%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU578^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 08:30:09 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 52 ( 17 unt; 0 typ; 5 def)
% Number of atoms : 1674 ( 443 equ; 0 cnn)
% Maximal formula atoms : 95 ( 32 avg)
% Number of connectives : 890 ( 49 ~; 40 |; 291 &; 123 @)
% ( 8 <=>; 379 =>; 0 <=; 0 <~>)
% Maximal formula depth : 99 ( 16 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 : 228 ( 225 usr; 112 con; 0-4 aty)
% Number of variables : 41 ( 0 sgn 33 !; 8 ?; 41 :)
% 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_112,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_113,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_114,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_115,type,
vNOT: $o > $o ).
thf(func_def_116,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_117,type,
vAND: $o > $o > $o ).
thf(func_def_118,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_119,type,
vIMP: $o > $o > $o ).
thf(func_def_120,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_121,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_122,type,
sP0: $i > $i > $o ).
thf(func_def_123,type,
sP1: $i > $o ).
thf(func_def_124,type,
sP2: $o ).
thf(func_def_126,type,
sK4: $i > $i ).
thf(func_def_128,type,
sK6: $i > $i ).
thf(func_def_129,type,
sK7: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_130,type,
sK8: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_131,type,
sK9: $i > $o ).
thf(func_def_132,type,
sK10: $i > $o ).
thf(func_def_135,type,
sK13: $i > $o ).
thf(func_def_137,type,
sK15: $i > $o ).
thf(func_def_140,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_141,type,
sK19: $i > $o ).
thf(func_def_143,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_144,type,
sK22: ( $i > $o ) > $i ).
thf(func_def_162,type,
sK40: ( $i > $o ) > $i ).
thf(func_def_163,type,
sK41: $i > $o ).
thf(func_def_164,type,
sK42: $i > $i ).
thf(func_def_170,type,
sK48: $i > $i ).
thf(func_def_172,type,
sK50: $o ).
thf(func_def_180,type,
sK58: $i > $i > $i ).
thf(func_def_186,type,
sK64: $i > $i > $i ).
thf(func_def_189,type,
sK67: $i > ( $i > $o ) > $i ).
thf(func_def_190,type,
sK68: $i > $o ).
thf(func_def_197,type,
sK75: $o ).
thf(func_def_198,type,
sK76: $o > $i > $i > $i ).
thf(func_def_200,type,
sK78: $i > $o ).
thf(func_def_206,type,
sK84: $i > $o ).
thf(func_def_211,type,
sK89: $i > $o ).
thf(func_def_213,type,
sK91: ( $i > $o ) > $i > $i ).
thf(func_def_214,type,
sK92: $i > $o ).
thf(func_def_215,type,
sK93: $i > $i > $i ).
thf(func_def_218,type,
sK96: $i > $o ).
thf(func_def_219,type,
sK97: $i > $i ).
thf(func_def_220,type,
sK98: ( $i > $o ) > $i ).
thf(func_def_221,type,
sK99: ( $i > $o ) > $i ).
thf(func_def_222,type,
sK100: $i > $o ).
thf(func_def_223,type,
sK101: $i > $i ).
thf(func_def_230,type,
sK108: $i > $o ).
thf(func_def_231,type,
sK109: $i > $o ).
thf(func_def_234,type,
sK112: $i > ( $i > $o ) > $i ).
thf(func_def_235,type,
sK113: $i > $o ).
thf(func_def_237,type,
sK115: $i > ( $i > $o ) > $i ).
thf(func_def_241,type,
sK119: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_242,type,
sK120: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_245,type,
sK123: $i > $o ).
thf(func_def_246,type,
sK124: $i > $o ).
thf(func_def_249,type,
sK127: $i > $i > $i ).
thf(func_def_253,type,
sK131: $o ).
thf(func_def_258,type,
sK136: $i > $o ).
thf(func_def_262,type,
sK140: $i > $i ).
thf(func_def_263,type,
sK141: $i > $i ).
thf(func_def_264,type,
sK142: $i > $i ).
thf(func_def_265,type,
sK143: $i > $i ).
thf(func_def_266,type,
sK144: $i > $i ).
