%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU594^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 08:30:14 AM UTC 2026
% Result : Theorem 0.20s 0.35s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 14 unt; 0 typ; 4 def)
% Number of atoms : 2144 ( 592 equ; 0 cnn)
% Maximal formula atoms : 112 ( 53 avg)
% Number of connectives : 1042 ( 31 ~; 21 |; 447 &; 94 @)
% ( 5 <=>; 444 =>; 0 <=; 0 <~>)
% Maximal formula depth : 117 ( 25 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 248 ( 245 usr; 128 con; 0-4 aty)
% Number of variables : 36 ( 0 sgn 26 !; 10 ?; 36 :)
% 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_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_130,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_131,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_132,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_133,type,
vAND: $o > $o > $o ).
thf(func_def_134,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_135,type,
vIMP: $o > $o > $o ).
thf(func_def_136,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_137,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_138,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_139,type,
vNOT: $o > $o ).
thf(func_def_140,type,
sP0: $i > $i > $o ).
thf(func_def_141,type,
sP1: $i > $o ).
thf(func_def_142,type,
sP2: $o ).
thf(func_def_149,type,
sK9: $i > $i ).
thf(func_def_152,type,
sK12: $i > $i ).
thf(func_def_153,type,
sK13: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_154,type,
sK14: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_155,type,
sK15: $i > $o ).
thf(func_def_156,type,
sK16: $i > $o ).
thf(func_def_165,type,
sK25: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_166,type,
sK26: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_167,type,
sK27: $i > $o ).
thf(func_def_168,type,
sK28: $i > $o ).
thf(func_def_169,type,
sK29: $i > $o ).
thf(func_def_172,type,
sK32: $i > ( $i > $o ) > $i ).
thf(func_def_174,type,
sK34: $i > $i ).
thf(func_def_175,type,
sK35: $i > $i ).
thf(func_def_176,type,
sK36: $i > $i ).
thf(func_def_177,type,
sK37: $i > $i ).
thf(func_def_178,type,
sK38: $i > $i ).
thf(func_def_179,type,
sK39: $i > $i > $i > $i ).
thf(func_def_180,type,
sK40: $i > $i ).
thf(func_def_181,type,
sK41: $i > $i ).
thf(func_def_182,type,
sK42: $i > $i ).
thf(func_def_183,type,
sK43: $i > $i ).
thf(func_def_184,type,
sK44: $i > $i > $i ).
thf(func_def_185,type,
sK45: $i > $i > $i > $i ).
thf(func_def_186,type,
sK46: $i > $i > $i > $i ).
thf(func_def_187,type,
sK47: $i > $i > $i > $i ).
thf(func_def_188,type,
sK48: $i > $i > $i ).
thf(func_def_189,type,
sK49: $i > $i > $i ).
thf(func_def_190,type,
sK50: $i > $i > $i ).
thf(func_def_191,type,
sK51: $i > $i > $i ).
thf(func_def_192,type,
sK52: $i > $i ).
thf(func_def_199,type,
sK59: $o ).
thf(func_def_202,type,
sK62: $i > $o ).
thf(func_def_204,type,
sK64: ( $i > $o ) > $i > $i ).
thf(func_def_209,type,
sK69: $i > $o ).
thf(func_def_216,type,
sK76: ( $i > $o ) > $i ).
thf(func_def_217,type,
sK77: $i > $o ).
thf(func_def_218,type,
sK78: $i > $i ).
thf(func_def_229,type,
sK89: $o ).
thf(func_def_234,type,
sK94: $i > $o ).
thf(func_def_236,type,
sK96: ( $i > $o ) > $i ).
thf(func_def_237,type,
sK97: ( $i > $o ) > $i ).
thf(func_def_244,type,
sK104: $i > $o ).
thf(func_def_253,type,
sK113: $i > ( $i > $i > $o ) > $i ).
thf(func_def_254,type,
sK114: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_255,type,
sK115: $i > ( $i > $i > $o ) > $i ).
