%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU556^1 : 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 : 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 08:30:03 AM UTC 2026
% Result : Theorem 0.22s 0.33s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 2
% Syntax : Number of formulae : 32 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 1682 ( 497 equ; 0 cnn)
% Maximal formula atoms : 76 ( 52 avg)
% Number of connectives : 805 ( 9 ~; 4 |; 308 &; 87 @)
% ( 0 <=>; 386 =>; 0 <=; 0 <~>)
% Maximal formula depth : 81 ( 23 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 224 ( 219 usr; 86 con; 0-4 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 61 ( 29 ^; 21 !; 11 ?; 61 :)
% 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_87,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_88,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_89,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_90,type,
vAND: $o > $o > $o ).
thf(func_def_91,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_92,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_93,type,
vIMP: $o > $o > $o ).
thf(func_def_94,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_95,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_96,type,
vNOT: $o > $o ).
thf(func_def_97,type,
sP0: $i > $i > $o ).
thf(func_def_98,type,
sP1: $i > $o ).
thf(func_def_99,type,
sP2: $i > $i > $o ).
thf(func_def_100,type,
sP3: $i > $i > $o ).
thf(func_def_101,type,
sP4: $o ).
thf(func_def_106,type,
sK9: $o > $i > $i > $i ).
thf(func_def_109,type,
sK12: $o ).
thf(func_def_110,type,
sK13: $i > $i ).
thf(func_def_112,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_113,type,
sK16: $i > $o ).
thf(func_def_114,type,
sK17: $i > $i ).
thf(func_def_115,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_116,type,
sK19: $i > $o ).
thf(func_def_124,type,
sK27: ( $i > $o ) > $i > $i ).
thf(func_def_126,type,
sK29: $i > $o ).
thf(func_def_130,type,
sK33: $i > $o ).
thf(func_def_134,type,
sK37: $o ).
thf(func_def_135,type,
sK38: $i > $o ).
thf(func_def_136,type,
sK39: ( $i > $o ) > $i ).
thf(func_def_138,type,
sK41: $i > $o ).
thf(func_def_140,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_141,type,
sK44: $i > $o ).
thf(func_def_142,type,
sK45: $i > $o ).
thf(func_def_143,type,
sK46: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_144,type,
sK47: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_145,type,
sK48: $i > $o ).
thf(func_def_149,type,
sK52: $i > $i ).
thf(func_def_153,type,
sK56: $i > $i > $i ).
thf(func_def_154,type,
sK57: $o ).
thf(func_def_155,type,
sK58: $i > $i > $i ).
thf(func_def_156,type,
sK59: $i > $i > $i ).
thf(func_def_157,type,
sK60: $i > $i > $i ).
thf(func_def_158,type,
sK61: $i > $i > $i ).
thf(func_def_159,type,
sK62: $i > $i > $i > $i ).
thf(func_def_160,type,
sK63: $i > $i ).
thf(func_def_161,type,
sK64: $i > $i ).
thf(func_def_162,type,
sK65: $i > $i ).
thf(func_def_163,type,
sK66: $i > $i ).
thf(func_def_164,type,
sK67: $i > $i > $i ).
thf(func_def_165,type,
sK68: $i > $i > $i > $i ).
thf(func_def_166,type,
sK69: $i > $i > $i > $i ).
thf(func_def_167,type,
sK70: $i > $i > $i ).
thf(func_def_168,type,
sK71: $i > $i > $i ).
thf(func_def_170,type,
sK73: $i > $i ).
thf(func_def_171,type,
sK74: $i > $i ).
thf(func_def_172,type,
sK75: $i > $i ).
thf(func_def_173,type,
sK76: $i > $i > $i ).
thf(func_def_174,type,
sK77: $i > $i > $i ).
thf(func_def_175,type,
sK78: $i > $i > $i ).
thf(func_def_180,type,
sK83: $o ).
