%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU529^1 : 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 : n003.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 0.22s 0.31s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 24 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 1060 ( 315 equ; 0 cnn)
% Maximal formula atoms : 48 ( 44 avg)
% Number of connectives : 644 ( 42 ~; 40 |; 204 &; 170 @)
% ( 4 <=>; 184 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 20 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 145 ( 142 usr; 58 con; 0-4 aty)
% Number of variables : 54 ( 0 ^; 39 !; 15 ?; 54 :)
% 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_59,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_60,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_61,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_62,type,
vAND: $o > $o > $o ).
thf(func_def_63,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_64,type,
vIMP: $o > $o > $o ).
thf(func_def_65,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_66,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_67,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_68,type,
vNOT: $o > $o ).
thf(func_def_69,type,
sP0: $i > $i > $o ).
thf(func_def_70,type,
sP1: $i > $o ).
thf(func_def_71,type,
sP2: $i > $i > $o ).
thf(func_def_72,type,
sP3: $i > $i > $o ).
thf(func_def_73,type,
sP4: $o ).
thf(func_def_76,type,
sK7: $i > $o ).
thf(func_def_80,type,
sK11: $i > $o ).
thf(func_def_82,type,
sK13: $i > $i ).
thf(func_def_84,type,
sK15: $i > $i ).
thf(func_def_85,type,
sK16: $i > $i > $i ).
thf(func_def_86,type,
sK17: $i > $i > $i ).
thf(func_def_87,type,
sK18: $i > $i > $i ).
thf(func_def_88,type,
sK19: $i > $i > $i ).
thf(func_def_89,type,
sK20: $i > $i > $i ).
thf(func_def_90,type,
sK21: $i > $i > $i > $i ).
thf(func_def_91,type,
sK22: $i > $i ).
thf(func_def_92,type,
sK23: $i > $i ).
thf(func_def_93,type,
sK24: $i > $i ).
thf(func_def_94,type,
sK25: $i > $i ).
thf(func_def_95,type,
sK26: $i > $i > $i > $i ).
thf(func_def_96,type,
sK27: $i > $i > $i > $i ).
thf(func_def_97,type,
sK28: $i > $i > $i ).
thf(func_def_98,type,
sK29: $i > $i > $i ).
thf(func_def_99,type,
sK30: $i > $i > $i ).
thf(func_def_101,type,
sK32: $i > $i ).
thf(func_def_102,type,
sK33: $i > $i ).
thf(func_def_103,type,
sK34: $i > $i ).
thf(func_def_105,type,
sK36: $i > $i > $o ).
thf(func_def_106,type,
sK37: $i > $i ).
thf(func_def_107,type,
sK38: $i > $i ).
thf(func_def_108,type,
sK39: ( $i > $i > $o ) > $i > $i ).
thf(func_def_109,type,
sK40: ( $i > $i > $o ) > $i > $i ).
thf(func_def_110,type,
sK41: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_116,type,
sK47: $i > $i > $i ).
thf(func_def_124,type,
sK55: $i > $i > $i ).
thf(func_def_125,type,
sK56: $i > $i > $i ).
thf(func_def_127,type,
sK58: $i > $o ).
thf(func_def_128,type,
sK59: $i > $i ).
thf(func_def_129,type,
sK60: ( $i > $o ) > $i ).
thf(func_def_130,type,
sK61: $o ).
thf(func_def_133,type,
sK64: $i > $o ).
thf(func_def_139,type,
sK70: $i > $i > $i ).
thf(func_def_143,type,
sK74: ( $i > $o ) > $i ).
thf(func_def_144,type,
sK75: $i > $o ).
thf(func_def_151,type,
sK82: $i > $i > $i ).
thf(func_def_153,type,
sK84: $i > $o ).
thf(func_def_154,type,
sK85: $i > $i ).
thf(func_def_155,type,
sK86: ( $i > $o ) > $i ).
thf(func_def_161,type,
sK92: $i > $i > $i ).
thf(func_def_165,type,
sK96: $o ).
thf(func_def_168,type,
sK99: $i > $o ).
thf(func_def_174,type,
sK105: $o ).
thf(func_def_175,type,
sK106: $o > $i > $i > $i ).
thf(func_def_176,type,
sK107: $i > $i ).
thf(func_def_179,type,
sK110: $i > $i ).
thf(func_def_189,type,
sK120: $o ).
thf(func_def_191,type,
sK122: $i > $o ).
thf(func_def_194,type,
sK125: $i > $i ).
