%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU592^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:13 AM UTC 2026
% Result : Theorem 0.20s 0.34s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 1739 ( 466 equ; 0 cnn)
% Maximal formula atoms : 109 ( 66 avg)
% Number of connectives : 911 ( 17 ~; 8 |; 327 &; 126 @)
% ( 1 <=>; 432 =>; 0 <=; 0 <~>)
% Maximal formula depth : 116 ( 32 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 284 ( 281 usr; 121 con; 0-4 aty)
% Number of variables : 64 ( 28 ^; 28 !; 8 ?; 64 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $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_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_128,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_129,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_130,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_131,type,
vAND: $o > $o > $o ).
thf(func_def_132,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_133,type,
vIMP: $o > $o > $o ).
thf(func_def_134,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_135,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_136,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_137,type,
vNOT: $o > $o ).
thf(func_def_138,type,
sP0: $o ).
thf(func_def_139,type,
sP1: $i > $i > $o ).
thf(func_def_140,type,
sP2: $i > $o ).
thf(func_def_141,type,
sP3: $i > $i > $o ).
thf(func_def_142,type,
sP4: $i > $i > $o ).
thf(func_def_147,type,
sK9: $i > $o ).
thf(func_def_152,type,
sK14: $i > $o ).
thf(func_def_158,type,
sK20: $i > $i > $i ).
thf(func_def_164,type,
sK26: $o ).
thf(func_def_168,type,
sK30: $o ).
thf(func_def_180,type,
sK42: $o ).
thf(func_def_182,type,
sK44: $i > $i > $o ).
thf(func_def_183,type,
sK45: $i > $i ).
thf(func_def_184,type,
sK46: $i > $i ).
thf(func_def_185,type,
sK47: ( $i > $i > $o ) > $i > $i ).
thf(func_def_186,type,
sK48: ( $i > $i > $o ) > $i > $i ).
thf(func_def_187,type,
sK49: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_190,type,
sK52: $i > $i > $i ).
thf(func_def_191,type,
sK53: $i > $i > $i ).
thf(func_def_192,type,
sK54: $i > $i > $i ).
thf(func_def_193,type,
sK55: $i > $i > $i ).
thf(func_def_194,type,
sK56: $i > $i > $i ).
thf(func_def_195,type,
sK57: $i > $i > $i > $i ).
thf(func_def_196,type,
sK58: $i > $i ).
thf(func_def_197,type,
sK59: $i > $i ).
thf(func_def_198,type,
sK60: $i > $i ).
thf(func_def_199,type,
sK61: $i > $i ).
thf(func_def_200,type,
sK62: $i > $i > $i > $i ).
thf(func_def_201,type,
sK63: $i > $i > $i > $i ).
thf(func_def_202,type,
sK64: $i > $i > $i ).
thf(func_def_203,type,
sK65: $i > $i > $i ).
thf(func_def_204,type,
sK66: $i > $i > $i ).
thf(func_def_205,type,
sK67: $i > $i ).
thf(func_def_207,type,
sK69: $i > $i ).
thf(func_def_208,type,
sK70: $i > $i ).
thf(func_def_211,type,
sK73: $i > $o ).
thf(func_def_213,type,
sK75: $i > $o ).
thf(func_def_219,type,
sK81: ( $i > $o ) > $i ).
thf(func_def_220,type,
sK82: $i > $o ).
thf(func_def_221,type,
sK83: $i > $i ).
thf(func_def_224,type,
sK86: $i > $o ).
thf(func_def_227,type,
sK89: $o > $i > $i > $i ).
thf(func_def_230,type,
sK92: $o ).
thf(func_def_233,type,
sK95: $i > $i ).
thf(func_def_236,type,
sK98: $i > $o ).
thf(func_def_238,type,
sK100: ( $i > $o ) > $i > $i ).
thf(func_def_239,type,
sK101: $i > $o ).
thf(func_def_241,type,
sK103: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_242,type,
sK104: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_245,type,
sK107: $i > $o ).
thf(func_def_246,type,
sK108: $i > $o ).
thf(func_def_248,type,
sK110: $i > $o ).
thf(func_def_250,type,
sK112: ( $i > $o ) > $i > $i ).
