%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU533^1 : 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 : n014.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 08:29:57 AM UTC 2026
% Result : Theorem 0.23s 0.35s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 1200 ( 336 equ; 0 cnn)
% Maximal formula atoms : 51 ( 27 avg)
% Number of connectives : 767 ( 64 ~; 61 |; 216 &; 222 @)
% ( 8 <=>; 196 =>; 0 <=; 0 <~>)
% Maximal formula depth : 57 ( 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 : 141 ( 138 usr; 66 con; 0-4 aty)
% Number of variables : 62 ( 0 sgn 47 !; 15 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_63,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_64,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_65,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_66,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_67,type,
vAND: $o > $o > $o ).
thf(func_def_68,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_69,type,
vIMP: $o > $o > $o ).
thf(func_def_70,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_71,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_72,type,
vNOT: $o > $o ).
thf(func_def_73,type,
sP0: $i > $i > $o ).
thf(func_def_74,type,
sP1: $i > $o ).
thf(func_def_75,type,
sP2: $o ).
thf(func_def_76,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_77,type,
sK4: $i > $o ).
thf(func_def_84,type,
sK11: $o ).
thf(func_def_88,type,
sK15: $i > $i ).
thf(func_def_94,type,
sK21: $i > $i ).
thf(func_def_97,type,
sK24: $i > $i ).
thf(func_def_99,type,
sK26: $i > $o ).
thf(func_def_107,type,
sK34: $o ).
thf(func_def_108,type,
sK35: $i > $o ).
thf(func_def_109,type,
sK36: ( $i > $o ) > $i ).
thf(func_def_110,type,
sK37: $i > $o ).
thf(func_def_111,type,
sK38: $i > $i ).
thf(func_def_115,type,
sK42: $i > $i ).
thf(func_def_116,type,
sK43: $i > $o ).
thf(func_def_119,type,
sK46: $i > $i ).
thf(func_def_121,type,
sK48: $i > $i ).
thf(func_def_125,type,
sK52: ( $i > $o ) > $i ).
thf(func_def_126,type,
sK53: $i > $o ).
thf(func_def_127,type,
sK54: $i > $i ).
thf(func_def_128,type,
sK55: $i > $i > $o ).
thf(func_def_130,type,
sK57: $i > $i ).
thf(func_def_131,type,
sK58: $i > $i ).
thf(func_def_132,type,
sK59: $i > ( $i > $i > $o ) > $i ).
thf(func_def_133,type,
sK60: $i > ( $i > $i > $o ) > $i ).
thf(func_def_134,type,
sK61: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_135,type,
sK62: $i > $i > $i ).
thf(func_def_136,type,
sK63: $i > $i > $i ).
thf(func_def_146,type,
sK73: $i > $o ).
thf(func_def_153,type,
sK80: $i > $o ).
thf(func_def_156,type,
sK83: $i > $i ).
thf(func_def_157,type,
sK84: $o ).
thf(func_def_161,type,
sK88: $i > $o ).
thf(func_def_167,type,
sK94: $i > $i > $i ).
thf(func_def_170,type,
sK97: $o > $i > $i > $i ).
thf(func_def_173,type,
sK100: $o ).
thf(func_def_178,type,
sK105: $i > $i > $i ).
thf(func_def_181,type,
sK108: $i > $i > $i ).
thf(func_def_185,type,
sK112: $i > $i > $i ).
thf(func_def_193,type,
sK120: $i > $i ).
thf(func_def_194,type,
sK121: $i > $i ).
thf(func_def_195,type,
sK122: $i > $i ).
thf(func_def_196,type,
sK123: $i > $i ).
thf(func_def_197,type,
sK124: $i > $i ).
thf(func_def_198,type,
sK125: $i > $i > $i > $i ).
thf(func_def_199,type,
sK126: $i > $i ).
thf(func_def_200,type,
sK127: $i > $i ).
thf(func_def_201,type,
sK128: $i > $i ).
thf(func_def_202,type,
sK129: $i > $i ).
thf(func_def_203,type,
sK130: $i > $i > $i ).
thf(func_def_204,type,
sK131: $i > $i > $i > $i ).
thf(func_def_205,type,
sK132: $i > $i > $i > $i ).
thf(func_def_206,type,
sK133: $i > $i > $i > $i ).
