%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU516^1 : 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 : n010.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 08:29:53 AM UTC 2026
% Result : Theorem 0.21s 0.29s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 12 unt; 0 typ; 1 def)
% Number of atoms : 892 ( 269 equ; 0 cnn)
% Maximal formula atoms : 35 ( 26 avg)
% Number of connectives : 612 ( 56 ~; 59 |; 156 &; 204 @)
% ( 5 <=>; 132 =>; 0 <=; 0 <~>)
% Maximal formula depth : 41 ( 13 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 124 ( 121 usr; 45 con; 0-4 aty)
% Number of variables : 66 ( 0 sgn 48 !; 18 ?; 66 :)
% 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_46,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vAND: $o > $o > $o ).
thf(func_def_48,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_51,type,
vIMP: $o > $o > $o ).
thf(func_def_52,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_53,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_54,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_55,type,
vNOT: $o > $o ).
thf(func_def_56,type,
sP0: $i > $i > $o ).
thf(func_def_57,type,
sP1: $i > $o ).
thf(func_def_58,type,
sP2: $i > $i > $o ).
thf(func_def_59,type,
sP3: $i > $i > $o ).
thf(func_def_60,type,
sP4: $o ).
thf(func_def_63,type,
sK7: $i > $o ).
thf(func_def_65,type,
sK9: $i > $i ).
thf(func_def_66,type,
sK10: $i > $i ).
thf(func_def_68,type,
sK12: ( $i > $o ) > $i ).
thf(func_def_69,type,
sK13: $i > $o ).
thf(func_def_70,type,
sK14: $i > $i ).
thf(func_def_75,type,
sK19: $i > $i > $i ).
thf(func_def_82,type,
sK26: $o ).
thf(func_def_90,type,
sK34: $i > $i > $i ).
thf(func_def_95,type,
sK39: $o ).
thf(func_def_97,type,
sK41: $i > $o ).
thf(func_def_100,type,
sK44: $i > $i > $i ).
thf(func_def_101,type,
sK45: $i > $i > $i ).
thf(func_def_102,type,
sK46: $i > $i > $i ).
thf(func_def_103,type,
sK47: $i > $i > $i ).
thf(func_def_104,type,
sK48: $i > $i > $i ).
thf(func_def_105,type,
sK49: $i > $i > $i > $i ).
thf(func_def_106,type,
sK50: $i > $i ).
thf(func_def_107,type,
sK51: $i > $i ).
thf(func_def_108,type,
sK52: $i > $i ).
thf(func_def_109,type,
sK53: $i > $i ).
thf(func_def_110,type,
sK54: $i > $i > $i ).
thf(func_def_111,type,
sK55: $i > $i > $i > $i ).
thf(func_def_112,type,
sK56: $i > $i > $i > $i ).
thf(func_def_113,type,
sK57: $i > $i > $i ).
thf(func_def_114,type,
sK58: $i > $i > $i ).
thf(func_def_116,type,
sK60: $i > $i ).
thf(func_def_117,type,
sK61: $i > $i ).
thf(func_def_118,type,
sK62: $i > $i ).
thf(func_def_119,type,
sK63: ( $i > $o ) > $i ).
thf(func_def_120,type,
sK64: $i > $o ).
thf(func_def_122,type,
sK66: $i > $o ).
thf(func_def_124,type,
sK68: $i > $o ).
thf(func_def_125,type,
sK69: $i > $o ).
thf(func_def_129,type,
sK73: $o ).
thf(func_def_131,type,
sK75: $i > $i > $o ).
thf(func_def_132,type,
sK76: $i > $i ).
thf(func_def_133,type,
sK77: $i > $i ).
thf(func_def_134,type,
sK78: ( $i > $i > $o ) > $i > $i ).
thf(func_def_135,type,
sK79: ( $i > $i > $o ) > $i > $i ).
thf(func_def_136,type,
sK80: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_139,type,
sK83: $i > $i ).
thf(func_def_140,type,
sK84: $i > $o ).
thf(func_def_146,type,
sK90: $i > $i > $i ).
thf(func_def_147,type,
sK91: $i > $i > $i ).
thf(func_def_148,type,
sK92: $i > $i > $i ).
thf(func_def_156,type,
sK100: $i > $i ).
thf(func_def_159,type,
sK103: $i > $i ).
thf(func_def_160,type,
sK104: $i > $i ).
