%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU622^1 : 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 : n009.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 08:30:22 AM UTC 2026
% Result : Theorem 0.83s 0.40s
% Output : Refutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 10
% Syntax : Number of formulae : 66 ( 22 unt; 0 typ; 7 def)
% Number of atoms : 2477 ( 644 equ; 0 cnn)
% Maximal formula atoms : 141 ( 37 avg)
% Number of connectives : 1361 ( 68 ~; 58 |; 429 &; 233 @)
% ( 11 <=>; 562 =>; 0 <=; 0 <~>)
% Maximal formula depth : 147 ( 18 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 : 291 ( 288 usr; 163 con; 0-4 aty)
% Number of variables : 60 ( 0 sgn 48 !; 12 ?; 60 :)
% 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_144,type,
setminusIRneg: $o ).
thf(func_def_145,type,
setminusLsub: $o ).
thf(func_def_146,type,
setminusSubset1: $o ).
thf(func_def_147,type,
symdiff: $i > $i > $i ).
thf(func_def_148,type,
symdiffE: $o ).
thf(func_def_149,type,
symdiffI1: $o ).
thf(func_def_150,type,
symdiffI2: $o ).
thf(func_def_151,type,
symdiffIneg1: $o ).
thf(func_def_152,type,
symdiffIneg2: $o ).
thf(func_def_153,type,
iskpair: $i > $o ).
thf(func_def_154,type,
secondinupair: $o ).
thf(func_def_155,type,
setukpairIL: $o ).
thf(func_def_156,type,
setukpairIR: $o ).
thf(func_def_157,type,
kpairiskpair: $o ).
thf(func_def_158,type,
kpair: $i > $i > $i ).
thf(func_def_159,type,
kpairp: $o ).
thf(func_def_160,type,
cartprod: $i > $i > $i ).
thf(func_def_161,type,
singletonsubset: $o ).
thf(func_def_164,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_165,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_166,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_167,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_168,type,
vNOT: $o > $o ).
thf(func_def_169,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_170,type,
vAND: $o > $o > $o ).
thf(func_def_171,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_172,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_173,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_174,type,
vIMP: $o > $o > $o ).
thf(func_def_175,type,
sP0: $i > $i > $o ).
thf(func_def_176,type,
sP1: $i > $o ).
thf(func_def_177,type,
sP2: $o ).
thf(func_def_183,type,
sK8: $o ).
thf(func_def_192,type,
sK17: $i > $o ).
thf(func_def_196,type,
sK21: $i > $o ).
thf(func_def_202,type,
sK27: $i > $i ).
thf(func_def_203,type,
sK28: $o ).
thf(func_def_204,type,
sK29: $i > ( $i > $o ) > $i ).
thf(func_def_205,type,
sK30: $i > $o ).
thf(func_def_210,type,
sK35: $i > $i ).
thf(func_def_216,type,
sK41: $i > $i ).
thf(func_def_221,type,
sK46: $o ).
thf(func_def_225,type,
sK50: $i > $o ).
thf(func_def_227,type,
sK52: ( $i > $o ) > $i > $i ).
thf(func_def_229,type,
sK54: $i > $o ).
thf(func_def_232,type,
sK57: $i > $i > $i ).
thf(func_def_237,type,
sK62: ( $i > $o ) > $i > $i ).
thf(func_def_239,type,
sK64: $i > $o ).
thf(func_def_241,type,
sK66: $i > $o ).
thf(func_def_244,type,
sK69: $i > $i > $i ).
thf(func_def_251,type,
sK76: $i > $o ).
thf(func_def_269,type,
sK94: ( $i > $o ) > $i > $i ).
thf(func_def_271,type,
sK96: $i > $o ).
thf(func_def_279,type,
sK104: $i > $o ).
thf(func_def_285,type,
sK110: $i > $i > $i ).
thf(func_def_286,type,
sK111: $i > $i > $i ).
thf(func_def_289,type,
sK114: $i > $i > $i ).
thf(func_def_290,type,
sK115: $i > $o ).
thf(func_def_292,type,
sK117: $i > ( $i > $o ) > $i ).
thf(func_def_309,type,
sK134: $i > $i > $i ).
thf(func_def_312,type,
sK137: $i > $o ).
thf(func_def_313,type,
sK138: $i > $o ).
thf(func_def_314,type,
sK139: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_315,type,
sK140: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_320,type,
sK145: $o ).
thf(func_def_324,type,
sK149: $i > $i > $i ).
thf(func_def_341,type,
sK166: $i > $o ).
thf(func_def_342,type,
sK167: $i > $i ).
thf(func_def_343,type,
sK168: ( $i > $o ) > $i ).
thf(func_def_344,type,
sK169: $i > $o ).
thf(func_def_345,type,
sK170: $i > $o ).
thf(func_def_346,type,
sK171: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_347,type,
sK172: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_376,type,
sK201: $i > $i > $i ).
thf(func_def_377,type,
sK202: $i > $o ).
thf(func_def_379,type,
sK204: $i > ( $i > $o ) > $i ).
