2995ds/46Mi)
% 5.47/2.19 % (6178)Instruction limit reached!
% 5.47/2.19 % (6178)------------------------------
% 5.47/2.19 % (6178)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.47/2.19 % (6178)Termination reason: Unknown
% 5.47/2.19 % (6178)Termination phase: Property scanning
% 5.47/2.19
% 5.47/2.19 % (6178)Memory used [KB]: 1791
% 5.47/2.19 % (6178)Time elapsed: 0.020 s
% 5.47/2.19 % (6178)Instructions burned: 41 (million)
% 5.47/2.19 % (6178)------------------------------
% 5.47/2.19 % (6178)------------------------------
% 5.47/2.19 % (6181)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_6029 for (2995ds/98Mi)
% 5.95/2.20 % (6159)Instruction limit reached!
% 5.95/2.20 % (6159)------------------------------
% 5.95/2.20 % (6159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.20 % (6159)Termination reason: Unknown
% 5.95/2.20 % (6159)Termination phase: Saturation
% 5.95/2.20
% 5.95/2.20 % (6159)Memory used [KB]: 9083
% 5.95/2.20 % (6159)Time elapsed: 0.363 s
% 5.95/2.20 % (6159)Instructions burned: 710 (million)
% 5.95/2.20 % (6159)------------------------------
% 5.95/2.20 % (6159)------------------------------
% 5.95/2.21 % (6180)Instruction limit reached!
% 5.95/2.21 % (6180)------------------------------
% 5.95/2.21 % (6180)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.21 % (6180)Termination reason: Unknown
% 5.95/2.21 % (6180)Termination phase: SInE selection
% 5.95/2.21
% 5.95/2.21 % (6180)Memory used [KB]: 1791
% 5.95/2.21 % (6180)Time elapsed: 0.023 s
% 5.95/2.21 % (6180)Instructions burned: 47 (million)
% 5.95/2.21 % (6180)------------------------------
% 5.95/2.21 % (6180)------------------------------
% 5.95/2.21 % (6182)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_6029 for (2995ds/507Mi)
% 5.95/2.21 % (6183)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_6029 for (2995ds/149Mi)
% 5.95/2.22 % (6184)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_6029 for (2995ds/39Mi)
% 5.95/2.24 % (6181)Instruction limit reached!
% 5.95/2.24 % (6181)------------------------------
% 5.95/2.24 % (6181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.24 % (6181)Termination reason: Unknown
% 5.95/2.24 % (6181)Termination phase: Saturation
% 5.95/2.24
% 5.95/2.24 % (6181)Memory used [KB]: 2046
% 5.95/2.24 % (6181)Time elapsed: 0.044 s
% 5.95/2.24 % (6181)Instructions burned: 99 (million)
% 5.95/2.24 % (6181)------------------------------
% 5.95/2.24 % (6181)------------------------------
% 5.95/2.24 % (6184)Instruction limit reached!
% 5.95/2.24 % (6184)------------------------------
% 5.95/2.24 % (6184)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.24 % (6184)Termination reason: Unknown
% 5.95/2.24 % (6184)Termination phase: Preprocessing 1
% 5.95/2.24
% 5.95/2.24 % (6184)Memory used [KB]: 1791
% 5.95/2.24 % (6184)Time elapsed: 0.019 s
% 5.95/2.24 % (6184)Instructions burned: 40 (million)
% 5.95/2.24 % (6184)------------------------------
% 5.95/2.24 % (6184)------------------------------
% 5.95/2.25 % (6185)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_6029 for (2995ds/6Mi)
% 5.95/2.26 % (6185)Instruction limit reached!
% 5.95/2.26 % (6185)------------------------------
% 5.95/2.26 % (6185)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.26 % (6185)Termination reason: Unknown
% 5.95/2.26 % (6185)Termination phase: shuffling
% 5.95/2.26
% 5.95/2.26 % (6185)Memory used [KB]: 1407
% 5.95/2.26 % (6185)Time elapsed: 0.005 s
% 5.95/2.26 % (6185)Instructions burned: 7 (million)
% 5.95/2.26 % (6185)------------------------------
% 5.95/2.26 % (6185)------------------------------
% 5.95/2.26 % (6186)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_6029 for (2994ds/1087Mi)
% 5.95/2.27 % (6187)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_6029 for (2994ds/47Mi)
% 5.95/2.28 % (6183)Instruction limit reached!
% 5.95/2.28 % (6183)------------------------------
% 5.95/2.28 % (6183)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.28 % (6183)Termination reason: Unknown
% 5.95/2.28 % (6183)Termination phase: Saturation
% 5.95/2.28
% 5.95/2.28 % (6183)Memory used [KB]: 7164
% 5.95/2.28 % (6183)Time elapsed: 0.072 s
% 5.95/2.28 % (6183)Instructions burned: 149 (million)
% 5.95/2.28 % (6183)------------------------------
% 5.95/2.28 % (6183)------------------------------
% 5.95/2.29 % (6161)Instruction limit reached!
% 5.95/2.29 % (6161)------------------------------
% 5.95/2.29 % (6161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.29 % (6161)Termination reason: Unknown
% 5.95/2.29 % (6161)Termination phase: Saturation
% 5.95/2.29
% 5.95/2.29 % (6161)Memory used [KB]: 10490
% 5.95/2.29 % (6161)Time elapsed: 0.441 s
% 5.95/2.29 % (6161)Instructions burned: 902 (million)
% 5.95/2.29 % (6161)------------------------------
% 5.95/2.29 % (6161)------------------------------
% 5.95/2.29 % (6187)Instruction limit reached!
% 5.95/2.29 % (6187)------------------------------
% 5.95/2.29 % (6187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.95/2.29 % (6187)Termination reason: Unknown
% 5.95/2.29 % (6187)Termination phase: Property scanning
% 5.95/2.29
% 5.95/2.29 % (6187)Memory used [KB]: 1918
% 5.95/2.29 % (6187)Time elapsed: 0.023 s
% 5.95/2.29 % (6187)Instructions burned: 47 (million)
% 5.95/2.29 % (6187)------------------------------
% 5.95/2.29 % (6187)------------------------------
% 6.45/2.30 % (6188)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_6029 for (2994ds/44Mi)
% 6.45/2.30 % (6189)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_6029 for (2994ds/432Mi)
% 6.45/2.31 % (6190)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_6029 for (2994ds/62Mi)
% 6.45/2.32 % (6188)Instruction limit reached!
% 6.45/2.32 % (6188)------------------------------
% 6.45/2.32 % (6188)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.32 % (6188)Termination reason: Unknown
% 6.45/2.32 % (6188)Termination phase: SInE selection
% 6.45/2.32
% 6.45/2.32 % (6188)Memory used [KB]: 1791
% 6.45/2.32 % (6188)Time elapsed: 0.022 s
% 6.45/2.32 % (6188)Instructions burned: 46 (million)
% 6.45/2.32 % (6188)------------------------------
% 6.45/2.32 % (6188)------------------------------
% 6.45/2.34 % (6191)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_6029 for (2994ds/31Mi)
% 6.45/2.34 % (6190)Instruction limit reached!
% 6.45/2.34 % (6190)------------------------------
% 6.45/2.34 % (6190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.34 % (6190)Termination reason: Unknown
% 6.45/2.34 % (6190)Termination phase: Function definition elimination
% 6.45/2.34
% 6.45/2.34 % (6190)Memory used [KB]: 1918
% 6.45/2.34 % (6190)Time elapsed: 0.029 s
% 6.45/2.34 % (6190)Instructions burned: 63 (million)
% 6.45/2.34 % (6190)------------------------------
% 6.45/2.34 % (6190)------------------------------
% 6.45/2.34 % (6179)Instruction limit reached!
% 6.45/2.34 % (6179)------------------------------
% 6.45/2.34 % (6179)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.34 % (6179)Termination reason: Unknown
% 6.45/2.34 % (6179)Termination phase: Saturation
% 6.45/2.34
% 6.45/2.34 % (6179)Memory used [KB]: 6652
% 6.45/2.34 % (6179)Time elapsed: 0.168 s
% 6.45/2.34 % (6179)Instructions burned: 448 (million)
% 6.45/2.34 % (6179)------------------------------
% 6.45/2.34 % (6179)------------------------------
% 6.45/2.35 % (6168)Instruction limit reached!
% 6.45/2.35 % (6168)------------------------------
% 6.45/2.35 % (6168)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.35 % (6168)Termination reason: Unknown
% 6.45/2.35 % (6168)Termination phase: Saturation
% 6.45/2.35
% 6.45/2.35 % (6168)Memory used [KB]: 8315
% 6.45/2.35 % (6168)Time elapsed: 0.441 s
% 6.45/2.35 % (6168)Instructions burned: 881 (million)
% 6.45/2.35 % (6168)------------------------------
% 6.45/2.35 % (6168)------------------------------
% 6.45/2.35 % (6191)Instruction limit reached!
% 6.45/2.35 % (6191)------------------------------
% 6.45/2.35 % (6191)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.35 % (6191)Termination reason: Unknown
% 6.45/2.35 % (6191)Termination phase: Property scanning
% 6.45/2.35
% 6.45/2.35 % (6191)Memory used [KB]: 1791
% 6.45/2.35 % (6191)Time elapsed: 0.017 s
% 6.45/2.35 % (6191)Instructions burned: 33 (million)
% 6.45/2.35 % (6191)------------------------------
% 6.45/2.35 % (6191)------------------------------
% 6.45/2.35 % (6192)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_6029 for (2994ds/96Mi)
% 6.45/2.36 % (6193)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_6029 for (2993ds/453Mi)
% 6.45/2.36 % (6194)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_6029 for (2993ds/71Mi)
% 6.45/2.37 % (6195)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_6029 for (2993ds/83Mi)
% 6.45/2.39 % (6194)Instruction limit reached!
% 6.45/2.39 % (6194)------------------------------
% 6.45/2.39 % (6194)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.45/2.39 % (6194)Termination reason: Unknown
% 6.45/2.39 % (6194)Termination phase: Property scanning
% 6.45/2.39
% 6.45/2.39 % (6194)Memory used [KB]: 2046
% 6.45/2.39 % (6194)Time elapsed: 0.033 s
% 6.45/2.39 % (6194)Instructions burned: 72 (million)
% 6.45/2.39 % (6194)------------------------------
% 6.45/2.39 % (6194)------------------------------
% 6.84/2.40 % (6192)Instruction limit reached!
% 6.84/2.40 % (6192)------------------------------
% 6.84/2.40 % (6192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.40 % (6192)Termination reason: Unknown
% 6.84/2.40 % (6192)Termination phase: Saturation
% 6.84/2.40
% 6.84/2.40 % (6192)Memory used [KB]: 6652
% 6.84/2.40 % (6192)Time elapsed: 0.045 s
% 6.84/2.40 % (6192)Instructions burned: 97 (million)
% 6.84/2.40 % (6192)------------------------------
% 6.84/2.40 % (6192)------------------------------
% 6.84/2.40 % (6195)Instruction limit reached!
% 6.84/2.40 % (6195)------------------------------
% 6.84/2.40 % (6195)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.40 % (6195)Termination reason: Unknown
% 6.84/2.40 % (6195)Termination phase: Property scanning
% 6.84/2.40
% 6.84/2.40 % (6195)Memory used [KB]: 1918
% 6.84/2.40 % (6195)Time elapsed: 0.037 s
% 6.84/2.40 % (6195)Instructions burned: 83 (million)
% 6.84/2.40 % (6195)------------------------------
% 6.84/2.40 % (6195)------------------------------
% 6.84/2.41 % (6196)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_6029 for (2993ds/11Mi)
% 6.84/2.41 % (6197)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_6029 for (2993ds/41Mi)
% 6.84/2.41 % (6196)Instruction limit reached!
% 6.84/2.41 % (6196)------------------------------
% 6.84/2.41 % (6196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.41 % (6196)Termination reason: Unknown
% 6.84/2.41 % (6196)Termination phase: shuffling
% 6.84/2.41
% 6.84/2.41 % (6196)Memory used [KB]: 1535
% 6.84/2.41 % (6196)Time elapsed: 0.007 s
% 6.84/2.41 % (6196)Instructions burned: 12 (million)
% 6.84/2.41 % (6196)------------------------------
% 6.84/2.41 % (6196)------------------------------
% 6.84/2.42 % (6198)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_6029 for (2993ds/6Mi)
% 6.84/2.42 % (6198)Instruction limit reached!
% 6.84/2.42 % (6198)------------------------------
% 6.84/2.42 % (6198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.42 % (6198)Termination reason: Unknown
% 6.84/2.42 % (6198)Termination phase: shuffling
% 6.84/2.42
% 6.84/2.42 % (6198)Memory used [KB]: 1407
% 6.84/2.42 % (6198)Time elapsed: 0.005 s
% 6.84/2.42 % (6198)Instructions burned: 8 (million)
% 6.84/2.42 % (6198)------------------------------
% 6.84/2.42 % (6198)------------------------------
% 6.84/2.43 % (6199)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_6029 for (2993ds/150Mi)
% 6.84/2.43 % (6197)Instruction limit reached!
% 6.84/2.43 % (6197)------------------------------
% 6.84/2.43 % (6197)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.43 % (6197)Termination reason: Unknown
% 6.84/2.43 % (6197)Termination phase: Preprocessing 3
% 6.84/2.43
% 6.84/2.43 % (6197)Memory used [KB]: 1918
% 6.84/2.43 % (6197)Time elapsed: 0.020 s
% 6.84/2.43 % (6197)Instructions burned: 42 (million)
% 6.84/2.43 % (6197)------------------------------
% 6.84/2.43 % (6197)------------------------------
% 6.84/2.44 % (6200)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_6029 for (2993ds/343Mi)
% 6.84/2.45 % (6201)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_6029 for (2993ds/109Mi)
% 6.84/2.45 % (6182)Instruction limit reached!