thf(func_def_161,type,
sK105: ( $i > $o ) > $i > $i ).
thf(func_def_162,type,
sK106: $i > ( $i > $o ) > $i ).
thf(func_def_163,type,
sK107: $i > ( $i > $o ) > $i ).
thf(func_def_164,type,
sK108: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_165,type,
sK109: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_166,type,
sK110: $i > ( $i > $o ) > $i ).
thf(func_def_167,type,
sK111: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_168,type,
sK112: $i > $i ).
thf(f4,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
<=> ( ( in @ X2 @ X1 )
| ( X2 = X0 ) ) )
= setadjoinAx ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(f36,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
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ( ( X2 = X0 )
| ( in @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(f37,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
=> ! [X0: $i,X2: $i,X1: $i] :
( ( in @ X2 @ ( setadjoin @ X0 @ X1 ) )
=> ( ( X2 = X0 )
| ( in @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
thf(f46,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
<=> ( ( in @ X1 @ X0 )
| ( X1 = X2 ) ) )
= setadjoinAx ),
inference(rectify,[],[f4]) ).
thf(f47,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( ( in @ X1 @ X0 )
= $true )
| ( X1 = X2 ) )
<=> ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true ) )
<=> ( setadjoinAx = $true ) ),
inference(fool_elimination,[],[f46]) ).
thf(f55,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ X2 ) )
=> ( ( X0 = X1 )
| ( in @ X1 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f37]) ).
thf(f56,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 )
=> ! [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
=> ( ( ( in @ X1 @ X2 )
= $true )
| ( X0 = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f55]) ).
thf(f126,plain,
( ? [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
!= $true )
& ( X0 != X1 )
& ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) ) )
& ( 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,[],[f56]) ).
thf(f127,plain,
( ( powersetAx = $true )
& ( prop2setE = $true )
& ? [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ X2 ) ) )
& ( X0 != X1 )
& ( ( in @ X1 @ X2 )
!= $true ) )
& ( setadjoinE = $true )
& ( notinemptyset = $true )
& ( noeltsimpempty = $true )
& ( setadjoinIR = $true )
& ( foundationAx = $true )
& ( omegaSAx = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( setbeta = $true )
& ( emptysetE = $true )
& ( setunionAx = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrI = $true )
& ( setextAx = $true )
& ( dsetconstrEL = $true )
& ( emptyI = $true )
& ( dsetconstrER = $true )
& ( emptysetAx = $true )
& ( omega0Ax = $true )
& ( wellorderingAx = $true )
& ( nonemptyE1 = $true )
& ( emptyinunitempty = $true )
& ( exuE3e = $true )
& ( setadjoinAx = $true )
& ( setext = $true )
& ( nonemptyI1 = $true )
& ( replAx = $true )
& ( descrp = $true )
& ( exuE1 = $true )
& ( nonemptyI = $true ) ),
inference(flattening,[],[f126]) ).
thf(f186,plain,
( ( powersetAx = $true )
& ( prop2setE = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
& ( X1 != X2 )
& ( ( in @ X1 @ X0 )
!= $true ) )
& ( setadjoinE = $true )
& ( notinemptyset = $true )
& ( noeltsimpempty = $true )
& ( setadjoinIR = $true )
& ( foundationAx = $true )
& ( omegaSAx = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( setbeta = $true )
& ( emptysetE = $true )
& ( setunionAx = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrI = $true )
& ( setextAx = $true )
& ( dsetconstrEL = $true )
& ( emptyI = $true )
& ( dsetconstrER = $true )
& ( emptysetAx = $true )
& ( omega0Ax = $true )
& ( wellorderingAx = $true )
& ( nonemptyE1 = $true )
& ( emptyinunitempty = $true )
& ( exuE3e = $true )
& ( setadjoinAx = $true )
& ( setext = $true )
& ( nonemptyI1 = $true )
& ( replAx = $true )
& ( descrp = $true )
& ( exuE1 = $true )
& ( nonemptyI = $true ) ),
inference(rectify,[],[f127]) ).
