%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU575^1 : 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 : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:30:08 AM UTC 2026
% Result : Theorem 0.21s 0.34s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 20 unt; 0 typ; 6 def)
% Number of atoms : 1716 ( 461 equ; 0 cnn)
% Maximal formula atoms : 94 ( 29 avg)
% Number of connectives : 903 ( 67 ~; 58 |; 288 &; 106 @)
% ( 10 <=>; 374 =>; 0 <=; 0 <~>)
% Maximal formula depth : 97 ( 14 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 : 227 ( 224 usr; 111 con; 0-4 aty)
% Number of variables : 43 ( 0 sgn 35 !; 8 ?; 43 :)
% 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_109,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_110,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_111,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_112,type,
vAND: $o > $o > $o ).
thf(func_def_113,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_114,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_115,type,
vIMP: $o > $o > $o ).
thf(func_def_116,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_117,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_118,type,
vNOT: $o > $o ).
thf(func_def_119,type,
sP0: $i > $i > $o ).
thf(func_def_120,type,
sP1: $i > $o ).
thf(func_def_121,type,
sP2: $o ).
thf(func_def_135,type,
sK16: $i > $o ).
thf(func_def_136,type,
sK17: $i > $o ).
thf(func_def_137,type,
sK18: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_138,type,
sK19: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_145,type,
sK26: $i > $o ).
thf(func_def_146,type,
sK27: $i > $i ).
thf(func_def_147,type,
sK28: ( $i > $o ) > $i ).
thf(func_def_149,type,
sK30: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_150,type,
sK31: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_151,type,
sK32: $i > $o ).
thf(func_def_152,type,
sK33: $i > $o ).
thf(func_def_155,type,
sK36: $i > $o ).
thf(func_def_156,type,
sK37: $i > $o ).
thf(func_def_162,type,
sK43: $i > $o ).
thf(func_def_164,type,
sK45: $o ).
thf(func_def_166,type,
sK47: $o ).
thf(func_def_169,type,
sK50: $i > $i ).
thf(func_def_171,type,
sK52: $i > $i ).
thf(func_def_173,type,
sK54: $i > ( $i > $o ) > $i ).
thf(func_def_174,type,
sK55: $i > $o ).
thf(func_def_178,type,
sK59: $i > $i > $i ).
thf(func_def_180,type,
sK61: $i > $i > $i ).
thf(func_def_183,type,
sK64: $i > $o ).
thf(func_def_188,type,
sK69: $i > $i ).
thf(func_def_199,type,
sK80: $i > $i > $i ).
thf(func_def_200,type,
sK81: $i > $o ).
thf(func_def_203,type,
sK84: $i > ( $i > $o ) > $i ).
thf(func_def_206,type,
sK87: $i > $i > $o ).
thf(func_def_208,type,
sK89: $i > $i ).
thf(func_def_209,type,
sK90: $i > $i ).
thf(func_def_210,type,
sK91: $i > ( $i > $i > $o ) > $i ).
thf(func_def_211,type,
sK92: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_212,type,
sK93: $i > ( $i > $i > $o ) > $i ).
thf(func_def_213,type,
sK94: ( $i > $o ) > $i ).
thf(func_def_214,type,
sK95: ( $i > $o ) > $i ).
thf(func_def_215,type,
sK96: $i > $o ).
thf(func_def_224,type,
sK105: $i > $i ).
thf(func_def_228,type,
sK109: $i > $o ).
thf(func_def_232,type,
sK113: $o ).
thf(func_def_233,type,
sK114: $o > $i > $i > $i ).
thf(func_def_234,type,
sK115: ( $i > $o ) > $i > $i ).
thf(func_def_236,type,
sK117: $i > $o ).
thf(func_def_238,type,
sK119: $i > $o ).
thf(func_def_241,type,
sK122: $i > ( $i > $o ) > $i ).
thf(func_def_249,type,
sK130: $i > $o ).
thf(func_def_250,type,
sK131: ( $i > $o ) > $i ).
thf(func_def_255,type,
sK136: $i > $i ).
thf(func_def_265,type,
sK146: $i > $o ).
thf(func_def_269,type,
sK150: ( $i > $o ) > $i ).
thf(func_def_270,type,
sK151: $i > $o ).