thf(func_def_256,type,
sK116: $i > $i > $o ).
thf(func_def_258,type,
sK118: $i > $i ).
thf(func_def_259,type,
sK119: $i > $i ).
thf(func_def_260,type,
sK120: ( $i > $o ) > $i > $i ).
thf(func_def_262,type,
sK122: $i > $o ).
thf(func_def_264,type,
sK124: $i > $o ).
thf(func_def_267,type,
sK127: $i > ( $i > $o ) > $i ).
thf(func_def_268,type,
sK128: $o ).
thf(func_def_280,type,
sK140: $o ).
thf(func_def_285,type,
sK145: $i > $i ).
thf(func_def_287,type,
sK147: $i > $i ).
thf(func_def_295,type,
sK155: $i > $o ).
thf(func_def_298,type,
sK158: $i > $o ).
thf(func_def_303,type,
sK163: $i > $o ).
thf(func_def_308,type,
sK168: $i > $o ).
thf(func_def_310,type,
sK170: ( $i > $o ) > $i > $i ).
thf(func_def_312,type,
sK172: $i > $o ).
thf(func_def_316,type,
sK176: $i > $o ).
thf(func_def_317,type,
sK177: ( $i > $o ) > $i ).
thf(func_def_318,type,
sK178: $o > $i > $i > $i ).
thf(func_def_321,type,
sK181: $o ).
thf(func_def_323,type,
sK183: $i > $o ).
thf(func_def_325,type,
sK185: $i > $o ).
thf(func_def_330,type,
sK190: $i > $i > $i ).
thf(func_def_345,type,
sK205: $i > $i > $i ).
thf(func_def_346,type,
sK206: $o ).
thf(func_def_347,type,
sK207: $i > $o ).
thf(func_def_349,type,
sK209: $i > ( $i > $o ) > $i ).
thf(func_def_350,type,
sK210: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_351,type,
sK211: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_354,type,
sK214: $i > $o ).
thf(func_def_355,type,
sK215: $i > $o ).
thf(func_def_357,type,
sK217: $i > $i ).
thf(func_def_365,type,
sK225: $i > $i > $i ).
thf(func_def_369,type,
sK229: $i > $i > $i ).
thf(func_def_375,type,
sK235: $i > $i > $i ).
thf(func_def_377,type,
sK237: $i > $o ).
thf(func_def_382,type,
sK242: $i > $o ).
thf(func_def_383,type,
sK243: $i > $o ).
thf(func_def_385,type,
sK245: $i > ( $i > $o ) > $i ).
thf(func_def_396,type,
sK256: $o ).
thf(func_def_402,type,
sK262: $i > $o ).
thf(func_def_411,type,
sK271: $i > $i > $i ).
thf(func_def_412,type,
sK272: $i > $o ).
thf(func_def_420,type,
sK280: $i > ( $i > $o ) > $i ).
thf(func_def_421,type,
sK281: $i > $o ).
thf(func_def_430,type,
sK290: $i > $i ).
thf(func_def_432,type,
sK292: ( $i > $o ) > $i ).
thf(func_def_433,type,
sK293: $i > $o ).
thf(func_def_434,type,
sK294: $i > $i ).
thf(func_def_439,type,
sK299: $i > $i > $i ).
thf(func_def_440,type,
sK300: $i > $i > $i ).
thf(f112,axiom,
( binintersectLsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(f114,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(f115,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f114]) ).
thf(f141,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( subset @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f115]) ).
thf(f142,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ! [X1: $i,X0: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
=> ( ( subset @ X1 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f141]) ).
thf(f175,plain,
( binintersectLsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X0 ) ) ),
inference(rectify,[],[f112]) ).
thf(f176,plain,
( ! [X1: $i,X0: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
<=> ( binintersectLsub = $true ) ),
inference(fool_elimination,[],[f175]) ).
thf(f390,plain,
( ? [X1: $i,X0: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
& ( ( subset @ X1 @ X0 )
!= $true ) )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f142]) ).