thf(func_def_380,type,
sK205: $o > $i > $i > $i ).
thf(func_def_383,type,
sK208: $o ).
thf(func_def_384,type,
sK209: $o ).
thf(func_def_386,type,
sK211: $i > $o ).
thf(func_def_389,type,
sK214: $i > $o ).
thf(func_def_406,type,
sK231: ( $i > $o ) > $i ).
thf(func_def_407,type,
sK232: $i > $o ).
thf(func_def_408,type,
sK233: $o ).
thf(func_def_417,type,
sK242: $i > $i ).
thf(func_def_436,type,
sK261: $i > $o ).
thf(func_def_439,type,
sK264: $i > ( $i > $o ) > $i ).
thf(func_def_443,type,
sK268: $i > $i > $i ).
thf(func_def_445,type,
sK270: $i > $i ).
thf(func_def_446,type,
sK271: $i > $i ).
thf(func_def_447,type,
sK272: $i > $i ).
thf(func_def_448,type,
sK273: $i > $i ).
thf(func_def_449,type,
sK274: $i > $i ).
thf(func_def_450,type,
sK275: $i > $i > $i > $i ).
thf(func_def_451,type,
sK276: $i > $i ).
thf(func_def_452,type,
sK277: $i > $i ).
thf(func_def_453,type,
sK278: $i > $i ).
thf(func_def_454,type,
sK279: $i > $i ).
thf(func_def_455,type,
sK280: $i > $i > $i ).
thf(func_def_456,type,
sK281: $i > $i > $i ).
thf(func_def_457,type,
sK282: $i > $i > $i > $i ).
thf(func_def_458,type,
sK283: $i > $i > $i > $i ).
thf(func_def_459,type,
sK284: $i > $i > $i > $i ).
thf(func_def_460,type,
sK285: $i > $i > $i ).
thf(func_def_461,type,
sK286: $i > $i > $i ).
thf(func_def_462,type,
sK287: $i > $i > $i ).
thf(func_def_464,type,
sK289: $i > $o ).
thf(func_def_465,type,
sK290: $i > $o ).
thf(func_def_466,type,
sK291: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_467,type,
sK292: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_475,type,
sK300: $i > $i ).
thf(func_def_477,type,
sK302: $i > $o ).
thf(func_def_479,type,
sK304: ( $i > $o ) > $i ).
thf(func_def_480,type,
sK305: ( $i > $o ) > $i ).
thf(func_def_484,type,
sK309: $i > $o ).
thf(func_def_489,type,
sK314: $i > $o ).
thf(func_def_493,type,
sK318: ( $i > $i > $o ) > $i > $i ).
thf(func_def_494,type,
sK319: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_495,type,
sK320: ( $i > $i > $o ) > $i > $i ).
thf(func_def_497,type,
sK322: $i > $i > $o ).
thf(func_def_498,type,
sK323: $i > $i ).
thf(func_def_499,type,
sK324: $i > $i ).
thf(func_def_503,type,
sK328: $i > $i ).
thf(func_def_505,type,
sK330: $i > $i ).
thf(func_def_511,type,
sK336: $i > $o ).
thf(func_def_513,type,
sK338: $i > $o ).
thf(func_def_515,type,
sK340: ( $i > $o ) > $i > $i ).
thf(func_def_516,type,
sK341: $i > $o ).
thf(func_def_517,type,
sK342: $i > $i ).
thf(func_def_518,type,
sK343: ( $i > $o ) > $i ).
thf(func_def_520,type,
sK345: $i > $o ).
thf(func_def_537,type,
sK362: $o ).
thf(f95,axiom,
( powersetI1
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(f143,axiom,
( singletonsubset
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ ( setadjoin @ X1 @ emptyset ) @ X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(f144,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
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(f145,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
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ X0 )
=> ( in @ ( setadjoin @ X1 @ emptyset ) @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f144]) ).
thf(f366,plain,
( powersetI1
= ( ! [X0: $i,X1: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
inference(rectify,[],[f95]) ).
thf(f367,plain,
( ( powersetI1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[],[f366]) ).
thf(f392,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
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ! [X0: $i,X1: $i] :
( ( in @ X0 @ X1 )
=> ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f145]) ).
thf(f393,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 )
=> ( ( setminusIRneg = $true )
=> ( ( setminusLsub = $true )
=> ( ( setminusSubset1 = $true )
=> ( ( symdiffE = $true )
=> ( ( symdiffI1 = $true )
=> ( ( symdiffI2 = $true )
=> ( ( symdiffIneg1 = $true )
=> ( ( symdiffIneg2 = $true )
=> ( ( secondinupair = $true )
=> ( ( setukpairIL = $true )
=> ( ( setukpairIR = $true )
=> ( ( kpairiskpair = $true )
=> ( ( kpairp = $true )
=> ( ( singletonsubset = $true )
=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f392]) ).
thf(f396,plain,
( singletonsubset
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ X1 )
=> ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 ) ) ) ),
inference(rectify,[],[f143]) ).
