%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU541^1 : 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 : n002.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 08:29:59 AM UTC 2026
% Result : Theorem 0.22s 0.29s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 1026 ( 279 equ; 0 cnn)
% Maximal formula atoms : 59 ( 38 avg)
% Number of connectives : 527 ( 24 ~; 15 |; 180 &; 71 @)
% ( 2 <=>; 235 =>; 0 <=; 0 <~>)
% Maximal formula depth : 63 ( 18 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 165 ( 162 usr; 67 con; 0-4 aty)
% Number of variables : 21 ( 4 ^; 13 !; 4 ?; 21 :)
% 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_72,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_73,type,
vAND: $o > $o > $o ).
thf(func_def_74,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_75,type,
vIMP: $o > $o > $o ).
thf(func_def_76,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_77,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_78,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_79,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_80,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_81,type,
vNOT: $o > $o ).
thf(func_def_82,type,
sP0: $o ).
thf(func_def_83,type,
sP1: $i > $i > $o ).
thf(func_def_84,type,
sP2: $i > $o ).
thf(func_def_85,type,
sP3: $i > $i > $o ).
thf(func_def_86,type,
sP4: $i > $i > $o ).
thf(func_def_90,type,
sK8: ( $i > $o ) > $i > $i ).
thf(func_def_92,type,
sK10: $i > $o ).
thf(func_def_94,type,
sK12: $i > $o ).
thf(func_def_96,type,
sK14: $i > $i > $o ).
thf(func_def_97,type,
sK15: $i > $i ).
thf(func_def_98,type,
sK16: $i > $i ).
thf(func_def_99,type,
sK17: ( $i > $i > $o ) > $i > $i ).
thf(func_def_100,type,
sK18: ( $i > $i > $o ) > $i > $i ).
thf(func_def_101,type,
sK19: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_103,type,
sK21: $i > $i ).
thf(func_def_104,type,
sK22: $i > $i > $i ).
thf(func_def_109,type,
sK27: $i > $o ).
thf(func_def_111,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_112,type,
sK30: $i > ( $i > $o ) > $i ).
thf(func_def_113,type,
sK31: $i > $o ).
thf(func_def_116,type,
sK34: $i > $o ).
thf(func_def_119,type,
sK37: $i > $i ).
thf(func_def_123,type,
sK41: $i > $o ).
thf(func_def_124,type,
sK42: $i > $o ).
thf(func_def_125,type,
sK43: $i > $i ).
thf(func_def_126,type,
sK44: ( $i > $o ) > $i ).
thf(func_def_132,type,
sK50: $i > $i > $i ).
thf(func_def_133,type,
sK51: $i > $o ).
thf(func_def_134,type,
sK52: ( $i > $o ) > $i ).
thf(func_def_142,type,
sK60: $i > $i ).
thf(func_def_145,type,
sK63: $i > $o ).
thf(func_def_147,type,
sK65: $i > $i > $i ).
thf(func_def_150,type,
sK68: $i > $o ).
thf(func_def_155,type,
sK73: $i > $i > $i ).
thf(func_def_156,type,
sK74: $i > $i > $i ).
thf(func_def_157,type,
sK75: $o > $i > $i > $i ).
thf(func_def_160,type,
sK78: $o ).
thf(func_def_162,type,
sK80: $i > $o ).
thf(func_def_171,type,
sK89: $o ).
thf(func_def_183,type,
sK101: $i > $i ).
thf(func_def_186,type,
sK104: $i > $i > $i ).
thf(func_def_189,type,
sK107: $i > $o ).
thf(func_def_190,type,
sK108: $i > $i ).
thf(func_def_191,type,
sK109: ( $i > $o ) > $i ).
thf(func_def_193,type,
sK111: $o ).
thf(func_def_195,type,
sK113: $o ).
thf(func_def_196,type,
sK114: $i > $o ).
thf(func_def_198,type,
sK116: $i > ( $i > $o ) > $i ).
thf(func_def_199,type,
sK117: $i > $o ).
thf(func_def_203,type,
sK121: $i > $o ).
thf(func_def_208,type,
sK126: $i > $i ).
thf(func_def_210,type,
sK128: $o ).
thf(func_def_211,type,
sK129: $i > $i > $i ).
