%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEU549^1 : 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 : n001.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 08:32:24 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 2
% Syntax : Number of formulae : 31 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 1332 ( 386 equ; 0 cnn)
% Maximal formula atoms : 69 ( 42 avg)
% Number of connectives : 669 ( 8 ~; 4 |; 212 &; 83 @)
% ( 0 <=>; 351 =>; 0 <=; 0 <~>)
% Maximal formula depth : 74 ( 20 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% Number of symbols : 143 ( 138 usr; 72 con; 0-4 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 57 ( 28 ^; 21 !; 8 ?; 57 :)
% 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_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_79,type,
vAND: $o > $o > $o ).
thf(func_def_80,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_81,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_82,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_83,type,
vIMP: $o > $o > $o ).
thf(func_def_84,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_85,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_86,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_87,type,
vIFF: $o > $o > $o ).
thf(func_def_88,type,
vNOT: $o > $o ).
thf(func_def_89,type,
vOR: $o > $o > $o ).
thf(func_def_90,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_91,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_94,type,
sK0: $i > $o ).
thf(func_def_98,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_99,type,
sK5: ( $i > $o ) > $i > $i ).
thf(func_def_100,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_101,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_102,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_103,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_104,type,
sK10: ( $i > $o ) > $i > $i ).
thf(func_def_105,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_106,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_107,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_108,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_109,type,
sK15: ( $i > $o ) > $i > $i ).
thf(func_def_110,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_111,type,
sK17: $i > $i ).
thf(func_def_112,type,
sK18: ( $i > $o ) > $i ).
thf(func_def_113,type,
sK19: ( $i > $o ) > $i > $i ).
thf(func_def_114,type,
sK20: $o > $i > $i > $i ).
thf(func_def_115,type,
sK21: $i > $i > $i ).
thf(func_def_116,type,
sK22: $i > $i ).
thf(func_def_117,type,
sK23: $i > $i ).
thf(func_def_118,type,
sK24: $i > $i ).
thf(func_def_119,type,
sK25: $i > $i > $i ).
thf(func_def_120,type,
sK26: $i > $i > $i ).
thf(func_def_121,type,
sK27: ( $i > $o ) > $i ).
thf(func_def_122,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_123,type,
sK29: ( $i > $o ) > $i ).
thf(func_def_124,type,
sK30: ( $i > $o ) > $i > $i ).
thf(func_def_125,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_126,type,
sK32: $i > $i ).
thf(func_def_127,type,
sK33: $i > $i > $i > $i ).
thf(func_def_128,type,
sK34: $i > $i > $i ).
thf(func_def_129,type,
sK35: $i > $i > $i ).
thf(func_def_130,type,
sK36: $i > $i > $i ).
thf(func_def_131,type,
sK37: $i > $i ).
thf(func_def_132,type,
sK38: $i > ( $i > $i > $o ) > $i ).
thf(func_def_133,type,
sK39: $i > ( $i > $i > $o ) > $i ).
thf(func_def_134,type,
sK40: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_135,type,
sK41: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_136,type,
sK42: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_137,type,
sK43: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_138,type,
sK44: $i > $i ).
thf(func_def_139,type,
sK45: $i > $i > $i ).
thf(func_def_140,type,
sK46: $i > $i > $i ).
thf(func_def_141,type,
sK47: $i > $i > $i ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(f68,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
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ! [X1: $i,X2: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(f69,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
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ! [X1: $i,X2: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f68]) ).
thf(f70,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f71,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f70]) ).
thf(f199,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
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ! [X2: $i,X3: $i] :
( ( X0 @ X2 )
=> ( ( X0 @ X3 )
=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f69]) ).
thf(f200,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 )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ! [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( ( X0 @ X3 )
= $true )
=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f199]) ).
thf(f201,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 )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ! [X1: $i,X2: $i] :
( ( ( X0 @ X1 )
= $true )
=> ( ( ( X0 @ X2 )
= $true )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f200]) ).
thf(f202,plain,
( ? [X0: $i > $o] :
( ? [X1: $i,X2: $i] :
( ( X1 != X2 )
& ( ( X0 @ X2 )
= $true )
& ( ( X0 @ X1 )
= $true ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( 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,[],[f201]) ).