thf(func_def_271,type,
sK152: $i > $i ).
thf(func_def_272,type,
sK153: $o ).
thf(func_def_281,type,
sK162: $i > $o ).
thf(func_def_283,type,
sK164: ( $i > $o ) > $i > $i ).
thf(func_def_290,type,
sK171: $i > $i > $i ).
thf(func_def_293,type,
sK174: $i > $i > $i ).
thf(func_def_294,type,
sK175: $i > $i > $i ).
thf(func_def_298,type,
sK179: $i > $o ).
thf(func_def_299,type,
sK180: $i > $o ).
thf(func_def_300,type,
sK181: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_301,type,
sK182: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_303,type,
sK184: $i > $i ).
thf(func_def_304,type,
sK185: $i > $i ).
thf(func_def_305,type,
sK186: $i > $i ).
thf(func_def_306,type,
sK187: $i > $i ).
thf(func_def_307,type,
sK188: $i > $i ).
thf(func_def_308,type,
sK189: $i > $i > $i > $i ).
thf(func_def_309,type,
sK190: $i > $i ).
thf(func_def_310,type,
sK191: $i > $i ).
thf(func_def_311,type,
sK192: $i > $i ).
thf(func_def_312,type,
sK193: $i > $i ).
thf(func_def_313,type,
sK194: $i > $i > $i ).
thf(func_def_314,type,
sK195: $i > $i > $i ).
thf(func_def_315,type,
sK196: $i > $i > $i > $i ).
thf(func_def_316,type,
sK197: $i > $i > $i > $i ).
thf(func_def_317,type,
sK198: $i > $i > $i > $i ).
thf(func_def_318,type,
sK199: $i > $i > $i ).
thf(func_def_319,type,
sK200: $i > $i > $i ).
thf(func_def_320,type,
sK201: $i > $i > $i ).
thf(func_def_326,type,
sK207: $o ).
thf(func_def_327,type,
sK208: ( $i > $o ) > $i > $i ).
thf(func_def_329,type,
sK210: $i > $o ).
thf(func_def_332,type,
sK213: $i > $i ).
thf(func_def_338,type,
sK219: $i > $o ).
thf(func_def_344,type,
sK225: $i > $o ).
thf(func_def_347,type,
sK228: $i > $i > $i ).
thf(func_def_351,type,
sK232: $i > $o ).
thf(func_def_354,type,
sK235: $i > ( $i > $o ) > $i ).
thf(func_def_358,type,
sK239: $i > $i > $i ).
thf(func_def_364,type,
sK245: $i > $o ).
thf(func_def_367,type,
sK248: $i > $i ).
thf(func_def_368,type,
sK249: $i > $o ).
thf(func_def_370,type,
sK251: $i > ( $i > $o ) > $i ).
thf(func_def_372,type,
sK253: $o ).
thf(func_def_373,type,
sK254: $i > $o ).
thf(f82,axiom,
( emptysetsubset
= ( ! [X0: $i] : ( subset @ emptyset @ X0 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(f93,axiom,
! [X1: $i,X0: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( subset @ X1 @ X0 )
=> ( X0 = X1 ) ) )
= setextsub ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(f94,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
=> ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(f95,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
=> ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
thf(f96,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
=> ! [X0: $i] :
( ( subset @ X0 @ emptyset )
=> ( X0 = emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f95]) ).
thf(f97,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 )
=> ! [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
=> ( emptyset = X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f96]) ).
thf(f232,plain,
( emptysetsubset
= ( ! [X0: $i] : ( subset @ emptyset @ X0 ) ) ),
inference(rectify,[],[f82]) ).
thf(f233,plain,
( ( emptysetsubset = $true )
<=> ! [X0: $i] :
( ( subset @ emptyset @ X0 )
= $true ) ),
inference(fool_elimination,[],[f232]) ).
thf(f254,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
=> ( ( subset @ X0 @ X1 )
=> ( X0 = X1 ) ) )
= setextsub ),
inference(rectify,[],[f93]) ).
thf(f255,plain,
( ( setextsub = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( subset @ X1 @ X0 )
= $true )
=> ( ( ( subset @ X0 @ X1 )
= $true )
=> ( X0 = X1 ) ) ) ),
inference(fool_elimination,[],[f254]) ).