thf(func_def_196,type,
sK127: $i > $i ).
thf(func_def_198,type,
sK129: $i > $i ).
thf(func_def_200,type,
sK131: $i > $o ).
thf(func_def_203,type,
sK134: $i > ( $i > $o ) > $i ).
thf(func_def_204,type,
sK135: ( $i > $o ) > $i > $i ).
thf(func_def_205,type,
sK136: ( $i > $o ) > $i > $i ).
thf(func_def_206,type,
sK137: $i > $i ).
thf(func_def_207,type,
sK138: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_208,type,
sK139: ( $i > $o ) > $i > $i ).
thf(func_def_209,type,
sK140: ( $i > $o ) > $i > $i ).
thf(func_def_210,type,
sK141: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_211,type,
sK142: $i > ( $i > $o ) > $i ).
thf(func_def_212,type,
sK143: $i > ( $i > $i > $o ) > $i > $i ).
thf(f4,axiom,
( setadjoinAx
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( X2 = X0 )
| ( in @ X2 @ X1 ) )
<=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(f49,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
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(f50,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
=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
=> ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f49]) ).
thf(f119,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
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f50]) ).
thf(f120,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 )
=> ! [X0: $i,X1: $i] :
( ( X0 = X1 )
=> ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f119]) ).
thf(f127,plain,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( X0 = X1 )
| ( in @ X0 @ X2 ) )
<=> ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f128,plain,
( ( setadjoinAx = $true )
<=> ! [X0: $i,X2: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
<=> ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f127]) ).
thf(f177,plain,
( ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
& ( X0 = X1 ) )
& ( 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,[],[f120]) ).
thf(f178,plain,
( ( nonemptyI = $true )
& ( powersetI = $true )
& ( dsetconstrEL = $true )
& ( emptysetAx = $true )
& ( prop2setE = $true )
& ( setadjoinE = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( omegaIndAx = $true )
& ( setbeta = $true )
& ( emptyinunitempty = $true )
& ? [X1: $i,X0: $i] :
( ( ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) )
!= $true )
& ( X0 = X1 ) )
& ( setoftrueEq = $true )
& ( dsetconstrER = $true )
& ( setadjoinIL = $true )
& ( setunionAx = $true )
& ( emptyinPowerset = $true )
& ( noeltsimpempty = $true )
& ( emptysetimpfalse = $true )
& ( powersetE = $true )
& ( wellorderingAx = $true )
& ( nonemptyI1 = $true )
& ( setunionE = $true )
& ( subPowSU = $true )
& ( emptysetE = $true )
& ( replAx = $true )
& ( exuE1 = $true )
& ( setadjoinIR = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( exuE2 = $true )
& ( setextAx = $true )
& ( nonemptyImpWitness = $true )
& ( powersetAx = $true )
& ( notinsingleton = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( notinemptyset = $true )
& ( emptyInPowerset = $true )
& ( setadjoinOr = $true )
& ( setunionI = $true )
& ( uniqinunit = $true )
& ( emptyI = $true )
& ( omegaSAx = $true )
& ( nonemptyE1 = $true ) ),
inference(flattening,[],[f177]) ).
thf(f246,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true ) ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) ) ),
inference(nnf_transformation,[],[f128]) ).
thf(f247,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true ) ) ) )
& ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( ( in @ X0 @ ( setadjoin @ X1 @ X2 ) )
!= $true ) ) )
| ( setadjoinAx != $true ) ) ),
inference(flattening,[],[f246]) ).
thf(f248,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( ( in @ X0 @ X1 )
!= $true )
& ( X0 != X2 ) )
| ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
!= $true ) )
& ( ( ( in @ X0 @ X1 )
= $true )
| ( X0 = X2 )
| ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
= $true ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( ( ( in @ X3 @ X4 )
!= $true )
& ( X3 != X5 ) ) )
& ( ( ( in @ X3 @ X4 )
= $true )
| ( X3 = X5 )
| ( $true
!= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(rectify,[],[f247]) ).
thf(f249,plain,
( ( ( setadjoinAx = $true )
| ( ( ( ( $true
!= ( in @ sK42 @ sK43 ) )
& ( sK42 != sK44 ) )
| ( $true
!= ( in @ sK42 @ ( setadjoin @ sK44 @ sK43 ) ) ) )
& ( ( $true
= ( in @ sK42 @ sK43 ) )
| ( sK42 = sK44 )
| ( $true
= ( in @ sK42 @ ( setadjoin @ sK44 @ sK43 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( ( ( in @ X3 @ X4 )
!= $true )
& ( X3 != X5 ) ) )
& ( ( ( in @ X3 @ X4 )
= $true )
| ( X3 = X5 )
| ( $true
!= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK42,sK43,sK44]),skolemize(X0,sK42),skolemize(X1,sK43),skolemize(X2,sK44)],[f248]) ).
