%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU552^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 08:30:02 AM UTC 2026
% Result : Theorem 0.18s 0.30s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 15 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 1077 ( 300 equ; 0 cnn)
% Maximal formula atoms : 71 ( 71 avg)
% Number of connectives : 539 ( 9 ~; 0 |; 210 &; 40 @)
% ( 0 <=>; 280 =>; 0 <=; 0 <~>)
% Maximal formula depth : 76 ( 35 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 191 ( 188 usr; 141 con; 0-4 aty)
% Number of variables : 24 ( 0 ^; 16 !; 8 ?; 24 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_82,type,
vIMP: $o > $o > $o ).
thf(func_def_83,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_84,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_85,type,
vIFF: $o > $o > $o ).
thf(func_def_86,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_87,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_88,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_89,type,
vAND: $o > $o > $o ).
thf(func_def_90,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_91,type,
vNOT: $o > $o ).
thf(func_def_92,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_93,type,
vOR: $o > $o > $o ).
thf(func_def_96,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_101,type,
sF4: $o ).
thf(func_def_102,type,
sF5: $o ).
thf(func_def_103,type,
sF6: $o ).
thf(func_def_104,type,
sF7: $o ).
thf(func_def_105,type,
sF8: $o ).
thf(func_def_106,type,
sF9: $o ).
thf(func_def_107,type,
sF10: $o ).
thf(func_def_109,type,
sF12: $o ).
thf(func_def_110,type,
sF13: $o ).
thf(func_def_111,type,
sF14: $o ).
thf(func_def_112,type,
sF15: $o ).
thf(func_def_113,type,
sF16: $o ).
thf(func_def_114,type,
sF17: $o ).
thf(func_def_115,type,
sF18: $o ).
thf(func_def_116,type,
sF19: $o ).
thf(func_def_117,type,
sF20: $o ).
thf(func_def_118,type,
sF21: $o ).
thf(func_def_119,type,
sF22: $o ).
thf(func_def_120,type,
sF23: $o ).
thf(func_def_121,type,
sF24: $o ).
thf(func_def_122,type,
sF25: $o ).
thf(func_def_123,type,
sF26: $o ).
thf(func_def_124,type,
sF27: $o ).
thf(func_def_125,type,
sF28: $o ).
thf(func_def_126,type,
sF29: $o ).
thf(func_def_127,type,
sF30: $o ).
thf(func_def_128,type,
sF31: $o ).
thf(func_def_129,type,
sF32: $o ).
thf(func_def_130,type,
sF33: $o ).
thf(func_def_131,type,
sF34: $o ).
thf(func_def_133,type,
sF36: $o ).
thf(func_def_134,type,
sF37: $o ).
thf(func_def_135,type,
sF38: $o ).
thf(func_def_136,type,
sF39: $o ).
thf(func_def_137,type,
sF40: $o ).
thf(func_def_138,type,
sF41: $o ).
thf(func_def_139,type,
sF42: $o ).
thf(func_def_140,type,
sF43: $o ).
thf(func_def_141,type,
sF44: $o ).
thf(func_def_142,type,
sF45: $o ).
thf(func_def_143,type,
sF46: $o ).
thf(func_def_144,type,
sF47: $o ).
thf(func_def_145,type,
sF48: $o ).
thf(func_def_146,type,
sF49: $o ).
thf(func_def_147,type,
sF50: $o ).
thf(func_def_148,type,
sF51: $o ).
thf(func_def_149,type,
sF52: $o ).
thf(func_def_150,type,
sF53: $o ).
thf(func_def_151,type,
sF54: $o ).
thf(func_def_152,type,
sF55: $o ).
thf(func_def_153,type,
sF56: $o ).
thf(func_def_154,type,
sF57: $o ).
thf(func_def_155,type,
sF58: $o ).
thf(func_def_156,type,
sF59: $o ).
thf(func_def_157,type,
sF60: $o ).
thf(func_def_158,type,
sF61: $o ).
thf(func_def_159,type,
sF62: $o ).
thf(func_def_160,type,
sF63: $o ).
thf(func_def_161,type,
sF64: $o ).
thf(func_def_162,type,
sF65: $o ).
thf(func_def_163,type,
sF66: $o ).
thf(func_def_164,type,
sF67: $o ).
thf(func_def_165,type,
sF68: $o ).
thf(func_def_166,type,
sF69: $o ).
thf(func_def_167,type,
sF70: $o ).
thf(func_def_168,type,
sK71: ( $i > $o ) > $i ).