thf(func_def_212,type,
sK130: $i > $i > $i ).
thf(func_def_213,type,
sK131: $i > $i > $i ).
thf(func_def_214,type,
sK132: $i > $i > $i ).
thf(func_def_215,type,
sK133: $i > $i > $i ).
thf(func_def_216,type,
sK134: $i > $i > $i > $i ).
thf(func_def_217,type,
sK135: $i > $i ).
thf(func_def_218,type,
sK136: $i > $i ).
thf(func_def_219,type,
sK137: $i > $i ).
thf(func_def_220,type,
sK138: $i > $i ).
thf(func_def_221,type,
sK139: $i > $i > $i ).
thf(func_def_222,type,
sK140: $i > $i > $i > $i ).
thf(func_def_223,type,
sK141: $i > $i > $i > $i ).
thf(func_def_224,type,
sK142: $i > $i > $i ).
thf(func_def_225,type,
sK143: $i > $i > $i ).
thf(func_def_226,type,
sK144: $i > $i ).
thf(func_def_228,type,
sK146: $i > $i ).
thf(func_def_229,type,
sK147: $i > $i ).
thf(func_def_232,type,
sK150: $o ).
thf(func_def_243,type,
sK161: $i > $i ).
thf(func_def_245,type,
sK163: $i > $i ).
thf(func_def_248,type,
sK166: ( $i > $o ) > $i > $i ).
thf(func_def_249,type,
sK167: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_250,type,
sK168: $i > $i ).
thf(func_def_251,type,
sK169: ( $i > $o ) > $i > $i ).
thf(func_def_252,type,
sK170: $i > ( $i > $o ) > $i ).
thf(func_def_253,type,
sK171: ( $i > $o ) > $i > $i ).
thf(func_def_254,type,
sK172: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_255,type,
sK173: ( $i > $o ) > $i > $i ).
thf(func_def_256,type,
sK174: ( $i > $o ) > $i > $i ).
thf(func_def_257,type,
sK175: $i > $i > ( $i > $i > $o ) > $i ).
thf(f59,axiom,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(f60,axiom,
( ( ^ [X0: $i] : ( in @ emptyset @ X0 ) )
= set2prop ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',set2prop) ).
thf(f61,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
=> ! [X0: $o] :
( X0
=> ( set2prop @ ( prop2set @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set2propI) ).
thf(f62,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
=> ! [X0: $o] :
( X0
=> ( set2prop @ ( prop2set @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f61]) ).
thf(f87,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
=> ! [X0: $o] :
( X0
=> ( set2prop @ ( prop2set @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f62]) ).
thf(f88,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 )
=> ! [X0: $o] :
( ( $true = X0 )
=> ( ( set2prop @ ( prop2set @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f87]) ).
thf(f114,plain,
( set2prop
= ( ^ [Y0: $i] : ( in @ emptyset @ Y0 ) ) ),
inference(fool_elimination,[],[f60]) ).
thf(f175,plain,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
inference(rectify,[],[f59]) ).
thf(f176,plain,
( ( prop2setI = $true )
<=> ! [X0: $o] :
( ( $true = X0 )
=> ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f175]) ).
thf(f209,plain,
( ? [X0: $o] :
( ( $true = X0 )
& ( ( set2prop @ ( prop2set @ X0 ) )
!= $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,[],[f88]) ).
