%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU557^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 08:30:03 AM UTC 2026
% Result : Theorem 1.01s 0.40s
% Output : Refutation 1.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 8
% Syntax : Number of formulae : 103 ( 36 unt; 0 typ; 5 def)
% Number of atoms : 1870 ( 547 equ; 0 cnn)
% Maximal formula atoms : 78 ( 18 avg)
% Number of connectives : 1212 ( 58 ~; 98 |; 322 &; 356 @)
% ( 8 <=>; 339 =>; 0 <=; 0 <~>)
% Maximal formula depth : 83 ( 9 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 42 ( 42 >; 0 *; 0 +; 0 <<)
% Number of symbols : 173 ( 168 usr; 84 con; 0-4 aty)
% ( 21 !!; 10 ??; 0 @@+; 0 @@-)
% Number of variables : 179 ( 0 sgn 76 !; 8 ?; 179 :)
% 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,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_87,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_88,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_89,type,
vIMP: $o > $o > $o ).
thf(func_def_90,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_91,type,
vIFF: $o > $o > $o ).
thf(func_def_92,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_93,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_94,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_95,type,
vAND: $o > $o > $o ).
thf(func_def_96,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_97,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_98,type,
vOR: $o > $o > $o ).
thf(func_def_99,type,
vNOT: $o > $o ).
thf(func_def_102,type,
sK0: $i > $o ).
thf(func_def_103,type,
sK1: $i > $o ).
thf(func_def_104,type,
sK2: $o > $i > $i > $i ).
thf(func_def_105,type,
sK3: ( $i > $o ) > $i ).
thf(func_def_106,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_108,type,
sK6: ( $i > $o ) > $i > $i ).
thf(func_def_109,type,
sK7: $i > $i > $i ).
thf(func_def_110,type,
sK8: $i > $i > $i ).
thf(func_def_111,type,
sK9: $i > $i > $i ).
thf(func_def_112,type,
sK10: $i > ( $i > $o ) > $i ).
thf(func_def_113,type,
sK11: $i > ( $i > $o ) > $i ).
thf(func_def_114,type,
sK12: $i > $i > $i ).
thf(func_def_115,type,
sK13: ( $i > $o ) > $i ).
thf(func_def_116,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_117,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_118,type,
sK16: ( $i > $o ) > $i > $i ).
thf(func_def_119,type,
sK17: $i > $i ).
thf(func_def_120,type,
sK18: $i > $i ).
thf(func_def_121,type,
sK19: $i > $i > $i ).
thf(func_def_122,type,
sK20: $i > $i > $i ).
thf(func_def_123,type,
sK21: $i > $i > $i ).
thf(func_def_124,type,
sK22: $i > $i > $i > $i ).
thf(func_def_125,type,
sK23: $i > ( $i > $i > $o ) > $i ).
thf(func_def_126,type,
sK24: $i > ( $i > $i > $o ) > $i ).
thf(func_def_127,type,
sK25: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_128,type,
sK26: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_129,type,
sK27: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_130,type,
sK28: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_131,type,
sK29: ( $i > $o ) > $i ).
thf(func_def_132,type,
sK30: ( $i > $o ) > $i > $i ).
thf(func_def_133,type,
sK31: ( $i > $o ) > $i > $i ).
thf(func_def_134,type,
sK32: ( $i > $o ) > $i ).
thf(func_def_135,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_136,type,
sK34: $i > $i > $i ).
thf(func_def_137,type,
sK35: $i > $i ).
thf(func_def_138,type,
sK36: $i > $i ).
thf(func_def_139,type,
sK37: $i > $i ).
thf(func_def_140,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_141,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_142,type,
sK40: $i > ( $i > $o ) > $i ).
thf(func_def_143,type,
sK41: $i > $i ).
thf(func_def_144,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_145,type,
sK43: $i > $i ).
thf(func_def_147,type,
sK45: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_148,type,
sK46: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_149,type,
sK47: ( $i > $o ) > $i ).
thf(func_def_150,type,
sK48: $i > ( $i > $o ) > $i ).
thf(func_def_151,type,
sK49: $i > ( $i > $o ) > $i ).
thf(func_def_152,type,
sK50: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK51: $i > ( $i > $o ) > $i ).
thf(func_def_154,type,
sK52: $i > ( $i > $o ) > $i ).
thf(func_def_155,type,
sK53: ( $i > $o ) > $i ).
thf(func_def_156,type,
sK54: $i > ( $i > $o ) > $i ).
thf(func_def_157,type,
sK55: $i > ( $i > $o ) > $i ).
thf(func_def_158,type,
sK56: ( $i > $o ) > $i ).
thf(func_def_159,type,
sK57: $i > ( $i > $o ) > $i ).
thf(func_def_160,type,
sK58: $i > ( $i > $o ) > $i ).
thf(func_def_161,type,
sK59: $i > $i > $i ).
thf(func_def_162,type,
sK60: ( $i > $o ) > $i > $i ).
thf(func_def_163,type,
sK61: ( $i > $o ) > $i ).
thf(func_def_164,type,
sK62: ( $i > $o ) > $i ).
thf(func_def_165,type,
sK63: ( $i > $o ) > $i ).
thf(func_def_166,type,
sK64: $i > ( $i > $o ) > $i ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(f13,axiom,
! [X0: $i > $o] :
( ( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ( X0
@ ( descr
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) )
= descrp ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descrp) ).
thf(f76,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
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ! [X1: $i > $o,X0: $i > $o] :
( ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X2 )
<=> ( X1 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X0 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',descr__Cong) ).
thf(f77,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
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ! [X1: $i > $o,X0: $i > $o] :
( ! [X3: $i,X2: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X2 )
<=> ( X1 @ X3 ) ) )
=> ( ( exu
@ ^ [X2: $i] : ( X0 @ X2 ) )
=> ( ( exu
@ ^ [X2: $i] : ( X1 @ X2 ) )
=> ( ( descr
@ ^ [X2: $i] : ( X1 @ X2 ) )
= ( descr
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f76]) ).