thf(func_def_182,type,
sK85: $i > $o ).
thf(func_def_185,type,
sK88: ( $i > $o ) > $i > $i ).
thf(func_def_187,type,
sK90: $i > $o ).
thf(func_def_189,type,
sK92: $i > $o ).
thf(func_def_190,type,
sK93: $i > $i ).
thf(func_def_191,type,
sK94: ( $i > $o ) > $i ).
thf(func_def_197,type,
sK100: $i > ( $i > $o ) > $i ).
thf(func_def_198,type,
sK101: $i > $o ).
thf(func_def_206,type,
sK109: $i > $i > $i ).
thf(func_def_211,type,
sK114: $i > $i > $i ).
thf(func_def_216,type,
sK119: $i > $o ).
thf(func_def_221,type,
sK124: $i > $o ).
thf(func_def_226,type,
sK129: $i > $o ).
thf(func_def_227,type,
sK130: $i > ( $i > $o ) > $i ).
thf(func_def_228,type,
sK131: $i > $o ).
thf(func_def_235,type,
sK138: $i > $i ).
thf(func_def_240,type,
sK143: $i > $i > $i ).
thf(func_def_246,type,
sK149: $i > $i ).
thf(func_def_252,type,
sK155: $i > ( $i > $o ) > $i ).
thf(func_def_253,type,
sK156: $i > $o ).
thf(func_def_256,type,
sK159: $i > $i ).
thf(func_def_258,type,
sK161: ( $i > $o ) > $i ).
thf(func_def_259,type,
sK162: ( $i > $o ) > $i ).
thf(func_def_260,type,
sK163: $i > $o ).
thf(func_def_267,type,
sK170: $i > $o ).
thf(func_def_269,type,
sK172: $i > $o ).
thf(func_def_272,type,
sK175: $o ).
thf(func_def_273,type,
sK176: $i > $o ).
thf(func_def_275,type,
sK178: $i > ( $i > $o ) > $i ).
thf(func_def_285,type,
sK188: $i > $o ).
thf(func_def_286,type,
sK189: $i > $o ).
thf(func_def_290,type,
sK193: $o ).
thf(func_def_291,type,
sK194: $i > $i ).
thf(func_def_293,type,
sK196: $i > $i ).
thf(func_def_296,type,
sK199: $i > $i > $o ).
thf(func_def_297,type,
sK200: $i > $i ).
thf(func_def_298,type,
sK201: $i > $i ).
thf(func_def_299,type,
sK202: ( $i > $i > $o ) > $i > $i ).
thf(func_def_300,type,
sK203: ( $i > $i > $o ) > $i > $i ).
thf(func_def_301,type,
sK204: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_307,type,
sK210: $i > ( $i > $o ) > $i ).
thf(func_def_308,type,
sK211: ( $i > $o ) > $i ).
thf(func_def_309,type,
sK212: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_310,type,
sK213: ( $i > $o ) > $i ).
thf(func_def_311,type,
sK214: ( $i > $o ) > $i ).
thf(func_def_312,type,
sK215: $i > $i ).
thf(func_def_313,type,
sK216: ( $i > $o ) > $i ).
thf(func_def_314,type,
sK217: ( $i > $o ) > $i > $i ).
thf(func_def_315,type,
sK218: $i > ( $i > $o ) > $i ).
thf(func_def_316,type,
sK219: ( $i > $o ) > $i ).
thf(func_def_317,type,
sK220: ( $i > $o ) > $i ).
thf(func_def_318,type,
sK221: ( $i > $o ) > $i > $i ).
thf(func_def_319,type,
sK222: ( $i > $o ) > $i ).
thf(func_def_320,type,
sK223: ( $i > $o ) > $i > $i ).
thf(func_def_321,type,
sK224: $i > ( $i > $o ) > $i ).
thf(func_def_322,type,
sK225: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_323,type,
sK226: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_324,type,
sK227: ( $i > $o ) > $i ).
