%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU527^1 : 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 : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:29:56 AM UTC 2026
% Result : Theorem 0.24s 0.33s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 21 unt; 0 typ; 6 def)
% Number of atoms : 1135 ( 316 equ; 0 cnn)
% Maximal formula atoms : 46 ( 18 avg)
% Number of connectives : 666 ( 69 ~; 61 |; 188 &; 158 @)
% ( 11 <=>; 179 =>; 0 <=; 0 <~>)
% Maximal formula depth : 51 ( 9 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 138 ( 135 usr; 63 con; 0-4 aty)
% Number of variables : 65 ( 0 sgn 51 !; 14 ?; 65 :)
% 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_57,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_59,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_60,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_61,type,
vNOT: $o > $o ).
thf(func_def_62,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_63,type,
vAND: $o > $o > $o ).
thf(func_def_64,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_65,type,
vIMP: $o > $o > $o ).
thf(func_def_66,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_67,type,
sP0: $i > $i > $o ).
thf(func_def_68,type,
sP1: $i > $o ).
thf(func_def_69,type,
sP2: $o ).
thf(func_def_72,type,
sK5: $o ).
thf(func_def_73,type,
sK6: $o > $i > $i > $i ).
thf(func_def_74,type,
sK7: $i > $o ).
thf(func_def_75,type,
sK8: $i > $i ).
thf(func_def_76,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_82,type,
sK15: $i > $i > $i ).
thf(func_def_83,type,
sK16: $i > $i > $i ).
thf(func_def_86,type,
sK19: $i > $o ).
thf(func_def_93,type,
sK26: $o ).
thf(func_def_96,type,
sK29: $i > $i ).
thf(func_def_97,type,
sK30: $i > $i ).
thf(func_def_103,type,
sK36: $i > $i > $i ).
thf(func_def_109,type,
sK42: $i > $i ).
thf(func_def_113,type,
sK46: $i > ( $i > $i > $o ) > $i ).
thf(func_def_114,type,
sK47: $i > ( $i > $i > $o ) > $i ).
thf(func_def_115,type,
sK48: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_116,type,
sK49: $i > $i > $o ).
thf(func_def_118,type,
sK51: $i > $i ).
thf(func_def_119,type,
sK52: $i > $i ).
thf(func_def_121,type,
sK54: $i > $i ).
thf(func_def_122,type,
sK55: $i > $i ).
thf(func_def_123,type,
sK56: $i > $i ).
thf(func_def_124,type,
sK57: $i > $i ).
thf(func_def_125,type,
sK58: $i > $i ).
thf(func_def_126,type,
sK59: $i > $i > $i > $i ).
thf(func_def_127,type,
sK60: $i > $i ).
thf(func_def_128,type,
sK61: $i > $i ).
thf(func_def_129,type,
sK62: $i > $i ).
thf(func_def_130,type,
sK63: $i > $i ).
thf(func_def_131,type,
sK64: $i > $i > $i ).
thf(func_def_132,type,
sK65: $i > $i > $i > $i ).
thf(func_def_133,type,
sK66: $i > $i > $i > $i ).
thf(func_def_134,type,
sK67: $i > $i > $i > $i ).
thf(func_def_135,type,
sK68: $i > $i > $i ).
thf(func_def_136,type,
sK69: $i > $i > $i ).
thf(func_def_137,type,
sK70: $i > $i > $i ).
thf(func_def_138,type,
sK71: $i > $i > $i ).
thf(func_def_142,type,
sK75: $i > $i > $i ).
thf(func_def_145,type,
sK78: $i > $o ).
thf(func_def_148,type,
sK81: $o ).
thf(func_def_153,type,
sK86: $i > $i > $i ).
thf(func_def_160,type,
sK93: $i > $o ).
thf(func_def_165,type,
sK98: ( $i > $o ) > $i ).
thf(func_def_166,type,
sK99: $i > $o ).