thf(f391,plain,
( ( exuI3 = $true )
& ( nonemptyI = $true )
& ( singletonsswitch = $true )
& ( inPowerset = $true )
& ( emptyInPowerset = $true )
& ( notequalI1 = $true )
& ( setextsub = $true )
& ( upairsetIR = $true )
& ( exuE2 = $true )
& ( dsetconstrI = $true )
& ( setadjoinOr = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinSub2 = $true )
& ( emptysetsubset = $true )
& ( notdallE = $true )
& ( prop2setE = $true )
& ( setbeta = $true )
& ( setadjoinAx = $true )
& ( setadjoinSub = $true )
& ( dsetconstrEL = $true )
& ( emptyinunitempty = $true )
& ( binunionE = $true )
& ( exu__Cong = $true )
& ( subsetI2 = $true )
& ( powersetAx = $true )
& ( nonemptyImpWitness = $true )
& ( setext = $true )
& ( eqinunit = $true )
& ( powersetI = $true )
& ( eqimpsubset1 = $true )
& ( wellorderingAx = $true )
& ( subsetI1 = $true )
& ( setadjoinIR = $true )
& ( exuI2 = $true )
& ( nonemptyE1 = $true )
& ( binintersectI = $true )
& ( binintersectSubset2 = $true )
& ( setunionAx = $true )
& ( subsetemptysetimpeq = $true )
& ( omegaIndAx = $true )
& ( powersetsubset = $true )
& ( notinsingleton = $true )
& ( upairset2IR = $true )
& ( upairsetIL = $true )
& ( subsetTrans = $true )
& ( binunionLsub = $true )
& ( subset2powerset = $true )
& ( prop2setI = $true )
& ( binunionEcases = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinIL = $true )
& ( powerset__Cong = $true )
& ( emptysetE = $true )
& ( powersetE = $true )
& ( emptyE1 = $true )
& ( subsetRefl = $true )
& ( binunionIL = $true )
& ( exuE3u = $true )
& ( setunionE = $true )
& ( notsubsetI = $true )
& ( binunionRsub = $true )
& ( exuE3e = $true )
& ( setadjoinE = $true )
& ( quantDeMorgan1 = $true )
& ( subsetE2 = $true )
& ( notinemptyset = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( notequalI2 = $true )
& ? [X1: $i,X0: $i] :
( ( ( binintersect @ X0 @ X1 )
= X1 )
& ( ( subset @ X1 @ X0 )
!= $true ) )
& ( subsetE = $true )
& ( dsetconstrER = $true )
& ( exuI1 = $true )
& ( uniqinunit = $true )
& ( binintersectLsub = $true )
& ( exuE1 = $true )
& ( setextAx = $true )
& ( noeltsimpempty = $true )
& ( nonemptyI1 = $true )
& ( exuEu = $true )
& ( inCongP = $true )
& ( omega__Cong = $true )
& ( upairsetE = $true )
& ( emptyinPowerset = $true )
& ( powersetI1 = $true )
& ( eqimpsubset2 = $true )
& ( binunionIR = $true )
& ( sepInPowerset = $true )
& ( in__Cong = $true )
& ( powersetE1 = $true )
& ( binintersectEL = $true )
& ( notdexE = $true )
& ( descr__Cong = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan2 = $true )
& ( sepSubset = $true )
& ( binintersectSubset5 = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( emptyset__Cong = $true )
& ( subPowSU = $true )
& ( emptysetAx = $true )
& ( vacuousDall = $true )
& ( emptysetimpfalse = $true )
& ( setadjoin__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( setunion__Cong = $true )
& ( prop2set2propI = $true )
& ( replAx = $true ) ),
inference(flattening,[],[f390]) ).
