%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU581^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:24 AM UTC 2026
% Result : Theorem 2.45s 1.88s
% Output : Refutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 1715 ( 464 equ; 0 cnn)
% Maximal formula atoms : 98 ( 45 avg)
% Number of connectives : 988 ( 39 ~; 24 |; 302 &; 226 @)
% ( 3 <=>; 394 =>; 0 <=; 0 <~>)
% Maximal formula depth : 106 ( 22 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 248 ( 245 usr; 103 con; 0-4 aty)
% Number of variables : 94 ( 24 ^; 52 !; 18 ?; 94 :)
% 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_125,type,
sP0: $i > $i > $i > $o ).
thf(func_def_126,type,
sP1: $i > $i > $o ).
thf(func_def_127,type,
sP2: $i > $i > $o ).
thf(func_def_128,type,
sP3: $i > $o ).
thf(func_def_129,type,
sP4: $i > $i > $o ).
thf(func_def_130,type,
sP5: $i > $i > $o ).
thf(func_def_131,type,
sP6: $i > ( $i > $o ) > $o ).
thf(func_def_134,type,
sP9: $i > $i > $o > $o ).
thf(func_def_135,type,
sP10: $i > $i > $i > $o ).
thf(func_def_136,type,
sP11: ( $i > $o ) > $o ).
thf(func_def_138,type,
sP13: $i > $i > $i > $o ).
thf(func_def_140,type,
sP15: $i > $o > $i > $o ).
thf(func_def_141,type,
sP16: ( $i > $o ) > $o ).
thf(func_def_142,type,
sP17: $i > ( $i > $i > $o ) > $i > $o ).
thf(func_def_143,type,
sP18: $i > ( $i > $i > $o ) > $o ).
thf(func_def_145,type,
sP20: $i > $o ).
thf(func_def_146,type,
sP21: ( $i > $o ) > $o ).
thf(func_def_147,type,
sP22: $i > $i > $o ).
thf(func_def_149,type,
sP24: ( $i > $o ) > $o ).
thf(func_def_150,type,
sP25: $i > $i > $o ).
thf(func_def_152,type,
sP27: ( $i > $o ) > $o ).
thf(func_def_153,type,
sP28: $i > $o ).
thf(func_def_154,type,
sP29: $i > $o ).
thf(func_def_155,type,
sP30: $i > ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(func_def_156,type,
sP31: $i > ( $i > $o ) > $o ).
thf(func_def_158,type,
sP33: $i > ( $i > $o ) > $o ).
thf(func_def_161,type,
sP36: $i > ( $i > $o ) > $o ).
thf(func_def_163,type,
sP38: ( $i > $o ) > $i > $o ).
thf(func_def_165,type,
sP40: ( $i > $o ) > $i > $o ).
thf(func_def_167,type,
sP42: $i > $i > $o ).
thf(func_def_173,type,
sK48: $i > $i > $i ).
thf(func_def_174,type,
sK49: $i > $i > $i ).
thf(func_def_175,type,
sK50: $i > $i > $i > $i ).
thf(func_def_176,type,
sK51: $i > $i > $i ).
thf(func_def_177,type,
sK52: $i > $i > $i ).
thf(func_def_178,type,
sK53: $i > $i > $i ).
thf(func_def_179,type,
sK54: $i > $i ).
thf(func_def_180,type,
sK55: $i > $i ).
thf(func_def_181,type,
sK56: $i > $i ).
thf(func_def_182,type,
sK57: $i > $i ).
thf(func_def_183,type,
sK58: $i > $i > $i ).
thf(func_def_184,type,
sK59: $i > $i > $i ).
thf(func_def_185,type,
sK60: $i > $i > $i ).
thf(func_def_186,type,
sK61: $i > $i > $i ).
thf(func_def_187,type,
sK62: $i > $i > $i ).
thf(func_def_188,type,
sK63: $i > $i > $i > $i ).
thf(func_def_189,type,
sK64: $i > $i > $i > $i ).
thf(func_def_190,type,
sK65: $i > $i ).
thf(func_def_194,type,
sK69: $i > $o ).
thf(func_def_196,type,
sK71: $i > $o ).
thf(func_def_197,type,
sK72: ( $i > $o ) > $i > $i ).
thf(func_def_198,type,
sK73: $i > ( $i > $o ) > $i ).
thf(func_def_201,type,
sK76: $i > $o ).
thf(func_def_202,type,
sK77: $i > $o ).
thf(func_def_203,type,
sK78: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_204,type,
sK79: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_210,type,
sK85: $i > $i > $i > $o ).
thf(func_def_216,type,
sK91: $i > ( $i > $o ) > $i ).
thf(func_def_217,type,
sK92: ( $i > $o ) > $i ).
thf(func_def_218,type,
sK93: $i > $o ).
thf(func_def_221,type,
sK96: $i > $i > $i ).
thf(func_def_225,type,
sK100: $i > $o > $i > $i ).
thf(func_def_233,type,
sK108: $i > $o ).
thf(func_def_234,type,
sK109: ( $i > $o ) > $i ).
thf(func_def_235,type,
sK110: $i > $o ).
thf(func_def_240,type,
sK115: ( $i > $o ) > $i ).
thf(func_def_241,type,
sK116: $i > ( $i > $o ) > $i ).
thf(func_def_242,type,
sK117: $i > $o ).
thf(func_def_243,type,
sK118: $i > $i > $o ).
thf(func_def_245,type,
sK120: $i > ( $i > $i > $o ) > $i ).
thf(func_def_246,type,
sK121: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_247,type,
sK122: $i > ( $i > $i > $o ) > $i ).
thf(func_def_248,type,
sK123: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_249,type,
sK124: $i > $i > $i ).
thf(func_def_250,type,
sK125: $i > $i ).
thf(func_def_255,type,
sK130: $i > $o ).
thf(func_def_264,type,
sK139: $i > $o ).
thf(func_def_266,type,
sK141: $i > $i ).
thf(func_def_271,type,
sK146: ( $i > $o ) > $i ).
thf(func_def_272,type,
sK147: $i > ( $i > $o ) > $i ).
thf(func_def_273,type,
sK148: $i > $o ).
thf(func_def_278,type,
sK153: $i > $o ).
thf(func_def_281,type,
sK156: $i > $i > $i ).
thf(func_def_282,type,
sK157: $i > $o ).
thf(func_def_288,type,
sK163: $i > $i ).
thf(func_def_291,type,
sK166: $i > $i > $i ).
thf(func_def_295,type,
sK170: $i > $o ).
thf(func_def_297,type,
sK172: $i > $i ).
thf(func_def_313,type,
sK188: $i > ( $i > $o ) > $i ).
thf(func_def_314,type,
sK189: ( $i > $o ) > $i ).
thf(func_def_315,type,
sK190: $i > $o ).
thf(func_def_318,type,
sK193: $i > $i > $i ).
thf(func_def_319,type,
sK194: $i > $i > $i ).
thf(func_def_320,type,
sK195: ( $i > $o ) > $i ).
thf(func_def_321,type,
sK196: ( $i > $o ) > $i ).
thf(func_def_322,type,
sK197: $i > $o ).
thf(func_def_328,type,
sK203: $i > $i ).
thf(func_def_329,type,
sK204: $i > $i ).
thf(func_def_335,type,
sK210: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_336,type,
sK211: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(func_def_339,type,
sK214: $i > $o ).
thf(func_def_340,type,
sK215: $i > $o ).
thf(func_def_345,type,
sK220: $i > $o ).
thf(func_def_347,type,
sK222: $i > ( $i > $o ) > $i ).
thf(func_def_348,type,
sK223: $i > ( $i > $o ) > $i ).
thf(func_def_354,type,
sK229: $i > $i ).
thf(func_def_356,type,
sK231: $i > $o ).
thf(func_def_361,type,
sK236: $i > $o ).
thf(func_def_362,type,
sK237: ( $i > $o ) > $i > $i ).
thf(func_def_363,type,
sK238: $i > ( $i > $o ) > $i ).
thf(func_def_364,type,
sK239: $i > $o ).
thf(func_def_372,type,
sK247: $i > $o ).
thf(func_def_379,type,
sK254: $i > $o ).
thf(func_def_388,type,
sK263: $i > $i > $i ).
thf(func_def_389,type,
sK264: $i > $o ).
thf(func_def_391,type,
sK266: $i > ( $i > $o ) > $i ).
thf(func_def_392,type,
sK267: $i > ( $i > $o ) > $i ).
thf(func_def_403,type,
sK278: $i > $o ).
thf(func_def_404,type,
sK279: ( $i > $o ) > $i > $i ).
thf(func_def_405,type,
sK280: ( $i > $o ) > $i > $i ).
thf(func_def_406,type,
sK281: $i > $o ).
thf(func_def_408,type,
sK283: $i > ( $i > $o ) > $i ).
thf(func_def_409,type,
sK284: ( $i > $o ) > $i > $i ).
thf(func_def_415,type,
sK290: $i > $i > $i ).
thf(func_def_419,type,
sK294: $i > $o ).
thf(func_def_420,type,
sK295: $i > $o ).
thf(func_def_421,type,
sK296: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_422,type,
sK297: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_425,type,
sK300: $i > $i > $i ).
thf(func_def_426,type,
sK301: $i > $o ).
thf(func_def_434,type,
ph309:
!>[X0: $tType] : X0 ).
thf(f2703,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f2700]) ).
thf(f2700,plain,
$true != $true,
inference(superposition,[status(thm)],[f1963,f2695]) ).
thf(f2695,plain,
! [X0: $i,X1: $i > $o] :
( $true
= ( subset @ ( dsetconstr @ X0 @ X1 ) @ X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f2691]) ).
thf(f2691,plain,
! [X0: $i,X1: $i > $o] :
( ( $true
= ( subset @ ( dsetconstr @ X0 @ X1 ) @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f1958,f2047]) ).
thf(f2047,plain,
! [X0: $i,X1: $i > $o] :
( $true
= ( in @ ( dsetconstr @ X0 @ X1 ) @ ( powerset @ X0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f2046]) ).
thf(f2046,plain,
! [X0: $i,X1: $i > $o] :
( $true
= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1739]) ).
thf(f1739,plain,
! [X0: $i,X1: $i > $o] :
( ( $true != $true )
| ( $true
= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1374,f1315]) ).
thf(f1315,plain,
sepInPowerset = $true,
inference(cnf_transformation,[status(thm)],[f727]) ).
thf(f727,plain,
( ( quantDeMorgan2 = $true )
& ( subsetE = $true )
& ( wellorderingAx = $true )
& ( emptyinPowerset = $true )
& ( descrp = $true )
& ( eqinunit = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( subsetI2 = $true )
& ( dsetconstrI = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstrEL = $true )
& ( omegaIndAx = $true )
& ( noeltsimpempty = $true )
& ( subsetE2 = $true )
& ( exuE1 = $true )
& ( exu__Cong = $true )
& ( emptysetAx = $true )
& ( notdexE = $true )
& ( exuE2 = $true )
& ( emptyset__Cong = $true )
& ( setext = $true )
& ( exuI2 = $true )
& ( replAx = $true )
& ( setadjoinIR = $true )
& ( setunion__Cong = $true )
& ( notinsingleton = $true )
& ( foundationAx = $true )
& ( emptysetsubset = $true )
& ( eqimpsubset1 = $true )
& ( setadjoinE = $true )
& ( exuEu = $true )
& ( sepInPowerset = $true )
& ( $true
!= ( subset
@ ( dsetconstr @ sK152
@ ^ [Y0: $i] : ( sK153 @ Y0 ) )
@ sK152 ) )
& ( omega0Ax = $true )
& ( setadjoinAx = $true )
& ( emptysetE = $true )
& ( setextsub = $true )
& ( singletonsswitch = $true )
& ( setadjoinSub = $true )
& ( setadjoinSub2 = $true )
& ( exuE3e = $true )
& ( descr__Cong = $true )
& ( powersetE = $true )
& ( quantDeMorgan1 = $true )
& ( prop2set2propI = $true )
& ( powersetI = $true )
& ( quantDeMorgan3 = $true )
& ( exuI1 = $true )
& ( powerset__Cong = $true )
& ( notinemptyset = $true )
& ( subsetTrans = $true )
& ( inCongP = $true )
& ( nonemptyE1 = $true )
& ( subsetI1 = $true )
& ( notsubsetI = $true )
& ( powersetE1 = $true )
& ( subsetRefl = $true )
& ( emptyE1 = $true )
& ( subsetemptysetimpeq = $true )
& ( omega__Cong = $true )
& ( nonemptyI = $true )
& ( emptyInPowerset = $true )
& ( setadjoinIL = $true )
& ( subPowSU = $true )
& ( in__Cong = $true )
& ( emptysetimpfalse = $true )
& ( nonemptyI1 = $true )
& ( inPowerset = $true )
& ( prop2setI = $true )
& ( setoftrueEq = $true )
& ( upairsetE = $true )
& ( setadjoinOr = $true )
& ( vacuousDall = $true )
& ( emptyI = $true )
& ( setunionE = $true )
& ( notdallE = $true )
& ( eqimpsubset2 = $true )
& ( setbeta = $true )
& ( powersetsubset = $true )
& ( subset2powerset = $true )
& ( notequalI1 = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setextAx = $true )
& ( exuE3u = $true )
& ( nonemptyImpWitness = $true )
& ( emptyinunitempty = $true )
& ( uniqinunit = $true )
& ( upairsetIL = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan4 = $true )
& ( powersetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( upairsetIR = $true )
& ( exuI3 = $true )
& ( notequalI2 = $true )
& ( setunionI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK152,sK153])],[f351,f726]) ).
thf(f726,plain,
( ? [X0: $i,X1: $i > $o] :
( $true
!= ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 ) )
=> ( $true
!= ( subset
@ ( dsetconstr @ sK152
@ ^ [Y0: $i] : ( sK153 @ Y0 ) )
@ sK152 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f351,plain,
( ( quantDeMorgan2 = $true )
& ( subsetE = $true )
& ( wellorderingAx = $true )
& ( emptyinPowerset = $true )
& ( descrp = $true )
& ( eqinunit = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( subsetI2 = $true )
& ( dsetconstrI = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstrEL = $true )
& ( omegaIndAx = $true )
& ( noeltsimpempty = $true )
& ( subsetE2 = $true )
& ( exuE1 = $true )
& ( exu__Cong = $true )
& ( emptysetAx = $true )
& ( notdexE = $true )
& ( exuE2 = $true )
& ( emptyset__Cong = $true )
& ( setext = $true )
& ( exuI2 = $true )
& ( replAx = $true )
& ( setadjoinIR = $true )
& ( setunion__Cong = $true )
& ( notinsingleton = $true )
& ( foundationAx = $true )
& ( emptysetsubset = $true )
& ( eqimpsubset1 = $true )
& ( setadjoinE = $true )
& ( exuEu = $true )
& ( sepInPowerset = $true )
& ? [X0: $i,X1: $i > $o] :
( $true
!= ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 ) )
& ( omega0Ax = $true )
& ( setadjoinAx = $true )
& ( emptysetE = $true )
& ( setextsub = $true )
& ( singletonsswitch = $true )
& ( setadjoinSub = $true )
& ( setadjoinSub2 = $true )
& ( exuE3e = $true )
& ( descr__Cong = $true )
& ( powersetE = $true )
& ( quantDeMorgan1 = $true )
& ( prop2set2propI = $true )
& ( powersetI = $true )
& ( quantDeMorgan3 = $true )
& ( exuI1 = $true )
& ( powerset__Cong = $true )
& ( notinemptyset = $true )
& ( subsetTrans = $true )
& ( inCongP = $true )
& ( nonemptyE1 = $true )
& ( subsetI1 = $true )
& ( notsubsetI = $true )
& ( powersetE1 = $true )
& ( subsetRefl = $true )
& ( emptyE1 = $true )
& ( subsetemptysetimpeq = $true )
& ( omega__Cong = $true )
& ( nonemptyI = $true )
& ( emptyInPowerset = $true )
& ( setadjoinIL = $true )
& ( subPowSU = $true )
& ( in__Cong = $true )
& ( emptysetimpfalse = $true )
& ( nonemptyI1 = $true )
& ( inPowerset = $true )
& ( prop2setI = $true )
& ( setoftrueEq = $true )
& ( upairsetE = $true )
& ( setadjoinOr = $true )
& ( vacuousDall = $true )
& ( emptyI = $true )
& ( setunionE = $true )
& ( notdallE = $true )
& ( eqimpsubset2 = $true )
& ( setbeta = $true )
& ( powersetsubset = $true )
& ( subset2powerset = $true )
& ( notequalI1 = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setextAx = $true )
& ( exuE3u = $true )
& ( nonemptyImpWitness = $true )
& ( emptyinunitempty = $true )
& ( uniqinunit = $true )
& ( upairsetIL = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan4 = $true )
& ( powersetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( upairsetIR = $true )
& ( exuI3 = $true )
& ( notequalI2 = $true )
& ( setunionI = $true ) ),
inference(flattening,[status(thm)],[f350]) ).
thf(f350,plain,
( ? [X0: $i,X1: $i > $o] :
( $true
!= ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 ) )
& ( 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)],[f152]) ).
thf(f152,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 )
=> ! [X0: $i,X1: $i > $o] :
( $true
= ( subset
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f151]) ).
thf(f151,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
=> ! [X0: $i,X1: $i > $o] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f101]) ).
thf(f101,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
=> ! [X3: $i,X0: $i > $o] :
( subset
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) )
@ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f100]) ).
thf(f100,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
=> ! [X3: $i,X0: $i > $o] :
( subset
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) )
@ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ChmJPLfBjb/DTF2THF_20010.p',sepSubset) ).
thf(f1374,plain,
! [X0: $i,X1: $i > $o] :
( ( $true
= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) )
| ( sepInPowerset != $true ) ),
inference(cnf_transformation,[status(thm)],[f762]) ).
thf(f762,plain,
( ( ! [X0: $i,X1: $i > $o] :
( $true
= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) )
| ( sepInPowerset != $true ) )
& ( ( sepInPowerset = $true )
| ( $true
!= ( in
@ ( dsetconstr @ sK169
@ ^ [Y0: $i] : ( sK170 @ Y0 ) )
@ ( powerset @ sK169 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK169,sK170])],[f760,f761]) ).
thf(f761,plain,
( ? [X2: $i,X3: $i > $o] :
( $true
!= ( in
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X3 @ Y0 ) )
@ ( powerset @ X2 ) ) )
=> ( $true
!= ( in
@ ( dsetconstr @ sK169
@ ^ [Y0: $i] : ( sK170 @ Y0 ) )
@ ( powerset @ sK169 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f760,plain,
( ( ! [X0: $i,X1: $i > $o] :
( $true
= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) )
| ( sepInPowerset != $true ) )
& ( ( sepInPowerset = $true )
| ? [X2: $i,X3: $i > $o] :
( $true
!= ( in
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X3 @ Y0 ) )
@ ( powerset @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f759]) ).