thf(f333,plain,
( ( setextsub = $true )
<=> ! [X1: $i,X0: $i] :
( ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true ) ) ),
inference(ennf_transformation,[],[f255]) ).
thf(f334,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) )
<=> ( setextsub = $true ) ),
inference(flattening,[],[f333]) ).
thf(f357,plain,
( ? [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
& ( emptyset != X0 ) )
& ( 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,[],[f97]) ).
thf(f358,plain,
( ( dsetconstrEL = $true )
& ( setextsub = $true )
& ( inCongP = $true )
& ( exuI1 = $true )
& ( prop2setI = $true )
& ( upairsetIR = $true )
& ( notdallE = $true )
& ( emptysetimpfalse = $true )
& ( subset2powerset = $true )
& ( subsetTrans = $true )
& ( prop2setE = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( nonemptyI1 = $true )
& ( omega__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( foundationAx = $true )
& ( setadjoinSub2 = $true )
& ( emptyinPowerset = $true )
& ( subsetE = $true )
& ( setadjoinIL = $true )
& ( subPowSU = $true )
& ( notequalI1 = $true )
& ( notinemptyset = $true )
& ( nonemptyImpWitness = $true )
& ( setext = $true )
& ( setoftrueEq = $true )
& ( setunionAx = $true )
& ( setunionI = $true )
& ( setadjoinIR = $true )
& ( quantDeMorgan3 = $true )
& ( subsetRefl = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( notequalI2 = $true )
& ( exuI2 = $true )
& ? [X0: $i] :
( ( ( subset @ X0 @ emptyset )
= $true )
& ( emptyset != X0 ) )
& ( dsetconstrER = $true )
& ( omega0Ax = $true )
& ( exuEu = $true )
& ( prop2set2propI = $true )
& ( nonemptyE1 = $true )
& ( subsetI1 = $true )
& ( emptyInPowerset = $true )
& ( singletonsswitch = $true )
& ( emptysetsubset = $true )
& ( replAx = $true )
& ( quantDeMorgan4 = $true )
& ( uniqinunit = $true )
& ( exuE1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptyE1 = $true )
& ( setadjoinSub = $true )
& ( emptyI = $true )
& ( setadjoinOr = $true )
& ( exuE3e = $true )
& ( emptysetE = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( exuE2 = $true )
& ( eqinunit = $true )
& ( notdexE = $true )
& ( exu__Cong = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstrI = $true )
& ( setadjoinE = $true )
& ( powerset__Cong = $true )
& ( setunion__Cong = $true )
& ( exuI3 = $true )
& ( powersetE = $true )
& ( upairsetIL = $true )
& ( exuE3u = $true )
& ( eqimpsubset1 = $true )
& ( upairsetE = $true )
& ( wellorderingAx = $true )
& ( vacuousDall = $true )
& ( noeltsimpempty = $true )
& ( setbeta = $true )
& ( descr__Cong = $true )
& ( in__Cong = $true )
& ( descrp = $true )
& ( powersetI = $true )
& ( dsetconstr__Cong = $true )
& ( setunionE = $true )
& ( subsetI2 = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( nonemptyI = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( emptyset__Cong = $true )
& ( emptysetAx = $true ) ),
inference(flattening,[],[f357]) ).
thf(f413,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
= $true )
& ( X0 != X1 )
& ( ( subset @ X1 @ X0 )
= $true ) ) ) ),
inference(nnf_transformation,[],[f334]) ).
thf(f414,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( subset @ X2 @ X3 ) )
& ( X2 != X3 )
& ( ( subset @ X3 @ X2 )
= $true ) ) ) ),
inference(rectify,[],[f413]) ).
thf(f415,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true ) )
| ( setextsub != $true ) )
& ( ( setextsub = $true )
| ( ( ( subset @ sK10 @ sK11 )
= $true )
& ( sK10 != sK11 )
& ( $true
= ( subset @ sK11 @ sK10 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10,sK11]),skolemize(X2,sK10),skolemize(X3,sK11)],[f414]) ).