thf(f772,plain,
( ( exuI3 = $true )
& ( nonemptyI = $true )
& ( singletonsswitch = $true )
& ( inPowerset = $true )
& ( emptyInPowerset = $true )
& ( notequalI1 = $true )
& ( setextsub = $true )
& ( upairsetIR = $true )
& ( exuE2 = $true )
& ( dsetconstrI = $true )
& ( setadjoinOr = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinSub2 = $true )
& ( emptysetsubset = $true )
& ( notdallE = $true )
& ( prop2setE = $true )
& ( setbeta = $true )
& ( setadjoinAx = $true )
& ( setadjoinSub = $true )
& ( dsetconstrEL = $true )
& ( emptyinunitempty = $true )
& ( binunionE = $true )
& ( exu__Cong = $true )
& ( subsetI2 = $true )
& ( powersetAx = $true )
& ( nonemptyImpWitness = $true )
& ( setext = $true )
& ( eqinunit = $true )
& ( powersetI = $true )
& ( eqimpsubset1 = $true )
& ( wellorderingAx = $true )
& ( subsetI1 = $true )
& ( setadjoinIR = $true )
& ( exuI2 = $true )
& ( nonemptyE1 = $true )
& ( binintersectI = $true )
& ( binintersectSubset2 = $true )
& ( setunionAx = $true )
& ( subsetemptysetimpeq = $true )
& ( omegaIndAx = $true )
& ( powersetsubset = $true )
& ( notinsingleton = $true )
& ( upairset2IR = $true )
& ( upairsetIL = $true )
& ( subsetTrans = $true )
& ( binunionLsub = $true )
& ( subset2powerset = $true )
& ( prop2setI = $true )
& ( binunionEcases = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinIL = $true )
& ( powerset__Cong = $true )
& ( emptysetE = $true )
& ( powersetE = $true )
& ( emptyE1 = $true )
& ( subsetRefl = $true )
& ( binunionIL = $true )
& ( exuE3u = $true )
& ( setunionE = $true )
& ( notsubsetI = $true )
& ( binunionRsub = $true )
& ( exuE3e = $true )
& ( setadjoinE = $true )
& ( quantDeMorgan1 = $true )
& ( subsetE2 = $true )
& ( notinemptyset = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( notequalI2 = $true )
& ? [X0: $i,X1: $i] :
( ( ( binintersect @ X1 @ X0 )
= X0 )
& ( ( subset @ X0 @ X1 )
!= $true ) )
& ( subsetE = $true )
& ( dsetconstrER = $true )
& ( exuI1 = $true )
& ( uniqinunit = $true )
& ( binintersectLsub = $true )
& ( exuE1 = $true )
& ( setextAx = $true )
& ( noeltsimpempty = $true )
& ( nonemptyI1 = $true )
& ( exuEu = $true )
& ( inCongP = $true )
& ( omega__Cong = $true )
& ( upairsetE = $true )
& ( emptyinPowerset = $true )
& ( powersetI1 = $true )
& ( eqimpsubset2 = $true )
& ( binunionIR = $true )
& ( sepInPowerset = $true )
& ( in__Cong = $true )
& ( powersetE1 = $true )
& ( binintersectEL = $true )
& ( notdexE = $true )
& ( descr__Cong = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan2 = $true )
& ( sepSubset = $true )
& ( binintersectSubset5 = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( emptyset__Cong = $true )
& ( subPowSU = $true )
& ( emptysetAx = $true )
& ( vacuousDall = $true )
& ( emptysetimpfalse = $true )
& ( setadjoin__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( setunion__Cong = $true )
& ( prop2set2propI = $true )
& ( replAx = $true ) ),
inference(rectify,[],[f391]) ).