thf(f759,plain,
( ( ! [X0: $i,X1: $i > $o] :
( $true
= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) )
| ( sepInPowerset != $true ) )
& ( ( sepInPowerset = $true )
| ? [X0: $i,X1: $i > $o] :
( $true
!= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f256]) ).
thf(f256,plain,
( ! [X0: $i,X1: $i > $o] :
( $true
= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) )
<=> ( sepInPowerset = $true ) ),
inference(fool_elimination,[status(thm)],[f255]) ).
thf(f255,plain,
! [X0: $i,X1: $i > $o] :
( ( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) )
= sepInPowerset ),
inference(rectify,[status(thm)],[f99]) ).
thf(f99,axiom,
! [X3: $i,X0: $i > $o] :
( ( in
@ ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) )
@ ( powerset @ X3 ) )
= sepInPowerset ),
file('/export/starexec/sandbox/tmp/tmp.ChmJPLfBjb/DTF2THF_20010.p',sepInPowerset) ).
thf(f1958,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( $true
= ( subset @ X3 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1864]) ).
thf(f1864,plain,
! [X2: $i,X3: $i] :
( ( $true != $true )
| ( $true
= ( subset @ X3 @ X2 ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f1549,f1291]) ).
thf(f1291,plain,
powersetE1 = $true,
inference(cnf_transformation,[status(thm)],[f727]) ).
thf(f1549,plain,
! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) )
| ( powersetE1 != $true ) ),
inference(cnf_transformation,[status(thm)],[f980]) ).
thf(f980,plain,
( ( ( powersetE1 = $true )
| ( ( $true
!= ( subset @ sK271 @ sK270 ) )
& ( $true
= ( in @ sK271 @ ( powerset @ sK270 ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) )
| ( powersetE1 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK270,sK271])],[f978,f979]) ).
thf(f979,plain,
( ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) )
=> ( ( $true
!= ( subset @ sK271 @ sK270 ) )
& ( $true
= ( in @ sK271 @ ( powerset @ sK270 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f978,plain,
( ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
| ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) )
| ( powersetE1 != $true ) ) ),
inference(rectify,[status(thm)],[f977]) ).
thf(f977,plain,
( ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ X1 @ X0 ) )
& ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) )
| ( powersetE1 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f423]) ).
thf(f423,plain,
( ( powersetE1 = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ X1 @ X0 ) )
| ( $true
!= ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f184]) ).
thf(f184,plain,
( ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( powerset @ X0 ) ) )
=> ( $true
= ( subset @ X1 @ X0 ) ) )
<=> ( powersetE1 = $true ) ),
inference(fool_elimination,[status(thm)],[f183]) ).
thf(f183,plain,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f96]) ).
thf(f96,axiom,
( powersetE1
= ( ! [X3: $i,X4: $i] :
( ( in @ X4 @ ( powerset @ X3 ) )
=> ( subset @ X4 @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.ChmJPLfBjb/DTF2THF_20010.p',powersetE1) ).
thf(f1963,plain,
( $true
!= ( subset @ ( dsetconstr @ sK152 @ sK153 ) @ sK152 ) ),
inference(beta_eta_normalization,[status(thm)],[f1314]) ).
thf(f1314,plain,
( $true
!= ( subset
@ ( dsetconstr @ sK152
@ ^ [Y0: $i] : ( sK153 @ Y0 ) )
@ sK152 ) ),
inference(cnf_transformation,[status(thm)],[f727]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU581^1 : 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
% 0.15/0.34 % Computer : n018.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:27:31 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU581^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Preliminary Notions - Relations on Sets - Subsets
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : (! A:i.! phi:i>o.subset (dsetconstr A (^ x:i.phi x)) A)
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC083g [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.40 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 212 ( 99 unt; 112 typ; 99 def)
% 0.29/0.46 % Number of atoms : 535 ( 148 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 98 ( 5 avg)
% 0.29/0.46 % Number of connectives : 837 ( 29 ~; 5 |; 27 &; 521 @)
% 0.29/0.46 % ( 14 <=>; 241 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 105 ( 2 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 55 ( 55 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 115 ( 112 usr; 101 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 294 ( 30 ^; 236 !; 28 ?; 294 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=259
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu_type,type,
% 0.29/0.46 exu: ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu,definition,
% 0.29/0.46 ( exu
% 0.29/0.46 = ( ^ [Xphi: $i > $o] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx_type,type,
% 0.29/0.46 setextAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx,definition,
% 0.29/0.46 ( setextAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xx @ B ) )
% 0.29/0.46 => ( A = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset_type,type,
% 0.29/0.46 emptyset: $i ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx_type,type,
% 0.29/0.46 emptysetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx,definition,
% 0.29/0.46 ( emptysetAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin_type,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx_type,type,
% 0.29/0.46 setadjoinAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx,definition,
% 0.29/0.46 ( setadjoinAx
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 <=> ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset_type,type,
% 0.29/0.46 powerset: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx_type,type,
% 0.29/0.46 powersetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx,definition,
% 0.29/0.46 ( powersetAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 <=> ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion_type,type,
% 0.29/0.46 setunion: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx_type,type,
% 0.29/0.46 setunionAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx,definition,
% 0.29/0.46 ( setunionAx
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 <=> ? [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega_type,type,
% 0.29/0.46 omega: $i ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax_type,type,
% 0.29/0.46 omega0Ax: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax,definition,
% 0.29/0.46 ( omega0Ax
% 0.29/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx_type,type,
% 0.29/0.46 omegaSAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx,definition,
% 0.29/0.46 ( omegaSAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx_type,type,
% 0.29/0.46 omegaIndAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx,definition,
% 0.29/0.46 ( omegaIndAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( ( in @ emptyset @ A )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ omega )
% 0.29/0.46 & ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(replAx_type,type,
% 0.29/0.46 replAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(replAx,definition,
% 0.29/0.46 ( replAx
% 0.29/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 <=> ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx_type,type,
% 0.29/0.46 foundationAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx,definition,
% 0.29/0.46 ( foundationAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ( ( in @ B @ A )
% 0.29/0.46 & ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx_type,type,
% 0.29/0.46 wellorderingAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx,definition,
% 0.29/0.46 ( wellorderingAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ? [B: $i] :
% 0.29/0.46 ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) ) )
% 0.29/0.46 & ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xy @ A ) )
% 0.29/0.46 => ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ( ( in @ Xx @ C )
% 0.29/0.46 <=> ( in @ Xy @ C ) ) )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 & ! [C: $i,D: $i] :
% 0.29/0.46 ( ( ( in @ C @ B )
% 0.29/0.46 & ( in @ D @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ D ) )
% 0.29/0.46 | ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ D )
% 0.29/0.46 => ( in @ Xx @ C ) ) ) )
% 0.29/0.46 & ! [C: $i] :
% 0.29/0.46 ( ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.46 => ? [D: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ D @ B )
% 0.29/0.46 & ( in @ Xx @ C )
% 0.29/0.46 & ~ ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ D )
% 0.29/0.46 & ( in @ Xy @ C ) )
% 0.29/0.46 & ! [E: $i] :
% 0.29/0.46 ( ( in @ E @ B )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ E )
% 0.29/0.46 => ( in @ Xy @ D ) )
% 0.29/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr_type,type,
% 0.29/0.46 descr: ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(descrp_type,type,
% 0.29/0.46 descrp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descrp,definition,
% 0.29/0.46 ( descrp
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 @ ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr_type,type,
% 0.29/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI_type,type,
% 0.29/0.46 dsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI,definition,
% 0.29/0.46 ( dsetconstrI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL_type,type,
% 0.29/0.46 dsetconstrEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL,definition,
% 0.29/0.46 ( dsetconstrEL
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER_type,type,
% 0.29/0.46 dsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER,definition,
% 0.29/0.46 ( dsetconstrER
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1_type,type,
% 0.29/0.46 exuE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1,definition,
% 0.29/0.46 ( exuE1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set_type,type,
% 0.29/0.46 prop2set: $o > $i ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE_type,type,
% 0.29/0.46 prop2setE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE,definition,
% 0.29/0.46 ( prop2setE
% 0.29/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE_type,type,
% 0.29/0.46 emptysetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE,definition,
% 0.29/0.46 ( emptysetE
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse_type,type,
% 0.29/0.46 emptysetimpfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse,definition,
% 0.29/0.46 ( emptysetimpfalse
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => $false ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset_type,type,
% 0.29/0.46 notinemptyset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset,definition,
% 0.29/0.46 ( notinemptyset
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e_type,type,
% 0.29/0.46 exuE3e: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e,definition,
% 0.29/0.46 ( exuE3e
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setext_type,type,
% 0.29/0.46 setext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setext,definition,
% 0.29/0.46 ( setext
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI_type,type,
% 0.29/0.46 emptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI,definition,
% 0.29/0.46 ( emptyI
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty_type,type,
% 0.29/0.46 noeltsimpempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty,definition,
% 0.29/0.46 ( noeltsimpempty
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta_type,type,
% 0.29/0.46 setbeta: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta,definition,
% 0.29/0.46 ( setbeta
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty_type,type,
% 0.29/0.46 nonempty: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty,definition,
% 0.29/0.46 ( nonempty
% 0.29/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1_type,type,
% 0.29/0.46 nonemptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1,definition,
% 0.29/0.46 ( nonemptyE1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI_type,type,
% 0.29/0.46 nonemptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI,definition,
% 0.29/0.46 ( nonemptyI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( nonempty
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1_type,type,
% 0.29/0.46 nonemptyI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1,definition,
% 0.29/0.46 ( nonemptyI1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL_type,type,
% 0.29/0.46 setadjoinIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL,definition,
% 0.29/0.46 ( setadjoinIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty_type,type,
% 0.29/0.46 emptyinunitempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty,definition,
% 0.29/0.46 ( emptyinunitempty
% 0.29/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR_type,type,
% 0.29/0.46 setadjoinIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR,definition,
% 0.29/0.46 ( setadjoinIR
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE_type,type,
% 0.29/0.46 setadjoinE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinE,definition,
% 0.29/0.46 ( setadjoinE
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ( ( Xy = Xx )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => ( ( ( in @ Xy @ A )
% 0.29/0.46 => Xphi )
% 0.29/0.46 => Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr_type,type,
% 0.29/0.46 setadjoinOr: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinOr,definition,
% 0.29/0.46 ( setadjoinOr
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 => ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq_type,type,
% 0.29/0.46 setoftrueEq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setoftrueEq,definition,
% 0.29/0.46 ( setoftrueEq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : $true )
% 0.29/0.46 = A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI_type,type,
% 0.29/0.46 powersetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI,definition,
% 0.29/0.46 ( powersetI
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset_type,type,
% 0.29/0.46 emptyinPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinPowerset,definition,
% 0.29/0.46 ( emptyinPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset_type,type,
% 0.29/0.46 emptyInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyInPowerset,definition,
% 0.29/0.46 ( emptyInPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE_type,type,
% 0.29/0.46 powersetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE,definition,
% 0.29/0.46 ( powersetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI_type,type,
% 0.29/0.46 setunionI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionI,definition,
% 0.29/0.46 ( setunionI
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE_type,type,
% 0.29/0.46 setunionE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionE,definition,
% 0.29/0.46 ( setunionE
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 => ! [Xphi: $o] :
% 0.29/0.46 ( ! [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( ( in @ B @ A )
% 0.29/0.46 => Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU_type,type,
% 0.29/0.46 subPowSU: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subPowSU,definition,
% 0.29/0.46 ( subPowSU
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2_type,type,
% 0.29/0.46 exuE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE2,definition,
% 0.29/0.46 ( exuE2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness_type,type,
% 0.29/0.46 nonemptyImpWitness: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyImpWitness,definition,
% 0.29/0.46 ( nonemptyImpWitness
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & $true ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit_type,type,
% 0.29/0.46 uniqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(uniqinunit,definition,
% 0.29/0.46 ( uniqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton_type,type,
% 0.29/0.46 notinsingleton: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinsingleton,definition,
% 0.29/0.46 ( notinsingleton
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx != Xy )
% 0.29/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit_type,type,
% 0.29/0.46 eqinunit: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqinunit,definition,
% 0.29/0.46 ( eqinunit
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch_type,type,
% 0.29/0.46 singletonsswitch: $o ).
% 0.29/0.46
% 0.29/0.46 thf(singletonsswitch,definition,
% 0.29/0.46 ( singletonsswitch
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE_type,type,
% 0.29/0.46 upairsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetE,definition,
% 0.29/0.46 ( upairsetE
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.46 => ( ( Xz = Xx )
% 0.29/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL_type,type,
% 0.29/0.46 upairsetIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIL,definition,
% 0.29/0.46 ( upairsetIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR_type,type,
% 0.29/0.46 upairsetIR: $o ).
% 0.29/0.46
% 0.29/0.46 thf(upairsetIR,definition,
% 0.29/0.46 ( upairsetIR
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1_type,type,
% 0.29/0.46 emptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyE1,definition,
% 0.29/0.46 ( emptyE1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = emptyset )
% 0.29/0.46 => $false ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall_type,type,
% 0.29/0.46 vacuousDall: $o ).
% 0.29/0.46
% 0.29/0.46 thf(vacuousDall,definition,
% 0.29/0.46 ( vacuousDall
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1_type,type,
% 0.29/0.46 quantDeMorgan1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan1,definition,
% 0.29/0.46 ( quantDeMorgan1
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2_type,type,
% 0.29/0.46 quantDeMorgan2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan2,definition,
% 0.29/0.46 ( quantDeMorgan2
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3_type,type,
% 0.29/0.46 quantDeMorgan3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan3,definition,
% 0.29/0.46 ( quantDeMorgan3
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4_type,type,
% 0.29/0.46 quantDeMorgan4: $o ).
% 0.29/0.46
% 0.29/0.46 thf(quantDeMorgan4,definition,
% 0.29/0.46 ( quantDeMorgan4
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) )
% 0.29/0.46 => ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI_type,type,
% 0.29/0.46 prop2setI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setI,definition,
% 0.29/0.46 ( prop2setI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(set2prop_type,type,
% 0.29/0.46 set2prop: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI_type,type,
% 0.29/0.46 prop2set2propI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set2propI,definition,
% 0.29/0.46 ( prop2set2propI
% 0.29/0.46 = ( ! [Xphi: $o] :
% 0.29/0.46 ( Xphi
% 0.29/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE_type,type,
% 0.29/0.46 notdexE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdexE,definition,
% 0.29/0.46 ( notdexE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE_type,type,
% 0.29/0.46 notdallE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notdallE,definition,
% 0.29/0.46 ( notdallE
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( ~ ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1_type,type,
% 0.29/0.46 exuI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI1,definition,
% 0.29/0.46 ( exuI1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3_type,type,
% 0.29/0.46 exuI3: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI3,definition,
% 0.29/0.46 ( exuI3
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2_type,type,
% 0.29/0.46 exuI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuI2,definition,
% 0.29/0.46 ( exuI2
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ? [Xx: $i] :
% 0.29/0.46 ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 <=> ( Xy = Xx ) )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP_type,type,
% 0.29/0.46 inCongP: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inCongP,definition,
% 0.29/0.46 ( inCongP
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong_type,type,
% 0.29/0.46 in__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(in__Cong,definition,
% 0.29/0.46 ( in__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u_type,type,
% 0.29/0.46 exuE3u: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3u,definition,
% 0.29/0.46 ( exuE3u
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong_type,type,
% 0.29/0.46 exu__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu__Cong,definition,
% 0.29/0.46 ( exu__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 <=> ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong_type,type,
% 0.29/0.46 emptyset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset__Cong,definition,
% 0.29/0.46 ( emptyset__Cong
% 0.29/0.46 = ( emptyset = emptyset ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong_type,type,
% 0.29/0.46 setadjoin__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin__Cong,definition,
% 0.29/0.46 ( setadjoin__Cong
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ! [Xz: $i,Xu: $i] :
% 0.29/0.46 ( ( Xz = Xu )
% 0.29/0.46 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong_type,type,
% 0.29/0.46 powerset__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powerset__Cong,definition,
% 0.29/0.46 ( powerset__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( powerset @ A )
% 0.29/0.46 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong_type,type,
% 0.29/0.46 setunion__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunion__Cong,definition,
% 0.29/0.46 ( setunion__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( ( setunion @ A )
% 0.29/0.46 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong_type,type,
% 0.29/0.46 omega__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega__Cong,definition,
% 0.29/0.46 ( omega__Cong
% 0.29/0.46 = ( omega = omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu_type,type,
% 0.29/0.46 exuEu: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuEu,definition,
% 0.29/0.46 ( exuEu
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 => ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong_type,type,
% 0.29/0.46 descr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descr__Cong,definition,
% 0.29/0.46 ( descr__Cong
% 0.29/0.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.46 => ( ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong_type,type,
% 0.29/0.46 dsetconstr__Cong: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr__Cong,definition,
% 0.29/0.46 ( dsetconstr__Cong
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ B )
% 0.29/0.46 => ( ( Xx = Xy )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.46 => ( ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 = ( dsetconstr @ B
% 0.29/0.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset_type,type,
% 0.29/0.46 subset: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(disjoint_type,type,
% 0.29/0.46 disjoint: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(setsmeet_type,type,
% 0.29/0.46 setsmeet: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1_type,type,
% 0.29/0.46 subsetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI1,definition,
% 0.29/0.46 ( subsetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2_type,type,
% 0.29/0.46 eqimpsubset2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset2,definition,
% 0.29/0.46 ( eqimpsubset2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1_type,type,
% 0.29/0.46 eqimpsubset1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(eqimpsubset1,definition,
% 0.29/0.46 ( eqimpsubset1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( A = B )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2_type,type,
% 0.29/0.46 subsetI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetI2,definition,
% 0.29/0.46 ( subsetI2
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset_type,type,
% 0.29/0.46 emptysetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetsubset,definition,
% 0.29/0.46 ( emptysetsubset
% 0.29/0.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE_type,type,
% 0.29/0.46 subsetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE,definition,
% 0.29/0.46 ( subsetE
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2_type,type,
% 0.29/0.46 subsetE2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetE2,definition,
% 0.29/0.46 ( subsetE2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI_type,type,
% 0.29/0.46 notsubsetI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notsubsetI,definition,
% 0.29/0.46 ( notsubsetI
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1_type,type,
% 0.29/0.46 notequalI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI1,definition,
% 0.29/0.46 ( notequalI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ~ ( subset @ A @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2_type,type,
% 0.29/0.46 notequalI2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notequalI2,definition,
% 0.29/0.46 ( notequalI2
% 0.29/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ~ ( in @ Xx @ B )
% 0.29/0.46 => ( A != B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl_type,type,
% 0.29/0.46 subsetRefl: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetRefl,definition,
% 0.29/0.46 ( subsetRefl
% 0.29/0.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans_type,type,
% 0.29/0.46 subsetTrans: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetTrans,definition,
% 0.29/0.46 ( subsetTrans
% 0.29/0.46 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ C )
% 0.29/0.46 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub_type,type,
% 0.29/0.46 setadjoinSub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub,definition,
% 0.29/0.46 ( setadjoinSub
% 0.29/0.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2_type,type,
% 0.29/0.46 setadjoinSub2: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinSub2,definition,
% 0.29/0.46 ( setadjoinSub2
% 0.29/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset_type,type,
% 0.29/0.46 subset2powerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subset2powerset,definition,
% 0.29/0.46 ( subset2powerset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub_type,type,
% 0.29/0.46 setextsub: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextsub,definition,
% 0.29/0.46 ( setextsub
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( ( subset @ B @ A )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq_type,type,
% 0.29/0.46 subsetemptysetimpeq: $o ).
