%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU545^1 : 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 : n018.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 08:30:00 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 34 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 1300 ( 387 equ; 0 cnn)
% Maximal formula atoms : 66 ( 38 avg)
% Number of connectives : 707 ( 27 ~; 25 |; 260 &; 113 @)
% ( 0 <=>; 271 =>; 0 <=; 0 <~>)
% Maximal formula depth : 71 ( 18 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 181 ( 176 usr; 73 con; 0-4 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 78 ( 28 ^; 38 !; 12 ?; 78 :)
% 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_76,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_77,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_78,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_79,type,
vAND: $o > $o > $o ).
thf(func_def_80,type,
db1:
!>[X0: $tType] : X0 ).
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,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_85,type,
vNOT: $o > $o ).
thf(func_def_86,type,
sP0: $o ).
thf(func_def_87,type,
sP1: $i > $i > $o ).
thf(func_def_88,type,
sP2: $i > $o ).
thf(func_def_89,type,
sP3: $i > $i > $o ).
thf(func_def_90,type,
sP4: $i > $i > $o ).
thf(func_def_102,type,
sK16: $i > $o ).
thf(func_def_105,type,
sK19: $i > $i ).
thf(func_def_112,type,
sK26: $i > $i > $i ).
thf(func_def_114,type,
sK28: $o ).
thf(func_def_115,type,
sK29: $i > $i > $o ).
thf(func_def_117,type,
sK31: $i > $i ).
thf(func_def_118,type,
sK32: $i > $i ).
thf(func_def_119,type,
sK33: $i > ( $i > $i > $o ) > $i ).
thf(func_def_120,type,
sK34: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_121,type,
sK35: $i > ( $i > $i > $o ) > $i ).
thf(func_def_123,type,
sK37: $i > $o ).
thf(func_def_125,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_128,type,
sK42: $o ).
thf(func_def_129,type,
sK43: $i > $i > $i ).
thf(func_def_133,type,
sK47: $i > $o ).
thf(func_def_135,type,
sK49: $i > $o ).
thf(func_def_137,type,
sK51: $i > ( $i > $o ) > $i ).
thf(func_def_139,type,
sK53: $i > $o ).
thf(func_def_141,type,
sK55: $i > $o ).
thf(func_def_142,type,
sK56: $i > $i ).
thf(func_def_143,type,
sK57: ( $i > $o ) > $i ).
thf(func_def_152,type,
sK66: $i > $i > $i ).
thf(func_def_156,type,
sK70: $i > $i > $i ).
thf(func_def_157,type,
sK71: $i > $i > $i ).
thf(func_def_158,type,
sK72: $i > $i > $i ).
thf(func_def_159,type,
sK73: $i > $i > $i ).
thf(func_def_160,type,
sK74: $i > $i > $i > $i ).
thf(func_def_161,type,
sK75: $i > $i ).
thf(func_def_162,type,
sK76: $i > $i ).
thf(func_def_163,type,
sK77: $i > $i ).
thf(func_def_164,type,
sK78: $i > $i ).
thf(func_def_165,type,
sK79: $i > $i > $i ).
thf(func_def_166,type,
sK80: $i > $i > $i > $i ).
thf(func_def_167,type,
sK81: $i > $i > $i > $i ).
thf(func_def_168,type,
sK82: $i > $i > $i ).
thf(func_def_169,type,
sK83: $i > $i > $i ).
thf(func_def_171,type,
sK85: $i > $i ).
thf(func_def_172,type,
sK86: $i > $i ).
thf(func_def_173,type,
sK87: $i > $i ).
thf(func_def_174,type,
sK88: $i > $i > $i ).
thf(func_def_176,type,
sK90: $i > $i ).
thf(func_def_178,type,
sK92: $i > $i ).
thf(func_def_181,type,
sK95: $o ).
thf(func_def_182,type,
sK96: $o > $i > $i > $i ).
thf(func_def_185,type,
sK99: $i > $o ).