thf(func_def_267,type,
sK145: $i > $i > $i > $i ).
thf(func_def_268,type,
sK146: $i > $i ).
thf(func_def_269,type,
sK147: $i > $i ).
thf(func_def_270,type,
sK148: $i > $i ).
thf(func_def_271,type,
sK149: $i > $i ).
thf(func_def_272,type,
sK150: $i > $i > $i ).
thf(func_def_273,type,
sK151: $i > $i > $i > $i ).
thf(func_def_274,type,
sK152: $i > $i > $i > $i ).
thf(func_def_275,type,
sK153: $i > $i > $i > $i ).
thf(func_def_276,type,
sK154: $i > $i > $i ).
thf(func_def_277,type,
sK155: $i > $i > $i ).
thf(func_def_278,type,
sK156: $i > $i > $i ).
thf(func_def_279,type,
sK157: $i > $i > $i ).
thf(func_def_282,type,
sK160: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_283,type,
sK161: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_284,type,
sK162: $i > $o ).
thf(func_def_285,type,
sK163: $i > $o ).
thf(func_def_287,type,
sK165: $i > $i ).
thf(func_def_303,type,
sK181: $i > ( $i > $o ) > $i ).
thf(func_def_304,type,
sK182: $i > $o ).
thf(func_def_306,type,
sK184: $o ).
thf(func_def_315,type,
sK193: $i > $o ).
thf(func_def_318,type,
sK196: $i > ( $i > $o ) > $i ).
thf(func_def_319,type,
sK197: $i > $o ).
thf(func_def_327,type,
sK205: $o ).
thf(func_def_329,type,
sK207: $i > $o ).
thf(func_def_334,type,
sK212: $i > $o ).
thf(func_def_338,type,
sK216: $i > $i ).
thf(func_def_340,type,
sK218: $i > $o ).
thf(func_def_344,type,
sK222: $i > $o ).
thf(func_def_346,type,
sK224: ( $i > $o ) > $i > $i ).
thf(func_def_350,type,
sK228: $o ).
thf(func_def_353,type,
sK231: $i > $i > $i ).
thf(func_def_354,type,
sK232: $i > $i > $i ).
thf(func_def_360,type,
sK238: $i > $i ).
thf(func_def_365,type,
sK243: $i > $i > $i ).
thf(func_def_366,type,
sK244: $i > $i > $i ).
thf(func_def_377,type,
sK255: ( $i > $i > $o ) > $i > $i ).
thf(func_def_378,type,
sK256: ( $i > $i > $o ) > $i > $i ).
thf(func_def_379,type,
sK257: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_381,type,
sK259: $i > $i > $o ).
thf(func_def_382,type,
sK260: $i > $i ).
thf(func_def_383,type,
sK261: $i > $i ).
thf(f88,axiom,
( subsetRefl
= ( ! [X0: $i] : ( subset @ X0 @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(f95,axiom,
( powersetI1
= ( ! [X1: $i,X0: $i] :
( ( subset @ X1 @ X0 )
=> ( in @ X1 @ ( powerset @ X0 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(f97,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
=> ! [X0: $i] : ( in @ X0 @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(f98,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
=> ! [X0: $i] : ( in @ X0 @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f97]) ).
thf(f135,plain,
( powersetI1
= ( ! [X0: $i,X1: $i] :
( ( subset @ X0 @ X1 )
=> ( in @ X0 @ ( powerset @ X1 ) ) ) ) ),
inference(rectify,[],[f95]) ).
thf(f136,plain,
( ( powersetI1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) ) ),
inference(fool_elimination,[],[f135]) ).
thf(f163,plain,
( subsetRefl
= ( ! [X0: $i] : ( subset @ X0 @ X0 ) ) ),
inference(rectify,[],[f88]) ).
thf(f164,plain,
( ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true )
<=> ( subsetRefl = $true ) ),
inference(fool_elimination,[],[f163]) ).
thf(f269,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
=> ! [X0: $i] : ( in @ X0 @ ( powerset @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f98]) ).
thf(f270,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 )
=> ! [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f269]) ).
thf(f342,plain,
( ? [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
!= $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,[],[f270]) ).
