%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU526^1 : 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 : n007.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 08:32:18 AM UTC 2026
% Result : Theorem 0.09s 0.27s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 920 ( 261 equ; 0 cnn)
% Maximal formula atoms : 45 ( 27 avg)
% Number of connectives : 475 ( 19 ~; 6 |; 133 &; 84 @)
% ( 0 <=>; 222 =>; 0 <=; 0 <~>)
% Maximal formula depth : 50 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 103 ( 98 usr; 48 con; 0-4 aty)
% ( 3 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 46 ( 19 ^; 18 !; 9 ?; 46 :)
% 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,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
vAND: $o > $o > $o ).
thf(func_def_56,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_58,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_59,type,
vIMP: $o > $o > $o ).
thf(func_def_60,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_61,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_62,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_63,type,
vIFF: $o > $o > $o ).
thf(func_def_64,type,
vNOT: $o > $o ).
thf(func_def_65,type,
vOR: $o > $o > $o ).
thf(func_def_66,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_67,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_71,type,
sK1: ( $i > $o ) > $i ).
thf(func_def_72,type,
sK2: ( $i > $o ) > $i > $i ).
thf(func_def_73,type,
sK3: $o > $i > $i > $i ).
thf(func_def_74,type,
sK4: $i > $i > $i ).
thf(func_def_75,type,
sK5: $i > $i ).
thf(func_def_76,type,
sK6: $i > $i ).
thf(func_def_77,type,
sK7: $i > $i ).
thf(func_def_78,type,
sK8: $i > $i > $i ).
thf(func_def_79,type,
sK9: $i > $i > $i ).
thf(func_def_80,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_81,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_82,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_83,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_84,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_85,type,
sK15: $i > $i ).
thf(func_def_86,type,
sK16: $i > $i > $i > $i ).
thf(func_def_87,type,
sK17: $i > $i > $i ).
thf(func_def_88,type,
sK18: $i > $i > $i ).
thf(func_def_89,type,
sK19: $i > $i > $i ).
thf(func_def_90,type,
sK20: $i > $i ).
thf(func_def_91,type,
sK21: $i > ( $i > $i > $o ) > $i ).
thf(func_def_92,type,
sK22: $i > ( $i > $i > $o ) > $i ).
thf(func_def_93,type,
sK23: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_94,type,
sK24: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_95,type,
sK25: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_96,type,
sK26: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_97,type,
sK27: $i > $i ).
thf(func_def_98,type,
sK28: $i > $i > $i ).
thf(func_def_99,type,
sK29: $i > $i > $i ).
thf(func_def_100,type,
sK30: $i > $i > $i ).
thf(f28,axiom,
( nonempty
= ( ^ [X0: $i] : ( X0 != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(f29,axiom,
( nonemptyE1
= ( ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] : ( in @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(f46,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
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] :
( $true
& ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(f47,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
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] :
( $true
& ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f46]) ).
thf(f100,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(fool_elimination,[],[f28]) ).
thf(f101,plain,
( nonemptyE1
= ( ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] : ( in @ X1 @ X0 ) ) ) ),
inference(rectify,[],[f29]) ).
thf(f102,plain,
( nonemptyE1
= ( !! @ $i
@ ^ [Y0: $i] :
( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[],[f101]) ).
thf(f133,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
=> ! [X0: $i] :
( ( nonempty @ X0 )
=> ? [X1: $i] :
( $true
& ( in @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f47]) ).
thf(f134,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 )
=> ! [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
=> ? [X1: $i] :
( $true
& ( ( in @ X1 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f133]) ).
thf(f135,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 )
=> ! [X0: $i] :
( ( ( nonempty @ X0 )
= $true )
=> ? [X1: $i] :
( ( in @ X1 @ X0 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(true_and_false_elimination,[],[f134]) ).
thf(f136,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
& ( ( nonempty @ X0 )
= $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,[],[f135]) ).
thf(f137,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
!= $true )
& ( ( nonempty @ X0 )
= $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,[],[f136]) ).
thf(f138,plain,
( ! [X1: $i] :
( $true
!= ( in @ X1 @ sK0 ) )
& ( $true
= ( nonempty @ sK0 ) )
& ( 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]),skolemize(X0,sK0)],[f137]) ).
thf(f166,plain,
( nonempty
= ( ^ [Y0: $i] : ( emptyset != Y0 ) ) ),
inference(cnf_transformation,[],[f100]) ).