thf(func_def_167,type,
sK100: $i > $o ).
thf(func_def_171,type,
sK104: $i > $o ).
thf(func_def_175,type,
sK108: $i > $i > $i ).
thf(func_def_177,type,
sK110: $i > $i ).
thf(func_def_181,type,
sK114: $o ).
thf(func_def_182,type,
sK115: ( $i > $o ) > $i ).
thf(func_def_183,type,
sK116: $i > $o ).
thf(func_def_184,type,
sK117: $i > $i ).
thf(func_def_187,type,
sK120: $i > $o ).
thf(func_def_189,type,
sK122: $i > $i ).
thf(func_def_191,type,
sK124: $i > $i ).
thf(func_def_194,type,
sK127: $i > $i ).
thf(f22,axiom,
! [X0: $i] :
( ( ~ ( in @ X0 @ emptyset ) )
= notinemptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(f36,axiom,
( setadjoinOr
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ( ( X2 = X0 )
| ( in @ X2 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(f47,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
=> ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(f48,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
=> ! [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
thf(f102,plain,
( setadjoinOr
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ( ( X2 = X0 )
| ( in @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f36]) ).
thf(f103,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true )
=> ( ( ( in @ X2 @ X1 )
= $true )
| ( X0 = X2 ) ) )
<=> ( setadjoinOr = $true ) ),
inference(fool_elimination,[],[f102]) ).
thf(f112,plain,
! [X0: $i] :
( ( ~ ( in @ X0 @ emptyset ) )
= notinemptyset ),
inference(rectify,[],[f22]) ).
thf(f113,plain,
( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
<=> ( notinemptyset = $true ) ),
inference(fool_elimination,[],[f112]) ).
thf(f128,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
=> ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f48]) ).
thf(f129,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 )
=> ! [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
=> ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f128]) ).
thf(f146,plain,
( ( notinemptyset = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(flattening,[],[f113]) ).
thf(f174,plain,
( ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( X0 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
!= $true ) )
<=> ( setadjoinOr = $true ) ),
inference(ennf_transformation,[],[f103]) ).
thf(f175,plain,
( ( setadjoinOr = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
| ( X0 = X2 ) ) ),
inference(flattening,[],[f174]) ).
thf(f180,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) )
& ( 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,[],[f129]) ).
thf(f181,plain,
( ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( setadjoinOr = $true )
& ( notinemptyset = $true )
& ( emptyinunitempty = $true )
& ( powersetE = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( exuE3e = $true )
& ( setext = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( nonemptyE1 = $true )
& ( subPowSU = $true )
& ( exuE2 = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( setextAx = $true )
& ( nonemptyImpWitness = $true )
& ( dsetconstrEL = $true )
& ( powersetI = $true )
& ( dsetconstrER = $true )
& ( emptyinPowerset = $true )
& ( setbeta = $true )
& ( nonemptyI = $true )
& ( omega0Ax = $true )
& ( prop2setE = $true )
& ( emptyInPowerset = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( powersetAx = $true )
& ( setunionI = $true )
& ( wellorderingAx = $true )
& ( setoftrueEq = $true )
& ( emptyI = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true )
& ( X0 != X1 ) )
& ( foundationAx = $true )
& ( setunionAx = $true )
& ( exuE1 = $true )
& ( dsetconstrI = $true )
& ( nonemptyI1 = $true ) ),
inference(flattening,[],[f180]) ).