thf(func_def_207,type,
sK134: $i > $i > $i ).
thf(func_def_208,type,
sK135: $i > $i > $i ).
thf(func_def_209,type,
sK136: $i > $i > $i ).
thf(func_def_210,type,
sK137: $i > $i > $i ).
thf(f4,axiom,
( setadjoinAx
= ( ! [X2: $i,X1: $i,X0: $i] :
( ( ( X2 = X0 )
| ( in @ X2 @ X1 ) )
<=> ( in @ X2 @ ( setadjoin @ X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(f53,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ! [X1: $i,X0: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(f54,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ! [X1: $i,X0: $i] : ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
thf(f135,plain,
( setadjoinAx
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( X2 = X0 )
| ( in @ X0 @ X1 ) )
<=> ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f136,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( ( $true
= ( in @ X0 @ X1 ) )
| ( X0 = X2 ) )
<=> ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) )
<=> ( setadjoinAx = $true ) ),
inference(fool_elimination,[],[f135]) ).
thf(f154,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ! [X0: $i,X1: $i] : ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f54]) ).
thf(f155,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f154]) ).
thf(f212,plain,
( ? [X1: $i,X0: $i] :
( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f155]) ).
thf(f213,plain,
( ( upairsetIL = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( setextAx = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrER = $true )
& ( subPowSU = $true )
& ( emptysetE = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrI = $true )
& ( eqinunit = $true )
& ( emptysetimpfalse = $true )
& ( exuE2 = $true )
& ( powersetAx = $true )
& ( setadjoinE = $true )
& ( singletonsswitch = $true )
& ? [X1: $i,X0: $i] :
( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) )
& ( prop2setE = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( setoftrueEq = $true )
& ( nonemptyImpWitness = $true )
& ( setunionAx = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( setunionE = $true )
& ( foundationAx = $true )
& ( emptyinunitempty = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( notinemptyset = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( exuE3e = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( emptyinPowerset = $true )
& ( setadjoinIL = $true )
& ( setadjoinAx = $true )
& ( emptyInPowerset = $true )
& ( uniqinunit = $true )
& ( upairsetE = $true )
& ( replAx = $true )
& ( emptyI = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( wellorderingAx = $true )
& ( notinsingleton = $true ) ),
inference(flattening,[],[f212]) ).
thf(f240,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( $true
= ( in @ X0 @ X1 ) )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) )
& ( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( $true
!= ( in @ X0 @ X1 ) )
& ( X0 != X2 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( $true
!= ( in @ X0 @ X1 ) )
& ( X0 != X2 ) ) )
& ( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( X0 = X2 ) ) ) ) ),
inference(nnf_transformation,[],[f136]) ).
thf(f241,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( ( $true
= ( in @ X0 @ X1 ) )
| ( X0 = X2 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) )
& ( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( $true
!= ( in @ X0 @ X1 ) )
& ( X0 != X2 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( ( $true
!= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( ( $true
!= ( in @ X0 @ X1 ) )
& ( X0 != X2 ) ) )
& ( ( $true
= ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) )
| ( $true
= ( in @ X0 @ X1 ) )
| ( X0 = X2 ) ) ) ) ),
inference(flattening,[],[f240]) ).
thf(f242,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) )
& ( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( $true
!= ( in @ X3 @ ( setadjoin @ X4 @ X5 ) ) )
| ( ( ( in @ X3 @ X5 )
!= $true )
& ( X3 != X4 ) ) )
& ( ( $true
= ( in @ X3 @ ( setadjoin @ X4 @ X5 ) ) )
| ( ( in @ X3 @ X5 )
= $true )
| ( X3 = X4 ) ) ) ) ),
inference(rectify,[],[f241]) ).
thf(f243,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( $true
= ( in @ X0 @ X2 ) )
| ( X0 = X1 )
| ( $true
!= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) ) )
& ( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( ( $true
!= ( in @ X0 @ X2 ) )
& ( X0 != X1 ) ) ) )
| ( setadjoinAx != $true ) )
& ( ( setadjoinAx = $true )
| ( ( ( $true
!= ( in @ sK16 @ ( setadjoin @ sK17 @ sK18 ) ) )
| ( ( $true
!= ( in @ sK16 @ sK18 ) )
& ( sK16 != sK17 ) ) )
& ( ( $true
= ( in @ sK16 @ ( setadjoin @ sK17 @ sK18 ) ) )
| ( $true
= ( in @ sK16 @ sK18 ) )
| ( sK16 = sK17 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16,sK17,sK18]),skolemize(X3,sK16),skolemize(X4,sK17),skolemize(X5,sK18)],[f242]) ).
