%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU608^1 : 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 : n002.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 08:30:18 AM UTC 2026
% Result : Theorem 0.68s 0.38s
% Output : Refutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 2853 ( 803 equ; 0 cnn)
% Maximal formula atoms : 126 ( 63 avg)
% Number of connectives : 1386 ( 53 ~; 31 |; 506 &; 160 @)
% ( 7 <=>; 629 =>; 0 <=; 0 <~>)
% Maximal formula depth : 134 ( 29 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 267 ( 264 usr; 144 con; 0-4 aty)
% Number of variables : 63 ( 0 sgn 48 !; 15 ?; 63 :)
% 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,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_133,type,
binintersectSubset1: $o ).
thf(func_def_134,type,
bs114d: $o ).
thf(func_def_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_137,type,
setminusI: $o ).
thf(func_def_138,type,
setminusEL: $o ).
thf(func_def_139,type,
setminusER: $o ).
thf(func_def_140,type,
setminusSubset2: $o ).
thf(func_def_141,type,
setminusERneg: $o ).
thf(func_def_142,type,
setminusELneg: $o ).
thf(func_def_143,type,
setminusILneg: $o ).
thf(func_def_146,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_147,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_148,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_149,type,
vAND: $o > $o > $o ).
thf(func_def_150,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_151,type,
vIMP: $o > $o > $o ).
thf(func_def_152,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_153,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_154,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_155,type,
vNOT: $o > $o ).
thf(func_def_156,type,
sP0: $i > $i > $o ).
thf(func_def_157,type,
sP1: $i > $o ).
thf(func_def_158,type,
sP2: $o ).
thf(func_def_167,type,
sK11: $i > $i ).
thf(func_def_169,type,
sK13: $i > $o ).
thf(func_def_172,type,
sK16: $i > $i ).
thf(func_def_173,type,
sK17: $i > $i ).
thf(func_def_181,type,
sK25: $i > $o ).
thf(func_def_183,type,
sK27: $i > $o ).
thf(func_def_187,type,
sK31: $i > $o ).
thf(func_def_192,type,
sK36: $i > $o ).
thf(func_def_193,type,
sK37: $i > $o ).
thf(func_def_194,type,
sK38: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_195,type,
sK39: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_196,type,
sK40: $i > $o ).
thf(func_def_199,type,
sK43: $i > $o ).
thf(func_def_200,type,
sK44: $i > $i ).
thf(func_def_201,type,
sK45: ( $i > $o ) > $i ).
thf(func_def_208,type,
sK52: $o ).
thf(func_def_209,type,
sK53: $o > $i > $i > $i ).
thf(func_def_215,type,
sK59: $o ).
thf(func_def_252,type,
sK96: $i > $i > $i ).
thf(func_def_255,type,
sK99: $i > $i > $i ).
thf(func_def_261,type,
sK105: $i > $o ).
thf(func_def_263,type,
sK107: ( $i > $o ) > $i > $i ).
thf(func_def_265,type,
sK109: $i > $i ).
thf(func_def_276,type,
sK120: $i > $i > $i ).
thf(func_def_279,type,
sK123: $i > $i ).
thf(func_def_289,type,
sK133: $i > $o ).
thf(func_def_292,type,
sK136: $i > ( $i > $o ) > $i ).
thf(func_def_300,type,
sK144: $i > $o ).
thf(func_def_301,type,
sK145: $i > $o ).
thf(func_def_302,type,
sK146: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_303,type,
sK147: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_305,type,
sK149: $i > $i ).
thf(func_def_306,type,
sK150: $i > $i ).
thf(func_def_307,type,
sK151: $i > $i ).
thf(func_def_308,type,
sK152: $i > $i ).
thf(func_def_309,type,
sK153: $i > $i ).
thf(func_def_310,type,
sK154: $i > $i > $i > $i ).
thf(func_def_311,type,
sK155: $i > $i ).
thf(func_def_312,type,
sK156: $i > $i ).
thf(func_def_313,type,
sK157: $i > $i ).
thf(func_def_314,type,
sK158: $i > $i ).
thf(func_def_315,type,
sK159: $i > $i > $i ).
thf(func_def_316,type,
sK160: $i > $i > $i > $i ).
thf(func_def_317,type,
sK161: $i > $i > $i > $i ).
thf(func_def_318,type,
sK162: $i > $i > $i > $i ).