thf(f203,plain,
( ? [X0: $i > $o] :
( ? [X1: $i,X2: $i] :
( ( X1 != X2 )
& ( ( X0 @ X2 )
= $true )
& ( ( X0 @ X1 )
= $true ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( 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(flattening,[],[f202]) ).
thf(f204,plain,
( ( sK1 != sK2 )
& ( $true
= ( sK0 @ sK2 ) )
& ( $true
= ( sK0 @ sK1 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( 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(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f203]) ).
thf(f205,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f71]) ).
thf(f337,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f204]) ).
thf(f338,plain,
( $true
= ( sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f204]) ).
thf(f339,plain,
( $true
= ( sK0 @ sK2 ) ),
inference(cnf_transformation,[],[f204]) ).
thf(f340,plain,
sK1 != sK2,
inference(cnf_transformation,[],[f204]) ).
thf(f408,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(definition_unfolding,[],[f337,f205]) ).
thf(f409,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f408]) ).
thf(f410,plain,
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK3 ) ),
inference(sigma_proxy_clausification,[],[f409]) ).
thf(f411,plain,
( $true
= ( ( sK0 @ sK3 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK3 = Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f410]) ).
thf(f412,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK3 = Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f411]) ).
thf(f414,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK3 = Y0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f412]) ).
thf(f415,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ X1 )
=> ( sK3 = X1 ) ) ),
inference(beta-eta_normalization,[],[f414]) ).
thf(f416,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( $true
= ( sK3 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f415]) ).
thf(f417,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK3 = X1 ) ),
inference(equality_proxy_clausification,[],[f416]) ).
thf(f1220,plain,
( ( $false = $true )
| ( sK1 = sK3 ) ),
inference(constrained_superposition,[],[f338,f417]) ).
thf(f1221,plain,
( ( $false = $true )
| ( sK2 = sK3 ) ),
inference(constrained_superposition,[],[f339,f417]) ).
thf(f1222,plain,
sK2 = sK3,
inference(trivial_inequality_removal,[],[f1221]) ).
thf(f1223,plain,
sK1 = sK3,
inference(trivial_inequality_removal,[],[f1220]) ).
thf(f1229,plain,
sK1 = sK2,
inference(constrained_superposition,[],[f1222,f1223]) ).
thf(f1231,plain,
$false,
inference(forward_subsumption_resolution,[],[f1229,f340]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU549^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n001.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 13:55:35 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.30 % (1278222)Will run a generic schedule for satisfiability detection.
% 0.20/0.30 % (1278233)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2598157758_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.30 % (1278234)% WARNING: option uhcvi not known.
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (1278236)dis+10_1_sil=32000:sp=arity:random_seed=2089966962:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.30 % (1278234)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=68985413:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.30 % (1278237)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1929613781:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.30 % (1278235)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=464114457:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.30 % (1278239)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3266243319:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.30 % (1278238)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3880176358:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (1278234)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (1278237)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.30 % (1278241)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1232867020:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.20/0.30 % (1278234)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.20/0.30 % Exception at run slice level
% 0.20/0.30 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.30 % (1278234) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1278222-1278234"...
% 0.20/0.30 % (1278236) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1278222-1278236"...
% 0.20/0.30 % (1278235) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1278222-1278235"...
% 0.20/0.30 % (1278236)...printing done.
% 0.20/0.30 % (1278234)...printing done.
% 0.20/0.30 % (1278237) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1278222-1278237"...
% 0.20/0.30 % (1278249)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=3287993199:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.30 % (1278234)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (1278234)------------------------------
% 0.20/0.30 % (1278234)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (1278234)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (1278234)CaDiCaL version: 2.1.3
% 0.20/0.30 % (1278234)Termination reason: Refutation
% 0.20/0.30 % (1278234)Time elapsed: 0.025 s
% 0.20/0.30 % (1278234)Peak memory usage: 13 MB
% 0.20/0.30 % (1278234)Instructions burned: 53 (million)
% 0.20/0.30 % (1278222)Success in time 0.066 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------