thf(f103,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f104,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f103]) ).
thf(f157,plain,
! [X0: $i > $o] :
( ( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ( X0
@ ( descr
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) )
= descrp ),
inference(rectify,[],[f13]) ).
thf(f158,plain,
( descrp
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( exu
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
=> ( Y0
@ ( descr
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[],[f157]) ).
thf(f207,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
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X1 @ X3 )
<=> ( X0 @ X2 ) ) )
=> ( ( exu
@ ^ [X4: $i] : ( X1 @ X4 ) )
=> ( ( exu
@ ^ [X5: $i] : ( X0 @ X5 ) )
=> ( ( descr
@ ^ [X6: $i] : ( X0 @ X6 ) )
= ( descr
@ ^ [X7: $i] : ( X1 @ X7 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f77]) ).
thf(f208,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 )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ! [X1: $i > $o,X0: $i > $o] :
( ! [X2: $i,X3: $i] :
( ( X2 = X3 )
=> ( ( X0 @ X2 )
= ( X1 @ X3 ) ) )
=> ( ( $true
= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
=> ( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ( ( descr
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
= ( descr
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f207]) ).
thf(f222,plain,
( ? [X1: $i > $o,X0: $i > $o] :
( ( ( descr
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ! [X3: $i,X2: $i] :
( ( X2 != X3 )
| ( ( X0 @ X2 )
= ( X1 @ X3 ) ) ) )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( 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,[],[f208]) ).
thf(f223,plain,
( ( exuE3u = $true )
& ( upairsetIR = $true )
& ( replAx = $true )
& ( quantDeMorgan3 = $true )
& ( dsetconstrEL = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( exuI1 = $true )
& ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( prop2set2propI = $true )
& ( dsetconstrI = $true )
& ( exuE3e = $true )
& ( exuE1 = $true )
& ( nonemptyI = $true )
& ( prop2setE = $true )
& ( emptysetAx = $true )
& ( emptyinunitempty = $true )
& ( subPowSU = $true )
& ( setunionI = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan2 = $true )
& ( omegaIndAx = $true )
& ( setadjoinAx = $true )
& ( upairsetE = $true )
& ( emptyInPowerset = $true )
& ( omega0Ax = $true )
& ( exuE2 = $true )
& ( exuEu = $true )
& ( setadjoinIR = $true )
& ( wellorderingAx = $true )
& ( powersetE = $true )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ( foundationAx = $true )
& ( powersetAx = $true )
& ( nonemptyImpWitness = $true )
& ( eqinunit = $true )
& ( notdexE = $true )
& ( vacuousDall = $true )
& ( inCongP = $true )
& ( prop2setI = $true )
& ( powerset__Cong = $true )
& ( emptyI = $true )
& ( singletonsswitch = $true )
& ( setadjoin__Cong = $true )
& ( notinemptyset = $true )
& ( nonemptyI1 = $true )
& ( exu__Cong = $true )
& ( setadjoinOr = $true )
& ( nonemptyE1 = $true )
& ? [X1: $i > $o,X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ! [X3: $i,X2: $i] :
( ( X2 != X3 )
| ( ( X0 @ X2 )
= ( X1 @ X3 ) ) )
& ( ( descr
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( setbeta = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( notdallE = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( descrp = $true )
& ( setunion__Cong = $true )
& ( upairsetIL = $true )
& ( notinsingleton = $true )
& ( dsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( omegaSAx = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan1 = $true )
& ( setextAx = $true )
& ( quantDeMorgan4 = $true )
& ( setext = $true )
& ( emptyinPowerset = $true )
& ( in__Cong = $true )
& ( setunionAx = $true )
& ( omega__Cong = $true ) ),
inference(flattening,[],[f222]) ).
thf(f224,plain,
( ( exuE3u = $true )
& ( upairsetIR = $true )
& ( replAx = $true )
& ( quantDeMorgan3 = $true )
& ( dsetconstrEL = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( exuI1 = $true )
& ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( prop2set2propI = $true )
& ( dsetconstrI = $true )
& ( exuE3e = $true )
& ( exuE1 = $true )
& ( nonemptyI = $true )
& ( prop2setE = $true )
& ( emptysetAx = $true )
& ( emptyinunitempty = $true )
& ( subPowSU = $true )
& ( setunionI = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan2 = $true )
& ( omegaIndAx = $true )
& ( setadjoinAx = $true )
& ( upairsetE = $true )
& ( emptyInPowerset = $true )
& ( omega0Ax = $true )
& ( exuE2 = $true )
& ( exuEu = $true )
& ( setadjoinIR = $true )
& ( wellorderingAx = $true )
& ( powersetE = $true )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ( foundationAx = $true )
& ( powersetAx = $true )
& ( nonemptyImpWitness = $true )
& ( eqinunit = $true )
& ( notdexE = $true )
& ( vacuousDall = $true )
& ( inCongP = $true )
& ( prop2setI = $true )
& ( powerset__Cong = $true )
& ( emptyI = $true )
& ( singletonsswitch = $true )
& ( setadjoin__Cong = $true )
& ( notinemptyset = $true )
& ( nonemptyI1 = $true )
& ( exu__Cong = $true )
& ( setadjoinOr = $true )
& ( nonemptyE1 = $true )
& ? [X0: $i > $o,X1: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( X0 @ X2 )
= ( X1 @ X3 ) ) )
& ( ( descr
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( setbeta = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( notdallE = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( descrp = $true )
& ( setunion__Cong = $true )
& ( upairsetIL = $true )
& ( notinsingleton = $true )
& ( dsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( omegaSAx = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan1 = $true )
& ( setextAx = $true )
& ( quantDeMorgan4 = $true )
& ( setext = $true )
& ( emptyinPowerset = $true )
& ( in__Cong = $true )
& ( setunionAx = $true )
& ( omega__Cong = $true ) ),
inference(rectify,[],[f223]) ).