% 6.84/2.45 % (6182)------------------------------
% 6.84/2.45 % (6182)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.45 % (6182)Termination reason: Unknown
% 6.84/2.45 % (6182)Termination phase: Saturation
% 6.84/2.45
% 6.84/2.45 % (6182)Memory used [KB]: 7419
% 6.84/2.45 % (6182)Time elapsed: 0.245 s
% 6.84/2.45 % (6182)Instructions burned: 507 (million)
% 6.84/2.45 % (6182)------------------------------
% 6.84/2.45 % (6182)------------------------------
% 6.84/2.47 % (6202)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_6029 for (2992ds/253Mi)
% 6.84/2.47 % (6189)Instruction limit reached!
% 6.84/2.47 % (6189)------------------------------
% 6.84/2.47 % (6189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.84/2.47 % (6189)Termination reason: Unknown
% 6.84/2.47 % (6189)Termination phase: Saturation
% 6.84/2.47
% 6.84/2.47 % (6189)Memory used [KB]: 3198
% 6.84/2.47 % (6189)Time elapsed: 0.173 s
% 6.84/2.47 % (6189)Instructions burned: 433 (million)
% 6.84/2.47 % (6189)------------------------------
% 6.84/2.47 % (6189)------------------------------
% 6.84/2.49 % (6203)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_6029 for (2992ds/140Mi)
% 7.48/2.50 % (6201)Instruction limit reached!
% 7.48/2.50 % (6201)------------------------------
% 7.48/2.50 % (6201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.50 % (6201)Termination reason: Unknown
% 7.48/2.50 % (6201)Termination phase: Saturation
% 7.48/2.50
% 7.48/2.50 % (6201)Memory used [KB]: 6780
% 7.48/2.50 % (6201)Time elapsed: 0.050 s
% 7.48/2.50 % (6201)Instructions burned: 109 (million)
% 7.48/2.50 % (6201)------------------------------
% 7.48/2.50 % (6201)------------------------------
% 7.48/2.50 % (6199)Instruction limit reached!
% 7.48/2.50 % (6199)------------------------------
% 7.48/2.50 % (6199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.50 % (6199)Termination reason: Unknown
% 7.48/2.50 % (6199)Termination phase: Saturation
% 7.48/2.50
% 7.48/2.50 % (6199)Memory used [KB]: 7931
% 7.48/2.50 % (6199)Time elapsed: 0.073 s
% 7.48/2.50 % (6199)Instructions burned: 150 (million)
% 7.48/2.50 % (6199)------------------------------
% 7.48/2.50 % (6199)------------------------------
% 7.48/2.51 % (6204)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_6029 for (2992ds/614Mi)
% 7.48/2.52 % (6205)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_6029 for (2992ds/202Mi)
% 7.48/2.53 % (6193)Instruction limit reached!
% 7.48/2.53 % (6193)------------------------------
% 7.48/2.53 % (6193)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.53 % (6193)Termination reason: Unknown
% 7.48/2.53 % (6193)Termination phase: Saturation
% 7.48/2.53
% 7.48/2.53 % (6193)Memory used [KB]: 6652
% 7.48/2.53 % (6193)Time elapsed: 0.172 s
% 7.48/2.53 % (6193)Instructions burned: 453 (million)
% 7.48/2.53 % (6193)------------------------------
% 7.48/2.53 % (6193)------------------------------
% 7.48/2.55 % (6206)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_6029 for (2992ds/339Mi)
% 7.48/2.55 % (6203)Instruction limit reached!
% 7.48/2.55 % (6203)------------------------------
% 7.48/2.55 % (6203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.55 % (6203)Termination reason: Unknown
% 7.48/2.55 % (6203)Termination phase: Saturation
% 7.48/2.55
% 7.48/2.55 % (6203)Memory used [KB]: 6652
% 7.48/2.55 % (6203)Time elapsed: 0.065 s
% 7.48/2.55 % (6203)Instructions burned: 141 (million)
% 7.48/2.55 % (6203)------------------------------
% 7.48/2.55 % (6203)------------------------------
% 7.48/2.57 % (6207)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_6029 for (2991ds/283Mi)
% 7.48/2.59 % (6202)Instruction limit reached!
% 7.48/2.59 % (6202)------------------------------
% 7.48/2.59 % (6202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.48/2.59 % (6202)Termination reason: Unknown
% 7.48/2.59 % (6202)Termination phase: Saturation
% 7.48/2.59
% 7.48/2.59 % (6202)Memory used [KB]: 8187
% 7.48/2.59 % (6202)Time elapsed: 0.126 s
% 7.48/2.59 % (6202)Instructions burned: 254 (million)
% 7.48/2.59 % (6202)------------------------------
% 7.48/2.59 % (6202)------------------------------
% 8.04/2.60 % (6200)Instruction limit reached!
% 8.04/2.60 % (6200)------------------------------
% 8.04/2.60 % (6200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.60 % (6200)Termination reason: Unknown
% 8.04/2.60 % (6200)Termination phase: Saturation
% 8.04/2.60
% 8.04/2.60 % (6200)Memory used [KB]: 7931
% 8.04/2.60 % (6200)Time elapsed: 0.162 s
% 8.04/2.60 % (6200)Instructions burned: 343 (million)
% 8.04/2.60 % (6200)------------------------------
% 8.04/2.60 % (6200)------------------------------
% 8.04/2.61 % (6208)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_6029 for (2991ds/134Mi)
% 8.04/2.62 % (6209)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_6029 for (2991ds/298Mi)
% 8.04/2.62 % (6205)Instruction limit reached!
% 8.04/2.62 % (6205)------------------------------
% 8.04/2.62 % (6205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.62 % (6205)Termination reason: Unknown
% 8.04/2.62 % (6205)Termination phase: Saturation
% 8.04/2.62
% 8.04/2.62 % (6205)Memory used [KB]: 8699
% 8.04/2.62 % (6205)Time elapsed: 0.101 s
% 8.04/2.62 % (6205)Instructions burned: 203 (million)
% 8.04/2.62 % (6205)------------------------------
% 8.04/2.62 % (6205)------------------------------
% 8.04/2.64 % (6210)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_6029 for (2991ds/192Mi)
% 8.04/2.67 % (6208)Instruction limit reached!
% 8.04/2.67 % (6208)------------------------------
% 8.04/2.67 % (6208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.67 % (6208)Termination reason: Unknown
% 8.04/2.67 % (6208)Termination phase: Saturation
% 8.04/2.67
% 8.04/2.67 % (6208)Memory used [KB]: 6908
% 8.04/2.67 % (6208)Time elapsed: 0.062 s
% 8.04/2.67 % (6208)Instructions burned: 134 (million)
% 8.04/2.67 % (6208)------------------------------
% 8.04/2.67 % (6208)------------------------------
% 8.04/2.68 % (6207)Instruction limit reached!
% 8.04/2.68 % (6207)------------------------------
% 8.04/2.68 % (6207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.04/2.68 % (6207)Termination reason: Unknown
% 8.04/2.68 % (6207)Termination phase: Saturation
% 8.04/2.68
% 8.04/2.68 % (6207)Memory used [KB]: 9338
% 8.04/2.68 % (6207)Time elapsed: 0.115 s
% 8.04/2.68 % (6207)Instructions burned: 284 (million)
% 8.04/2.68 % (6207)------------------------------
% 8.04/2.68 % (6207)------------------------------
% 8.04/2.69 % (6211)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_6029 for (2990ds/258Mi)
% 8.54/2.70 % (6212)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_6029 for (2990ds/90Mi)
% 8.54/2.71 % (6206)Instruction limit reached!
% 8.54/2.71 % (6206)------------------------------
% 8.54/2.71 % (6206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.71 % (6206)Termination reason: Unknown
% 8.54/2.71 % (6206)Termination phase: Saturation
% 8.54/2.71
% 8.54/2.71 % (6206)Memory used [KB]: 7803
% 8.54/2.71 % (6206)Time elapsed: 0.160 s
% 8.54/2.71 % (6206)Instructions burned: 340 (million)
% 8.54/2.71 % (6206)------------------------------
% 8.54/2.71 % (6206)------------------------------
% 8.54/2.72 % (6213)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_6029 for (2990ds/231Mi)
% 8.54/2.72 % (6210)Instruction limit reached!
% 8.54/2.72 % (6210)------------------------------
% 8.54/2.72 % (6210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.72 % (6210)Termination reason: Unknown
% 8.54/2.72 % (6210)Termination phase: Saturation
% 8.54/2.72
% 8.54/2.72 % (6210)Memory used [KB]: 7419
% 8.54/2.72 % (6210)Time elapsed: 0.091 s
% 8.54/2.72 % (6210)Instructions burned: 193 (million)
% 8.54/2.72 % (6210)------------------------------
% 8.54/2.72 % (6210)------------------------------
% 8.54/2.74 % (6214)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_6029 for (2990ds/458Mi)
% 8.54/2.74 % (6212)Instruction limit reached!
% 8.54/2.74 % (6212)------------------------------
% 8.54/2.74 % (6212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.74 % (6212)Termination reason: Unknown
% 8.54/2.74 % (6212)Termination phase: Saturation
% 8.54/2.74
% 8.54/2.74 % (6212)Memory used [KB]: 2430
% 8.54/2.74 % (6212)Time elapsed: 0.043 s
% 8.54/2.74 % (6212)Instructions burned: 91 (million)
% 8.54/2.74 % (6212)------------------------------
% 8.54/2.74 % (6212)------------------------------
% 8.54/2.74 % (6209)Instruction limit reached!
% 8.54/2.74 % (6209)------------------------------
% 8.54/2.74 % (6209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.74 % (6209)Termination reason: Unknown
% 8.54/2.74 % (6209)Termination phase: Saturation
% 8.54/2.74
% 8.54/2.74 % (6209)Memory used [KB]: 6652
% 8.54/2.74 % (6209)Time elapsed: 0.126 s
% 8.54/2.74 % (6209)Instructions burned: 300 (million)
% 8.54/2.74 % (6209)------------------------------
% 8.54/2.74 % (6209)------------------------------
% 8.54/2.76 % (6215)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_6029 for (2989ds/31Mi)
% 8.54/2.76 % (6216)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_6029 for (2989ds/297Mi)
% 8.54/2.77 % (6215)Instruction limit reached!
% 8.54/2.77 % (6215)------------------------------
% 8.54/2.77 % (6215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.54/2.77 % (6215)Termination reason: Unknown
% 8.54/2.77 % (6215)Termination phase: Property scanning
% 8.54/2.77
% 8.54/2.77 % (6215)Memory used [KB]: 1791
% 8.54/2.77 % (6215)Time elapsed: 0.016 s
% 8.54/2.77 % (6215)Instructions burned: 31 (million)
% 8.54/2.77 % (6215)------------------------------
% 8.54/2.77 % (6215)------------------------------
% 8.54/2.79 % (6217)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_6029 for (2989ds/987Mi)
% 9.04/2.81 % (6186)Instruction limit reached!
% 9.04/2.81 % (6186)------------------------------
% 9.04/2.81 % (6186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.04/2.81 % (6186)Termination reason: Unknown
% 9.04/2.81 % (6186)Termination phase: Saturation
% 9.04/2.81
% 9.04/2.81 % (6186)Memory used [KB]: 10362
% 9.04/2.81 % (6186)Time elapsed: 0.550 s
% 9.04/2.81 % (6186)Instructions burned: 1087 (million)
% 9.04/2.81 % (6186)------------------------------
% 9.04/2.81 % (6186)------------------------------
% 9.04/2.81 % (6211)Instruction limit reached!
% 9.04/2.81 % (6211)------------------------------
% 9.04/2.81 % (6211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.04/2.81 % (6211)Termination reason: Unknown
% 9.04/2.81 % (6211)Termination phase: Saturation
% 9.04/2.81
% 9.04/2.81 % (6211)Memory used [KB]: 7547
% 9.04/2.81 % (6211)Time elapsed: 0.122 s
% 9.04/2.81 % (6211)Instructions burned: 259 (million)
% 9.04/2.81 % (6211)------------------------------
% 9.04/2.81 % (6211)------------------------------
% 9.04/2.81 % (6204)Instruction limit reached!
% 9.04/2.81 % (6204)------------------------------
% 9.04/2.81 % (6204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.04/2.81 % (6204)Termination reason: Unknown
% 9.04/2.81 % (6204)Termination phase: Saturation
% 9.04/2.81
% 9.04/2.81 % (6204)Memory used [KB]: 8443
% 9.04/2.81 % (6204)Time elapsed: 0.299 s
% 9.04/2.81 % (6204)Instructions burned: 614 (million)
% 9.04/2.81 % (6204)------------------------------
% 9.04/2.81 % (6204)------------------------------
% 9.04/2.82 % (6218)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_6029 for (2989ds/182Mi)
% 9.04/2.82 % (6219)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_6029 for (2989ds/182Mi)
% 9.04/2.83 % (6220)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_6029 for (2989ds/154Mi)
% 9.04/2.83 % (6213)Instruction limit reached!