thf(func_def_187,type,
sK101: $i > $o ).
thf(func_def_188,type,
sK102: ( $i > $o ) > $i ).
thf(func_def_189,type,
sK103: $i > $o ).
thf(func_def_190,type,
sK104: $i > $i ).
thf(func_def_194,type,
sK108: $i > $o ).
thf(func_def_197,type,
sK111: $i > ( $i > $o ) > $i ).
thf(func_def_202,type,
sK116: $i > $i ).
thf(func_def_206,type,
sK120: $o ).
thf(func_def_207,type,
sK121: ( $i > $o ) > $i > $i ).
thf(func_def_209,type,
sK123: $i > $o ).
thf(func_def_215,type,
sK129: $i > $o ).
thf(func_def_218,type,
sK132: $i > $o ).
thf(func_def_221,type,
sK135: $i > $o ).
thf(func_def_223,type,
sK137: ( $i > $o ) > $i > $i ).
thf(func_def_225,type,
sK139: $i > $o ).
thf(func_def_227,type,
sK141: ( $i > $o ) > $i > $i ).
thf(func_def_228,type,
sK142: $i > $i ).
thf(func_def_230,type,
sK144: $i > $o ).
thf(func_def_234,type,
sK148: $i > $i ).
thf(func_def_235,type,
sK149: ( $i > $o ) > $i ).
thf(func_def_236,type,
sK150: $i > $o ).
thf(func_def_237,type,
sK151: $i > $i > $i ).
thf(func_def_241,type,
sK155: $i > $i ).
thf(func_def_246,type,
sK160: $o ).
thf(func_def_248,type,
sK162: $o ).
thf(func_def_249,type,
sK163: $i > $o ).
thf(func_def_252,type,
sK166: $i > $o ).
thf(func_def_255,type,
sK169: $i > ( $i > $o ) > $i ).
thf(func_def_256,type,
sK170: $i > $i > $i ).
thf(func_def_257,type,
sK171: $i > $i > $i ).
thf(func_def_265,type,
sK179: $i > ( $i > $o ) > $i ).
thf(func_def_266,type,
sK180: $i > $i ).
thf(func_def_267,type,
sK181: $i > ( $i > $o ) > $i ).
thf(func_def_268,type,
sK182: ( $i > $o ) > $i ).
thf(func_def_269,type,
sK183: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_270,type,
sK184: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_271,type,
sK185: $i > ( $i > $o ) > $i ).
thf(func_def_272,type,
sK186: ( $i > $o ) > $i ).
thf(func_def_273,type,
sK187: $i > ( $i > $o ) > $i ).
thf(func_def_274,type,
sK188: ( $i > $o ) > $i > $i ).
thf(func_def_275,type,
sK189: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_276,type,
sK190: $i > $i ).
thf(func_def_277,type,
sK191: ( $i > $o ) > $i > $i ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(f64,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
=> ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X2: $i,X1: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(f65,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
=> ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X2: $i,X1: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f64]) ).
thf(f92,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f93,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f92]) ).
thf(f98,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
=> ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X2: $i,X3: $i] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X4: $i] : ( X0 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f65]) ).
thf(f99,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 )
=> ! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ! [X2: $i,X3: $i] :
( ( $true
= ( X0 @ X3 ) )
=> ( ( ( X0 @ X2 )
= $true )
=> ( X2 = X3 ) ) )
=> ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f98]) ).
thf(f233,plain,
( ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true )
& ! [X2: $i,X3: $i] :
( ( X2 = X3 )
| ( ( X0 @ X2 )
!= $true )
| ( $true
!= ( X0 @ X3 ) ) )
& ? [X1: $i] :
( ( X0 @ X1 )
= $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,[],[f99]) ).