thf(f773,plain,
( ( exuI3 = $true )
& ( nonemptyI = $true )
& ( singletonsswitch = $true )
& ( inPowerset = $true )
& ( emptyInPowerset = $true )
& ( notequalI1 = $true )
& ( setextsub = $true )
& ( upairsetIR = $true )
& ( exuE2 = $true )
& ( dsetconstrI = $true )
& ( setadjoinOr = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinSub2 = $true )
& ( emptysetsubset = $true )
& ( notdallE = $true )
& ( prop2setE = $true )
& ( setbeta = $true )
& ( setadjoinAx = $true )
& ( setadjoinSub = $true )
& ( dsetconstrEL = $true )
& ( emptyinunitempty = $true )
& ( binunionE = $true )
& ( exu__Cong = $true )
& ( subsetI2 = $true )
& ( powersetAx = $true )
& ( nonemptyImpWitness = $true )
& ( setext = $true )
& ( eqinunit = $true )
& ( powersetI = $true )
& ( eqimpsubset1 = $true )
& ( wellorderingAx = $true )
& ( subsetI1 = $true )
& ( setadjoinIR = $true )
& ( exuI2 = $true )
& ( nonemptyE1 = $true )
& ( binintersectI = $true )
& ( binintersectSubset2 = $true )
& ( setunionAx = $true )
& ( subsetemptysetimpeq = $true )
& ( omegaIndAx = $true )
& ( powersetsubset = $true )
& ( notinsingleton = $true )
& ( upairset2IR = $true )
& ( upairsetIL = $true )
& ( subsetTrans = $true )
& ( binunionLsub = $true )
& ( subset2powerset = $true )
& ( prop2setI = $true )
& ( binunionEcases = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinIL = $true )
& ( powerset__Cong = $true )
& ( emptysetE = $true )
& ( powersetE = $true )
& ( emptyE1 = $true )
& ( subsetRefl = $true )
& ( binunionIL = $true )
& ( exuE3u = $true )
& ( setunionE = $true )
& ( notsubsetI = $true )
& ( binunionRsub = $true )
& ( exuE3e = $true )
& ( setadjoinE = $true )
& ( quantDeMorgan1 = $true )
& ( subsetE2 = $true )
& ( notinemptyset = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( notequalI2 = $true )
& ( ( binintersect @ sK268 @ sK267 )
= sK267 )
& ( ( subset @ sK267 @ sK268 )
!= $true )
& ( subsetE = $true )
& ( dsetconstrER = $true )
& ( exuI1 = $true )
& ( uniqinunit = $true )
& ( binintersectLsub = $true )
& ( exuE1 = $true )
& ( setextAx = $true )
& ( noeltsimpempty = $true )
& ( nonemptyI1 = $true )
& ( exuEu = $true )
& ( inCongP = $true )
& ( omega__Cong = $true )
& ( upairsetE = $true )
& ( emptyinPowerset = $true )
& ( powersetI1 = $true )
& ( eqimpsubset2 = $true )
& ( binunionIR = $true )
& ( sepInPowerset = $true )
& ( in__Cong = $true )
& ( powersetE1 = $true )
& ( binintersectEL = $true )
& ( notdexE = $true )
& ( descr__Cong = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan2 = $true )
& ( sepSubset = $true )
& ( binintersectSubset5 = $true )
& ( emptyI = $true )
& ( foundationAx = $true )
& ( emptyset__Cong = $true )
& ( subPowSU = $true )
& ( emptysetAx = $true )
& ( vacuousDall = $true )
& ( emptysetimpfalse = $true )
& ( setadjoin__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( setunion__Cong = $true )
& ( prop2set2propI = $true )
& ( replAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK267,sK268]),skolemize(X0,sK267),skolemize(X1,sK268)],[f772]) ).
thf(f790,plain,
( ( ! [X1: $i,X0: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ? [X1: $i,X0: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[],[f176]) ).
thf(f791,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ? [X2: $i,X3: $i] :
( ( subset @ ( binintersect @ X3 @ X2 ) @ X3 )
!= $true ) ) ),
inference(rectify,[],[f790]) ).
thf(f792,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ( binintersectLsub != $true ) )
& ( ( binintersectLsub = $true )
| ( ( subset @ ( binintersect @ sK285 @ sK284 ) @ sK285 )
!= $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK284,sK285]),skolemize(X2,sK284),skolemize(X3,sK285)],[f791]) ).