thf(f237,plain,
( ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( setadjoinOr = $true )
& ( notinemptyset = $true )
& ( emptyinunitempty = $true )
& ( powersetE = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( exuE3e = $true )
& ( setext = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( nonemptyE1 = $true )
& ( subPowSU = $true )
& ( exuE2 = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( setextAx = $true )
& ( nonemptyImpWitness = $true )
& ( dsetconstrEL = $true )
& ( powersetI = $true )
& ( dsetconstrER = $true )
& ( emptyinPowerset = $true )
& ( setbeta = $true )
& ( nonemptyI = $true )
& ( omega0Ax = $true )
& ( prop2setE = $true )
& ( emptyInPowerset = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( powersetAx = $true )
& ( setunionI = $true )
& ( wellorderingAx = $true )
& ( setoftrueEq = $true )
& ( emptyI = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
= $true )
& ( X0 != X1 ) )
& ( foundationAx = $true )
& ( setunionAx = $true )
& ( exuE1 = $true )
& ( dsetconstrI = $true )
& ( nonemptyI1 = $true ) ),
inference(rectify,[],[f181]) ).
thf(f238,plain,
( ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( setadjoinOr = $true )
& ( notinemptyset = $true )
& ( emptyinunitempty = $true )
& ( powersetE = $true )
& ( setadjoinAx = $true )
& ( omegaSAx = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( exuE3e = $true )
& ( setext = $true )
& ( emptysetAx = $true )
& ( omegaIndAx = $true )
& ( nonemptyE1 = $true )
& ( subPowSU = $true )
& ( exuE2 = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( setextAx = $true )
& ( nonemptyImpWitness = $true )
& ( dsetconstrEL = $true )
& ( powersetI = $true )
& ( dsetconstrER = $true )
& ( emptyinPowerset = $true )
& ( setbeta = $true )
& ( nonemptyI = $true )
& ( omega0Ax = $true )
& ( prop2setE = $true )
& ( emptyInPowerset = $true )
& ( setadjoinIR = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( powersetAx = $true )
& ( setunionI = $true )
& ( wellorderingAx = $true )
& ( setoftrueEq = $true )
& ( emptyI = $true )
& ( ( in @ sK40 @ ( setadjoin @ sK41 @ emptyset ) )
= $true )
& ( sK40 != sK41 )
& ( foundationAx = $true )
& ( setunionAx = $true )
& ( exuE1 = $true )
& ( dsetconstrI = $true )
& ( nonemptyI1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK40,sK41]),skolemize(X0,sK40),skolemize(X1,sK41)],[f237]) ).
thf(f282,plain,
( ( ( setadjoinOr = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
!= $true )
& ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
= $true )
& ( X0 != X2 ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
| ( X0 = X2 ) )
| ( setadjoinOr != $true ) ) ),
inference(nnf_transformation,[],[f175]) ).
thf(f283,plain,
( ( ( setadjoinOr = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
& ( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
= $true )
& ( X0 != X1 ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
!= $true )
| ( X3 = X4 ) )
| ( setadjoinOr != $true ) ) ),
inference(rectify,[],[f282]) ).
thf(f284,plain,
( ( ( setadjoinOr = $true )
| ( ( ( in @ sK91 @ sK92 )
!= $true )
& ( ( in @ sK91 @ ( setadjoin @ sK90 @ sK92 ) )
= $true )
& ( sK91 != sK90 ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
!= $true )
| ( X3 = X4 ) )
| ( setadjoinOr != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK90,sK91,sK92]),skolemize(X0,sK90),skolemize(X1,sK91),skolemize(X2,sK92)],[f283]) ).
thf(f291,plain,
( ( ( notinemptyset = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ) ),
inference(nnf_transformation,[],[f146]) ).
thf(f292,plain,
( ( ( notinemptyset = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ) ),
inference(rectify,[],[f291]) ).
thf(f293,plain,
( ( ( notinemptyset = $true )
| ( ( in @ sK95 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(X0,sK95)],[f292]) ).
thf(f394,plain,
sK40 != sK41,
inference(cnf_transformation,[],[f238]) ).
thf(f395,plain,
( ( in @ sK40 @ ( setadjoin @ sK41 @ emptyset ) )
= $true ),
inference(cnf_transformation,[],[f238]) ).
thf(f430,plain,
notinemptyset = $true,
inference(cnf_transformation,[],[f238]) ).
thf(f431,plain,
setadjoinOr = $true,
inference(cnf_transformation,[],[f238]) ).
