%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU543^1 : 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 : n006.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 0.22s 0.32s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 15 ( 4 unt; 0 typ; 0 def)
% Number of atoms : 1339 ( 385 equ; 0 cnn)
% Maximal formula atoms : 63 ( 89 avg)
% Number of connectives : 647 ( 25 ~; 6 |; 249 &; 62 @)
% ( 0 <=>; 305 =>; 0 <=; 0 <~>)
% Maximal formula depth : 69 ( 40 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 171 ( 168 usr; 70 con; 0-4 aty)
% Number of variables : 34 ( 0 ^; 20 !; 14 ?; 34 :)
% 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,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_73,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_76,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_77,type,
vNOT: $o > $o ).
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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_81,type,
vIMP: $o > $o > $o ).
thf(func_def_82,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_83,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_84,type,
sP0: $i > $i > $o ).
thf(func_def_85,type,
sP1: $i > $o ).
thf(func_def_86,type,
sP2: $i > $i > $o ).
thf(func_def_87,type,
sP3: $i > $i > $o ).
thf(func_def_88,type,
sP4: $o ).
thf(func_def_91,type,
sK7: $i > $i > $i ).
thf(func_def_95,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_97,type,
sK13: $i > $o ).
thf(func_def_100,type,
sK16: $o ).
thf(func_def_102,type,
sK18: $i > $i > $i ).
thf(func_def_103,type,
sK19: $i > $i > $i ).
thf(func_def_104,type,
sK20: $i > $i > $i ).
thf(func_def_105,type,
sK21: $i > $i > $i ).
thf(func_def_106,type,
sK22: $i > $i > $i > $i ).
thf(func_def_107,type,
sK23: $i > $i ).
thf(func_def_108,type,
sK24: $i > $i ).
thf(func_def_109,type,
sK25: $i > $i ).
thf(func_def_110,type,
sK26: $i > $i ).
thf(func_def_111,type,
sK27: $i > $i > $i ).
thf(func_def_112,type,
sK28: $i > $i > $i > $i ).
thf(func_def_113,type,
sK29: $i > $i > $i > $i ).
thf(func_def_114,type,
sK30: $i > $i > $i ).
thf(func_def_115,type,
sK31: $i > $i > $i ).
thf(func_def_117,type,
sK33: $i > $i ).
thf(func_def_118,type,
sK34: $i > $i ).
thf(func_def_119,type,
sK35: $i > $i ).
thf(func_def_120,type,
sK36: $i > $i > $i ).
thf(func_def_124,type,
sK40: $o ).
thf(func_def_125,type,
sK41: $i > $o ).
thf(func_def_126,type,
sK42: $i > $i > $o ).
thf(func_def_128,type,
sK44: $i > $i ).
thf(func_def_129,type,
sK45: $i > $i ).
thf(func_def_130,type,
sK46: $i > ( $i > $i > $o ) > $i ).
thf(func_def_131,type,
sK47: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_132,type,
sK48: $i > ( $i > $i > $o ) > $i ).
thf(func_def_138,type,
sK54: $i > $i > $i ).
thf(func_def_144,type,
sK60: $i > $i ).
thf(func_def_147,type,
sK63: $o ).
thf(func_def_149,type,
sK65: $i > $i > $i ).
thf(func_def_150,type,
sK66: $i > $i > $i ).
thf(func_def_154,type,
sK70: $i > $o ).
thf(func_def_157,type,
sK73: $i > $o ).
thf(func_def_159,type,
sK75: ( $i > $o ) > $i > $i ).
thf(func_def_161,type,
sK77: $i > $o ).
thf(func_def_163,type,
sK79: $o > $i > $i > $i ).
thf(func_def_166,type,
sK82: $o ).
thf(func_def_167,type,
sK83: $i > $o ).
thf(func_def_168,type,
sK84: $i > $i ).
thf(func_def_169,type,
sK85: ( $i > $o ) > $i ).
thf(func_def_170,type,
sK86: $i > ( $i > $o ) > $i ).
thf(func_def_171,type,
sK87: $i > $o ).
thf(func_def_176,type,
sK92: $i > $o ).
thf(func_def_181,type,
sK97: $i > $i > $i ).
thf(func_def_182,type,
sK98: $i > $o ).
thf(func_def_185,type,
sK101: $i > ( $i > $o ) > $i ).
thf(func_def_189,type,
sK105: $o ).
thf(func_def_192,type,
sK108: $i > $o ).
thf(func_def_193,type,
sK109: $i > $i ).
thf(func_def_194,type,
sK110: ( $i > $o ) > $i ).
thf(func_def_195,type,
sK111: $i > $o ).
thf(func_def_196,type,
sK112: ( $i > $o ) > $i ).