thf(f470,plain,
( ( dsetconstrEL = $true )
& ( setextsub = $true )
& ( inCongP = $true )
& ( exuI1 = $true )
& ( prop2setI = $true )
& ( upairsetIR = $true )
& ( notdallE = $true )
& ( emptysetimpfalse = $true )
& ( subset2powerset = $true )
& ( subsetTrans = $true )
& ( prop2setE = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( nonemptyI1 = $true )
& ( omega__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( foundationAx = $true )
& ( setadjoinSub2 = $true )
& ( emptyinPowerset = $true )
& ( subsetE = $true )
& ( setadjoinIL = $true )
& ( subPowSU = $true )
& ( notequalI1 = $true )
& ( notinemptyset = $true )
& ( nonemptyImpWitness = $true )
& ( setext = $true )
& ( setoftrueEq = $true )
& ( setunionAx = $true )
& ( setunionI = $true )
& ( setadjoinIR = $true )
& ( quantDeMorgan3 = $true )
& ( subsetRefl = $true )
& ( powersetAx = $true )
& ( setadjoin__Cong = $true )
& ( notequalI2 = $true )
& ( exuI2 = $true )
& ( $true
= ( subset @ sK60 @ emptyset ) )
& ( emptyset != sK60 )
& ( dsetconstrER = $true )
& ( omega0Ax = $true )
& ( exuEu = $true )
& ( prop2set2propI = $true )
& ( nonemptyE1 = $true )
& ( subsetI1 = $true )
& ( emptyInPowerset = $true )
& ( singletonsswitch = $true )
& ( emptysetsubset = $true )
& ( replAx = $true )
& ( quantDeMorgan4 = $true )
& ( uniqinunit = $true )
& ( exuE1 = $true )
& ( quantDeMorgan2 = $true )
& ( emptyE1 = $true )
& ( setadjoinSub = $true )
& ( emptyI = $true )
& ( setadjoinOr = $true )
& ( exuE3e = $true )
& ( emptysetE = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( exuE2 = $true )
& ( eqinunit = $true )
& ( notdexE = $true )
& ( exu__Cong = $true )
& ( eqimpsubset2 = $true )
& ( dsetconstrI = $true )
& ( setadjoinE = $true )
& ( powerset__Cong = $true )
& ( setunion__Cong = $true )
& ( exuI3 = $true )
& ( powersetE = $true )
& ( upairsetIL = $true )
& ( exuE3u = $true )
& ( eqimpsubset1 = $true )
& ( upairsetE = $true )
& ( wellorderingAx = $true )
& ( vacuousDall = $true )
& ( noeltsimpempty = $true )
& ( setbeta = $true )
& ( descr__Cong = $true )
& ( in__Cong = $true )
& ( descrp = $true )
& ( powersetI = $true )
& ( dsetconstr__Cong = $true )
& ( setunionE = $true )
& ( subsetI2 = $true )
& ( omegaSAx = $true )
& ( emptyinunitempty = $true )
& ( nonemptyI = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( emptyset__Cong = $true )
& ( emptysetAx = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(X0,sK60)],[f358]) ).
thf(f552,plain,
( ( ( emptysetsubset = $true )
| ? [X0: $i] :
( ( subset @ emptyset @ X0 )
!= $true ) )
& ( ! [X0: $i] :
( ( subset @ emptyset @ X0 )
= $true )
| ( emptysetsubset != $true ) ) ),
inference(nnf_transformation,[],[f233]) ).
thf(f553,plain,
( ( ( emptysetsubset = $true )
| ? [X0: $i] :
( ( subset @ emptyset @ X0 )
!= $true ) )
& ( ! [X1: $i] :
( $true
= ( subset @ emptyset @ X1 ) )
| ( emptysetsubset != $true ) ) ),
inference(rectify,[],[f552]) ).
thf(f554,plain,
( ( ( emptysetsubset = $true )
| ( $true
!= ( subset @ emptyset @ sK142 ) ) )
& ( ! [X1: $i] :
( $true
= ( subset @ emptyset @ X1 ) )
| ( emptysetsubset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(X0,sK142)],[f553]) ).
thf(f688,plain,
! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( setextsub != $true ) ),
inference(cnf_transformation,[],[f415]) ).
thf(f806,plain,
emptysetsubset = $true,
inference(cnf_transformation,[],[f470]) ).
thf(f815,plain,
emptyset != sK60,
inference(cnf_transformation,[],[f470]) ).