thf(f1243,plain,
binintersectLsub = $true,
inference(cnf_transformation,[],[f773]) ).
thf(f1248,plain,
( ( subset @ sK267 @ sK268 )
!= $true ),
inference(cnf_transformation,[],[f773]) ).
thf(f1249,plain,
( ( binintersect @ sK268 @ sK267 )
= sK267 ),
inference(cnf_transformation,[],[f773]) ).
thf(f1343,plain,
! [X0: $i,X1: $i] :
( ( binintersectLsub != $true )
| ( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f792]) ).
thf(f1590,definition,
( spl302_18
<=> ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl302_18])],[avatar_definition]) ).
thf(f1591,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X1 @ X0 ) @ X1 )
= $true )
| ~ spl302_18 ),
inference(avatar_component_clause,[],[f1590]) ).
thf(f1593,definition,
( spl302_19
<=> ( binintersectLsub = $true ) ),
introduced(definition,[new_symbols(definition,[spl302_19])],[avatar_definition]) ).
thf(f1596,plain,
( spl302_18
| ~ spl302_19 ),
inference(avatar_split_clause,[],[f1343,f1593,f1590]) ).
thf(f1957,definition,
( spl302_102
<=> ( ( subset @ sK267 @ sK268 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl302_102])],[avatar_definition]) ).
thf(f1959,plain,
( ( ( subset @ sK267 @ sK268 )
!= $true )
| spl302_102 ),
inference(avatar_component_clause,[],[f1957]) ).
thf(f1960,plain,
~ spl302_102,
inference(avatar_split_clause,[],[f1248,f1957]) ).
thf(f2530,plain,
spl302_19,
inference(avatar_split_clause,[],[f1243,f1593]) ).
thf(f3894,definition,
( spl302_511
<=> ( ( binintersect @ sK268 @ sK267 )
= sK267 ) ),
introduced(definition,[new_symbols(definition,[spl302_511])],[avatar_definition]) ).
thf(f3896,plain,
( ( ( binintersect @ sK268 @ sK267 )
= sK267 )
| ~ spl302_511 ),
inference(avatar_component_clause,[],[f3894]) ).
thf(f3897,plain,
spl302_511,
inference(avatar_split_clause,[],[f1249,f3894]) ).
thf(f4108,plain,
( ( ( subset @ sK267 @ sK268 )
= $true )
| ~ spl302_18
| ~ spl302_511 ),
inference(superposition,[],[f1591,f3896]) ).
thf(f4111,plain,
( $false
| ~ spl302_18
| spl302_102
| ~ spl302_511 ),
inference(forward_subsumption_resolution,[],[f4108,f1959]) ).
thf(f4112,plain,
( ~ spl302_18
| spl302_102
| ~ spl302_511 ),
inference(avatar_contradiction_clause,[],[f4111]) ).
cnf(s9,plain,
( spl302_18
| ~ spl302_19 ),
inference(sat_conversion,[],[f1596]) ).
cnf(s59,plain,
~ spl302_102,
inference(sat_conversion,[],[f1960]) ).
cnf(s170,plain,
spl302_19,
inference(sat_conversion,[],[f2530]) ).
cnf(s516,plain,
spl302_511,
inference(sat_conversion,[],[f3897]) ).
cnf(s541,plain,
( ~ spl302_18
| spl302_102
| ~ spl302_511 ),
inference(sat_conversion,[],[f4112]) ).
cnf(s661,plain,
~ spl302_18,
inference(rat,[],[s541,s516,s59]) ).
cnf(s675,plain,
$false,
inference(rat,[],[s9,s170,s661]) ).
thf(f4113,plain,
$false,
inference(avatar_sat_refutation,[],[s675]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU594^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.17 % Computer : n003.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Sep 29 13:57:46 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 Running higher-order theorem proving
% 0.07/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.35 % (2542385)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.35 % (2542391)lrs+10_16_si=on:nwc=1.5:random_seed=2179965323:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.35 % (2542396)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.35 % (2542396)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
% 0.20/0.35 % (2542391)Instruction limit reached!