thf(func_def_197,type,
sK113: $i > $i > $i ).
thf(func_def_200,type,
sK116: ( $i > $o ) > $i > $i ).
thf(func_def_202,type,
sK118: $i > $o ).
thf(func_def_207,type,
sK123: $i > $i ).
thf(func_def_208,type,
sK124: $i > $i ).
thf(func_def_210,type,
sK126: $i > $i ).
thf(func_def_223,type,
sK139: $i > $o ).
thf(func_def_225,type,
sK141: $i > $o ).
thf(func_def_230,type,
sK146: $i > $o ).
thf(func_def_232,type,
sK148: $o ).
thf(func_def_235,type,
sK151: $i > $o ).
thf(func_def_239,type,
sK155: $i > $o ).
thf(func_def_252,type,
sK168: $i > $i ).
thf(func_def_254,type,
sK170: $i > $i ).
thf(func_def_256,type,
sK172: $i > $i ).
thf(func_def_257,type,
sK173: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_258,type,
sK174: $i > ( $i > $o ) > $i ).
thf(func_def_259,type,
sK175: $i > $i ).
thf(func_def_260,type,
sK176: ( $i > $o ) > $i > $i ).
thf(func_def_261,type,
sK177: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_262,type,
sK178: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_263,type,
sK179: ( $i > $o ) > $i > $i ).
thf(func_def_264,type,
sK180: ( $i > $o ) > $i > $i ).
thf(func_def_265,type,
sK181: $i > ( $i > $o ) > $i ).
thf(func_def_266,type,
sK182: ( $i > $o ) > $i > $i ).
thf(f62,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
=> ! [X0: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(f63,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
=> ! [X0: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) )
=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ~ ( X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f62]) ).
thf(f179,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
=> ! [X0: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( in @ X2 @ X0 )
=> ( X1 @ X2 ) )
=> ? [X3: $i] :
( ( in @ X3 @ X0 )
& ~ ( X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f63]) ).
thf(f180,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 )
=> ! [X0: $i,X1: $i > $o] :
( ~ ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( X1 @ X2 )
= $true ) )
=> ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( X1 @ X3 )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f179]) ).
thf(f202,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 )
=> ! [X1: $i > $o,X0: $i] :
( ~ ! [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
=> ( ( X1 @ X2 )
= $true ) )
=> ? [X3: $i] :
( ( ( X1 @ X3 )
!= $true )
& ( ( in @ X3 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f180]) ).
thf(f225,plain,
( ? [X0: $i,X1: $i > $o] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $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,[],[f202]) ).
thf(f226,plain,
( ( emptyinunitempty = $true )
& ( omegaIndAx = $true )
& ( notinemptyset = $true )
& ( setunionE = $true )
& ( wellorderingAx = $true )
& ( exuE3e = $true )
& ( nonemptyE1 = $true )
& ( powersetE = $true )
& ( emptysetimpfalse = $true )
& ( subPowSU = $true )
& ( emptyE1 = $true )
& ( upairsetE = $true )
& ( setadjoinE = $true )
& ( prop2setE = $true )
& ( exuE2 = $true )
& ( quantDeMorgan1 = $true )
& ( setunionAx = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( emptysetAx = $true )
& ( exuE1 = $true )
& ( setadjoinIR = $true )
& ( emptyInPowerset = $true )
& ( uniqinunit = $true )
& ( setextAx = $true )
& ( emptysetE = $true )
& ( setunionI = $true )
& ( dsetconstrEL = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan2 = $true )
& ( setbeta = $true )
& ( notinsingleton = $true )
& ( upairsetIL = $true )
& ( setadjoinOr = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( setext = $true )
& ( powersetAx = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( descrp = $true )
& ( emptyI = $true )
& ( singletonsswitch = $true )
& ( upairsetIR = $true )
& ( dsetconstrI = $true )
& ( foundationAx = $true )
& ? [X0: $i,X1: $i > $o] :
( ! [X3: $i] :
( ( ( X1 @ X3 )
= $true )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
!= $true ) ) )
& ( powersetI = $true )
& ( noeltsimpempty = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( setadjoinIL = $true )
& ( notdexE = $true )
& ( quantDeMorgan4 = $true ) ),
inference(flattening,[],[f225]) ).