% 0.29/0.46
% 0.29/0.46 thf(subsetemptysetimpeq,definition,
% 0.29/0.46 ( subsetemptysetimpeq
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( subset @ A @ emptyset )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1_type,type,
% 0.29/0.46 powersetI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetI1,definition,
% 0.29/0.46 ( powersetI1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ B @ A )
% 0.29/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1_type,type,
% 0.29/0.46 powersetE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetE1,definition,
% 0.29/0.46 ( powersetE1
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset_type,type,
% 0.29/0.46 inPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(inPowerset,definition,
% 0.29/0.46 ( inPowerset
% 0.29/0.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset_type,type,
% 0.29/0.46 powersetsubset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetsubset,definition,
% 0.29/0.46 ( powersetsubset
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( subset @ A @ B )
% 0.29/0.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset_type,type,
% 0.29/0.46 sepInPowerset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(sepInPowerset,definition,
% 0.29/0.46 ( sepInPowerset
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( in
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(sepSubset,conjecture,
% 0.29/0.46 ( setextAx
% 0.29/0.46 => ( emptysetAx
% 0.29/0.46 => ( setadjoinAx
% 0.29/0.46 => ( powersetAx
% 0.29/0.46 => ( setunionAx
% 0.29/0.46 => ( omega0Ax
% 0.29/0.46 => ( omegaSAx
% 0.29/0.46 => ( omegaIndAx
% 0.29/0.46 => ( replAx
% 0.29/0.46 => ( foundationAx
% 0.29/0.46 => ( wellorderingAx
% 0.29/0.46 => ( descrp
% 0.29/0.46 => ( dsetconstrI
% 0.29/0.46 => ( dsetconstrEL
% 0.29/0.46 => ( dsetconstrER
% 0.29/0.46 => ( exuE1
% 0.29/0.46 => ( prop2setE
% 0.29/0.46 => ( emptysetE
% 0.29/0.46 => ( emptysetimpfalse
% 0.29/0.46 => ( notinemptyset
% 0.29/0.46 => ( exuE3e
% 0.29/0.46 => ( setext
% 0.29/0.46 => ( emptyI
% 0.29/0.46 => ( noeltsimpempty
% 0.29/0.46 => ( setbeta
% 0.29/0.46 => ( nonemptyE1
% 0.29/0.46 => ( nonemptyI
% 0.29/0.46 => ( nonemptyI1
% 0.29/0.46 => ( setadjoinIL
% 0.29/0.46 => ( emptyinunitempty
% 0.29/0.46 => ( setadjoinIR
% 0.29/0.46 => ( setadjoinE
% 0.29/0.46 => ( setadjoinOr
% 0.29/0.46 => ( setoftrueEq
% 0.29/0.46 => ( powersetI
% 0.29/0.46 => ( emptyinPowerset
% 0.29/0.46 => ( emptyInPowerset
% 0.29/0.46 => ( powersetE
% 0.29/0.46 => ( setunionI
% 0.29/0.46 => ( setunionE
% 0.29/0.46 => ( subPowSU
% 0.29/0.46 => ( exuE2
% 0.29/0.46 => ( nonemptyImpWitness
% 0.29/0.46 => ( uniqinunit
% 0.29/0.46 => ( notinsingleton
% 0.29/0.46 => ( eqinunit
% 0.29/0.46 => ( singletonsswitch
% 0.29/0.46 => ( upairsetE
% 0.29/0.46 => ( upairsetIL
% 0.29/0.46 => ( upairsetIR
% 0.29/0.46 => ( emptyE1
% 0.29/0.46 => ( vacuousDall
% 0.29/0.46 => ( quantDeMorgan1
% 0.29/0.46 => ( quantDeMorgan2
% 0.29/0.46 => ( quantDeMorgan3
% 0.29/0.46 => ( quantDeMorgan4
% 0.29/0.46 => ( prop2setI
% 0.29/0.46 => ( prop2set2propI
% 0.29/0.46 => ( notdexE
% 0.29/0.46 => ( notdallE
% 0.29/0.46 => ( exuI1
% 0.29/0.46 => ( exuI3
% 0.29/0.46 => ( exuI2
% 0.29/0.46 => ( inCongP
% 0.29/0.46 => ( in__Cong
% 0.29/0.46 => ( exuE3u
% 0.29/0.46 => ( exu__Cong
% 0.29/0.46 => ( emptyset__Cong
% 0.29/0.46 => ( setadjoin__Cong
% 0.29/0.46 => ( powerset__Cong
% 0.29/0.46 => ( setunion__Cong
% 0.29/0.46 => ( omega__Cong
% 0.29/0.46 => ( exuEu
% 0.29/0.46 => ( descr__Cong
% 0.29/0.46 => ( dsetconstr__Cong
% 0.29/0.46 => ( subsetI1
% 0.29/0.46 => ( eqimpsubset2
% 0.29/0.46 => ( eqimpsubset1
% 0.29/0.46 => ( subsetI2
% 0.29/0.46 => ( emptysetsubset
% 0.29/0.46 => ( subsetE
% 0.29/0.46 => ( subsetE2
% 0.29/0.46 => ( notsubsetI
% 0.29/0.46 => ( notequalI1
% 0.29/0.46 => ( notequalI2
% 0.29/0.46 => ( subsetRefl
% 0.29/0.46 => ( subsetTrans
% 0.29/0.46 => ( setadjoinSub
% 0.29/0.46 => ( setadjoinSub2
% 0.29/0.46 => ( subset2powerset
% 0.29/0.46 => ( setextsub
% 0.29/0.46 => ( subsetemptysetimpeq
% 0.29/0.46 => ( powersetI1
% 0.29/0.46 => ( powersetE1
% 0.29/0.46 => ( inPowerset
% 0.29/0.46 => ( powersetsubset
% 0.29/0.46 => ( sepInPowerset
% 0.29/0.46 => ! [A: $i,Xphi: $i > $o] :
% 0.29/0.46 ( subset
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 ------------------------
% 2.29/1.45 ---- Embedded in THF ---
% 2.29/1.45 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.29/1.45 %%% Generated on Tue Feb 24 12:27:32 EST 2026
% 2.29/1.45 %%% using '$$dhol' embedding, version 1.3.0.
% 2.29/1.45 %%% Logic specification used:
% 2.29/1.45 %%% thf(spec, logic, $$dhol).
% 2.29/1.45
% 2.29/1.45 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.ChmJPLfBjb/DTF2DTF20010.p
% See solution above
% 2.29/1.45 ------------------------
% 2.29/1.46 ---- Cleaned THF ---
% 2.29/1.46 thf(in_type,type,
% 2.29/1.46 in: $i > $i > $o ).
% 2.29/1.46
% 2.29/1.46 thf(exu_type,type,
% 2.29/1.46 exu: ( $i > $o ) > $o ).
% 2.29/1.46
% 2.29/1.46 thf(exu,definition,
% 2.29/1.46 ( exu
% 2.29/1.46 = ( ^ [Xphi: $i > $o] :
% 2.29/1.46 ? [Xx: $i] :
% 2.29/1.46 ( ( Xphi @ Xx )
% 2.29/1.46 & ! [Xy: $i] :
% 2.29/1.46 ( ( Xphi @ Xy )
% 2.29/1.46 => ( Xx = Xy ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setextAx_type,type,
% 2.29/1.46 setextAx: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setextAx,definition,
% 2.29/1.46 ( setextAx
% 2.29/1.46 = ( ! [A: $i,B: $i] :
% 2.29/1.46 ( ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ A )
% 2.29/1.46 <=> ( in @ Xx @ B ) )
% 2.29/1.46 => ( A = B ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(emptyset_type,type,
% 2.29/1.46 emptyset: $i ).
% 2.29/1.46
% 2.29/1.46 thf(emptysetAx_type,type,
% 2.29/1.46 emptysetAx: $o ).
% 2.29/1.46
% 2.29/1.46 thf(emptysetAx,definition,
% 2.29/1.46 ( emptysetAx
% 2.29/1.46 = ( ! [Xx: $i] :
% 2.29/1.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoin_type,type,
% 2.29/1.46 setadjoin: $i > $i > $i ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoinAx_type,type,
% 2.29/1.46 setadjoinAx: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoinAx,definition,
% 2.29/1.46 ( setadjoinAx
% 2.29/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.29/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.29/1.46 <=> ( ( Xy = Xx )
% 2.29/1.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(powerset_type,type,
% 2.29/1.46 powerset: $i > $i ).
% 2.29/1.46
% 2.29/1.46 thf(powersetAx_type,type,
% 2.29/1.46 powersetAx: $o ).
% 2.29/1.46
% 2.29/1.46 thf(powersetAx,definition,
% 2.29/1.46 ( powersetAx
% 2.29/1.46 = ( ! [A: $i,B: $i] :
% 2.29/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.29/1.46 <=> ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ B )
% 2.29/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setunion_type,type,
% 2.29/1.46 setunion: $i > $i ).
% 2.29/1.46
% 2.29/1.46 thf(setunionAx_type,type,
% 2.29/1.46 setunionAx: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setunionAx,definition,
% 2.29/1.46 ( setunionAx
% 2.29/1.46 = ( ! [A: $i,Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ ( setunion @ A ) )
% 2.29/1.46 <=> ? [B: $i] :
% 2.29/1.46 ( ( in @ Xx @ B )
% 2.29/1.46 & ( in @ B @ A ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(omega_type,type,
% 2.29/1.46 omega: $i ).
% 2.29/1.46
% 2.29/1.46 thf(omega0Ax_type,type,
% 2.29/1.46 omega0Ax: $o ).
% 2.29/1.46
% 2.29/1.46 thf(omega0Ax,definition,
% 2.29/1.46 ( omega0Ax
% 2.29/1.46 = ( in @ emptyset @ omega ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(omegaSAx_type,type,
% 2.29/1.46 omegaSAx: $o ).
% 2.29/1.46
% 2.29/1.46 thf(omegaSAx,definition,
% 2.29/1.46 ( omegaSAx
% 2.29/1.46 = ( ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ omega )
% 2.29/1.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(omegaIndAx_type,type,
% 2.29/1.46 omegaIndAx: $o ).
% 2.29/1.46
% 2.29/1.46 thf(omegaIndAx,definition,
% 2.29/1.46 ( omegaIndAx
% 2.29/1.46 = ( ! [A: $i] :
% 2.29/1.46 ( ( ( in @ emptyset @ A )
% 2.29/1.46 & ! [Xx: $i] :
% 2.29/1.46 ( ( ( in @ Xx @ omega )
% 2.29/1.46 & ( in @ Xx @ A ) )
% 2.29/1.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.29/1.46 => ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ omega )
% 2.29/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(replAx_type,type,
% 2.29/1.46 replAx: $o ).
% 2.29/1.46
% 2.29/1.46 thf(replAx,definition,
% 2.29/1.46 ( replAx
% 2.29/1.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.29/1.46 ( ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ A )
% 2.29/1.46 => ( exu
% 2.29/1.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.29/1.46 => ? [B: $i] :
% 2.29/1.46 ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ B )
% 2.29/1.46 <=> ? [Xy: $i] :
% 2.29/1.46 ( ( in @ Xy @ A )
% 2.29/1.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(foundationAx_type,type,
% 2.29/1.46 foundationAx: $o ).
% 2.29/1.46
% 2.29/1.46 thf(foundationAx,definition,
% 2.29/1.46 ( foundationAx
% 2.29/1.46 = ( ! [A: $i] :
% 2.29/1.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.29/1.46 => ? [B: $i] :
% 2.29/1.46 ( ( in @ B @ A )
% 2.29/1.46 & ~ ? [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ B )
% 2.29/1.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(wellorderingAx_type,type,
% 2.29/1.46 wellorderingAx: $o ).
% 2.29/1.46
% 2.29/1.46 thf(wellorderingAx,definition,
% 2.29/1.46 ( wellorderingAx
% 2.29/1.46 = ( ! [A: $i] :
% 2.29/1.46 ? [B: $i] :
% 2.29/1.46 ( ! [C: $i] :
% 2.29/1.46 ( ( in @ C @ B )
% 2.29/1.46 => ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ C )
% 2.29/1.46 => ( in @ Xx @ A ) ) )
% 2.29/1.46 & ! [Xx: $i,Xy: $i] :
% 2.29/1.46 ( ( ( in @ Xx @ A )
% 2.29/1.46 & ( in @ Xy @ A ) )
% 2.29/1.46 => ( ! [C: $i] :
% 2.29/1.46 ( ( in @ C @ B )
% 2.29/1.46 => ( ( in @ Xx @ C )
% 2.29/1.46 <=> ( in @ Xy @ C ) ) )
% 2.29/1.46 => ( Xx = Xy ) ) )
% 2.29/1.46 & ! [C: $i,D: $i] :
% 2.29/1.46 ( ( ( in @ C @ B )
% 2.29/1.46 & ( in @ D @ B ) )
% 2.29/1.46 => ( ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ C )
% 2.29/1.46 => ( in @ Xx @ D ) )
% 2.29/1.46 | ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ D )
% 2.29/1.46 => ( in @ Xx @ C ) ) ) )
% 2.29/1.46 & ! [C: $i] :
% 2.29/1.46 ( ( ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ C )
% 2.29/1.46 => ( in @ Xx @ A ) )
% 2.29/1.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.29/1.46 => ? [D: $i,Xx: $i] :
% 2.29/1.46 ( ( in @ D @ B )
% 2.29/1.46 & ( in @ Xx @ C )
% 2.29/1.46 & ~ ? [Xy: $i] :
% 2.29/1.46 ( ( in @ Xy @ D )
% 2.29/1.46 & ( in @ Xy @ C ) )
% 2.29/1.46 & ! [E: $i] :
% 2.29/1.46 ( ( in @ E @ B )
% 2.29/1.46 => ( ! [Xy: $i] :
% 2.29/1.46 ( ( in @ Xy @ E )
% 2.29/1.46 => ( in @ Xy @ D ) )
% 2.29/1.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(descr_type,type,
% 2.29/1.46 descr: ( $i > $o ) > $i ).
% 2.29/1.46
% 2.29/1.46 thf(descrp_type,type,
% 2.29/1.46 descrp: $o ).
% 2.29/1.46
% 2.29/1.46 thf(descrp,definition,
% 2.29/1.46 ( descrp
% 2.29/1.46 = ( ! [Xphi: $i > $o] :
% 2.29/1.46 ( ( exu
% 2.29/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.46 => ( Xphi
% 2.29/1.46 @ ( descr
% 2.29/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(dsetconstr_type,type,
% 2.29/1.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.29/1.46
% 2.29/1.46 thf(dsetconstrI_type,type,
% 2.29/1.46 dsetconstrI: $o ).
% 2.29/1.46
% 2.29/1.46 thf(dsetconstrI,definition,
% 2.29/1.46 ( dsetconstrI
% 2.29/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ A )
% 2.29/1.46 => ( ( Xphi @ Xx )
% 2.29/1.46 => ( in @ Xx
% 2.29/1.46 @ ( dsetconstr @ A
% 2.29/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(dsetconstrEL_type,type,
% 2.29/1.46 dsetconstrEL: $o ).
% 2.29/1.46
% 2.29/1.46 thf(dsetconstrEL,definition,
% 2.29/1.46 ( dsetconstrEL
% 2.29/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.29/1.46 ( ( in @ Xx
% 2.29/1.46 @ ( dsetconstr @ A
% 2.29/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.29/1.46 => ( in @ Xx @ A ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(dsetconstrER_type,type,
% 2.29/1.46 dsetconstrER: $o ).
% 2.29/1.46
% 2.29/1.46 thf(dsetconstrER,definition,
% 2.29/1.46 ( dsetconstrER
% 2.29/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.29/1.46 ( ( in @ Xx
% 2.29/1.46 @ ( dsetconstr @ A
% 2.29/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.29/1.46 => ( Xphi @ Xx ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(exuE1_type,type,
% 2.29/1.46 exuE1: $o ).
% 2.29/1.46
% 2.29/1.46 thf(exuE1,definition,
% 2.29/1.46 ( exuE1
% 2.29/1.46 = ( ! [Xphi: $i > $o] :
% 2.29/1.46 ( ( exu
% 2.29/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.46 => ? [Xx: $i] :
% 2.29/1.46 ( ( Xphi @ Xx )
% 2.29/1.46 & ! [Xy: $i] :
% 2.29/1.46 ( ( Xphi @ Xy )
% 2.29/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(prop2set_type,type,
% 2.29/1.46 prop2set: $o > $i ).
% 2.29/1.46
% 2.29/1.46 thf(prop2setE_type,type,
% 2.29/1.46 prop2setE: $o ).
% 2.29/1.46
% 2.29/1.46 thf(prop2setE,definition,
% 2.29/1.46 ( prop2setE
% 2.29/1.46 = ( ! [Xphi: $o,Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.29/1.46 => Xphi ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(emptysetE_type,type,
% 2.29/1.46 emptysetE: $o ).
% 2.29/1.46
% 2.29/1.46 thf(emptysetE,definition,
% 2.29/1.46 ( emptysetE
% 2.29/1.46 = ( ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ emptyset )
% 2.29/1.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(emptysetimpfalse_type,type,
% 2.29/1.46 emptysetimpfalse: $o ).
% 2.29/1.46
% 2.29/1.46 thf(emptysetimpfalse,definition,
% 2.29/1.46 ( emptysetimpfalse
% 2.29/1.46 = ( ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ emptyset )
% 2.29/1.46 => $false ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(notinemptyset_type,type,
% 2.29/1.46 notinemptyset: $o ).
% 2.29/1.46
% 2.29/1.46 thf(notinemptyset,definition,
% 2.29/1.46 ( notinemptyset
% 2.29/1.46 = ( ! [Xx: $i] :
% 2.29/1.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(exuE3e_type,type,
% 2.29/1.46 exuE3e: $o ).
% 2.29/1.46
% 2.29/1.46 thf(exuE3e,definition,
% 2.29/1.46 ( exuE3e
% 2.29/1.46 = ( ! [Xphi: $i > $o] :
% 2.29/1.46 ( ( exu
% 2.29/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setext_type,type,
% 2.29/1.46 setext: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setext,definition,
% 2.29/1.46 ( setext
% 2.29/1.46 = ( ! [A: $i,B: $i] :
% 2.29/1.46 ( ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ A )
% 2.29/1.46 => ( in @ Xx @ B ) )
% 2.29/1.46 => ( ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ B )
% 2.29/1.46 => ( in @ Xx @ A ) )
% 2.29/1.46 => ( A = B ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(emptyI_type,type,
% 2.29/1.46 emptyI: $o ).