thf(f234,plain,
( ( uniqinunit = $true )
& ( notdexE = $true )
& ( emptysetAx = $true )
& ( emptysetE = $true )
& ( upairsetE = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIR = $true )
& ( notinsingleton = $true )
& ( replAx = $true )
& ( subPowSU = $true )
& ( setadjoinOr = $true )
& ? [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
& ! [X3: $i,X2: $i] :
( ( $true
!= ( X0 @ X3 ) )
| ( ( X0 @ X2 )
!= $true )
| ( X2 = X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true ) )
& ( prop2setI = $true )
& ( noeltsimpempty = $true )
& ( omegaIndAx = $true )
& ( dsetconstrER = $true )
& ( emptyE1 = $true )
& ( omega0Ax = $true )
& ( setadjoinIL = $true )
& ( vacuousDall = $true )
& ( dsetconstrI = $true )
& ( omegaSAx = $true )
& ( setunionAx = $true )
& ( emptyI = $true )
& ( wellorderingAx = $true )
& ( descrp = $true )
& ( emptyInPowerset = $true )
& ( setadjoinAx = $true )
& ( notinemptyset = $true )
& ( prop2set2propI = $true )
& ( setunionI = $true )
& ( emptyinunitempty = $true )
& ( exuI1 = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan3 = $true )
& ( powersetE = $true )
& ( nonemptyI = $true )
& ( powersetI = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( exuE3e = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( upairsetIR = $true )
& ( emptyinPowerset = $true )
& ( setadjoinE = $true )
& ( upairsetIL = $true )
& ( notdallE = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( setunionE = $true )
& ( setext = $true )
& ( exuE2 = $true )
& ( singletonsswitch = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( eqinunit = $true ) ),
inference(flattening,[],[f233]) ).
thf(f295,plain,
( ( uniqinunit = $true )
& ( notdexE = $true )
& ( emptysetAx = $true )
& ( emptysetE = $true )
& ( upairsetE = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIR = $true )
& ( notinsingleton = $true )
& ( replAx = $true )
& ( subPowSU = $true )
& ( setadjoinOr = $true )
& ? [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
& ! [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( $true
!= ( X0 @ X3 ) )
| ( X2 = X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
!= $true ) )
& ( prop2setI = $true )
& ( noeltsimpempty = $true )
& ( omegaIndAx = $true )
& ( dsetconstrER = $true )
& ( emptyE1 = $true )
& ( omega0Ax = $true )
& ( setadjoinIL = $true )
& ( vacuousDall = $true )
& ( dsetconstrI = $true )
& ( omegaSAx = $true )
& ( setunionAx = $true )
& ( emptyI = $true )
& ( wellorderingAx = $true )
& ( descrp = $true )
& ( emptyInPowerset = $true )
& ( setadjoinAx = $true )
& ( notinemptyset = $true )
& ( prop2set2propI = $true )
& ( setunionI = $true )
& ( emptyinunitempty = $true )
& ( exuI1 = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan3 = $true )
& ( powersetE = $true )
& ( nonemptyI = $true )
& ( powersetI = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( exuE3e = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( upairsetIR = $true )
& ( emptyinPowerset = $true )
& ( setadjoinE = $true )
& ( upairsetIL = $true )
& ( notdallE = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( setunionE = $true )
& ( setext = $true )
& ( exuE2 = $true )
& ( singletonsswitch = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( eqinunit = $true ) ),
inference(rectify,[],[f234]) ).