thf(f368,plain,
( ( upairsetIL = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( setextAx = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrER = $true )
& ( subPowSU = $true )
& ( emptysetE = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrI = $true )
& ( eqinunit = $true )
& ( emptysetimpfalse = $true )
& ( exuE2 = $true )
& ( powersetAx = $true )
& ( setadjoinE = $true )
& ( singletonsswitch = $true )
& ? [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
!= $true )
& ( prop2setE = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( setoftrueEq = $true )
& ( nonemptyImpWitness = $true )
& ( setunionAx = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( setunionE = $true )
& ( foundationAx = $true )
& ( emptyinunitempty = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( notinemptyset = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( exuE3e = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( emptyinPowerset = $true )
& ( setadjoinIL = $true )
& ( setadjoinAx = $true )
& ( emptyInPowerset = $true )
& ( uniqinunit = $true )
& ( upairsetE = $true )
& ( replAx = $true )
& ( emptyI = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( wellorderingAx = $true )
& ( notinsingleton = $true ) ),
inference(rectify,[],[f213]) ).
thf(f369,plain,
( ( upairsetIL = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( setextAx = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrER = $true )
& ( subPowSU = $true )
& ( emptysetE = $true )
& ( nonemptyE1 = $true )
& ( dsetconstrI = $true )
& ( eqinunit = $true )
& ( emptysetimpfalse = $true )
& ( exuE2 = $true )
& ( powersetAx = $true )
& ( setadjoinE = $true )
& ( singletonsswitch = $true )
& ( $true
!= ( in @ sK139 @ ( setadjoin @ sK138 @ ( setadjoin @ sK139 @ emptyset ) ) ) )
& ( prop2setE = $true )
& ( nonemptyI1 = $true )
& ( emptysetAx = $true )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( setoftrueEq = $true )
& ( nonemptyImpWitness = $true )
& ( setunionAx = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( setunionE = $true )
& ( foundationAx = $true )
& ( emptyinunitempty = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( notinemptyset = $true )
& ( setunionI = $true )
& ( descrp = $true )
& ( exuE3e = $true )
& ( powersetE = $true )
& ( setadjoinOr = $true )
& ( emptyinPowerset = $true )
& ( setadjoinIL = $true )
& ( setadjoinAx = $true )
& ( emptyInPowerset = $true )
& ( uniqinunit = $true )
& ( upairsetE = $true )
& ( replAx = $true )
& ( emptyI = $true )
& ( omega0Ax = $true )
& ( exuE1 = $true )
& ( wellorderingAx = $true )
& ( notinsingleton = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK138,sK139]),skolemize(X0,sK138),skolemize(X1,sK139)],[f368]) ).
thf(f398,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( X0 != X1 )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[],[f243]) ).
thf(f399,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X2 ) )
| ( setadjoinAx != $true ) ),
inference(cnf_transformation,[],[f243]) ).
thf(f604,plain,
setadjoinAx = $true,
inference(cnf_transformation,[],[f369]) ).
thf(f628,plain,
( $true
!= ( in @ sK139 @ ( setadjoin @ sK138 @ ( setadjoin @ sK139 @ emptyset ) ) ) ),
inference(cnf_transformation,[],[f369]) ).
thf(f652,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X2 ) ) )
| ( setadjoinAx != $true ) ),
inference(equality_resolution,[],[f398]) ).
thf(f1025,definition,
( spl141_74
<=> ( setadjoinAx = $true ) ),
introduced(definition,[new_symbols(definition,[spl141_74])],[avatar_definition]) ).
thf(f1135,definition,
( spl141_99
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl141_99])],[avatar_definition]) ).
thf(f1136,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ ( setadjoin @ X1 @ X2 ) ) )
| ( $true
!= ( in @ X0 @ X2 ) ) )
| ~ spl141_99 ),
inference(avatar_component_clause,[],[f1135]) ).
thf(f1137,plain,
( ~ spl141_74
| spl141_99 ),
inference(avatar_split_clause,[],[f399,f1135,f1025]) ).