thf(f433,plain,
( ( emptyinunitempty = $true )
& ( omegaIndAx = $true )
& ( notinemptyset = $true )
& ( setunionE = $true )
& ( wellorderingAx = $true )
& ( exuE3e = $true )
& ( nonemptyE1 = $true )
& ( powersetE = $true )
& ( emptysetimpfalse = $true )
& ( subPowSU = $true )
& ( emptyE1 = $true )
& ( upairsetE = $true )
& ( setadjoinE = $true )
& ( prop2setE = $true )
& ( exuE2 = $true )
& ( quantDeMorgan1 = $true )
& ( setunionAx = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( emptysetAx = $true )
& ( exuE1 = $true )
& ( setadjoinIR = $true )
& ( emptyInPowerset = $true )
& ( uniqinunit = $true )
& ( setextAx = $true )
& ( emptysetE = $true )
& ( setunionI = $true )
& ( dsetconstrEL = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan2 = $true )
& ( setbeta = $true )
& ( notinsingleton = $true )
& ( upairsetIL = $true )
& ( setadjoinOr = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( setext = $true )
& ( powersetAx = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( descrp = $true )
& ( emptyI = $true )
& ( singletonsswitch = $true )
& ( upairsetIR = $true )
& ( dsetconstrI = $true )
& ( foundationAx = $true )
& ? [X0: $i,X1: $i > $o] :
( ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
| ( ( in @ X2 @ X0 )
!= $true ) )
& ? [X3: $i] :
( ( ( in @ X3 @ X0 )
= $true )
& ( ( X1 @ X3 )
!= $true ) ) )
& ( powersetI = $true )
& ( noeltsimpempty = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( setadjoinIL = $true )
& ( notdexE = $true )
& ( quantDeMorgan4 = $true ) ),
inference(rectify,[],[f226]) ).
thf(f434,plain,
( ( emptyinunitempty = $true )
& ( omegaIndAx = $true )
& ( notinemptyset = $true )
& ( setunionE = $true )
& ( wellorderingAx = $true )
& ( exuE3e = $true )
& ( nonemptyE1 = $true )
& ( powersetE = $true )
& ( emptysetimpfalse = $true )
& ( subPowSU = $true )
& ( emptyE1 = $true )
& ( upairsetE = $true )
& ( setadjoinE = $true )
& ( prop2setE = $true )
& ( exuE2 = $true )
& ( quantDeMorgan1 = $true )
& ( setunionAx = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( emptysetAx = $true )
& ( exuE1 = $true )
& ( setadjoinIR = $true )
& ( emptyInPowerset = $true )
& ( uniqinunit = $true )
& ( setextAx = $true )
& ( emptysetE = $true )
& ( setunionI = $true )
& ( dsetconstrEL = $true )
& ( vacuousDall = $true )
& ( quantDeMorgan3 = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( quantDeMorgan2 = $true )
& ( setbeta = $true )
& ( notinsingleton = $true )
& ( upairsetIL = $true )
& ( setadjoinOr = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( setext = $true )
& ( powersetAx = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( descrp = $true )
& ( emptyI = $true )
& ( singletonsswitch = $true )
& ( upairsetIR = $true )
& ( dsetconstrI = $true )
& ( foundationAx = $true )
& ! [X2: $i] :
( ( $true
= ( sK155 @ X2 ) )
| ( $true
!= ( in @ X2 @ sK154 ) ) )
& ( $true
= ( in @ sK156 @ sK154 ) )
& ( $true
!= ( sK155 @ sK156 ) )
& ( powersetI = $true )
& ( noeltsimpempty = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( setadjoinIL = $true )
& ( notdexE = $true )
& ( quantDeMorgan4 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK154,sK155,sK156]),skolemize(X0,sK154),skolemize(X1,sK155),skolemize(X3,sK156)],[f433]) ).
thf(f700,plain,
( $true
!= ( sK155 @ sK156 ) ),
inference(cnf_transformation,[],[f434]) ).
thf(f701,plain,
( $true
= ( in @ sK156 @ sK154 ) ),
inference(cnf_transformation,[],[f434]) ).
thf(f702,plain,
! [X2: $i] :
( ( $true
!= ( in @ X2 @ sK154 ) )
| ( $true
= ( sK155 @ X2 ) ) ),
inference(cnf_transformation,[],[f434]) ).
thf(f1238,plain,
( ( $true
= ( sK155 @ sK156 ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f702,f701]) ).
thf(f1239,plain,
( $true
= ( sK155 @ sK156 ) ),
inference(trivial_inequality_removal,[],[f1238]) ).
thf(f1240,plain,
$false,
inference(forward_subsumption_resolution,[],[f1239,f700]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU543^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n006.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Tue Sep 29 13:48:55 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.32 % (747335)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.32 % (747342)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=111361088:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.32 % (747342)Instruction limit reached!