% 0.20/0.35 % (2542391)------------------------------
% 0.20/0.35 % (2542391)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542391)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542391)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542391)Termination reason: Instruction limit
% 0.20/0.35 % (2542391)Termination phase: Preprocessing 3
% 0.20/0.35 % (2542391)Time elapsed: 0.005 s
% 0.20/0.35 % (2542391)Peak memory usage: 10 MB
% 0.20/0.35 % (2542391)Instructions burned: 22 (million)
% 0.20/0.35 % (2542390)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=202603121:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.35 % (2542392)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=195165395:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.35 % (2542394)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=607577348:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.35 % (2542393)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=4110819035: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)
% 0.20/0.35 % (2542395)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2038818375:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.35 % (2542396)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=2971716612:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.35 % (2542392)Instruction limit reached!
% 0.20/0.35 % (2542392)------------------------------
% 0.20/0.35 % (2542392)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542392)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542392)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542392)Termination reason: Instruction limit
% 0.20/0.35 % (2542392)Termination phase: shuffling
% 0.20/0.35 % (2542392)Time elapsed: 0.002 s
% 0.20/0.35 % (2542392)Peak memory usage: 9 MB
% 0.20/0.35 % (2542392)Instructions burned: 4 (million)
% 0.20/0.35 % (2542398)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=643215441:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (2542398)Instruction limit reached!
% 0.20/0.35 % (2542398)------------------------------
% 0.20/0.35 % (2542398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542398)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542398)Termination reason: Instruction limit
% 0.20/0.35 % (2542398)Termination phase: shuffling
% 0.20/0.35 % (2542398)Time elapsed: 0.001 s
% 0.20/0.35 % (2542398)Peak memory usage: 9 MB
% 0.20/0.35 % (2542398)Instructions burned: 4 (million)
% 0.20/0.35 % (2542394)Instruction limit reached!
% 0.20/0.35 % (2542394)------------------------------
% 0.20/0.35 % (2542394)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542394)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542394)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542394)Termination reason: Instruction limit
% 0.20/0.35 % (2542394)Termination phase: Preprocessing 3
% 0.20/0.35 % (2542394)Time elapsed: 0.013 s
% 0.20/0.35 % (2542394)Peak memory usage: 11 MB
% 0.20/0.35 % (2542394)Instructions burned: 26 (million)
% 0.20/0.35 % (2542407)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (2542405)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1607629365:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.35 % (2542407)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1576305234:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.35 % (2542407)Instruction limit reached!
% 0.20/0.35 % (2542407)------------------------------
% 0.20/0.35 % (2542407)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542407)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542407)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542407)Termination reason: Instruction limit
% 0.20/0.35 % (2542407)Termination phase: shuffling
% 0.20/0.35 % (2542407)Time elapsed: 0.002 s
% 0.20/0.35 % (2542407)Peak memory usage: 9 MB
% 0.20/0.35 % (2542407)Instructions burned: 8 (million)
% 0.20/0.35 % (2542405)Instruction limit reached!
% 0.20/0.35 % (2542405)------------------------------
% 0.20/0.35 % (2542405)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542405)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542405)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542405)Termination reason: Instruction limit
% 0.20/0.35 % (2542405)Termination phase: shuffling
% 0.20/0.35 % (2542405)Time elapsed: 0.003 s
% 0.20/0.35 % (2542405)Peak memory usage: 9 MB
% 0.20/0.35 % (2542405)Instructions burned: 6 (million)
% 0.20/0.35 % (2542408)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3295746505:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.35 % (2542395)Instruction limit reached!
% 0.20/0.35 % (2542395)------------------------------
% 0.20/0.35 % (2542395)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542395)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542395)Termination reason: Instruction limit
% 0.20/0.35 % (2542395)Termination phase: Saturation
% 0.20/0.35 % (2542395)Time elapsed: 0.035 s
% 0.20/0.35 % (2542395)Peak memory usage: 12 MB
% 0.20/0.35 % (2542395)Instructions burned: 76 (million)
% 0.20/0.35 % (2542408)Instruction limit reached!