thf(f187,plain,
( ( powersetAx = $true )
& ( prop2setE = $true )
& ( ( in @ sK32 @ ( setadjoin @ sK33 @ sK31 ) )
= $true )
& ( sK32 != sK33 )
& ( ( in @ sK32 @ sK31 )
!= $true )
& ( setadjoinE = $true )
& ( notinemptyset = $true )
& ( noeltsimpempty = $true )
& ( setadjoinIR = $true )
& ( foundationAx = $true )
& ( omegaSAx = $true )
& ( omegaIndAx = $true )
& ( setadjoinIL = $true )
& ( setbeta = $true )
& ( emptysetE = $true )
& ( setunionAx = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrI = $true )
& ( setextAx = $true )
& ( dsetconstrEL = $true )
& ( emptyI = $true )
& ( dsetconstrER = $true )
& ( emptysetAx = $true )
& ( omega0Ax = $true )
& ( wellorderingAx = $true )
& ( nonemptyE1 = $true )
& ( emptyinunitempty = $true )
& ( exuE3e = $true )
& ( setadjoinAx = $true )
& ( setext = $true )
& ( nonemptyI1 = $true )
& ( replAx = $true )
& ( descrp = $true )
& ( exuE1 = $true )
& ( nonemptyI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31,sK32,sK33]),skolemize(X0,sK31),skolemize(X1,sK32),skolemize(X2,sK33)],[f186]) ).
thf(f249,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( ( in @ X1 @ X0 )
= $true )
| ( X1 = X2 )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) )
& ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
| ( ( ( in @ X1 @ X0 )
!= $true )
& ( X1 != X2 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true )
| ( ( ( in @ X1 @ X0 )
!= $true )
& ( X1 != X2 ) ) )
& ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( X1 = X2 ) ) ) ) ),
inference(nnf_transformation,[],[f47]) ).
thf(f250,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( ( in @ X1 @ X0 )
= $true )
| ( X1 = X2 )
| ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true ) )
& ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
| ( ( ( in @ X1 @ X0 )
!= $true )
& ( X1 != X2 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
!= $true )
| ( ( ( in @ X1 @ X0 )
!= $true )
& ( X1 != X2 ) ) )
& ( ( ( in @ X1 @ ( setadjoin @ X2 @ X0 ) )
= $true )
| ( ( in @ X1 @ X0 )
= $true )
| ( X1 = X2 ) ) ) ) ),
inference(flattening,[],[f249]) ).
thf(f251,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
!= $true ) )
& ( ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( ( ( in @ X2 @ X0 )
!= $true )
& ( X1 != X2 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( ( in @ X5 @ ( setadjoin @ X4 @ X3 ) )
!= $true )
| ( ( ( in @ X5 @ X3 )
!= $true )
& ( X4 != X5 ) ) )
& ( ( ( in @ X5 @ ( setadjoin @ X4 @ X3 ) )
= $true )
| ( ( in @ X5 @ X3 )
= $true )
| ( X4 = X5 ) ) ) ) ),
inference(rectify,[],[f250]) ).
thf(f252,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
!= $true ) )
& ( ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
= $true )
| ( ( ( in @ X2 @ X0 )
!= $true )
& ( X1 != X2 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ( ( ( ( in @ sK97 @ ( setadjoin @ sK96 @ sK95 ) )
!= $true )
| ( ( ( in @ sK97 @ sK95 )
!= $true )
& ( sK96 != sK97 ) ) )
& ( ( ( in @ sK97 @ ( setadjoin @ sK96 @ sK95 ) )
= $true )
| ( ( in @ sK97 @ sK95 )
= $true )
| ( sK96 = sK97 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK95,sK96,sK97]),skolemize(X3,sK95),skolemize(X4,sK96),skolemize(X5,sK97)],[f251]) ).
thf(f309,plain,
setadjoinAx = $true,
inference(cnf_transformation,[],[f187]) ).
thf(f333,plain,
( ( in @ sK32 @ sK31 )
!= $true ),
inference(cnf_transformation,[],[f187]) ).
thf(f334,plain,
sK32 != sK33,
inference(cnf_transformation,[],[f187]) ).
thf(f335,plain,
( ( in @ sK32 @ ( setadjoin @ sK33 @ sK31 ) )
= $true ),
inference(cnf_transformation,[],[f187]) ).
thf(f443,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
!= $true )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[],[f252]) ).
thf(f563,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
!= $true )
| ( X1 = X2 )
| ( $true != $true )
| ( ( in @ X2 @ X0 )
= $true ) ),
inference(definition_unfolding,[],[f443,f309]) ).