thf(f343,plain,
( ( descrp = $true )
& ( uniqinunit = $true )
& ( upairsetIL = $true )
& ( setoftrueEq = $true )
& ( eqinunit = $true )
& ( setunionAx = $true )
& ( exu__Cong = $true )
& ( exuEu = $true )
& ( setadjoin__Cong = $true )
& ( inCongP = $true )
& ( dsetconstrI = $true )
& ( emptyE1 = $true )
& ( powersetI1 = $true )
& ( omega__Cong = $true )
& ( dsetconstrEL = $true )
& ( descr__Cong = $true )
& ( setadjoinSub2 = $true )
& ( exuE3u = $true )
& ( subsetE2 = $true )
& ( subset2powerset = $true )
& ( powersetAx = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan2 = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( exuE3e = $true )
& ( subsetI1 = $true )
& ( prop2set2propI = $true )
& ( notinemptyset = $true )
& ( in__Cong = $true )
& ( emptysetAx = $true )
& ( exuI3 = $true )
& ( subsetI2 = $true )
& ( emptyinunitempty = $true )
& ( notsubsetI = $true )
& ( powersetE1 = $true )
& ( subPowSU = $true )
& ( setunion__Cong = $true )
& ( emptyset__Cong = $true )
& ( prop2setI = $true )
& ( emptyI = $true )
& ( exuE2 = $true )
& ( emptyInPowerset = $true )
& ( nonemptyI1 = $true )
& ( exuI1 = $true )
& ( powersetE = $true )
& ( foundationAx = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinIR = $true )
& ( exuE1 = $true )
& ( quantDeMorgan1 = $true )
& ( setextsub = $true )
& ( emptysetsubset = $true )
& ( setbeta = $true )
& ( emptyinPowerset = $true )
& ( setadjoinAx = $true )
& ( eqimpsubset1 = $true )
& ( subsetemptysetimpeq = $true )
& ( noeltsimpempty = $true )
& ( dsetconstr__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetE = $true )
& ( subsetRefl = $true )
& ( setextAx = $true )
& ( upairsetE = $true )
& ( vacuousDall = $true )
& ( omegaIndAx = $true )
& ( subsetE = $true )
& ( nonemptyE1 = $true )
& ( setunionE = $true )
& ( powerset__Cong = $true )
& ? [X0: $i] :
( ( in @ X0 @ ( powerset @ X0 ) )
!= $true )
& ( singletonsswitch = $true )
& ( notinsingleton = $true )
& ( powersetI = $true )
& ( notequalI2 = $true )
& ( notdexE = $true )
& ( setadjoinIL = $true )
& ( notdallE = $true )
& ( dsetconstrER = $true )
& ( setunionI = $true )
& ( notequalI1 = $true )
& ( setadjoinOr = $true )
& ( omega0Ax = $true )
& ( exuI2 = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( eqimpsubset2 = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinSub = $true )
& ( wellorderingAx = $true )
& ( setadjoinE = $true )
& ( omegaSAx = $true )
& ( subsetTrans = $true )
& ( prop2setE = $true ) ),
inference(flattening,[],[f342]) ).
thf(f409,plain,
( ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
<=> ( powersetI1 = $true ) ),
inference(ennf_transformation,[],[f136]) ).
thf(f532,plain,
( ( ! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( in @ X0 @ ( powerset @ X1 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f409]) ).
thf(f533,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( subset @ X3 @ X2 ) )
& ( $true
!= ( in @ X3 @ ( powerset @ X2 ) ) ) ) ) ),
inference(rectify,[],[f532]) ).
thf(f534,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) )
| ( powersetI1 != $true ) )
& ( ( powersetI1 = $true )
| ( ( ( subset @ sK104 @ sK103 )
= $true )
& ( $true
!= ( in @ sK104 @ ( powerset @ sK103 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK103,sK104]),skolemize(X2,sK103),skolemize(X3,sK104)],[f533]) ).
thf(f569,plain,
( ( ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true )
| ( subsetRefl != $true ) )
& ( ( subsetRefl = $true )
| ? [X0: $i] :
( ( subset @ X0 @ X0 )
!= $true ) ) ),
inference(nnf_transformation,[],[f164]) ).