% 0.20/0.35 % (2542408)------------------------------
% 0.20/0.35 % (2542408)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542408)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542408)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542408)Termination reason: Instruction limit
% 0.20/0.35 % (2542408)Termination phase: Property scanning
% 0.20/0.35 % (2542408)Time elapsed: 0.006 s
% 0.20/0.35 % (2542408)Peak memory usage: 10 MB
% 0.20/0.35 % (2542408)Instructions burned: 14 (million)
% 0.20/0.35 % (2542411)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
% 0.20/0.35 % (2542411)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.35 % (2542390)Instruction limit reached!
% 0.20/0.35 % (2542390)------------------------------
% 0.20/0.35 % (2542390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542390)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542390)Termination reason: Instruction limit
% 0.20/0.35 % (2542390)Termination phase: Saturation
% 0.20/0.35 % (2542390)Time elapsed: 0.041 s
% 0.20/0.35 % (2542390)Peak memory usage: 13 MB
% 0.20/0.35 % (2542390)Instructions burned: 88 (million)
% 0.20/0.35 % (2542411)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=565404132:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.35 % (2542412)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=3282960788:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.35 % (2542415)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.20/0.35 % (2542414)lrs+10_1_si=on:cs=on:random_seed=3146834197:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.20/0.35 % (2542411)Instruction limit reached!
% 0.20/0.35 % (2542411)------------------------------
% 0.20/0.35 % (2542411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542411)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542411)Termination reason: Instruction limit
% 0.20/0.35 % (2542411)Termination phase: Property scanning
% 0.20/0.35 % (2542411)Time elapsed: 0.013 s
% 0.20/0.35 % (2542411)Peak memory usage: 10 MB
% 0.20/0.35 % (2542411)Instructions burned: 29 (million)
% 0.20/0.35 % (2542393) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2542385-2542393"...
% 0.20/0.35 % (2542415)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=323237082:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.35 % (2542415)Instruction limit reached!
% 0.20/0.35 % (2542415)------------------------------
% 0.20/0.35 % (2542415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542415)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542415)Termination reason: Instruction limit
% 0.20/0.35 % (2542415)Termination phase: shuffling
% 0.20/0.35 % (2542415)Time elapsed: 0.001 s
% 0.20/0.35 % (2542415)Peak memory usage: 9 MB
% 0.20/0.35 % (2542415)Instructions burned: 2 (million)
% 0.20/0.35 % (2542416)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=340789021:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.20/0.35 % (2542414)Instruction limit reached!
% 0.20/0.35 % (2542414)------------------------------
% 0.20/0.35 % (2542414)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542414)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542414)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542414)Termination reason: Instruction limit
% 0.20/0.35 % (2542414)Termination phase: Property scanning
% 0.20/0.35 % (2542414)Time elapsed: 0.006 s
% 0.20/0.35 % (2542414)Peak memory usage: 10 MB
% 0.20/0.35 % (2542414)Instructions burned: 12 (million)
% 0.20/0.35 % (2542393)...printing done.
% 0.20/0.35 % (2542393)Refutation found. Thanks to Tanya!
% 0.20/0.35 % SZS status Theorem for theBenchmark
% 0.20/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.35 % (2542393)------------------------------
% 0.20/0.35 % (2542393)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.35 % (2542393)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.35 % (2542393)CaDiCaL version: 2.1.3
% 0.20/0.35 % (2542393)Termination reason: Refutation
% 0.20/0.35 % (2542393)Time elapsed: 0.060 s
% 0.20/0.35 % (2542393)Peak memory usage: 15 MB
% 0.20/0.35 % (2542393)Instructions burned: 119 (million)
% 0.20/0.35 % (2542385)Success in time 0.106 s
% 0.20/0.35 % Vampire exiting
%------------------------------------------------------------------------------