thf(func_def_319,type,
sK163: $i > $i > $i ).
thf(func_def_320,type,
sK164: $i > $i > $i ).
thf(func_def_321,type,
sK165: $i > $i > $i ).
thf(func_def_322,type,
sK166: $i > $i > $i ).
thf(func_def_324,type,
sK168: $i > $o ).
thf(func_def_326,type,
sK170: ( $i > $o ) > $i > $i ).
thf(func_def_327,type,
sK171: ( $i > $o ) > $i ).
thf(func_def_328,type,
sK172: ( $i > $o ) > $i ).
thf(func_def_329,type,
sK173: $i > $o ).
thf(func_def_334,type,
sK178: $i > $o ).
thf(func_def_335,type,
sK179: $i > $i ).
thf(func_def_336,type,
sK180: ( $i > $o ) > $i ).
thf(func_def_337,type,
sK181: ( $i > $o ) > $i > $i ).
thf(func_def_339,type,
sK183: $i > $o ).
thf(func_def_350,type,
sK194: $i > $i > $o ).
thf(func_def_351,type,
sK195: $i > $i ).
thf(func_def_352,type,
sK196: $i > $i ).
thf(func_def_353,type,
sK197: ( $i > $i > $o ) > $i > $i ).
thf(func_def_354,type,
sK198: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_355,type,
sK199: ( $i > $i > $o ) > $i > $i ).
thf(func_def_363,type,
sK207: $i > $o ).
thf(func_def_365,type,
sK209: $i > ( $i > $o ) > $i ).
thf(func_def_367,type,
sK211: $i > $o ).
thf(func_def_369,type,
sK213: $o ).
thf(func_def_370,type,
sK214: ( $i > $o ) > $i > $i ).
thf(func_def_372,type,
sK216: $i > $o ).
thf(func_def_378,type,
sK222: $i > $o ).
thf(func_def_380,type,
sK224: $i > $o ).
thf(func_def_384,type,
sK228: $i > $i > $i ).
thf(func_def_385,type,
sK229: $i > $i > $i ).
thf(func_def_391,type,
sK235: $i > $i > $i ).
thf(func_def_393,type,
sK237: $o ).
thf(func_def_396,type,
sK240: $i > $i ).
thf(func_def_397,type,
sK241: $i > $i > $i ).
thf(func_def_400,type,
sK244: $i > $o ).
thf(func_def_403,type,
sK247: $i > ( $i > $o ) > $i ).
thf(func_def_404,type,
sK248: $i > $o ).
thf(func_def_405,type,
sK249: ( $i > $o ) > $i ).
thf(func_def_419,type,
sK263: $i > $i > $i ).
thf(func_def_426,type,
sK270: $o ).
thf(func_def_429,type,
sK273: $i > $o ).
thf(func_def_444,type,
sK288: $i > $o ).
thf(func_def_446,type,
sK290: $i > ( $i > $o ) > $i ).
thf(func_def_452,type,
sK296: $o ).
thf(func_def_457,type,
sK301: $i > $i ).
thf(func_def_459,type,
sK303: $i > $o ).
thf(func_def_473,type,
sK317: $i > $o ).
thf(func_def_474,type,
sK318: $i > $o ).
thf(func_def_475,type,
sK319: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_476,type,
sK320: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_477,type,
sK321: $i > $o ).
thf(func_def_481,type,
sK325: $i > $o ).
thf(func_def_484,type,
sK328: $o ).
thf(func_def_485,type,
sK329: $i > $i > $i ).
thf(f122,axiom,
! [X2: $i,X1: $i,X0: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
=> ~ ( in @ X2 @ X1 ) )
= setminusER ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusER) ).
thf(f127,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
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(f128,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
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f127]) ).
thf(f194,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
=> ~ ( in @ X0 @ X1 ) )
= setminusER ),
inference(rectify,[],[f122]) ).
thf(f195,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
=> ( $true
!= ( in @ X0 @ X1 ) ) )
<=> ( setminusER = $true ) ),
inference(fool_elimination,[],[f194]) ).
thf(f196,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
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ~ ( in @ X2 @ ( setminus @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f128]) ).
thf(f197,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 )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f196]) ).
thf(f384,plain,
( ( setminusER = $true )
<=> ! [X1: $i,X0: $i,X2: $i] :
( ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true )
=> ( $true
!= ( in @ X0 @ X1 ) ) ) ),
inference(flattening,[],[f195]) ).