thf(f519,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( setadjoinOr != $true )
| ( X3 = X4 )
| ( ( in @ X4 @ X5 )
= $true )
| ( ( in @ X4 @ ( setadjoin @ X3 @ X5 ) )
!= $true ) ),
inference(cnf_transformation,[],[f284]) ).
thf(f530,plain,
! [X1: $i] :
( ( notinemptyset != $true )
| ( ( in @ X1 @ emptyset )
!= $true ) ),
inference(cnf_transformation,[],[f293]) ).
thf(f903,definition,
( spl128_62
<=> ( notinemptyset = $true ) ),
introduced(definition,[new_symbols(definition,[spl128_62])],[avatar_definition]) ).
thf(f927,definition,
( spl128_67
<=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl128_67])],[avatar_definition]) ).
thf(f928,plain,
( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ~ spl128_67 ),
inference(avatar_component_clause,[],[f927]) ).
thf(f935,definition,
( spl128_69
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( X0 = X2 )
| ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
!= $true )
| ( ( in @ X0 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl128_69])],[avatar_definition]) ).
thf(f936,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
!= $true )
| ( X0 = X2 )
| ( ( in @ X0 @ X1 )
= $true ) )
| ~ spl128_69 ),
inference(avatar_component_clause,[],[f935]) ).
thf(f1078,definition,
( spl128_101
<=> ( setadjoinOr = $true ) ),
introduced(definition,[new_symbols(definition,[spl128_101])],[avatar_definition]) ).
thf(f1120,plain,
spl128_101,
inference(avatar_split_clause,[],[f431,f1078]) ).
thf(f1409,plain,
( spl128_69
| ~ spl128_101 ),
inference(avatar_split_clause,[],[f519,f1078,f935]) ).
thf(f1496,plain,
spl128_62,
inference(avatar_split_clause,[],[f430,f903]) ).
thf(f1517,definition,
( spl128_195
<=> ( sK40 = sK41 ) ),
introduced(definition,[new_symbols(definition,[spl128_195])],[avatar_definition]) ).
thf(f1519,plain,
( ( sK40 != sK41 )
| spl128_195 ),
inference(avatar_component_clause,[],[f1517]) ).
thf(f1520,plain,
~ spl128_195,
inference(avatar_split_clause,[],[f394,f1517]) ).
thf(f1558,plain,
( ~ spl128_62
| spl128_67 ),
inference(avatar_split_clause,[],[f530,f927,f903]) ).
thf(f1644,definition,
( spl128_222
<=> ( ( in @ sK40 @ ( setadjoin @ sK41 @ emptyset ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl128_222])],[avatar_definition]) ).
thf(f1646,plain,
( ( ( in @ sK40 @ ( setadjoin @ sK41 @ emptyset ) )
= $true )
| ~ spl128_222 ),
inference(avatar_component_clause,[],[f1644]) ).
thf(f1647,plain,
spl128_222,
inference(avatar_split_clause,[],[f395,f1644]) ).
thf(f1784,plain,
( ( $true != $true )
| ( ( in @ sK40 @ emptyset )
= $true )
| ( sK40 = sK41 )
| ~ spl128_69
| ~ spl128_222 ),
inference(superposition,[],[f936,f1646]) ).
thf(f1796,plain,
( ( ( in @ sK40 @ emptyset )
= $true )
| ( sK40 = sK41 )
| ~ spl128_69
| ~ spl128_222 ),
inference(trivial_inequality_removal,[],[f1784]) ).
thf(f1797,plain,
( ( sK40 = sK41 )
| ~ spl128_67
| ~ spl128_69
| ~ spl128_222 ),
inference(forward_subsumption_resolution,[],[f1796,f928]) ).
thf(f1798,plain,
( $false
| ~ spl128_67
| ~ spl128_69
| spl128_195
| ~ spl128_222 ),
inference(forward_subsumption_resolution,[],[f1797,f1519]) ).