thf(f816,plain,
( $true
= ( subset @ sK60 @ emptyset ) ),
inference(cnf_transformation,[],[f470]) ).
thf(f851,plain,
setextsub = $true,
inference(cnf_transformation,[],[f470]) ).
thf(f966,plain,
! [X1: $i] :
( ( emptysetsubset != $true )
| ( $true
= ( subset @ emptyset @ X1 ) ) ),
inference(cnf_transformation,[],[f554]) ).
thf(f1577,definition,
( spl257_64
<=> ! [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
| ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl257_64])],[avatar_definition]) ).
thf(f1578,plain,
( ! [X0: $i,X1: $i] :
( ( ( subset @ X1 @ X0 )
!= $true )
| ( X0 = X1 )
| ( ( subset @ X0 @ X1 )
!= $true ) )
| ~ spl257_64 ),
inference(avatar_component_clause,[],[f1577]) ).
thf(f1580,definition,
( spl257_65
<=> ( setextsub = $true ) ),
introduced(definition,[new_symbols(definition,[spl257_65])],[avatar_definition]) ).
thf(f1583,plain,
( spl257_64
| ~ spl257_65 ),
inference(avatar_split_clause,[],[f688,f1580,f1577]) ).
thf(f1871,definition,
( spl257_131
<=> ( emptysetsubset = $true ) ),
introduced(definition,[new_symbols(definition,[spl257_131])],[avatar_definition]) ).
thf(f2059,plain,
spl257_131,
inference(avatar_split_clause,[],[f806,f1871]) ).
thf(f3235,plain,
spl257_65,
inference(avatar_split_clause,[],[f851,f1580]) ).
thf(f3323,definition,
( spl257_440
<=> ( emptyset = sK60 ) ),
introduced(definition,[new_symbols(definition,[spl257_440])],[avatar_definition]) ).
thf(f3325,plain,
( ( emptyset != sK60 )
| spl257_440 ),
inference(avatar_component_clause,[],[f3323]) ).
thf(f3326,plain,
~ spl257_440,
inference(avatar_split_clause,[],[f815,f3323]) ).
thf(f3339,definition,
( spl257_443
<=> ( $true
= ( subset @ sK60 @ emptyset ) ) ),
introduced(definition,[new_symbols(definition,[spl257_443])],[avatar_definition]) ).
thf(f3341,plain,
( ( $true
= ( subset @ sK60 @ emptyset ) )
| ~ spl257_443 ),
inference(avatar_component_clause,[],[f3339]) ).
thf(f3342,plain,
spl257_443,
inference(avatar_split_clause,[],[f816,f3339]) ).
thf(f3350,definition,
( spl257_445
<=> ! [X1: $i] :
( $true
= ( subset @ emptyset @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl257_445])],[avatar_definition]) ).
thf(f3351,plain,
( ! [X1: $i] :
( $true
= ( subset @ emptyset @ X1 ) )
| ~ spl257_445 ),
inference(avatar_component_clause,[],[f3350]) ).
thf(f3352,plain,
( ~ spl257_131
| spl257_445 ),
inference(avatar_split_clause,[],[f966,f3350,f1871]) ).
thf(f3547,plain,
( ( ( subset @ emptyset @ sK60 )
!= $true )
| ( emptyset = sK60 )
| ( $true != $true )
| ~ spl257_64
| ~ spl257_443 ),
inference(superposition,[],[f1578,f3341]) ).
thf(f3552,plain,
( ( emptyset = sK60 )
| ( ( subset @ emptyset @ sK60 )
!= $true )
| ~ spl257_64
| ~ spl257_443 ),
inference(trivial_inequality_removal,[],[f3547]) ).
thf(f3553,plain,
( ( ( subset @ emptyset @ sK60 )
!= $true )
| ~ spl257_64
| spl257_440
| ~ spl257_443 ),
inference(forward_subsumption_resolution,[],[f3552,f3325]) ).
thf(f3554,plain,
( $false
| ~ spl257_64
| spl257_440
| ~ spl257_443
| ~ spl257_445 ),
inference(forward_subsumption_resolution,[],[f3553,f3351]) ).
thf(f3555,plain,
( ~ spl257_64
| spl257_440
| ~ spl257_443
| ~ spl257_445 ),
inference(avatar_contradiction_clause,[],[f3554]) ).