thf(f385,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 )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ( ( setminusER = $true )
=> ( ( setminusSubset2 = $true )
=> ( ( setminusERneg = $true )
=> ( ( setminusELneg = $true )
=> ( ( setminusILneg = $true )
=> ! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
=> ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
!= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[],[f197]) ).
thf(f463,plain,
( ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( setminusILneg = $true )
& ( setminusELneg = $true )
& ( setminusERneg = $true )
& ( setminusSubset2 = $true )
& ( setminusER = $true )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( 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,[],[f385]) ).
thf(f464,plain,
( ( exuE3e = $true )
& ( notdexE = $true )
& ( exu__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( setoftrueEq = $true )
& ( notequalI2 = $true )
& ( quantDeMorgan1 = $true )
& ( subsetRefl = $true )
& ( singletonsswitch = $true )
& ( setadjoinSub = $true )
& ( emptyE1 = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true )
& ( binunionLsub = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( exuI2 = $true )
& ( notinsingleton = $true )
& ( powersetAx = $true )
& ( notequalI1 = $true )
& ( subsetTrans = $true )
& ( emptysetE = $true )
& ( inPowerset = $true )
& ( descr__Cong = $true )
& ( subsetE2 = $true )
& ? [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ ( setminus @ X0 @ X1 ) )
= $true )
& ( ( in @ X2 @ X1 )
= $true ) )
& ( sepInPowerset = $true )
& ( setminusERneg = $true )
& ( setext = $true )
& ( eqinunit = $true )
& ( prop2set2propI = $true )
& ( binintersectI = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( nonemptyE1 = $true )
& ( exuE2 = $true )
& ( dsetconstrI = $true )
& ( setunion__Cong = $true )
& ( emptysetsubset = $true )
& ( setadjoinAx = $true )
& ( eqimpsubset1 = $true )
& ( powerset__Cong = $true )
& ( setunionAx = $true )
& ( dsetconstrEL = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrER = $true )
& ( notdallE = $true )
& ( subsetE = $true )
& ( powersetE1 = $true )
& ( emptyInPowerset = $true )
& ( setbeta = $true )
& ( binintersectSubset4 = $true )
& ( quantDeMorgan2 = $true )
& ( binunionE = $true )
& ( emptyset__Cong = $true )
& ( upairsetE = $true )
& ( setminusILneg = $true )
& ( subsetI1 = $true )
& ( setadjoinIR = $true )
& ( binunionIL = $true )
& ( exuI3 = $true )
& ( powersetI1 = $true )
& ( setunionE = $true )
& ( emptysetimpfalse = $true )
& ( notsubsetI = $true )
& ( binunionRsub = $true )
& ( nonemptyI1 = $true )
& ( omegaIndAx = $true )
& ( powersetsubset = $true )
& ( setadjoinSub2 = $true )
& ( binintersectER = $true )
& ( bs114d = $true )
& ( foundationAx = $true )
& ( emptyinunitempty = $true )
& ( exuEu = $true )
& ( noeltsimpempty = $true )
& ( binunionIR = $true )
& ( setminusEL = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan3 = $true )
& ( setminusER = $true )
& ( binintersectRsub = $true )
& ( setminusELneg = $true )
& ( omega__Cong = $true )
& ( omegaSAx = $true )
& ( exuE1 = $true )
& ( powersetI = $true )
& ( setextsub = $true )
& ( binintersectEL = $true )
& ( upairsetIL = $true )
& ( setextAx = $true )
& ( binintersectSubset2 = $true )
& ( setminusSubset2 = $true )
& ( exuE3u = $true )
& ( subPowSU = $true )
& ( binintersectSubset5 = $true )
& ( powersetE = $true )
& ( setunionI = $true )
& ( binintersectLsub = $true )
& ( in__Cong = $true )
& ( setadjoin__Cong = $true )
& ( binunionEcases = $true )
& ( dsetconstr__Cong = $true )
& ( eqimpsubset2 = $true )
& ( subset2powerset = $true )
& ( subsetI2 = $true )
& ( prop2setE = $true )
& ( uniqinunit = $true )
& ( binintersectSubset1 = $true )
& ( omega0Ax = $true )
& ( upairset2IR = $true )
& ( prop2setI = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( replAx = $true )
& ( wellorderingAx = $true )
& ( emptysetAx = $true )
& ( sepSubset = $true )
& ( descrp = $true )
& ( exuI1 = $true )
& ( nonemptyImpWitness = $true )
& ( setminusI = $true )
& ( emptyinPowerset = $true )
& ( disjointsetsI1 = $true ) ),
inference(flattening,[],[f463]) ).