thf(f296,plain,
( ( uniqinunit = $true )
& ( notdexE = $true )
& ( emptysetAx = $true )
& ( emptysetE = $true )
& ( upairsetE = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIR = $true )
& ( notinsingleton = $true )
& ( replAx = $true )
& ( subPowSU = $true )
& ( setadjoinOr = $true )
& ( $true
= ( sK16 @ sK17 ) )
& ! [X2: $i,X3: $i] :
( ( $true
!= ( sK16 @ X2 ) )
| ( $true
!= ( sK16 @ X3 ) )
| ( X2 = X3 ) )
& ( ( exu
@ ^ [Y0: $i] : ( sK16 @ Y0 ) )
!= $true )
& ( prop2setI = $true )
& ( noeltsimpempty = $true )
& ( omegaIndAx = $true )
& ( dsetconstrER = $true )
& ( emptyE1 = $true )
& ( omega0Ax = $true )
& ( setadjoinIL = $true )
& ( vacuousDall = $true )
& ( dsetconstrI = $true )
& ( omegaSAx = $true )
& ( setunionAx = $true )
& ( emptyI = $true )
& ( wellorderingAx = $true )
& ( descrp = $true )
& ( emptyInPowerset = $true )
& ( setadjoinAx = $true )
& ( notinemptyset = $true )
& ( prop2set2propI = $true )
& ( setunionI = $true )
& ( emptyinunitempty = $true )
& ( exuI1 = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan3 = $true )
& ( powersetE = $true )
& ( nonemptyI = $true )
& ( powersetI = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( exuE3e = $true )
& ( setbeta = $true )
& ( prop2setE = $true )
& ( upairsetIR = $true )
& ( emptyinPowerset = $true )
& ( setadjoinE = $true )
& ( upairsetIL = $true )
& ( notdallE = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan4 = $true )
& ( nonemptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( setunionE = $true )
& ( setext = $true )
& ( exuE2 = $true )
& ( singletonsswitch = $true )
& ( powersetAx = $true )
& ( exuE1 = $true )
& ( eqinunit = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17]),skolemize(X0,sK16),skolemize(X1,sK17)],[f295]) ).
thf(f538,plain,
( ( exu
@ ^ [Y0: $i] : ( sK16 @ Y0 ) )
!= $true ),
inference(cnf_transformation,[],[f296]) ).
thf(f539,plain,
! [X2: $i,X3: $i] :
( ( $true
!= ( sK16 @ X3 ) )
| ( $true
!= ( sK16 @ X2 ) )
| ( X2 = X3 ) ),
inference(cnf_transformation,[],[f296]) ).
thf(f540,plain,
( $true
= ( sK16 @ sK17 ) ),
inference(cnf_transformation,[],[f296]) ).
thf(f702,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f93]) ).
thf(f822,plain,
( $true
!= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK16 @ Y0 ) ) ),
inference(definition_unfolding,[],[f538,f702]) ).
thf(f1061,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK16 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK16 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
!= $true ),
inference(beta-eta_normalization,[],[f822]) ).
thf(f1062,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( sK16 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK16 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f1061]) ).
thf(f1063,plain,
! [X1: $i] :
( $false
= ( ( sK16 @ X1 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK16 @ Y0 )
=> ( X1 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f1062]) ).
thf(f1064,plain,
! [X1: $i] :
( ( $false
= ( sK16 @ X1 ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK16 @ Y0 )
=> ( X1 = Y0 ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f1063]) ).
thf(f1065,plain,
! [X1: $i] :
( ( $false
= ( ^ [Y0: $i] :
( ( sK16 @ Y0 )
=> ( X1 = Y0 ) )
@ ( sK180 @ X1 ) ) )
| ( $false
= ( sK16 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f1064]) ).
thf(f1066,plain,
! [X1: $i] :
( ( $false
= ( ( sK16 @ ( sK180 @ X1 ) )
=> ( X1
= ( sK180 @ X1 ) ) ) )
| ( $false
= ( sK16 @ X1 ) ) ),
inference(beta-eta_normalization,[],[f1065]) ).
thf(f1067,plain,
! [X1: $i] :
( ( $false
= ( X1
= ( sK180 @ X1 ) ) )
| ( $false
= ( sK16 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1066]) ).
thf(f1068,plain,
! [X1: $i] :
( ( $true
= ( sK16 @ ( sK180 @ X1 ) ) )
| ( $false
= ( sK16 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f1066]) ).
thf(f1069,plain,
! [X1: $i] :
( ( ( sK180 @ X1 )
!= X1 )
| ( $false
= ( sK16 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f1067]) ).
