%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU512^1 : 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 : n017.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 08:29:52 AM UTC 2026
% Result : Theorem 0.21s 0.30s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 11 unt; 0 typ; 3 def)
% Number of atoms : 766 ( 222 equ; 0 cnn)
% Maximal formula atoms : 29 ( 20 avg)
% Number of connectives : 524 ( 51 ~; 48 |; 132 &; 174 @)
% ( 7 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 10 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 : 110 ( 107 usr; 41 con; 0-4 aty)
% Number of variables : 53 ( 0 sgn 38 !; 15 ?; 53 :)
% 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_42,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_43,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_44,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_45,type,
vAND: $o > $o > $o ).
thf(func_def_46,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_47,type,
vIMP: $o > $o > $o ).
thf(func_def_48,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_49,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_50,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_51,type,
vNOT: $o > $o ).
thf(func_def_52,type,
sP0: $i > $i > $o ).
thf(func_def_53,type,
sP1: $i > $o ).
thf(func_def_54,type,
sP2: $o ).
thf(func_def_59,type,
sK7: $i > $o ).
thf(func_def_60,type,
sK8: $i > $i ).
thf(func_def_62,type,
sK10: $i > $i ).
thf(func_def_65,type,
sK13: $i > $i ).
thf(func_def_68,type,
sK16: $i > $o ).
thf(func_def_70,type,
sK18: $i > $o ).
thf(func_def_71,type,
sK19: $i > $i ).
thf(func_def_75,type,
sK23: $i > $o ).
thf(func_def_77,type,
sK25: $i > $o ).
thf(func_def_80,type,
sK28: $i > $i > $i ).
thf(func_def_84,type,
sK32: $i > $i > $i ).
thf(func_def_88,type,
sK36: $i > $i ).
thf(func_def_89,type,
sK37: $i > $i ).
thf(func_def_90,type,
sK38: $i > $i ).
thf(func_def_91,type,
sK39: $i > $i ).
thf(func_def_92,type,
sK40: $i > $i ).
thf(func_def_93,type,
sK41: $i > $i > $i > $i ).
thf(func_def_94,type,
sK42: $i > $i ).
thf(func_def_95,type,
sK43: $i > $i ).
thf(func_def_96,type,
sK44: $i > $i ).
thf(func_def_97,type,
sK45: $i > $i ).
thf(func_def_98,type,
sK46: $i > $i > $i ).
thf(func_def_99,type,
sK47: $i > $i > $i > $i ).
thf(func_def_100,type,
sK48: $i > $i > $i > $i ).
thf(func_def_101,type,
sK49: $i > $i > $i > $i ).
thf(func_def_102,type,
sK50: $i > $i > $i ).
thf(func_def_103,type,
sK51: $i > $i > $i ).
thf(func_def_104,type,
sK52: $i > $i > $i ).
thf(func_def_105,type,
sK53: $i > $i > $i ).
thf(func_def_107,type,
sK55: $i > $i ).
thf(func_def_116,type,
sK64: $i > $i ).
thf(func_def_117,type,
sK65: $i > $i > $i ).
thf(func_def_121,type,
sK69: ( $i > $i > $o ) > $i > $i ).
thf(func_def_122,type,
sK70: ( $i > $i > $o ) > $i > $i ).
thf(func_def_123,type,
sK71: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_125,type,
sK73: $i > $i > $o ).
thf(func_def_126,type,
sK74: $i > $i ).
thf(func_def_127,type,
sK75: $i > $i ).
thf(func_def_130,type,
sK78: $o ).
thf(func_def_131,type,
sK79: $i > $i > $i ).
thf(func_def_132,type,
sK80: $i > $i > $i ).
thf(func_def_135,type,
sK83: ( $i > $o ) > $i ).
thf(func_def_136,type,
sK84: $i > $o ).
thf(func_def_137,type,
sK85: $i > $i ).
thf(func_def_138,type,
sK86: ( $i > $o ) > $i ).
thf(func_def_139,type,
sK87: $i > $o ).
thf(func_def_141,type,
sK89: $o ).
thf(func_def_144,type,
sK92: $i > $o ).
thf(f4,axiom,
( setadjoinAx
= ( ! [X2: $i,X0: $i,X1: $i] :
( ( ( X2 = X0 )
| ( in @ X2 @ X1 ) )
<=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(f32,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
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(f33,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
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
thf(f46,plain,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( X0 = X1 )
| ( in @ X0 @ X2 ) )
<=> ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f47,plain,
( ( setadjoinAx = $true )
<=> ! [X2: $i,X1: $i,X0: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
<=> ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f46]) ).
thf(f69,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
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f33]) ).
thf(f70,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 )
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f69]) ).
thf(f104,plain,
( ? [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $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,[],[f70]) ).
