%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU535^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 08:29:58 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 890 ( 237 equ; 0 cnn)
% Maximal formula atoms : 53 ( 44 avg)
% Number of connectives : 447 ( 21 ~; 8 |; 159 &; 49 @)
% ( 2 <=>; 208 =>; 0 <=; 0 <~>)
% Maximal formula depth : 58 ( 21 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 6 >; 0 *; 0 +; 0 <<)
% Number of symbols : 150 ( 147 usr; 61 con; 0-4 aty)
% Number of variables : 24 ( 0 ^; 18 !; 6 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_64,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_67,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_68,type,
vNOT: $o > $o ).
thf(func_def_69,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_70,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_71,type,
vAND: $o > $o > $o ).
thf(func_def_72,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_73,type,
vIMP: $o > $o > $o ).
thf(func_def_74,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_75,type,
sP0: $o ).
thf(func_def_76,type,
sP1: $i > $i > $o ).
thf(func_def_77,type,
sP2: $i > $o ).
thf(func_def_78,type,
sP3: $i > $i > $o ).
thf(func_def_79,type,
sP4: $i > $i > $o ).
thf(func_def_82,type,
sK7: $i > $i ).
thf(func_def_83,type,
sK8: $i > $i ).
thf(func_def_86,type,
sK11: $i > $o ).
thf(func_def_95,type,
sK20: $i > $i > $o ).
thf(func_def_97,type,
sK22: $i > $i ).
thf(func_def_98,type,
sK23: $i > $i ).
thf(func_def_99,type,
sK24: $i > ( $i > $i > $o ) > $i ).
thf(func_def_100,type,
sK25: $i > ( $i > $i > $o ) > $i ).
thf(func_def_101,type,
sK26: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_102,type,
sK27: $o ).
thf(func_def_109,type,
sK34: $i > $i > $i ).
thf(func_def_112,type,
sK37: $i > $i ).
thf(func_def_113,type,
sK38: $i > $o ).
thf(func_def_120,type,
sK45: $i > $o ).
thf(func_def_123,type,
sK48: $i > $o ).
thf(func_def_124,type,
sK49: $i > $i ).
thf(func_def_125,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_126,type,
sK51: $i > $o ).
thf(func_def_127,type,
sK52: ( $i > $o ) > $i ).
thf(func_def_130,type,
sK55: $i > $o ).
thf(func_def_131,type,
sK56: $i > $o ).
thf(func_def_136,type,
sK61: $i > $i ).
thf(func_def_138,type,
sK63: $i > $i > $i ).
thf(func_def_139,type,
sK64: $i > $i > $i ).
thf(func_def_148,type,
sK73: $i > $i > $i ).
thf(func_def_151,type,
sK76: $i > $i > $i ).
thf(func_def_154,type,
sK79: $i > $o ).
thf(func_def_156,type,
sK81: $i > $i ).
thf(func_def_161,type,
sK86: $i > $i ).
thf(func_def_170,type,
sK95: $o ).
thf(func_def_173,type,
sK98: $o ).
thf(func_def_174,type,
sK99: $o > $i > $i > $i ).
thf(func_def_175,type,
sK100: $i > $i > $i ).
thf(func_def_176,type,
sK101: $i > $i > $i ).
thf(func_def_177,type,
sK102: $i > $i > $i ).
thf(func_def_178,type,
sK103: $i > $i > $i ).
thf(func_def_179,type,
sK104: $i > $i > $i ).
thf(func_def_180,type,
sK105: $i > $i > $i > $i ).
thf(func_def_181,type,
sK106: $i > $i ).
thf(func_def_182,type,
sK107: $i > $i ).
thf(func_def_183,type,
sK108: $i > $i ).
thf(func_def_184,type,
sK109: $i > $i ).
thf(func_def_185,type,
sK110: $i > $i > $i > $i ).
thf(func_def_186,type,
sK111: $i > $i > $i > $i ).
thf(func_def_187,type,
sK112: $i > $i > $i ).
thf(func_def_188,type,
sK113: $i > $i > $i ).
thf(func_def_189,type,
sK114: $i > $i > $i ).
thf(func_def_190,type,
sK115: $i > $i ).
thf(func_def_192,type,
sK117: $i > $i ).
thf(func_def_193,type,
sK118: $i > $i ).
thf(func_def_194,type,
sK119: ( $i > $o ) > $i ).
thf(func_def_195,type,
sK120: $i > $o ).
thf(func_def_196,type,
sK121: $i > $i ).
thf(func_def_197,type,
sK122: $i > $o ).
thf(func_def_208,type,
sK133: $i > $i ).
thf(func_def_211,type,
sK136: $i > $i > $i ).
thf(func_def_219,type,
sK144: $o ).
thf(func_def_221,type,
sK146: $i > $o ).
thf(func_def_223,type,
sK148: ( $i > $o ) > $i > $i ).
thf(func_def_224,type,
sK149: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_225,type,
sK150: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_226,type,
sK151: $i > ( $i > $o ) > $i ).