cnf(s42,plain,
( spl257_64
| ~ spl257_65 ),
inference(sat_conversion,[],[f1583]) ).
cnf(s129,plain,
spl257_131,
inference(sat_conversion,[],[f2059]) ).
cnf(s415,plain,
spl257_65,
inference(sat_conversion,[],[f3235]) ).
cnf(s439,plain,
~ spl257_440,
inference(sat_conversion,[],[f3326]) ).
cnf(s443,plain,
spl257_443,
inference(sat_conversion,[],[f3342]) ).
cnf(s446,plain,
( ~ spl257_131
| spl257_445 ),
inference(sat_conversion,[],[f3352]) ).
cnf(s468,plain,
( ~ spl257_64
| spl257_440
| ~ spl257_443
| ~ spl257_445 ),
inference(sat_conversion,[],[f3555]) ).
cnf(s541,plain,
spl257_445,
inference(rat,[],[s446,s129]) ).
cnf(s542,plain,
~ spl257_64,
inference(rat,[],[s468,s439,s443,s541]) ).
cnf(s575,plain,
$false,
inference(rat,[],[s42,s415,s542]) ).
thf(f3556,plain,
$false,
inference(avatar_sat_refutation,[],[s575]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU575^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n008.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 13:52:09 UTC 2026
% 0.09/0.17 % CPUTime :
% 0.09/0.17 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 Running higher-order theorem proving
% 0.09/0.22 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
% 0.21/0.34 % (3188759)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.34 % (3188765)lrs+10_16_si=on:nwc=1.5:random_seed=1218886138:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.34 % (3188770)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.34 % (3188770)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
% 0.21/0.34 % (3188765)Instruction limit reached!
% 0.21/0.34 % (3188765)------------------------------
% 0.21/0.34 % (3188765)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188765)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188765)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188765)Termination reason: Instruction limit
% 0.21/0.34 % (3188765)Termination phase: Property scanning
% 0.21/0.34 % (3188765)Time elapsed: 0.005 s
% 0.21/0.34 % (3188765)Peak memory usage: 10 MB
% 0.21/0.34 % (3188765)Instructions burned: 23 (million)
% 0.21/0.34 % (3188764)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2061264055:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.34 % (3188766)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1457274153:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.34 % (3188769)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3032243543:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.34 % (3188768)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=2658857860:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.34 % (3188767)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=3167463630: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)
% 0.21/0.34 % (3188770)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=3859659006:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.34 % (3188766)Instruction limit reached!
% 0.21/0.34 % (3188766)------------------------------
% 0.21/0.34 % (3188766)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188766)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188766)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188766)Termination reason: Instruction limit
% 0.21/0.34 % (3188766)Termination phase: shuffling
% 0.21/0.34 % (3188766)Time elapsed: 0.002 s
% 0.21/0.34 % (3188766)Peak memory usage: 10 MB
% 0.21/0.34 % (3188766)Instructions burned: 3 (million)
% 0.21/0.34 % (3188772)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1413740157:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.34 % (3188772)Instruction limit reached!
% 0.21/0.34 % (3188772)------------------------------
% 0.21/0.34 % (3188772)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188772)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188772)Termination reason: Instruction limit
% 0.21/0.34 % (3188772)Termination phase: shuffling
% 0.21/0.34 % (3188772)Time elapsed: 0.001 s
% 0.21/0.34 % (3188772)Peak memory usage: 10 MB
% 0.21/0.34 % (3188772)Instructions burned: 4 (million)
% 0.21/0.34 % (3188768)Instruction limit reached!
% 0.21/0.34 % (3188768)------------------------------
% 0.21/0.34 % (3188768)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188768)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188768)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188768)Termination reason: Instruction limit
% 0.21/0.34 % (3188768)Termination phase: Preprocessing 3
% 0.21/0.34 % (3188768)Time elapsed: 0.013 s
% 0.21/0.34 % (3188768)Peak memory usage: 11 MB
% 0.21/0.34 % (3188768)Instructions burned: 25 (million)
% 0.21/0.34 % (3188781)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.34 % (3188781)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2895709619:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.34 % (3188779)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3223671790:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.34 % (3188781)Instruction limit reached!