thf(f105,plain,
( ( omegaSAx = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrEL = $true )
& ( setadjoinAx = $true )
& ? [X1: $i,X0: $i] :
( ( in @ X0 @ ( setadjoin @ X0 @ X1 ) )
!= $true )
& ( foundationAx = $true )
& ( omegaIndAx = $true )
& ( exuE3e = $true )
& ( emptysetE = $true )
& ( notinemptyset = $true )
& ( setbeta = $true )
& ( omega0Ax = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( nonemptyI1 = $true )
& ( nonemptyE1 = $true )
& ( setext = $true )
& ( emptyI = $true )
& ( dsetconstrI = $true )
& ( setextAx = $true )
& ( emptysetimpfalse = $true )
& ( setunionAx = $true )
& ( wellorderingAx = $true )
& ( exuE1 = $true )
& ( emptysetAx = $true )
& ( descrp = $true )
& ( nonemptyI = $true ) ),
inference(flattening,[],[f104]) ).
thf(f137,plain,
( ( omegaSAx = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrEL = $true )
& ( setadjoinAx = $true )
& ? [X0: $i,X1: $i] :
( $true
!= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
& ( foundationAx = $true )
& ( omegaIndAx = $true )
& ( exuE3e = $true )
& ( emptysetE = $true )
& ( notinemptyset = $true )
& ( setbeta = $true )
& ( omega0Ax = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( nonemptyI1 = $true )
& ( nonemptyE1 = $true )
& ( setext = $true )
& ( emptyI = $true )
& ( dsetconstrI = $true )
& ( setextAx = $true )
& ( emptysetimpfalse = $true )
& ( setunionAx = $true )
& ( wellorderingAx = $true )
& ( exuE1 = $true )
& ( emptysetAx = $true )
& ( descrp = $true )
& ( nonemptyI = $true ) ),
inference(rectify,[],[f105]) ).
thf(f138,plain,
( ( omegaSAx = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrEL = $true )
& ( setadjoinAx = $true )
& ( $true
!= ( in @ sK4 @ ( setadjoin @ sK4 @ sK3 ) ) )
& ( foundationAx = $true )
& ( omegaIndAx = $true )
& ( exuE3e = $true )
& ( emptysetE = $true )
& ( notinemptyset = $true )
& ( setbeta = $true )
& ( omega0Ax = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( nonemptyI1 = $true )
& ( nonemptyE1 = $true )
& ( setext = $true )
& ( emptyI = $true )
& ( dsetconstrI = $true )
& ( setextAx = $true )
& ( emptysetimpfalse = $true )
& ( setunionAx = $true )
& ( wellorderingAx = $true )
& ( exuE1 = $true )
& ( emptysetAx = $true )
& ( descrp = $true )
& ( nonemptyI = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f137]) ).
thf(f194,plain,
( ( ( setadjoinAx = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(nnf_transformation,[],[f47]) ).
thf(f195,plain,
( ( ( setadjoinAx = $true )
| ? [X2: $i,X1: $i,X0: $i] :
( ( ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) ) )
& ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) ) )
& ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(flattening,[],[f194]) ).
thf(f196,plain,
( ( ( setadjoinAx = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( ( ( ( in @ X2 @ X0 )
!= $true )
& ( X1 != X2 ) )
| ( $true
!= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) )
& ( ( ( in @ X2 @ X0 )
= $true )
| ( X1 = X2 )
| ( $true
= ( in @ X2 @ ( setadjoin @ X1 @ X0 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( $true
= ( in @ X5 @ ( setadjoin @ X4 @ X3 ) ) )
| ( ( $true
!= ( in @ X5 @ X3 ) )
& ( X4 != X5 ) ) )
& ( ( $true
= ( in @ X5 @ X3 ) )
| ( X4 = X5 )
| ( $true
!= ( in @ X5 @ ( setadjoin @ X4 @ X3 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(rectify,[],[f195]) ).
thf(f197,plain,
( ( ( setadjoinAx = $true )
| ( ( ( ( $true
!= ( in @ sK61 @ sK59 ) )
& ( sK61 != sK60 ) )
| ( $true
!= ( in @ sK61 @ ( setadjoin @ sK60 @ sK59 ) ) ) )
& ( ( $true
= ( in @ sK61 @ sK59 ) )
| ( sK61 = sK60 )
| ( $true
= ( in @ sK61 @ ( setadjoin @ sK60 @ sK59 ) ) ) ) ) )
& ( ! [X3: $i,X4: $i,X5: $i] :
( ( ( $true
= ( in @ X5 @ ( setadjoin @ X4 @ X3 ) ) )
| ( ( $true
!= ( in @ X5 @ X3 ) )
& ( X4 != X5 ) ) )
& ( ( $true
= ( in @ X5 @ X3 ) )
| ( X4 = X5 )
| ( $true
!= ( in @ X5 @ ( setadjoin @ X4 @ X3 ) ) ) ) )
| ( setadjoinAx != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK59,sK60,sK61]),skolemize(X0,sK59),skolemize(X1,sK60),skolemize(X2,sK61)],[f196]) ).
thf(f253,plain,
( $true
!= ( in @ sK4 @ ( setadjoin @ sK4 @ sK3 ) ) ),
inference(cnf_transformation,[],[f138]) ).
