%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU522^1 : 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 : n004.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 08:32:17 AM UTC 2026
% Result : Theorem 1.08s 0.41s
% Output : Refutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 778 ( 203 equ; 0 cnn)
% Maximal formula atoms : 41 ( 25 avg)
% Number of connectives : 532 ( 8 ~; 9 |; 133 &; 203 @)
% ( 2 <=>; 160 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 97 ( 92 usr; 45 con; 0-4 aty)
% ( 8 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 65 ( 20 ^; 37 !; 8 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
vAND: $o > $o > $o ).
thf(func_def_52,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_54,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_55,type,
vIMP: $o > $o > $o ).
thf(func_def_56,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_57,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_58,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_59,type,
vIFF: $o > $o > $o ).
thf(func_def_60,type,
vNOT: $o > $o ).
thf(func_def_61,type,
vOR: $o > $o > $o ).
thf(func_def_62,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_63,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_69,type,
sK3: $i > $i > $i ).
thf(func_def_70,type,
sK4: $i > $i ).
thf(func_def_71,type,
sK5: $i > $i ).
thf(func_def_72,type,
sK6: $i > $i ).
thf(func_def_73,type,
sK7: $i > $i > $i ).
thf(func_def_74,type,
sK8: $i > $i > $i ).
thf(func_def_75,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_76,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_77,type,
sK11: ( $i > $o ) > $i ).
thf(func_def_78,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_79,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_80,type,
sK14: $i > $i ).
thf(func_def_81,type,
sK15: $i > $i > $i > $i ).
thf(func_def_82,type,
sK16: $i > $i > $i ).
thf(func_def_83,type,
sK17: $i > $i > $i ).
thf(func_def_84,type,
sK18: $i > $i > $i ).
thf(func_def_85,type,
sK19: $i > $i ).
thf(func_def_86,type,
sK20: $i > ( $i > $i > $o ) > $i ).
thf(func_def_87,type,
sK21: $i > ( $i > $i > $o ) > $i ).
thf(func_def_88,type,
sK22: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_89,type,
sK23: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_90,type,
sK24: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_91,type,
sK25: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_92,type,
sK26: $i > $i ).
thf(func_def_93,type,
sK27: $i > $i > $i ).
thf(func_def_94,type,
sK28: $i > $i > $i ).
thf(func_def_95,type,
sK29: $i > $i > $i ).
thf(f6,axiom,
( setunionAx
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
<=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( in @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(f42,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(f43,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
thf(f54,plain,
( setunionAx
= ( ! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X0 ) )
<=> ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( in @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f55,plain,
( setunionAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f54]) ).
thf(f121,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f43]) ).
thf(f122,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
= $true )
=> ( ( ( in @ X2 @ X0 )
= $true )
=> ( ( in @ X1 @ ( setunion @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f121]) ).
thf(f123,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setunion @ X0 ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X1 @ X2 )
= $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,[],[f122]) ).
thf(f124,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setunion @ X0 ) )
!= $true )
& ( ( in @ X2 @ X0 )
= $true )
& ( ( in @ X1 @ X2 )
= $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,[],[f123]) ).
thf(f125,plain,
( ( $true
!= ( in @ sK1 @ ( setunion @ sK0 ) ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK1 @ sK2 ) )
& ( 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)],[f124]) ).
thf(f131,plain,
( setunionAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f55]) ).
thf(f171,plain,
setunionAx = $true,
inference(cnf_transformation,[],[f125]) ).
thf(f205,plain,
( $true
= ( in @ sK1 @ sK2 ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f206,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f207,plain,
( $true
!= ( in @ sK1 @ ( setunion @ sK0 ) ) ),
inference(cnf_transformation,[],[f125]) ).
thf(f214,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f131,f171]) ).
thf(f631,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( setunion @ Y1 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ Y2 )
& ( in @ Y2 @ Y1 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f214]) ).
thf(f632,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setunion @ Y0 ) )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
& ( in @ Y1 @ Y0 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f631]) ).