thf(f491,plain,
( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true ) )
<=> ( setminusER = $true ) ),
inference(ennf_transformation,[],[f384]) ).
thf(f628,plain,
( ( exuE3e = $true )
& ( notdexE = $true )
& ( exu__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( setoftrueEq = $true )
& ( notequalI2 = $true )
& ( quantDeMorgan1 = $true )
& ( subsetRefl = $true )
& ( singletonsswitch = $true )
& ( setadjoinSub = $true )
& ( emptyE1 = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true )
& ( binunionLsub = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( exuI2 = $true )
& ( notinsingleton = $true )
& ( powersetAx = $true )
& ( notequalI1 = $true )
& ( subsetTrans = $true )
& ( emptysetE = $true )
& ( inPowerset = $true )
& ( descr__Cong = $true )
& ( subsetE2 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
& ( ( in @ X0 @ X2 )
= $true ) )
& ( sepInPowerset = $true )
& ( setminusERneg = $true )
& ( setext = $true )
& ( eqinunit = $true )
& ( prop2set2propI = $true )
& ( binintersectI = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( nonemptyE1 = $true )
& ( exuE2 = $true )
& ( dsetconstrI = $true )
& ( setunion__Cong = $true )
& ( emptysetsubset = $true )
& ( setadjoinAx = $true )
& ( eqimpsubset1 = $true )
& ( powerset__Cong = $true )
& ( setunionAx = $true )
& ( dsetconstrEL = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrER = $true )
& ( notdallE = $true )
& ( subsetE = $true )
& ( powersetE1 = $true )
& ( emptyInPowerset = $true )
& ( setbeta = $true )
& ( binintersectSubset4 = $true )
& ( quantDeMorgan2 = $true )
& ( binunionE = $true )
& ( emptyset__Cong = $true )
& ( upairsetE = $true )
& ( setminusILneg = $true )
& ( subsetI1 = $true )
& ( setadjoinIR = $true )
& ( binunionIL = $true )
& ( exuI3 = $true )
& ( powersetI1 = $true )
& ( setunionE = $true )
& ( emptysetimpfalse = $true )
& ( notsubsetI = $true )
& ( binunionRsub = $true )
& ( nonemptyI1 = $true )
& ( omegaIndAx = $true )
& ( powersetsubset = $true )
& ( setadjoinSub2 = $true )
& ( binintersectER = $true )
& ( bs114d = $true )
& ( foundationAx = $true )
& ( emptyinunitempty = $true )
& ( exuEu = $true )
& ( noeltsimpempty = $true )
& ( binunionIR = $true )
& ( setminusEL = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan3 = $true )
& ( setminusER = $true )
& ( binintersectRsub = $true )
& ( setminusELneg = $true )
& ( omega__Cong = $true )
& ( omegaSAx = $true )
& ( exuE1 = $true )
& ( powersetI = $true )
& ( setextsub = $true )
& ( binintersectEL = $true )
& ( upairsetIL = $true )
& ( setextAx = $true )
& ( binintersectSubset2 = $true )
& ( setminusSubset2 = $true )
& ( exuE3u = $true )
& ( subPowSU = $true )
& ( binintersectSubset5 = $true )
& ( powersetE = $true )
& ( setunionI = $true )
& ( binintersectLsub = $true )
& ( in__Cong = $true )
& ( setadjoin__Cong = $true )
& ( binunionEcases = $true )
& ( dsetconstr__Cong = $true )
& ( eqimpsubset2 = $true )
& ( subset2powerset = $true )
& ( subsetI2 = $true )
& ( prop2setE = $true )
& ( uniqinunit = $true )
& ( binintersectSubset1 = $true )
& ( omega0Ax = $true )
& ( upairset2IR = $true )
& ( prop2setI = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( replAx = $true )
& ( wellorderingAx = $true )
& ( emptysetAx = $true )
& ( sepSubset = $true )
& ( descrp = $true )
& ( exuI1 = $true )
& ( nonemptyImpWitness = $true )
& ( setminusI = $true )
& ( emptyinPowerset = $true )
& ( disjointsetsI1 = $true ) ),
inference(rectify,[],[f464]) ).