% 0.22/0.32 % (747342)------------------------------
% 0.22/0.32 % (747342)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (747342)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (747342)CaDiCaL version: 2.1.3
% 0.22/0.32 % (747342)Termination reason: Instruction limit
% 0.22/0.32 % (747342)Termination phase: shuffling
% 0.22/0.32 % (747342)Time elapsed: 0.001 s
% 0.22/0.32 % (747342)Peak memory usage: 9 MB
% 0.22/0.32 % (747342)Instructions burned: 3 (million)
% 0.22/0.32 % (747346)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.32 % (747346)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
% 0.22/0.32 % (747340)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=520357923:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.32 % (747344)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3819308774:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.32 % (747341)lrs+10_16_si=on:nwc=1.5:random_seed=3614029306:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.32 % (747343)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=1593740416: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)
% 0.22/0.32 % (747345)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4022936090:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.32 % (747346)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=3813843294:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.32 % (747348)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2268232989:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.32 % (747348)Instruction limit reached!
% 0.22/0.32 % (747348)------------------------------
% 0.22/0.32 % (747348)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (747348)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (747348)CaDiCaL version: 2.1.3
% 0.22/0.32 % (747348)Termination reason: Instruction limit
% 0.22/0.32 % (747348)Termination phase: shuffling
% 0.22/0.32 % (747348)Time elapsed: 0.001 s
% 0.22/0.32 % (747348)Peak memory usage: 9 MB
% 0.22/0.32 % (747348)Instructions burned: 4 (million)
% 0.22/0.32 % (747341)Instruction limit reached!
% 0.22/0.32 % (747341)------------------------------
% 0.22/0.32 % (747341)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (747341)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (747341)CaDiCaL version: 2.1.3
% 0.22/0.32 % (747341)Termination reason: Instruction limit
% 0.22/0.32 % (747341)Termination phase: Function definition elimination
% 0.22/0.32 % (747341)Time elapsed: 0.008 s
% 0.22/0.32 % (747341)Peak memory usage: 10 MB
% 0.22/0.32 % (747341)Instructions burned: 19 (million)
% 0.22/0.32 % (747344)Instruction limit reached!
% 0.22/0.32 % (747344)------------------------------
% 0.22/0.32 % (747344)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (747344)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (747344)CaDiCaL version: 2.1.3
% 0.22/0.32 % (747344)Termination reason: Instruction limit
% 0.22/0.32 % (747344)Termination phase: Property scanning
% 0.22/0.32 % (747344)Time elapsed: 0.012 s
% 0.22/0.32 % (747344)Peak memory usage: 11 MB
% 0.22/0.32 % (747344)Instructions burned: 24 (million)
% 0.22/0.32 % (747356)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=799102031:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.32 % (747356)Instruction limit reached!
% 0.22/0.32 % (747356)------------------------------
% 0.22/0.32 % (747356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (747356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (747356)CaDiCaL version: 2.1.3
% 0.22/0.32 % (747356)Termination reason: Instruction limit
% 0.22/0.32 % (747356)Termination phase: Property scanning
% 0.22/0.32 % (747356)Time elapsed: 0.002 s
% 0.22/0.32 % (747356)Peak memory usage: 10 MB
% 0.22/0.32 % (747356)Instructions burned: 8 (million)
% 0.22/0.32 % (747357)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.32 % (747360)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
% 0.22/0.32 % (747360)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.32 % (747357)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1743270449:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.32 % (747340) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-747335-747340"...
% 0.22/0.32 % (747360)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2116634425:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.32 % (747358)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=4056789423:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.32 % (747340)...printing done.
% 0.22/0.32 % (747343) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-747335-747343"...
% 0.22/0.32 % (747357)Instruction limit reached!
% 0.22/0.32 % (747357)------------------------------
% 0.22/0.32 % (747357)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (747357)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (747357)CaDiCaL version: 2.1.3
% 0.22/0.32 % (747357)Termination reason: Instruction limit
% 0.22/0.32 % (747357)Termination phase: Property scanning
% 0.22/0.32 % (747357)Time elapsed: 0.004 s
% 0.22/0.32 % (747357)Peak memory usage: 9 MB
% 0.22/0.32 % (747357)Instructions burned: 9 (million)
% 0.22/0.32 % (747340)Refutation found. Thanks to Tanya!
% 0.22/0.32 % SZS status Theorem for theBenchmark
% 0.22/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.32 % (747340)------------------------------
% 0.22/0.32 % (747340)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.32 % (747340)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.32 % (747340)CaDiCaL version: 2.1.3
% 0.22/0.32 % (747340)Termination reason: Refutation
% 0.22/0.32 % (747340)Time elapsed: 0.031 s
% 0.22/0.32 % (747340)Peak memory usage: 13 MB
% 0.22/0.32 % (747340)Instructions burned: 62 (million)
% 0.22/0.32 % (747335)Success in time 0.068 s
% 0.22/0.32 % Vampire exiting
%------------------------------------------------------------------------------