% 9.04/2.83 % (6213)------------------------------
% 9.04/2.83 % (6213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.04/2.83 % (6213)Termination reason: Unknown
% 9.04/2.83 % (6213)Termination phase: Saturation
% 9.04/2.83
% 9.04/2.83 % (6213)Memory used [KB]: 10874
% 9.04/2.83 % (6213)Time elapsed: 0.110 s
% 9.04/2.83 % (6213)Instructions burned: 231 (million)
% 9.04/2.83 % (6213)------------------------------
% 9.04/2.83 % (6213)------------------------------
% 9.04/2.85 % (6221)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_6029 for (2989ds/79Mi)
% 9.04/2.87 % (6216)Instruction limit reached!
% 9.04/2.87 % (6216)------------------------------
% 9.04/2.87 % (6216)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.04/2.87 % (6216)Termination reason: Unknown
% 9.04/2.87 % (6216)Termination phase: Saturation
% 9.04/2.87
% 9.04/2.87 % (6216)Memory used [KB]: 8187
% 9.04/2.87 % (6216)Time elapsed: 0.117 s
% 9.04/2.87 % (6216)Instructions burned: 298 (million)
% 9.04/2.87 % (6216)------------------------------
% 9.04/2.87 % (6216)------------------------------
% 9.04/2.88 % (6221)Instruction limit reached!
% 9.04/2.88 % (6221)------------------------------
% 9.04/2.88 % (6221)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.04/2.88 % (6221)Termination reason: Unknown
% 9.04/2.88 % (6221)Termination phase: Saturation
% 9.04/2.88
% 9.04/2.88 % (6221)Memory used [KB]: 6524
% 9.04/2.88 % (6221)Time elapsed: 0.037 s
% 9.04/2.88 % (6221)Instructions burned: 80 (million)
% 9.04/2.88 % (6221)------------------------------
% 9.04/2.88 % (6221)------------------------------
% 9.04/2.89 % (6222)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_6029 for (2988ds/216Mi)
% 9.04/2.89 % (6220)Instruction limit reached!
% 9.04/2.89 % (6220)------------------------------
% 9.04/2.89 % (6220)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.04/2.89 % (6220)Termination reason: Unknown
% 9.04/2.89 % (6220)Termination phase: Saturation
% 9.04/2.89
% 9.04/2.89 % (6220)Memory used [KB]: 6652
% 9.04/2.89 % (6220)Time elapsed: 0.066 s
% 9.04/2.89 % (6220)Instructions burned: 154 (million)
% 9.04/2.89 % (6220)------------------------------
% 9.04/2.89 % (6220)------------------------------
% 10.45/2.90 % (6223)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_6029 for (2988ds/114Mi)
% 10.45/2.91 % (6218)Instruction limit reached!
% 10.45/2.91 % (6218)------------------------------
% 10.45/2.91 % (6218)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.45/2.91 % (6218)Termination reason: Unknown
% 10.45/2.91 % (6218)Termination phase: Saturation
% 10.45/2.91
% 10.45/2.91 % (6218)Memory used [KB]: 7419
% 10.45/2.91 % (6218)Time elapsed: 0.085 s
% 10.45/2.91 % (6218)Instructions burned: 182 (million)
% 10.45/2.91 % (6218)------------------------------
% 10.45/2.91 % (6218)------------------------------
% 10.45/2.91 % (6224)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_6029 for (2988ds/922Mi)
% 10.45/2.91 % (6219)Instruction limit reached!
% 10.45/2.91 % (6219)------------------------------
% 10.45/2.91 % (6219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.45/2.91 % (6219)Termination reason: Unknown
% 10.45/2.91 % (6219)Termination phase: Saturation
% 10.45/2.91
% 10.45/2.91 % (6219)Memory used [KB]: 9722
% 10.45/2.91 % (6219)Time elapsed: 0.089 s
% 10.45/2.91 % (6219)Instructions burned: 183 (million)
% 10.45/2.91 % (6219)------------------------------
% 10.45/2.91 % (6219)------------------------------
% 10.45/2.92 % (6225)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_6029 for (2988ds/182Mi)
% 10.45/2.93 % (6226)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_6029 for (2988ds/164Mi)
% 10.45/2.95 % (6223)Instruction limit reached!
% 10.45/2.95 % (6223)------------------------------
% 10.45/2.95 % (6223)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.45/2.95 % (6223)Termination reason: Unknown
% 10.45/2.95 % (6223)Termination phase: Saturation
% 10.45/2.95
% 10.45/2.95 % (6223)Memory used [KB]: 6908
% 10.45/2.95 % (6223)Time elapsed: 0.053 s
% 10.45/2.95 % (6223)Instructions burned: 115 (million)
% 10.45/2.95 % (6223)------------------------------
% 10.45/2.95 % (6223)------------------------------
% 10.45/2.96 % (6214)Instruction limit reached!
% 10.45/2.96 % (6214)------------------------------
% 10.45/2.96 % (6214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.45/2.96 % (6214)Termination reason: Unknown
% 10.45/2.96 % (6214)Termination phase: Saturation
% 10.45/2.96
% 10.45/2.96 % (6214)Memory used [KB]: 7931
% 10.45/2.96 % (6214)Time elapsed: 0.222 s
% 10.45/2.96 % (6214)Instructions burned: 458 (million)
% 10.45/2.96 % (6214)------------------------------
% 10.45/2.96 % (6214)------------------------------
% 10.45/2.97 % (6227)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_6029 for (2987ds/50Mi)
% 10.45/2.98 % (6222)Instruction limit reached!
% 10.45/2.98 % (6222)------------------------------
% 10.45/2.98 % (6222)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.45/2.98 % (6222)Termination reason: Unknown
% 10.45/2.98 % (6222)Termination phase: Saturation
% 10.45/2.98
% 10.45/2.98 % (6222)Memory used [KB]: 6652
% 10.45/2.98 % (6222)Time elapsed: 0.089 s
% 10.45/2.98 % (6222)Instructions burned: 218 (million)
% 10.45/2.98 % (6222)------------------------------
% 10.45/2.98 % (6222)------------------------------
% 10.45/2.98 % (6228)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_6029 for (2987ds/368Mi)
% 10.45/2.99 % (6227)Instruction limit reached!
% 10.45/2.99 % (6227)------------------------------
% 10.45/2.99 % (6227)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.45/2.99 % (6227)Termination reason: Unknown
% 10.45/2.99 % (6227)Termination phase: Property scanning
% 10.45/2.99
% 10.45/2.99 % (6227)Memory used [KB]: 1791
% 10.45/2.99 % (6227)Time elapsed: 0.024 s
% 10.45/2.99 % (6227)Instructions burned: 50 (million)
% 10.45/2.99 % (6227)------------------------------
% 10.45/2.99 % (6227)------------------------------
% 10.45/2.99 % (6229)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_6029 for (2987ds/1021Mi)
% 10.45/3.00 % (6225)Instruction limit reached!
% 10.45/3.00 % (6225)------------------------------
% 10.45/3.00 % (6225)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.45/3.00 % (6225)Termination reason: Unknown
% 10.45/3.00 % (6225)Termination phase: Saturation
% 10.45/3.00
% 10.45/3.00 % (6225)Memory used [KB]: 6652
% 10.45/3.00 % (6225)Time elapsed: 0.078 s
% 10.45/3.00 % (6225)Instructions burned: 183 (million)
% 10.45/3.00 % (6225)------------------------------
% 10.45/3.00 % (6225)------------------------------
% 10.45/3.00 % (6226)Instruction limit reached!
% 10.45/3.00 % (6226)------------------------------
% 10.45/3.00 % (6226)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.45/3.00 % (6226)Termination reason: Unknown
% 10.45/3.00 % (6226)Termination phase: Saturation
% 10.45/3.00
% 10.45/3.00 % (6226)Memory used [KB]: 2430
% 10.45/3.00 % (6226)Time elapsed: 0.076 s
% 10.45/3.00 % (6226)Instructions burned: 165 (million)
% 10.45/3.00 % (6226)------------------------------
% 10.45/3.00 % (6226)------------------------------
% 10.45/3.01 % (6230)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_6029 for (2987ds/267Mi)
% 10.45/3.02 % (6231)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_6029 for (2987ds/204Mi)
% 10.45/3.02 % (6232)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_6029 for (2987ds/26Mi)
% 11.77/3.03 % (6232)Instruction limit reached!
% 11.77/3.03 % (6232)------------------------------
% 11.77/3.03 % (6232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.77/3.03 % (6232)Termination reason: Unknown
% 11.77/3.03 % (6232)Termination phase: Property scanning
% 11.77/3.03
% 11.77/3.03 % (6232)Memory used [KB]: 1791
% 11.77/3.03 % (6232)Time elapsed: 0.014 s
% 11.77/3.03 % (6232)Instructions burned: 26 (million)
% 11.77/3.03 % (6232)------------------------------
% 11.77/3.03 % (6232)------------------------------
% 11.77/3.05 % (6233)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_6029 for (2987ds/53Mi)
% 11.77/3.07 % (6233)Instruction limit reached!
% 11.77/3.07 % (6233)------------------------------
% 11.77/3.07 % (6233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.77/3.07 % (6233)Termination reason: Unknown
% 11.77/3.07 % (6233)Termination phase: Property scanning
% 11.77/3.07
% 11.77/3.07 % (6233)Memory used [KB]: 1791
% 11.77/3.07 % (6233)Time elapsed: 0.026 s
% 11.77/3.07 % (6233)Instructions burned: 54 (million)
% 11.77/3.07 % (6233)------------------------------
% 11.77/3.07 % (6233)------------------------------
% 11.77/3.09 % (6234)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_6029 for (2986ds/4436Mi)
% 11.77/3.11 % (6231)Instruction limit reached!
% 11.77/3.11 % (6231)------------------------------
% 11.77/3.11 % (6231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.77/3.11 % (6231)Termination reason: Unknown
% 11.77/3.11 % (6231)Termination phase: Saturation
% 11.77/3.11
% 11.77/3.11 % (6231)Memory used [KB]: 7419
% 11.77/3.11 % (6231)Time elapsed: 0.093 s
% 11.77/3.11 % (6231)Instructions burned: 205 (million)
% 11.77/3.11 % (6231)------------------------------
% 11.77/3.11 % (6231)------------------------------
% 11.77/3.11 % (6230)Instruction limit reached!
% 11.77/3.11 % (6230)------------------------------
% 11.77/3.11 % (6230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.77/3.11 % (6230)Termination reason: Unknown
% 11.77/3.11 % (6230)Termination phase: Saturation
% 11.77/3.11
% 11.77/3.11 % (6230)Memory used [KB]: 8699
% 11.77/3.11 % (6230)Time elapsed: 0.108 s
% 11.77/3.11 % (6230)Instructions burned: 269 (million)
% 11.77/3.11 % (6230)------------------------------
% 11.77/3.11 % (6230)------------------------------
% 11.77/3.12 % (6235)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_6029 for (2986ds/1539Mi)
% 12.45/3.13 % (6236)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_6029 for (2986ds/408Mi)
% 12.45/3.15 % (6217)Instruction limit reached!
% 12.45/3.15 % (6217)------------------------------
% 12.45/3.15 % (6217)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.45/3.15 % (6217)Termination reason: Unknown
% 12.45/3.15 % (6217)Termination phase: Saturation
% 12.45/3.15
% 12.45/3.15 % (6217)Memory used [KB]: 10106
% 12.45/3.15 % (6217)Time elapsed: 0.364 s
% 12.45/3.15 % (6217)Instructions burned: 988 (million)
% 12.45/3.15 % (6217)------------------------------
% 12.45/3.15 % (6217)------------------------------
% 12.45/3.16 % (6228)Instruction limit reached!
% 12.45/3.16 % (6228)------------------------------
% 12.45/3.16 % (6228)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.45/3.16 % (6228)Termination reason: Unknown
% 12.45/3.16 % (6228)Termination phase: Saturation
% 12.45/3.16
% 12.45/3.16 % (6228)Memory used [KB]: 8059
% 12.45/3.16 % (6228)Time elapsed: 0.181 s
% 12.45/3.16 % (6228)Instructions burned: 369 (million)
% 12.45/3.16 % (6228)------------------------------
% 12.45/3.16 % (6228)------------------------------
% 12.45/3.17 % (6237)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_6029 for (2985ds/5205Mi)
% 12.45/3.17 % (6238)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_6029 for (2985ds/1913Mi)
% 12.86/3.34 % (6236)Instruction limit reached!
% 12.86/3.34 % (6236)------------------------------
% 12.86/3.34 % (6236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.86/3.34 % (6236)Termination reason: Unknown
% 12.86/3.34 % (6236)Termination phase: Saturation
% 12.86/3.34
% 12.86/3.34 % (6236)Memory used [KB]: 9210
% 12.86/3.34 % (6236)Time elapsed: 0.210 s
% 12.86/3.34 % (6236)Instructions burned: 409 (million)
% 12.86/3.34 % (6236)------------------------------
% 12.86/3.34 % (6236)------------------------------
% 12.86/3.35 % (6239)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_6029 for (2984ds/4350Mi)
% 12.86/3.37 % (6224)Instruction limit reached!
% 12.86/3.37 % (6224)------------------------------
% 12.86/3.37 % (6224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.86/3.37 % (6224)Termination reason: Unknown
% 12.86/3.37 % (6224)Termination phase: Saturation
% 12.86/3.37
% 12.86/3.37 % (6224)Memory used [KB]: 9594
% 12.86/3.37 % (6224)Time elapsed: 0.465 s
% 12.86/3.37 % (6224)Instructions burned: 922 (million)
% 12.86/3.37 % (6224)------------------------------
% 12.86/3.37 % (6224)------------------------------
% 12.86/3.39 % (6240)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_6029 for (2983ds/68Mi)
% 13.27/3.42 % (6240)Instruction limit reached!