thf(f629,plain,
( ( exuE3e = $true )
& ( notdexE = $true )
& ( exu__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( setoftrueEq = $true )
& ( notequalI2 = $true )
& ( quantDeMorgan1 = $true )
& ( subsetRefl = $true )
& ( singletonsswitch = $true )
& ( setadjoinSub = $true )
& ( emptyE1 = $true )
& ( setadjoinE = $true )
& ( setadjoinIL = $true )
& ( binunionLsub = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( exuI2 = $true )
& ( notinsingleton = $true )
& ( powersetAx = $true )
& ( notequalI1 = $true )
& ( subsetTrans = $true )
& ( emptysetE = $true )
& ( inPowerset = $true )
& ( descr__Cong = $true )
& ( subsetE2 = $true )
& ( $true
= ( in @ sK80 @ ( setminus @ sK81 @ sK82 ) ) )
& ( $true
= ( in @ sK80 @ sK82 ) )
& ( sepInPowerset = $true )
& ( setminusERneg = $true )
& ( setext = $true )
& ( eqinunit = $true )
& ( prop2set2propI = $true )
& ( binintersectI = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( nonemptyE1 = $true )
& ( exuE2 = $true )
& ( dsetconstrI = $true )
& ( setunion__Cong = $true )
& ( emptysetsubset = $true )
& ( setadjoinAx = $true )
& ( eqimpsubset1 = $true )
& ( powerset__Cong = $true )
& ( setunionAx = $true )
& ( dsetconstrEL = $true )
& ( subsetemptysetimpeq = $true )
& ( binintersectSubset3 = $true )
& ( dsetconstrER = $true )
& ( notdallE = $true )
& ( subsetE = $true )
& ( powersetE1 = $true )
& ( emptyInPowerset = $true )
& ( setbeta = $true )
& ( binintersectSubset4 = $true )
& ( quantDeMorgan2 = $true )
& ( binunionE = $true )
& ( emptyset__Cong = $true )
& ( upairsetE = $true )
& ( setminusILneg = $true )
& ( subsetI1 = $true )
& ( setadjoinIR = $true )
& ( binunionIL = $true )
& ( exuI3 = $true )
& ( powersetI1 = $true )
& ( setunionE = $true )
& ( emptysetimpfalse = $true )
& ( notsubsetI = $true )
& ( binunionRsub = $true )
& ( nonemptyI1 = $true )
& ( omegaIndAx = $true )
& ( powersetsubset = $true )
& ( setadjoinSub2 = $true )
& ( binintersectER = $true )
& ( bs114d = $true )
& ( foundationAx = $true )
& ( emptyinunitempty = $true )
& ( exuEu = $true )
& ( noeltsimpempty = $true )
& ( binunionIR = $true )
& ( setminusEL = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan3 = $true )
& ( setminusER = $true )
& ( binintersectRsub = $true )
& ( setminusELneg = $true )
& ( omega__Cong = $true )
& ( omegaSAx = $true )
& ( exuE1 = $true )
& ( powersetI = $true )
& ( setextsub = $true )
& ( binintersectEL = $true )
& ( upairsetIL = $true )
& ( setextAx = $true )
& ( binintersectSubset2 = $true )
& ( setminusSubset2 = $true )
& ( exuE3u = $true )
& ( subPowSU = $true )
& ( binintersectSubset5 = $true )
& ( powersetE = $true )
& ( setunionI = $true )
& ( binintersectLsub = $true )
& ( in__Cong = $true )
& ( setadjoin__Cong = $true )
& ( binunionEcases = $true )
& ( dsetconstr__Cong = $true )
& ( eqimpsubset2 = $true )
& ( subset2powerset = $true )
& ( subsetI2 = $true )
& ( prop2setE = $true )
& ( uniqinunit = $true )
& ( binintersectSubset1 = $true )
& ( omega0Ax = $true )
& ( upairset2IR = $true )
& ( prop2setI = $true )
& ( setadjoinOr = $true )
& ( emptyI = $true )
& ( replAx = $true )
& ( wellorderingAx = $true )
& ( emptysetAx = $true )
& ( sepSubset = $true )
& ( descrp = $true )
& ( exuI1 = $true )
& ( nonemptyImpWitness = $true )
& ( setminusI = $true )
& ( emptyinPowerset = $true )
& ( disjointsetsI1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK80,sK81,sK82]),skolemize(X0,sK80),skolemize(X1,sK81),skolemize(X2,sK82)],[f628]) ).