thf(func_def_255,type,
sK117: $i > $o ).
thf(func_def_269,type,
sK131: $i > $i ).
thf(func_def_271,type,
sK133: $i > $i ).
thf(func_def_272,type,
sK134: $i > $o ).
thf(func_def_273,type,
sK135: $i > $o ).
thf(func_def_274,type,
sK136: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_275,type,
sK137: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_277,type,
sK139: $i > $i ).
thf(func_def_279,type,
sK141: $i > $i ).
thf(func_def_281,type,
sK143: $i > $i ).
thf(func_def_283,type,
sK145: $i > $i > $i ).
thf(func_def_288,type,
sK150: $i > $o ).
thf(func_def_291,type,
sK153: $i > ( $i > $o ) > $i ).
thf(func_def_292,type,
sK154: $i > $o ).
thf(func_def_302,type,
sK164: $o ).
thf(func_def_305,type,
sK167: $o ).
thf(func_def_306,type,
sK168: $i > $o ).
thf(func_def_307,type,
sK169: $i > $i ).
thf(func_def_308,type,
sK170: ( $i > $o ) > $i ).
thf(func_def_309,type,
sK171: $i > ( $i > $o ) > $i ).
thf(func_def_310,type,
sK172: $i > $o ).
thf(func_def_312,type,
sK174: $i > $i > $i ).
thf(func_def_318,type,
sK180: $i > $o ).
thf(func_def_321,type,
sK183: $i > $o ).
thf(func_def_322,type,
sK184: ( $i > $o ) > $i ).
thf(func_def_326,type,
sK188: $i > $o ).
thf(func_def_329,type,
sK191: $i > ( $i > $o ) > $i ).
thf(func_def_330,type,
sK192: $o ).
thf(func_def_333,type,
sK195: $i > $o ).
thf(func_def_337,type,
sK199: $i > $o ).
thf(func_def_346,type,
sK208: $i > $o ).
thf(func_def_355,type,
sK217: $i > $i ).
thf(func_def_358,type,
sK220: $i > ( $i > $o ) > $i ).
thf(func_def_359,type,
sK221: $i > $o ).
thf(func_def_368,type,
sK230: $i > $o ).
thf(func_def_369,type,
sK231: $i > $o ).
thf(func_def_370,type,
sK232: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_371,type,
sK233: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_382,type,
sK244: $i > $i > $i ).
thf(func_def_394,type,
sK256: $i > $i > $i ).
thf(func_def_395,type,
sK257: $i > $i > $i ).
thf(func_def_400,type,
sK262: $i > ( $i > $o ) > $i ).
thf(func_def_401,type,
sK263: $i > $o ).
thf(func_def_416,type,
sK278: $i > $o ).
thf(func_def_419,type,
sK281: $i > ( $i > $o ) > $i ).
thf(func_def_420,type,
sK282: $i > $i > $i ).
thf(func_def_426,type,
sK288: $i > $o ).
thf(func_def_428,type,
sK290: ( $i > $o ) > $i ).
thf(func_def_429,type,
sK291: ( $i > $o ) > $i ).
thf(func_def_432,type,
sK294: $i > $i > $i ).
thf(func_def_438,type,
sK300: ( $i > $o ) > $i ).
thf(func_def_439,type,
sK301: $i > ( $i > $o ) > $i ).
thf(func_def_440,type,
sK302: $i > $i ).
thf(func_def_441,type,
sK303: $i > ( $i > $o ) > $i ).
thf(func_def_442,type,
sK304: ( $i > $o ) > $i ).
thf(func_def_443,type,
sK305: ( $i > $o ) > $i ).
thf(func_def_444,type,
sK306: ( $i > $o ) > $i ).
thf(func_def_445,type,
sK307: ( $i > $o ) > $i > $i ).
thf(func_def_446,type,
sK308: ( $i > $o ) > $i > $i ).
thf(func_def_447,type,
sK309: ( $i > $o ) > $i ).
thf(func_def_448,type,
sK310: ( $i > $o ) > $i > $i ).
thf(func_def_449,type,
sK311: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_450,type,
sK312: ( $i > $o ) > $i ).
thf(func_def_451,type,
sK313: $i > ( $i > $o ) > $i ).