thf(func_def_227,type,
sK152: $i > ( $i > $o ) > $i ).
thf(func_def_228,type,
sK153: ( $i > $o ) > $i > $i ).
thf(func_def_229,type,
sK154: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_230,type,
sK155: $i > ( $i > $o ) > $i ).
thf(func_def_231,type,
sK156: ( $i > $o ) > $i > $i ).
thf(func_def_232,type,
sK157: $i > $i ).
thf(f22,axiom,
( notinemptyset
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(f55,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
=> ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(f56,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
=> ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
thf(f67,plain,
( notinemptyset
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
inference(rectify,[],[f22]) ).
thf(f68,plain,
( ( notinemptyset = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(fool_elimination,[],[f67]) ).
thf(f101,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
=> ! [X0: $i > $o,X1: $i] :
( ( in @ X1 @ emptyset )
=> ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f56]) ).
thf(f102,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 )
=> ! [X0: $i > $o,X1: $i] :
( ( ( in @ X1 @ emptyset )
= $true )
=> ( ( X0 @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f101]) ).
thf(f163,plain,
( ( notinemptyset = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(flattening,[],[f68]) ).
thf(f196,plain,
( ? [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
& ( ( in @ X1 @ emptyset )
= $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,[],[f102]) ).
thf(f197,plain,
( ( emptysetimpfalse = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( omegaIndAx = $true )
& ( nonemptyImpWitness = $true )
& ( powersetI = $true )
& ( dsetconstrER = $true )
& ( replAx = $true )
& ( setadjoinOr = $true )
& ( upairsetE = $true )
& ( upairsetIR = $true )
& ( exuE3e = $true )
& ( dsetconstrI = $true )
& ( setunionE = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( emptyI = $true )
& ( setunionAx = $true )
& ( setadjoinAx = $true )
& ( setbeta = $true )
& ( eqinunit = $true )
& ( setextAx = $true )
& ( emptysetAx = $true )
& ( setadjoinE = $true )
& ( omega0Ax = $true )
& ( emptyinunitempty = $true )
& ( exuE1 = $true )
& ( setadjoinIL = $true )
& ? [X0: $i > $o,X1: $i] :
( ( ( X0 @ X1 )
!= $true )
& ( ( in @ X1 @ emptyset )
= $true ) )
& ( powersetE = $true )
& ( prop2setE = $true )
& ( notinemptyset = $true )
& ( singletonsswitch = $true )
& ( emptyE1 = $true )
& ( exuE2 = $true )
& ( notinsingleton = $true )
& ( setadjoinIR = $true )
& ( subPowSU = $true )
& ( dsetconstrEL = $true )
& ( emptyinPowerset = $true )
& ( setoftrueEq = $true )
& ( uniqinunit = $true )
& ( noeltsimpempty = $true )
& ( nonemptyE1 = $true )
& ( setunionI = $true )
& ( emptysetE = $true )
& ( powersetAx = $true )
& ( foundationAx = $true )
& ( nonemptyI = $true )
& ( setext = $true )
& ( nonemptyI1 = $true )
& ( upairsetIL = $true ) ),
inference(flattening,[],[f196]) ).
thf(f237,plain,
( ( ( notinemptyset = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ) ),
inference(nnf_transformation,[],[f163]) ).
thf(f238,plain,
( ( ( notinemptyset = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ) ),
inference(rectify,[],[f237]) ).
thf(f239,plain,
( ( ( notinemptyset = $true )
| ( $true
= ( in @ sK9 @ emptyset ) ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(X0,sK9)],[f238]) ).
thf(f296,plain,
( ( emptysetimpfalse = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( omegaIndAx = $true )
& ( nonemptyImpWitness = $true )
& ( powersetI = $true )
& ( dsetconstrER = $true )
& ( replAx = $true )
& ( setadjoinOr = $true )
& ( upairsetE = $true )
& ( upairsetIR = $true )
& ( exuE3e = $true )
& ( dsetconstrI = $true )
& ( setunionE = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( emptyI = $true )
& ( setunionAx = $true )
& ( setadjoinAx = $true )
& ( setbeta = $true )
& ( eqinunit = $true )
& ( setextAx = $true )
& ( emptysetAx = $true )
& ( setadjoinE = $true )
& ( omega0Ax = $true )
& ( emptyinunitempty = $true )
& ( exuE1 = $true )
& ( setadjoinIL = $true )
& ( $true
!= ( sK56 @ sK57 ) )
& ( $true
= ( in @ sK57 @ emptyset ) )
& ( powersetE = $true )
& ( prop2setE = $true )
& ( notinemptyset = $true )
& ( singletonsswitch = $true )
& ( emptyE1 = $true )
& ( exuE2 = $true )
& ( notinsingleton = $true )
& ( setadjoinIR = $true )
& ( subPowSU = $true )
& ( dsetconstrEL = $true )
& ( emptyinPowerset = $true )
& ( setoftrueEq = $true )
& ( uniqinunit = $true )
& ( noeltsimpempty = $true )
& ( nonemptyE1 = $true )
& ( setunionI = $true )
& ( emptysetE = $true )
& ( powersetAx = $true )
& ( foundationAx = $true )
& ( nonemptyI = $true )
& ( setext = $true )
& ( nonemptyI1 = $true )
& ( upairsetIL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56,sK57]),skolemize(X0,sK56),skolemize(X1,sK57)],[f197]) ).
