%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU534^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 08:32:20 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 3
% Syntax : Number of formulae : 38 ( 22 unt; 0 typ; 0 def)
% Number of atoms : 1273 ( 373 equ; 0 cnn)
% Maximal formula atoms : 54 ( 33 avg)
% Number of connectives : 732 ( 21 ~; 11 |; 162 &; 190 @)
% ( 0 <=>; 333 =>; 0 <=; 0 <~>)
% Maximal formula depth : 59 ( 15 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 113 ( 109 usr; 56 con; 0-4 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 95 ( 39 ^; 44 !; 12 ?; 95 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_63,type,
vAND: $o > $o > $o ).
thf(func_def_64,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_65,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_66,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_67,type,
vIMP: $o > $o > $o ).
thf(func_def_68,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_69,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_70,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_71,type,
vIFF: $o > $o > $o ).
thf(func_def_72,type,
vNOT: $o > $o ).
thf(func_def_73,type,
vOR: $o > $o > $o ).
thf(func_def_74,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_75,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_79,type,
sK1: $i > $o ).
thf(func_def_81,type,
sK3: $i > $i ).
thf(func_def_82,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_83,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_84,type,
sK6: $o > $i > $i > $i ).
thf(func_def_85,type,
sK7: $i > $i > $i ).
thf(func_def_86,type,
sK8: $i > $i ).
thf(func_def_87,type,
sK9: $i > $i ).
thf(func_def_88,type,
sK10: $i > $i ).
thf(func_def_89,type,
sK11: $i > $i > $i ).
thf(func_def_90,type,
sK12: $i > $i > $i ).
thf(func_def_91,type,
sK13: ( $i > $o ) > $i ).
thf(func_def_92,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_93,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_94,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_95,type,
sK17: ( $i > $o ) > $i > $i ).
thf(func_def_96,type,
sK18: $i > $i ).
thf(func_def_97,type,
sK19: $i > $i > $i > $i ).
thf(func_def_98,type,
sK20: $i > $i > $i ).
thf(func_def_99,type,
sK21: $i > $i > $i ).
thf(func_def_100,type,
sK22: $i > $i > $i ).
thf(func_def_101,type,
sK23: $i > $i ).
thf(func_def_102,type,
sK24: $i > ( $i > $i > $o ) > $i ).
thf(func_def_103,type,
sK25: $i > ( $i > $i > $o ) > $i ).
thf(func_def_104,type,
sK26: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_105,type,
sK27: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_106,type,
sK28: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_107,type,
sK29: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_108,type,
sK30: $i > $i ).
thf(func_def_109,type,
sK31: $i > $i > $i ).
thf(func_def_110,type,
sK32: $i > $i > $i ).
thf(func_def_111,type,
sK33: $i > $i > $i ).
thf(f28,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(f30,axiom,
( nonemptyI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(f54,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
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ( ( ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(f55,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
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ( ( ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
= emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
thf(f108,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f111,plain,
( nonemptyI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X2 @ X0 )
=> ( ( X1 @ X2 )
=> ( nonempty
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
inference(rectify,[],[f30]) ).
thf(f112,plain,
( nonemptyI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( nonempty
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f111]) ).
thf(f157,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
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( X1 @ X2 )
& ( in @ X2 @ X0 ) )
=> ( ( ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) )
= emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f55]) ).
thf(f158,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 )
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f157]) ).
thf(f159,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 )
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( emptyset
!= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(true_and_false_elimination,[],[f158]) ).
thf(f160,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 )
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $true ) )
=> ( emptyset
!= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f159]) ).
thf(f161,plain,
( ? [X0: $i,X1: $i > $o] :
( ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $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,[],[f160]) ).
thf(f162,plain,
( ? [X0: $i,X1: $i > $o] :
( ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ? [X2: $i] :
( ( ( X1 @ X2 )
= $true )
& ( ( in @ X2 @ X0 )
= $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(flattening,[],[f161]) ).
thf(f163,plain,
( ( emptyset
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
& ( $true
= ( sK1 @ sK2 ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( 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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f162]) ).
thf(f191,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f108]) ).
thf(f193,plain,
( nonemptyI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( nonempty
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f112]) ).
thf(f243,plain,
nonemptyI = $true,
inference(cnf_transformation,[],[f163]) ).
thf(f267,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f163]) ).