thf(f397,plain,
( ( singletonsubset = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( in @ X0 @ X1 ) )
=> ( $true
= ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 ) ) ) ),
inference(fool_elimination,[],[f396]) ).
thf(f468,plain,
( ( singletonsubset = $true )
<=> ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[],[f397]) ).
thf(f559,plain,
( ? [X0: $i,X1: $i] :
( ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) )
!= $true )
& ( $true
= ( in @ X0 @ X1 ) ) )
& ( singletonsubset = $true )
& ( kpairp = $true )
& ( kpairiskpair = $true )
& ( setukpairIR = $true )
& ( setukpairIL = $true )
& ( secondinupair = $true )
& ( symdiffIneg2 = $true )
& ( symdiffIneg1 = $true )
& ( symdiffI2 = $true )
& ( symdiffI1 = $true )
& ( symdiffE = $true )
& ( setminusSubset1 = $true )
& ( setminusLsub = $true )
& ( setminusIRneg = $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,[],[f393]) ).
thf(f560,plain,
( ( notdexE = $true )
& ( setadjoinIR = $true )
& ( emptysetAx = $true )
& ( exuE1 = $true )
& ( binintersectER = $true )
& ( eqimpsubset1 = $true )
& ( prop2setI = $true )
& ( binunionLsub = $true )
& ( subPowSU = $true )
& ( symdiffIneg1 = $true )
& ( wellorderingAx = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( quantDeMorgan1 = $true )
& ( prop2set2propI = $true )
& ( setminusSubset1 = $true )
& ( setminusILneg = $true )
& ( exuEu = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( omegaIndAx = $true )
& ( nonemptyI1 = $true )
& ( kpairp = $true )
& ( powerset__Cong = $true )
& ( binintersectLsub = $true )
& ( setoftrueEq = $true )
& ( binunionE = $true )
& ( setadjoinAx = $true )
& ( notequalI1 = $true )
& ( setext = $true )
& ( exu__Cong = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ? [X0: $i,X1: $i] :
( ( ( in @ ( setadjoin @ X0 @ emptyset ) @ ( powerset @ X1 ) )
!= $true )
& ( $true
= ( in @ X0 @ X1 ) ) )
& ( symdiffE = $true )
& ( binunionIR = $true )
& ( upairsetIR = $true )
& ( uniqinunit = $true )
& ( notequalI2 = $true )
& ( foundationAx = $true )
& ( binintersectSubset1 = $true )
& ( quantDeMorgan2 = $true )
& ( noeltsimpempty = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( setukpairIL = $true )
& ( notinsingleton = $true )
& ( subsetE = $true )
& ( binunionRsub = $true )
& ( dsetconstrI = $true )
& ( setminusERneg = $true )
& ( binintersectSubset2 = $true )
& ( setminusI = $true )
& ( binintersectI = $true )
& ( upairset2IR = $true )
& ( exuI2 = $true )
& ( subsetE2 = $true )
& ( singletonsubset = $true )
& ( setminusER = $true )
& ( setukpairIR = $true )
& ( emptyE1 = $true )
& ( sepInPowerset = $true )
& ( setminusIRneg = $true )
& ( setadjoinSub = $true )
& ( binunionIL = $true )
& ( powersetE = $true )
& ( quantDeMorgan4 = $true )
& ( emptyI = $true )
& ( binintersectSubset4 = $true )
& ( symdiffIneg2 = $true )
& ( emptysetimpfalse = $true )
& ( inPowerset = $true )
& ( exuE2 = $true )
& ( powersetAx = $true )
& ( omega__Cong = $true )
& ( kpairiskpair = $true )
& ( setminusELneg = $true )
& ( disjointsetsI1 = $true )
& ( dsetconstrER = $true )
& ( eqinunit = $true )
& ( prop2setE = $true )
& ( notsubsetI = $true )
& ( dsetconstrEL = $true )
& ( upairsetE = $true )
& ( exuE3u = $true )
& ( descrp = $true )
& ( symdiffI2 = $true )
& ( powersetI = $true )
& ( exuI3 = $true )
& ( setunion__Cong = $true )
& ( subsetRefl = $true )
& ( quantDeMorgan3 = $true )
& ( powersetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( upairsetIL = $true )
& ( setbeta = $true )
& ( emptysetsubset = $true )
& ( binintersectSubset5 = $true )
& ( symdiffI1 = $true )
& ( exuE3e = $true )
& ( emptysetE = $true )
& ( exuI1 = $true )
& ( binintersectSubset3 = $true )
& ( subset2powerset = $true )
& ( emptyinPowerset = $true )
& ( powersetE1 = $true )
& ( setminusSubset2 = $true )
& ( eqimpsubset2 = $true )
& ( setadjoinE = $true )
& ( setadjoin__Cong = $true )
& ( setminusEL = $true )
& ( setminusLsub = $true )
& ( secondinupair = $true )
& ( binintersectRsub = $true )
& ( emptyinunitempty = $true )
& ( subsetI1 = $true )
& ( binintersectEL = $true )
& ( subsetI2 = $true )
& ( setunionI = $true )
& ( setunionE = $true )
& ( subsetemptysetimpeq = $true )
& ( vacuousDall = $true )
& ( descr__Cong = $true )
& ( sepSubset = $true )
& ( in__Cong = $true )
& ( notdallE = $true )
& ( setadjoinOr = $true )
& ( setadjoinSub2 = $true )
& ( singletonsswitch = $true )
& ( bs114d = $true )
& ( setadjoinIL = $true )
& ( binunionEcases = $true )
& ( omega0Ax = $true )
& ( subsetTrans = $true )
& ( inCongP = $true )
& ( dsetconstr__Cong = $true )
& ( replAx = $true )
& ( powersetI1 = $true ) ),
inference(flattening,[],[f559]) ).