thf(f210,plain,
( ( emptysetimpfalse = $true )
& ( nonemptyI = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE = $true )
& ( setadjoinIL = $true )
& ( setadjoinOr = $true )
& ( omega0Ax = $true )
& ( powersetAx = $true )
& ( emptyinunitempty = $true )
& ( exuE1 = $true )
& ( upairsetIR = $true )
& ( emptyI = $true )
& ( quantDeMorgan4 = $true )
& ( emptyInPowerset = $true )
& ( emptysetE = $true )
& ( setunionE = $true )
& ( exuE3e = $true )
& ( dsetconstrI = $true )
& ? [X0: $o] :
( ( $true = X0 )
& ( ( set2prop @ ( prop2set @ X0 ) )
!= $true ) )
& ( subPowSU = $true )
& ( emptyinPowerset = $true )
& ( prop2setI = $true )
& ( vacuousDall = $true )
& ( uniqinunit = $true )
& ( notinsingleton = $true )
& ( dsetconstrER = $true )
& ( setunionAx = $true )
& ( wellorderingAx = $true )
& ( notinemptyset = $true )
& ( nonemptyE1 = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( eqinunit = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyI1 = $true )
& ( powersetI = $true )
& ( quantDeMorgan3 = $true )
& ( noeltsimpempty = $true )
& ( foundationAx = $true )
& ( quantDeMorgan2 = $true )
& ( dsetconstrEL = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptysetAx = $true )
& ( setoftrueEq = $true )
& ( setbeta = $true )
& ( singletonsswitch = $true )
& ( upairsetIL = $true )
& ( setext = $true )
& ( omegaIndAx = $true )
& ( emptyE1 = $true )
& ( exuE2 = $true )
& ( prop2setE = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( setunionI = $true )
& ( upairsetE = $true )
& ( setadjoinAx = $true ) ),
inference(flattening,[],[f209]) ).
thf(f253,plain,
( ! [X0: $o] :
( ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true )
| ( $true != X0 ) )
<=> ( prop2setI = $true ) ),
inference(ennf_transformation,[],[f176]) ).
thf(f398,plain,
( ( ! [X0: $o] :
( ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true )
| ( $true != X0 ) )
| ( prop2setI != $true ) )
& ( ( prop2setI = $true )
| ? [X0: $o] :
( ( ( in @ emptyset @ ( prop2set @ X0 ) )
!= $true )
& ( $true = X0 ) ) ) ),
inference(nnf_transformation,[],[f253]) ).
thf(f399,plain,
( ( ! [X0: $o] :
( ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true )
| ( $true != X0 ) )
| ( prop2setI != $true ) )
& ( ( prop2setI = $true )
| ? [X1: $o] :
( ( ( in @ emptyset @ ( prop2set @ X1 ) )
!= $true )
& ( $true = X1 ) ) ) ),
inference(rectify,[],[f398]) ).
thf(f400,plain,
( ( ! [X0: $o] :
( ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true )
| ( $true != X0 ) )
| ( prop2setI != $true ) )
& ( ( prop2setI = $true )
| ( ( $true
!= ( in @ emptyset @ ( prop2set @ sK128 ) ) )
& ( sK128 = $true ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(X1,sK128)],[f399]) ).
thf(f419,plain,
( ( emptysetimpfalse = $true )
& ( nonemptyI = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE = $true )
& ( setadjoinIL = $true )
& ( setadjoinOr = $true )
& ( omega0Ax = $true )
& ( powersetAx = $true )
& ( emptyinunitempty = $true )
& ( exuE1 = $true )
& ( upairsetIR = $true )
& ( emptyI = $true )
& ( quantDeMorgan4 = $true )
& ( emptyInPowerset = $true )
& ( emptysetE = $true )
& ( setunionE = $true )
& ( exuE3e = $true )
& ( dsetconstrI = $true )
& ( $true = sK150 )
& ( ( set2prop @ ( prop2set @ sK150 ) )
!= $true )
& ( subPowSU = $true )
& ( emptyinPowerset = $true )
& ( prop2setI = $true )
& ( vacuousDall = $true )
& ( uniqinunit = $true )
& ( notinsingleton = $true )
& ( dsetconstrER = $true )
& ( setunionAx = $true )
& ( wellorderingAx = $true )
& ( notinemptyset = $true )
& ( nonemptyE1 = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( eqinunit = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyI1 = $true )
& ( powersetI = $true )
& ( quantDeMorgan3 = $true )
& ( noeltsimpempty = $true )
& ( foundationAx = $true )
& ( quantDeMorgan2 = $true )
& ( dsetconstrEL = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptysetAx = $true )
& ( setoftrueEq = $true )
& ( setbeta = $true )
& ( singletonsswitch = $true )
& ( upairsetIL = $true )
& ( setext = $true )
& ( omegaIndAx = $true )
& ( emptyE1 = $true )
& ( exuE2 = $true )
& ( prop2setE = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( setunionI = $true )
& ( upairsetE = $true )
& ( setadjoinAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(X0,sK150)],[f210]) ).
thf(f516,plain,
( set2prop
= ( ^ [Y0: $i] : ( in @ emptyset @ Y0 ) ) ),
inference(cnf_transformation,[],[f114]) ).