thf(func_def_325,type,
sK228: ( $i > $o ) > $i > $i ).
thf(func_def_326,type,
sK229: ( $i > $o ) > $i > $i ).
thf(func_def_327,type,
sK230: ( $i > $o ) > $i ).
thf(func_def_328,type,
sK231: ( $i > $o ) > $i > $i ).
thf(func_def_329,type,
sK232: ( $i > $o ) > $i > $i ).
thf(func_def_330,type,
sK233: ( $i > $o ) > $i ).
thf(func_def_331,type,
sK234: ( $i > $o ) > $i > $i ).
thf(func_def_332,type,
sK235: ( $i > $o ) > $i > $i ).
thf(func_def_333,type,
sK236: ( $i > $o ) > $i ).
thf(func_def_334,type,
sK237: ( $i > $o ) > $i > $i ).
thf(func_def_336,type,
sK239: ( $i > $o ) > $i ).
thf(func_def_337,type,
sK240: $i > ( $i > $o ) > $i ).
thf(func_def_338,type,
sK241: ( $i > $o ) > $i ).
thf(func_def_339,type,
sK242: ( $i > $o ) > $i > $i ).
thf(func_def_340,type,
sK243: ( $i > $o ) > $i > $i ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) )
= exu ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(f75,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
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ! [X2: $i,X1: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(f76,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
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ! [X2: $i,X1: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f75]) ).
thf(f105,plain,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) )
& ( X0 @ X1 ) ) )
= exu ),
inference(rectify,[],[f1]) ).
thf(f106,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f105]) ).
thf(f174,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
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ! [X2: $i,X3: $i] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f76]) ).
thf(f175,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 )
=> ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ! [X2: $i,X3: $i] :
( ( ( X0 @ X3 )
= $true )
=> ( ( ( X0 @ X2 )
= $true )
=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f174]) ).
thf(f237,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 )
=> ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ! [X1: $i,X2: $i] :
( ( ( X0 @ X2 )
= $true )
=> ( ( ( X0 @ X1 )
= $true )
=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f175]) ).
thf(f256,plain,
( ? [X0: $i > $o] :
( ? [X1: $i,X2: $i] :
( ( X1 != X2 )
& ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $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,[],[f237]) ).
thf(f257,plain,
( ( emptysetE = $true )
& ( emptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( uniqinunit = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( powersetE = $true )
& ( emptysetimpfalse = $true )
& ( setoftrueEq = $true )
& ( subPowSU = $true )
& ( prop2setI = $true )
& ( setext = $true )
& ( emptysetAx = $true )
& ( vacuousDall = $true )
& ( in__Cong = $true )
& ( upairsetIL = $true )
& ( powersetAx = $true )
& ( foundationAx = $true )
& ( powerset__Cong = $true )
& ( exuE3e = $true )
& ( dsetconstrER = $true )
& ( exuI1 = $true )
& ( eqinunit = $true )
& ( dsetconstrEL = $true )
& ( notdallE = $true )
& ( nonemptyI1 = $true )
& ( emptyI = $true )
& ( setadjoinIL = $true )
& ( setadjoinAx = $true )
& ( setunion__Cong = $true )
& ( exuI3 = $true )
& ( prop2setE = $true )
& ( setextAx = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIR = $true )
& ( replAx = $true )
& ( exuE1 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ? [X0: $i > $o] :
( ? [X2: $i,X1: $i] :
( ( X1 != X2 )
& ( ( X0 @ X2 )
= $true )
& ( ( X0 @ X1 )
= $true ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( inCongP = $true )
& ( nonemptyI = $true )
& ( omegaIndAx = $true )
& ( upairsetE = $true )
& ( omega__Cong = $true )
& ( singletonsswitch = $true )
& ( notinsingleton = $true )
& ( setadjoinOr = $true )
& ( emptyset__Cong = $true )
& ( prop2set2propI = $true )
& ( setunionI = $true )
& ( notdexE = $true )
& ( descrp = $true )
& ( exuE3u = $true )
& ( notinemptyset = $true )
& ( quantDeMorgan4 = $true )
& ( setunionE = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( wellorderingAx = $true )
& ( dsetconstrI = $true )
& ( exuE2 = $true )
& ( emptyinPowerset = $true )
& ( setadjoin__Cong = $true )
& ( exu__Cong = $true )
& ( setadjoinE = $true )
& ( setunionAx = $true )
& ( upairsetIR = $true )
& ( emptyInPowerset = $true )
& ( emptyinunitempty = $true )
& ( exuI2 = $true ) ),
inference(flattening,[],[f256]) ).