% 13.27/3.42 % (6240)------------------------------
% 13.27/3.42 % (6240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.27/3.42 % (6240)Termination reason: Unknown
% 13.27/3.42 % (6240)Termination phase: Function definition elimination
% 13.27/3.42
% 13.27/3.42 % (6240)Memory used [KB]: 1918
% 13.27/3.42 % (6240)Time elapsed: 0.032 s
% 13.27/3.42 % (6240)Instructions burned: 69 (million)
% 13.27/3.42 % (6240)------------------------------
% 13.27/3.42 % (6240)------------------------------
% 13.27/3.44 % (6241)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_6029 for (2983ds/358Mi)
% 13.43/3.51 % (6229)Instruction limit reached!
% 13.43/3.51 % (6229)------------------------------
% 13.43/3.51 % (6229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.43/3.51 % (6229)Termination reason: Unknown
% 13.43/3.51 % (6229)Termination phase: Saturation
% 13.43/3.51
% 13.43/3.51 % (6229)Memory used [KB]: 9978
% 13.43/3.51 % (6229)Time elapsed: 0.516 s
% 13.43/3.51 % (6229)Instructions burned: 1022 (million)
% 13.43/3.51 % (6229)------------------------------
% 13.43/3.51 % (6229)------------------------------
% 13.43/3.53 % (6242)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_6029 for (2982ds/31Mi)
% 13.43/3.54 % (6242)Instruction limit reached!
% 13.43/3.54 % (6242)------------------------------
% 13.43/3.54 % (6242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.43/3.54 % (6242)Termination reason: Unknown
% 13.43/3.54 % (6242)Termination phase: Property scanning
% 13.43/3.54
% 13.43/3.54 % (6242)Memory used [KB]: 1791
% 13.43/3.54 % (6242)Time elapsed: 0.016 s
% 13.43/3.54 % (6242)Instructions burned: 32 (million)
% 13.43/3.54 % (6242)------------------------------
% 13.43/3.54 % (6242)------------------------------
% 13.43/3.56 % (6243)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_6029 for (2981ds/279Mi)
% 13.49/3.60 % (6241)Instruction limit reached!
% 13.49/3.60 % (6241)------------------------------
% 13.49/3.60 % (6241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.49/3.60 % (6241)Termination reason: Unknown
% 13.49/3.60 % (6241)Termination phase: Saturation
% 13.49/3.60
% 13.49/3.60 % (6241)Memory used [KB]: 7675
% 13.49/3.60 % (6241)Time elapsed: 0.193 s
% 13.49/3.60 % (6241)Instructions burned: 358 (million)
% 13.49/3.60 % (6241)------------------------------
% 13.49/3.60 % (6241)------------------------------
% 13.49/3.62 % (6244)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_6029 for (2981ds/258Mi)
% 13.49/3.67 % (6243)Instruction limit reached!
% 13.49/3.67 % (6243)------------------------------
% 13.49/3.67 % (6243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.49/3.67 % (6243)Termination reason: Unknown
% 13.49/3.67 % (6243)Termination phase: Saturation
% 13.49/3.67
% 13.49/3.67 % (6243)Memory used [KB]: 6780
% 13.49/3.67 % (6243)Time elapsed: 0.111 s
% 13.49/3.67 % (6243)Instructions burned: 281 (million)
% 13.49/3.67 % (6243)------------------------------
% 13.49/3.67 % (6243)------------------------------
% 13.49/3.68 % (6245)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_6029 for (2980ds/26Mi)
% 13.49/3.69 % (6245)Instruction limit reached!
% 13.49/3.69 % (6245)------------------------------
% 13.49/3.69 % (6245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.49/3.69 % (6245)Termination reason: Unknown
% 13.49/3.69 % (6245)Termination phase: Property scanning
% 13.49/3.69
% 13.49/3.69 % (6245)Memory used [KB]: 1791
% 13.49/3.69 % (6245)Time elapsed: 0.014 s
% 13.49/3.69 % (6245)Instructions burned: 26 (million)
% 13.49/3.69 % (6245)------------------------------
% 13.49/3.69 % (6245)------------------------------
% 13.82/3.71 % (6246)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_6029 for (2980ds/995Mi)
% 13.82/3.74 % (6244)Instruction limit reached!
% 13.82/3.74 % (6244)------------------------------
% 13.82/3.74 % (6244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.82/3.74 % (6244)Termination reason: Unknown
% 13.82/3.74 % (6244)Termination phase: Saturation
% 13.82/3.74
% 13.82/3.74 % (6244)Memory used [KB]: 7803
% 13.82/3.74 % (6244)Time elapsed: 0.122 s
% 13.82/3.74 % (6244)Instructions burned: 260 (million)
% 13.82/3.74 % (6244)------------------------------
% 13.82/3.74 % (6244)------------------------------
% 13.82/3.76 % (6247)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_6029 for (2979ds/373Mi)
% 13.96/3.89 % (6235)Instruction limit reached!
% 13.96/3.89 % (6235)------------------------------
% 13.96/3.89 % (6235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.89 % (6235)Termination reason: Unknown
% 13.96/3.89 % (6235)Termination phase: Saturation
% 13.96/3.89
% 13.96/3.89 % (6235)Memory used [KB]: 8699
% 13.96/3.89 % (6235)Time elapsed: 0.764 s
% 13.96/3.89 % (6235)Instructions burned: 1539 (million)
% 13.96/3.89 % (6235)------------------------------
% 13.96/3.89 % (6235)------------------------------
% 14.74/3.90 % (6248)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_6029 for (2978ds/253Mi)
% 14.74/3.94 % (6247)Instruction limit reached!
% 14.74/3.94 % (6247)------------------------------
% 14.74/3.94 % (6247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.74/3.94 % (6247)Termination reason: Unknown
% 14.74/3.94 % (6247)Termination phase: Saturation
% 14.74/3.94
% 14.74/3.94 % (6247)Memory used [KB]: 7803
% 14.74/3.94 % (6247)Time elapsed: 0.182 s
% 14.74/3.94 % (6247)Instructions burned: 373 (million)
% 14.74/3.94 % (6247)------------------------------
% 14.74/3.94 % (6247)------------------------------
% 14.74/3.96 % (6249)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_6029 for (2977ds/832Mi)
% 14.74/4.00 % (6248)Instruction limit reached!
% 14.74/4.00 % (6248)------------------------------
% 14.74/4.00 % (6248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.74/4.00 % (6248)Termination reason: Unknown
% 14.74/4.00 % (6248)Termination phase: Saturation
% 14.74/4.00
% 14.74/4.00 % (6248)Memory used [KB]: 6780
% 14.74/4.00 % (6248)Time elapsed: 0.102 s
% 14.74/4.00 % (6248)Instructions burned: 255 (million)
% 14.74/4.00 % (6248)------------------------------
% 14.74/4.00 % (6248)------------------------------
% 14.74/4.02 % (6250)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_6029 for (2977ds/668Mi)
% 18.76/4.07 % (6246)Instruction limit reached!
% 18.76/4.07 % (6246)------------------------------
% 18.76/4.07 % (6246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.76/4.07 % (6246)Termination reason: Unknown
% 18.76/4.07 % (6246)Termination phase: Saturation
% 18.76/4.07
% 18.76/4.07 % (6246)Memory used [KB]: 9594
% 18.76/4.07 % (6246)Time elapsed: 0.363 s
% 18.76/4.07 % (6246)Instructions burned: 996 (million)
% 18.76/4.07 % (6246)------------------------------
% 18.76/4.07 % (6246)------------------------------
% 18.76/4.09 % (6251)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_6029 for (2976ds/40Mi)
% 18.76/4.11 % (6251)Instruction limit reached!
% 18.76/4.11 % (6251)------------------------------
% 18.76/4.11 % (6251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.76/4.11 % (6251)Termination reason: Unknown
% 18.76/4.11 % (6251)Termination phase: Property scanning
% 18.76/4.11
% 18.76/4.11 % (6251)Memory used [KB]: 1791
% 18.76/4.11 % (6251)Time elapsed: 0.019 s
% 18.76/4.11 % (6251)Instructions burned: 40 (million)
% 18.76/4.11 % (6251)------------------------------
% 18.76/4.11 % (6251)------------------------------
% 18.76/4.11 % (6238)Instruction limit reached!
% 18.76/4.11 % (6238)------------------------------
% 18.76/4.11 % (6238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.76/4.11 % (6238)Termination reason: Unknown
% 18.76/4.11 % (6238)Termination phase: Saturation
% 18.76/4.11
% 18.76/4.11 % (6238)Memory used [KB]: 4221
% 18.76/4.11 % (6238)Time elapsed: 0.937 s
% 18.76/4.11 % (6238)Instructions burned: 1913 (million)
% 18.76/4.11 % (6238)------------------------------
% 18.76/4.11 % (6238)------------------------------
% 18.76/4.12 % (6252)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_6029 for (2976ds/294Mi)
% 18.76/4.13 % (6253)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_6029 for (2976ds/187Mi)
% 19.67/4.21 % (6253)Instruction limit reached!
% 19.67/4.21 % (6253)------------------------------
% 19.67/4.21 % (6253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.67/4.21 % (6253)Termination reason: Unknown
% 19.67/4.21 % (6253)Termination phase: Saturation
% 19.67/4.21
% 19.67/4.21 % (6253)Memory used [KB]: 7419
% 19.67/4.21 % (6253)Time elapsed: 0.086 s
% 19.67/4.21 % (6253)Instructions burned: 187 (million)
% 19.67/4.21 % (6253)------------------------------
% 19.67/4.21 % (6253)------------------------------
% 19.67/4.23 % (6254)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_6029 for (2975ds/371Mi)
% 19.67/4.25 % (6252)Instruction limit reached!
% 19.67/4.25 % (6252)------------------------------
% 19.67/4.25 % (6252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.67/4.25 % (6252)Termination reason: Unknown
% 19.67/4.25 % (6252)Termination phase: Saturation
% 19.67/4.25
% 19.67/4.25 % (6252)Memory used [KB]: 6652
% 19.67/4.25 % (6252)Time elapsed: 0.124 s
% 19.67/4.25 % (6252)Instructions burned: 294 (million)
% 19.67/4.25 % (6252)------------------------------
% 19.67/4.25 % (6252)------------------------------
% 19.67/4.26 % (6255)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_6029 for (2974ds/1827Mi)
% 19.67/4.27 % (6250)Instruction limit reached!
% 19.67/4.27 % (6250)------------------------------
% 19.67/4.27 % (6250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.67/4.27 % (6250)Termination reason: Unknown
% 19.67/4.27 % (6250)Termination phase: Saturation
% 19.67/4.27
% 19.67/4.27 % (6250)Memory used [KB]: 14200
% 19.67/4.27 % (6250)Time elapsed: 0.249 s
% 19.67/4.27 % (6250)Instructions burned: 669 (million)
% 19.67/4.27 % (6250)------------------------------
% 19.67/4.27 % (6250)------------------------------
% 19.67/4.29 % (6256)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_6029 for (2974ds/70Mi)
% 20.57/4.32 % (6256)Instruction limit reached!
% 20.57/4.32 % (6256)------------------------------
% 20.57/4.32 % (6256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/4.32 % (6256)Termination reason: Unknown
% 20.57/4.32 % (6256)Termination phase: Property scanning
% 20.57/4.32
% 20.57/4.32 % (6256)Memory used [KB]: 2046
% 20.57/4.32 % (6256)Time elapsed: 0.032 s
% 20.57/4.32 % (6256)Instructions burned: 70 (million)
% 20.57/4.32 % (6256)------------------------------
% 20.57/4.32 % (6256)------------------------------
% 20.57/4.33 % (6257)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_6029 for (2974ds/316Mi)
% 20.57/4.37 % (6249)Instruction limit reached!
% 20.57/4.37 % (6249)------------------------------
% 20.57/4.37 % (6249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.57/4.37 % (6249)Termination reason: Unknown
% 20.57/4.37 % (6249)Termination phase: Saturation
% 20.57/4.37
% 20.57/4.37 % (6249)Memory used [KB]: 9210
% 20.57/4.37 % (6249)Time elapsed: 0.413 s
% 20.57/4.37 % (6249)Instructions burned: 832 (million)
% 20.57/4.37 % (6249)------------------------------
% 20.57/4.37 % (6249)------------------------------
% 20.57/4.38 % (6258)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_6029 for (2973ds/932Mi)
% 20.99/4.40 % (6254)Instruction limit reached!
% 20.99/4.40 % (6254)------------------------------
% 20.99/4.40 % (6254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.99/4.40 % (6254)Termination reason: Unknown
% 20.99/4.40 % (6254)Termination phase: Saturation
% 20.99/4.40
% 20.99/4.40 % (6254)Memory used [KB]: 7931
% 20.99/4.40 % (6254)Time elapsed: 0.178 s
% 20.99/4.40 % (6254)Instructions burned: 371 (million)
% 20.99/4.40 % (6254)------------------------------
% 20.99/4.40 % (6254)------------------------------
% 20.99/4.42 % (6259)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_6029 for (2973ds/4714Mi)
% 20.99/4.46 % (6257)Instruction limit reached!