thf(f633,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X1 @ ( setunion @ Y0 ) )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ Y1 )
& ( in @ Y1 @ Y0 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f632]) ).
thf(f634,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X1 @ ( setunion @ X2 ) )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
& ( in @ Y0 @ X2 ) ) ) ) ),
inference(beta-eta_normalization,[],[f633]) ).
thf(f635,plain,
! [X2: $i,X1: $i] :
( ( in @ X1 @ ( setunion @ X2 ) )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
& ( in @ Y0 @ X2 ) ) ) ),
inference(iff_proxy_clausification,[],[f634]) ).
thf(f636,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
& ( in @ Y0 @ X2 ) ) ) ) ),
inference(iff_proxy_clausification,[],[f635]) ).
thf(f642,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ^ [Y0: $i] :
( ( in @ X1 @ Y0 )
& ( in @ Y0 @ X2 ) )
@ X3 ) ) ),
inference(pi_proxy_clausification,[],[f636]) ).
thf(f643,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( $false
= ( ( in @ X1 @ X3 )
& ( in @ X3 @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f642]) ).
thf(f644,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setunion @ X2 ) ) )
| ( ( in @ X3 @ X2 )
= $false )
| ( $false
= ( in @ X1 @ X3 ) ) ),
inference(and_proxy_clausification,[],[f643]) ).
thf(f2494,plain,
! [X0: $i] :
( ( $true != $true )
| ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ sK1 @ X0 ) ) ),
inference(constrained_superposition,[],[f207,f644]) ).
thf(f2578,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( $false
= ( in @ sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2494]) ).
thf(f2671,plain,
( ( $false = $true )
| ( $false
= ( in @ sK1 @ sK2 ) ) ),
inference(constrained_superposition,[],[f206,f2578]) ).
thf(f2702,plain,
( $false
= ( in @ sK1 @ sK2 ) ),
inference(trivial_inequality_removal,[],[f2671]) ).
thf(f2789,plain,
$false = $true,
inference(constrained_superposition,[],[f205,f2702]) ).
thf(f2805,plain,
$false,
inference(trivial_inequality_removal,[],[f2789]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU522^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.18 % Computer : n004.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:47:52 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 Running first-order model finding
% 0.09/0.20 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
% 1.08/0.41 % (1312117)Will run a generic schedule for satisfiability detection.
% 1.08/0.41 % (1312122)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=923436038_2999 on theBenchmark for (2999ds/0Mi)
% 1.08/0.41 % (1312123)% WARNING: option uhcvi not known.
% 1.08/0.41 % Exception at run slice level
% 1.08/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.08/0.41 % (1312123)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3340475456:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 1.08/0.41 % (1312124)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1457973370:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 1.08/0.41 % (1312125)dis+10_1_sil=32000:sp=arity:random_seed=3962464694:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 1.08/0.41 % (1312123)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.41 % (1312127)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1287270187:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 1.08/0.41 % (1312130)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1053829900:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 1.08/0.41 % (1312123)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.08/0.41 % (1312128)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2279920459:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 1.08/0.41 % Exception at run slice level
% 1.08/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.08/0.41 % (1312126)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1944486509:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 1.08/0.41 % (1312126)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.41 % (1312138)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=1519242442:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 1.08/0.41 % (1312126)Instruction limit reached!
% 1.08/0.41 % (1312126)------------------------------
% 1.08/0.41 % (1312126)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.41 % (1312126)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.41 % (1312126)CaDiCaL version: 2.1.3
% 1.08/0.41 % (1312126)Termination reason: Instruction limit
% 1.08/0.41 % (1312126)Termination phase: Saturation
% 1.08/0.41 % (1312126)Time elapsed: 0.035 s
% 1.08/0.41 % (1312126)Peak memory usage: 13 MB
% 1.08/0.41 % (1312126)Instructions burned: 118 (million)
% 1.08/0.41 % (1312125)Instruction limit reached!