thf(f630,plain,
! [X0: $o] :
( ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true )
| ( $true != X0 )
| ( prop2setI != $true ) ),
inference(cnf_transformation,[],[f400]) ).
thf(f707,plain,
prop2setI = $true,
inference(cnf_transformation,[],[f419]) ).
thf(f710,plain,
( ( set2prop @ ( prop2set @ sK150 ) )
!= $true ),
inference(cnf_transformation,[],[f419]) ).
thf(f711,plain,
$true = sK150,
inference(cnf_transformation,[],[f419]) ).
thf(f932,plain,
! [X0: $o] :
( ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true )
| ( $true != X0 )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f630,f707]) ).
thf(f945,plain,
( $true
!= ( ^ [Y0: $i] : ( in @ emptyset @ Y0 )
@ ( prop2set @ $true ) ) ),
inference(definition_unfolding,[],[f710,f516,f711]) ).
thf(f972,plain,
( ( $true != $true )
| ( $true
= ( in @ emptyset @ ( prop2set @ $true ) ) ) ),
inference(equality_resolution,[],[f932]) ).
thf(f1113,plain,
( $true
!= ( in @ emptyset @ ( prop2set @ $true ) ) ),
inference(beta-eta_normalization,[],[f945]) ).
thf(f1139,plain,
( $true
= ( in @ emptyset @ ( prop2set @ $true ) ) ),
inference(trivial_inequality_removal,[],[f972]) ).
thf(f1225,plain,
$false,
inference(forward_subsumption_resolution,[],[f1139,f1113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU541^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n002.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:51:38 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.22/0.29 % (1316159)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.29 % (1316170)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3840494618:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.29 % (1316171)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.29 % (1316171)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
% 0.22/0.29 % (1316164)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4240692675:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.29 % (1316165)lrs+10_16_si=on:nwc=1.5:random_seed=1603592467:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.29 % (1316168)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=2708836164: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)
% 0.22/0.29 % (1316167)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1362763050:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.29 % (1316171)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=3379956236:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.29 % (1316169)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=14814581:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.29 % (1316167)Instruction limit reached!
% 0.22/0.29 % (1316167)------------------------------
% 0.22/0.29 % (1316167)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (1316167)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (1316167)CaDiCaL version: 2.1.3
% 0.22/0.29 % (1316167)Termination reason: Instruction limit
% 0.22/0.29 % (1316167)Termination phase: shuffling
% 0.22/0.29 % (1316167)Time elapsed: 0.002 s
% 0.22/0.29 % (1316167)Peak memory usage: 10 MB
% 0.22/0.29 % (1316167)Instructions burned: 4 (million)
% 0.22/0.29 % (1316170) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1316159-1316170"...
% 0.22/0.29 % (1316165)Instruction limit reached!
% 0.22/0.29 % (1316165)------------------------------
% 0.22/0.29 % (1316165)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.29 % (1316165)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.29 % (1316165)CaDiCaL version: 2.1.3
% 0.22/0.29 % (1316165)Termination reason: Instruction limit
% 0.22/0.29 % (1316165)Termination phase: Function definition elimination
% 0.22/0.29 % (1316165)Time elapsed: 0.008 s
% 0.22/0.29 % (1316165)Peak memory usage: 10 MB
% 0.22/0.29 % (1316165)Instructions burned: 19 (million)
% 0.22/0.29 % (1316170)...printing done.
% 0.22/0.29 % (1316170)Refutation found. Thanks to Tanya!
% 0.22/0.29 % SZS status Theorem for theBenchmark
% 0.22/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.30 % (1316170)------------------------------
% 0.22/0.30 % (1316170)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.30 % (1316170)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.30 % (1316170)CaDiCaL version: 2.1.3
% 0.22/0.30 % (1316170)Termination reason: Refutation
% 0.22/0.30 % (1316170)Time elapsed: 0.016 s
% 0.22/0.30 % (1316170)Peak memory usage: 13 MB
% 0.22/0.30 % (1316170)Instructions burned: 59 (million)
% 0.22/0.30 % (1316159)Success in time 0.036 s
% 0.22/0.30 % Vampire exiting
%------------------------------------------------------------------------------