thf(f1345,plain,
! [X0: $i] :
( ( sK17 = X0 )
| ( $true != $true )
| ( $true
!= ( sK16 @ X0 ) ) ),
inference(constrained_superposition,[],[f539,f540]) ).
thf(f1346,plain,
! [X0: $i] :
( ( $true
!= ( sK16 @ X0 ) )
| ( sK17 = X0 ) ),
inference(trivial_inequality_removal,[],[f1345]) ).
thf(f1351,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( sK16 @ X0 ) )
| ( ( sK180 @ X0 )
= sK17 ) ),
inference(constrained_superposition,[],[f1346,f1068]) ).
thf(f1354,plain,
! [X0: $i] :
( ( ( sK180 @ X0 )
= sK17 )
| ( $false
= ( sK16 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1351]) ).
thf(f1356,plain,
! [X0: $i] :
( ( $false
= ( sK16 @ X0 ) )
| ( sK17 != X0 )
| ( $false
= ( sK16 @ X0 ) ) ),
inference(constrained_superposition,[],[f1069,f1354]) ).
thf(f1357,plain,
! [X0: $i] :
( ( sK17 != X0 )
| ( $false
= ( sK16 @ X0 ) ) ),
inference(duplicate_literal_removal,[],[f1356]) ).
thf(f1360,plain,
( ( sK16 @ sK17 )
= $false ),
inference(equality_resolution,[],[f1357]) ).
thf(f1362,plain,
$true = $false,
inference(forward_demodulation,[],[f1360,f540]) ).
thf(f1363,plain,
$false,
inference(trivial_inequality_removal,[],[f1362]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU545^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.19 % Computer : n018.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Sep 29 13:51:42 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.07/0.25 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
% 0.21/0.30 % (101410)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (101415)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=144638274:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (101421)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (101421)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
% 0.21/0.30 % (101416)lrs+10_16_si=on:nwc=1.5:random_seed=2052576353:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (101418)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=6189624: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)
% 0.21/0.30 % (101420)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=246219006:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (101419)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=104920575:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (101417)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3935961136:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (101421)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=2210367024:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (101417)Instruction limit reached!
% 0.21/0.30 % (101417)------------------------------
% 0.21/0.30 % (101417)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (101417)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (101417)CaDiCaL version: 2.1.3
% 0.21/0.30 % (101417)Termination reason: Instruction limit
% 0.21/0.30 % (101417)Termination phase: shuffling
% 0.21/0.30 % (101417)Time elapsed: 0.002 s
% 0.21/0.30 % (101417)Peak memory usage: 10 MB
% 0.21/0.30 % (101417)Instructions burned: 4 (million)
% 0.21/0.30 % (101416)Instruction limit reached!
% 0.21/0.30 % (101416)------------------------------
% 0.21/0.30 % (101416)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (101416)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (101416)CaDiCaL version: 2.1.3
% 0.21/0.30 % (101416)Termination reason: Instruction limit
% 0.21/0.30 % (101416)Termination phase: Function definition elimination
% 0.21/0.30 % (101416)Time elapsed: 0.008 s
% 0.21/0.30 % (101416)Peak memory usage: 10 MB
% 0.21/0.30 % (101416)Instructions burned: 19 (million)
% 0.21/0.30 % (101415) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-101410-101415"...
% 0.21/0.30 % (101415)...printing done.
% 0.21/0.30 % (101415)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (101415)------------------------------
% 0.21/0.30 % (101415)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (101415)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (101415)CaDiCaL version: 2.1.3
% 0.21/0.30 % (101415)Termination reason: Refutation
% 0.21/0.30 % (101415)Time elapsed: 0.019 s
% 0.21/0.30 % (101415)Peak memory usage: 13 MB
% 0.21/0.30 % (101415)Instructions burned: 67 (million)
% 0.21/0.30 % (101410)Success in time 0.037 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------