thf(f361,plain,
( ( emptysetE = $true )
& ( emptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( uniqinunit = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( powersetE = $true )
& ( emptysetimpfalse = $true )
& ( setoftrueEq = $true )
& ( subPowSU = $true )
& ( prop2setI = $true )
& ( setext = $true )
& ( emptysetAx = $true )
& ( vacuousDall = $true )
& ( in__Cong = $true )
& ( upairsetIL = $true )
& ( powersetAx = $true )
& ( foundationAx = $true )
& ( powerset__Cong = $true )
& ( exuE3e = $true )
& ( dsetconstrER = $true )
& ( exuI1 = $true )
& ( eqinunit = $true )
& ( dsetconstrEL = $true )
& ( notdallE = $true )
& ( nonemptyI1 = $true )
& ( emptyI = $true )
& ( setadjoinIL = $true )
& ( setadjoinAx = $true )
& ( setunion__Cong = $true )
& ( exuI3 = $true )
& ( prop2setE = $true )
& ( setextAx = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIR = $true )
& ( replAx = $true )
& ( exuE1 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ? [X0: $i > $o] :
( ? [X1: $i,X2: $i] :
( ( X1 != X2 )
& ( ( X0 @ X1 )
= $true )
& ( ( X0 @ X2 )
= $true ) )
& ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true ) )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( inCongP = $true )
& ( nonemptyI = $true )
& ( omegaIndAx = $true )
& ( upairsetE = $true )
& ( omega__Cong = $true )
& ( singletonsswitch = $true )
& ( notinsingleton = $true )
& ( setadjoinOr = $true )
& ( emptyset__Cong = $true )
& ( prop2set2propI = $true )
& ( setunionI = $true )
& ( notdexE = $true )
& ( descrp = $true )
& ( exuE3u = $true )
& ( notinemptyset = $true )
& ( quantDeMorgan4 = $true )
& ( setunionE = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( wellorderingAx = $true )
& ( dsetconstrI = $true )
& ( exuE2 = $true )
& ( emptyinPowerset = $true )
& ( setadjoin__Cong = $true )
& ( exu__Cong = $true )
& ( setadjoinE = $true )
& ( setunionAx = $true )
& ( upairsetIR = $true )
& ( emptyInPowerset = $true )
& ( emptyinunitempty = $true )
& ( exuI2 = $true ) ),
inference(rectify,[],[f257]) ).