thf(f593,plain,
( ( powersetI1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
inference(ennf_transformation,[],[f367]) ).
thf(f819,plain,
( ( notdexE = $true )
& ( setadjoinIR = $true )
& ( emptysetAx = $true )
& ( exuE1 = $true )
& ( binintersectER = $true )
& ( eqimpsubset1 = $true )
& ( prop2setI = $true )
& ( binunionLsub = $true )
& ( subPowSU = $true )
& ( symdiffIneg1 = $true )
& ( wellorderingAx = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( quantDeMorgan1 = $true )
& ( prop2set2propI = $true )
& ( setminusSubset1 = $true )
& ( setminusILneg = $true )
& ( exuEu = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( omegaIndAx = $true )
& ( nonemptyI1 = $true )
& ( kpairp = $true )
& ( powerset__Cong = $true )
& ( binintersectLsub = $true )
& ( setoftrueEq = $true )
& ( binunionE = $true )
& ( setadjoinAx = $true )
& ( notequalI1 = $true )
& ( setext = $true )
& ( exu__Cong = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( ( in @ ( setadjoin @ sK189 @ emptyset ) @ ( powerset @ sK190 ) )
!= $true )
& ( ( in @ sK189 @ sK190 )
= $true )
& ( symdiffE = $true )
& ( binunionIR = $true )
& ( upairsetIR = $true )
& ( uniqinunit = $true )
& ( notequalI2 = $true )
& ( foundationAx = $true )
& ( binintersectSubset1 = $true )
& ( quantDeMorgan2 = $true )
& ( noeltsimpempty = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( emptyInPowerset = $true )
& ( setukpairIL = $true )
& ( notinsingleton = $true )
& ( subsetE = $true )
& ( binunionRsub = $true )
& ( dsetconstrI = $true )
& ( setminusERneg = $true )
& ( binintersectSubset2 = $true )
& ( setminusI = $true )
& ( binintersectI = $true )
& ( upairset2IR = $true )
& ( exuI2 = $true )
& ( subsetE2 = $true )
& ( singletonsubset = $true )
& ( setminusER = $true )
& ( setukpairIR = $true )
& ( emptyE1 = $true )
& ( sepInPowerset = $true )
& ( setminusIRneg = $true )
& ( setadjoinSub = $true )
& ( binunionIL = $true )
& ( powersetE = $true )
& ( quantDeMorgan4 = $true )
& ( emptyI = $true )
& ( binintersectSubset4 = $true )
& ( symdiffIneg2 = $true )
& ( emptysetimpfalse = $true )
& ( inPowerset = $true )
& ( exuE2 = $true )
& ( powersetAx = $true )
& ( omega__Cong = $true )
& ( kpairiskpair = $true )
& ( setminusELneg = $true )
& ( disjointsetsI1 = $true )
& ( dsetconstrER = $true )
& ( eqinunit = $true )
& ( prop2setE = $true )
& ( notsubsetI = $true )
& ( dsetconstrEL = $true )
& ( upairsetE = $true )
& ( exuE3u = $true )
& ( descrp = $true )
& ( symdiffI2 = $true )
& ( powersetI = $true )
& ( exuI3 = $true )
& ( setunion__Cong = $true )
& ( subsetRefl = $true )
& ( quantDeMorgan3 = $true )
& ( powersetsubset = $true )
& ( nonemptyImpWitness = $true )
& ( upairsetIL = $true )
& ( setbeta = $true )
& ( emptysetsubset = $true )
& ( binintersectSubset5 = $true )
& ( symdiffI1 = $true )
& ( exuE3e = $true )
& ( emptysetE = $true )
& ( exuI1 = $true )
& ( binintersectSubset3 = $true )
& ( subset2powerset = $true )
& ( emptyinPowerset = $true )
& ( powersetE1 = $true )
& ( setminusSubset2 = $true )
& ( eqimpsubset2 = $true )
& ( setadjoinE = $true )
& ( setadjoin__Cong = $true )
& ( setminusEL = $true )
& ( setminusLsub = $true )
& ( secondinupair = $true )
& ( binintersectRsub = $true )
& ( emptyinunitempty = $true )
& ( subsetI1 = $true )
& ( binintersectEL = $true )
& ( subsetI2 = $true )
& ( setunionI = $true )
& ( setunionE = $true )
& ( subsetemptysetimpeq = $true )
& ( vacuousDall = $true )
& ( descr__Cong = $true )
& ( sepSubset = $true )
& ( in__Cong = $true )
& ( notdallE = $true )
& ( setadjoinOr = $true )
& ( setadjoinSub2 = $true )
& ( singletonsswitch = $true )
& ( bs114d = $true )
& ( setadjoinIL = $true )
& ( binunionEcases = $true )
& ( omega0Ax = $true )
& ( subsetTrans = $true )
& ( inCongP = $true )
& ( dsetconstr__Cong = $true )
& ( replAx = $true )
& ( powersetI1 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK189,sK190]),skolemize(X0,sK189),skolemize(X1,sK190)],[f560]) ).