thf(f225,plain,
( ( exuE3u = $true )
& ( upairsetIR = $true )
& ( replAx = $true )
& ( quantDeMorgan3 = $true )
& ( dsetconstrEL = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( exuI1 = $true )
& ( noeltsimpempty = $true )
& ( setadjoinE = $true )
& ( prop2set2propI = $true )
& ( dsetconstrI = $true )
& ( exuE3e = $true )
& ( exuE1 = $true )
& ( nonemptyI = $true )
& ( prop2setE = $true )
& ( emptysetAx = $true )
& ( emptyinunitempty = $true )
& ( subPowSU = $true )
& ( setunionI = $true )
& ( emptyE1 = $true )
& ( quantDeMorgan2 = $true )
& ( omegaIndAx = $true )
& ( setadjoinAx = $true )
& ( upairsetE = $true )
& ( emptyInPowerset = $true )
& ( omega0Ax = $true )
& ( exuE2 = $true )
& ( exuEu = $true )
& ( setadjoinIR = $true )
& ( wellorderingAx = $true )
& ( powersetE = $true )
& ( uniqinunit = $true )
& ( setunionE = $true )
& ( foundationAx = $true )
& ( powersetAx = $true )
& ( nonemptyImpWitness = $true )
& ( eqinunit = $true )
& ( notdexE = $true )
& ( vacuousDall = $true )
& ( inCongP = $true )
& ( prop2setI = $true )
& ( powerset__Cong = $true )
& ( emptyI = $true )
& ( singletonsswitch = $true )
& ( setadjoin__Cong = $true )
& ( notinemptyset = $true )
& ( nonemptyI1 = $true )
& ( exu__Cong = $true )
& ( setadjoinOr = $true )
& ( nonemptyE1 = $true )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( sK1 @ X3 )
= ( sK0 @ X2 ) ) )
& ( ( descr
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ( setbeta = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( notdallE = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( descrp = $true )
& ( setunion__Cong = $true )
& ( upairsetIL = $true )
& ( notinsingleton = $true )
& ( dsetconstrER = $true )
& ( emptyset__Cong = $true )
& ( omegaSAx = $true )
& ( emptysetimpfalse = $true )
& ( quantDeMorgan1 = $true )
& ( setextAx = $true )
& ( quantDeMorgan4 = $true )
& ( setext = $true )
& ( emptyinPowerset = $true )
& ( in__Cong = $true )
& ( setunionAx = $true )
& ( omega__Cong = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f224]) ).
thf(f236,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f104]) ).
thf(f247,plain,
( descrp
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( exu
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
=> ( Y0
@ ( descr
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[],[f158]) ).
thf(f291,plain,
descrp = $true,
inference(cnf_transformation,[],[f225]) ).
thf(f298,plain,
( ( descr
@ ^ [Y0: $i] : ( sK1 @ Y0 ) )
!= ( descr
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f299,plain,
! [X2: $i,X3: $i] :
( ( X2 != X3 )
| ( ( sK1 @ X3 )
= ( sK0 @ X2 ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f300,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f301,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(cnf_transformation,[],[f225]) ).
thf(f399,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) )
& ( Y1 @ Y2 ) ) )
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
=> ( Y0
@ ( descr
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[],[f247,f291,f236]) ).
thf(f428,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK1 @ Y0 ) ) ),
inference(definition_unfolding,[],[f301,f236]) ).
thf(f429,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(definition_unfolding,[],[f300,f236]) ).
thf(f455,plain,
! [X3: $i] :
( ( sK0 @ X3 )
= ( sK1 @ X3 ) ),
inference(equality_resolution,[],[f299]) ).
thf(f492,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK1 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f428]) ).
thf(f493,plain,
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK1 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK1 @ Y0 ) )
@ sK5 ) ),
inference(sigma_proxy_clausification,[],[f492]) ).
thf(f494,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) )
& ( sK1 @ sK5 ) ) ),
inference(beta-eta_normalization,[],[f493]) ).
thf(f496,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f494]) ).
thf(f497,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK1 @ Y0 )
=> ( sK5 = Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f496]) ).
thf(f498,plain,
! [X1: $i] :
( $true
= ( ( sK1 @ X1 )
=> ( sK5 = X1 ) ) ),
inference(beta-eta_normalization,[],[f497]) ).
thf(f499,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( $true
= ( sK5 = X1 ) ) ),
inference(imp_proxy_clausification,[],[f498]) ).
thf(f500,plain,
! [X1: $i] :
( ( $false
= ( sK1 @ X1 ) )
| ( sK5 = X1 ) ),
inference(equality_proxy_clausification,[],[f499]) ).
thf(f768,plain,
( ( descr @ sK0 )
!= ( descr @ sK1 ) ),
inference(beta-eta_normalization,[],[f298]) ).
thf(f956,plain,
! [X3: $i] :
( ( $true
= ( sK1 @ X3 ) )
| ( ( sK0 @ X3 )
= $false ) ),
inference(iff_proxy_clausification,[],[f455]) ).
thf(f1141,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) ) ),
inference(beta-eta_normalization,[],[f429]) ).
thf(f1142,plain,
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) )
@ sK44 ) ),
inference(sigma_proxy_clausification,[],[f1141]) ).
thf(f1143,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK44 = Y0 ) ) )
& ( sK0 @ sK44 ) ) ),
inference(beta-eta_normalization,[],[f1142]) ).
thf(f1144,plain,
( $true
= ( sK0 @ sK44 ) ),
inference(and_proxy_clausification,[],[f1143]) ).
thf(f1306,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ^ [Y1: $i > $o] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y1 @ Y3 )
=> ( Y2 = Y3 ) ) )
& ( Y1 @ Y2 ) ) )
@ ^ [Y1: $i] : ( Y0 @ Y1 ) )
=> ( Y0
@ ( descr
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f399]) ).