% 0.21/0.34 % (3188781)------------------------------
% 0.21/0.34 % (3188781)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188781)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188781)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188781)Termination reason: Instruction limit
% 0.21/0.34 % (3188781)Termination phase: shuffling
% 0.21/0.34 % (3188781)Time elapsed: 0.002 s
% 0.21/0.34 % (3188781)Peak memory usage: 10 MB
% 0.21/0.34 % (3188781)Instructions burned: 8 (million)
% 0.21/0.34 % (3188779)Instruction limit reached!
% 0.21/0.34 % (3188779)------------------------------
% 0.21/0.34 % (3188779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188779)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188779)Termination reason: Instruction limit
% 0.21/0.34 % (3188779)Termination phase: shuffling
% 0.21/0.34 % (3188779)Time elapsed: 0.003 s
% 0.21/0.34 % (3188779)Peak memory usage: 10 MB
% 0.21/0.34 % (3188779)Instructions burned: 6 (million)
% 0.21/0.34 % (3188785)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
% 0.21/0.34 % (3188785)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.34 % (3188782)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1117178621:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.34 % (3188785)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1662590712:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.34 % (3188769)Instruction limit reached!
% 0.21/0.34 % (3188769)------------------------------
% 0.21/0.34 % (3188769)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188769)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188769)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188769)Termination reason: Instruction limit
% 0.21/0.34 % (3188769)Termination phase: Saturation
% 0.21/0.34 % (3188769)Time elapsed: 0.036 s
% 0.21/0.34 % (3188769)Peak memory usage: 13 MB
% 0.21/0.34 % (3188769)Instructions burned: 75 (million)
% 0.21/0.34 % (3188782)Instruction limit reached!
% 0.21/0.34 % (3188782)------------------------------
% 0.21/0.34 % (3188782)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188782)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188782)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188782)Termination reason: Instruction limit
% 0.21/0.34 % (3188782)Termination phase: Property scanning
% 0.21/0.34 % (3188782)Time elapsed: 0.006 s
% 0.21/0.34 % (3188782)Peak memory usage: 10 MB
% 0.21/0.34 % (3188782)Instructions burned: 14 (million)
% 0.21/0.34 % (3188785)Instruction limit reached!
% 0.21/0.34 % (3188785)------------------------------
% 0.21/0.34 % (3188785)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188785)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188785)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188785)Termination reason: Instruction limit
% 0.21/0.34 % (3188785)Termination phase: Property scanning
% 0.21/0.34 % (3188785)Time elapsed: 0.006 s
% 0.21/0.34 % (3188785)Peak memory usage: 10 MB
% 0.21/0.34 % (3188785)Instructions burned: 29 (million)
% 0.21/0.34 % (3188764)Instruction limit reached!
% 0.21/0.34 % (3188764)------------------------------
% 0.21/0.34 % (3188764)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188764)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188764)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188764)Termination reason: Instruction limit
% 0.21/0.34 % (3188764)Termination phase: Saturation
% 0.21/0.34 % (3188764)Time elapsed: 0.042 s
% 0.21/0.34 % (3188764)Peak memory usage: 13 MB
% 0.21/0.34 % (3188764)Instructions burned: 88 (million)
% 0.21/0.34 % (3188786)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=640862085:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.34 % (3188791)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2431935681:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.21/0.34 % (3188767) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3188759-3188767"...
% 0.21/0.34 % (3188790)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.34 % (3188789)lrs+10_1_si=on:cs=on:random_seed=2493888049:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.34 % (3188767)...printing done.
% 0.21/0.34 % (3188767)Refutation found. Thanks to Tanya!
% 0.21/0.34 % SZS status Theorem for theBenchmark
% 0.21/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.34 % (3188767)------------------------------
% 0.21/0.34 % (3188767)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.34 % (3188767)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.34 % (3188767)CaDiCaL version: 2.1.3
% 0.21/0.34 % (3188767)Termination reason: Refutation
% 0.21/0.34 % (3188767)Time elapsed: 0.054 s
% 0.21/0.34 % (3188767)Peak memory usage: 15 MB
% 0.21/0.34 % (3188767)Instructions burned: 105 (million)
% 0.21/0.34 % (3188759)Success in time 0.104 s
% 0.21/0.34 % Vampire exiting
%------------------------------------------------------------------------------