% 2.29/1.46
% 2.29/1.46 thf(emptyI,definition,
% 2.29/1.46 ( emptyI
% 2.29/1.46 = ( ! [A: $i] :
% 2.29/1.46 ( ! [Xx: $i] :
% 2.29/1.46 ~ ( in @ Xx @ A )
% 2.29/1.46 => ( A = emptyset ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(noeltsimpempty_type,type,
% 2.29/1.46 noeltsimpempty: $o ).
% 2.29/1.46
% 2.29/1.46 thf(noeltsimpempty,definition,
% 2.29/1.46 ( noeltsimpempty
% 2.29/1.46 = ( ! [A: $i] :
% 2.29/1.46 ( ! [Xx: $i] :
% 2.29/1.46 ~ ( in @ Xx @ A )
% 2.29/1.46 => ( A = emptyset ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setbeta_type,type,
% 2.29/1.46 setbeta: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setbeta,definition,
% 2.29/1.46 ( setbeta
% 2.29/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ A )
% 2.29/1.46 => ( ( in @ Xx
% 2.29/1.46 @ ( dsetconstr @ A
% 2.29/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.29/1.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(nonempty_type,type,
% 2.29/1.46 nonempty: $i > $o ).
% 2.29/1.46
% 2.29/1.46 thf(nonempty,definition,
% 2.29/1.46 ( nonempty
% 2.29/1.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(nonemptyE1_type,type,
% 2.29/1.46 nonemptyE1: $o ).
% 2.29/1.46
% 2.29/1.46 thf(nonemptyE1,definition,
% 2.29/1.46 ( nonemptyE1
% 2.29/1.46 = ( ! [A: $i] :
% 2.29/1.46 ( ( nonempty @ A )
% 2.29/1.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(nonemptyI_type,type,
% 2.29/1.46 nonemptyI: $o ).
% 2.29/1.46
% 2.29/1.46 thf(nonemptyI,definition,
% 2.29/1.46 ( nonemptyI
% 2.29/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ A )
% 2.29/1.46 => ( ( Xphi @ Xx )
% 2.29/1.46 => ( nonempty
% 2.29/1.46 @ ( dsetconstr @ A
% 2.29/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(nonemptyI1_type,type,
% 2.29/1.46 nonemptyI1: $o ).
% 2.29/1.46
% 2.29/1.46 thf(nonemptyI1,definition,
% 2.29/1.46 ( nonemptyI1
% 2.29/1.46 = ( ! [A: $i] :
% 2.29/1.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.29/1.46 => ( nonempty @ A ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoinIL_type,type,
% 2.29/1.46 setadjoinIL: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoinIL,definition,
% 2.29/1.46 ( setadjoinIL
% 2.29/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(emptyinunitempty_type,type,
% 2.29/1.46 emptyinunitempty: $o ).
% 2.29/1.46
% 2.29/1.46 thf(emptyinunitempty,definition,
% 2.29/1.46 ( emptyinunitempty
% 2.29/1.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoinIR_type,type,
% 2.29/1.46 setadjoinIR: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoinIR,definition,
% 2.29/1.46 ( setadjoinIR
% 2.29/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.29/1.46 ( ( in @ Xy @ A )
% 2.29/1.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoinE_type,type,
% 2.29/1.46 setadjoinE: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoinE,definition,
% 2.29/1.46 ( setadjoinE
% 2.29/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.29/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.29/1.46 => ! [Xphi: $o] :
% 2.29/1.46 ( ( ( Xy = Xx )
% 2.29/1.46 => Xphi )
% 2.29/1.46 => ( ( ( in @ Xy @ A )
% 2.29/1.46 => Xphi )
% 2.29/1.46 => Xphi ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoinOr_type,type,
% 2.29/1.46 setadjoinOr: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setadjoinOr,definition,
% 2.29/1.46 ( setadjoinOr
% 2.29/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.29/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.29/1.46 => ( ( Xy = Xx )
% 2.29/1.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setoftrueEq_type,type,
% 2.29/1.46 setoftrueEq: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setoftrueEq,definition,
% 2.29/1.46 ( setoftrueEq
% 2.29/1.46 = ( ! [A: $i] :
% 2.29/1.46 ( ( dsetconstr @ A
% 2.29/1.46 @ ^ [Xx: $i] : $true )
% 2.29/1.46 = A ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(powersetI_type,type,
% 2.29/1.46 powersetI: $o ).
% 2.29/1.46
% 2.29/1.46 thf(powersetI,definition,
% 2.29/1.46 ( powersetI
% 2.29/1.46 = ( ! [A: $i,B: $i] :
% 2.29/1.46 ( ! [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ B )
% 2.29/1.46 => ( in @ Xx @ A ) )
% 2.29/1.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(emptyinPowerset_type,type,
% 2.29/1.46 emptyinPowerset: $o ).
% 2.29/1.46
% 2.29/1.46 thf(emptyinPowerset,definition,
% 2.29/1.46 ( emptyinPowerset
% 2.29/1.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(emptyInPowerset_type,type,
% 2.29/1.46 emptyInPowerset: $o ).
% 2.29/1.46
% 2.29/1.46 thf(emptyInPowerset,definition,
% 2.29/1.46 ( emptyInPowerset
% 2.29/1.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(powersetE_type,type,
% 2.29/1.46 powersetE: $o ).
% 2.29/1.46
% 2.29/1.46 thf(powersetE,definition,
% 2.29/1.46 ( powersetE
% 2.29/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.29/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.29/1.46 => ( ( in @ Xx @ B )
% 2.29/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setunionI_type,type,
% 2.29/1.46 setunionI: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setunionI,definition,
% 2.29/1.46 ( setunionI
% 2.29/1.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.29/1.46 ( ( in @ Xx @ B )
% 2.29/1.46 => ( ( in @ B @ A )
% 2.29/1.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(setunionE_type,type,
% 2.29/1.46 setunionE: $o ).
% 2.29/1.46
% 2.29/1.46 thf(setunionE,definition,
% 2.29/1.46 ( setunionE
% 2.29/1.46 = ( ! [A: $i,Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ ( setunion @ A ) )
% 2.29/1.46 => ! [Xphi: $o] :
% 2.29/1.46 ( ! [B: $i] :
% 2.29/1.46 ( ( in @ Xx @ B )
% 2.29/1.46 => ( ( in @ B @ A )
% 2.29/1.46 => Xphi ) )
% 2.29/1.46 => Xphi ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(subPowSU_type,type,
% 2.29/1.46 subPowSU: $o ).
% 2.29/1.46
% 2.29/1.46 thf(subPowSU,definition,
% 2.29/1.46 ( subPowSU
% 2.29/1.46 = ( ! [A: $i,Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ A )
% 2.29/1.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(exuE2_type,type,
% 2.29/1.46 exuE2: $o ).
% 2.29/1.46
% 2.29/1.46 thf(exuE2,definition,
% 2.29/1.46 ( exuE2
% 2.29/1.46 = ( ! [Xphi: $i > $o] :
% 2.29/1.46 ( ( exu
% 2.29/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.46 => ? [Xx: $i] :
% 2.29/1.46 ! [Xy: $i] :
% 2.29/1.46 ( ( Xphi @ Xy )
% 2.29/1.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(nonemptyImpWitness_type,type,
% 2.29/1.46 nonemptyImpWitness: $o ).
% 2.29/1.46
% 2.29/1.46 thf(nonemptyImpWitness,definition,
% 2.29/1.46 ( nonemptyImpWitness
% 2.29/1.46 = ( ! [A: $i] :
% 2.29/1.46 ( ( nonempty @ A )
% 2.29/1.46 => ? [Xx: $i] :
% 2.29/1.46 ( ( in @ Xx @ A )
% 2.29/1.46 & $true ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(uniqinunit_type,type,
% 2.29/1.46 uniqinunit: $o ).
% 2.29/1.46
% 2.29/1.46 thf(uniqinunit,definition,
% 2.29/1.46 ( uniqinunit
% 2.29/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.29/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.29/1.46 => ( Xx = Xy ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(notinsingleton_type,type,
% 2.29/1.46 notinsingleton: $o ).
% 2.29/1.46
% 2.29/1.46 thf(notinsingleton,definition,
% 2.29/1.46 ( notinsingleton
% 2.29/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.29/1.46 ( ( Xx != Xy )
% 2.29/1.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.29/1.46
% 2.29/1.46 thf(eqinunit_type,type,
% 2.29/1.47 eqinunit: $o ).
% 2.29/1.47
% 2.29/1.47 thf(eqinunit,definition,
% 2.29/1.47 ( eqinunit
% 2.29/1.47 = ( ! [Xx: $i,Xy: $i] :
% 2.29/1.47 ( ( Xx = Xy )
% 2.29/1.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(singletonsswitch_type,type,
% 2.29/1.47 singletonsswitch: $o ).
% 2.29/1.47
% 2.29/1.47 thf(singletonsswitch,definition,
% 2.29/1.47 ( singletonsswitch
% 2.29/1.47 = ( ! [Xx: $i,Xy: $i] :
% 2.29/1.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.29/1.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(upairsetE_type,type,
% 2.29/1.47 upairsetE: $o ).
% 2.29/1.47
% 2.29/1.47 thf(upairsetE,definition,
% 2.29/1.47 ( upairsetE
% 2.29/1.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.29/1.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.29/1.47 => ( ( Xz = Xx )
% 2.29/1.47 | ( Xz = Xy ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(upairsetIL_type,type,
% 2.29/1.47 upairsetIL: $o ).
% 2.29/1.47
% 2.29/1.47 thf(upairsetIL,definition,
% 2.29/1.47 ( upairsetIL
% 2.29/1.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(upairsetIR_type,type,
% 2.29/1.47 upairsetIR: $o ).
% 2.29/1.47
% 2.29/1.47 thf(upairsetIR,definition,
% 2.29/1.47 ( upairsetIR
% 2.29/1.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(emptyE1_type,type,
% 2.29/1.47 emptyE1: $o ).
% 2.29/1.47
% 2.29/1.47 thf(emptyE1,definition,
% 2.29/1.47 ( emptyE1
% 2.29/1.47 = ( ! [A: $i,Xphi: $i > $o] :
% 2.29/1.47 ( ? [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 & ( Xphi @ Xx ) )
% 2.29/1.47 => ( ( ( dsetconstr @ A
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.47 = emptyset )
% 2.29/1.47 => $false ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(vacuousDall_type,type,
% 2.29/1.47 vacuousDall: $o ).
% 2.29/1.47
% 2.29/1.47 thf(vacuousDall,definition,
% 2.29/1.47 ( vacuousDall
% 2.29/1.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ emptyset )
% 2.29/1.47 => ( Xphi @ Xx ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(quantDeMorgan1_type,type,
% 2.29/1.47 quantDeMorgan1: $o ).
% 2.29/1.47
% 2.29/1.47 thf(quantDeMorgan1,definition,
% 2.29/1.47 ( quantDeMorgan1
% 2.29/1.47 = ( ! [A: $i,Xphi: $i > $o] :
% 2.29/1.47 ( ~ ! [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ( Xphi @ Xx ) )
% 2.29/1.47 => ? [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(quantDeMorgan2_type,type,
% 2.29/1.47 quantDeMorgan2: $o ).
% 2.29/1.47
% 2.29/1.47 thf(quantDeMorgan2,definition,
% 2.29/1.47 ( quantDeMorgan2
% 2.29/1.47 = ( ! [A: $i,Xphi: $i > $o] :
% 2.29/1.47 ( ! [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ~ ( Xphi @ Xx ) )
% 2.29/1.47 => ~ ? [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(quantDeMorgan3_type,type,
% 2.29/1.47 quantDeMorgan3: $o ).
% 2.29/1.47
% 2.29/1.47 thf(quantDeMorgan3,definition,
% 2.29/1.47 ( quantDeMorgan3
% 2.29/1.47 = ( ! [A: $i,Xphi: $i > $o] :
% 2.29/1.47 ( ~ ? [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 & ( Xphi @ Xx ) )
% 2.29/1.47 => ! [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(quantDeMorgan4_type,type,
% 2.29/1.47 quantDeMorgan4: $o ).
% 2.29/1.47
% 2.29/1.47 thf(quantDeMorgan4,definition,
% 2.29/1.47 ( quantDeMorgan4
% 2.29/1.47 = ( ! [A: $i,Xphi: $i > $o] :
% 2.29/1.47 ( ? [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 & ~ ( Xphi @ Xx ) )
% 2.29/1.47 => ~ ! [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(prop2setI_type,type,
% 2.29/1.47 prop2setI: $o ).
% 2.29/1.47
% 2.29/1.47 thf(prop2setI,definition,
% 2.29/1.47 ( prop2setI
% 2.29/1.47 = ( ! [Xphi: $o] :
% 2.29/1.47 ( Xphi
% 2.29/1.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(set2prop_type,type,
% 2.29/1.47 set2prop: $i > $o ).
% 2.29/1.47
% 2.29/1.47 thf(prop2set2propI_type,type,
% 2.29/1.47 prop2set2propI: $o ).
% 2.29/1.47
% 2.29/1.47 thf(prop2set2propI,definition,
% 2.29/1.47 ( prop2set2propI
% 2.29/1.47 = ( ! [Xphi: $o] :
% 2.29/1.47 ( Xphi
% 2.29/1.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(notdexE_type,type,
% 2.29/1.47 notdexE: $o ).
% 2.29/1.47
% 2.29/1.47 thf(notdexE,definition,
% 2.29/1.47 ( notdexE
% 2.29/1.47 = ( ! [A: $i,Xphi: $i > $o] :
% 2.29/1.47 ( ~ ? [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 & ( Xphi @ Xx ) )
% 2.29/1.47 => ! [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(notdallE_type,type,
% 2.29/1.47 notdallE: $o ).
% 2.29/1.47
% 2.29/1.47 thf(notdallE,definition,
% 2.29/1.47 ( notdallE
% 2.29/1.47 = ( ! [A: $i,Xphi: $i > $o] :
% 2.29/1.47 ( ~ ! [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ( Xphi @ Xx ) )
% 2.29/1.47 => ? [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(exuI1_type,type,
% 2.29/1.47 exuI1: $o ).
% 2.29/1.47
% 2.29/1.47 thf(exuI1,definition,
% 2.29/1.47 ( exuI1
% 2.29/1.47 = ( ! [Xphi: $i > $o] :
% 2.29/1.47 ( ? [Xx: $i] :
% 2.29/1.47 ( ( Xphi @ Xx )
% 2.29/1.47 & ! [Xy: $i] :
% 2.29/1.47 ( ( Xphi @ Xy )
% 2.29/1.47 => ( Xx = Xy ) ) )
% 2.29/1.47 => ( exu
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(exuI3_type,type,
% 2.29/1.47 exuI3: $o ).
% 2.29/1.47
% 2.29/1.47 thf(exuI3,definition,
% 2.29/1.47 ( exuI3
% 2.29/1.47 = ( ! [Xphi: $i > $o] :
% 2.29/1.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.29/1.47 => ( ! [Xx: $i,Xy: $i] :
% 2.29/1.47 ( ( Xphi @ Xx )
% 2.29/1.47 => ( ( Xphi @ Xy )
% 2.29/1.47 => ( Xx = Xy ) ) )
% 2.29/1.47 => ( exu
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(exuI2_type,type,
% 2.29/1.47 exuI2: $o ).
% 2.29/1.47
% 2.29/1.47 thf(exuI2,definition,
% 2.29/1.47 ( exuI2
% 2.29/1.47 = ( ! [Xphi: $i > $o] :
% 2.29/1.47 ( ? [Xx: $i] :
% 2.29/1.47 ! [Xy: $i] :
% 2.29/1.47 ( ( Xphi @ Xy )
% 2.29/1.47 <=> ( Xy = Xx ) )
% 2.29/1.47 => ( exu
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(inCongP_type,type,
% 2.29/1.47 inCongP: $o ).
% 2.29/1.47
% 2.29/1.47 thf(inCongP,definition,
% 2.29/1.47 ( inCongP
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( A = B )
% 2.29/1.47 => ! [Xx: $i,Xy: $i] :
% 2.29/1.47 ( ( Xx = Xy )
% 2.29/1.47 => ( ( in @ Xx @ A )
% 2.29/1.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(in__Cong_type,type,
% 2.29/1.47 in__Cong: $o ).
% 2.29/1.47
% 2.29/1.47 thf(in__Cong,definition,
% 2.29/1.47 ( in__Cong
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( A = B )
% 2.29/1.47 => ! [Xx: $i,Xy: $i] :
% 2.29/1.47 ( ( Xx = Xy )
% 2.29/1.47 => ( ( in @ Xx @ A )
% 2.29/1.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(exuE3u_type,type,
% 2.29/1.47 exuE3u: $o ).
% 2.29/1.47
% 2.29/1.47 thf(exuE3u,definition,
% 2.29/1.47 ( exuE3u
% 2.29/1.47 = ( ! [Xphi: $i > $o] :
% 2.29/1.47 ( ( exu
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.47 => ! [Xx: $i,Xy: $i] :
% 2.29/1.47 ( ( Xphi @ Xx )
% 2.29/1.47 => ( ( Xphi @ Xy )
% 2.29/1.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(exu__Cong_type,type,
% 2.29/1.47 exu__Cong: $o ).
% 2.29/1.47
% 2.29/1.47 thf(exu__Cong,definition,
% 2.29/1.47 ( exu__Cong
% 2.29/1.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.29/1.47 ( ! [Xx: $i,Xy: $i] :
% 2.29/1.47 ( ( Xx = Xy )
% 2.29/1.47 => ( ( Xphi @ Xx )
% 2.29/1.47 <=> ( Xpsi @ Xy ) ) )
% 2.29/1.47 => ( ( exu
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.47 <=> ( exu
% 2.29/1.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(emptyset__Cong_type,type,
% 2.29/1.47 emptyset__Cong: $o ).
% 2.29/1.47
% 2.29/1.47 thf(emptyset__Cong,definition,
% 2.29/1.47 ( emptyset__Cong
% 2.29/1.47 = ( emptyset = emptyset ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(setadjoin__Cong_type,type,
% 2.29/1.47 setadjoin__Cong: $o ).
% 2.29/1.47
% 2.29/1.47 thf(setadjoin__Cong,definition,
% 2.29/1.47 ( setadjoin__Cong
% 2.29/1.47 = ( ! [Xx: $i,Xy: $i] :
% 2.29/1.47 ( ( Xx = Xy )
% 2.29/1.47 => ! [Xz: $i,Xu: $i] :
% 2.29/1.47 ( ( Xz = Xu )
% 2.29/1.47 => ( ( setadjoin @ Xx @ Xz )
% 2.29/1.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(powerset__Cong_type,type,
% 2.29/1.47 powerset__Cong: $o ).
% 2.29/1.47
% 2.29/1.47 thf(powerset__Cong,definition,
% 2.29/1.47 ( powerset__Cong
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( A = B )
% 2.29/1.47 => ( ( powerset @ A )
% 2.29/1.47 = ( powerset @ B ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(setunion__Cong_type,type,
% 2.29/1.47 setunion__Cong: $o ).