thf(func_def_169,type,
sK72: ( $i > $o ) > $i > $i ).
thf(func_def_170,type,
sK73: ( $i > $o ) > $i > $i ).
thf(func_def_171,type,
sK74: $i > $o ).
thf(func_def_173,type,
sK76: $i > $i ).
thf(func_def_174,type,
sK77: ( $i > $o ) > $i > $i ).
thf(func_def_175,type,
sK78: $i > $o ).
thf(func_def_180,type,
sK83: $i > $o ).
thf(func_def_187,type,
sK90: ( $i > $o ) > $i ).
thf(func_def_188,type,
sK91: ( $i > $o ) > $i > $i ).
thf(func_def_189,type,
sK92: $i > $o ).
thf(func_def_191,type,
sK94: $i > $i ).
thf(func_def_194,type,
sK97: $i > $o ).
thf(func_def_196,type,
sK99: $i > $i ).
thf(func_def_197,type,
sK100: ( $i > $o ) > $i ).
thf(func_def_198,type,
sK101: ( $i > $o ) > $i > $i ).
thf(func_def_205,type,
sK108: $o ).
thf(func_def_207,type,
sK110: $i > $o ).
thf(func_def_209,type,
sK112: $i > ( $i > $o ) > $i ).
thf(func_def_211,type,
sK114: $i > $o ).
thf(func_def_213,type,
sK116: $i > $i ).
thf(func_def_214,type,
sK117: ( $i > $o ) > $i ).
thf(func_def_215,type,
sK118: ( $i > $o ) > $i ).
thf(func_def_216,type,
sK119: ( $i > $o ) > $i ).
thf(func_def_217,type,
sK120: ( $i > $o ) > $i ).
thf(f71,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
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X0 @ X2 )
= ( setadjoin @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(f72,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
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X0 @ X2 )
= ( setadjoin @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f71]) ).
thf(f203,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
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X0 @ X2 )
= ( setadjoin @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f72]) ).
thf(f204,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 )
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( setadjoin @ X0 @ X2 )
= ( setadjoin @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f203]) ).
thf(f209,plain,
( ? [X0: $i,X1: $i] :
( ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ X0 @ X2 )
!= ( setadjoin @ X1 @ X3 ) ) )
& ( X0 = X1 ) )
& ( 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,[],[f204]) ).
thf(f210,plain,
( ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( setadjoinIL = $true )
& ( emptyI = $true )
& ( quantDeMorgan1 = $true )
& ( quantDeMorgan2 = $true )
& ( vacuousDall = $true )
& ( noeltsimpempty = $true )
& ( descrp = $true )
& ( omega0Ax = $true )
& ? [X0: $i,X1: $i] :
( ? [X2: $i,X3: $i] :
( ( X2 = X3 )
& ( ( setadjoin @ X0 @ X2 )
!= ( setadjoin @ X1 @ X3 ) ) )
& ( X0 = X1 ) )
& ( emptysetAx = $true )
& ( setbeta = $true )
& ( emptyinunitempty = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( upairsetIL = $true )
& ( exuE1 = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( quantDeMorgan4 = $true )
& ( dsetconstrEL = $true )
& ( emptyinPowerset = $true )
& ( setunionE = $true )
& ( notdallE = $true )
& ( exuE2 = $true )
& ( exuI3 = $true )
& ( omegaIndAx = $true )
& ( nonemptyImpWitness = $true )
& ( omegaSAx = $true )
& ( replAx = $true )
& ( setoftrueEq = $true )
& ( setadjoinIR = $true )
& ( nonemptyI1 = $true )
& ( inCongP = $true )
& ( prop2set2propI = $true )
& ( exuI1 = $true )
& ( in__Cong = $true )
& ( powersetI = $true )
& ( dsetconstrI = $true )
& ( nonemptyE1 = $true )
& ( quantDeMorgan3 = $true )
& ( exuE3u = $true )
& ( notinemptyset = $true )
& ( notdexE = $true )
& ( powersetAx = $true )
& ( emptyInPowerset = $true )
& ( upairsetE = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( emptysetE = $true )
& ( setunionAx = $true )
& ( prop2setI = $true )
& ( setextAx = $true )
& ( uniqinunit = $true )
& ( nonemptyI = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinAx = $true )
& ( dsetconstrER = $true )
& ( foundationAx = $true )
& ( setunionI = $true )
& ( exuI2 = $true )
& ( subPowSU = $true )
& ( eqinunit = $true )
& ( prop2setE = $true )
& ( setadjoinE = $true )
& ( upairsetIR = $true )
& ( singletonsswitch = $true )
& ( notinsingleton = $true ) ),
inference(flattening,[],[f209]) ).