thf(f1799,plain,
( ~ spl128_67
| ~ spl128_69
| spl128_195
| ~ spl128_222 ),
inference(avatar_contradiction_clause,[],[f1798]) ).
cnf(s83,plain,
spl128_101,
inference(sat_conversion,[],[f1120]) ).
cnf(s157,plain,
( spl128_69
| ~ spl128_101 ),
inference(sat_conversion,[],[f1409]) ).
cnf(s182,plain,
spl128_62,
inference(sat_conversion,[],[f1496]) ).
cnf(s187,plain,
~ spl128_195,
inference(sat_conversion,[],[f1520]) ).
cnf(s199,plain,
( ~ spl128_62
| spl128_67 ),
inference(sat_conversion,[],[f1558]) ).
cnf(s222,plain,
spl128_222,
inference(sat_conversion,[],[f1647]) ).
cnf(s236,plain,
( ~ spl128_67
| ~ spl128_69
| spl128_195
| ~ spl128_222 ),
inference(sat_conversion,[],[f1799]) ).
cnf(s237,plain,
spl128_67,
inference(rat,[],[s199,s182]) ).
cnf(s238,plain,
~ spl128_69,
inference(rat,[],[s236,s222,s187,s237]) ).
cnf(s244,plain,
~ spl128_101,
inference(rat,[],[s157,s238]) ).
cnf(s267,plain,
$false,
inference(rat,[],[s83,s244]) ).
thf(f1800,plain,
$false,
inference(avatar_sat_refutation,[],[s267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU527^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n011.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 13:48:16 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.24 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
% 0.24/0.33 % (123218)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.33 % (123237)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=4117338755:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.33 % (123244)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.33 % (123244)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
% 0.24/0.33 % (123239)lrs+10_16_si=on:nwc=1.5:random_seed=3772275541:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.33 % (123243)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3533165044:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.33 % (123240)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2824758249:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.33 % (123242)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3168634025:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.33 % (123241)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=475823983: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)
% 0.24/0.33 % (123244)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=4266820505:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.33 % (123240)Instruction limit reached!
% 0.24/0.33 % (123240)------------------------------
% 0.24/0.33 % (123240)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (123240)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (123240)CaDiCaL version: 2.1.3
% 0.24/0.33 % (123240)Termination reason: Instruction limit
% 0.24/0.33 % (123240)Termination phase: shuffling
% 0.24/0.33 % (123240)Time elapsed: 0.002 s
% 0.24/0.33 % (123240)Peak memory usage: 9 MB
% 0.24/0.33 % (123240)Instructions burned: 4 (million)
% 0.24/0.33 % (123239)Instruction limit reached!
% 0.24/0.33 % (123239)------------------------------
% 0.24/0.33 % (123239)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (123239)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (123239)CaDiCaL version: 2.1.3
% 0.24/0.33 % (123239)Termination reason: Instruction limit
% 0.24/0.33 % (123239)Termination phase: Saturation
% 0.24/0.33 % (123239)Time elapsed: 0.008 s
% 0.24/0.33 % (123239)Peak memory usage: 10 MB
% 0.24/0.33 % (123239)Instructions burned: 20 (million)
% 0.24/0.33 % (123242)Instruction limit reached!
% 0.24/0.33 % (123242)------------------------------
% 0.24/0.33 % (123242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (123242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (123242)CaDiCaL version: 2.1.3
% 0.24/0.33 % (123242)Termination reason: Instruction limit
% 0.24/0.33 % (123242)Termination phase: Property scanning
% 0.24/0.33 % (123242)Time elapsed: 0.012 s
% 0.24/0.33 % (123242)Peak memory usage: 11 MB
% 0.24/0.33 % (123242)Instructions burned: 25 (million)
% 0.24/0.33 % (123237)Instruction limit reached!