thf(f906,plain,
( ( ! [X0: $i,X2: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ X1 ) )
| ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
!= $true ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X0: $i,X2: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
& ( ( in @ X0 @ ( setminus @ X2 @ X1 ) )
= $true ) ) ) ),
inference(nnf_transformation,[],[f491]) ).
thf(f907,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X3 @ X5 )
= $true )
& ( ( in @ X3 @ ( setminus @ X4 @ X5 ) )
= $true ) ) ) ),
inference(rectify,[],[f906]) ).
thf(f908,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X2 )
!= $true )
| ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) ) )
| ( setminusER != $true ) )
& ( ( setminusER = $true )
| ( ( ( in @ sK335 @ sK337 )
= $true )
& ( $true
= ( in @ sK335 @ ( setminus @ sK336 @ sK337 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK335,sK336,sK337]),skolemize(X3,sK335),skolemize(X4,sK336),skolemize(X5,sK337)],[f907]) ).
thf(f1063,plain,
setminusER = $true,
inference(cnf_transformation,[],[f629]) ).
thf(f1119,plain,
( $true
= ( in @ sK80 @ sK82 ) ),
inference(cnf_transformation,[],[f629]) ).
thf(f1120,plain,
( $true
= ( in @ sK80 @ ( setminus @ sK81 @ sK82 ) ) ),
inference(cnf_transformation,[],[f629]) ).
thf(f1523,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( setminusER != $true )
| ( ( in @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f908]) ).
thf(f2657,definition,
( spl340_221
<=> ( $true
= ( in @ sK80 @ ( setminus @ sK81 @ sK82 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl340_221])],[avatar_definition]) ).
thf(f2659,plain,
( ( $true
= ( in @ sK80 @ ( setminus @ sK81 @ sK82 ) ) )
| ~ spl340_221 ),
inference(avatar_component_clause,[],[f2657]) ).
thf(f2660,plain,
spl340_221,
inference(avatar_split_clause,[],[f1120,f2657]) ).
thf(f3393,definition,
( spl340_375
<=> ( setminusER = $true ) ),
introduced(definition,[new_symbols(definition,[spl340_375])],[avatar_definition]) ).
thf(f3969,plain,
spl340_375,
inference(avatar_split_clause,[],[f1063,f3393]) ).
thf(f4134,definition,
( spl340_529
<=> ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X2 )
!= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl340_529])],[avatar_definition]) ).
thf(f4135,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X0 @ ( setminus @ X1 @ X2 ) ) )
| ( ( in @ X0 @ X2 )
!= $true ) )
| ~ spl340_529 ),
inference(avatar_component_clause,[],[f4134]) ).
thf(f4136,plain,
( ~ spl340_375
| spl340_529 ),
inference(avatar_split_clause,[],[f1523,f4134,f3393]) ).
thf(f4365,definition,
( spl340_576
<=> ( $true
= ( in @ sK80 @ sK82 ) ) ),
introduced(definition,[new_symbols(definition,[spl340_576])],[avatar_definition]) ).
thf(f4367,plain,
( ( $true
= ( in @ sK80 @ sK82 ) )
| ~ spl340_576 ),
inference(avatar_component_clause,[],[f4365]) ).
thf(f4368,plain,
spl340_576,
inference(avatar_split_clause,[],[f1119,f4365]) ).
thf(f4425,plain,
( ( $true
!= ( in @ sK80 @ sK82 ) )
| ( $true != $true )
| ~ spl340_221
| ~ spl340_529 ),
inference(superposition,[],[f4135,f2659]) ).
thf(f4426,plain,
( ( $true
!= ( in @ sK80 @ sK82 ) )
| ~ spl340_221
| ~ spl340_529 ),
inference(trivial_inequality_removal,[],[f4425]) ).
thf(f4427,plain,
( $false
| ~ spl340_221
| ~ spl340_529
| ~ spl340_576 ),
inference(forward_subsumption_resolution,[],[f4426,f4367]) ).
thf(f4428,plain,
( ~ spl340_221
| ~ spl340_529
| ~ spl340_576 ),
inference(avatar_contradiction_clause,[],[f4427]) ).
cnf(s159,plain,
spl340_221,
inference(sat_conversion,[],[f2660]) ).