thf(f570,plain,
( ( ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true )
| ( subsetRefl != $true ) )
& ( ( subsetRefl = $true )
| ? [X1: $i] :
( $true
!= ( subset @ X1 @ X1 ) ) ) ),
inference(rectify,[],[f569]) ).
thf(f571,plain,
( ( ! [X0: $i] :
( ( subset @ X0 @ X0 )
= $true )
| ( subsetRefl != $true ) )
& ( ( subsetRefl = $true )
| ( $true
!= ( subset @ sK135 @ sK135 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(X1,sK135)],[f570]) ).
thf(f594,plain,
( ( descrp = $true )
& ( uniqinunit = $true )
& ( upairsetIL = $true )
& ( setoftrueEq = $true )
& ( eqinunit = $true )
& ( setunionAx = $true )
& ( exu__Cong = $true )
& ( exuEu = $true )
& ( setadjoin__Cong = $true )
& ( inCongP = $true )
& ( dsetconstrI = $true )
& ( emptyE1 = $true )
& ( powersetI1 = $true )
& ( omega__Cong = $true )
& ( dsetconstrEL = $true )
& ( descr__Cong = $true )
& ( setadjoinSub2 = $true )
& ( exuE3u = $true )
& ( subsetE2 = $true )
& ( subset2powerset = $true )
& ( powersetAx = $true )
& ( upairsetIR = $true )
& ( quantDeMorgan2 = $true )
& ( setext = $true )
& ( nonemptyI = $true )
& ( exuE3e = $true )
& ( subsetI1 = $true )
& ( prop2set2propI = $true )
& ( notinemptyset = $true )
& ( in__Cong = $true )
& ( emptysetAx = $true )
& ( exuI3 = $true )
& ( subsetI2 = $true )
& ( emptyinunitempty = $true )
& ( notsubsetI = $true )
& ( powersetE1 = $true )
& ( subPowSU = $true )
& ( setunion__Cong = $true )
& ( emptyset__Cong = $true )
& ( prop2setI = $true )
& ( emptyI = $true )
& ( exuE2 = $true )
& ( emptyInPowerset = $true )
& ( nonemptyI1 = $true )
& ( exuI1 = $true )
& ( powersetE = $true )
& ( foundationAx = $true )
& ( quantDeMorgan3 = $true )
& ( setadjoinIR = $true )
& ( exuE1 = $true )
& ( quantDeMorgan1 = $true )
& ( setextsub = $true )
& ( emptysetsubset = $true )
& ( setbeta = $true )
& ( emptyinPowerset = $true )
& ( setadjoinAx = $true )
& ( eqimpsubset1 = $true )
& ( subsetemptysetimpeq = $true )
& ( noeltsimpempty = $true )
& ( dsetconstr__Cong = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetE = $true )
& ( subsetRefl = $true )
& ( setextAx = $true )
& ( upairsetE = $true )
& ( vacuousDall = $true )
& ( omegaIndAx = $true )
& ( subsetE = $true )
& ( nonemptyE1 = $true )
& ( setunionE = $true )
& ( powerset__Cong = $true )
& ( $true
!= ( in @ sK166 @ ( powerset @ sK166 ) ) )
& ( singletonsswitch = $true )
& ( notinsingleton = $true )
& ( powersetI = $true )
& ( notequalI2 = $true )
& ( notdexE = $true )
& ( setadjoinIL = $true )
& ( notdallE = $true )
& ( dsetconstrER = $true )
& ( setunionI = $true )
& ( notequalI1 = $true )
& ( setadjoinOr = $true )
& ( omega0Ax = $true )
& ( exuI2 = $true )
& ( emptysetimpfalse = $true )
& ( replAx = $true )
& ( eqimpsubset2 = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinSub = $true )
& ( wellorderingAx = $true )
& ( setadjoinE = $true )
& ( omegaSAx = $true )
& ( subsetTrans = $true )
& ( prop2setE = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(X0,sK166)],[f343]) ).
thf(f842,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( powersetI1 != $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ),
inference(cnf_transformation,[],[f534]) ).