thf(f1307,plain,
! [X1: $i > $o] :
( $true
= ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( X1 @ Y0 ) ) )
=> ( X1 @ ( descr @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1306]) ).
thf(f1308,plain,
! [X1: $i > $o] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( X1 @ Y0 ) ) )
= $false )
| ( $true
= ( X1 @ ( descr @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f1307]) ).
thf(f1309,plain,
! [X2: $i,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( X1 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( X1 @ Y0 ) )
@ X2 )
= $false )
| ( $true
= ( X1 @ ( descr @ X1 ) ) ) ),
inference(pi_proxy_clausification,[],[f1308]) ).
thf(f1310,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X2 = Y0 ) ) )
& ( X1 @ X2 ) ) )
| ( $true
= ( X1 @ ( descr @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f1309]) ).
thf(f1311,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( X1 @ ( descr @ X1 ) ) )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X2 = Y0 ) ) )
= $false )
| ( ( X1 @ X2 )
= $false ) ),
inference(and_proxy_clausification,[],[f1310]) ).
thf(f1312,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $false )
| ( $true
= ( X1 @ ( descr @ X1 ) ) )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X2 = Y0 ) )
@ ( sK60 @ X1 @ X2 ) )
= $false ) ),
inference(sigma_proxy_clausification,[],[f1311]) ).
thf(f1313,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( X1 @ ( descr @ X1 ) ) )
| ( ( X1 @ X2 )
= $false )
| ( ( ( X1 @ ( sK60 @ X1 @ X2 ) )
=> ( X2
= ( sK60 @ X1 @ X2 ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f1312]) ).
thf(f1314,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ X2 )
= $false )
| ( $false
= ( X2
= ( sK60 @ X1 @ X2 ) ) )
| ( $true
= ( X1 @ ( descr @ X1 ) ) ) ),
inference(imp_proxy_clausification,[],[f1313]) ).
thf(f1315,plain,
! [X2: $i,X1: $i > $o] :
( ( ( X1 @ ( sK60 @ X1 @ X2 ) )
= $true )
| ( $true
= ( X1 @ ( descr @ X1 ) ) )
| ( ( X1 @ X2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f1313]) ).
thf(f1316,plain,
! [X2: $i,X1: $i > $o] :
( ( ( sK60 @ X1 @ X2 )
!= X2 )
| ( $true
= ( X1 @ ( descr @ X1 ) ) )
| ( ( X1 @ X2 )
= $false ) ),
inference(equality_proxy_clausification,[],[f1314]) ).
thf(f1491,plain,
! [X0: $i] :
( ( $true = $false )
| ( sK5 = X0 )
| ( ( sK0 @ X0 )
= $false ) ),
inference(superposition,[],[f956,f500]) ).
thf(f1495,plain,
! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( sK5 = X0 ) ),
inference(trivial_inequality_removal,[],[f1491]) ).
thf(f2386,plain,
! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( $true = $false )
| ( $true
= ( sK0 @ ( descr @ sK0 ) ) )
| ( sK5
= ( sK60 @ sK0 @ X0 ) ) ),
inference(superposition,[],[f1315,f1495]) ).
thf(f2389,plain,
! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $true = $false )
| ( $true
= ( sK1 @ ( descr @ sK1 ) ) )
| ( sK5
= ( sK60 @ sK1 @ X0 ) ) ),
inference(superposition,[],[f1315,f500]) ).
thf(f2405,plain,
! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( sK5
= ( sK60 @ sK0 @ X0 ) )
| ( $true
= ( sK0 @ ( descr @ sK0 ) ) ) ),
inference(trivial_inequality_removal,[],[f2386]) ).
thf(f2407,plain,
! [X0: $i] :
( ( $true
= ( sK1 @ ( descr @ sK1 ) ) )
| ( sK5
= ( sK60 @ sK1 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f2389]) ).
thf(f2417,definition,
( spl65_16
<=> ( $true
= ( sK1 @ ( descr @ sK1 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl65_16])],[avatar_definition]) ).
thf(f2418,plain,
( ( $true
!= ( sK1 @ ( descr @ sK1 ) ) )
| spl65_16 ),
inference(avatar_component_clause,[],[f2417]) ).
thf(f2419,plain,
( ( $true
= ( sK1 @ ( descr @ sK1 ) ) )
| ~ spl65_16 ),
inference(avatar_component_clause,[],[f2417]) ).
thf(f2425,definition,
( spl65_18
<=> ! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( sK5
= ( sK60 @ sK0 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl65_18])],[avatar_definition]) ).
thf(f2426,plain,
( ! [X0: $i] :
( ( sK5
= ( sK60 @ sK0 @ X0 ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl65_18 ),
inference(avatar_component_clause,[],[f2425]) ).
thf(f2428,definition,
( spl65_19
<=> ( $true
= ( sK0 @ ( descr @ sK0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl65_19])],[avatar_definition]) ).
thf(f2430,plain,
( ( $true
= ( sK0 @ ( descr @ sK0 ) ) )
| ~ spl65_19 ),
inference(avatar_component_clause,[],[f2428]) ).
thf(f2431,plain,
( spl65_18
| spl65_19 ),
inference(avatar_split_clause,[],[f2405,f2428,f2425]) ).
thf(f2433,definition,
( spl65_20
<=> ! [X0: $i] :
( ( sK5
= ( sK60 @ sK1 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl65_20])],[avatar_definition]) ).
thf(f2434,plain,
( ! [X0: $i] :
( ( sK5
= ( sK60 @ sK1 @ X0 ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl65_20 ),
inference(avatar_component_clause,[],[f2433]) ).
thf(f2435,plain,
( spl65_16
| spl65_20 ),
inference(avatar_split_clause,[],[f2407,f2433,f2417]) ).