thf(func_def_452,type,
sK314: $i > ( $i > $o ) > $i ).
thf(func_def_453,type,
sK315: ( $i > $o ) > $i > $i ).
thf(func_def_454,type,
sK316: ( $i > $o ) > $i > $i ).
thf(func_def_455,type,
sK317: $i > ( $i > $o ) > $i ).
thf(func_def_456,type,
sK318: ( $i > $o ) > $i ).
thf(func_def_457,type,
sK319: ( $i > $o ) > $i ).
thf(func_def_458,type,
sK320: ( $i > $o ) > $i ).
thf(func_def_459,type,
sK321: ( $i > $o ) > $i > $i ).
thf(func_def_460,type,
sK322: ( $i > $o ) > $i ).
thf(func_def_461,type,
sK323: ( $i > $o ) > $i > $i ).
thf(func_def_462,type,
sK324: ( $i > $o ) > $i > $i ).
thf(func_def_463,type,
sK325: ( $i > $o ) > $i ).
thf(func_def_464,type,
sK326: ( $i > $o ) > $i > $i ).
thf(func_def_465,type,
sK327: ( $i > $o ) > $i > $i ).
thf(func_def_466,type,
sK328: ( $i > $o ) > $i ).
thf(func_def_467,type,
sK329: ( $i > $o ) > $i > $i ).
thf(func_def_468,type,
sK330: ( $i > $o ) > $i > $i ).
thf(func_def_469,type,
sK331: $i > ( $i > $o ) > $i ).
thf(func_def_470,type,
sK332: ( $i > $o ) > $i > $i ).
thf(func_def_471,type,
sK333: ( $i > $o ) > $i > $i ).
thf(func_def_472,type,
sK334: $i > ( $i > $o ) > $i ).
thf(func_def_473,type,
sK335: ( $i > $o ) > $i ).
thf(func_def_474,type,
sK336: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_475,type,
sK337: $i > ( $i > $o ) > $i ).
thf(func_def_476,type,
sK338: ( $i > $o ) > $i > $i ).
thf(func_def_477,type,
sK339: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_478,type,
sK340: $i > ( $i > $o ) > $i ).
thf(f100,axiom,
( sepSubset
= ( ! [X1: $i > $o,X0: $i] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(f108,axiom,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersect) ).
thf(f112,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(f113,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f112]) ).
thf(f191,plain,
( binintersect
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[],[f108]) ).
thf(f192,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f191]) ).
thf(f227,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f113]) ).
thf(f228,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ! [X1: $i,X0: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f227]) ).
thf(f231,plain,
( sepSubset
= ( ! [X0: $i > $o,X1: $i] :
( subset
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
@ X1 ) ) ),
inference(rectify,[],[f100]) ).
thf(f232,plain,
( ( sepSubset = $true )
<=> ! [X0: $i > $o,X1: $i] :
( $true
= ( subset
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ X1 ) ) ),
inference(fool_elimination,[],[f231]) ).
thf(f447,plain,
( ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
!= $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f228]) ).