thf(f211,plain,
( ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( setadjoinIL = $true )
& ( emptyI = $true )
& ( quantDeMorgan1 = $true )
& ( quantDeMorgan2 = $true )
& ( vacuousDall = $true )
& ( noeltsimpempty = $true )
& ( descrp = $true )
& ( omega0Ax = $true )
& ( sK3 = sK2 )
& ( ( setadjoin @ sK0 @ sK2 )
!= ( setadjoin @ sK1 @ sK3 ) )
& ( sK1 = sK0 )
& ( emptysetAx = $true )
& ( setbeta = $true )
& ( emptyinunitempty = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( upairsetIL = $true )
& ( exuE1 = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( quantDeMorgan4 = $true )
& ( dsetconstrEL = $true )
& ( emptyinPowerset = $true )
& ( setunionE = $true )
& ( notdallE = $true )
& ( exuE2 = $true )
& ( exuI3 = $true )
& ( omegaIndAx = $true )
& ( nonemptyImpWitness = $true )
& ( omegaSAx = $true )
& ( replAx = $true )
& ( setoftrueEq = $true )
& ( setadjoinIR = $true )
& ( nonemptyI1 = $true )
& ( inCongP = $true )
& ( prop2set2propI = $true )
& ( exuI1 = $true )
& ( in__Cong = $true )
& ( powersetI = $true )
& ( dsetconstrI = $true )
& ( nonemptyE1 = $true )
& ( quantDeMorgan3 = $true )
& ( exuE3u = $true )
& ( notinemptyset = $true )
& ( notdexE = $true )
& ( powersetAx = $true )
& ( emptyInPowerset = $true )
& ( upairsetE = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( emptysetE = $true )
& ( setunionAx = $true )
& ( prop2setI = $true )
& ( setextAx = $true )
& ( uniqinunit = $true )
& ( nonemptyI = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinAx = $true )
& ( dsetconstrER = $true )
& ( foundationAx = $true )
& ( setunionI = $true )
& ( exuI2 = $true )
& ( subPowSU = $true )
& ( eqinunit = $true )
& ( prop2setE = $true )
& ( setadjoinE = $true )
& ( upairsetIR = $true )
& ( singletonsswitch = $true )
& ( notinsingleton = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f210]) ).
thf(f277,plain,
sK1 = sK0,
inference(cnf_transformation,[],[f211]) ).
thf(f278,plain,
( ( setadjoin @ sK0 @ sK2 )
!= ( setadjoin @ sK1 @ sK3 ) ),
inference(cnf_transformation,[],[f211]) ).
thf(f279,plain,
sK3 = sK2,
inference(cnf_transformation,[],[f211]) ).
thf(f362,plain,
( ( setadjoin @ sK0 @ sK2 )
!= ( setadjoin @ sK0 @ sK2 ) ),
inference(definition_unfolding,[],[f278,f277,f279]) ).
thf(f442,definition,
( sF11
= ( setadjoin @ sK0 @ sK2 ) ),
introduced(definition,[new_symbols(definition,[sF11])],[function_definition]) ).
thf(f443,plain,
( ( setadjoin @ sK0 @ sK2 )
= sF11 ),
inference(reorient_equations,[],[f442]) ).
thf(f444,plain,
sF11 != sF11,
inference(definition_folding,[],[f362,f443,f443]) ).
thf(f1000,plain,
$false,
inference(trivial_inequality_removal,[],[f444]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU552^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.16 % Computer : n005.cluster.edu
% 0.09/0.16 % Model : x86_64 x86_64
% 0.09/0.16 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.16 % Memory : 8046.5625MB
% 0.09/0.16 % OS : Linux 6.8.0-71-generic
% 0.09/0.16 % CPULimit : 300
% 0.09/0.16 % WCLimit : 300
% 0.09/0.16 % DateTime : Tue Sep 29 13:49:31 UTC 2026
% 0.09/0.16 % CPUTime :
% 0.09/0.16 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 Running higher-order theorem proving
% 0.09/0.22 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
% 0.18/0.30 % (1698379)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.18/0.30 % (1698388)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2290977748:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.18/0.30 % (1698390)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.18/0.30 % (1698390)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
% 0.18/0.30 % (1698384)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2008188994:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.18/0.30 % (1698385)lrs+10_16_si=on:nwc=1.5:random_seed=1508923835:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.18/0.30 % (1698386)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=289366784:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.18/0.30 % (1698388)Instruction limit reached!