thf(f889,plain,
! [X0: $i] :
( ( subsetRefl != $true )
| ( ( subset @ X0 @ X0 )
= $true ) ),
inference(cnf_transformation,[],[f571]) ).
thf(f974,plain,
( $true
!= ( in @ sK166 @ ( powerset @ sK166 ) ) ),
inference(cnf_transformation,[],[f594]) ).
thf(f983,plain,
subsetRefl = $true,
inference(cnf_transformation,[],[f594]) ).
thf(f1033,plain,
powersetI1 = $true,
inference(cnf_transformation,[],[f594]) ).
thf(f1937,definition,
( spl262_138
<=> ( powersetI1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl262_138])],[avatar_definition]) ).
thf(f1941,definition,
( spl262_139
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( ( in @ X1 @ ( powerset @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl262_139])],[avatar_definition]) ).
thf(f1942,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X1 @ ( powerset @ X0 ) )
= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ~ spl262_139 ),
inference(avatar_component_clause,[],[f1941]) ).
thf(f1943,plain,
( ~ spl262_138
| spl262_139 ),
inference(avatar_split_clause,[],[f842,f1941,f1937]) ).
thf(f2672,definition,
( spl262_299
<=> ! [X1: $i] :
( $true
= ( subset @ X1 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl262_299])],[avatar_definition]) ).
thf(f2673,plain,
( ! [X1: $i] :
( $true
= ( subset @ X1 @ X1 ) )
| ~ spl262_299 ),
inference(avatar_component_clause,[],[f2672]) ).
thf(f2831,definition,
( spl262_333
<=> ( $true
= ( in @ sK166 @ ( powerset @ sK166 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl262_333])],[avatar_definition]) ).
thf(f2833,plain,
( ( $true
!= ( in @ sK166 @ ( powerset @ sK166 ) ) )
| spl262_333 ),
inference(avatar_component_clause,[],[f2831]) ).
thf(f2834,plain,
~ spl262_333,
inference(avatar_split_clause,[],[f974,f2831]) ).
thf(f3348,definition,
( spl262_439
<=> ( subsetRefl = $true ) ),
introduced(definition,[new_symbols(definition,[spl262_439])],[avatar_definition]) ).
thf(f3351,plain,
( spl262_299
| ~ spl262_439 ),
inference(avatar_split_clause,[],[f889,f3348,f2672]) ).
thf(f3447,plain,
spl262_439,
inference(avatar_split_clause,[],[f983,f3348]) ).
thf(f3458,plain,
spl262_138,
inference(avatar_split_clause,[],[f1033,f1937]) ).
thf(f3640,plain,
( ( $true
!= ( subset @ sK166 @ sK166 ) )
| ( $true != $true )
| ~ spl262_139
| spl262_333 ),
inference(superposition,[],[f2833,f1942]) ).
thf(f3641,plain,
( ( $true
!= ( subset @ sK166 @ sK166 ) )
| ~ spl262_139
| spl262_333 ),
inference(trivial_inequality_removal,[],[f3640]) ).
thf(f3644,plain,
( $false
| ~ spl262_139
| ~ spl262_299
| spl262_333 ),
inference(forward_subsumption_resolution,[],[f3641,f2673]) ).
thf(f3645,plain,
( ~ spl262_139
| ~ spl262_299
| spl262_333 ),
inference(avatar_contradiction_clause,[],[f3644]) ).
cnf(s101,plain,
( ~ spl262_138
| spl262_139 ),
inference(sat_conversion,[],[f1943]) ).
cnf(s288,plain,
~ spl262_333,
inference(sat_conversion,[],[f2834]) ).
cnf(s434,plain,
( spl262_299
| ~ spl262_439 ),
inference(sat_conversion,[],[f3351]) ).
cnf(s462,plain,
spl262_439,
inference(sat_conversion,[],[f3447]) ).
cnf(s465,plain,
spl262_138,
inference(sat_conversion,[],[f3458]) ).
cnf(s479,plain,
( ~ spl262_139
| ~ spl262_299
| spl262_333 ),
inference(sat_conversion,[],[f3645]) ).
cnf(s481,plain,
spl262_299,
inference(rat,[],[s434,s462]) ).