thf(f448,plain,
( ( inCongP = $true )
& ( upairsetIL = $true )
& ( binintersectEL = $true )
& ( uniqinunit = $true )
& ( binunionIR = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyInPowerset = $true )
& ( quantDeMorgan4 = $true )
& ( binunionE = $true )
& ( omegaSAx = $true )
& ( setunionI = $true )
& ( inPowerset = $true )
& ( subsetTrans = $true )
& ( setadjoinAx = $true )
& ( setextAx = $true )
& ( notdallE = $true )
& ( nonemptyI = $true )
& ( notequalI1 = $true )
& ( setoftrueEq = $true )
& ( upairsetIR = $true )
& ( omega__Cong = $true )
& ( eqimpsubset2 = $true )
& ( descr__Cong = $true )
& ( emptysetE = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset5 = $true )
& ( setext = $true )
& ( setadjoin__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( powersetE = $true )
& ( notinemptyset = $true )
& ( powersetE1 = $true )
& ( subsetE2 = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetAx = $true )
& ( omega0Ax = $true )
& ( dsetconstr__Cong = $true )
& ( upairset2IR = $true )
& ( setunionAx = $true )
& ( noeltsimpempty = $true )
& ( sepInPowerset = $true )
& ( setunionE = $true )
& ( emptyE1 = $true )
& ( exuI2 = $true )
& ( nonemptyI1 = $true )
& ( subsetI2 = $true )
& ( sepSubset = $true )
& ( dsetconstrEL = $true )
& ( subsetE = $true )
& ( notsubsetI = $true )
& ( setunion__Cong = $true )
& ( subset2powerset = $true )
& ( notequalI2 = $true )
& ( foundationAx = $true )
& ( subPowSU = $true )
& ( exuI3 = $true )
& ( notinsingleton = $true )
& ( vacuousDall = $true )
& ( exuE3e = $true )
& ( setadjoinIR = $true )
& ( powersetsubset = $true )
& ( prop2set2propI = $true )
& ( dsetconstrER = $true )
& ( powersetAx = $true )
& ( in__Cong = $true )
& ( dsetconstrI = $true )
& ( setadjoinSub = $true )
& ( setadjoinSub2 = $true )
& ( setbeta = $true )
& ( eqinunit = $true )
& ( prop2setE = $true )
& ( binunionLsub = $true )
& ( emptysetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( exuEu = $true )
& ( exuE2 = $true )
& ( replAx = $true )
& ( subsetI1 = $true )
& ( powersetI = $true )
& ( prop2setI = $true )
& ( notdexE = $true )
& ( emptyinPowerset = $true )
& ( descrp = $true )
& ( setadjoinE = $true )
& ( emptyI = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan2 = $true )
& ( wellorderingAx = $true )
& ( exu__Cong = $true )
& ( setextsub = $true )
& ( nonemptyE1 = $true )
& ( powersetI1 = $true )
& ( exuE1 = $true )
& ( binunionRsub = $true )
& ( exuI1 = $true )
& ( exuE3u = $true )
& ( eqimpsubset1 = $true )
& ( emptyset__Cong = $true )
& ( binintersectI = $true )
& ( subsetRefl = $true )
& ( binunionIL = $true )
& ( upairsetE = $true )
& ( binunionEcases = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
!= $true )
& ( setadjoinOr = $true )
& ( powerset__Cong = $true ) ),
inference(flattening,[],[f447]) ).
thf(f690,plain,
( ( ( sepSubset = $true )
| ? [X0: $i > $o,X1: $i] :
( $true
!= ( subset
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ X1 ) ) )
& ( ! [X0: $i > $o,X1: $i] :
( $true
= ( subset
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ X1 ) )
| ( sepSubset != $true ) ) ),
inference(nnf_transformation,[],[f232]) ).
thf(f691,plain,
( ( ( sepSubset = $true )
| ? [X0: $i > $o,X1: $i] :
( $true
!= ( subset
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ X1 ) ) )
& ( ! [X2: $i > $o,X3: $i] :
( $true
= ( subset
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X3 ) )
| ( sepSubset != $true ) ) ),
inference(rectify,[],[f690]) ).
thf(f692,plain,
( ( ( sepSubset = $true )
| ( $true
!= ( subset
@ ( dsetconstr @ sK200
@ ^ [Y0: $i] : ( sK199 @ Y0 ) )
@ sK200 ) ) )
& ( ! [X2: $i > $o,X3: $i] :
( $true
= ( subset
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X3 ) )
| ( sepSubset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK199,sK200]),skolemize(X0,sK199),skolemize(X1,sK200)],[f691]) ).