% 20.99/4.46 % (6257)------------------------------
% 20.99/4.46 % (6257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.99/4.46 % (6257)Termination reason: Unknown
% 20.99/4.46 % (6257)Termination phase: Saturation
% 20.99/4.46
% 20.99/4.46 % (6257)Memory used [KB]: 7547
% 20.99/4.46 % (6257)Time elapsed: 0.130 s
% 20.99/4.46 % (6257)Instructions burned: 319 (million)
% 20.99/4.46 % (6257)------------------------------
% 20.99/4.46 % (6257)------------------------------
% 20.99/4.48 % (6260)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_6029 for (2972ds/8250Mi)
% 22.22/4.76 % (6258)Instruction limit reached!
% 22.22/4.76 % (6258)------------------------------
% 22.22/4.76 % (6258)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.22/4.76 % (6258)Termination reason: Unknown
% 22.22/4.76 % (6258)Termination phase: Saturation
% 22.22/4.76
% 22.22/4.76 % (6258)Memory used [KB]: 10234
% 22.22/4.76 % (6258)Time elapsed: 0.374 s
% 22.22/4.76 % (6258)Instructions burned: 934 (million)
% 22.22/4.76 % (6258)------------------------------
% 22.22/4.76 % (6258)------------------------------
% 22.22/4.77 % (6261)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_6029 for (2969ds/770Mi)
% 25.84/5.09 % (6237)Instruction limit reached!
% 25.84/5.09 % (6237)------------------------------
% 25.84/5.09 % (6237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.84/5.09 % (6237)Termination reason: Unknown
% 25.84/5.09 % (6237)Termination phase: Saturation
% 25.84/5.09
% 25.84/5.09 % (6237)Memory used [KB]: 10106
% 25.84/5.09 % (6237)Time elapsed: 1.926 s
% 25.84/5.09 % (6237)Instructions burned: 5205 (million)
% 25.84/5.09 % (6237)------------------------------
% 25.84/5.09 % (6237)------------------------------
% 25.84/5.11 % (6262)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_6029 for (2966ds/794Mi)
% 25.84/5.12 % (6261)Instruction limit reached!
% 25.84/5.12 % (6261)------------------------------
% 25.84/5.12 % (6261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.84/5.12 % (6261)Termination reason: Unknown
% 25.84/5.12 % (6261)Termination phase: Saturation
% 25.84/5.12
% 25.84/5.12 % (6261)Memory used [KB]: 6908
% 25.84/5.12 % (6261)Time elapsed: 0.344 s
% 25.84/5.12 % (6261)Instructions burned: 770 (million)
% 25.84/5.12 % (6261)------------------------------
% 25.84/5.12 % (6261)------------------------------
% 25.84/5.13 % (6263)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_6029 for (2966ds/464Mi)
% 26.51/5.15 % (6255)Instruction limit reached!
% 26.51/5.15 % (6255)------------------------------
% 26.51/5.15 % (6255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.51/5.15 % (6255)Termination reason: Unknown
% 26.51/5.15 % (6255)Termination phase: Saturation
% 26.51/5.15
% 26.51/5.15 % (6255)Memory used [KB]: 15735
% 26.51/5.15 % (6255)Time elapsed: 0.900 s
% 26.51/5.15 % (6255)Instructions burned: 1828 (million)
% 26.51/5.15 % (6255)------------------------------
% 26.51/5.15 % (6255)------------------------------
% 26.51/5.17 % (6264)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_6029 for (2965ds/1376Mi)
% 27.19/5.32 % (6234)Instruction limit reached!
% 27.19/5.32 % (6234)------------------------------
% 27.19/5.32 % (6234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.19/5.32 % (6234)Termination reason: Unknown
% 27.19/5.32 % (6234)Termination phase: Saturation
% 27.19/5.32
% 27.19/5.32 % (6234)Memory used [KB]: 16502
% 27.19/5.32 % (6234)Time elapsed: 2.236 s
% 27.19/5.32 % (6234)Instructions burned: 4436 (million)
% 27.19/5.32 % (6234)------------------------------
% 27.19/5.32 % (6234)------------------------------
% 27.19/5.34 % (6265)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_6029 for (2964ds/906Mi)
% 27.19/5.35 % (6263)Instruction limit reached!
% 27.19/5.35 % (6263)------------------------------
% 27.19/5.35 % (6263)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.19/5.35 % (6263)Termination reason: Unknown
% 27.19/5.35 % (6263)Termination phase: Saturation
% 27.19/5.35
% 27.19/5.35 % (6263)Memory used [KB]: 8059
% 27.19/5.35 % (6263)Time elapsed: 0.220 s
% 27.19/5.35 % (6263)Instructions burned: 465 (million)
% 27.19/5.35 % (6263)------------------------------
% 27.19/5.35 % (6263)------------------------------
% 27.19/5.37 % (6266)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_6029 for (2963ds/434Mi)
% 28.05/5.50 % (6262)Instruction limit reached!
% 28.05/5.50 % (6262)------------------------------
% 28.05/5.50 % (6262)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.05/5.50 % (6262)Termination reason: Unknown
% 28.05/5.50 % (6262)Termination phase: Saturation
% 28.05/5.50
% 28.05/5.50 % (6262)Memory used [KB]: 4221
% 28.05/5.50 % (6262)Time elapsed: 0.394 s
% 28.05/5.50 % (6262)Instructions burned: 795 (million)
% 28.05/5.50 % (6262)------------------------------
% 28.05/5.50 % (6262)------------------------------
% 28.05/5.50 % (6239)Instruction limit reached!
% 28.05/5.50 % (6239)------------------------------
% 28.05/5.50 % (6239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.05/5.50 % (6239)Termination reason: Unknown
% 28.05/5.50 % (6239)Termination phase: Saturation
% 28.05/5.50
% 28.05/5.50 % (6239)Memory used [KB]: 11001
% 28.05/5.50 % (6239)Time elapsed: 2.171 s
% 28.05/5.50 % (6239)Instructions burned: 4350 (million)
% 28.05/5.50 % (6239)------------------------------
% 28.05/5.50 % (6239)------------------------------
% 28.05/5.52 % (6267)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_6029 for (2962ds/865Mi)
% 28.05/5.52 % (6268)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_6029 for (2962ds/593Mi)
% 28.05/5.58 % (6266)Instruction limit reached!
% 28.05/5.58 % (6266)------------------------------
% 28.05/5.58 % (6266)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.05/5.58 % (6266)Termination reason: Unknown
% 28.05/5.58 % (6266)Termination phase: Saturation
% 28.05/5.58
% 28.05/5.58 % (6266)Memory used [KB]: 9083
% 28.05/5.58 % (6266)Time elapsed: 0.218 s
% 28.05/5.58 % (6266)Instructions burned: 434 (million)
% 28.05/5.58 % (6266)------------------------------
% 28.05/5.58 % (6266)------------------------------
% 28.91/5.60 % (6269)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_6029 for (2961ds/443Mi)
% 29.11/5.71 % (6264)Instruction limit reached!
% 29.11/5.71 % (6264)------------------------------
% 29.11/5.71 % (6264)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.11/5.71 % (6264)Termination reason: Unknown
% 29.11/5.71 % (6264)Termination phase: Saturation
% 29.11/5.71
% 29.11/5.71 % (6264)Memory used [KB]: 8315
% 29.11/5.71 % (6264)Time elapsed: 0.539 s
% 29.11/5.71 % (6264)Instructions burned: 1376 (million)
% 29.11/5.71 % (6264)------------------------------
% 29.11/5.71 % (6264)------------------------------
% 29.11/5.73 % (6270)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_6029 for (2960ds/594Mi)
% 29.11/5.74 % (6268)Instruction limit reached!
% 29.11/5.74 % (6268)------------------------------
% 29.11/5.74 % (6268)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.11/5.74 % (6268)Termination reason: Unknown
% 29.11/5.74 % (6268)Termination phase: Saturation
% 29.11/5.74
% 29.11/5.74 % (6268)Memory used [KB]: 6780
% 29.11/5.74 % (6268)Time elapsed: 0.218 s
% 29.11/5.74 % (6268)Instructions burned: 593 (million)
% 29.11/5.74 % (6268)------------------------------
% 29.11/5.74 % (6268)------------------------------
% 29.11/5.75 % (6271)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_6029 for (2960ds/327Mi)
% 29.11/5.78 % (6265)Instruction limit reached!
% 29.11/5.78 % (6265)------------------------------
% 29.11/5.78 % (6265)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.11/5.78 % (6265)Termination reason: Unknown
% 29.11/5.78 % (6265)Termination phase: Saturation
% 29.11/5.78
% 29.11/5.78 % (6265)Memory used [KB]: 9722
% 29.11/5.78 % (6265)Time elapsed: 0.437 s
% 29.11/5.78 % (6265)Instructions burned: 907 (million)
% 29.11/5.78 % (6265)------------------------------
% 29.11/5.78 % (6265)------------------------------
% 29.11/5.79 % (6272)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_6029 for (2959ds/5411Mi)
% 30.55/5.82 % (6269)Instruction limit reached!
% 30.55/5.82 % (6269)------------------------------
% 30.55/5.82 % (6269)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.55/5.82 % (6269)Termination reason: Unknown
% 30.55/5.82 % (6269)Termination phase: Saturation
% 30.55/5.82
% 30.55/5.82 % (6269)Memory used [KB]: 8059
% 30.55/5.82 % (6269)Time elapsed: 0.220 s
% 30.55/5.82 % (6269)Instructions burned: 444 (million)
% 30.55/5.82 % (6269)------------------------------
% 30.55/5.82 % (6269)------------------------------
% 30.55/5.84 % (6273)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_6029 for (2959ds/1762Mi)
% 30.99/5.92 % (6271)Instruction limit reached!
% 30.99/5.92 % (6271)------------------------------
% 30.99/5.92 % (6271)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.99/5.92 % (6271)Termination reason: Unknown
% 30.99/5.92 % (6271)Termination phase: Saturation
% 30.99/5.92
% 30.99/5.92 % (6271)Memory used [KB]: 9466
% 30.99/5.92 % (6271)Time elapsed: 0.169 s
% 30.99/5.92 % (6271)Instructions burned: 327 (million)
% 30.99/5.92 % (6271)------------------------------
% 30.99/5.92 % (6271)------------------------------
% 30.99/5.94 % (6274)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_6029 for (2958ds/96Mi)
% 30.99/5.94 % (6267)Instruction limit reached!
% 30.99/5.94 % (6267)------------------------------
% 30.99/5.94 % (6267)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.99/5.94 % (6267)Termination reason: Unknown
% 30.99/5.94 % (6267)Termination phase: Saturation
% 30.99/5.94
% 30.99/5.94 % (6267)Memory used [KB]: 8827
% 30.99/5.94 % (6267)Time elapsed: 0.419 s
% 30.99/5.94 % (6267)Instructions burned: 865 (million)
% 30.99/5.94 % (6267)------------------------------
% 30.99/5.94 % (6267)------------------------------
% 30.99/5.95 % (6275)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_6029 for (2957ds/503Mi)
% 30.99/5.98 % (6274)Instruction limit reached!
% 30.99/5.98 % (6274)------------------------------
% 30.99/5.98 % (6274)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.99/5.98 % (6274)Termination reason: Unknown
% 30.99/5.98 % (6274)Termination phase: Saturation
% 30.99/5.98
% 30.99/5.98 % (6274)Memory used [KB]: 6524
% 30.99/5.98 % (6274)Time elapsed: 0.044 s
% 30.99/5.98 % (6274)Instructions burned: 97 (million)
% 30.99/5.98 % (6274)------------------------------
% 30.99/5.98 % (6274)------------------------------
% 30.99/6.00 % (6276)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_6029 for (2957ds/90Mi)
% 30.99/6.01 % (6270)Instruction limit reached!
% 30.99/6.01 % (6270)------------------------------
% 30.99/6.01 % (6270)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.99/6.01 % (6270)Termination reason: Unknown
% 30.99/6.01 % (6270)Termination phase: Saturation
% 30.99/6.01
% 30.99/6.01 % (6270)Memory used [KB]: 8059
% 30.99/6.01 % (6270)Time elapsed: 0.290 s
% 30.99/6.01 % (6270)Instructions burned: 594 (million)
% 30.99/6.01 % (6270)------------------------------
% 30.99/6.01 % (6270)------------------------------
% 32.76/6.03 % (6277)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_6029 for (2957ds/593Mi)
% 32.76/6.04 % (6276)Instruction limit reached!
% 32.76/6.04 % (6276)------------------------------
% 32.76/6.04 % (6276)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.76/6.04 % (6276)Termination reason: Unknown
% 32.76/6.04 % (6276)Termination phase: Property scanning
% 32.76/6.04
% 32.76/6.04 % (6276)Memory used [KB]: 2430
% 32.76/6.04 % (6276)Time elapsed: 0.042 s
% 32.76/6.04 % (6276)Instructions burned: 90 (million)
% 32.76/6.04 % (6276)------------------------------
% 32.76/6.04 % (6276)------------------------------
% 32.76/6.05 % (6278)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_6029 for (2956ds/1512Mi)
% 32.76/6.06 % (6259)Instruction limit reached!
% 32.76/6.06 % (6259)------------------------------
% 32.76/6.06 % (6259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.76/6.06 % (6259)Termination reason: Unknown
% 32.76/6.06 % (6259)Termination phase: Saturation
% 32.76/6.06
% 32.76/6.06 % (6259)Memory used [KB]: 7164
% 32.76/6.06 % (6259)Time elapsed: 1.642 s
% 32.76/6.06 % (6259)Instructions burned: 4714 (million)
% 32.76/6.06 % (6259)------------------------------
% 32.76/6.06 % (6259)------------------------------
% 32.76/6.08 % (6279)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_6029 for (2956ds/569Mi)
% 33.23/6.15 % (6260)First to succeed.