thf(f1228,definition,
( spl141_119
<=> ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl141_119])],[avatar_definition]) ).
thf(f1229,plain,
( ! [X0: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X1 @ X0 ) ) )
| ~ spl141_119 ),
inference(avatar_component_clause,[],[f1228]) ).
thf(f1289,definition,
( spl141_132
<=> ( $true
= ( in @ sK139 @ ( setadjoin @ sK138 @ ( setadjoin @ sK139 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl141_132])],[avatar_definition]) ).
thf(f1291,plain,
( ( $true
!= ( in @ sK139 @ ( setadjoin @ sK138 @ ( setadjoin @ sK139 @ emptyset ) ) ) )
| spl141_132 ),
inference(avatar_component_clause,[],[f1289]) ).
thf(f1292,plain,
~ spl141_132,
inference(avatar_split_clause,[],[f628,f1289]) ).
thf(f1497,plain,
spl141_74,
inference(avatar_split_clause,[],[f604,f1025]) ).
thf(f1627,plain,
( spl141_119
| ~ spl141_74 ),
inference(avatar_split_clause,[],[f652,f1025,f1228]) ).
thf(f1980,plain,
( ( $true
!= ( in @ sK139 @ ( setadjoin @ sK139 @ emptyset ) ) )
| ( $true != $true )
| ~ spl141_99
| spl141_132 ),
inference(superposition,[],[f1291,f1136]) ).
thf(f1982,plain,
( ( $true
!= ( in @ sK139 @ ( setadjoin @ sK139 @ emptyset ) ) )
| ~ spl141_99
| spl141_132 ),
inference(trivial_inequality_removal,[],[f1980]) ).
thf(f1986,plain,
( $false
| ~ spl141_99
| ~ spl141_119
| spl141_132 ),
inference(forward_subsumption_resolution,[],[f1982,f1229]) ).
thf(f1987,plain,
( ~ spl141_99
| ~ spl141_119
| spl141_132 ),
inference(avatar_contradiction_clause,[],[f1986]) ).
cnf(s75,plain,
( ~ spl141_74
| spl141_99 ),
inference(sat_conversion,[],[f1137]) ).
cnf(s112,plain,
~ spl141_132,
inference(sat_conversion,[],[f1292]) ).
cnf(s164,plain,
spl141_74,
inference(sat_conversion,[],[f1497]) ).
cnf(s200,plain,
( ~ spl141_74
| spl141_119 ),
inference(sat_conversion,[],[f1627]) ).
cnf(s259,plain,
( ~ spl141_99
| ~ spl141_119
| spl141_132 ),
inference(sat_conversion,[],[f1987]) ).
cnf(s267,plain,
spl141_119,
inference(rat,[],[s200,s164]) ).
cnf(s277,plain,
~ spl141_99,
inference(rat,[],[s259,s267,s112]) ).
cnf(s296,plain,
$false,
inference(rat,[],[s75,s277,s164]) ).
thf(f1988,plain,
$false,
inference(avatar_sat_refutation,[],[s296]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU533^1 : 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 : n014.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 13:48:30 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running higher-order theorem proving
% 0.09/0.25 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
% 0.23/0.35 % (2689209)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.35 % (2689216)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1331178914:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.35 % (2689216)Instruction limit reached!
% 0.23/0.35 % (2689216)------------------------------
% 0.23/0.35 % (2689216)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (2689216)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (2689216)CaDiCaL version: 2.1.3
% 0.23/0.35 % (2689216)Termination reason: Instruction limit
% 0.23/0.35 % (2689216)Termination phase: Property scanning
% 0.23/0.35 % (2689216)Time elapsed: 0.002 s
% 0.23/0.35 % (2689216)Peak memory usage: 10 MB
% 0.23/0.35 % (2689216)Instructions burned: 7 (million)
% 0.23/0.35 % (2689220)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.35 % (2689220)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
% 0.23/0.35 % (2689215)lrs+10_16_si=on:nwc=1.5:random_seed=467543433:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.35 % (2689214)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3341439943:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.35 % (2689219)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3403861112:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.35 % (2689217)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=1273789550: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)
% 0.23/0.35 % (2689220)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=2778985872:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.35 % (2689218)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2609893102:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.35 % (2689222)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2494780307:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.35 % (2689222)Instruction limit reached!