thf(f790,plain,
( ( inCongP = $true )
& ( upairsetIL = $true )
& ( binintersectEL = $true )
& ( uniqinunit = $true )
& ( binunionIR = $true )
& ( subsetemptysetimpeq = $true )
& ( emptyInPowerset = $true )
& ( quantDeMorgan4 = $true )
& ( binunionE = $true )
& ( omegaSAx = $true )
& ( setunionI = $true )
& ( inPowerset = $true )
& ( subsetTrans = $true )
& ( setadjoinAx = $true )
& ( setextAx = $true )
& ( notdallE = $true )
& ( nonemptyI = $true )
& ( notequalI1 = $true )
& ( setoftrueEq = $true )
& ( upairsetIR = $true )
& ( omega__Cong = $true )
& ( eqimpsubset2 = $true )
& ( descr__Cong = $true )
& ( emptysetE = $true )
& ( singletonsswitch = $true )
& ( binintersectSubset5 = $true )
& ( setext = $true )
& ( setadjoin__Cong = $true )
& ( quantDeMorgan3 = $true )
& ( powersetE = $true )
& ( notinemptyset = $true )
& ( powersetE1 = $true )
& ( subsetE2 = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan1 = $true )
& ( emptysetAx = $true )
& ( omega0Ax = $true )
& ( dsetconstr__Cong = $true )
& ( upairset2IR = $true )
& ( setunionAx = $true )
& ( noeltsimpempty = $true )
& ( sepInPowerset = $true )
& ( setunionE = $true )
& ( emptyE1 = $true )
& ( exuI2 = $true )
& ( nonemptyI1 = $true )
& ( subsetI2 = $true )
& ( sepSubset = $true )
& ( dsetconstrEL = $true )
& ( subsetE = $true )
& ( notsubsetI = $true )
& ( setunion__Cong = $true )
& ( subset2powerset = $true )
& ( notequalI2 = $true )
& ( foundationAx = $true )
& ( subPowSU = $true )
& ( exuI3 = $true )
& ( notinsingleton = $true )
& ( vacuousDall = $true )
& ( exuE3e = $true )
& ( setadjoinIR = $true )
& ( powersetsubset = $true )
& ( prop2set2propI = $true )
& ( dsetconstrER = $true )
& ( powersetAx = $true )
& ( in__Cong = $true )
& ( dsetconstrI = $true )
& ( setadjoinSub = $true )
& ( setadjoinSub2 = $true )
& ( setbeta = $true )
& ( eqinunit = $true )
& ( prop2setE = $true )
& ( binunionLsub = $true )
& ( emptysetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( exuEu = $true )
& ( exuE2 = $true )
& ( replAx = $true )
& ( subsetI1 = $true )
& ( powersetI = $true )
& ( prop2setI = $true )
& ( notdexE = $true )
& ( emptyinPowerset = $true )
& ( descrp = $true )
& ( setadjoinE = $true )
& ( emptyI = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan2 = $true )
& ( wellorderingAx = $true )
& ( exu__Cong = $true )
& ( setextsub = $true )
& ( nonemptyE1 = $true )
& ( powersetI1 = $true )
& ( exuE1 = $true )
& ( binunionRsub = $true )
& ( exuI1 = $true )
& ( exuE3u = $true )
& ( eqimpsubset1 = $true )
& ( emptyset__Cong = $true )
& ( binintersectI = $true )
& ( subsetRefl = $true )
& ( binunionIL = $true )
& ( upairsetE = $true )
& ( binunionEcases = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( $true
!= ( subset @ ( binintersect @ sK286 @ sK287 ) @ sK286 ) )
& ( setadjoinOr = $true )
& ( powerset__Cong = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK286,sK287]),skolemize(X0,sK286),skolemize(X1,sK287)],[f448]) ).
thf(f1097,plain,
! [X2: $i > $o,X3: $i] :
( ( $true
= ( subset
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X3 ) )
| ( sepSubset != $true ) ),
inference(cnf_transformation,[],[f692]) ).
thf(f1116,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f192]) ).
thf(f1225,plain,
( $true
!= ( subset @ ( binintersect @ sK286 @ sK287 ) @ sK286 ) ),
inference(cnf_transformation,[],[f790]) ).
thf(f1284,plain,
sepSubset = $true,
inference(cnf_transformation,[],[f790]) ).
thf(f1608,plain,
! [X2: $i > $o,X3: $i] :
( ( $true != $true )
| ( $true
= ( subset
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X3 ) ) ),
inference(definition_unfolding,[],[f1097,f1284]) ).
thf(f1731,plain,
( $true
!= ( subset
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK286
@ sK287 )
@ sK286 ) ),
inference(definition_unfolding,[],[f1225,f1116]) ).
thf(f1801,plain,
! [X2: $i > $o,X3: $i] :
( $true
= ( subset
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X2 @ Y0 ) )
@ X3 ) ),
inference(trivial_inequality_removal,[],[f1608]) ).