thf(f268,plain,
( $true
= ( sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f163]) ).
thf(f269,plain,
( emptyset
= ( dsetconstr @ sK0
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f163]) ).
thf(f298,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( ^ [Y3: $i] : ( emptyset != Y3 )
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[],[f193,f243,f191]) ).
thf(f322,plain,
( emptyset
= ( dsetconstr @ sK0 @ sK1 ) ),
inference(beta-eta_normalization,[],[f269]) ).
thf(f496,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
=> ( ( Y1 @ Y0 )
=> ( ^ [Y3: $i] : ( emptyset != Y3 )
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f298]) ).
thf(f497,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( Y0 @ X1 )
=> ( emptyset
!= ( dsetconstr @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f496]) ).
thf(f498,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
=> ( ( Y0 @ X1 )
=> ( emptyset
!= ( dsetconstr @ Y1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f497]) ).
thf(f499,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( X2 @ X1 )
=> ( emptyset
!= ( dsetconstr @ Y0 @ X2 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f498]) ).
thf(f500,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
=> ( ( X2 @ X1 )
=> ( emptyset
!= ( dsetconstr @ Y0 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f499]) ).
thf(f501,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X1 @ X3 )
=> ( ( X2 @ X1 )
=> ( emptyset
!= ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f500]) ).
thf(f502,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X1 @ X3 )
= $false )
| ( $true
= ( ( X2 @ X1 )
=> ( emptyset
!= ( dsetconstr @ X3 @ X2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f501]) ).
thf(f503,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X1 @ X3 )
= $false )
| ( $false
= ( X2 @ X1 ) )
| ( $true
= ( emptyset
!= ( dsetconstr @ X3 @ X2 ) ) ) ),
inference(imp_proxy_clausification,[],[f502]) ).
thf(f504,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X1 @ X3 )
= $false )
| ( $false
= ( X2 @ X1 ) )
| ( $false
= ( emptyset
= ( dsetconstr @ X3 @ X2 ) ) ) ),
inference(not_proxy_clausification,[],[f503]) ).
thf(f505,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( emptyset
!= ( dsetconstr @ X3 @ X2 ) )
| ( $false
= ( X2 @ X1 ) )
| ( ( in @ X1 @ X3 )
= $false ) ),
inference(equality_proxy_clausification,[],[f504]) ).
thf(f1003,plain,
! [X0: $i] :
( ( emptyset != emptyset )
| ( $false
= ( sK1 @ X0 ) )
| ( $false
= ( in @ X0 @ sK0 ) ) ),
inference(constrained_superposition,[],[f505,f322]) ).
thf(f1007,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f1003]) ).
thf(f1020,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK2 ) ) ),
inference(constrained_superposition,[],[f267,f1007]) ).
thf(f1021,plain,
( $false
= ( sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f1020]) ).
thf(f1079,plain,
$false = $true,
inference(constrained_superposition,[],[f268,f1021]) ).
thf(f1080,plain,
$false,
inference(trivial_inequality_removal,[],[f1079]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU534^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.17 % Computer : n001.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Sep 29 13:54:36 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.21 Running first-order model finding
% 0.08/0.21 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.27 % (1274889)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (1274900)% WARNING: option uhcvi not known.
% 0.19/0.27 % (1274900)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1890305481:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.27 % (1274900)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (1274900)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.27 % (1274899)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4012757924_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.27 % (1274901)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1034432141:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (1274902)dis+10_1_sil=32000:sp=arity:random_seed=1731133726:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.27 % (1274903)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4197963732:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.19/0.27 % (1274905)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=638347390:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.19/0.27 % (1274904)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=701820921:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.19/0.27 % (1274903)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.27 % (1274900) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1274889-1274900"...
% 0.19/0.27 % Exception at run slice level
% 0.19/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.27 % (1274900)...printing done.
% 0.19/0.27 % (1274900)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (1274900)------------------------------
% 0.19/0.27 % (1274900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1274900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1274900)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1274900)Termination reason: Refutation
% 0.19/0.27 % (1274900)Time elapsed: 0.016 s
% 0.19/0.27 % (1274900)Peak memory usage: 13 MB
% 0.19/0.27 % (1274900)Instructions burned: 58 (million)
% 0.19/0.27 % (1274889)Success in time 0.054 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------