% 1.08/0.41 % (1312125)------------------------------
% 1.08/0.41 % (1312125)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.41 % (1312125)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.41 % (1312125)CaDiCaL version: 2.1.3
% 1.08/0.41 % (1312125)Termination reason: Instruction limit
% 1.08/0.41 % (1312125)Termination phase: Saturation
% 1.08/0.41 % (1312125)Time elapsed: 0.058 s
% 1.08/0.41 % (1312125)Peak memory usage: 13 MB
% 1.08/0.41 % (1312125)Instructions burned: 104 (million)
% 1.08/0.41 % (1312140)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=1728389564:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 1.08/0.41 % (1312140)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 1.08/0.41 % (1312140)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 1.08/0.41 % (1312127)Instruction limit reached!
% 1.08/0.41 % (1312127)------------------------------
% 1.08/0.41 % (1312127)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.41 % (1312127)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.41 % (1312127)CaDiCaL version: 2.1.3
% 1.08/0.41 % (1312127)Termination reason: Instruction limit
% 1.08/0.41 % (1312127)Termination phase: Saturation
% 1.08/0.41 % (1312127)Time elapsed: 0.066 s
% 1.08/0.41 % (1312127)Peak memory usage: 13 MB
% 1.08/0.41 % (1312127)Instructions burned: 131 (million)
% 1.08/0.41 % (1312142)ott-21_1_sil=16000:fs=off:random_seed=3878626493:i=180:av=off:fsr=off_2998 on theBenchmark for (2998ds/180Mi)
% 1.08/0.41 % (1312128)Instruction limit reached!
% 1.08/0.41 % (1312128)------------------------------
% 1.08/0.41 % (1312128)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.41 % (1312128)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.41 % (1312128)CaDiCaL version: 2.1.3
% 1.08/0.41 % (1312128)Termination reason: Instruction limit
% 1.08/0.41 % (1312128)Termination phase: Saturation
% 1.08/0.41 % (1312128)Time elapsed: 0.078 s
% 1.08/0.41 % (1312128)Peak memory usage: 13 MB
% 1.08/0.41 % (1312128)Instructions burned: 159 (million)
% 1.08/0.41 % (1312143)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=673617499:i=477:bd=all_2998 on theBenchmark for (2998ds/477Mi)
% 1.08/0.41 % (1312146)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3509257134:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 1.08/0.41 % Exception at run slice level
% 1.08/0.41 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 1.08/0.41 % (1312138)Instruction limit reached!
% 1.08/0.41 % (1312138)------------------------------
% 1.08/0.41 % (1312138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.41 % (1312138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.41 % (1312138)CaDiCaL version: 2.1.3
% 1.08/0.41 % (1312138)Termination reason: Instruction limit
% 1.08/0.41 % (1312138)Termination phase: Saturation
% 1.08/0.41 % (1312138)Time elapsed: 0.098 s
% 1.08/0.41 % (1312138)Peak memory usage: 12 MB
% 1.08/0.41 % (1312138)Instructions burned: 133 (million)
% 1.08/0.41 % (1312148)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=919880557:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 1.08/0.41 % (1312123) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1312117-1312123"...
% 1.08/0.41 % (1312123)...printing done.
% 1.08/0.41 % (1312123)Refutation found. Thanks to Tanya!
% 1.08/0.41 % SZS status Theorem for theBenchmark
% 1.08/0.41 % SZS output start Proof for theBenchmark
% See solution above
% 1.08/0.41 % (1312123)------------------------------
% 1.08/0.41 % (1312123)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.08/0.41 % (1312123)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.08/0.41 % (1312123)CaDiCaL version: 2.1.3
% 1.08/0.41 % (1312123)Termination reason: Refutation
% 1.08/0.41 % (1312123)Time elapsed: 0.146 s
% 1.08/0.41 % (1312123)Peak memory usage: 14 MB
% 1.08/0.41 % (1312123)Instructions burned: 302 (million)
% 1.08/0.41 % (1312117)Success in time 0.194 s
% 1.08/0.41 % Vampire exiting
%------------------------------------------------------------------------------