thf(f362,plain,
( ( emptysetE = $true )
& ( emptyE1 = $true )
& ( nonemptyImpWitness = $true )
& ( uniqinunit = $true )
& ( powersetI = $true )
& ( omegaSAx = $true )
& ( powersetE = $true )
& ( emptysetimpfalse = $true )
& ( setoftrueEq = $true )
& ( subPowSU = $true )
& ( prop2setI = $true )
& ( setext = $true )
& ( emptysetAx = $true )
& ( vacuousDall = $true )
& ( in__Cong = $true )
& ( upairsetIL = $true )
& ( powersetAx = $true )
& ( foundationAx = $true )
& ( powerset__Cong = $true )
& ( exuE3e = $true )
& ( dsetconstrER = $true )
& ( exuI1 = $true )
& ( eqinunit = $true )
& ( dsetconstrEL = $true )
& ( notdallE = $true )
& ( nonemptyI1 = $true )
& ( emptyI = $true )
& ( setadjoinIL = $true )
& ( setadjoinAx = $true )
& ( setunion__Cong = $true )
& ( exuI3 = $true )
& ( prop2setE = $true )
& ( setextAx = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIR = $true )
& ( replAx = $true )
& ( exuE1 = $true )
& ( nonemptyE1 = $true )
& ( omega0Ax = $true )
& ( sK50 != sK49 )
& ( ( sK48 @ sK49 )
= $true )
& ( ( sK48 @ sK50 )
= $true )
& ( ( exu
@ ^ [Y0: $i] : ( sK48 @ Y0 ) )
= $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( inCongP = $true )
& ( nonemptyI = $true )
& ( omegaIndAx = $true )
& ( upairsetE = $true )
& ( omega__Cong = $true )
& ( singletonsswitch = $true )
& ( notinsingleton = $true )
& ( setadjoinOr = $true )
& ( emptyset__Cong = $true )
& ( prop2set2propI = $true )
& ( setunionI = $true )
& ( notdexE = $true )
& ( descrp = $true )
& ( exuE3u = $true )
& ( notinemptyset = $true )
& ( quantDeMorgan4 = $true )
& ( setunionE = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( wellorderingAx = $true )
& ( dsetconstrI = $true )
& ( exuE2 = $true )
& ( emptyinPowerset = $true )
& ( setadjoin__Cong = $true )
& ( exu__Cong = $true )
& ( setadjoinE = $true )
& ( setunionAx = $true )
& ( upairsetIR = $true )
& ( emptyInPowerset = $true )
& ( emptyinunitempty = $true )
& ( exuI2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK48,sK49,sK50]),skolemize(X0,sK48),skolemize(X1,sK49),skolemize(X2,sK50)],[f361]) ).
thf(f638,plain,
( ( exu
@ ^ [Y0: $i] : ( sK48 @ Y0 ) )
= $true ),
inference(cnf_transformation,[],[f362]) ).
thf(f639,plain,
( ( sK48 @ sK50 )
= $true ),
inference(cnf_transformation,[],[f362]) ).
thf(f640,plain,
( ( sK48 @ sK49 )
= $true ),
inference(cnf_transformation,[],[f362]) ).
thf(f641,plain,
sK50 != sK49,
inference(cnf_transformation,[],[f362]) ).
thf(f812,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f106]) ).
thf(f994,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
& ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) ) ) )
@ ^ [Y0: $i] : ( sK48 @ Y0 ) )
= $true ),
inference(definition_unfolding,[],[f638,f812]) ).
thf(f1586,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( sK48 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK48 @ Y1 )
=> ( Y0 = Y1 ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f994]) ).
thf(f1587,plain,
( ( ^ [Y0: $i] :
( ( sK48 @ Y0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( sK48 @ Y1 )
=> ( Y0 = Y1 ) ) ) )
@ sK238 )
= $true ),
inference(sigma_proxy_clausification,[],[f1586]) ).
thf(f1588,plain,
( ( ( sK48 @ sK238 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK48 @ Y0 )
=> ( sK238 = Y0 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f1587]) ).
thf(f1589,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK48 @ Y0 )
=> ( sK238 = Y0 ) ) )
= $true ),
inference(and_proxy_clausification,[],[f1588]) ).
thf(f1591,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( sK48 @ Y0 )
=> ( sK238 = Y0 ) )
@ X1 )
= $true ),
inference(pi_proxy_clausification,[],[f1589]) ).
thf(f1592,plain,
! [X1: $i] :
( ( ( sK48 @ X1 )
=> ( sK238 = X1 ) )
= $true ),
inference(beta-eta_normalization,[],[f1591]) ).