thf(f638,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 )
| ( ( in @ X2 @ ( setadjoin @ X1 @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[],[f563]) ).
thf(f753,definition,
( spl113_6
<=> ! [X6: $i,X4: $i,X5: $i] :
( ( X4 = X5 )
| ( ( in @ X5 @ X6 )
= $true )
| ( ( in @ X5 @ ( setadjoin @ X4 @ X6 ) )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl113_6])],[avatar_definition]) ).
thf(f754,plain,
( ! [X6: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ ( setadjoin @ X4 @ X6 ) )
!= $true )
| ( ( in @ X5 @ X6 )
= $true )
| ( X4 = X5 ) )
| ~ spl113_6 ),
inference(avatar_component_clause,[],[f753]) ).
thf(f766,plain,
spl113_6,
inference(avatar_split_clause,[],[f638,f753]) ).
thf(f903,plain,
( ( sK32 = sK33 )
| ( ( in @ sK32 @ sK31 )
= $true )
| ( $true != $true )
| ~ spl113_6 ),
inference(constrained_superposition,[],[f754,f335]) ).
thf(f906,plain,
( ( sK32 = sK33 )
| ( ( in @ sK32 @ sK31 )
= $true )
| ~ spl113_6 ),
inference(trivial_inequality_removal,[],[f903]) ).
thf(f912,plain,
( ( ( in @ sK32 @ sK31 )
= $true )
| ~ spl113_6 ),
inference(forward_subsumption_resolution,[],[f906,f334]) ).
thf(f916,plain,
( $false
| ~ spl113_6 ),
inference(forward_subsumption_resolution,[],[f912,f333]) ).
thf(f917,plain,
~ spl113_6,
inference(avatar_contradiction_clause,[],[f916]) ).
cnf(s9,plain,
spl113_6,
inference(sat_conversion,[],[f766]) ).
cnf(s22,plain,
~ spl113_6,
inference(sat_conversion,[],[f917]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s9,s22]) ).
thf(f918,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU516^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:48:03 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.29 % (2880440)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.29 % (2880459)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=780840593:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.29 % (2880460)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.29 % (2880460)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.21/0.29 % (2880455)lrs+10_16_si=on:nwc=1.5:random_seed=3922541500:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.29 % (2880454)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=411726843:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.29 % (2880456)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=677657690:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.29 % (2880457)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=3493708007:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.29 % (2880458)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2909447590:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.29 % (2880460)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=3285881726:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.29 % (2880456)Instruction limit reached!
% 0.21/0.29 % (2880456)------------------------------
% 0.21/0.29 % (2880456)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2880456)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2880456)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2880456)Termination reason: Instruction limit
% 0.21/0.29 % (2880456)Termination phase: shuffling
% 0.21/0.29 % (2880456)Time elapsed: 0.002 s
% 0.21/0.29 % (2880456)Peak memory usage: 9 MB
% 0.21/0.29 % (2880456)Instructions burned: 4 (million)
% 0.21/0.29 % (2880459) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2880440-2880459"...
% 0.21/0.29 % (2880455)Instruction limit reached!
% 0.21/0.29 % (2880455)------------------------------
% 0.21/0.29 % (2880455)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.29 % (2880455)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.29 % (2880455)CaDiCaL version: 2.1.3
% 0.21/0.29 % (2880455)Termination reason: Instruction limit
% 0.21/0.29 % (2880455)Termination phase: Saturation
% 0.21/0.29 % (2880455)Time elapsed: 0.008 s
% 0.21/0.29 % (2880455)Peak memory usage: 11 MB
% 0.21/0.29 % (2880455)Instructions burned: 18 (million)
% 0.21/0.29 % (2880459)...printing done.
% 0.21/0.29 % (2880459)Refutation found. Thanks to Tanya!
% 0.21/0.29 % SZS status Theorem for theBenchmark
% 0.21/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (2880459)------------------------------
% 0.21/0.30 % (2880459)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (2880459)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (2880459)CaDiCaL version: 2.1.3
% 0.21/0.30 % (2880459)Termination reason: Refutation
% 0.21/0.30 % (2880459)Time elapsed: 0.017 s
% 0.21/0.30 % (2880459)Peak memory usage: 14 MB
% 0.21/0.30 % (2880459)Instructions burned: 61 (million)
% 0.21/0.30 % (2880440)Success in time 0.051 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------