% 33.23/6.16 % (6260)Refutation found. Thanks to Tanya!
% 33.23/6.16 % SZS status Theorem for DTF2THF_6029
% 33.23/6.16 % SZS output start Proof for DTF2THF_6029
% 33.23/6.16 thf(func_def_0, type, in: $i > $i > $o).
% 33.23/6.16 thf(func_def_1, type, exu: ($i > $o) > $o).
% 33.23/6.16 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 33.23/6.16 thf(func_def_8, type, powerset: $i > $i).
% 33.23/6.16 thf(func_def_10, type, setunion: $i > $i).
% 33.23/6.16 thf(func_def_19, type, descr: ($i > $o) > $i).
% 33.23/6.16 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_26, type, prop2set: $o > $i).
% 33.23/6.16 thf(func_def_36, type, nonempty: $i > $o).
% 33.23/6.16 thf(func_def_69, type, set2prop: $i > $o).
% 33.23/6.16 thf(func_def_88, type, subset: $i > $i > $o).
% 33.23/6.16 thf(func_def_89, type, disjoint: $i > $i > $o).
% 33.23/6.16 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 33.23/6.16 thf(func_def_114, type, binunion: $i > $i > $i).
% 33.23/6.16 thf(func_def_122, type, binintersect: $i > $i > $i).
% 33.23/6.16 thf(func_def_135, type, regular: $i > $o).
% 33.23/6.16 thf(func_def_136, type, setminus: $i > $i > $i).
% 33.23/6.16 thf(func_def_147, type, symdiff: $i > $i > $i).
% 33.23/6.16 thf(func_def_153, type, iskpair: $i > $o).
% 33.23/6.16 thf(func_def_158, type, kpair: $i > $i > $i).
% 33.23/6.16 thf(func_def_160, type, cartprod: $i > $i > $i).
% 33.23/6.16 thf(func_def_177, type, singleton: $i > $o).
% 33.23/6.16 thf(func_def_179, type, ex1: $i > ($i > $o) > $o).
% 33.23/6.16 thf(func_def_184, type, atmost1p: $i > $o).
% 33.23/6.16 thf(func_def_185, type, atleast2p: $i > $o).
% 33.23/6.16 thf(func_def_186, type, atmost2p: $i > $o).
% 33.23/6.16 thf(func_def_187, type, upairsetp: $i > $o).
% 33.23/6.16 thf(func_def_191, type, kfst: $i > $i).
% 33.23/6.16 thf(func_def_205, type, sP0: $i > $i > $o).
% 33.23/6.16 thf(func_def_206, type, sP1: $i > $o).
% 33.23/6.16 thf(func_def_207, type, sP2: $i > $i > $o).
% 33.23/6.16 thf(func_def_208, type, sP3: $i > $i > $o).
% 33.23/6.16 thf(func_def_209, type, sP4: $i > $o > $i > $i > $o).
% 33.23/6.16 thf(func_def_219, type, sK14: $i > $i).
% 33.23/6.16 thf(func_def_220, type, sK15: $i > $i > $i).
% 33.23/6.16 thf(func_def_236, type, sK31: $i > $i > $i).
% 33.23/6.16 thf(func_def_237, type, sK32: $i > $i > $i).
% 33.23/6.16 thf(func_def_238, type, sK33: $i > $i > $i).
% 33.23/6.16 thf(func_def_239, type, sK34: $i > $i > $i).
% 33.23/6.16 thf(func_def_240, type, sK35: $i > $i > $i).
% 33.23/6.16 thf(func_def_241, type, sK36: $i > $i > $i > $i).
% 33.23/6.16 thf(func_def_242, type, sK37: $i > $i).
% 33.23/6.16 thf(func_def_243, type, sK38: $i > $i).
% 33.23/6.16 thf(func_def_244, type, sK39: $i > $i).
% 33.23/6.16 thf(func_def_245, type, sK40: $i > $i).
% 33.23/6.16 thf(func_def_246, type, sK41: $i > $i > $i).
% 33.23/6.16 thf(func_def_247, type, sK42: $i > $i > $i > $i).
% 33.23/6.16 thf(func_def_248, type, sK43: $i > $i > $i > $i).
% 33.23/6.16 thf(func_def_249, type, sK44: $i > $i > $i).
% 33.23/6.16 thf(func_def_250, type, sK45: $i > $i > $i).
% 33.23/6.16 thf(func_def_252, type, sK47: $i > $i).
% 33.23/6.16 thf(func_def_253, type, sK48: $i > $i).
% 33.23/6.16 thf(func_def_254, type, sK49: $i > $i).
% 33.23/6.16 thf(func_def_283, type, sK78: $i > $o).
% 33.23/6.16 thf(func_def_297, type, sK92: $i > $o).
% 33.23/6.16 thf(func_def_303, type, sK98: $i > $o).
% 33.23/6.16 thf(func_def_305, type, sK100: ($i > $o) > $i).
% 33.23/6.16 thf(func_def_306, type, sK101: ($i > $o) > $i).
% 33.23/6.16 thf(func_def_308, type, sK103: $i > $o).
% 33.23/6.16 thf(func_def_318, type, sK113: $i > $i).
% 33.23/6.16 thf(func_def_327, type, sK122: $i > $o).
% 33.23/6.16 thf(func_def_328, type, sK123: $i > $o).
% 33.23/6.16 thf(func_def_329, type, sK124: ($i > $o) > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_330, type, sK125: ($i > $o) > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_342, type, sK137: $i > $o).
% 33.23/6.16 thf(func_def_343, type, sK138: $i > $o).
% 33.23/6.16 thf(func_def_345, type, sK140: $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_348, type, sK143: $i > $o).
% 33.23/6.16 thf(func_def_356, type, sK151: $i > $o).
% 33.23/6.16 thf(func_def_359, type, sK154: $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_360, type, sK155: $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_361, type, sK156: $i > $i > $i).
% 33.23/6.16 thf(func_def_366, type, sK161: $i > $i).
% 33.23/6.16 thf(func_def_371, type, sK166: $i > $i).
% 33.23/6.16 thf(func_def_377, type, sK172: ($i > $o) > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_378, type, sK173: ($i > $o) > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_379, type, sK174: $i > $o).
% 33.23/6.16 thf(func_def_380, type, sK175: $i > $o).
% 33.23/6.16 thf(func_def_381, type, sK176: $i > $o).
% 33.23/6.16 thf(func_def_384, type, sK179: ($i > $o) > $i > $i).
% 33.23/6.16 thf(func_def_386, type, sK181: $i > $o).
% 33.23/6.16 thf(func_def_387, type, sK182: $i > $i > $i).
% 33.23/6.16 thf(func_def_390, type, sK185: $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_391, type, sK186: $i > $o).
% 33.23/6.16 thf(func_def_397, type, sK192: $i > $i > $i).
% 33.23/6.16 thf(func_def_404, type, sK199: $i > $i).
% 33.23/6.16 thf(func_def_406, type, sK201: $i > $i).
% 33.23/6.16 thf(func_def_408, type, sK203: $i > $i > $i).
% 33.23/6.16 thf(func_def_409, type, sK204: $i > $i > $i).
% 33.23/6.16 thf(func_def_412, type, sK207: $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_413, type, sK208: $i > $o).
% 33.23/6.16 thf(func_def_427, type, sK222: ($i > $o) > $i).
% 33.23/6.16 thf(func_def_428, type, sK223: $i > $o).
% 33.23/6.16 thf(func_def_429, type, sK224: $i > $i).
% 33.23/6.16 thf(func_def_430, type, sK225: $i > $i > $o).
% 33.23/6.16 thf(func_def_432, type, sK227: $i > $i).
% 33.23/6.16 thf(func_def_433, type, sK228: $i > $i).
% 33.23/6.16 thf(func_def_434, type, sK229: $i > ($i > $i > $o) > $i).
% 33.23/6.16 thf(func_def_435, type, sK230: $i > ($i > $i > $o) > $i).
% 33.23/6.16 thf(func_def_436, type, sK231: $i > $i > ($i > $i > $o) > $i).
% 33.23/6.16 thf(func_def_447, type, sK242: $i > $o).
% 33.23/6.16 thf(func_def_457, type, sK252: $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_458, type, sK253: $i > $o).
% 33.23/6.16 thf(func_def_466, type, sK261: $i > $o).
% 33.23/6.16 thf(func_def_467, type, sK262: $i > $i).
% 33.23/6.16 thf(func_def_468, type, sK263: ($i > $o) > $i).
% 33.23/6.16 thf(func_def_475, type, sK270: $i > $o).
% 33.23/6.16 thf(func_def_477, type, sK272: ($i > $o) > $i > $i).
% 33.23/6.16 thf(func_def_478, type, sK273: ($i > $o) > $i > $i).
% 33.23/6.16 thf(func_def_481, type, sK276: $i > $i > $i).
% 33.23/6.16 thf(func_def_489, type, sK284: $i > $o).
% 33.23/6.16 thf(func_def_492, type, sK287: $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_496, type, sK291: $i > $o).
% 33.23/6.16 thf(func_def_499, type, sK294: $i > $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_516, type, sK311: $i > $o).
% 33.23/6.16 thf(func_def_517, type, sK312: $i > $o).
% 33.23/6.16 thf(func_def_518, type, sK313: ($i > $o) > ($i > $o) > $i > $i > $i).
% 33.23/6.16 thf(func_def_519, type, sK314: ($i > $o) > ($i > $o) > $i > $i > $i).
% 33.23/6.16 thf(func_def_520, type, sK315: $i > $o).
% 33.23/6.16 thf(func_def_526, type, sK321: $i > $i > $i > $i).
% 33.23/6.16 thf(func_def_527, type, sK322: $i > $i > $i > $i).
% 33.23/6.16 thf(func_def_553, type, sK348: $i > $o).
% 33.23/6.16 thf(func_def_556, type, sK351: $i > $i > $i).
% 33.23/6.16 thf(func_def_563, type, sK358: $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_564, type, sK359: $i > $o).
% 33.23/6.16 thf(func_def_578, type, sK373: $i > $o).
% 33.23/6.16 thf(func_def_585, type, sK380: $i > ($i > $o) > $i).
% 33.23/6.16 thf(func_def_586, type, sK381: $i > $o).
% 33.23/6.16 thf(func_def_603, type, sK398: $o > $i > $i > $i).
% 33.23/6.16 thf(func_def_606, type, sK401: $i > $i > $i).
% 33.23/6.16 thf(func_def_609, type, sK404: $i > $o).
% 33.23/6.16 thf(func_def_616, type, sK411: $i > $i).
% 33.23/6.16 thf(func_def_638, type, sK433: $i > $i > $i).
% 33.23/6.16 thf(func_def_643, type, sK438: ($i > $o) > $i).
% 33.23/6.16 thf(func_def_644, type, sK439: $i > $o).
% 33.23/6.16 thf(func_def_645, type, sK440: ($i > $o) > $i > $i).
% 33.23/6.16 thf(func_def_647, type, sK442: $i > $o).
% 33.23/6.16 thf(func_def_649, type, sK444: $i > $o).
% 33.23/6.16 thf(func_def_658, type, ph453: !>[X0: $tType]:(X0)).
% 33.23/6.16 thf(f16757,plain,(
% 33.23/6.16 $false),
% 33.23/6.16 inference(avatar_sat_refutation,[status(thm)],[f3073,f3082,f3792,f5120,f5410,f16756])).
% 33.23/6.16 thf(f16756,plain,(
% 33.23/6.16 ~spl452_148 | ~spl452_150 | ~spl452_587),
% 33.23/6.16 inference(avatar_contradiction_clause,[status(thm)],[f16755])).
% 33.23/6.16 thf(f16755,plain,(
% 33.23/6.16 $false | (~spl452_148 | ~spl452_150 | ~spl452_587)),
% 33.23/6.16 inference(subsumption_resolution,[status(thm)],[f16754,f2070])).
% 33.23/6.16 thf(f2070,plain,(
% 33.23/6.16 ($true != (in @ (kfst @ sK386) @ sK385))),
% 33.23/6.16 inference(cnf_transformation,[status(thm)],[f1355])).