thf(f313,plain,
( ( nonemptyI = $true )
& ( powersetI = $true )
& ( dsetconstrEL = $true )
& ( emptysetAx = $true )
& ( prop2setE = $true )
& ( setadjoinE = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( omegaIndAx = $true )
& ( setbeta = $true )
& ( emptyinunitempty = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
!= $true )
& ( X0 = X1 ) )
& ( setoftrueEq = $true )
& ( dsetconstrER = $true )
& ( setadjoinIL = $true )
& ( setunionAx = $true )
& ( emptyinPowerset = $true )
& ( noeltsimpempty = $true )
& ( emptysetimpfalse = $true )
& ( powersetE = $true )
& ( wellorderingAx = $true )
& ( nonemptyI1 = $true )
& ( setunionE = $true )
& ( subPowSU = $true )
& ( emptysetE = $true )
& ( replAx = $true )
& ( exuE1 = $true )
& ( setadjoinIR = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( exuE2 = $true )
& ( setextAx = $true )
& ( nonemptyImpWitness = $true )
& ( powersetAx = $true )
& ( notinsingleton = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( notinemptyset = $true )
& ( emptyInPowerset = $true )
& ( setadjoinOr = $true )
& ( setunionI = $true )
& ( uniqinunit = $true )
& ( emptyI = $true )
& ( omegaSAx = $true )
& ( nonemptyE1 = $true ) ),
inference(rectify,[],[f178]) ).
thf(f314,plain,
( ( nonemptyI = $true )
& ( powersetI = $true )
& ( dsetconstrEL = $true )
& ( emptysetAx = $true )
& ( prop2setE = $true )
& ( setadjoinE = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( omegaIndAx = $true )
& ( setbeta = $true )
& ( emptyinunitempty = $true )
& ( ( in @ sK100 @ ( setadjoin @ sK101 @ emptyset ) )
!= $true )
& ( sK100 = sK101 )
& ( setoftrueEq = $true )
& ( dsetconstrER = $true )
& ( setadjoinIL = $true )
& ( setunionAx = $true )
& ( emptyinPowerset = $true )
& ( noeltsimpempty = $true )
& ( emptysetimpfalse = $true )
& ( powersetE = $true )
& ( wellorderingAx = $true )
& ( nonemptyI1 = $true )
& ( setunionE = $true )
& ( subPowSU = $true )
& ( emptysetE = $true )
& ( replAx = $true )
& ( exuE1 = $true )
& ( setadjoinIR = $true )
& ( setadjoinAx = $true )
& ( omega0Ax = $true )
& ( exuE2 = $true )
& ( setextAx = $true )
& ( nonemptyImpWitness = $true )
& ( powersetAx = $true )
& ( notinsingleton = $true )
& ( foundationAx = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( notinemptyset = $true )
& ( emptyInPowerset = $true )
& ( setadjoinOr = $true )
& ( setunionI = $true )
& ( uniqinunit = $true )
& ( emptyI = $true )
& ( omegaSAx = $true )
& ( nonemptyE1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK100,sK101]),skolemize(X0,sK100),skolemize(X1,sK101)],[f313]) ).
thf(f424,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( X3 != X5 )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[],[f249]) ).
thf(f526,plain,
setadjoinAx = $true,
inference(cnf_transformation,[],[f314]) ).
thf(f543,plain,
sK100 = sK101,
inference(cnf_transformation,[],[f314]) ).
thf(f544,plain,
( ( in @ sK100 @ ( setadjoin @ sK101 @ emptyset ) )
!= $true ),
inference(cnf_transformation,[],[f314]) ).
thf(f646,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X3 @ ( setadjoin @ X5 @ X4 ) ) )
| ( X3 != X5 )
| ( $true != $true ) ),
inference(definition_unfolding,[],[f424,f526]) ).
thf(f727,plain,
( ( in @ sK101 @ ( setadjoin @ sK101 @ emptyset ) )
!= $true ),
inference(definition_unfolding,[],[f544,f543]) ).