thf(f2444,plain,
( ( sK5
= ( descr @ sK1 ) )
| ( $true = $false )
| ~ spl65_16 ),
inference(superposition,[],[f500,f2419]) ).
thf(f2446,plain,
( ( sK5
= ( descr @ sK1 ) )
| ~ spl65_16 ),
inference(trivial_inequality_removal,[],[f2444]) ).
thf(f2477,definition,
( spl65_21
<=> ! [X0: $i] :
( ( sK0 @ X0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl65_21])],[avatar_definition]) ).
thf(f2478,plain,
( ! [X0: $i] :
( ( sK0 @ X0 )
= $false )
| ~ spl65_21 ),
inference(avatar_component_clause,[],[f2477]) ).
thf(f2792,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ ( descr @ sK0 ) ) )
| ( ( sK0 @ X0 )
= $false )
| ( ( sK0 @ X0 )
= $false )
| ( sK5 != X0 ) )
| ~ spl65_18 ),
inference(superposition,[],[f1316,f2426]) ).
thf(f2794,plain,
( ! [X0: $i] :
( ( ( sK0 @ X0 )
= $false )
| ( sK5 != X0 )
| ( $true
= ( sK0 @ ( descr @ sK0 ) ) ) )
| ~ spl65_18 ),
inference(duplicate_literal_removal,[],[f2792]) ).
thf(f2795,plain,
( ! [X0: $i] :
( ( $true
= ( sK0 @ ( descr @ sK0 ) ) )
| ( ( sK0 @ X0 )
= $false ) )
| ~ spl65_18 ),
inference(forward_subsumption_resolution,[],[f2794,f1495]) ).
thf(f2796,plain,
( spl65_19
| spl65_21
| ~ spl65_18 ),
inference(avatar_split_clause,[],[f2795,f2425,f2477,f2428]) ).
thf(f2845,plain,
( ( sK5
= ( descr @ sK0 ) )
| ( $true = $false )
| ~ spl65_19 ),
inference(superposition,[],[f1495,f2430]) ).
thf(f2849,plain,
( ( sK5
= ( descr @ sK0 ) )
| ~ spl65_19 ),
inference(trivial_inequality_removal,[],[f2845]) ).
thf(f2900,plain,
( ( sK5
!= ( descr @ sK1 ) )
| ~ spl65_19 ),
inference(superposition,[],[f768,f2849]) ).
thf(f2901,plain,
( $false
| ~ spl65_16
| ~ spl65_19 ),
inference(forward_subsumption_resolution,[],[f2900,f2446]) ).
thf(f2902,plain,
( ~ spl65_16
| ~ spl65_19 ),
inference(avatar_contradiction_clause,[],[f2901]) ).
thf(f3033,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( sK5 != X0 )
| ( $true
= ( sK1 @ ( descr @ sK1 ) ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl65_20 ),
inference(superposition,[],[f1316,f2434]) ).
thf(f3035,plain,
( ! [X0: $i] :
( ( $false
= ( sK1 @ X0 ) )
| ( $true
= ( sK1 @ ( descr @ sK1 ) ) )
| ( sK5 != X0 ) )
| ~ spl65_20 ),
inference(duplicate_literal_removal,[],[f3033]) ).
thf(f3036,plain,
( ! [X0: $i] :
( ( $true
= ( sK1 @ ( descr @ sK1 ) ) )
| ( $false
= ( sK1 @ X0 ) ) )
| ~ spl65_20 ),
inference(forward_subsumption_resolution,[],[f3035,f500]) ).
thf(f3037,plain,
( ! [X0: $i] :
( $false
= ( sK1 @ X0 ) )
| spl65_16
| ~ spl65_20 ),
inference(forward_subsumption_resolution,[],[f3036,f2418]) ).
thf(f3057,plain,
( ! [X0: $i] :
( ( $true = $false )
| ( ( sK0 @ X0 )
= $false ) )
| spl65_16
| ~ spl65_20 ),
inference(superposition,[],[f956,f3037]) ).
thf(f3078,plain,
( ! [X0: $i] :
( ( sK0 @ X0 )
= $false )
| spl65_16
| ~ spl65_20 ),
inference(trivial_inequality_removal,[],[f3057]) ).
thf(f3095,plain,
( spl65_21
| spl65_16
| ~ spl65_20 ),
inference(avatar_split_clause,[],[f3078,f2433,f2417,f2477]) ).
thf(f3100,plain,
( ( $true = $false )
| ~ spl65_21 ),
inference(superposition,[],[f2478,f1144]) ).
thf(f3147,plain,
( $false
| ~ spl65_21 ),
inference(trivial_inequality_removal,[],[f3100]) ).
thf(f3148,plain,
~ spl65_21,
inference(avatar_contradiction_clause,[],[f3147]) ).
cnf(s23,plain,
( spl65_18
| spl65_19 ),
inference(sat_conversion,[],[f2431]) ).
cnf(s24,plain,
( spl65_16
| spl65_20 ),
inference(sat_conversion,[],[f2435]) ).
cnf(s31,plain,
( ~ spl65_18
| spl65_19
| spl65_21 ),
inference(sat_conversion,[],[f2796]) ).
cnf(s32,plain,
( ~ spl65_16
| ~ spl65_19 ),
inference(sat_conversion,[],[f2902]) ).
cnf(s37,plain,
( spl65_16
| ~ spl65_20
| spl65_21 ),
inference(sat_conversion,[],[f3095]) ).
cnf(s44,plain,
~ spl65_21,
inference(sat_conversion,[],[f3148]) ).
cnf(s45,plain,
( spl65_16
| ~ spl65_20 ),
inference(rat,[],[s37,s44]) ).
cnf(s46,plain,
( ~ spl65_18
| spl65_19 ),
inference(rat,[],[s31,s44]) ).
cnf(s48,plain,
spl65_16,
inference(rat,[],[s24,s45]) ).