% 0.23/0.35 % (2689222)------------------------------
% 0.23/0.35 % (2689222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (2689222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (2689222)CaDiCaL version: 2.1.3
% 0.23/0.35 % (2689222)Termination reason: Instruction limit
% 0.23/0.35 % (2689222)Termination phase: shuffling
% 0.23/0.35 % (2689222)Time elapsed: 0.001 s
% 0.23/0.35 % (2689222)Peak memory usage: 9 MB
% 0.23/0.35 % (2689222)Instructions burned: 3 (million)
% 0.23/0.35 % (2689215)Instruction limit reached!
% 0.23/0.35 % (2689215)------------------------------
% 0.23/0.35 % (2689215)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (2689215)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (2689215)CaDiCaL version: 2.1.3
% 0.23/0.35 % (2689215)Termination reason: Instruction limit
% 0.23/0.35 % (2689215)Termination phase: Property scanning
% 0.23/0.35 % (2689215)Time elapsed: 0.008 s
% 0.23/0.35 % (2689215)Peak memory usage: 10 MB
% 0.23/0.35 % (2689215)Instructions burned: 20 (million)
% 0.23/0.35 % (2689230)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3767446904:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.35 % (2689218)Instruction limit reached!
% 0.23/0.35 % (2689218)------------------------------
% 0.23/0.35 % (2689218)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (2689218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (2689218)CaDiCaL version: 2.1.3
% 0.23/0.35 % (2689218)Termination reason: Instruction limit
% 0.23/0.35 % (2689218)Termination phase: Property scanning
% 0.23/0.35 % (2689218)Time elapsed: 0.013 s
% 0.23/0.35 % (2689218)Peak memory usage: 11 MB
% 0.23/0.35 % (2689218)Instructions burned: 26 (million)
% 0.23/0.35 % (2689230)Instruction limit reached!
% 0.23/0.35 % (2689230)------------------------------
% 0.23/0.35 % (2689230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (2689230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (2689230)CaDiCaL version: 2.1.3
% 0.23/0.35 % (2689230)Termination reason: Instruction limit
% 0.23/0.35 % (2689230)Termination phase: Property scanning
% 0.23/0.35 % (2689230)Time elapsed: 0.002 s
% 0.23/0.35 % (2689230)Peak memory usage: 10 MB
% 0.23/0.35 % (2689230)Instructions burned: 7 (million)
% 0.23/0.35 % (2689234)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
% 0.23/0.35 % (2689234)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.35 % (2689234)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3152473045:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.23/0.35 % (2689231)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.35 % (2689219) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2689209-2689219"...
% 0.23/0.35 % (2689217) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2689209-2689217"...
% 0.23/0.35 % (2689234)Instruction limit reached!
% 0.23/0.35 % (2689234)------------------------------
% 0.23/0.35 % (2689234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (2689234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (2689234)CaDiCaL version: 2.1.3
% 0.23/0.35 % (2689234)Termination reason: Instruction limit
% 0.23/0.35 % (2689234)Termination phase: Saturation
% 0.23/0.35 % (2689234)Time elapsed: 0.006 s
% 0.23/0.35 % (2689234)Peak memory usage: 11 MB
% 0.23/0.35 % (2689234)Instructions burned: 28 (million)
% 0.23/0.35 % (2689219)...printing done.
% 0.23/0.35 % (2689217)...printing done.
% 0.23/0.35 % (2689214) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2689209-2689214"...
% 0.23/0.35 % (2689231)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1684116259:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/0.35 % (2689217)Refutation found. Thanks to Tanya!
% 0.23/0.35 % SZS status Theorem for theBenchmark
% 0.23/0.35 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.35 % (2689217)------------------------------
% 0.23/0.35 % (2689217)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.35 % (2689217)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.35 % (2689217)CaDiCaL version: 2.1.3
% 0.23/0.35 % (2689217)Termination reason: Refutation
% 0.23/0.35 % (2689217)Time elapsed: 0.036 s
% 0.23/0.35 % (2689217)Peak memory usage: 14 MB
% 0.23/0.35 % (2689217)Instructions burned: 69 (million)
% 0.23/0.35 % (2689209)Success in time 0.086 s
% 0.23/0.35 % Vampire exiting
%------------------------------------------------------------------------------