% 33.23/6.16 thf(f1355,plain,(
% 33.23/6.16 (emptyinunitempty = $true) & (setunionsingleton2 = $true) & (upairsetIL = $true) & (uniqinunit = $true) & (notequalI2 = $true) & (subsetTrans = $true) & (symdiffI1 = $true) & (binintersectSubset2 = $true) & (exuI2 = $true) & (bs114d = $true) & (exuI1 = $true) & (setadjoinOr = $true) & (setoftrueEq = $true) & (dsetconstr__Cong = $true) & (sepInPowerset = $true) & (vacuousDall = $true) & (sepSubset = $true) & (setukpairIR = $true) & (binunionIL = $true) & (quantDeMorgan4 = $true) & (descr__Cong = $true) & (emptysetE = $true) & (quantDeMorgan3 = $true) & (setadjoinSub = $true) & (setextsub = $true) & (ubforcartprodlem2 = $true) & (setunionsingleton = $true) & (omega0Ax = $true) & (powersetE = $true) & (subsetE2 = $true) & (ex1I2 = $true) & (setunionAx = $true) & (exuE3e = $true) & (emptysetAx = $true) & (setminusSubset1 = $true) & (nonemptyE1 = $true) & (noeltsimpempty = $true) & (omega__Cong = $true) & (singletonsuniq = $true) & (binintersectSubset5 = $true) & (binintersectER = $true) & (descrp = $true) & (setadjoinIR = $true) & (foundationAx = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (nonemptyI1 = $true) & (setadjoinIL = $true) & (nonemptyI = $true) & (setunion__Cong = $true) & (quantDeMorgan2 = $true) & (singletonprop = $true) & (setukpairinjL1 = $true) & (theprop = $true) & (ex1E1 = $true) & (in__Cong = $true) & (setadjoin__Cong = $true) & (nonemptyImpWitness = $true) & (prop2setI = $true) & (setadjoinAx = $true) & (subsetI1 = $true) & (exuI3 = $true) & (singletonsswitch = $true) & (symdiffI2 = $true) & (exu__Cong = $true) & (symdiffIneg2 = $true) & (omegaIndAx = $true) & (wellorderingAx = $true) & (upairsubunion = $true) & (subPowSU = $true) & (subsetE = $true) & (singletoninpowunion = $true) & (subsetRefl = $true) & (setminusLsub = $true) & (omegaSAx = $true) & (binintersectLsub = $true) & (setextAx = $true) & (eqimpsubset1 = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (kpairp = $true) & (setminusSubset2 = $true) & (binintersectSubset1 = $true) & (binintersectEL = $true) & (exuE2 = $true) & (binintersectRsub = $true) & (setunionE = $true) & (binintersectSubset3 = $true) & (dsetconstrI = $true) & (setunionI = $true) & (symdiffE = $true) & (subset2powerset = $true) & (replAx = $true) & (emptyset__Cong = $true) & (emptyE1 = $true) & (eqimpsubset2 = $true) & (setminusIRneg = $true) & (setukpairIL = $true) & (emptyinPowerset = $true) & (($true != (in @ (kfst @ sK386) @ sK385)) & ((in @ sK386 @ (cartprod @ sK385 @ sK384)) = $true)) & (exuEu = $true) & (notinemptyset = $true) & (kfstsingleton = $true) & (setminusI = $true) & (emptyInPowerset = $true) & (notdallE = $true) & (kpairiskpair = $true) & (setminusERneg = $true) & (binunionE = $true) & (binintersectSubset4 = $true) & (prop2set2propI = $true) & (powerset__Cong = $true) & (notsubsetI = $true) & (singletoninpowerset = $true) & (powersetI = $true) & (setunionE2 = $true) & (upairinpowunion = $true) & (setunionsingleton1 = $true) & (notdexE = $true) & (emptyI = $true) & (powersetsubset = $true) & (cartprodmempair1 = $true) & (emptysetimpfalse = $true) & (kfstpairEq = $true) & (upairset2IR = $true) & (upairsetE = $true) & (ex1I = $true) & (quantDeMorgan1 = $true) & (binunionRsub = $true) & (binintersectI = $true) & (powersetAx = $true) & (binunionIR = $true) & (dsetconstrEL = $true) & (ubforcartprodlem3 = $true) & (setminusER = $true) & (symdiffIneg1 = $true) & (emptysetsubset = $true) & (setadjoinSub2 = $true) & (subsetI2 = $true) & (setadjoinE = $true) & (upairset2E = $true) & (ubforcartprodlem1 = $true) & (setbeta = $true) & (singletonsubset = $true) & (setminusILneg = $true) & (setminusEL = $true) & (upairsetIR = $true) & (subsetemptysetimpeq = $true) & (cartprodmempair = $true) & (exuE1 = $true) & (inCongP = $true) & (eqinunit = $true) & (notinsingleton = $true) & (binunionLsub = $true) & (inPowerset = $true) & (notequalI1 = $true) & (setminusELneg = $true) & (cartprodpairin = $true) & (disjointsetsI1 = $true) & (binunionEcases = $true) & (exuE3u = $true) & (secondinupair = $true) & (setext = $true)),
% 33.23/6.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK384,sK385,sK386])],[f573,f1354])).
% 33.23/6.16 thf(f1354,plain,(
% 33.23/6.16 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (kfst @ X2) @ X1)) & ((in @ X2 @ (cartprod @ X1 @ X0)) = $true)) => (($true != (in @ (kfst @ sK386) @ sK385)) & ((in @ sK386 @ (cartprod @ sK385 @ sK384)) = $true))),
% 33.23/6.16 introduced(definition,[],[choice_axiom])).
% 33.23/6.16 thf(f573,plain,(
% 33.23/6.16 (emptyinunitempty = $true) & (setunionsingleton2 = $true) & (upairsetIL = $true) & (uniqinunit = $true) & (notequalI2 = $true) & (subsetTrans = $true) & (symdiffI1 = $true) & (binintersectSubset2 = $true) & (exuI2 = $true) & (bs114d = $true) & (exuI1 = $true) & (setadjoinOr = $true) & (setoftrueEq = $true) & (dsetconstr__Cong = $true) & (sepInPowerset = $true) & (vacuousDall = $true) & (sepSubset = $true) & (setukpairIR = $true) & (binunionIL = $true) & (quantDeMorgan4 = $true) & (descr__Cong = $true) & (emptysetE = $true) & (quantDeMorgan3 = $true) & (setadjoinSub = $true) & (setextsub = $true) & (ubforcartprodlem2 = $true) & (setunionsingleton = $true) & (omega0Ax = $true) & (powersetE = $true) & (subsetE2 = $true) & (ex1I2 = $true) & (setunionAx = $true) & (exuE3e = $true) & (emptysetAx = $true) & (setminusSubset1 = $true) & (nonemptyE1 = $true) & (noeltsimpempty = $true) & (omega__Cong = $true) & (singletonsuniq = $true) & (binintersectSubset5 = $true) & (binintersectER = $true) & (descrp = $true) & (setadjoinIR = $true) & (foundationAx = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (nonemptyI1 = $true) & (setadjoinIL = $true) & (nonemptyI = $true) & (setunion__Cong = $true) & (quantDeMorgan2 = $true) & (singletonprop = $true) & (setukpairinjL1 = $true) & (theprop = $true) & (ex1E1 = $true) & (in__Cong = $true) & (setadjoin__Cong = $true) & (nonemptyImpWitness = $true) & (prop2setI = $true) & (setadjoinAx = $true) & (subsetI1 = $true) & (exuI3 = $true) & (singletonsswitch = $true) & (symdiffI2 = $true) & (exu__Cong = $true) & (symdiffIneg2 = $true) & (omegaIndAx = $true) & (wellorderingAx = $true) & (upairsubunion = $true) & (subPowSU = $true) & (subsetE = $true) & (singletoninpowunion = $true) & (subsetRefl = $true) & (setminusLsub = $true) & (omegaSAx = $true) & (binintersectLsub = $true) & (setextAx = $true) & (eqimpsubset1 = $true) & (powersetE1 = $true) & (powersetI1 = $true) & (kpairp = $true) & (setminusSubset2 = $true) & (binintersectSubset1 = $true) & (binintersectEL = $true) & (exuE2 = $true) & (binintersectRsub = $true) & (setunionE = $true) & (binintersectSubset3 = $true) & (dsetconstrI = $true) & (setunionI = $true) & (symdiffE = $true) & (subset2powerset = $true) & (replAx = $true) & (emptyset__Cong = $true) & (emptyE1 = $true) & (eqimpsubset2 = $true) & (setminusIRneg = $true) & (setukpairIL = $true) & (emptyinPowerset = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (kfst @ X2) @ X1)) & ((in @ X2 @ (cartprod @ X1 @ X0)) = $true)) & (exuEu = $true) & (notinemptyset = $true) & (kfstsingleton = $true) & (setminusI = $true) & (emptyInPowerset = $true) & (notdallE = $true) & (kpairiskpair = $true) & (setminusERneg = $true) & (binunionE = $true) & (binintersectSubset4 = $true) & (prop2set2propI = $true) & (powerset__Cong = $true) & (notsubsetI = $true) & (singletoninpowerset = $true) & (powersetI = $true) & (setunionE2 = $true) & (upairinpowunion = $true) & (setunionsingleton1 = $true) & (notdexE = $true) & (emptyI = $true) & (powersetsubset = $true) & (cartprodmempair1 = $true) & (emptysetimpfalse = $true) & (kfstpairEq = $true) & (upairset2IR = $true) & (upairsetE = $true) & (ex1I = $true) & (quantDeMorgan1 = $true) & (binunionRsub = $true) & (binintersectI = $true) & (powersetAx = $true) & (binunionIR = $true) & (dsetconstrEL = $true) & (ubforcartprodlem3 = $true) & (setminusER = $true) & (symdiffIneg1 = $true) & (emptysetsubset = $true) & (setadjoinSub2 = $true) & (subsetI2 = $true) & (setadjoinE = $true) & (upairset2E = $true) & (ubforcartprodlem1 = $true) & (setbeta = $true) & (singletonsubset = $true) & (setminusILneg = $true) & (setminusEL = $true) & (upairsetIR = $true) & (subsetemptysetimpeq = $true) & (cartprodmempair = $true) & (exuE1 = $true) & (inCongP = $true) & (eqinunit = $true) & (notinsingleton = $true) & (binunionLsub = $true) & (inPowerset = $true) & (notequalI1 = $true) & (setminusELneg = $true) & (cartprodpairin = $true) & (disjointsetsI1 = $true) & (binunionEcases = $true) & (exuE3u = $true) & (secondinupair = $true) & (setext = $true)),
% 33.23/6.16 inference(flattening,[status(thm)],[f572])).
% 33.23/6.16 thf(f572,plain,(
% 33.23/6.16 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ (kfst @ X2) @ X1)) & ((in @ X2 @ (cartprod @ X1 @ X0)) = $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)),
% 33.23/6.16 inference(ennf_transformation,[status(thm)],[f379])).
% 33.23/6.16 thf(f379,plain,(
% 33.23/6.16 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (cartprod @ X1 @ X0)) = $true) => ($true = (in @ (kfst @ X2) @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 33.23/6.16 inference(fool_elimination,[status(thm)],[f378])).
% 33.23/6.16 thf(f378,plain,(
% 33.23/6.16 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (cartprod @ X1 @ X0)) => (in @ (kfst @ X2) @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 33.23/6.16 inference(rectify,[status(thm)],[f170])).
% 33.23/6.16 thf(f170,negated_conjecture,(
% 33.23/6.16 ~(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 => ! [X4 : $i,X3 : $i,X10 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (kfst @ X10) @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 33.23/6.16 inference(negated_conjecture,[status(cth)],[f169])).
% 33.23/6.16 thf(f169,conjecture,(
% 33.23/6.16 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 => ! [X4 : $i,X3 : $i,X10 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => (in @ (kfst @ X10) @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 33.23/6.16 file('/export/starexec/sandbox/tmp/tmp.BWMLOxAvmL/DTF2THF_6029.p',cartprodfstin)).
% 33.23/6.16 thf(f16754,plain,(
% 33.23/6.16 ($true = (in @ (kfst @ sK386) @ sK385)) | (~spl452_148 | ~spl452_150 | ~spl452_587)),
% 33.23/6.16 inference(backward_demodulation,[status(thm)],[f10216,f16752])).
% 33.23/6.16 thf(f16752,plain,(
% 33.23/6.16 ((sK321 @ sK384 @ sK385 @ sK386) = (kfst @ sK386)) | (~spl452_148 | ~spl452_587)),
% 33.23/6.16 inference(superposition,[status(thm)],[f3072,f10830])).
% 33.23/6.16 thf(f10830,plain,(
% 33.23/6.16 (sK386 = (kpair @ (sK321 @ sK384 @ sK385 @ sK386) @ (sK322 @ sK384 @ sK385 @ sK386))) | ~spl452_587),
% 33.23/6.16 inference(trivial_inequality_removal,[status(thm)],[f10811])).
% 33.23/6.16 thf(f10811,plain,(
% 33.23/6.16 ($true != $true) | (sK386 = (kpair @ (sK321 @ sK384 @ sK385 @ sK386) @ (sK322 @ sK384 @ sK385 @ sK386))) | ~spl452_587),
% 33.23/6.16 inference(superposition,[status(thm)],[f5119,f2069])).
% 33.23/6.16 thf(f2069,plain,(
% 33.23/6.16 ((in @ sK386 @ (cartprod @ sK385 @ sK384)) = $true)),
% 33.23/6.16 inference(cnf_transformation,[status(thm)],[f1355])).
% 33.23/6.16 thf(f5119,plain,(
% 33.23/6.16 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ X5 @ (cartprod @ X6 @ X7)) != $true) | ((kpair @ (sK321 @ X7 @ X6 @ X5) @ (sK322 @ X7 @ X6 @ X5)) = X5)) ) | ~spl452_587),
% 33.23/6.16 inference(avatar_component_clause,[status(thm)],[f5118])).
% 33.23/6.16 thf(f5118,definition,(
% 33.23/6.16 spl452_587 <=> ! [X6 : $i,X5 : $i,X7 : $i] : (((kpair @ (sK321 @ X7 @ X6 @ X5) @ (sK322 @ X7 @ X6 @ X5)) = X5) | ((in @ X5 @ (cartprod @ X6 @ X7)) != $true))),
% 33.23/6.16 introduced(definition,[new_symbols(naming,[spl452_587])],[avatar_definition])).
% 33.23/6.16 thf(f3072,plain,(
% 33.23/6.16 ( ! [X2 : $i,X3 : $i] : (((kfst @ (kpair @ X2 @ X3)) = X2)) ) | ~spl452_148),
% 33.23/6.16 inference(avatar_component_clause,[status(thm)],[f3071])).
% 33.23/6.16 thf(f3071,definition,(
% 33.23/6.16 spl452_148 <=> ! [X2 : $i,X3 : $i] : ((kfst @ (kpair @ X2 @ X3)) = X2)),
% 33.23/6.16 introduced(definition,[new_symbols(naming,[spl452_148])],[avatar_definition])).