cnf(s480,plain,
spl340_375,
inference(sat_conversion,[],[f3969]) ).
cnf(s519,plain,
( ~ spl340_375
| spl340_529 ),
inference(sat_conversion,[],[f4136]) ).
cnf(s589,plain,
spl340_576,
inference(sat_conversion,[],[f4368]) ).
cnf(s597,plain,
( ~ spl340_221
| ~ spl340_529
| ~ spl340_576 ),
inference(sat_conversion,[],[f4428]) ).
cnf(s602,plain,
spl340_529,
inference(rat,[],[s519,s480]) ).
cnf(s603,plain,
~ spl340_221,
inference(rat,[],[s597,s589,s602]) ).
cnf(s677,plain,
$false,
inference(rat,[],[s159,s603]) ).
thf(f4429,plain,
$false,
inference(avatar_sat_refutation,[],[s677]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU608^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:00:07 UTC 2026
% 0.08/0.20 % CPUTime :
% 0.08/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.26 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
% 0.68/0.38 % (1327699)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.68/0.38 % (1327705)lrs+10_16_si=on:nwc=1.5:random_seed=2802665893:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.68/0.38 % (1327710)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.68/0.38 % (1327710)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
% 0.68/0.38 % (1327705)Instruction limit reached!
% 0.68/0.38 % (1327705)------------------------------
% 0.68/0.38 % (1327705)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327705)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327705)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327705)Termination reason: Instruction limit
% 0.68/0.38 % (1327705)Termination phase: Property scanning
% 0.68/0.38 % (1327705)Time elapsed: 0.005 s
% 0.68/0.38 % (1327705)Peak memory usage: 10 MB
% 0.68/0.38 % (1327705)Instructions burned: 22 (million)
% 0.68/0.38 % (1327708)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2658351222:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.68/0.38 % (1327704)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=159098554:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.68/0.38 % (1327706)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=4109189600:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.68/0.38 % (1327707)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=1687301724: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)
% 0.68/0.38 % (1327710)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=2025951373:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.68/0.38 % (1327709)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1106495054:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.68/0.38 % (1327706)Instruction limit reached!
% 0.68/0.38 % (1327706)------------------------------
% 0.68/0.38 % (1327706)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327706)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327706)Termination reason: Instruction limit
% 0.68/0.38 % (1327706)Termination phase: shuffling
% 0.68/0.38 % (1327706)Time elapsed: 0.003 s
% 0.68/0.38 % (1327706)Peak memory usage: 10 MB
% 0.68/0.38 % (1327706)Instructions burned: 6 (million)
% 0.68/0.38 % (1327712)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=62019604:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.38 % (1327708)Instruction limit reached!
% 0.68/0.38 % (1327708)------------------------------
% 0.68/0.38 % (1327708)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327708)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327712)Instruction limit reached!
% 0.68/0.38 % (1327712)------------------------------
% 0.68/0.38 % (1327712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327708)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327708)Termination reason: Instruction limit
% 0.68/0.38 % (1327708)Termination phase: Preprocessing 3
% 0.68/0.38 % (1327708)Time elapsed: 0.013 s
% 0.68/0.38 % (1327712)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327712)Termination reason: Instruction limit
% 0.68/0.38 % (1327712)Termination phase: shuffling
% 0.68/0.38 % (1327708)Peak memory usage: 11 MB
% 0.68/0.38 % (1327712)Time elapsed: 0.001 s
% 0.68/0.38 % (1327712)Peak memory usage: 10 MB
% 0.68/0.38 % (1327712)Instructions burned: 4 (million)
% 0.68/0.38 % (1327708)Instructions burned: 25 (million)
% 0.68/0.38 % (1327721)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.38 % (1327721)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2195584179:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.68/0.38 % (1327719)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1886202124:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.68/0.38 % (1327721)Instruction limit reached!
% 0.68/0.38 % (1327721)------------------------------
% 0.68/0.38 % (1327721)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327721)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327721)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327721)Termination reason: Instruction limit
% 0.68/0.38 % (1327721)Termination phase: shuffling
% 0.68/0.38 % (1327721)Time elapsed: 0.003 s
% 0.68/0.38 % (1327721)Peak memory usage: 10 MB
% 0.68/0.38 % (1327721)Instructions burned: 11 (million)
% 0.68/0.38 % (1327719)Instruction limit reached!