thf(f859,plain,
( ( ( powersetI1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
& ( ( in @ X1 @ ( powerset @ X0 ) )
!= $true ) ) )
& ( ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI1 != $true ) ) ),
inference(nnf_transformation,[],[f593]) ).
thf(f860,plain,
( ( ( powersetI1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
| ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) ) )
| ( powersetI1 != $true ) ) ),
inference(rectify,[],[f859]) ).
thf(f861,plain,
( ( ( powersetI1 = $true )
| ( ( ( subset @ sK221 @ sK222 )
= $true )
& ( ( in @ sK221 @ ( powerset @ sK222 ) )
!= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( $true
!= ( subset @ X2 @ X3 ) )
| ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) ) )
| ( powersetI1 != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK221,sK222]),skolemize(X0,sK221),skolemize(X1,sK222)],[f860]) ).
thf(f996,plain,
( ( ( singletonsubset = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 ) )
& ( $true
= ( in @ X0 @ X1 ) ) ) )
& ( ! [X0: $i,X1: $i] :
( ( $true
= ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 ) )
| ( $true
!= ( in @ X0 @ X1 ) ) )
| ( singletonsubset != $true ) ) ),
inference(nnf_transformation,[],[f468]) ).
thf(f997,plain,
( ( ( singletonsubset = $true )
| ? [X0: $i,X1: $i] :
( ( $true
!= ( subset @ ( setadjoin @ X0 @ emptyset ) @ X1 ) )
& ( $true
= ( in @ X0 @ X1 ) ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 )
= $true )
| ( ( in @ X2 @ X3 )
!= $true ) )
| ( singletonsubset != $true ) ) ),
inference(rectify,[],[f996]) ).
thf(f998,plain,
( ( ( singletonsubset = $true )
| ( ( ( subset @ ( setadjoin @ sK352 @ emptyset ) @ sK353 )
!= $true )
& ( ( in @ sK352 @ sK353 )
= $true ) ) )
& ( ! [X2: $i,X3: $i] :
( ( ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 )
= $true )
| ( ( in @ X2 @ X3 )
!= $true ) )
| ( singletonsubset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK352,sK353]),skolemize(X0,sK352),skolemize(X1,sK353)],[f997]) ).
thf(f1279,plain,
powersetI1 = $true,
inference(cnf_transformation,[],[f819]) ).
thf(f1359,plain,
singletonsubset = $true,
inference(cnf_transformation,[],[f819]) ).
thf(f1384,plain,
( ( in @ sK189 @ sK190 )
= $true ),
inference(cnf_transformation,[],[f819]) ).
thf(f1385,plain,
( ( in @ ( setadjoin @ sK189 @ emptyset ) @ ( powerset @ sK190 ) )
!= $true ),
inference(cnf_transformation,[],[f819]) ).
thf(f1465,plain,
! [X2: $i,X3: $i] :
( ( powersetI1 != $true )
| ( $true
!= ( subset @ X2 @ X3 ) )
| ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) ) ),
inference(cnf_transformation,[],[f861]) ).
thf(f1663,plain,
! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X3 )
!= $true )
| ( ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 )
= $true )
| ( singletonsubset != $true ) ),
inference(cnf_transformation,[],[f998]) ).
thf(f2829,definition,
( spl374_220
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl374_220])],[avatar_definition]) ).
thf(f2830,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ~ spl374_220 ),
inference(avatar_component_clause,[],[f2829]) ).
thf(f2846,definition,
( spl374_224
<=> ( singletonsubset = $true ) ),
introduced(definition,[new_symbols(definition,[spl374_224])],[avatar_definition]) ).
thf(f3140,definition,
( spl374_286
<=> ( ( in @ sK189 @ sK190 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl374_286])],[avatar_definition]) ).
thf(f3142,plain,
( ( ( in @ sK189 @ sK190 )
= $true )
| ~ spl374_286 ),
inference(avatar_component_clause,[],[f3140]) ).
thf(f3143,plain,
spl374_286,
inference(avatar_split_clause,[],[f1384,f3140]) ).
thf(f3164,definition,
( spl374_291
<=> ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X3 )
!= $true )
| ( ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl374_291])],[avatar_definition]) ).