thf(f254,plain,
setadjoinAx = $true,
inference(cnf_transformation,[],[f138]) ).
thf(f354,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( $true
= ( in @ X5 @ ( setadjoin @ X4 @ X3 ) ) )
| ( X4 != X5 )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[],[f197]) ).
thf(f411,plain,
! [X3: $i,X5: $i] :
( ( setadjoinAx != $true )
| ( $true
= ( in @ X5 @ ( setadjoin @ X5 @ X3 ) ) ) ),
inference(equality_resolution,[],[f354]) ).
thf(f557,definition,
( spl93_25
<=> ! [X5: $i,X3: $i] :
( $true
= ( in @ X5 @ ( setadjoin @ X5 @ X3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl93_25])],[avatar_definition]) ).
thf(f558,plain,
( ! [X3: $i,X5: $i] :
( $true
= ( in @ X5 @ ( setadjoin @ X5 @ X3 ) ) )
| ~ spl93_25 ),
inference(avatar_component_clause,[],[f557]) ).
thf(f560,definition,
( spl93_26
<=> ( setadjoinAx = $true ) ),
introduced(definition,[new_symbols(definition,[spl93_26])],[avatar_definition]) ).
thf(f563,plain,
( spl93_25
| ~ spl93_26 ),
inference(avatar_split_clause,[],[f411,f560,f557]) ).
thf(f605,plain,
spl93_26,
inference(avatar_split_clause,[],[f254,f560]) ).
thf(f1162,definition,
( spl93_159
<=> ( $true
= ( in @ sK4 @ ( setadjoin @ sK4 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl93_159])],[avatar_definition]) ).
thf(f1164,plain,
( ( $true
!= ( in @ sK4 @ ( setadjoin @ sK4 @ sK3 ) ) )
| spl93_159 ),
inference(avatar_component_clause,[],[f1162]) ).
thf(f1165,plain,
~ spl93_159,
inference(avatar_split_clause,[],[f253,f1162]) ).
thf(f1246,plain,
( ( $true != $true )
| ~ spl93_25
| spl93_159 ),
inference(superposition,[],[f1164,f558]) ).
thf(f1249,plain,
( $false
| ~ spl93_25
| spl93_159 ),
inference(trivial_inequality_removal,[],[f1246]) ).
thf(f1250,plain,
( ~ spl93_25
| spl93_159 ),
inference(avatar_contradiction_clause,[],[f1249]) ).
cnf(s17,plain,
( spl93_25
| ~ spl93_26 ),
inference(sat_conversion,[],[f563]) ).
cnf(s25,plain,
spl93_26,
inference(sat_conversion,[],[f605]) ).
cnf(s155,plain,
~ spl93_159,
inference(sat_conversion,[],[f1165]) ).
cnf(s167,plain,
( ~ spl93_25
| spl93_159 ),
inference(sat_conversion,[],[f1250]) ).
cnf(s169,plain,
~ spl93_25,
inference(rat,[],[s167,s155]) ).
cnf(s213,plain,
$false,
inference(rat,[],[s17,s25,s169]) ).
thf(f1251,plain,
$false,
inference(avatar_sat_refutation,[],[s213]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU512^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n017.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 13:42:52 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.30 % (357957)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.30 % (357965)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=3167520326: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)
% 0.21/0.30 % (357968)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.30 % (357968)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
% 0.21/0.30 % (357962)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2140634342:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.30 % (357963)lrs+10_16_si=on:nwc=1.5:random_seed=4198758999:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.30 % (357964)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2253922948:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.30 % (357966)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1131239597:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.30 % (357967)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1695013651:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.30 % (357968)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=825380105:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.30 % (357964)Instruction limit reached!
% 0.21/0.30 % (357964)------------------------------
% 0.21/0.30 % (357964)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (357964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (357964)CaDiCaL version: 2.1.3
% 0.21/0.30 % (357964)Termination reason: Instruction limit
% 0.21/0.30 % (357964)Termination phase: Property scanning
% 0.21/0.30 % (357964)Time elapsed: 0.003 s
% 0.21/0.30 % (357964)Peak memory usage: 10 MB
% 0.21/0.30 % (357964)Instructions burned: 5 (million)
% 0.21/0.30 % (357965) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-357957-357965"...
% 0.21/0.30 % (357965)...printing done.
% 0.21/0.30 % (357965)Refutation found. Thanks to Tanya!
% 0.21/0.30 % SZS status Theorem for theBenchmark
% 0.21/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.30 % (357965)------------------------------
% 0.21/0.30 % (357965)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.30 % (357965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.30 % (357965)CaDiCaL version: 2.1.3
% 0.21/0.30 % (357965)Termination reason: Refutation
% 0.21/0.30 % (357965)Time elapsed: 0.013 s
% 0.21/0.30 % (357965)Peak memory usage: 13 MB
% 0.21/0.30 % (357965)Instructions burned: 45 (million)
% 0.21/0.30 % (357957)Success in time 0.054 s
% 0.21/0.30 % Vampire exiting
%------------------------------------------------------------------------------