thf(f167,plain,
( nonemptyE1
= ( !! @ $i
@ ^ [Y0: $i] :
( ( nonempty @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f102]) ).
thf(f209,plain,
nonemptyE1 = $true,
inference(cnf_transformation,[],[f138]) ).
thf(f226,plain,
( $true
= ( nonempty @ sK0 ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f227,plain,
! [X1: $i] :
( $true
!= ( in @ X1 @ sK0 ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f255,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( emptyset != Y1 )
@ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) ) ) ),
inference(definition_unfolding,[],[f167,f209,f166]) ).
thf(f272,plain,
( $true
= ( ^ [Y0: $i] : ( emptyset != Y0 )
@ sK0 ) ),
inference(definition_unfolding,[],[f226,f166]) ).
thf(f273,plain,
( $true
= ( emptyset != sK0 ) ),
inference(beta-eta_normalization,[],[f272]) ).
thf(f274,plain,
( $false
= ( emptyset = sK0 ) ),
inference(not_proxy_clausification,[],[f273]) ).
thf(f275,plain,
emptyset != sK0,
inference(equality_proxy_clausification,[],[f274]) ).
thf(f407,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( ^ [Y1: $i] : ( emptyset != Y1 )
@ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] : ( in @ Y1 @ Y0 ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f255]) ).
thf(f408,plain,
! [X1: $i] :
( $true
= ( ( emptyset != X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f407]) ).
thf(f409,plain,
! [X1: $i] :
( ( $false
= ( emptyset != X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f408]) ).
thf(f410,plain,
! [X1: $i] :
( ( $true
= ( emptyset = X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f409]) ).
thf(f411,plain,
! [X1: $i] :
( ( emptyset = X1 )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] : ( in @ Y0 @ X1 ) ) ) ),
inference(equality_proxy_clausification,[],[f410]) ).
thf(f412,plain,
! [X1: $i] :
( ( emptyset = X1 )
| ( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ X1 )
@ ( sK5 @ X1 ) ) ) ),
inference(sigma_proxy_clausification,[],[f411]) ).
thf(f413,plain,
! [X1: $i] :
( ( $true
= ( in @ ( sK5 @ X1 ) @ X1 ) )
| ( emptyset = X1 ) ),
inference(beta-eta_normalization,[],[f412]) ).
thf(f823,plain,
( ( $true != $true )
| ( emptyset = sK0 ) ),
inference(constrained_superposition,[],[f227,f413]) ).
thf(f824,plain,
emptyset = sK0,
inference(trivial_inequality_removal,[],[f823]) ).
thf(f827,plain,
$false,
inference(forward_subsumption_resolution,[],[f824,f275]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU526^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n007.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:46:11 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.27 % (3385561)Will run a generic schedule for satisfiability detection.
% 0.09/0.27 % (3385568)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=685474749_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.27 % (3385569)% WARNING: option uhcvi not known.
% 0.09/0.27 % Exception at run slice level
% 0.09/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.27 % (3385569)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1163781622:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.27 % (3385570)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=952897791:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.27 % (3385572)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2488954704:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.27 % (3385571)dis+10_1_sil=32000:sp=arity:random_seed=3301464147:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.27 % (3385569)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.27 % (3385572)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.27 % (3385577)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3747275817:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.09/0.27 % (3385569)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.09/0.27 % Exception at run slice level
% 0.09/0.27 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.27 % (3385569) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3385561-3385569"...
% 0.09/0.27 % (3385574)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1095986125:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.27 % (3385572) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3385561-3385572"...
% 0.09/0.27 % (3385570) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3385561-3385570"...
% 0.09/0.27 % (3385569)...printing done.
% 0.09/0.27 % (3385573)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3148252951:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.27 % (3385569)Refutation found. Thanks to Tanya!
% 0.09/0.27 % SZS status Theorem for theBenchmark
% 0.09/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.27 % (3385569)------------------------------
% 0.09/0.27 % (3385569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.27 % (3385569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.27 % (3385569)CaDiCaL version: 2.1.3
% 0.09/0.27 % (3385569)Termination reason: Refutation
% 0.09/0.27 % (3385569)Time elapsed: 0.019 s
% 0.09/0.27 % (3385569)Peak memory usage: 12 MB
% 0.09/0.27 % (3385569)Instructions burned: 38 (million)
% 0.09/0.27 % (3385561)Success in time 0.052 s
% 0.09/0.27 % Vampire exiting
%------------------------------------------------------------------------------