% 33.23/6.16 thf(f10216,plain,(
% 33.23/6.16 ((in @ (sK321 @ sK384 @ sK385 @ sK386) @ sK385) = $true) | ~spl452_150),
% 33.23/6.16 inference(trivial_inequality_removal,[status(thm)],[f10195])).
% 33.23/6.16 thf(f10195,plain,(
% 33.23/6.16 ($true != $true) | ((in @ (sK321 @ sK384 @ sK385 @ sK386) @ sK385) = $true) | ~spl452_150),
% 33.23/6.16 inference(superposition,[status(thm)],[f3081,f2069])).
% 33.23/6.16 thf(f3081,plain,(
% 33.23/6.16 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ X5 @ (cartprod @ X6 @ X7)) != $true) | ((in @ (sK321 @ X7 @ X6 @ X5) @ X6) = $true)) ) | ~spl452_150),
% 33.23/6.16 inference(avatar_component_clause,[status(thm)],[f3080])).
% 33.23/6.16 thf(f3080,definition,(
% 33.23/6.16 spl452_150 <=> ! [X6 : $i,X5 : $i,X7 : $i] : (((in @ (sK321 @ X7 @ X6 @ X5) @ X6) = $true) | ((in @ X5 @ (cartprod @ X6 @ X7)) != $true))),
% 33.23/6.16 introduced(definition,[new_symbols(naming,[spl452_150])],[avatar_definition])).
% 33.23/6.16 thf(f5410,plain,(
% 33.23/6.16 spl452_6),
% 33.23/6.16 inference(avatar_split_clause,[status(thm)],[f2045,f2447])).
% 33.23/6.16 thf(f2447,definition,(
% 33.23/6.16 spl452_6 <=> (kfstpairEq = $true)),
% 33.23/6.16 introduced(definition,[new_symbols(naming,[spl452_6])],[avatar_definition])).
% 33.23/6.16 thf(f2045,plain,(
% 33.23/6.16 (kfstpairEq = $true)),
% 33.23/6.16 inference(cnf_transformation,[status(thm)],[f1355])).
% 33.23/6.16 thf(f5120,plain,(
% 33.23/6.16 ~spl452_42 | spl452_587),
% 33.23/6.16 inference(avatar_split_clause,[status(thm)],[f1925,f5118,f2604])).
% 33.23/6.16 thf(f2604,definition,(
% 33.23/6.16 spl452_42 <=> (cartprodmempair1 = $true)),
% 33.23/6.16 introduced(definition,[new_symbols(naming,[spl452_42])],[avatar_definition])).
% 33.23/6.16 thf(f1925,plain,(
% 33.23/6.16 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((kpair @ (sK321 @ X7 @ X6 @ X5) @ (sK322 @ X7 @ X6 @ X5)) = X5) | ((in @ X5 @ (cartprod @ X6 @ X7)) != $true) | (cartprodmempair1 != $true)) )),
% 33.23/6.16 inference(cnf_transformation,[status(thm)],[f1258])).
% 33.23/6.16 thf(f1258,plain,(
% 33.23/6.16 ((cartprodmempair1 = $true) | (! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != sK318) | ((in @ X4 @ sK320) != $true)) | ($true != (in @ X3 @ sK319))) & ((in @ sK318 @ (cartprod @ sK319 @ sK320)) = $true))) & (! [X5 : $i,X6 : $i,X7 : $i] : (((((kpair @ (sK321 @ X7 @ X6 @ X5) @ (sK322 @ X7 @ X6 @ X5)) = X5) & ($true = (in @ (sK322 @ X7 @ X6 @ X5) @ X7))) & ((in @ (sK321 @ X7 @ X6 @ X5) @ X6) = $true)) | ((in @ X5 @ (cartprod @ X6 @ X7)) != $true)) | (cartprodmempair1 != $true))),
% 33.23/6.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK318,sK319,sK320,sK321,sK322])],[f1254,f1257,f1256,f1255])).
% 33.23/6.16 thf(f1255,plain,(
% 33.23/6.16 ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != X0) | ((in @ X4 @ X2) != $true)) | ($true != (in @ X3 @ X1))) & ($true = (in @ X0 @ (cartprod @ X1 @ X2)))) => (! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != sK318) | ((in @ X4 @ sK320) != $true)) | ($true != (in @ X3 @ sK319))) & ((in @ sK318 @ (cartprod @ sK319 @ sK320)) = $true))),
% 33.23/6.16 introduced(definition,[],[choice_axiom])).
% 33.23/6.16 thf(f1256,plain,(
% 33.23/6.16 ! [X5 : $i,X6 : $i,X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : (((kpair @ X8 @ X9) = X5) & ($true = (in @ X9 @ X7))) & ($true = (in @ X8 @ X6))) => (? [X9 : $i] : (((kpair @ (sK321 @ X7 @ X6 @ X5) @ X9) = X5) & ($true = (in @ X9 @ X7))) & ((in @ (sK321 @ X7 @ X6 @ X5) @ X6) = $true)))),
% 33.23/6.16 introduced(definition,[],[choice_axiom])).
% 33.23/6.16 thf(f1257,plain,(
% 33.23/6.16 ! [X5 : $i,X6 : $i,X7 : $i] : (? [X9 : $i] : (((kpair @ (sK321 @ X7 @ X6 @ X5) @ X9) = X5) & ($true = (in @ X9 @ X7))) => (((kpair @ (sK321 @ X7 @ X6 @ X5) @ (sK322 @ X7 @ X6 @ X5)) = X5) & ($true = (in @ (sK322 @ X7 @ X6 @ X5) @ X7))))),
% 33.23/6.16 introduced(definition,[],[choice_axiom])).
% 33.23/6.16 thf(f1254,plain,(
% 33.23/6.16 ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != X0) | ((in @ X4 @ X2) != $true)) | ($true != (in @ X3 @ X1))) & ($true = (in @ X0 @ (cartprod @ X1 @ X2))))) & (! [X5 : $i,X6 : $i,X7 : $i] : (? [X8 : $i] : (? [X9 : $i] : (((kpair @ X8 @ X9) = X5) & ($true = (in @ X9 @ X7))) & ($true = (in @ X8 @ X6))) | ((in @ X5 @ (cartprod @ X6 @ X7)) != $true)) | (cartprodmempair1 != $true))),
% 33.23/6.16 inference(rectify,[status(thm)],[f1253])).
% 33.23/6.16 thf(f1253,plain,(
% 33.23/6.16 ((cartprodmempair1 = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (! [X3 : $i] : (! [X4 : $i] : (((kpair @ X3 @ X4) != X0) | ((in @ X4 @ X2) != $true)) | ($true != (in @ X3 @ X1))) & ($true = (in @ X0 @ (cartprod @ X1 @ X2))))) & (! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((kpair @ X3 @ X4) = X0) & ((in @ X4 @ X2) = $true)) & ($true = (in @ X3 @ X1))) | ($true != (in @ X0 @ (cartprod @ X1 @ X2)))) | (cartprodmempair1 != $true))),
% 33.23/6.16 inference(nnf_transformation,[status(thm)],[f668])).
% 33.23/6.16 thf(f668,plain,(
% 33.23/6.16 (cartprodmempair1 = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (? [X3 : $i] : (? [X4 : $i] : (((kpair @ X3 @ X4) = X0) & ((in @ X4 @ X2) = $true)) & ($true = (in @ X3 @ X1))) | ($true != (in @ X0 @ (cartprod @ X1 @ X2))))),
% 33.23/6.16 inference(ennf_transformation,[status(thm)],[f214])).
% 33.23/6.16 thf(f214,plain,(
% 33.23/6.16 ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (cartprod @ X1 @ X2))) => ? [X3 : $i] : (? [X4 : $i] : (((kpair @ X3 @ X4) = X0) & ((in @ X4 @ X2) = $true)) & ($true = (in @ X3 @ X1)))) <=> (cartprodmempair1 = $true)),
% 33.23/6.16 inference(fool_elimination,[status(thm)],[f213])).
% 33.23/6.16 thf(f213,plain,(
% 33.23/6.16 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (cartprod @ X1 @ X2)) => ? [X3 : $i] : ((in @ X3 @ X1) & ? [X4 : $i] : ((in @ X4 @ X2) & ((kpair @ X3 @ X4) = X0)))) = cartprodmempair1)),
% 33.23/6.16 inference(rectify,[status(thm)],[f152])).
% 33.23/6.16 thf(f152,axiom,(
% 33.23/6.16 (! [X10 : $i,X3 : $i,X4 : $i] : ((in @ X10 @ (cartprod @ X3 @ X4)) => ? [X1 : $i] : ((in @ X1 @ X3) & ? [X2 : $i] : ((in @ X2 @ X4) & ((kpair @ X1 @ X2) = X10)))) = cartprodmempair1)),
% 33.23/6.16 file('/export/starexec/sandbox/tmp/tmp.BWMLOxAvmL/DTF2THF_6029.p',cartprodmempair1)).
% 33.23/6.16 thf(f3792,plain,(
% 33.23/6.16 spl452_42),
% 33.23/6.16 inference(avatar_split_clause,[status(thm)],[f2047,f2604])).
% 33.23/6.16 thf(f2047,plain,(
% 33.23/6.16 (cartprodmempair1 = $true)),
% 33.23/6.16 inference(cnf_transformation,[status(thm)],[f1355])).
% 33.23/6.16 thf(f3082,plain,(
% 33.23/6.16 ~spl452_42 | spl452_150),
% 33.23/6.16 inference(avatar_split_clause,[status(thm)],[f1923,f3080,f2604])).
% 33.23/6.16 thf(f1923,plain,(
% 33.23/6.16 ( ! [X6 : $i,X7 : $i,X5 : $i] : (((in @ (sK321 @ X7 @ X6 @ X5) @ X6) = $true) | ((in @ X5 @ (cartprod @ X6 @ X7)) != $true) | (cartprodmempair1 != $true)) )),
% 33.23/6.16 inference(cnf_transformation,[status(thm)],[f1258])).
% 33.23/6.16 thf(f3073,plain,(
% 33.23/6.16 spl452_148 | ~spl452_6),
% 33.23/6.16 inference(avatar_split_clause,[status(thm)],[f1707,f2447,f3071])).
% 33.23/6.16 thf(f1707,plain,(
% 33.23/6.16 ( ! [X2 : $i,X3 : $i] : (((kfst @ (kpair @ X2 @ X3)) = X2) | (kfstpairEq != $true)) )),
% 33.23/6.16 inference(cnf_transformation,[status(thm)],[f999])).
% 33.23/6.16 thf(f999,plain,(
% 33.23/6.16 ((kfstpairEq = $true) | (sK163 != (kfst @ (kpair @ sK163 @ sK164)))) & (! [X2 : $i,X3 : $i] : ((kfst @ (kpair @ X2 @ X3)) = X2) | (kfstpairEq != $true))),
% 33.23/6.16 inference(skolemisation,[status(esa),new_symbols(skolem,[sK163,sK164])],[f997,f998])).
% 33.23/6.16 thf(f998,plain,(
% 33.23/6.16 ? [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X0 @ X1)) != X0) => (sK163 != (kfst @ (kpair @ sK163 @ sK164)))),
% 33.23/6.16 introduced(definition,[],[choice_axiom])).
% 33.23/6.16 thf(f997,plain,(
% 33.23/6.16 ((kfstpairEq = $true) | ? [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X0 @ X1)) != X0)) & (! [X2 : $i,X3 : $i] : ((kfst @ (kpair @ X2 @ X3)) = X2) | (kfstpairEq != $true))),
% 33.23/6.16 inference(rectify,[status(thm)],[f996])).
% 33.23/6.16 thf(f996,plain,(
% 33.23/6.16 ((kfstpairEq = $true) | ? [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X0 @ X1)) != X0)) & (! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X0 @ X1)) = X0) | (kfstpairEq != $true))),
% 33.23/6.16 inference(nnf_transformation,[status(thm)],[f222])).
% 33.23/6.16 thf(f222,plain,(
% 33.23/6.16 (kfstpairEq = $true) <=> ! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X0 @ X1)) = X0)),
% 33.23/6.16 inference(fool_elimination,[status(thm)],[f221])).
% 33.23/6.16 thf(f221,plain,(
% 33.23/6.16 (kfstpairEq = ! [X0 : $i,X1 : $i] : ((kfst @ (kpair @ X0 @ X1)) = X0))),
% 33.23/6.16 inference(rectify,[status(thm)],[f168])).
% 33.23/6.16 thf(f168,axiom,(
% 33.23/6.16 (kfstpairEq = ! [X1 : $i,X2 : $i] : ((kfst @ (kpair @ X1 @ X2)) = X1))),
% 33.23/6.16 file('/export/starexec/sandbox/tmp/tmp.BWMLOxAvmL/DTF2THF_6029.p',kfstpairEq)).
% 33.23/6.16 % SZS output end Proof for DTF2THF_6029
% 33.23/6.16 % (6260)------------------------------
% 33.23/6.16 % (6260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.23/6.16 % (6260)Termination reason: Refutation
% 33.23/6.16
% 33.23/6.16 % (6260)Memory used [KB]: 15991
% 33.23/6.16 % (6260)Time elapsed: 1.680 s
% 33.23/6.16 % (6260)Instructions burned: 3274 (million)
% 33.23/6.16 % (6260)------------------------------
% 33.23/6.16 % (6260)------------------------------
% 33.23/6.16 % (6138)Success in time 4.428 s
%------------------------------------------------------------------------------