thf(f1593,plain,
! [X1: $i] :
( ( ( sK48 @ X1 )
= $false )
| ( ( sK238 = X1 )
= $true ) ),
inference(imp_proxy_clausification,[],[f1592]) ).
thf(f1594,plain,
! [X1: $i] :
( ( ( sK48 @ X1 )
= $false )
| ( sK238 = X1 ) ),
inference(equality_proxy_clausification,[],[f1593]) ).
thf(f1733,plain,
( ( $false = $true )
| ( sK238 = sK50 ) ),
inference(constrained_superposition,[],[f1594,f639]) ).
thf(f1734,plain,
( ( sK238 = sK49 )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f640,f1594]) ).
thf(f1736,plain,
sK238 = sK50,
inference(trivial_inequality_removal,[],[f1733]) ).
thf(f1737,plain,
sK238 = sK49,
inference(trivial_inequality_removal,[],[f1734]) ).
thf(f1740,plain,
sK50 = sK49,
inference(forward_demodulation,[],[f1737,f1736]) ).
thf(f1742,plain,
$false,
inference(forward_subsumption_resolution,[],[f1740,f641]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU556^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n001.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 13:55:50 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 Running higher-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.22/0.33 % (1279185)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.33 % (1279198)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4294212381:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.22/0.33 % (1279200)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.33 % (1279200)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
% 0.22/0.33 % (1279198)Instruction limit reached!
% 0.22/0.33 % (1279198)------------------------------
% 0.22/0.33 % (1279198)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1279198)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1279198)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1279198)Termination reason: Instruction limit
% 0.22/0.33 % (1279198)Termination phase: Property scanning
% 0.22/0.33 % (1279198)Time elapsed: 0.006 s
% 0.22/0.33 % (1279198)Peak memory usage: 11 MB
% 0.22/0.33 % (1279198)Instructions burned: 25 (million)
% 0.22/0.33 % (1279194)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3102255837:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.22/0.33 % (1279195)lrs+10_16_si=on:nwc=1.5:random_seed=3355777479:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.22/0.33 % (1279196)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=291740324:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.22/0.33 % (1279199)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1032994378:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.22/0.33 % (1279197)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=1992966321: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)
% 0.22/0.33 % (1279200)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=438991878:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.22/0.33 % (1279196)Instruction limit reached!
% 0.22/0.33 % (1279196)------------------------------
% 0.22/0.33 % (1279196)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1279196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1279196)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1279196)Termination reason: Instruction limit
% 0.22/0.33 % (1279196)Termination phase: shuffling
% 0.22/0.33 % (1279196)Time elapsed: 0.002 s
% 0.22/0.33 % (1279196)Peak memory usage: 10 MB
% 0.22/0.33 % (1279196)Instructions burned: 4 (million)
% 0.22/0.33 % (1279195)Instruction limit reached!
% 0.22/0.33 % (1279195)------------------------------
% 0.22/0.33 % (1279195)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1279195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1279195)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1279195)Termination reason: Instruction limit
% 0.22/0.33 % (1279195)Termination phase: Property scanning
% 0.22/0.33 % (1279195)Time elapsed: 0.008 s
% 0.22/0.33 % (1279195)Peak memory usage: 10 MB
% 0.22/0.33 % (1279195)Instructions burned: 19 (million)
% 0.22/0.33 % (1279214)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=110912963:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.22/0.33 % (1279214)Instruction limit reached!
% 0.22/0.33 % (1279214)------------------------------
% 0.22/0.33 % (1279214)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1279214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1279214)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1279214)Termination reason: Instruction limit
% 0.22/0.33 % (1279214)Termination phase: shuffling
% 0.22/0.33 % (1279214)Time elapsed: 0.001 s
% 0.22/0.33 % (1279214)Peak memory usage: 10 MB
% 0.22/0.33 % (1279214)Instructions burned: 4 (million)
% 0.22/0.33 % (1279230)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3152943564:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.22/0.33 % (1279222)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=454111878:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.22/0.33 % (1279228)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.33 % (1279230)Instruction limit reached!