% 0.18/0.30 % (1698388)------------------------------
% 0.18/0.30 % (1698388)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (1698389)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1552388547:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.18/0.30 % (1698388)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (1698388)CaDiCaL version: 2.1.3
% 0.18/0.30 % (1698388)Termination reason: Instruction limit
% 0.18/0.30 % (1698388)Termination phase: Property scanning
% 0.18/0.30 % (1698388)Time elapsed: 0.007 s
% 0.18/0.30 % (1698388)Peak memory usage: 11 MB
% 0.18/0.30 % (1698387)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=4021835944: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)
% 0.18/0.30 % (1698388)Instructions burned: 28 (million)
% 0.18/0.30 % (1698390)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=3531024632:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.18/0.30 % (1698386)Instruction limit reached!
% 0.18/0.30 % (1698386)------------------------------
% 0.18/0.30 % (1698386)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (1698386)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (1698386)CaDiCaL version: 2.1.3
% 0.18/0.30 % (1698386)Termination reason: Instruction limit
% 0.18/0.30 % (1698386)Termination phase: shuffling
% 0.18/0.30 % (1698386)Time elapsed: 0.002 s
% 0.18/0.30 % (1698386)Peak memory usage: 10 MB
% 0.18/0.30 % (1698386)Instructions burned: 4 (million)
% 0.18/0.30 % (1698385)Instruction limit reached!
% 0.18/0.30 % (1698385)------------------------------
% 0.18/0.30 % (1698385)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (1698385)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (1698385)CaDiCaL version: 2.1.3
% 0.18/0.30 % (1698385)Termination reason: Instruction limit
% 0.18/0.30 % (1698385)Termination phase: Property scanning
% 0.18/0.30 % (1698385)Time elapsed: 0.008 s
% 0.18/0.30 % (1698385)Peak memory usage: 10 MB
% 0.18/0.30 % (1698385)Instructions burned: 19 (million)
% 0.18/0.30 % (1698400)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.18/0.30 % (1698398)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2928795945:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.18/0.30 % (1698400)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3880926482:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.18/0.30 % (1698390) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1698379-1698390"...
% 0.18/0.30 % (1698399)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3997104435:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.18/0.30 % (1698398)Instruction limit reached!
% 0.18/0.30 % (1698398)------------------------------
% 0.18/0.30 % (1698398)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (1698398)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (1698398)CaDiCaL version: 2.1.3
% 0.18/0.30 % (1698398)Termination reason: Instruction limit
% 0.18/0.30 % (1698398)Termination phase: shuffling
% 0.18/0.30 % (1698398)Time elapsed: 0.002 s
% 0.18/0.30 % (1698398)Peak memory usage: 10 MB
% 0.18/0.30 % (1698398)Instructions burned: 4 (million)
% 0.18/0.30 % (1698400)Instruction limit reached!
% 0.18/0.30 % (1698400)------------------------------
% 0.18/0.30 % (1698400)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (1698400)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (1698400)CaDiCaL version: 2.1.3
% 0.18/0.30 % (1698400)Termination reason: Instruction limit
% 0.18/0.30 % (1698400)Termination phase: Property scanning
% 0.18/0.30 % (1698400)Time elapsed: 0.002 s
% 0.18/0.30 % (1698400)Peak memory usage: 10 MB
% 0.18/0.30 % (1698400)Instructions burned: 9 (million)
% 0.18/0.30 % (1698389) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1698379-1698389"...
% 0.18/0.30 % (1698390)...printing done.
% 0.18/0.30 % (1698384) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1698379-1698384"...
% 0.18/0.30 % (1698390)Refutation found. Thanks to Tanya!
% 0.18/0.30 % SZS status Theorem for theBenchmark
% 0.18/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.30 % (1698390)------------------------------
% 0.18/0.30 % (1698390)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.30 % (1698390)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.30 % (1698390)CaDiCaL version: 2.1.3
% 0.18/0.30 % (1698390)Termination reason: Refutation
% 0.18/0.30 % (1698390)Time elapsed: 0.022 s
% 0.18/0.30 % (1698390)Peak memory usage: 12 MB
% 0.18/0.30 % (1698390)Instructions burned: 48 (million)
% 0.18/0.30 % (1698379)Success in time 0.075 s
% 0.18/0.30 % Vampire exiting
%------------------------------------------------------------------------------