thf(f1802,plain,
! [X2: $i > $o,X3: $i] :
( ( subset @ ( dsetconstr @ X3 @ X2 ) @ X3 )
= $true ),
inference(beta-eta_normalization,[],[f1801]) ).
thf(f1864,plain,
( $true
!= ( subset
@ ( dsetconstr @ sK286
@ ^ [Y0: $i] : ( in @ Y0 @ sK287 ) )
@ sK286 ) ),
inference(beta-eta_normalization,[],[f1731]) ).
thf(f2367,plain,
$false,
inference(forward_subsumption_resolution,[],[f1864,f1802]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU592^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.21 % Computer : n007.cluster.edu
% 0.07/0.21 % Model : x86_64 x86_64
% 0.07/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.21 % Memory : 8046.5625MB
% 0.07/0.21 % OS : Linux 6.8.0-71-generic
% 0.07/0.21 % CPULimit : 300
% 0.07/0.21 % WCLimit : 300
% 0.07/0.21 % DateTime : Tue Sep 29 13:51:27 UTC 2026
% 0.07/0.22 % CPUTime :
% 0.07/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.25 Running higher-order theorem proving
% 0.20/0.28 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.34 % (3400500)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.34 % (3400505)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1893814492:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.34 % (3400511)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.34 % (3400511)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.34 % (3400506)lrs+10_16_si=on:nwc=1.5:random_seed=3781266585:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.34 % (3400507)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3991394822:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.34 % (3400509)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4220782806:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.34 % (3400508)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=420142656:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.34 % (3400510)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1344716179:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.34 % (3400511)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=15951559:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.34 % (3400507)Instruction limit reached!
% 0.20/0.34 % (3400507)------------------------------
% 0.20/0.34 % (3400507)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3400507)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3400507)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3400507)Termination reason: Instruction limit
% 0.20/0.34 % (3400507)Termination phase: shuffling
% 0.20/0.34 % (3400507)Time elapsed: 0.002 s
% 0.20/0.34 % (3400507)Peak memory usage: 10 MB
% 0.20/0.34 % (3400507)Instructions burned: 4 (million)
% 0.20/0.34 % (3400506)Instruction limit reached!
% 0.20/0.34 % (3400506)------------------------------
% 0.20/0.34 % (3400506)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3400506)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3400506)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3400506)Termination reason: Instruction limit
% 0.20/0.34 % (3400506)Termination phase: Property scanning
% 0.20/0.34 % (3400506)Time elapsed: 0.010 s
% 0.20/0.34 % (3400506)Peak memory usage: 10 MB
% 0.20/0.34 % (3400506)Instructions burned: 20 (million)
% 0.20/0.34 % (3400505) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3400500-3400505"...
% 0.20/0.34 % (3400509)Instruction limit reached!
% 0.20/0.34 % (3400509)------------------------------
% 0.20/0.34 % (3400509)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3400509)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3400509)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3400509)Termination reason: Instruction limit
% 0.20/0.34 % (3400509)Termination phase: Preprocessing 3
% 0.20/0.34 % (3400509)Time elapsed: 0.012 s
% 0.20/0.34 % (3400509)Peak memory usage: 11 MB
% 0.20/0.34 % (3400509)Instructions burned: 25 (million)
% 0.20/0.34 % (3400505)...printing done.
% 0.20/0.34 % (3400505)Refutation found. Thanks to Tanya!
% 0.20/0.34 % SZS status Theorem for theBenchmark
% 0.20/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.34 % (3400505)------------------------------
% 0.20/0.34 % (3400505)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.34 % (3400505)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.34 % (3400505)CaDiCaL version: 2.1.3
% 0.20/0.34 % (3400505)Termination reason: Refutation
% 0.20/0.34 % (3400505)Time elapsed: 0.022 s
% 0.20/0.34 % (3400505)Peak memory usage: 13 MB
% 0.20/0.34 % (3400505)Instructions burned: 86 (million)
% 0.20/0.34 % (3400500)Success in time 0.055 s
% 0.20/0.34 % Vampire exiting
%------------------------------------------------------------------------------