cnf(s500,plain,
~ spl262_139,
inference(rat,[],[s479,s481,s288]) ).
cnf(s551,plain,
$false,
inference(rat,[],[s101,s500,s465]) ).
thf(f3646,plain,
$false,
inference(avatar_sat_refutation,[],[s551]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU578^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.17 % Computer : n009.cluster.edu
% 0.11/0.17 % Model : x86_64 x86_64
% 0.11/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.17 % Memory : 8046.5625MB
% 0.11/0.17 % OS : Linux 6.8.0-71-generic
% 0.11/0.17 % CPULimit : 300
% 0.11/0.17 % WCLimit : 300
% 0.11/0.17 % DateTime : Tue Sep 29 13:52:01 UTC 2026
% 0.11/0.17 % CPUTime :
% 0.11/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.20 Running higher-order theorem proving
% 0.11/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.31 % (4031890)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (4031896)lrs+10_16_si=on:nwc=1.5:random_seed=2316630159:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (4031901)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (4031901)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
% 0.21/0.31 % (4031896)Instruction limit reached!
% 0.21/0.31 % (4031896)------------------------------
% 0.21/0.31 % (4031896)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031896)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031896)Termination reason: Instruction limit
% 0.21/0.31 % (4031896)Termination phase: Property scanning
% 0.21/0.31 % (4031896)Time elapsed: 0.005 s
% 0.21/0.31 % (4031896)Peak memory usage: 10 MB
% 0.21/0.31 % (4031896)Instructions burned: 22 (million)
% 0.21/0.31 % (4031895)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=404738600:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (4031897)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=100820017:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (4031899)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1930659165:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (4031900)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=458968281:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (4031898)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=234709994: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)
% 0.21/0.31 % (4031901)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=3805989442:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (4031897)Instruction limit reached!
% 0.21/0.31 % (4031897)------------------------------
% 0.21/0.31 % (4031897)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031897)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031897)Termination reason: Instruction limit
% 0.21/0.31 % (4031897)Termination phase: shuffling
% 0.21/0.31 % (4031897)Time elapsed: 0.003 s
% 0.21/0.31 % (4031897)Peak memory usage: 10 MB
% 0.21/0.31 % (4031897)Instructions burned: 7 (million)
% 0.21/0.31 % (4031903)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=4026958796:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (4031903)Instruction limit reached!
% 0.21/0.31 % (4031903)------------------------------
% 0.21/0.31 % (4031903)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031903)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031903)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031903)Termination reason: Instruction limit
% 0.21/0.31 % (4031903)Termination phase: shuffling
% 0.21/0.31 % (4031903)Time elapsed: 0.001 s
% 0.21/0.31 % (4031903)Peak memory usage: 10 MB
% 0.21/0.31 % (4031903)Instructions burned: 4 (million)
% 0.21/0.31 % (4031899)Instruction limit reached!
% 0.21/0.31 % (4031899)------------------------------
% 0.21/0.31 % (4031899)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031899)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031899)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031899)Termination reason: Instruction limit
% 0.21/0.31 % (4031899)Termination phase: Preprocessing 3
% 0.21/0.31 % (4031899)Time elapsed: 0.013 s
% 0.21/0.31 % (4031899)Peak memory usage: 11 MB
% 0.21/0.31 % (4031899)Instructions burned: 26 (million)
% 0.21/0.31 % (4031912)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.31 % (4031912)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2652482500:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.31 % (4031912)Instruction limit reached!
% 0.21/0.31 % (4031912)------------------------------
% 0.21/0.31 % (4031912)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031912)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031912)Termination reason: Instruction limit
% 0.21/0.31 % (4031912)Termination phase: shuffling
% 0.21/0.31 % (4031912)Time elapsed: 0.002 s
% 0.21/0.31 % (4031912)Peak memory usage: 10 MB
% 0.21/0.31 % (4031912)Instructions burned: 9 (million)
% 0.21/0.31 % (4031910)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3608854380:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.31 % (4031910)Instruction limit reached!