% 2.29/1.47
% 2.29/1.47 thf(setunion__Cong,definition,
% 2.29/1.47 ( setunion__Cong
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( A = B )
% 2.29/1.47 => ( ( setunion @ A )
% 2.29/1.47 = ( setunion @ B ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(omega__Cong_type,type,
% 2.29/1.47 omega__Cong: $o ).
% 2.29/1.47
% 2.29/1.47 thf(omega__Cong,definition,
% 2.29/1.47 ( omega__Cong
% 2.29/1.47 = ( omega = omega ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(exuEu_type,type,
% 2.29/1.47 exuEu: $o ).
% 2.29/1.47
% 2.29/1.47 thf(exuEu,definition,
% 2.29/1.47 ( exuEu
% 2.29/1.47 = ( ! [Xphi: $i > $o] :
% 2.29/1.47 ( ( exu
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.47 => ! [Xx: $i,Xy: $i] :
% 2.29/1.47 ( ( Xphi @ Xx )
% 2.29/1.47 => ( ( Xphi @ Xy )
% 2.29/1.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(descr__Cong_type,type,
% 2.29/1.47 descr__Cong: $o ).
% 2.29/1.47
% 2.29/1.47 thf(descr__Cong,definition,
% 2.29/1.47 ( descr__Cong
% 2.29/1.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.29/1.47 ( ! [Xx: $i,Xy: $i] :
% 2.29/1.47 ( ( Xx = Xy )
% 2.29/1.47 => ( ( Xphi @ Xx )
% 2.29/1.47 <=> ( Xpsi @ Xy ) ) )
% 2.29/1.47 => ( ( exu
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.47 => ( ( exu
% 2.29/1.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.29/1.47 => ( ( descr
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.47 = ( descr
% 2.29/1.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(dsetconstr__Cong_type,type,
% 2.29/1.47 dsetconstr__Cong: $o ).
% 2.29/1.47
% 2.29/1.47 thf(dsetconstr__Cong,definition,
% 2.29/1.47 ( dsetconstr__Cong
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( A = B )
% 2.29/1.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.29/1.47 ( ! [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ! [Xy: $i] :
% 2.29/1.47 ( ( in @ Xy @ B )
% 2.29/1.47 => ( ( Xx = Xy )
% 2.29/1.47 => ( ( Xphi @ Xx )
% 2.29/1.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.29/1.47 => ( ( dsetconstr @ A
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.47 = ( dsetconstr @ B
% 2.29/1.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(subset_type,type,
% 2.29/1.47 subset: $i > $i > $o ).
% 2.29/1.47
% 2.29/1.47 thf(disjoint_type,type,
% 2.29/1.47 disjoint: $i > $i > $o ).
% 2.29/1.47
% 2.29/1.47 thf(setsmeet_type,type,
% 2.29/1.47 setsmeet: $i > $i > $o ).
% 2.29/1.47
% 2.29/1.47 thf(subsetI1_type,type,
% 2.29/1.47 subsetI1: $o ).
% 2.29/1.47
% 2.29/1.47 thf(subsetI1,definition,
% 2.29/1.47 ( subsetI1
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ! [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ( in @ Xx @ B ) )
% 2.29/1.47 => ( subset @ A @ B ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(eqimpsubset2_type,type,
% 2.29/1.47 eqimpsubset2: $o ).
% 2.29/1.47
% 2.29/1.47 thf(eqimpsubset2,definition,
% 2.29/1.47 ( eqimpsubset2
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( A = B )
% 2.29/1.47 => ( subset @ B @ A ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(eqimpsubset1_type,type,
% 2.29/1.47 eqimpsubset1: $o ).
% 2.29/1.47
% 2.29/1.47 thf(eqimpsubset1,definition,
% 2.29/1.47 ( eqimpsubset1
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( A = B )
% 2.29/1.47 => ( subset @ A @ B ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(subsetI2_type,type,
% 2.29/1.47 subsetI2: $o ).
% 2.29/1.47
% 2.29/1.47 thf(subsetI2,definition,
% 2.29/1.47 ( subsetI2
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ! [Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ( in @ Xx @ B ) )
% 2.29/1.47 => ( subset @ A @ B ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(emptysetsubset_type,type,
% 2.29/1.47 emptysetsubset: $o ).
% 2.29/1.47
% 2.29/1.47 thf(emptysetsubset,definition,
% 2.29/1.47 ( emptysetsubset
% 2.29/1.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(subsetE_type,type,
% 2.29/1.47 subsetE: $o ).
% 2.29/1.47
% 2.29/1.47 thf(subsetE,definition,
% 2.29/1.47 ( subsetE
% 2.29/1.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.29/1.47 ( ( subset @ A @ B )
% 2.29/1.47 => ( ( in @ Xx @ A )
% 2.29/1.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(subsetE2_type,type,
% 2.29/1.47 subsetE2: $o ).
% 2.29/1.47
% 2.29/1.47 thf(subsetE2,definition,
% 2.29/1.47 ( subsetE2
% 2.29/1.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.29/1.47 ( ( subset @ A @ B )
% 2.29/1.47 => ( ~ ( in @ Xx @ B )
% 2.29/1.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(notsubsetI_type,type,
% 2.29/1.47 notsubsetI: $o ).
% 2.29/1.47
% 2.29/1.47 thf(notsubsetI,definition,
% 2.29/1.47 ( notsubsetI
% 2.29/1.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ( ~ ( in @ Xx @ B )
% 2.29/1.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(notequalI1_type,type,
% 2.29/1.47 notequalI1: $o ).
% 2.29/1.47
% 2.29/1.47 thf(notequalI1,definition,
% 2.29/1.47 ( notequalI1
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ~ ( subset @ A @ B )
% 2.29/1.47 => ( A != B ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(notequalI2_type,type,
% 2.29/1.47 notequalI2: $o ).
% 2.29/1.47
% 2.29/1.47 thf(notequalI2,definition,
% 2.29/1.47 ( notequalI2
% 2.29/1.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.29/1.47 ( ( in @ Xx @ A )
% 2.29/1.47 => ( ~ ( in @ Xx @ B )
% 2.29/1.47 => ( A != B ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(subsetRefl_type,type,
% 2.29/1.47 subsetRefl: $o ).
% 2.29/1.47
% 2.29/1.47 thf(subsetRefl,definition,
% 2.29/1.47 ( subsetRefl
% 2.29/1.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(subsetTrans_type,type,
% 2.29/1.47 subsetTrans: $o ).
% 2.29/1.47
% 2.29/1.47 thf(subsetTrans,definition,
% 2.29/1.47 ( subsetTrans
% 2.29/1.47 = ( ! [A: $i,B: $i,C: $i] :
% 2.29/1.47 ( ( subset @ A @ B )
% 2.29/1.47 => ( ( subset @ B @ C )
% 2.29/1.47 => ( subset @ A @ C ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(setadjoinSub_type,type,
% 2.29/1.47 setadjoinSub: $o ).
% 2.29/1.47
% 2.29/1.47 thf(setadjoinSub,definition,
% 2.29/1.47 ( setadjoinSub
% 2.29/1.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(setadjoinSub2_type,type,
% 2.29/1.47 setadjoinSub2: $o ).
% 2.29/1.47
% 2.29/1.47 thf(setadjoinSub2,definition,
% 2.29/1.47 ( setadjoinSub2
% 2.29/1.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.29/1.47 ( ( subset @ A @ B )
% 2.29/1.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(subset2powerset_type,type,
% 2.29/1.47 subset2powerset: $o ).
% 2.29/1.47
% 2.29/1.47 thf(subset2powerset,definition,
% 2.29/1.47 ( subset2powerset
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( subset @ A @ B )
% 2.29/1.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(setextsub_type,type,
% 2.29/1.47 setextsub: $o ).
% 2.29/1.47
% 2.29/1.47 thf(setextsub,definition,
% 2.29/1.47 ( setextsub
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( subset @ A @ B )
% 2.29/1.47 => ( ( subset @ B @ A )
% 2.29/1.47 => ( A = B ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(subsetemptysetimpeq_type,type,
% 2.29/1.47 subsetemptysetimpeq: $o ).
% 2.29/1.47
% 2.29/1.47 thf(subsetemptysetimpeq,definition,
% 2.29/1.47 ( subsetemptysetimpeq
% 2.29/1.47 = ( ! [A: $i] :
% 2.29/1.47 ( ( subset @ A @ emptyset )
% 2.29/1.47 => ( A = emptyset ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(powersetI1_type,type,
% 2.29/1.47 powersetI1: $o ).
% 2.29/1.47
% 2.29/1.47 thf(powersetI1,definition,
% 2.29/1.47 ( powersetI1
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( subset @ B @ A )
% 2.29/1.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(powersetE1_type,type,
% 2.29/1.47 powersetE1: $o ).
% 2.29/1.47
% 2.29/1.47 thf(powersetE1,definition,
% 2.29/1.47 ( powersetE1
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( in @ B @ ( powerset @ A ) )
% 2.29/1.47 => ( subset @ B @ A ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(inPowerset_type,type,
% 2.29/1.47 inPowerset: $o ).
% 2.29/1.47
% 2.29/1.47 thf(inPowerset,definition,
% 2.29/1.47 ( inPowerset
% 2.29/1.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(powersetsubset_type,type,
% 2.29/1.47 powersetsubset: $o ).
% 2.29/1.47
% 2.29/1.47 thf(powersetsubset,definition,
% 2.29/1.47 ( powersetsubset
% 2.29/1.47 = ( ! [A: $i,B: $i] :
% 2.29/1.47 ( ( subset @ A @ B )
% 2.29/1.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(sepInPowerset_type,type,
% 2.29/1.47 sepInPowerset: $o ).
% 2.29/1.47
% 2.29/1.47 thf(sepInPowerset,definition,
% 2.29/1.47 ( sepInPowerset
% 2.29/1.47 = ( ! [A: $i,Xphi: $i > $o] :
% 2.29/1.47 ( in
% 2.29/1.47 @ ( dsetconstr @ A
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.47 @ ( powerset @ A ) ) ) ) ).
% 2.29/1.47
% 2.29/1.47 thf(sepSubset,conjecture,
% 2.29/1.47 ( setextAx
% 2.29/1.47 => ( emptysetAx
% 2.29/1.47 => ( setadjoinAx
% 2.29/1.47 => ( powersetAx
% 2.29/1.47 => ( setunionAx
% 2.29/1.47 => ( omega0Ax
% 2.29/1.47 => ( omegaSAx
% 2.29/1.47 => ( omegaIndAx
% 2.29/1.47 => ( replAx
% 2.29/1.47 => ( foundationAx
% 2.29/1.47 => ( wellorderingAx
% 2.29/1.47 => ( descrp
% 2.29/1.47 => ( dsetconstrI
% 2.29/1.47 => ( dsetconstrEL
% 2.29/1.47 => ( dsetconstrER
% 2.29/1.47 => ( exuE1
% 2.29/1.47 => ( prop2setE
% 2.29/1.47 => ( emptysetE
% 2.29/1.47 => ( emptysetimpfalse
% 2.29/1.47 => ( notinemptyset
% 2.29/1.47 => ( exuE3e
% 2.29/1.47 => ( setext
% 2.29/1.47 => ( emptyI
% 2.29/1.47 => ( noeltsimpempty
% 2.29/1.47 => ( setbeta
% 2.29/1.47 => ( nonemptyE1
% 2.29/1.47 => ( nonemptyI
% 2.29/1.47 => ( nonemptyI1
% 2.29/1.47 => ( setadjoinIL
% 2.29/1.47 => ( emptyinunitempty
% 2.29/1.47 => ( setadjoinIR
% 2.29/1.47 => ( setadjoinE
% 2.29/1.47 => ( setadjoinOr
% 2.29/1.47 => ( setoftrueEq
% 2.29/1.47 => ( powersetI
% 2.29/1.47 => ( emptyinPowerset
% 2.29/1.47 => ( emptyInPowerset
% 2.29/1.47 => ( powersetE
% 2.29/1.47 => ( setunionI
% 2.29/1.47 => ( setunionE
% 2.29/1.47 => ( subPowSU
% 2.29/1.47 => ( exuE2
% 2.29/1.47 => ( nonemptyImpWitness
% 2.29/1.47 => ( uniqinunit
% 2.29/1.47 => ( notinsingleton
% 2.29/1.47 => ( eqinunit
% 2.29/1.47 => ( singletonsswitch
% 2.29/1.47 => ( upairsetE
% 2.29/1.47 => ( upairsetIL
% 2.29/1.47 => ( upairsetIR
% 2.29/1.47 => ( emptyE1
% 2.29/1.47 => ( vacuousDall
% 2.29/1.47 => ( quantDeMorgan1
% 2.29/1.47 => ( quantDeMorgan2
% 2.29/1.47 => ( quantDeMorgan3
% 2.29/1.47 => ( quantDeMorgan4
% 2.29/1.47 => ( prop2setI
% 2.29/1.47 => ( prop2set2propI
% 2.29/1.47 => ( notdexE
% 2.29/1.47 => ( notdallE
% 2.29/1.47 => ( exuI1
% 2.29/1.47 => ( exuI3
% 2.29/1.47 => ( exuI2
% 2.29/1.47 => ( inCongP
% 2.29/1.47 => ( in__Cong
% 2.29/1.47 => ( exuE3u
% 2.29/1.47 => ( exu__Cong
% 2.29/1.47 => ( emptyset__Cong
% 2.29/1.47 => ( setadjoin__Cong
% 2.29/1.47 => ( powerset__Cong
% 2.29/1.47 => ( setunion__Cong
% 2.29/1.47 => ( omega__Cong
% 2.29/1.47 => ( exuEu
% 2.29/1.47 => ( descr__Cong
% 2.29/1.47 => ( dsetconstr__Cong
% 2.29/1.47 => ( subsetI1
% 2.29/1.47 => ( eqimpsubset2
% 2.29/1.47 => ( eqimpsubset1
% 2.29/1.47 => ( subsetI2
% 2.29/1.47 => ( emptysetsubset
% 2.29/1.47 => ( subsetE
% 2.29/1.47 => ( subsetE2
% 2.29/1.47 => ( notsubsetI
% 2.29/1.47 => ( notequalI1
% 2.29/1.47 => ( notequalI2
% 2.29/1.47 => ( subsetRefl
% 2.29/1.47 => ( subsetTrans
% 2.29/1.47 => ( setadjoinSub
% 2.29/1.47 => ( setadjoinSub2
% 2.29/1.47 => ( subset2powerset
% 2.29/1.47 => ( setextsub
% 2.29/1.47 => ( subsetemptysetimpeq
% 2.29/1.47 => ( powersetI1
% 2.29/1.47 => ( powersetE1
% 2.29/1.47 => ( inPowerset
% 2.29/1.47 => ( powersetsubset
% 2.29/1.47 => ( sepInPowerset
% 2.29/1.47 => ! [A: $i,Xphi: $i > $o] :
% 2.29/1.47 ( subset
% 2.29/1.47 @ ( dsetconstr @ A
% 2.29/1.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.29/1.47 @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.29/1.47 ------------------------
% 2.29/1.48 % (20285)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/183Mi)
% 2.29/1.48 % (20291)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/18Mi)
% 2.29/1.49 % (20291)Instruction limit reached!
% 2.29/1.49 % (20291)------------------------------
% 2.29/1.49 % (20291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.49 % (20291)Termination reason: Unknown
% 2.29/1.49 % (20291)Termination phase: Preprocessing 3
% 2.29/1.49
% 2.29/1.49 % (20291)Memory used [KB]: 1535
% 2.29/1.49 % (20291)Time elapsed: 0.007 s
% 2.29/1.49 % (20291)Instructions burned: 18 (million)
% 2.29/1.49 % (20291)------------------------------
% 2.29/1.49 % (20291)------------------------------
% 2.29/1.49 % (20286)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_20010 for (2999ds/4Mi)
% 2.29/1.49 % (20288)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/2Mi)
% 2.29/1.49 % (20287)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_20010 for (2999ds/27Mi)
% 2.29/1.49 % (20289)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_20010 for (2999ds/2Mi)
% 2.29/1.49 % (20290)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_20010 for (2999ds/275Mi)
% 2.29/1.49 % (20288)Instruction limit reached!
% 2.29/1.49 % (20288)------------------------------
% 2.29/1.49 % (20288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.49 % (20288)Termination reason: Unknown
% 2.29/1.49 % (20288)Termination phase: shuffling
% 2.29/1.49
% 2.29/1.49 % (20288)Memory used [KB]: 1151
% 2.29/1.49 % (20288)Time elapsed: 0.003 s
% 2.29/1.49 % (20288)Instructions burned: 2 (million)
% 2.29/1.49 % (20288)------------------------------
% 2.29/1.49 % (20288)------------------------------
% 2.29/1.49 % (20289)Instruction limit reached!
% 2.29/1.49 % (20289)------------------------------
% 2.29/1.49 % (20289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.49 % (20289)Termination reason: Unknown
% 2.29/1.49 % (20289)Termination phase: shuffling
% 2.29/1.49
% 2.29/1.49 % (20289)Memory used [KB]: 1151
% 2.29/1.49 % (20289)Time elapsed: 0.003 s
% 2.29/1.49 % (20289)Instructions burned: 2 (million)
% 2.29/1.49 % (20289)------------------------------
% 2.29/1.49 % (20289)------------------------------
% 2.29/1.49 % (20286)Instruction limit reached!
% 2.29/1.49 % (20286)------------------------------
% 2.29/1.49 % (20286)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.29/1.49 % (20286)Termination reason: Unknown
% 2.29/1.49 % (20286)Termination phase: shuffling
% 2.29/1.49
% 2.29/1.49 % (20286)Memory used [KB]: 1151
% 2.29/1.49 % (20286)Time elapsed: 0.004 s
% 2.29/1.49 % (20286)Instructions burned: 4 (million)
% 2.29/1.49 % (20286)------------------------------
% 2.29/1.49 % (20286)------------------------------
% 2.29/1.50 % (20292)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/3Mi)
% 2.45/1.50 % (20292)Instruction limit reached!
% 2.45/1.50 % (20292)------------------------------
% 2.45/1.50 % (20292)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.50 % (20292)Termination reason: Unknown
% 2.45/1.50 % (20292)Termination phase: shuffling
% 2.45/1.50
% 2.45/1.50 % (20292)Memory used [KB]: 1151
% 2.45/1.50 % (20292)Time elapsed: 0.003 s
% 2.45/1.50 % (20292)Instructions burned: 4 (million)
% 2.45/1.50 % (20292)------------------------------
% 2.45/1.50 % (20292)------------------------------
% 2.45/1.50 % (20287)Instruction limit reached!
% 2.45/1.50 % (20287)------------------------------
% 2.45/1.50 % (20287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.50 % (20287)Termination reason: Unknown
% 2.45/1.50 % (20287)Termination phase: Property scanning
% 2.45/1.50
% 2.45/1.50 % (20287)Memory used [KB]: 1535
% 2.45/1.50 % (20287)Time elapsed: 0.016 s
% 2.45/1.50 % (20287)Instructions burned: 27 (million)
% 2.45/1.50 % (20287)------------------------------
% 2.45/1.50 % (20287)------------------------------
% 2.45/1.51 % (20293)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_20010 for (2999ds/37Mi)
% 2.45/1.51 % (20294)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_20010 for (2999ds/15Mi)
% 2.45/1.51 % (20295)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_20010 for (2999ds/3Mi)
% 2.45/1.51 % (20296)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_20010 for (2999ds/1041Mi)
% 2.45/1.51 % (20295)Instruction limit reached!