cnf(s49,plain,
~ spl65_19,
inference(rat,[],[s32,s48]) ).
cnf(s50,plain,
~ spl65_18,
inference(rat,[],[s46,s49]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s23,s49,s50]) ).
thf(f3150,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU557^1 : TPTP v9.3.1. Bugfixed v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n008.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 13:50:39 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 Running higher-order theorem proving
% 0.11/0.23 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
% 0.33/0.35 % (3185744)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.33/0.35 % (3185754)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1738687847:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.33/0.35 % (3185755)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.33/0.35 % (3185755)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
% 0.33/0.35 % (3185750)lrs+10_16_si=on:nwc=1.5:random_seed=3374897160:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.33/0.35 % (3185749)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3546052187:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.33/0.35 % (3185751)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3128422052:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.33/0.35 % (3185753)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3340485638:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.33/0.35 % (3185752)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=2792916161: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)
% 0.33/0.35 % (3185755)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=577979699:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.33/0.35 % (3185751)Instruction limit reached!
% 0.33/0.35 % (3185751)------------------------------
% 0.33/0.35 % (3185751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.35 % (3185751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.35 % (3185751)CaDiCaL version: 2.1.3
% 0.33/0.35 % (3185751)Termination reason: Instruction limit
% 0.33/0.35 % (3185751)Termination phase: shuffling
% 0.33/0.35 % (3185751)Time elapsed: 0.002 s
% 0.33/0.35 % (3185751)Peak memory usage: 10 MB
% 0.33/0.35 % (3185751)Instructions burned: 3 (million)
% 0.33/0.35 % (3185750)Instruction limit reached!
% 0.33/0.35 % (3185750)------------------------------
% 0.33/0.35 % (3185750)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.35 % (3185750)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.35 % (3185750)CaDiCaL version: 2.1.3
% 0.33/0.35 % (3185750)Termination reason: Instruction limit
% 0.33/0.35 % (3185750)Termination phase: Property scanning
% 0.33/0.35 % (3185750)Time elapsed: 0.008 s
% 0.33/0.35 % (3185750)Peak memory usage: 10 MB
% 0.33/0.35 % (3185750)Instructions burned: 18 (million)
% 0.33/0.35 % (3185754)Instruction limit reached!
% 0.33/0.35 % (3185754)------------------------------
% 0.33/0.35 % (3185754)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.35 % (3185754)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.35 % (3185754)CaDiCaL version: 2.1.3
% 0.33/0.35 % (3185754)Termination reason: Instruction limit
% 0.33/0.35 % (3185754)Termination phase: Saturation
% 0.33/0.35 % (3185754)Time elapsed: 0.020 s
% 0.33/0.35 % (3185754)Peak memory usage: 13 MB
% 0.33/0.35 % (3185754)Instructions burned: 78 (million)
% 0.33/0.35 % (3185753)Instruction limit reached!
% 0.33/0.35 % (3185753)------------------------------
% 0.33/0.35 % (3185753)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.33/0.35 % (3185753)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.33/0.35 % (3185753)CaDiCaL version: 2.1.3
% 0.33/0.35 % (3185753)Termination reason: Instruction limit
% 0.33/0.35 % (3185753)Termination phase: Property scanning
% 0.33/0.35 % (3185753)Time elapsed: 0.013 s
% 0.33/0.35 % (3185753)Peak memory usage: 11 MB
% 0.33/0.35 % (3185753)Instructions burned: 26 (million)
% 0.33/0.35 % (3185763)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2230908299:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.33/0.35 % (3185763)Instruction limit reached!
% 0.33/0.35 % (3185763)------------------------------
% 0.33/0.35 % (3185763)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.38 % (3185763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.38 % (3185763)CaDiCaL version: 2.1.3
% 1.01/0.38 % (3185763)Termination reason: Instruction limit
% 1.01/0.38 % (3185763)Termination phase: shuffling
% 1.01/0.38 % (3185763)Time elapsed: 0.001 s
% 1.01/0.38 % (3185763)Peak memory usage: 10 MB
% 1.01/0.38 % (3185763)Instructions burned: 3 (million)
% 1.01/0.38 % (3185766)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=33077970:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 1.01/0.38 % (3185764)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3601802202:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 1.01/0.38 % (3185764)Instruction limit reached!
% 1.01/0.38 % (3185764)------------------------------
% 1.01/0.38 % (3185764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.38 % (3185764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.38 % (3185764)CaDiCaL version: 2.1.3
% 1.01/0.38 % (3185764)Termination reason: Instruction limit
% 1.01/0.38 % (3185764)Termination phase: shuffling
% 1.01/0.38 % (3185764)Time elapsed: 0.002 s
% 1.01/0.38 % (3185764)Peak memory usage: 10 MB
% 1.01/0.38 % (3185764)Instructions burned: 5 (million)
% 1.01/0.38 % (3185766)Instruction limit reached!
% 1.01/0.38 % (3185766)------------------------------
% 1.01/0.38 % (3185766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.38 % (3185766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.38 % (3185766)CaDiCaL version: 2.1.3
% 1.01/0.38 % (3185766)Termination reason: Instruction limit
% 1.01/0.38 % (3185766)Termination phase: SInE selection
% 1.01/0.38 % (3185766)Time elapsed: 0.004 s
% 1.01/0.38 % (3185766)Peak memory usage: 10 MB
% 1.01/0.38 % (3185766)Instructions burned: 16 (million)
% 1.01/0.38 % (3185765)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.01/0.38 % (3185765)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=3566027120:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 1.01/0.38 % (3185768)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
% 1.01/0.38 % (3185768)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 1.01/0.38 % (3185765)Instruction limit reached!