% 0.21/0.31 % (4031910)------------------------------
% 0.21/0.31 % (4031910)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031910)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031910)Termination reason: Instruction limit
% 0.21/0.31 % (4031910)Termination phase: shuffling
% 0.21/0.31 % (4031910)Time elapsed: 0.003 s
% 0.21/0.31 % (4031910)Peak memory usage: 10 MB
% 0.21/0.31 % (4031910)Instructions burned: 7 (million)
% 0.21/0.31 % (4031915)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
% 0.21/0.31 % (4031915)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.31 % (4031915)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2867059923:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.31 % (4031913)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1388842876:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.31 % (4031900)Instruction limit reached!
% 0.21/0.31 % (4031900)------------------------------
% 0.21/0.31 % (4031900)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031900)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031900)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031900)Termination reason: Instruction limit
% 0.21/0.31 % (4031900)Termination phase: Saturation
% 0.21/0.31 % (4031900)Time elapsed: 0.036 s
% 0.21/0.31 % (4031900)Peak memory usage: 13 MB
% 0.21/0.31 % (4031900)Instructions burned: 76 (million)
% 0.21/0.31 % (4031915)Instruction limit reached!
% 0.21/0.31 % (4031915)------------------------------
% 0.21/0.31 % (4031915)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031915)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031915)Termination reason: Instruction limit
% 0.21/0.31 % (4031915)Termination phase: Property scanning
% 0.21/0.31 % (4031915)Time elapsed: 0.006 s
% 0.21/0.31 % (4031915)Peak memory usage: 10 MB
% 0.21/0.31 % (4031915)Instructions burned: 29 (million)
% 0.21/0.31 % (4031913)Instruction limit reached!
% 0.21/0.31 % (4031913)------------------------------
% 0.21/0.31 % (4031913)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031913)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031913)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031913)Termination reason: Instruction limit
% 0.21/0.31 % (4031913)Termination phase: Property scanning
% 0.21/0.31 % (4031913)Time elapsed: 0.005 s
% 0.21/0.31 % (4031913)Peak memory usage: 10 MB
% 0.21/0.31 % (4031913)Instructions burned: 12 (million)
% 0.21/0.31 % (4031895)Instruction limit reached!
% 0.21/0.31 % (4031895)------------------------------
% 0.21/0.31 % (4031895)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031895)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031895)Termination reason: Instruction limit
% 0.21/0.31 % (4031895)Termination phase: Saturation
% 0.21/0.31 % (4031895)Time elapsed: 0.041 s
% 0.21/0.31 % (4031895)Peak memory usage: 13 MB
% 0.21/0.31 % (4031895)Instructions burned: 88 (million)
% 0.21/0.31 % (4031917)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=1581560016:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.31 % (4031921)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.31 % (4031921)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=3923519610:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (4031921)Instruction limit reached!
% 0.21/0.31 % (4031921)------------------------------
% 0.21/0.31 % (4031921)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (4031921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (4031921)CaDiCaL version: 2.1.3
% 0.21/0.31 % (4031921)Termination reason: Instruction limit
% 0.21/0.31 % (4031921)Termination phase: shuffling
% 0.21/0.31 % (4031921)Time elapsed: 0.001 s
% 0.21/0.31 % (4031921)Peak memory usage: 10 MB
% 0.21/0.31 % (4031921)Instructions burned: 4 (million)
% 0.21/0.31 % (4031898) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4031890-4031898"...
% 0.21/0.31 % (4031920)lrs+10_1_si=on:cs=on:random_seed=3473037342:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.31 % (4031922)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2056834118:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.21/0.31 % (4031898)...printing done.
% 0.21/0.31 % (4031898)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.32 % (4031898)------------------------------
% 0.21/0.32 % (4031898)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.32 % (4031898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.32 % (4031898)CaDiCaL version: 2.1.3
% 0.21/0.32 % (4031898)Termination reason: Refutation
% 0.21/0.32 % (4031898)Time elapsed: 0.056 s
% 0.21/0.32 % (4031898)Peak memory usage: 15 MB
% 0.21/0.32 % (4031898)Instructions burned: 107 (million)
% 0.21/0.32 % (4031890)Success in time 0.085 s
% 0.21/0.32 % Vampire exiting
%------------------------------------------------------------------------------