% 0.68/0.38 % (1327719)------------------------------
% 0.68/0.38 % (1327719)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327719)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327719)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327719)Termination reason: Instruction limit
% 0.68/0.38 % (1327719)Termination phase: shuffling
% 0.68/0.38 % (1327719)Time elapsed: 0.003 s
% 0.68/0.38 % (1327719)Peak memory usage: 10 MB
% 0.68/0.38 % (1327719)Instructions burned: 5 (million)
% 0.68/0.38 % (1327722)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2532331470:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.68/0.38 % (1327709)Instruction limit reached!
% 0.68/0.38 % (1327709)------------------------------
% 0.68/0.38 % (1327709)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327709)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327709)Termination reason: Instruction limit
% 0.68/0.38 % (1327709)Termination phase: Saturation
% 0.68/0.38 % (1327709)Time elapsed: 0.036 s
% 0.68/0.38 % (1327709)Peak memory usage: 13 MB
% 0.68/0.38 % (1327709)Instructions burned: 77 (million)
% 0.68/0.38 % (1327725)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
% 0.68/0.38 % (1327725)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.68/0.38 % (1327722)Instruction limit reached!
% 0.68/0.38 % (1327722)------------------------------
% 0.68/0.38 % (1327722)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327722)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327722)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327722)Termination reason: Instruction limit
% 0.68/0.38 % (1327722)Termination phase: Property scanning
% 0.68/0.38 % (1327722)Time elapsed: 0.007 s
% 0.68/0.38 % (1327722)Peak memory usage: 10 MB
% 0.68/0.38 % (1327722)Instructions burned: 13 (million)
% 0.68/0.38 % (1327725)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3085812762:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.68/0.38 % (1327704)Instruction limit reached!
% 0.68/0.38 % (1327704)------------------------------
% 0.68/0.38 % (1327704)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327704)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327704)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327704)Termination reason: Instruction limit
% 0.68/0.38 % (1327704)Termination phase: Saturation
% 0.68/0.38 % (1327704)Time elapsed: 0.047 s
% 0.68/0.38 % (1327704)Peak memory usage: 13 MB
% 0.68/0.38 % (1327704)Instructions burned: 88 (million)
% 0.68/0.38 % (1327726)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=2242212459:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.68/0.38 % (1327725)Instruction limit reached!
% 0.68/0.38 % (1327725)------------------------------
% 0.68/0.38 % (1327725)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327725)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327725)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327725)Termination reason: Instruction limit
% 0.68/0.38 % (1327725)Termination phase: Property scanning
% 0.68/0.38 % (1327725)Time elapsed: 0.011 s
% 0.68/0.38 % (1327725)Peak memory usage: 11 MB
% 0.68/0.38 % (1327725)Instructions burned: 29 (million)
% 0.68/0.38 % (1327729)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.68/0.38 % (1327707) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1327699-1327707"...
% 0.68/0.38 % (1327729)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=3980769389:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.68/0.38 % (1327728)lrs+10_1_si=on:cs=on:random_seed=3210625809:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.68/0.38 % (1327707)...printing done.
% 0.68/0.38 % (1327731)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2441127450:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.68/0.38 % (1327729)Instruction limit reached!
% 0.68/0.38 % (1327729)------------------------------
% 0.68/0.38 % (1327729)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327729)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327729)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327729)Termination reason: Instruction limit
% 0.68/0.38 % (1327729)Termination phase: shuffling
% 0.68/0.38 % (1327729)Time elapsed: 0.003 s
% 0.68/0.38 % (1327729)Peak memory usage: 10 MB
% 0.68/0.38 % (1327729)Instructions burned: 5 (million)
% 0.68/0.38 % (1327707)Refutation found. Thanks to Tanya!
% 0.68/0.38 % SZS status Theorem for theBenchmark
% 0.68/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.68/0.38 % (1327707)------------------------------
% 0.68/0.38 % (1327707)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.68/0.38 % (1327707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.38 % (1327707)CaDiCaL version: 2.1.3
% 0.68/0.38 % (1327707)Termination reason: Refutation
% 0.68/0.38 % (1327707)Time elapsed: 0.062 s
% 0.68/0.38 % (1327707)Peak memory usage: 15 MB
% 0.68/0.38 % (1327707)Instructions burned: 122 (million)
% 0.68/0.38 % (1327699)Success in time 0.112 s
% 0.68/0.38 % Vampire exiting
%------------------------------------------------------------------------------