% 1.01/0.38 % (3185765)------------------------------
% 1.01/0.38 % (3185765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.38 % (3185765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.38 % (3185765)CaDiCaL version: 2.1.3
% 1.01/0.38 % (3185765)Termination reason: Instruction limit
% 1.01/0.38 % (3185765)Termination phase: shuffling
% 1.01/0.38 % (3185765)Time elapsed: 0.003 s
% 1.01/0.38 % (3185765)Peak memory usage: 10 MB
% 1.01/0.38 % (3185765)Instructions burned: 7 (million)
% 1.01/0.38 % (3185771)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=1029210047:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 1.01/0.38 % (3185768)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3249473006:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 1.01/0.38 % (3185749)Instruction limit reached!
% 1.01/0.38 % (3185749)------------------------------
% 1.01/0.38 % (3185749)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.38 % (3185749)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.38 % (3185749)CaDiCaL version: 2.1.3
% 1.01/0.38 % (3185749)Termination reason: Instruction limit
% 1.01/0.38 % (3185749)Termination phase: Saturation
% 1.01/0.38 % (3185749)Time elapsed: 0.043 s
% 1.01/0.38 % (3185749)Peak memory usage: 13 MB
% 1.01/0.38 % (3185749)Instructions burned: 87 (million)
% 1.01/0.38 % (3185772)lrs+10_1_si=on:cs=on:random_seed=3574092488:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 1.01/0.38 % (3185774)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 1.01/0.40 % (3185772)Instruction limit reached!
% 1.01/0.40 % (3185772)------------------------------
% 1.01/0.40 % (3185772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185772)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185772)Termination reason: Instruction limit
% 1.01/0.40 % (3185772)Termination phase: Property scanning
% 1.01/0.40 % (3185772)Time elapsed: 0.004 s
% 1.01/0.40 % (3185772)Peak memory usage: 10 MB
% 1.01/0.40 % (3185772)Instructions burned: 9 (million)
% 1.01/0.40 % (3185768)Instruction limit reached!
% 1.01/0.40 % (3185768)------------------------------
% 1.01/0.40 % (3185768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185768)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185768)Termination reason: Instruction limit
% 1.01/0.40 % (3185768)Termination phase: Property scanning
% 1.01/0.40 % (3185768)Time elapsed: 0.012 s
% 1.01/0.40 % (3185768)Peak memory usage: 11 MB
% 1.01/0.40 % (3185768)Instructions burned: 28 (million)
% 1.01/0.40 % (3185774)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1108310739:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 1.01/0.40 % (3185774)Instruction limit reached!
% 1.01/0.40 % (3185774)------------------------------
% 1.01/0.40 % (3185774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185774)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185774)Termination reason: Instruction limit
% 1.01/0.40 % (3185774)Termination phase: shuffling
% 1.01/0.40 % (3185774)Time elapsed: 0.002 s
% 1.01/0.40 % (3185774)Peak memory usage: 10 MB
% 1.01/0.40 % (3185774)Instructions burned: 4 (million)
% 1.01/0.40 % (3185771)Instruction limit reached!
% 1.01/0.40 % (3185771)------------------------------
% 1.01/0.40 % (3185771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185771)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185771)Termination reason: Instruction limit
% 1.01/0.40 % (3185771)Termination phase: Saturation
% 1.01/0.40 % (3185771)Time elapsed: 0.020 s
% 1.01/0.40 % (3185771)Peak memory usage: 13 MB
% 1.01/0.40 % (3185771)Instructions burned: 91 (million)
% 1.01/0.40 % (3185777)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3456779798:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 1.01/0.40 % (3185755)Instruction limit reached!
% 1.01/0.40 % (3185755)------------------------------
% 1.01/0.40 % (3185755)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185755)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185755)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185755)Termination reason: Instruction limit
% 1.01/0.40 % (3185755)Termination phase: Saturation
% 1.01/0.40 % (3185755)Time elapsed: 0.067 s
% 1.01/0.40 % (3185755)Peak memory usage: 14 MB
% 1.01/0.40 % (3185755)Instructions burned: 158 (million)
% 1.01/0.40 % (3185781)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2601756806:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 1.01/0.40 % (3185788)dis+1010_1_sil=128000:si=on:uwa=off:random_seed=512826757:st=3:s2a=on:i=327:sd=3:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/327Mi)
% 1.01/0.40 % (3185782)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2757221348:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/25Mi)
% 1.01/0.40 % (3185786)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=3486580893:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2999 on theBenchmark for (2999ds/14Mi)
% 1.01/0.40 % (3185777)Instruction limit reached!
% 1.01/0.40 % (3185777)------------------------------
% 1.01/0.40 % (3185777)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185777)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185777)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185777)Termination reason: Instruction limit
% 1.01/0.40 % (3185777)Termination phase: Property scanning
% 1.01/0.40 % (3185777)Time elapsed: 0.018 s
% 1.01/0.40 % (3185777)Peak memory usage: 11 MB
% 1.01/0.40 % (3185777)Instructions burned: 38 (million)
% 1.01/0.40 % (3185786)Instruction limit reached!
% 1.01/0.40 % (3185786)------------------------------
% 1.01/0.40 % (3185786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185786)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185786)Termination reason: Instruction limit
% 1.01/0.40 % (3185786)Termination phase: Naming
% 1.01/0.40 % (3185786)Time elapsed: 0.007 s
% 1.01/0.40 % (3185786)Peak memory usage: 10 MB
% 1.01/0.40 % (3185786)Instructions burned: 16 (million)
% 1.01/0.40 % (3185782)Instruction limit reached!
% 1.01/0.40 % (3185782)------------------------------
% 1.01/0.40 % (3185782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185782)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185782)Termination reason: Instruction limit
% 1.01/0.40 % (3185782)Termination phase: Property scanning
% 1.01/0.40 % (3185782)Time elapsed: 0.013 s
% 1.01/0.40 % (3185793)dis+10_1_anc=all_dependent:to=kbo:sil=128000:si=on:chr=on:random_seed=2752904679:uwa_fpi=on:i=14:aac=none:rtra=on:fe=abstraction_2998 on theBenchmark for (2998ds/14Mi)
% 1.01/0.40 % (3185782)Peak memory usage: 11 MB
% 1.01/0.40 % (3185782)Instructions burned: 26 (million)
% 1.01/0.40 % (3185793)Instruction limit reached!