thf(f401,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
!= $true )
| ( notinemptyset != $true ) ),
inference(cnf_transformation,[],[f239]) ).
thf(f492,plain,
notinemptyset = $true,
inference(cnf_transformation,[],[f296]) ).
thf(f495,plain,
( $true
= ( in @ sK57 @ emptyset ) ),
inference(cnf_transformation,[],[f296]) ).
thf(f682,plain,
! [X1: $i] :
( ( $true != $true )
| ( ( in @ X1 @ emptyset )
!= $true ) ),
inference(definition_unfolding,[],[f401,f492]) ).
thf(f870,plain,
! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true ),
inference(trivial_inequality_removal,[],[f682]) ).
thf(f1068,plain,
$false,
inference(forward_subsumption_resolution,[],[f495,f870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU535^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.20 % Computer : n018.cluster.edu
% 0.08/0.20 % Model : x86_64 x86_64
% 0.08/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.20 % Memory : 8046.5625MB
% 0.08/0.20 % OS : Linux 6.8.0-71-generic
% 0.08/0.20 % CPULimit : 300
% 0.08/0.20 % WCLimit : 300
% 0.08/0.20 % DateTime : Tue Sep 29 13:50:56 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.23 Running higher-order theorem proving
% 0.08/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.31 % (98645)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (98654)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4243385158:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (98656)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (98656)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
% 0.21/0.31 % (98651)lrs+10_16_si=on:nwc=1.5:random_seed=964684873:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (98654)Instruction limit reached!
% 0.21/0.31 % (98654)------------------------------
% 0.21/0.31 % (98654)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (98654)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (98654)CaDiCaL version: 2.1.3
% 0.21/0.31 % (98654)Termination reason: Instruction limit
% 0.21/0.31 % (98654)Termination phase: Property scanning
% 0.21/0.31 % (98654)Time elapsed: 0.007 s
% 0.21/0.31 % (98654)Peak memory usage: 11 MB
% 0.21/0.31 % (98654)Instructions burned: 27 (million)
% 0.21/0.31 % (98650)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1981309971:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (98652)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3573907626:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (98653)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=2571060173: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)
% 0.21/0.31 % (98655)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3240931259:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (98656)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=3736791108:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (98652)Instruction limit reached!
% 0.21/0.31 % (98652)------------------------------
% 0.21/0.31 % (98652)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (98652)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (98652)CaDiCaL version: 2.1.3
% 0.21/0.31 % (98652)Termination reason: Instruction limit
% 0.21/0.31 % (98652)Termination phase: Property scanning
% 0.21/0.31 % (98652)Time elapsed: 0.003 s
% 0.21/0.31 % (98652)Peak memory usage: 10 MB
% 0.21/0.31 % (98652)Instructions burned: 7 (million)
% 0.21/0.31 % (98651)Instruction limit reached!
% 0.21/0.31 % (98651)------------------------------
% 0.21/0.31 % (98651)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (98651)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (98651)CaDiCaL version: 2.1.3
% 0.21/0.31 % (98651)Termination reason: Instruction limit
% 0.21/0.31 % (98651)Termination phase: Property scanning
% 0.21/0.31 % (98651)Time elapsed: 0.009 s
% 0.21/0.31 % (98651)Peak memory usage: 11 MB
% 0.21/0.31 % (98651)Instructions burned: 20 (million)
% 0.21/0.31 % (98662)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=366726114:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (98662)Instruction limit reached!
% 0.21/0.31 % (98662)------------------------------
% 0.21/0.31 % (98662)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (98662)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (98662)CaDiCaL version: 2.1.3
% 0.21/0.31 % (98662)Termination reason: Instruction limit
% 0.21/0.31 % (98662)Termination phase: Property scanning
% 0.21/0.31 % (98662)Time elapsed: 0.004 s
% 0.21/0.31 % (98662)Peak memory usage: 11 MB
% 0.21/0.31 % (98662)Instructions burned: 18 (million)
% 0.21/0.31 % (98655) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-98645-98655"...
% 0.21/0.31 % (98655)...printing done.
% 0.21/0.31 % (98665)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3287649158:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.31 % (98655)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (98655)------------------------------
% 0.21/0.31 % (98655)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (98655)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (98655)CaDiCaL version: 2.1.3
% 0.21/0.31 % (98655)Termination reason: Refutation
% 0.21/0.31 % (98655)Time elapsed: 0.022 s
% 0.21/0.31 % (98655)Peak memory usage: 12 MB
% 0.21/0.31 % (98655)Instructions burned: 44 (million)
% 0.21/0.31 % (98645)Success in time 0.059 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------