thf(f3165,plain,
( ! [X2: $i,X3: $i] :
( ( ( subset @ ( setadjoin @ X2 @ emptyset ) @ X3 )
= $true )
| ( ( in @ X2 @ X3 )
!= $true ) )
| ~ spl374_291 ),
inference(avatar_component_clause,[],[f3164]) ).
thf(f3166,plain,
( spl374_291
| ~ spl374_224 ),
inference(avatar_split_clause,[],[f1663,f2846,f3164]) ).
thf(f3596,definition,
( spl374_380
<=> ( powersetI1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl374_380])],[avatar_definition]) ).
thf(f3599,plain,
( spl374_220
| ~ spl374_380 ),
inference(avatar_split_clause,[],[f1465,f3596,f2829]) ).
thf(f3986,plain,
spl374_380,
inference(avatar_split_clause,[],[f1279,f3596]) ).
thf(f4479,plain,
spl374_224,
inference(avatar_split_clause,[],[f1359,f2846]) ).
thf(f4661,definition,
( spl374_600
<=> ( ( in @ ( setadjoin @ sK189 @ emptyset ) @ ( powerset @ sK190 ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl374_600])],[avatar_definition]) ).
thf(f4663,plain,
( ( ( in @ ( setadjoin @ sK189 @ emptyset ) @ ( powerset @ sK190 ) )
!= $true )
| spl374_600 ),
inference(avatar_component_clause,[],[f4661]) ).
thf(f4664,plain,
~ spl374_600,
inference(avatar_split_clause,[],[f1385,f4661]) ).
thf(f5134,plain,
( ( ( subset @ ( setadjoin @ sK189 @ emptyset ) @ sK190 )
!= $true )
| ( $true != $true )
| ~ spl374_220
| spl374_600 ),
inference(superposition,[],[f4663,f2830]) ).
thf(f5141,plain,
( ( ( subset @ ( setadjoin @ sK189 @ emptyset ) @ sK190 )
!= $true )
| ~ spl374_220
| spl374_600 ),
inference(trivial_inequality_removal,[],[f5134]) ).
thf(f5146,definition,
( spl374_641
<=> ( ( subset @ ( setadjoin @ sK189 @ emptyset ) @ sK190 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl374_641])],[avatar_definition]) ).
thf(f5148,plain,
( ( ( subset @ ( setadjoin @ sK189 @ emptyset ) @ sK190 )
!= $true )
| spl374_641 ),
inference(avatar_component_clause,[],[f5146]) ).
thf(f5149,plain,
( ~ spl374_641
| ~ spl374_220
| spl374_600 ),
inference(avatar_split_clause,[],[f5141,f4661,f2829,f5146]) ).
thf(f5360,plain,
( ( $true != $true )
| ( ( in @ sK189 @ sK190 )
!= $true )
| ~ spl374_291
| spl374_641 ),
inference(superposition,[],[f5148,f3165]) ).
thf(f5361,plain,
( ( ( in @ sK189 @ sK190 )
!= $true )
| ~ spl374_291
| spl374_641 ),
inference(trivial_inequality_removal,[],[f5360]) ).
thf(f5364,plain,
( $false
| ~ spl374_286
| ~ spl374_291
| spl374_641 ),
inference(forward_subsumption_resolution,[],[f5361,f3142]) ).
thf(f5365,plain,
( ~ spl374_286
| ~ spl374_291
| spl374_641 ),
inference(avatar_contradiction_clause,[],[f5364]) ).
cnf(s221,plain,
spl374_286,
inference(sat_conversion,[],[f3143]) ).
cnf(s225,plain,
( ~ spl374_224
| spl374_291 ),
inference(sat_conversion,[],[f3166]) ).
cnf(s329,plain,
( spl374_220
| ~ spl374_380 ),
inference(sat_conversion,[],[f3599]) ).
cnf(s431,plain,
spl374_380,
inference(sat_conversion,[],[f3986]) ).
cnf(s564,plain,
spl374_224,
inference(sat_conversion,[],[f4479]) ).
cnf(s611,plain,
~ spl374_600,
inference(sat_conversion,[],[f4664]) ).
cnf(s666,plain,
( ~ spl374_220
| spl374_600
| ~ spl374_641 ),
inference(sat_conversion,[],[f5149]) ).
cnf(s675,plain,
( ~ spl374_286
| ~ spl374_291
| spl374_641 ),
inference(sat_conversion,[],[f5365]) ).
cnf(s714,plain,
spl374_220,
inference(rat,[],[s329,s431]) ).
cnf(s715,plain,
~ spl374_641,
inference(rat,[],[s666,s611,s714]) ).
cnf(s757,plain,
spl374_291,
inference(rat,[],[s225,s564]) ).
cnf(s758,plain,
~ spl374_286,
inference(rat,[],[s675,s715,s757]) ).
cnf(s759,plain,
$false,
inference(rat,[],[s221,s758]) ).
thf(f5366,plain,
$false,
inference(avatar_sat_refutation,[],[s759]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU622^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n009.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:59:00 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.24 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
% 0.83/0.40 % (4043761)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.83/0.40 % (4043768)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=3950807841:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.83/0.40 % (4043768)Instruction limit reached!