thf(f779,plain,
! [X4: $i,X5: $i] :
( ( $true != $true )
| ( ( in @ X5 @ ( setadjoin @ X5 @ X4 ) )
= $true ) ),
inference(equality_resolution,[],[f646]) ).
thf(f864,plain,
! [X4: $i,X5: $i] :
( ( in @ X5 @ ( setadjoin @ X5 @ X4 ) )
= $true ),
inference(trivial_inequality_removal,[],[f779]) ).
thf(f1030,plain,
$false,
inference(forward_subsumption_resolution,[],[f727,f864]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU529^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n003.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:50:14 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 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
% 0.22/0.31 % (2529344)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.31 % (2529361)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.31 % (2529361)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
% 0.22/0.31 % (2529361)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=3592115961:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.31 % (2529354)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3634194079:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.31 % (2529355)lrs+10_16_si=on:nwc=1.5:random_seed=3118436948:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.31 % (2529356)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1579892097:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.31 % (2529358)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3407338463:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.31 % (2529357)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=1143879715: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)
% 0.22/0.31 % (2529360)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4004930135:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.31 % (2529356)Instruction limit reached!
% 0.22/0.31 % (2529356)------------------------------
% 0.22/0.31 % (2529356)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (2529356)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (2529356)CaDiCaL version: 2.1.3
% 0.22/0.31 % (2529356)Termination reason: Instruction limit
% 0.22/0.31 % (2529356)Termination phase: shuffling
% 0.22/0.31 % (2529356)Time elapsed: 0.002 s
% 0.22/0.31 % (2529356)Peak memory usage: 9 MB
% 0.22/0.31 % (2529356)Instructions burned: 4 (million)
% 0.22/0.31 % (2529355)Instruction limit reached!
% 0.22/0.31 % (2529355)------------------------------
% 0.22/0.31 % (2529355)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (2529355)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (2529355)CaDiCaL version: 2.1.3
% 0.22/0.31 % (2529355)Termination reason: Instruction limit
% 0.22/0.31 % (2529355)Termination phase: Property scanning
% 0.22/0.31 % (2529355)Time elapsed: 0.008 s
% 0.22/0.31 % (2529355)Peak memory usage: 10 MB
% 0.22/0.31 % (2529355)Instructions burned: 19 (million)
% 0.22/0.31 % (2529358)Instruction limit reached!
% 0.22/0.31 % (2529358)------------------------------
% 0.22/0.31 % (2529358)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (2529358)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (2529358)CaDiCaL version: 2.1.3
% 0.22/0.31 % (2529358)Termination reason: Instruction limit
% 0.22/0.31 % (2529358)Termination phase: Property scanning
% 0.22/0.31 % (2529358)Time elapsed: 0.012 s
% 0.22/0.31 % (2529358)Peak memory usage: 11 MB
% 0.22/0.31 % (2529358)Instructions burned: 25 (million)
% 0.22/0.31 % (2529376)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3476972102:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.31 % (2529354) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2529344-2529354"...
% 0.22/0.31 % (2529360) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2529344-2529360"...
% 0.22/0.31 % (2529376)Instruction limit reached!
% 0.22/0.31 % (2529376)------------------------------
% 0.22/0.31 % (2529376)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (2529376)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (2529376)CaDiCaL version: 2.1.3
% 0.22/0.31 % (2529376)Termination reason: Instruction limit
% 0.22/0.31 % (2529376)Termination phase: shuffling
% 0.22/0.31 % (2529376)Time elapsed: 0.002 s
% 0.22/0.31 % (2529376)Peak memory usage: 9 MB
% 0.22/0.31 % (2529376)Instructions burned: 4 (million)
% 0.22/0.31 % (2529354)...printing done.
% 0.22/0.31 % (2529360)...printing done.
% 0.22/0.31 % (2529354)Refutation found. Thanks to Tanya!
% 0.22/0.31 % SZS status Theorem for theBenchmark
% 0.22/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.31 % (2529354)------------------------------
% 0.22/0.31 % (2529354)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.31 % (2529354)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.31 % (2529354)CaDiCaL version: 2.1.3
% 0.22/0.31 % (2529354)Termination reason: Refutation
% 0.22/0.31 % (2529354)Time elapsed: 0.025 s
% 0.22/0.31 % (2529354)Peak memory usage: 12 MB
% 0.22/0.31 % (2529354)Instructions burned: 49 (million)
% 0.22/0.31 % (2529344)Success in time 0.052 s
% 0.22/0.31 % Vampire exiting
%------------------------------------------------------------------------------