% 0.22/0.33 % (1279230)------------------------------
% 0.22/0.33 % (1279230)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1279230)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1279230)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1279230)Termination reason: Instruction limit
% 0.22/0.33 % (1279230)Termination phase: Property scanning
% 0.22/0.33 % (1279230)Time elapsed: 0.003 s
% 0.22/0.33 % (1279230)Peak memory usage: 10 MB
% 0.22/0.33 % (1279230)Instructions burned: 14 (million)
% 0.22/0.33 % (1279222)Instruction limit reached!
% 0.22/0.33 % (1279222)------------------------------
% 0.22/0.33 % (1279222)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1279222)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1279222)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1279222)Termination reason: Instruction limit
% 0.22/0.33 % (1279222)Termination phase: shuffling
% 0.22/0.33 % (1279222)Time elapsed: 0.003 s
% 0.22/0.33 % (1279222)Peak memory usage: 10 MB
% 0.22/0.33 % (1279222)Instructions burned: 6 (million)
% 0.22/0.33 % (1279228)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1907347117:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.22/0.33 % (1279228)Instruction limit reached!
% 0.22/0.33 % (1279228)------------------------------
% 0.22/0.33 % (1279228)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1279228)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1279228)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1279228)Termination reason: Instruction limit
% 0.22/0.33 % (1279228)Termination phase: Property scanning
% 0.22/0.33 % (1279228)Time elapsed: 0.004 s
% 0.22/0.33 % (1279228)Peak memory usage: 10 MB
% 0.22/0.33 % (1279228)Instructions burned: 9 (million)
% 0.22/0.33 % (1279242)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
% 0.22/0.33 % (1279242)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.22/0.33 % (1279242)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1481170056:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.22/0.33 % (1279199)Instruction limit reached!
% 0.22/0.33 % (1279199)------------------------------
% 0.22/0.33 % (1279199)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1279199)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1279199)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1279199)Termination reason: Instruction limit
% 0.22/0.33 % (1279199)Termination phase: Saturation
% 0.22/0.33 % (1279199)Time elapsed: 0.036 s
% 0.22/0.33 % (1279199)Peak memory usage: 13 MB
% 0.22/0.33 % (1279199)Instructions burned: 76 (million)
% 0.22/0.33 % (1279194) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1279185-1279194"...
% 0.22/0.33 % (1279194)...printing done.
% 0.22/0.33 % (1279242)Instruction limit reached!
% 0.22/0.33 % (1279242)------------------------------
% 0.22/0.33 % (1279242)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1279242)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1279242)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1279242)Termination reason: Instruction limit
% 0.22/0.33 % (1279242)Termination phase: Property scanning
% 0.22/0.33 % (1279242)Time elapsed: 0.006 s
% 0.22/0.33 % (1279242)Peak memory usage: 11 MB
% 0.22/0.33 % (1279242)Instructions burned: 29 (million)
% 0.22/0.33 % (1279194)Refutation found. Thanks to Tanya!
% 0.22/0.33 % SZS status Theorem for theBenchmark
% 0.22/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.33 % (1279194)------------------------------
% 0.22/0.33 % (1279194)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.33 % (1279194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.33 % (1279194)CaDiCaL version: 2.1.3
% 0.22/0.33 % (1279194)Termination reason: Refutation
% 0.22/0.33 % (1279194)Time elapsed: 0.040 s
% 0.22/0.33 % (1279194)Peak memory usage: 13 MB
% 0.22/0.33 % (1279194)Instructions burned: 82 (million)
% 0.22/0.33 % (1279185)Success in time 0.077 s
% 0.22/0.33 % Vampire exiting
%------------------------------------------------------------------------------