% 2.45/1.51 % (20295)------------------------------
% 2.45/1.51 % (20295)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.51 % (20295)Termination reason: Unknown
% 2.45/1.51 % (20295)Termination phase: shuffling
% 2.45/1.51
% 2.45/1.51 % (20295)Memory used [KB]: 1151
% 2.45/1.51 % (20295)Time elapsed: 0.004 s
% 2.45/1.51 % (20295)Instructions burned: 4 (million)
% 2.45/1.51 % (20295)------------------------------
% 2.45/1.51 % (20295)------------------------------
% 2.45/1.51 % (20294)Instruction limit reached!
% 2.45/1.51 % (20294)------------------------------
% 2.45/1.51 % (20294)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.51 % (20294)Termination reason: Unknown
% 2.45/1.51 % (20294)Termination phase: Preprocessing 3
% 2.45/1.51
% 2.45/1.51 % (20294)Memory used [KB]: 1407
% 2.45/1.51 % (20294)Time elapsed: 0.011 s
% 2.45/1.51 % (20294)Instructions burned: 16 (million)
% 2.45/1.51 % (20294)------------------------------
% 2.45/1.51 % (20294)------------------------------
% 2.45/1.52 % (20297)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/7Mi)
% 2.45/1.52 % (20297)Instruction limit reached!
% 2.45/1.52 % (20297)------------------------------
% 2.45/1.52 % (20297)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.52 % (20297)Termination reason: Unknown
% 2.45/1.52 % (20297)Termination phase: shuffling
% 2.45/1.52
% 2.45/1.52 % (20297)Memory used [KB]: 1279
% 2.45/1.52 % (20297)Time elapsed: 0.006 s
% 2.45/1.52 % (20297)Instructions burned: 8 (million)
% 2.45/1.52 % (20297)------------------------------
% 2.45/1.52 % (20297)------------------------------
% 2.45/1.52 % (20293)Instruction limit reached!
% 2.45/1.52 % (20293)------------------------------
% 2.45/1.52 % (20293)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.52 % (20293)Termination reason: Unknown
% 2.45/1.52 % (20293)Termination phase: Property scanning
% 2.45/1.52
% 2.45/1.52 % (20293)Memory used [KB]: 1535
% 2.45/1.52 % (20293)Time elapsed: 0.020 s
% 2.45/1.52 % (20293)Instructions burned: 38 (million)
% 2.45/1.52 % (20293)------------------------------
% 2.45/1.52 % (20293)------------------------------
% 2.45/1.53 % (20298)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/16Mi)
% 2.45/1.53 % (20299)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_20010 for (2999ds/3Mi)
% 2.45/1.53 % (20298)Instruction limit reached!
% 2.45/1.53 % (20298)------------------------------
% 2.45/1.53 % (20298)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.53 % (20298)Termination reason: Unknown
% 2.45/1.53 % (20298)Termination phase: Property scanning
% 2.45/1.53
% 2.45/1.53 % (20298)Memory used [KB]: 1407
% 2.45/1.53 % (20298)Time elapsed: 0.010 s
% 2.45/1.53 % (20298)Instructions burned: 16 (million)
% 2.45/1.53 % (20298)------------------------------
% 2.45/1.53 % (20298)------------------------------
% 2.45/1.53 % (20299)Instruction limit reached!
% 2.45/1.53 % (20299)------------------------------
% 2.45/1.53 % (20299)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.53 % (20299)Termination reason: Unknown
% 2.45/1.53 % (20299)Termination phase: shuffling
% 2.45/1.53
% 2.45/1.53 % (20299)Memory used [KB]: 1151
% 2.45/1.53 % (20299)Time elapsed: 0.004 s
% 2.45/1.53 % (20299)Instructions burned: 4 (million)
% 2.45/1.53 % (20299)------------------------------
% 2.45/1.53 % (20299)------------------------------
% 2.45/1.54 % (20285)Instruction limit reached!
% 2.45/1.54 % (20285)------------------------------
% 2.45/1.54 % (20285)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.54 % (20285)Termination reason: Unknown
% 2.45/1.54 % (20285)Termination phase: Saturation
% 2.45/1.54
% 2.45/1.54 % (20285)Memory used [KB]: 6908
% 2.45/1.54 % (20285)Time elapsed: 0.059 s
% 2.45/1.54 % (20285)Instructions burned: 184 (million)
% 2.45/1.54 % (20285)------------------------------
% 2.45/1.54 % (20285)------------------------------
% 2.45/1.54 % (20300)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_20010 for (2999ds/3Mi)
% 2.45/1.54 % (20300)Instruction limit reached!
% 2.45/1.54 % (20300)------------------------------
% 2.45/1.54 % (20300)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.54 % (20300)Termination reason: Unknown
% 2.45/1.54 % (20300)Termination phase: shuffling
% 2.45/1.54
% 2.45/1.54 % (20300)Memory used [KB]: 1151
% 2.45/1.54 % (20300)Time elapsed: 0.003 s
% 2.45/1.54 % (20300)Instructions burned: 3 (million)
% 2.45/1.54 % (20300)------------------------------
% 2.45/1.54 % (20300)------------------------------
% 2.45/1.54 % (20301)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/7Mi)
% 2.45/1.55 % (20301)Instruction limit reached!
% 2.45/1.55 % (20301)------------------------------
% 2.45/1.55 % (20301)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.55 % (20301)Termination reason: Unknown
% 2.45/1.55 % (20301)Termination phase: shuffling
% 2.45/1.55
% 2.45/1.55 % (20301)Memory used [KB]: 1279
% 2.45/1.55 % (20301)Time elapsed: 0.006 s
% 2.45/1.55 % (20301)Instructions burned: 8 (million)
% 2.45/1.55 % (20301)------------------------------
% 2.45/1.55 % (20301)------------------------------
% 2.45/1.55 % (20304)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/18Mi)
% 2.45/1.55 % (20302)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/3Mi)
% 2.45/1.55 % (20303)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/4Mi)
% 2.45/1.55 % (20304)Instruction limit reached!
% 2.45/1.55 % (20304)------------------------------
% 2.45/1.55 % (20304)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.55 % (20304)Termination reason: Unknown
% 2.45/1.55 % (20304)Termination phase: Property scanning
% 2.45/1.55
% 2.45/1.55 % (20304)Memory used [KB]: 1407
% 2.45/1.55 % (20304)Time elapsed: 0.007 s
% 2.45/1.55 % (20304)Instructions burned: 18 (million)
% 2.45/1.55 % (20304)------------------------------
% 2.45/1.55 % (20304)------------------------------
% 2.45/1.55 % (20302)Instruction limit reached!
% 2.45/1.55 % (20302)------------------------------
% 2.45/1.55 % (20302)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.55 % (20302)Termination reason: Unknown
% 2.45/1.55 % (20302)Termination phase: shuffling
% 2.45/1.55
% 2.45/1.55 % (20302)Memory used [KB]: 1151
% 2.45/1.55 % (20302)Time elapsed: 0.004 s
% 2.45/1.55 % (20302)Instructions burned: 4 (million)
% 2.45/1.55 % (20302)------------------------------
% 2.45/1.55 % (20302)------------------------------
% 2.45/1.55 % (20303)Instruction limit reached!
% 2.45/1.55 % (20303)------------------------------
% 2.45/1.55 % (20303)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.55 % (20303)Termination reason: Unknown
% 2.45/1.55 % (20303)Termination phase: shuffling
% 2.45/1.55
% 2.45/1.55 % (20303)Memory used [KB]: 1151
% 2.45/1.55 % (20303)Time elapsed: 0.004 s
% 2.45/1.55 % (20303)Instructions burned: 4 (million)
% 2.45/1.55 % (20303)------------------------------
% 2.45/1.55 % (20303)------------------------------
% 2.45/1.56 % (20305)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/710Mi)
% 2.45/1.56 % (20306)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/6Mi)
% 2.45/1.57 % (20306)Instruction limit reached!
% 2.45/1.57 % (20306)------------------------------
% 2.45/1.57 % (20306)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.57 % (20306)Termination reason: Unknown
% 2.45/1.57 % (20306)Termination phase: shuffling
% 2.45/1.57
% 2.45/1.57 % (20306)Memory used [KB]: 1279
% 2.45/1.57 % (20306)Time elapsed: 0.005 s
% 2.45/1.57 % (20306)Instructions burned: 6 (million)
% 2.45/1.57 % (20306)------------------------------
% 2.45/1.57 % (20306)------------------------------
% 2.45/1.57 % (20308)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_20010 for (2999ds/21Mi)
% 2.45/1.57 % (20307)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_20010 for (2999ds/902Mi)
% 2.45/1.57 % (20309)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/5Mi)
% 2.45/1.57 % (20308)Instruction limit reached!
% 2.45/1.57 % (20308)------------------------------
% 2.45/1.57 % (20308)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.57 % (20308)Termination reason: Unknown
% 2.45/1.57 % (20308)Termination phase: SInE selection
% 2.45/1.57
% 2.45/1.57 % (20308)Memory used [KB]: 1407
% 2.45/1.57 % (20308)Time elapsed: 0.008 s
% 2.45/1.57 % (20308)Instructions burned: 24 (million)
% 2.45/1.57 % (20308)------------------------------
% 2.45/1.57 % (20308)------------------------------
% 2.45/1.57 % (20309)Instruction limit reached!
% 2.45/1.57 % (20309)------------------------------
% 2.45/1.57 % (20309)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.57 % (20309)Termination reason: Unknown
% 2.45/1.57 % (20309)Termination phase: shuffling
% 2.45/1.57
% 2.45/1.57 % (20309)Memory used [KB]: 1279
% 2.45/1.57 % (20309)Time elapsed: 0.005 s
% 2.45/1.57 % (20309)Instructions burned: 6 (million)
% 2.45/1.57 % (20309)------------------------------
% 2.45/1.57 % (20309)------------------------------
% 2.45/1.58 % (20310)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_20010 for (2999ds/6Mi)
% 2.45/1.58 % (20311)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_20010 for (2999ds/377Mi)
% 2.45/1.59 % (20310)Instruction limit reached!
% 2.45/1.59 % (20310)------------------------------
% 2.45/1.59 % (20310)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.59 % (20310)Termination reason: Unknown
% 2.45/1.59 % (20310)Termination phase: shuffling
% 2.45/1.59
% 2.45/1.59 % (20310)Memory used [KB]: 1279
% 2.45/1.59 % (20310)Time elapsed: 0.005 s
% 2.45/1.59 % (20310)Instructions burned: 6 (million)
% 2.45/1.59 % (20310)------------------------------
% 2.45/1.59 % (20310)------------------------------
% 2.45/1.59 % (20312)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_20010 for (2999ds/779Mi)
% 2.45/1.59 % (20290)Instruction limit reached!
% 2.45/1.59 % (20290)------------------------------
% 2.45/1.59 % (20290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.59 % (20290)Termination reason: Unknown
% 2.45/1.59 % (20290)Termination phase: Saturation
% 2.45/1.59
% 2.45/1.59 % (20290)Memory used [KB]: 7547
% 2.45/1.59 % (20290)Time elapsed: 0.107 s
% 2.45/1.59 % (20290)Instructions burned: 275 (million)
% 2.45/1.59 % (20290)------------------------------
% 2.45/1.59 % (20290)------------------------------
% 2.45/1.60 % (20313)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_20010 for (2998ds/19Mi)
% 2.45/1.60 % (20314)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_20010 for (2998ds/879Mi)
% 2.45/1.61 % (20313)Instruction limit reached!
% 2.45/1.61 % (20313)------------------------------
% 2.45/1.61 % (20313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.61 % (20313)Termination reason: Unknown
% 2.45/1.61 % (20313)Termination phase: Property scanning
% 2.45/1.61
% 2.45/1.61 % (20313)Memory used [KB]: 1407
% 2.45/1.61 % (20313)Time elapsed: 0.009 s
% 2.45/1.61 % (20313)Instructions burned: 21 (million)
% 2.45/1.61 % (20313)------------------------------
% 2.45/1.61 % (20313)------------------------------
% 2.45/1.62 % (20315)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_20010 for (2998ds/17Mi)
% 2.45/1.62 % (20315)Instruction limit reached!
% 2.45/1.62 % (20315)------------------------------
% 2.45/1.62 % (20315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.62 % (20315)Termination reason: Unknown
% 2.45/1.62 % (20315)Termination phase: Property scanning
% 2.45/1.62
% 2.45/1.62 % (20315)Memory used [KB]: 1407
% 2.45/1.62 % (20315)Time elapsed: 0.007 s
% 2.45/1.62 % (20315)Instructions burned: 18 (million)
% 2.45/1.62 % (20315)------------------------------
% 2.45/1.62 % (20315)------------------------------
% 2.45/1.63 % (20316)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_20010 for (2998ds/3Mi)
% 2.45/1.63 % (20316)Instruction limit reached!
% 2.45/1.63 % (20316)------------------------------
% 2.45/1.63 % (20316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.63 % (20316)Termination reason: Unknown
% 2.45/1.63 % (20316)Termination phase: shuffling
% 2.45/1.63
% 2.45/1.63 % (20316)Memory used [KB]: 1151
% 2.45/1.63 % (20316)Time elapsed: 0.003 s
% 2.45/1.63 % (20316)Instructions burned: 4 (million)
% 2.45/1.63 % (20316)------------------------------
% 2.45/1.63 % (20316)------------------------------
% 2.45/1.64 % (20317)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_20010 for (2998ds/30Mi)
% 2.45/1.65 % (20317)Instruction limit reached!
% 2.45/1.65 % (20317)------------------------------
% 2.45/1.65 % (20317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.65 % (20317)Termination reason: Unknown
% 2.45/1.65 % (20317)Termination phase: Function definition elimination
% 2.45/1.65
% 2.45/1.65 % (20317)Memory used [KB]: 1535
% 2.45/1.65 % (20317)Time elapsed: 0.011 s
% 2.45/1.65 % (20317)Instructions burned: 33 (million)
% 2.45/1.65 % (20317)------------------------------
% 2.45/1.65 % (20317)------------------------------
% 2.45/1.66 % (20318)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_20010 for (2998ds/127Mi)
% 2.45/1.70 % (20318)Instruction limit reached!
% 2.45/1.70 % (20318)------------------------------
% 2.45/1.70 % (20318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.70 % (20318)Termination reason: Unknown
% 2.45/1.70 % (20318)Termination phase: Saturation
% 2.45/1.70
% 2.45/1.70 % (20318)Memory used [KB]: 6780
% 2.45/1.70 % (20318)Time elapsed: 0.041 s
% 2.45/1.70 % (20318)Instructions burned: 128 (million)
% 2.45/1.70 % (20318)------------------------------
% 2.45/1.70 % (20318)------------------------------
% 2.45/1.70 % (20311)Instruction limit reached!
% 2.45/1.70 % (20311)------------------------------
% 2.45/1.70 % (20311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.70 % (20311)Termination reason: Unknown
% 2.45/1.70 % (20311)Termination phase: Saturation
% 2.45/1.70
% 2.45/1.70 % (20311)Memory used [KB]: 7164
% 2.45/1.70 % (20311)Time elapsed: 0.122 s
% 2.45/1.70 % (20311)Instructions burned: 378 (million)
% 2.45/1.70 % (20311)------------------------------
% 2.45/1.70 % (20311)------------------------------
% 2.45/1.71 % (20319)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_20010 for (2997ds/100Mi)
% 2.45/1.71 % (20320)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_20010 for (2997ds/3Mi)
% 2.45/1.72 % (20320)Instruction limit reached!
% 2.45/1.72 % (20320)------------------------------
% 2.45/1.72 % (20320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.72 % (20320)Termination reason: Unknown
% 2.45/1.72 % (20320)Termination phase: shuffling
% 2.45/1.72
% 2.45/1.72 % (20320)Memory used [KB]: 1151
% 2.45/1.72 % (20320)Time elapsed: 0.002 s
% 2.45/1.72 % (20320)Instructions burned: 4 (million)
% 2.45/1.72 % (20320)------------------------------
% 2.45/1.72 % (20320)------------------------------
% 2.45/1.73 % (20321)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_20010 for (2997ds/20Mi)
% 2.45/1.73 % (20321)Instruction limit reached!
% 2.45/1.73 % (20321)------------------------------
% 2.45/1.73 % (20321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.73 % (20321)Termination reason: Unknown
% 2.45/1.73 % (20321)Termination phase: Preprocessing 3
% 2.45/1.73
% 2.45/1.73 % (20321)Memory used [KB]: 1407
% 2.45/1.73 % (20321)Time elapsed: 0.008 s
% 2.45/1.73 % (20321)Instructions burned: 20 (million)
% 2.45/1.73 % (20321)------------------------------
% 2.45/1.73 % (20321)------------------------------
% 2.45/1.74 % (20322)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_20010 for (2997ds/86Mi)
% 2.45/1.74 % (20319)Instruction limit reached!
% 2.45/1.74 % (20319)------------------------------
% 2.45/1.74 % (20319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.74 % (20319)Termination reason: Unknown
% 2.45/1.74 % (20319)Termination phase: Saturation
% 2.45/1.74
% 2.45/1.74 % (20319)Memory used [KB]: 6268
% 2.45/1.74 % (20319)Time elapsed: 0.031 s
% 2.45/1.74 % (20319)Instructions burned: 100 (million)
% 2.45/1.74 % (20319)------------------------------
% 2.45/1.74 % (20319)------------------------------
% 2.45/1.75 % (20323)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_20010 for (2997ds/107Mi)
% 2.45/1.76 % (20296)Instruction limit reached!
% 2.45/1.76 % (20296)------------------------------
% 2.45/1.76 % (20296)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.76 % (20296)Termination reason: Unknown
% 2.45/1.76 % (20296)Termination phase: Saturation
% 2.45/1.76
% 2.45/1.76 % (20296)Memory used [KB]: 7547
% 2.45/1.76 % (20296)Time elapsed: 0.253 s
% 2.45/1.76 % (20296)Instructions burned: 1043 (million)
% 2.45/1.76 % (20296)------------------------------
% 2.45/1.76 % (20296)------------------------------
% 2.45/1.77 % (20322)Instruction limit reached!
% 2.45/1.77 % (20322)------------------------------
% 2.45/1.77 % (20322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.77 % (20322)Termination reason: Unknown
% 2.45/1.77 % (20322)Termination phase: Saturation
% 2.45/1.77
% 2.45/1.77 % (20322)Memory used [KB]: 6396
% 2.45/1.77 % (20322)Time elapsed: 0.027 s
% 2.45/1.77 % (20322)Instructions burned: 88 (million)
% 2.45/1.77 % (20322)------------------------------
% 2.45/1.77 % (20322)------------------------------
% 2.45/1.77 % (20324)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_20010 for (2997ds/39Mi)
% 2.45/1.78 % (20325)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_20010 for (2997ds/448Mi)
% 2.45/1.78 % (20324)Instruction limit reached!