% 0.83/0.40 % (4043768)------------------------------
% 0.83/0.40 % (4043768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043768)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043768)Termination reason: Instruction limit
% 0.83/0.40 % (4043768)Termination phase: shuffling
% 0.83/0.40 % (4043768)Time elapsed: 0.001 s
% 0.83/0.40 % (4043768)Peak memory usage: 10 MB
% 0.83/0.40 % (4043768)Instructions burned: 4 (million)
% 0.83/0.40 % (4043767)lrs+10_16_si=on:nwc=1.5:random_seed=1529291049:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.83/0.40 % (4043766)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2000681822:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.83/0.40 % (4043770)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2894377246:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.83/0.40 % (4043772)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.83/0.40 % (4043772)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
% 0.83/0.40 % (4043769)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=3293264090: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)
% 0.83/0.40 % (4043774)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2995073215:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.83/0.40 % (4043771)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3848006546:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.83/0.40 % (4043774)Instruction limit reached!
% 0.83/0.40 % (4043774)------------------------------
% 0.83/0.40 % (4043774)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043774)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043774)Termination reason: Instruction limit
% 0.83/0.40 % (4043774)Termination phase: shuffling
% 0.83/0.40 % (4043774)Time elapsed: 0.001 s
% 0.83/0.40 % (4043774)Peak memory usage: 10 MB
% 0.83/0.40 % (4043774)Instructions burned: 3 (million)
% 0.83/0.40 % (4043772)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=707778673:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.83/0.40 % (4043767)Instruction limit reached!
% 0.83/0.40 % (4043767)------------------------------
% 0.83/0.40 % (4043767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043767)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043767)Termination reason: Instruction limit
% 0.83/0.40 % (4043767)Termination phase: Property scanning
% 0.83/0.40 % (4043767)Time elapsed: 0.008 s
% 0.83/0.40 % (4043767)Peak memory usage: 10 MB
% 0.83/0.40 % (4043767)Instructions burned: 19 (million)
% 0.83/0.40 % (4043770)Instruction limit reached!
% 0.83/0.40 % (4043770)------------------------------
% 0.83/0.40 % (4043770)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043770)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043770)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043770)Termination reason: Instruction limit
% 0.83/0.40 % (4043770)Termination phase: Preprocessing 3
% 0.83/0.40 % (4043770)Time elapsed: 0.012 s
% 0.83/0.40 % (4043770)Peak memory usage: 11 MB
% 0.83/0.40 % (4043770)Instructions burned: 25 (million)
% 0.83/0.40 % (4043781)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1833253926:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.83/0.40 % (4043781)Instruction limit reached!
% 0.83/0.40 % (4043781)------------------------------
% 0.83/0.40 % (4043781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043781)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043781)Termination reason: Instruction limit
% 0.83/0.40 % (4043781)Termination phase: shuffling
% 0.83/0.40 % (4043781)Time elapsed: 0.002 s
% 0.83/0.40 % (4043781)Peak memory usage: 10 MB
% 0.83/0.40 % (4043781)Instructions burned: 11 (million)
% 0.83/0.40 % (4043783)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.83/0.40 % (4043786)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
% 0.83/0.40 % (4043786)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.83/0.40 % (4043783)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1196686543:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.83/0.40 % (4043786)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1274239248:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.83/0.40 % (4043784)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=2245655691:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.83/0.40 % (4043783)Instruction limit reached!
% 0.83/0.40 % (4043783)------------------------------
% 0.83/0.40 % (4043783)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043783)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043783)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043783)Termination reason: Instruction limit
% 0.83/0.40 % (4043783)Termination phase: shuffling
% 0.83/0.40 % (4043783)Time elapsed: 0.004 s
% 0.83/0.40 % (4043783)Peak memory usage: 10 MB
% 0.83/0.40 % (4043783)Instructions burned: 8 (million)
% 0.83/0.40 % (4043786)Instruction limit reached!
% 0.83/0.40 % (4043786)------------------------------
% 0.83/0.40 % (4043786)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043786)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043786)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043786)Termination reason: Instruction limit
% 0.83/0.40 % (4043786)Termination phase: Property scanning
% 0.83/0.40 % (4043786)Time elapsed: 0.007 s
% 0.83/0.40 % (4043786)Peak memory usage: 10 MB
% 0.83/0.40 % (4043786)Instructions burned: 31 (million)
% 0.83/0.40 % (4043766)Instruction limit reached!
% 0.83/0.40 % (4043766)------------------------------
% 0.83/0.40 % (4043766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043766)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043766)Termination reason: Instruction limit
% 0.83/0.40 % (4043766)Termination phase: Saturation
% 0.83/0.40 % (4043766)Time elapsed: 0.040 s
% 0.83/0.40 % (4043766)Peak memory usage: 13 MB
% 0.83/0.40 % (4043766)Instructions burned: 87 (million)
% 0.83/0.40 % (4043784)Instruction limit reached!