% 1.01/0.40 % (3185793)------------------------------
% 1.01/0.40 % (3185793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185793)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185793)Termination reason: Instruction limit
% 1.01/0.40 % (3185793)Termination phase: Preprocessing 3
% 1.01/0.40 % (3185793)Time elapsed: 0.007 s
% 1.01/0.40 % (3185793)Peak memory usage: 10 MB
% 1.01/0.40 % (3185793)Instructions burned: 16 (million)
% 1.01/0.40 % (3185804)ott+21_20_to=lpo:sil=128000:tgt=ground:si=on:sp=arity:lma=off:uwa=off:foolp=on:random_seed=1397266032:st=4:i=2:add=off:sd=3:nm=16:fsr=off:rtra=on:ss=axioms:sgt=8:ntd=on_2998 on theBenchmark for (2998ds/2Mi)
% 1.01/0.40 % (3185804)Instruction limit reached!
% 1.01/0.40 % (3185804)------------------------------
% 1.01/0.40 % (3185804)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185804)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185804)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185804)Termination reason: Instruction limit
% 1.01/0.40 % (3185804)Termination phase: shuffling
% 1.01/0.40 % (3185804)Time elapsed: 0.002 s
% 1.01/0.40 % (3185804)Peak memory usage: 10 MB
% 1.01/0.40 % (3185804)Instructions burned: 5 (million)
% 1.01/0.40 % (3185808)ott+1004_1_sil=128000:cnfonf=lazy_pi_sigma_gen:si=on:sp=unary_frequency:cbe=off:uwa=off:nwc=1:random_seed=137708071:i=26:ep=R:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/26Mi)
% 1.01/0.40 % (3185810)dis+1002_16_sil=128000:si=on:sp=occurrence:random_seed=4023031419:cond=fast:i=23:hud=1:av=off:rtra=on:fe=abstraction:ntd=on_2998 on theBenchmark for (2998ds/23Mi)
% 1.01/0.40 % (3185814)lrs+1002_1024_sil=128000:tgt=ground:fde=none:e2e=on:si=on:uwa=off:nwc=1:random_seed=2170063670:cond=on:i=60:rtra=on:ntd=on_2998 on theBenchmark for (2998ds/60Mi)
% 1.01/0.40 % (3185810)Instruction limit reached!
% 1.01/0.40 % (3185810)------------------------------
% 1.01/0.40 % (3185810)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185810)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185810)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185810)Termination reason: Instruction limit
% 1.01/0.40 % (3185810)Termination phase: Function definition elimination
% 1.01/0.40 % (3185810)Time elapsed: 0.010 s
% 1.01/0.40 % (3185810)Peak memory usage: 11 MB
% 1.01/0.40 % (3185810)Instructions burned: 23 (million)
% 1.01/0.40 % (3185808)Instruction limit reached!
% 1.01/0.40 % (3185808)------------------------------
% 1.01/0.40 % (3185808)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185808)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185808)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185808)Termination reason: Instruction limit
% 1.01/0.40 % (3185808)Termination phase: Property scanning
% 1.01/0.40 % (3185808)Time elapsed: 0.011 s
% 1.01/0.40 % (3185808)Peak memory usage: 10 MB
% 1.01/0.40 % (3185808)Instructions burned: 27 (million)
% 1.01/0.40 % (3185819)WARNING Broken Constraint: if sine_to_age_generality_threshold(10) 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
% 1.01/0.40 % (3185819)WARNING Broken Constraint: if lrs_weight_limit_only(on) has been set then saturation_algorithm(otter) is equal to lrs
% 1.01/0.40 % (3185819)ott+21_1_to=kbo:sil=128000:cnfonf=lazy_gen:bsd=on:si=on:sp=const_frequency:lma=off:uwa=off:foolp=on:s2agt=10:lwlo=on:random_seed=3032179525:i=14:add=off:nm=40:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.01/0.40 % (3185819)Instruction limit reached!
% 1.01/0.40 % (3185819)------------------------------
% 1.01/0.40 % (3185819)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.40 % (3185819)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.40 % (3185819)CaDiCaL version: 2.1.3
% 1.01/0.40 % (3185819)Termination reason: Instruction limit
% 1.01/0.40 % (3185819)Termination phase: Property scanning
% 1.01/0.40 % (3185819)Time elapsed: 0.006 s
% 1.01/0.40 % (3185819)Peak memory usage: 10 MB
% 1.01/0.40 % (3185819)Instructions burned: 15 (million)
% 1.01/0.40 % (3185788) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3185744-3185788"...
% 1.01/0.40 % (3185828)WARNING Broken Constraint: if choice_reasoning(on) has been set then choice_ax(on) is equal to off
% 1.01/0.40 % (3185788)...printing done.
% 1.01/0.40 % (3185788)Refutation found. Thanks to Tanya!
% 1.01/0.40 % SZS status Theorem for theBenchmark
% 1.01/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 1.01/0.41 % (3185788)------------------------------
% 1.01/0.41 % (3185788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.01/0.41 % (3185788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.01/0.41 % (3185788)CaDiCaL version: 2.1.3
% 1.01/0.41 % (3185788)Termination reason: Refutation
% 1.01/0.41 % (3185788)Time elapsed: 0.060 s
% 1.01/0.41 % (3185788)Peak memory usage: 14 MB
% 1.01/0.41 % (3185788)Instructions burned: 222 (million)
% 1.01/0.41 % (3185744)Success in time 0.17 s
% 1.01/0.41 % Vampire exiting
%------------------------------------------------------------------------------