% 2.45/1.78 % (20324)------------------------------
% 2.45/1.78 % (20324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.78 % (20324)Termination reason: Unknown
% 2.45/1.78 % (20324)Termination phase: Property scanning
% 2.45/1.78
% 2.45/1.78 % (20324)Memory used [KB]: 1535
% 2.45/1.78 % (20324)Time elapsed: 0.011 s
% 2.45/1.78 % (20324)Instructions burned: 39 (million)
% 2.45/1.78 % (20324)------------------------------
% 2.45/1.78 % (20324)------------------------------
% 2.45/1.78 % (20323)Instruction limit reached!
% 2.45/1.78 % (20323)------------------------------
% 2.45/1.78 % (20323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.78 % (20323)Termination reason: Unknown
% 2.45/1.78 % (20323)Termination phase: Saturation
% 2.45/1.78
% 2.45/1.78 % (20323)Memory used [KB]: 6652
% 2.45/1.78 % (20323)Time elapsed: 0.033 s
% 2.45/1.78 % (20323)Instructions burned: 109 (million)
% 2.45/1.78 % (20323)------------------------------
% 2.45/1.78 % (20323)------------------------------
% 2.45/1.79 % (20326)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_20010 for (2997ds/46Mi)
% 2.45/1.79 % (20327)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_20010 for (2997ds/98Mi)
% 2.45/1.80 % (20326)Instruction limit reached!
% 2.45/1.80 % (20326)------------------------------
% 2.45/1.80 % (20326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.80 % (20326)Termination reason: Unknown
% 2.45/1.80 % (20326)Termination phase: Property scanning
% 2.45/1.80
% 2.45/1.80 % (20326)Memory used [KB]: 1535
% 2.45/1.80 % (20326)Time elapsed: 0.013 s
% 2.45/1.80 % (20326)Instructions burned: 47 (million)
% 2.45/1.80 % (20326)------------------------------
% 2.45/1.80 % (20326)------------------------------
% 2.45/1.80 % (20305)Instruction limit reached!
% 2.45/1.80 % (20305)------------------------------
% 2.45/1.80 % (20305)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.80 % (20305)Termination reason: Unknown
% 2.45/1.80 % (20305)Termination phase: Saturation
% 2.45/1.80
% 2.45/1.80 % (20305)Memory used [KB]: 8571
% 2.45/1.80 % (20305)Time elapsed: 0.245 s
% 2.45/1.80 % (20305)Instructions burned: 712 (million)
% 2.45/1.80 % (20305)------------------------------
% 2.45/1.80 % (20305)------------------------------
% 2.45/1.80 % (20312)Instruction limit reached!
% 2.45/1.80 % (20312)------------------------------
% 2.45/1.80 % (20312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.80 % (20312)Termination reason: Unknown
% 2.45/1.80 % (20312)Termination phase: Saturation
% 2.45/1.80
% 2.45/1.80 % (20312)Memory used [KB]: 7036
% 2.45/1.80 % (20312)Time elapsed: 0.213 s
% 2.45/1.80 % (20312)Instructions burned: 780 (million)
% 2.45/1.80 % (20312)------------------------------
% 2.45/1.80 % (20312)------------------------------
% 2.45/1.81 % (20328)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_20010 for (2996ds/507Mi)
% 2.45/1.81 % (20329)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_20010 for (2996ds/149Mi)
% 2.45/1.81 % (20330)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_20010 for (2996ds/39Mi)
% 2.45/1.82 % (20327)Instruction limit reached!
% 2.45/1.82 % (20327)------------------------------
% 2.45/1.82 % (20327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.82 % (20327)Termination reason: Unknown
% 2.45/1.82 % (20327)Termination phase: Saturation
% 2.45/1.82
% 2.45/1.82 % (20327)Memory used [KB]: 1663
% 2.45/1.82 % (20327)Time elapsed: 0.028 s
% 2.45/1.82 % (20327)Instructions burned: 98 (million)
% 2.45/1.82 % (20327)------------------------------
% 2.45/1.82 % (20327)------------------------------
% 2.45/1.82 % (20330)Instruction limit reached!
% 2.45/1.82 % (20330)------------------------------
% 2.45/1.82 % (20330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.82 % (20330)Termination reason: Unknown
% 2.45/1.82 % (20330)Termination phase: Property scanning
% 2.45/1.82
% 2.45/1.82 % (20330)Memory used [KB]: 1535
% 2.45/1.82 % (20330)Time elapsed: 0.013 s
% 2.45/1.82 % (20330)Instructions burned: 41 (million)
% 2.45/1.82 % (20330)------------------------------
% 2.45/1.82 % (20330)------------------------------
% 2.45/1.83 % (20331)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_20010 for (2996ds/6Mi)
% 2.45/1.83 % (20332)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_20010 for (2996ds/1087Mi)
% 2.45/1.83 % (20331)Instruction limit reached!
% 2.45/1.83 % (20331)------------------------------
% 2.45/1.83 % (20331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.83 % (20331)Termination reason: Unknown
% 2.45/1.83 % (20331)Termination phase: shuffling
% 2.45/1.83
% 2.45/1.83 % (20331)Memory used [KB]: 1279
% 2.45/1.83 % (20331)Time elapsed: 0.004 s
% 2.45/1.83 % (20331)Instructions burned: 8 (million)
% 2.45/1.83 % (20331)------------------------------
% 2.45/1.83 % (20331)------------------------------
% 2.45/1.84 % (20333)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_20010 for (2996ds/47Mi)
% 2.45/1.85 % (20307)Instruction limit reached!
% 2.45/1.85 % (20307)------------------------------
% 2.45/1.85 % (20307)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.85 % (20307)Termination reason: Unknown
% 2.45/1.85 % (20307)Termination phase: Saturation
% 2.45/1.85
% 2.45/1.85 % (20307)Memory used [KB]: 9466
% 2.45/1.85 % (20307)Time elapsed: 0.285 s
% 2.45/1.85 % (20307)Instructions burned: 904 (million)
% 2.45/1.85 % (20307)------------------------------
% 2.45/1.85 % (20307)------------------------------
% 2.45/1.86 % (20329)Instruction limit reached!
% 2.45/1.86 % (20329)------------------------------
% 2.45/1.86 % (20329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.86 % (20329)Termination reason: Unknown
% 2.45/1.86 % (20329)Termination phase: Saturation
% 2.45/1.86
% 2.45/1.86 % (20329)Memory used [KB]: 6652
% 2.45/1.86 % (20329)Time elapsed: 0.068 s
% 2.45/1.86 % (20329)Instructions burned: 149 (million)
% 2.45/1.86 % (20329)------------------------------
% 2.45/1.86 % (20329)------------------------------
% 2.45/1.86 % (20333)Instruction limit reached!
% 2.45/1.86 % (20333)------------------------------
% 2.45/1.86 % (20333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.86 % (20333)Termination reason: Unknown
% 2.45/1.86 % (20333)Termination phase: Saturation
% 2.45/1.86
% 2.45/1.86 % (20333)Memory used [KB]: 6012
% 2.45/1.86 % (20333)Time elapsed: 0.015 s
% 2.45/1.86 % (20333)Instructions burned: 48 (million)
% 2.45/1.86 % (20333)------------------------------
% 2.45/1.86 % (20333)------------------------------
% 2.45/1.86 % (20334)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_20010 for (2996ds/44Mi)
% 2.45/1.86 % (20335)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_20010 for (2996ds/432Mi)
% 2.45/1.87 % (20336)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_20010 for (2996ds/62Mi)
% 2.45/1.87 % (20334)Instruction limit reached!
% 2.45/1.87 % (20334)------------------------------
% 2.45/1.87 % (20334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.87 % (20334)Termination reason: Unknown
% 2.45/1.87 % (20334)Termination phase: Property scanning
% 2.45/1.87
% 2.45/1.87 % (20334)Memory used [KB]: 1535
% 2.45/1.87 % (20334)Time elapsed: 0.012 s
% 2.45/1.87 % (20334)Instructions burned: 44 (million)
% 2.45/1.87 % (20334)------------------------------
% 2.45/1.87 % (20334)------------------------------
% 2.45/1.88 % (20332)First to succeed.
% 2.45/1.88 % (20332)Refutation found. Thanks to Tanya!
% 2.45/1.88 % SZS status Theorem for DTF2THF_20010
% 2.45/1.88 % SZS output start Proof for DTF2THF_20010
% 2.45/1.88 thf(func_def_0, type, in: $i > $i > $o).
% 2.45/1.88 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.45/1.88 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.45/1.88 thf(func_def_8, type, powerset: $i > $i).
% 2.45/1.88 thf(func_def_10, type, setunion: $i > $i).
% 2.45/1.88 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.45/1.88 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_26, type, prop2set: $o > $i).
% 2.45/1.88 thf(func_def_36, type, nonempty: $i > $o).
% 2.45/1.88 thf(func_def_69, type, set2prop: $i > $o).
% 2.45/1.88 thf(func_def_88, type, subset: $i > $i > $o).
% 2.45/1.88 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.45/1.88 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.45/1.88 thf(func_def_125, type, sP0: $i > $i > $i > $o).
% 2.45/1.88 thf(func_def_126, type, sP1: $i > $i > $o).
% 2.45/1.88 thf(func_def_127, type, sP2: $i > $i > $o).
% 2.45/1.88 thf(func_def_128, type, sP3: $i > $o).
% 2.45/1.88 thf(func_def_129, type, sP4: $i > $i > $o).
% 2.45/1.88 thf(func_def_130, type, sP5: $i > $i > $o).
% 2.45/1.88 thf(func_def_131, type, sP6: $i > ($i > $o) > $o).
% 2.45/1.88 thf(func_def_134, type, sP9: $i > $i > $o > $o).
% 2.45/1.88 thf(func_def_135, type, sP10: $i > $i > $i > $o).
% 2.45/1.88 thf(func_def_136, type, sP11: ($i > $o) > $o).
% 2.45/1.88 thf(func_def_138, type, sP13: $i > $i > $i > $o).
% 2.45/1.88 thf(func_def_140, type, sP15: $i > $o > $i > $o).
% 2.45/1.88 thf(func_def_141, type, sP16: ($i > $o) > $o).
% 2.45/1.88 thf(func_def_142, type, sP17: $i > ($i > $i > $o) > $i > $o).
% 2.45/1.88 thf(func_def_143, type, sP18: $i > ($i > $i > $o) > $o).
% 2.45/1.88 thf(func_def_145, type, sP20: $i > $o).
% 2.45/1.88 thf(func_def_146, type, sP21: ($i > $o) > $o).
% 2.45/1.88 thf(func_def_147, type, sP22: $i > $i > $o).
% 2.45/1.88 thf(func_def_149, type, sP24: ($i > $o) > $o).
% 2.45/1.88 thf(func_def_150, type, sP25: $i > $i > $o).
% 2.45/1.88 thf(func_def_152, type, sP27: ($i > $o) > $o).
% 2.45/1.88 thf(func_def_153, type, sP28: $i > $o).
% 2.45/1.88 thf(func_def_154, type, sP29: $i > $o).
% 2.45/1.88 thf(func_def_155, type, sP30: $i > ($i > $o) > ($i > $o) > $i > $o).
% 2.45/1.88 thf(func_def_156, type, sP31: $i > ($i > $o) > $o).
% 2.45/1.88 thf(func_def_158, type, sP33: $i > ($i > $o) > $o).
% 2.45/1.88 thf(func_def_161, type, sP36: $i > ($i > $o) > $o).
% 2.45/1.88 thf(func_def_163, type, sP38: ($i > $o) > $i > $o).
% 2.45/1.88 thf(func_def_165, type, sP40: ($i > $o) > $i > $o).
% 2.45/1.88 thf(func_def_167, type, sP42: $i > $i > $o).
% 2.45/1.88 thf(func_def_173, type, sK48: $i > $i > $i).
% 2.45/1.88 thf(func_def_174, type, sK49: $i > $i > $i).
% 2.45/1.88 thf(func_def_175, type, sK50: $i > $i > $i > $i).
% 2.45/1.88 thf(func_def_176, type, sK51: $i > $i > $i).
% 2.45/1.88 thf(func_def_177, type, sK52: $i > $i > $i).
% 2.45/1.88 thf(func_def_178, type, sK53: $i > $i > $i).
% 2.45/1.88 thf(func_def_179, type, sK54: $i > $i).
% 2.45/1.88 thf(func_def_180, type, sK55: $i > $i).
% 2.45/1.88 thf(func_def_181, type, sK56: $i > $i).
% 2.45/1.88 thf(func_def_182, type, sK57: $i > $i).
% 2.45/1.88 thf(func_def_183, type, sK58: $i > $i > $i).
% 2.45/1.88 thf(func_def_184, type, sK59: $i > $i > $i).
% 2.45/1.88 thf(func_def_185, type, sK60: $i > $i > $i).
% 2.45/1.88 thf(func_def_186, type, sK61: $i > $i > $i).
% 2.45/1.88 thf(func_def_187, type, sK62: $i > $i > $i).
% 2.45/1.88 thf(func_def_188, type, sK63: $i > $i > $i > $i).
% 2.45/1.88 thf(func_def_189, type, sK64: $i > $i > $i > $i).
% 2.45/1.88 thf(func_def_190, type, sK65: $i > $i).
% 2.45/1.88 thf(func_def_194, type, sK69: $i > $o).
% 2.45/1.88 thf(func_def_196, type, sK71: $i > $o).
% 2.45/1.88 thf(func_def_197, type, sK72: ($i > $o) > $i > $i).
% 2.45/1.88 thf(func_def_198, type, sK73: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_201, type, sK76: $i > $o).
% 2.45/1.88 thf(func_def_202, type, sK77: $i > $o).
% 2.45/1.88 thf(func_def_203, type, sK78: ($i > $o) > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_204, type, sK79: ($i > $o) > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_210, type, sK85: $i > $i > $i > $o).
% 2.45/1.88 thf(func_def_216, type, sK91: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_217, type, sK92: ($i > $o) > $i).
% 2.45/1.88 thf(func_def_218, type, sK93: $i > $o).
% 2.45/1.88 thf(func_def_221, type, sK96: $i > $i > $i).
% 2.45/1.88 thf(func_def_225, type, sK100: $i > $o > $i > $i).
% 2.45/1.88 thf(func_def_233, type, sK108: $i > $o).
% 2.45/1.88 thf(func_def_234, type, sK109: ($i > $o) > $i).
% 2.45/1.88 thf(func_def_235, type, sK110: $i > $o).
% 2.45/1.88 thf(func_def_240, type, sK115: ($i > $o) > $i).
% 2.45/1.88 thf(func_def_241, type, sK116: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_242, type, sK117: $i > $o).
% 2.45/1.88 thf(func_def_243, type, sK118: $i > $i > $o).
% 2.45/1.88 thf(func_def_245, type, sK120: $i > ($i > $i > $o) > $i).
% 2.45/1.88 thf(func_def_246, type, sK121: $i > $i > ($i > $i > $o) > $i).
% 2.45/1.88 thf(func_def_247, type, sK122: $i > ($i > $i > $o) > $i).
% 2.45/1.88 thf(func_def_248, type, sK123: $i > ($i > $i > $o) > $i > $i).
% 2.45/1.88 thf(func_def_249, type, sK124: $i > $i > $i).
% 2.45/1.88 thf(func_def_250, type, sK125: $i > $i).
% 2.45/1.88 thf(func_def_255, type, sK130: $i > $o).
% 2.45/1.88 thf(func_def_264, type, sK139: $i > $o).
% 2.45/1.88 thf(func_def_266, type, sK141: $i > $i).
% 2.45/1.88 thf(func_def_271, type, sK146: ($i > $o) > $i).
% 2.45/1.88 thf(func_def_272, type, sK147: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_273, type, sK148: $i > $o).
% 2.45/1.88 thf(func_def_278, type, sK153: $i > $o).
% 2.45/1.88 thf(func_def_281, type, sK156: $i > $i > $i).
% 2.45/1.88 thf(func_def_282, type, sK157: $i > $o).
% 2.45/1.88 thf(func_def_288, type, sK163: $i > $i).
% 2.45/1.88 thf(func_def_291, type, sK166: $i > $i > $i).
% 2.45/1.88 thf(func_def_295, type, sK170: $i > $o).
% 2.45/1.88 thf(func_def_297, type, sK172: $i > $i).
% 2.45/1.88 thf(func_def_313, type, sK188: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_314, type, sK189: ($i > $o) > $i).
% 2.45/1.88 thf(func_def_315, type, sK190: $i > $o).
% 2.45/1.88 thf(func_def_318, type, sK193: $i > $i > $i).
% 2.45/1.88 thf(func_def_319, type, sK194: $i > $i > $i).
% 2.45/1.88 thf(func_def_320, type, sK195: ($i > $o) > $i).
% 2.45/1.88 thf(func_def_321, type, sK196: ($i > $o) > $i).
% 2.45/1.88 thf(func_def_322, type, sK197: $i > $o).
% 2.45/1.88 thf(func_def_328, type, sK203: $i > $i).
% 2.45/1.88 thf(func_def_329, type, sK204: $i > $i).
% 2.45/1.88 thf(func_def_335, type, sK210: $i > ($i > $o) > ($i > $o) > $i > $i).
% 2.45/1.88 thf(func_def_336, type, sK211: $i > ($i > $o) > ($i > $o) > $i > $i).
% 2.45/1.88 thf(func_def_339, type, sK214: $i > $o).
% 2.45/1.88 thf(func_def_340, type, sK215: $i > $o).
% 2.45/1.88 thf(func_def_345, type, sK220: $i > $o).
% 2.45/1.88 thf(func_def_347, type, sK222: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_348, type, sK223: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_354, type, sK229: $i > $i).
% 2.45/1.88 thf(func_def_356, type, sK231: $i > $o).
% 2.45/1.88 thf(func_def_361, type, sK236: $i > $o).
% 2.45/1.88 thf(func_def_362, type, sK237: ($i > $o) > $i > $i).
% 2.45/1.88 thf(func_def_363, type, sK238: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_364, type, sK239: $i > $o).
% 2.45/1.88 thf(func_def_372, type, sK247: $i > $o).
% 2.45/1.88 thf(func_def_379, type, sK254: $i > $o).
% 2.45/1.88 thf(func_def_388, type, sK263: $i > $i > $i).
% 2.45/1.88 thf(func_def_389, type, sK264: $i > $o).
% 2.45/1.88 thf(func_def_391, type, sK266: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_392, type, sK267: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_403, type, sK278: $i > $o).
% 2.45/1.88 thf(func_def_404, type, sK279: ($i > $o) > $i > $i).
% 2.45/1.88 thf(func_def_405, type, sK280: ($i > $o) > $i > $i).
% 2.45/1.88 thf(func_def_406, type, sK281: $i > $o).