% 0.24/0.33 % (123237)------------------------------
% 0.24/0.33 % (123237)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (123237)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (123237)CaDiCaL version: 2.1.3
% 0.24/0.33 % (123237)Termination reason: Instruction limit
% 0.24/0.33 % (123237)Termination phase: Saturation
% 0.24/0.33 % (123237)Time elapsed: 0.025 s
% 0.24/0.33 % (123237)Peak memory usage: 13 MB
% 0.24/0.33 % (123237)Instructions burned: 90 (million)
% 0.24/0.33 % (123257)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=130212399:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.24/0.33 % (123257)Instruction limit reached!
% 0.24/0.33 % (123257)------------------------------
% 0.24/0.33 % (123257)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (123257)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (123257)CaDiCaL version: 2.1.3
% 0.24/0.33 % (123257)Termination reason: Instruction limit
% 0.24/0.33 % (123257)Termination phase: shuffling
% 0.24/0.33 % (123257)Time elapsed: 0.002 s
% 0.24/0.33 % (123257)Peak memory usage: 9 MB
% 0.24/0.33 % (123257)Instructions burned: 4 (million)
% 0.24/0.33 % (123266)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=807736633:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.24/0.33 % (123261)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=2132432930:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.24/0.33 % (123263)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.24/0.33 % (123266)Instruction limit reached!
% 0.24/0.33 % (123266)------------------------------
% 0.24/0.33 % (123266)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (123266)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (123266)CaDiCaL version: 2.1.3
% 0.24/0.33 % (123266)Termination reason: Instruction limit
% 0.24/0.33 % (123266)Termination phase: Property scanning
% 0.24/0.33 % (123266)Time elapsed: 0.003 s
% 0.24/0.33 % (123266)Peak memory usage: 10 MB
% 0.24/0.33 % (123266)Instructions burned: 13 (million)
% 0.24/0.33 % (123261)Instruction limit reached!
% 0.24/0.33 % (123261)------------------------------
% 0.24/0.33 % (123261)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (123261)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (123261)CaDiCaL version: 2.1.3
% 0.24/0.33 % (123261)Termination reason: Instruction limit
% 0.24/0.33 % (123261)Termination phase: Property scanning
% 0.24/0.33 % (123261)Time elapsed: 0.003 s
% 0.24/0.33 % (123261)Peak memory usage: 10 MB
% 0.24/0.33 % (123261)Instructions burned: 6 (million)
% 0.24/0.33 % (123263)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2097295116:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.24/0.33 % (123241) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-123218-123241"...
% 0.24/0.33 % (123241)...printing done.
% 0.24/0.33 % (123263)Instruction limit reached!
% 0.24/0.33 % (123263)------------------------------
% 0.24/0.33 % (123263)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (123263)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (123263)CaDiCaL version: 2.1.3
% 0.24/0.33 % (123263)Termination reason: Instruction limit
% 0.24/0.33 % (123263)Termination phase: Property scanning
% 0.24/0.33 % (123263)Time elapsed: 0.004 s
% 0.24/0.33 % (123263)Peak memory usage: 10 MB
% 0.24/0.33 % (123263)Instructions burned: 8 (million)
% 0.24/0.33 % (123243) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-123218-123243"...
% 0.24/0.33 % (123241)Refutation found. Thanks to Tanya!
% 0.24/0.33 % SZS status Theorem for theBenchmark
% 0.24/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.33 % (123241)------------------------------
% 0.24/0.33 % (123241)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.33 % (123241)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.33 % (123241)CaDiCaL version: 2.1.3
% 0.24/0.33 % (123241)Termination reason: Refutation
% 0.24/0.33 % (123241)Time elapsed: 0.034 s
% 0.24/0.33 % (123241)Peak memory usage: 14 MB
% 0.24/0.33 % (123241)Instructions burned: 64 (million)
% 0.24/0.33 % (123218)Success in time 0.082 s
% 0.24/0.33 % Vampire exiting
%------------------------------------------------------------------------------