% 0.83/0.40 % (4043784)------------------------------
% 0.83/0.40 % (4043784)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043784)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043784)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043784)Termination reason: Instruction limit
% 0.83/0.40 % (4043784)Termination phase: Property scanning
% 0.83/0.40 % (4043784)Time elapsed: 0.009 s
% 0.83/0.40 % (4043784)Peak memory usage: 10 MB
% 0.83/0.40 % (4043784)Instructions burned: 21 (million)
% 0.83/0.40 % (4043791)lrs+10_1_si=on:cs=on:random_seed=3865399583:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.83/0.40 % (4043791)Instruction limit reached!
% 0.83/0.40 % (4043791)------------------------------
% 0.83/0.40 % (4043791)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043791)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043791)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043791)Termination reason: Instruction limit
% 0.83/0.40 % (4043791)Termination phase: shuffling
% 0.83/0.40 % (4043791)Time elapsed: 0.004 s
% 0.83/0.40 % (4043791)Peak memory usage: 10 MB
% 0.83/0.40 % (4043791)Instructions burned: 15 (million)
% 0.83/0.40 % (4043790)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=2425311360:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.83/0.40 % (4043792)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.83/0.40 % (4043792)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=4236908187:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.83/0.40 % (4043793)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=1462248840:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.83/0.40 % (4043795)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=4261418649:st=2:i=249:sd=1:rtra=on:ss=axioms_2998 on theBenchmark for (2998ds/249Mi)
% 0.83/0.40 % (4043792)Instruction limit reached!
% 0.83/0.40 % (4043792)------------------------------
% 0.83/0.40 % (4043792)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043792)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043792)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043792)Termination reason: Instruction limit
% 0.83/0.40 % (4043792)Termination phase: shuffling
% 0.83/0.40 % (4043792)Time elapsed: 0.003 s
% 0.83/0.40 % (4043792)Peak memory usage: 10 MB
% 0.83/0.40 % (4043792)Instructions burned: 7 (million)
% 0.83/0.40 % (4043771)Instruction limit reached!
% 0.83/0.40 % (4043771)------------------------------
% 0.83/0.40 % (4043771)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043771)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043771)Termination reason: Instruction limit
% 0.83/0.40 % (4043771)Termination phase: Property scanning
% 0.83/0.40 % (4043771)Time elapsed: 0.062 s
% 0.83/0.40 % (4043771)Peak memory usage: 12 MB
% 0.83/0.40 % (4043771)Instructions burned: 75 (million)
% 0.83/0.40 % (4043793)Instruction limit reached!
% 0.83/0.40 % (4043793)------------------------------
% 0.83/0.40 % (4043793)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043793)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043793)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043793)Termination reason: Instruction limit
% 0.83/0.40 % (4043793)Termination phase: Preprocessing 3
% 0.83/0.40 % (4043793)Time elapsed: 0.018 s
% 0.83/0.40 % (4043793)Peak memory usage: 11 MB
% 0.83/0.40 % (4043793)Instructions burned: 39 (million)
% 0.83/0.40 % (4043800)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2251947382:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.83/0.40 % (4043769) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-4043761-4043769"...
% 0.83/0.40 % (4043801)lrs+10_16:1_sil=128000:si=on:lma=off:urr=on:uwa=interpreted_only:random_seed=1446794541:i=14:kws=precedence:aac=none:nm=10:rtra=on:er=filter:ntd=on_2998 on theBenchmark for (2998ds/14Mi)
% 0.83/0.40 % (4043790)Instruction limit reached!
% 0.83/0.40 % (4043790)------------------------------
% 0.83/0.40 % (4043790)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.40 % (4043790)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.40 % (4043790)CaDiCaL version: 2.1.3
% 0.83/0.40 % (4043790)Termination reason: Instruction limit
% 0.83/0.40 % (4043790)Termination phase: Saturation
% 0.83/0.40 % (4043790)Time elapsed: 0.038 s
% 0.83/0.40 % (4043790)Peak memory usage: 13 MB
% 0.83/0.40 % (4043790)Instructions burned: 87 (million)
% 0.83/0.40 % (4043769)...printing done.
% 0.83/0.40 % (4043769)Refutation found. Thanks to Tanya!
% 0.83/0.40 % SZS status Theorem for theBenchmark
% 0.83/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.83/0.41 % (4043769)------------------------------
% 0.83/0.41 % (4043769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.83/0.41 % (4043769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.83/0.41 % (4043769)CaDiCaL version: 2.1.3
% 0.83/0.41 % (4043769)Termination reason: Refutation
% 0.83/0.41 % (4043769)Time elapsed: 0.094 s
% 0.83/0.41 % (4043769)Peak memory usage: 16 MB
% 0.83/0.41 % (4043769)Instructions burned: 180 (million)
% 0.83/0.41 % (4043761)Success in time 0.156 s
% 0.83/0.41 % Vampire exiting
%------------------------------------------------------------------------------