% 2.45/1.88 thf(func_def_408, type, sK283: $i > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_409, type, sK284: ($i > $o) > $i > $i).
% 2.45/1.88 thf(func_def_415, type, sK290: $i > $i > $i).
% 2.45/1.88 thf(func_def_419, type, sK294: $i > $o).
% 2.45/1.88 thf(func_def_420, type, sK295: $i > $o).
% 2.45/1.88 thf(func_def_421, type, sK296: ($i > $o) > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_422, type, sK297: ($i > $o) > ($i > $o) > $i).
% 2.45/1.88 thf(func_def_425, type, sK300: $i > $i > $i).
% 2.45/1.88 thf(func_def_426, type, sK301: $i > $o).
% 2.45/1.88 thf(func_def_434, type, ph309: !>[X0: $tType]:(X0)).
% 2.45/1.88 thf(f2703,plain,(
% 2.45/1.88 $false),
% 2.45/1.88 inference(trivial_inequality_removal,[status(thm)],[f2700])).
% 2.45/1.88 thf(f2700,plain,(
% 2.45/1.88 ($true != $true)),
% 2.45/1.88 inference(superposition,[status(thm)],[f1963,f2695])).
% 2.45/1.88 thf(f2695,plain,(
% 2.45/1.88 ( ! [X0 : $i,X1 : $i > $o] : (($true = (subset @ (dsetconstr @ X0 @ X1) @ X0))) )),
% 2.45/1.88 inference(trivial_inequality_removal,[status(thm)],[f2691])).
% 2.45/1.88 thf(f2691,plain,(
% 2.45/1.88 ( ! [X0 : $i,X1 : $i > $o] : (($true = (subset @ (dsetconstr @ X0 @ X1) @ X0)) | ($true != $true)) )),
% 2.45/1.88 inference(superposition,[status(thm)],[f1958,f2047])).
% 2.45/1.88 thf(f2047,plain,(
% 2.45/1.88 ( ! [X0 : $i,X1 : $i > $o] : (($true = (in @ (dsetconstr @ X0 @ X1) @ (powerset @ X0)))) )),
% 2.45/1.88 inference(beta_eta_normalization,[status(thm)],[f2046])).
% 2.45/1.88 thf(f2046,plain,(
% 2.45/1.88 ( ! [X0 : $i,X1 : $i > $o] : (($true = (in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0)))) )),
% 2.45/1.88 inference(trivial_inequality_removal,[status(thm)],[f1739])).
% 2.45/1.88 thf(f1739,plain,(
% 2.45/1.88 ( ! [X0 : $i,X1 : $i > $o] : (($true != $true) | ($true = (in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0)))) )),
% 2.45/1.88 inference(definition_unfolding,[status(thm)],[f1374,f1315])).
% 2.45/1.88 thf(f1315,plain,(
% 2.45/1.88 (sepInPowerset = $true)),
% 2.45/1.88 inference(cnf_transformation,[status(thm)],[f727])).
% 2.45/1.88 thf(f727,plain,(
% 2.45/1.88 (quantDeMorgan2 = $true) & (subsetE = $true) & (wellorderingAx = $true) & (emptyinPowerset = $true) & (descrp = $true) & (eqinunit = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (subsetI2 = $true) & (dsetconstrI = $true) & (setadjoin__Cong = $true) & (dsetconstrEL = $true) & (omegaIndAx = $true) & (noeltsimpempty = $true) & (subsetE2 = $true) & (exuE1 = $true) & (exu__Cong = $true) & (emptysetAx = $true) & (notdexE = $true) & (exuE2 = $true) & (emptyset__Cong = $true) & (setext = $true) & (exuI2 = $true) & (replAx = $true) & (setadjoinIR = $true) & (setunion__Cong = $true) & (notinsingleton = $true) & (foundationAx = $true) & (emptysetsubset = $true) & (eqimpsubset1 = $true) & (setadjoinE = $true) & (exuEu = $true) & (sepInPowerset = $true) & ($true != (subset @ (dsetconstr @ sK152 @ (^[Y0 : $i]: (sK153 @ Y0))) @ sK152)) & (omega0Ax = $true) & (setadjoinAx = $true) & (emptysetE = $true) & (setextsub = $true) & (singletonsswitch = $true) & (setadjoinSub = $true) & (setadjoinSub2 = $true) & (exuE3e = $true) & (descr__Cong = $true) & (powersetE = $true) & (quantDeMorgan1 = $true) & (prop2set2propI = $true) & (powersetI = $true) & (quantDeMorgan3 = $true) & (exuI1 = $true) & (powerset__Cong = $true) & (notinemptyset = $true) & (subsetTrans = $true) & (inCongP = $true) & (nonemptyE1 = $true) & (subsetI1 = $true) & (notsubsetI = $true) & (powersetE1 = $true) & (subsetRefl = $true) & (emptyE1 = $true) & (subsetemptysetimpeq = $true) & (omega__Cong = $true) & (nonemptyI = $true) & (emptyInPowerset = $true) & (setadjoinIL = $true) & (subPowSU = $true) & (in__Cong = $true) & (emptysetimpfalse = $true) & (nonemptyI1 = $true) & (inPowerset = $true) & (prop2setI = $true) & (setoftrueEq = $true) & (upairsetE = $true) & (setadjoinOr = $true) & (vacuousDall = $true) & (emptyI = $true) & (setunionE = $true) & (notdallE = $true) & (eqimpsubset2 = $true) & (setbeta = $true) & (powersetsubset = $true) & (subset2powerset = $true) & (notequalI1 = $true) & (setunionAx = $true) & (powersetAx = $true) & (setextAx = $true) & (exuE3u = $true) & (nonemptyImpWitness = $true) & (emptyinunitempty = $true) & (uniqinunit = $true) & (upairsetIL = $true) & (omegaSAx = $true) & (quantDeMorgan4 = $true) & (powersetI1 = $true) & (dsetconstr__Cong = $true) & (upairsetIR = $true) & (exuI3 = $true) & (notequalI2 = $true) & (setunionI = $true)),
% 2.45/1.88 inference(skolemisation,[status(esa),new_symbols(skolem,[sK152,sK153])],[f351,f726])).
% 2.45/1.88 thf(f726,plain,(
% 2.45/1.88 ? [X0 : $i,X1 : $i > $o] : ($true != (subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ X0)) => ($true != (subset @ (dsetconstr @ sK152 @ (^[Y0 : $i]: (sK153 @ Y0))) @ sK152))),
% 2.45/1.88 introduced(definition,[],[choice_axiom])).
% 2.45/1.88 thf(f351,plain,(
% 2.45/1.88 (quantDeMorgan2 = $true) & (subsetE = $true) & (wellorderingAx = $true) & (emptyinPowerset = $true) & (descrp = $true) & (eqinunit = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (subsetI2 = $true) & (dsetconstrI = $true) & (setadjoin__Cong = $true) & (dsetconstrEL = $true) & (omegaIndAx = $true) & (noeltsimpempty = $true) & (subsetE2 = $true) & (exuE1 = $true) & (exu__Cong = $true) & (emptysetAx = $true) & (notdexE = $true) & (exuE2 = $true) & (emptyset__Cong = $true) & (setext = $true) & (exuI2 = $true) & (replAx = $true) & (setadjoinIR = $true) & (setunion__Cong = $true) & (notinsingleton = $true) & (foundationAx = $true) & (emptysetsubset = $true) & (eqimpsubset1 = $true) & (setadjoinE = $true) & (exuEu = $true) & (sepInPowerset = $true) & ? [X0 : $i,X1 : $i > $o] : ($true != (subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ X0)) & (omega0Ax = $true) & (setadjoinAx = $true) & (emptysetE = $true) & (setextsub = $true) & (singletonsswitch = $true) & (setadjoinSub = $true) & (setadjoinSub2 = $true) & (exuE3e = $true) & (descr__Cong = $true) & (powersetE = $true) & (quantDeMorgan1 = $true) & (prop2set2propI = $true) & (powersetI = $true) & (quantDeMorgan3 = $true) & (exuI1 = $true) & (powerset__Cong = $true) & (notinemptyset = $true) & (subsetTrans = $true) & (inCongP = $true) & (nonemptyE1 = $true) & (subsetI1 = $true) & (notsubsetI = $true) & (powersetE1 = $true) & (subsetRefl = $true) & (emptyE1 = $true) & (subsetemptysetimpeq = $true) & (omega__Cong = $true) & (nonemptyI = $true) & (emptyInPowerset = $true) & (setadjoinIL = $true) & (subPowSU = $true) & (in__Cong = $true) & (emptysetimpfalse = $true) & (nonemptyI1 = $true) & (inPowerset = $true) & (prop2setI = $true) & (setoftrueEq = $true) & (upairsetE = $true) & (setadjoinOr = $true) & (vacuousDall = $true) & (emptyI = $true) & (setunionE = $true) & (notdallE = $true) & (eqimpsubset2 = $true) & (setbeta = $true) & (powersetsubset = $true) & (subset2powerset = $true) & (notequalI1 = $true) & (setunionAx = $true) & (powersetAx = $true) & (setextAx = $true) & (exuE3u = $true) & (nonemptyImpWitness = $true) & (emptyinunitempty = $true) & (uniqinunit = $true) & (upairsetIL = $true) & (omegaSAx = $true) & (quantDeMorgan4 = $true) & (powersetI1 = $true) & (dsetconstr__Cong = $true) & (upairsetIR = $true) & (exuI3 = $true) & (notequalI2 = $true) & (setunionI = $true)),
% 2.45/1.88 inference(flattening,[status(thm)],[f350])).
% 2.45/1.88 thf(f350,plain,(
% 2.45/1.88 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i > $o] : ($true != (subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ X0)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.45/1.88 inference(ennf_transformation,[status(thm)],[f152])).
% 2.45/1.88 thf(f152,plain,(
% 2.45/1.88 ~((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) => ! [X0 : $i,X1 : $i > $o] : ($true = (subset @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.45/1.88 inference(fool_elimination,[status(thm)],[f151])).
% 2.45/1.88 thf(f151,plain,(
% 2.45/1.88 ~(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 => ! [X0 : $i,X1 : $i > $o] : (subset @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.45/1.88 inference(rectify,[status(thm)],[f101])).
% 2.45/1.88 thf(f101,negated_conjecture,(
% 2.45/1.88 ~(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 => ! [X3 : $i,X0 : $i > $o] : (subset @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.45/1.88 inference(negated_conjecture,[status(cth)],[f100])).
% 2.45/1.88 thf(f100,conjecture,(
% 2.45/1.88 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 => ! [X3 : $i,X0 : $i > $o] : (subset @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.45/1.88 file('/export/starexec/sandbox/tmp/tmp.ChmJPLfBjb/DTF2THF_20010.p',sepSubset)).
% 2.45/1.88 thf(f1374,plain,(
% 2.45/1.88 ( ! [X0 : $i,X1 : $i > $o] : (($true = (in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0))) | (sepInPowerset != $true)) )),
% 2.45/1.88 inference(cnf_transformation,[status(thm)],[f762])).
% 2.45/1.88 thf(f762,plain,(
% 2.45/1.88 (! [X0 : $i,X1 : $i > $o] : ($true = (in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0))) | (sepInPowerset != $true)) & ((sepInPowerset = $true) | ($true != (in @ (dsetconstr @ sK169 @ (^[Y0 : $i]: (sK170 @ Y0))) @ (powerset @ sK169))))),
% 2.45/1.88 inference(skolemisation,[status(esa),new_symbols(skolem,[sK169,sK170])],[f760,f761])).
% 2.45/1.88 thf(f761,plain,(
% 2.45/1.88 ? [X2 : $i,X3 : $i > $o] : ($true != (in @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X3 @ Y0))) @ (powerset @ X2))) => ($true != (in @ (dsetconstr @ sK169 @ (^[Y0 : $i]: (sK170 @ Y0))) @ (powerset @ sK169)))),
% 2.45/1.88 introduced(definition,[],[choice_axiom])).
% 2.45/1.88 thf(f760,plain,(
% 2.45/1.88 (! [X0 : $i,X1 : $i > $o] : ($true = (in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0))) | (sepInPowerset != $true)) & ((sepInPowerset = $true) | ? [X2 : $i,X3 : $i > $o] : ($true != (in @ (dsetconstr @ X2 @ (^[Y0 : $i]: (X3 @ Y0))) @ (powerset @ X2))))),
% 2.45/1.88 inference(rectify,[status(thm)],[f759])).
% 2.45/1.88 thf(f759,plain,(
% 2.45/1.88 (! [X0 : $i,X1 : $i > $o] : ($true = (in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0))) | (sepInPowerset != $true)) & ((sepInPowerset = $true) | ? [X0 : $i,X1 : $i > $o] : ($true != (in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0))))),
% 2.45/1.88 inference(nnf_transformation,[status(thm)],[f256])).
% 2.45/1.88 thf(f256,plain,(
% 2.45/1.88 ! [X0 : $i,X1 : $i > $o] : ($true = (in @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))) @ (powerset @ X0))) <=> (sepInPowerset = $true)),
% 2.45/1.88 inference(fool_elimination,[status(thm)],[f255])).
% 2.45/1.88 thf(f255,plain,(
% 2.45/1.88 (! [X0 : $i,X1 : $i > $o] : (in @ (dsetconstr @ X0 @ (^[X2 : $i] : (X1 @ X2))) @ (powerset @ X0)) = sepInPowerset)),
% 2.45/1.88 inference(rectify,[status(thm)],[f99])).
% 2.45/1.88 thf(f99,axiom,(
% 2.45/1.88 (! [X3 : $i,X0 : $i > $o] : (in @ (dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) @ (powerset @ X3)) = sepInPowerset)),
% 2.45/1.88 file('/export/starexec/sandbox/tmp/tmp.ChmJPLfBjb/DTF2THF_20010.p',sepInPowerset)).
% 2.45/1.88 thf(f1958,plain,(
% 2.45/1.88 ( ! [X2 : $i,X3 : $i] : (($true != (in @ X3 @ (powerset @ X2))) | ($true = (subset @ X3 @ X2))) )),
% 2.45/1.88 inference(trivial_inequality_removal,[status(thm)],[f1864])).
% 2.45/1.88 thf(f1864,plain,(
% 2.45/1.88 ( ! [X2 : $i,X3 : $i] : (($true != $true) | ($true = (subset @ X3 @ X2)) | ($true != (in @ X3 @ (powerset @ X2)))) )),
% 2.45/1.88 inference(definition_unfolding,[status(thm)],[f1549,f1291])).
% 2.45/1.88 thf(f1291,plain,(
% 2.45/1.88 (powersetE1 = $true)),
% 2.45/1.88 inference(cnf_transformation,[status(thm)],[f727])).
% 2.45/1.88 thf(f1549,plain,(
% 2.45/1.88 ( ! [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ X2)) | ($true != (in @ X3 @ (powerset @ X2))) | (powersetE1 != $true)) )),
% 2.45/1.88 inference(cnf_transformation,[status(thm)],[f980])).
% 2.45/1.88 thf(f980,plain,(
% 2.45/1.88 ((powersetE1 = $true) | (($true != (subset @ sK271 @ sK270)) & ($true = (in @ sK271 @ (powerset @ sK270))))) & (! [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ X2)) | ($true != (in @ X3 @ (powerset @ X2)))) | (powersetE1 != $true))),
% 2.45/1.88 inference(skolemisation,[status(esa),new_symbols(skolem,[sK270,sK271])],[f978,f979])).
% 2.45/1.88 thf(f979,plain,(
% 2.45/1.88 ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ($true = (in @ X1 @ (powerset @ X0)))) => (($true != (subset @ sK271 @ sK270)) & ($true = (in @ sK271 @ (powerset @ sK270))))),
% 2.45/1.88 introduced(definition,[],[choice_axiom])).
% 2.45/1.88 thf(f978,plain,(
% 2.45/1.88 ((powersetE1 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ($true = (in @ X1 @ (powerset @ X0))))) & (! [X2 : $i,X3 : $i] : (($true = (subset @ X3 @ X2)) | ($true != (in @ X3 @ (powerset @ X2)))) | (powersetE1 != $true))),
% 2.45/1.88 inference(rectify,[status(thm)],[f977])).
% 2.45/1.88 thf(f977,plain,(
% 2.45/1.88 ((powersetE1 = $true) | ? [X0 : $i,X1 : $i] : (($true != (subset @ X1 @ X0)) & ($true = (in @ X1 @ (powerset @ X0))))) & (! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ($true != (in @ X1 @ (powerset @ X0)))) | (powersetE1 != $true))),
% 2.45/1.88 inference(nnf_transformation,[status(thm)],[f423])).
% 2.45/1.88 thf(f423,plain,(
% 2.45/1.88 (powersetE1 = $true) <=> ! [X0 : $i,X1 : $i] : (($true = (subset @ X1 @ X0)) | ($true != (in @ X1 @ (powerset @ X0))))),
% 2.45/1.88 inference(ennf_transformation,[status(thm)],[f184])).
% 2.45/1.88 thf(f184,plain,(
% 2.45/1.88 ! [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (powerset @ X0))) => ($true = (subset @ X1 @ X0))) <=> (powersetE1 = $true)),
% 2.45/1.88 inference(fool_elimination,[status(thm)],[f183])).
% 2.45/1.88 thf(f183,plain,(
% 2.45/1.88 (powersetE1 = ! [X0 : $i,X1 : $i] : ((in @ X1 @ (powerset @ X0)) => (subset @ X1 @ X0)))),
% 2.45/1.88 inference(rectify,[status(thm)],[f96])).
% 2.45/1.88 thf(f96,axiom,(
% 2.45/1.88 (powersetE1 = ! [X3 : $i,X4 : $i] : ((in @ X4 @ (powerset @ X3)) => (subset @ X4 @ X3)))),
% 2.45/1.88 file('/export/starexec/sandbox/tmp/tmp.ChmJPLfBjb/DTF2THF_20010.p',powersetE1)).
% 2.45/1.88 thf(f1963,plain,(
% 2.45/1.88 ($true != (subset @ (dsetconstr @ sK152 @ sK153) @ sK152))),
% 2.45/1.88 inference(beta_eta_normalization,[status(thm)],[f1314])).
% 2.45/1.88 thf(f1314,plain,(
% 2.45/1.88 ($true != (subset @ (dsetconstr @ sK152 @ (^[Y0 : $i]: (sK153 @ Y0))) @ sK152))),
% 2.45/1.88 inference(cnf_transformation,[status(thm)],[f727])).
% 2.45/1.88 % SZS output end Proof for DTF2THF_20010
% 2.45/1.88 % (20332)------------------------------
% 2.45/1.88 % (20332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.88 % (20332)Termination reason: Refutation
% 2.45/1.88
% 2.45/1.88 % (20332)Memory used [KB]: 7547
% 2.45/1.88 % (20332)Time elapsed: 0.070 s
% 2.45/1.88 % (20332)Instructions burned: 131 (million)
% 2.45/1.88 % (20332)------------------------------
% 2.45/1.88 % (20332)------------------------------
% 2.45/1.88 % (20284)Success in time 0.412 s
%------------------------------------------------------------------------------