%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU581^1 : 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 : n018.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 08:30:10 AM UTC 2026
% Result : Theorem 0.23s 0.36s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 19 unt; 0 typ; 5 def)
% Number of atoms : 1739 ( 459 equ; 0 cnn)
% Maximal formula atoms : 98 ( 31 avg)
% Number of connectives : 998 ( 55 ~; 44 |; 300 &; 200 @)
% ( 8 <=>; 391 =>; 0 <=; 0 <~>)
% Maximal formula depth : 106 ( 16 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 20 >; 0 *; 0 +; 0 <<)
% Number of symbols : 233 ( 230 usr; 115 con; 0-4 aty)
% Number of variables : 82 ( 0 sgn 52 !; 12 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_115,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_116,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_117,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_118,type,
vAND: $o > $o > $o ).
thf(func_def_119,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_120,type,
vIMP: $o > $o > $o ).
thf(func_def_121,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_122,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_123,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_124,type,
vNOT: $o > $o ).
thf(func_def_125,type,
sP0: $i > $i > $o ).
thf(func_def_126,type,
sP1: $i > $o ).
thf(func_def_127,type,
sP2: $o ).
thf(func_def_128,type,
sK3: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_129,type,
sK4: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_130,type,
sK5: $i > $o ).
thf(func_def_131,type,
sK6: $i > $o ).
thf(func_def_136,type,
sK11: $i > $i ).
thf(func_def_142,type,
sK17: $i > $o ).
thf(func_def_145,type,
sK20: $i > $i ).
thf(func_def_148,type,
sK23: $i > $i ).
thf(func_def_149,type,
sK24: ( $i > $o ) > $i ).
thf(func_def_150,type,
sK25: $i > $o ).
thf(func_def_151,type,
sK26: $i > $i ).
thf(func_def_152,type,
sK27: $o ).
thf(func_def_154,type,
sK29: $i > $o ).
thf(func_def_156,type,
sK31: $i > $i ).
thf(func_def_161,type,
sK36: $i > $o ).
thf(func_def_162,type,
sK37: $i > $i > $i ).
thf(func_def_169,type,
sK44: $i > $i > $i ).
thf(func_def_172,type,
sK47: $i > $i > $o ).
thf(func_def_174,type,
sK49: $i > $i ).
thf(func_def_175,type,
sK50: $i > $i ).
thf(func_def_176,type,
sK51: $i > ( $i > $i > $o ) > $i ).
thf(func_def_177,type,
sK52: $i > ( $i > $i > $o ) > $i ).
thf(func_def_178,type,
sK53: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_179,type,
sK54: ( $i > $o ) > $i ).
thf(func_def_180,type,
sK55: ( $i > $o ) > $i ).
thf(func_def_181,type,
sK56: $i > $o ).
thf(func_def_183,type,
sK58: $i > $o ).
thf(func_def_187,type,
sK62: $i > $o ).
thf(func_def_191,type,
sK66: $i > $o ).
thf(func_def_193,type,
sK68: $i > ( $i > $o ) > $i ).
thf(func_def_196,type,
sK71: $i > $o ).
thf(func_def_198,type,
sK73: $i > $o ).
thf(func_def_201,type,
sK76: $i > ( $i > $o ) > $i ).
thf(func_def_204,type,
sK79: $i > $i > $i ).
thf(func_def_214,type,
sK89: $i > $o ).
thf(func_def_217,type,
sK92: $o ).
thf(func_def_221,type,
sK96: $i > ( $i > $o ) > $i ).
thf(func_def_222,type,
sK97: $i > $o ).
thf(func_def_225,type,
sK100: $i > $i > $i ).
thf(func_def_229,type,
sK104: $i > $o ).
thf(func_def_231,type,
sK106: ( $i > $o ) > $i > $i ).
thf(func_def_235,type,
sK110: ( $i > $o ) > $i ).
thf(func_def_236,type,
sK111: $i > $o ).
thf(func_def_237,type,
sK112: $i > $i ).
thf(func_def_240,type,
sK115: $i > $i > $i ).
thf(func_def_248,type,
sK123: ( $i > $o ) > $i > $i ).
thf(func_def_250,type,
sK125: $i > $o ).
thf(func_def_254,type,
sK129: $i > $o ).
thf(func_def_256,type,
sK131: $i > ( $i > $o ) > $i ).
thf(func_def_259,type,
sK134: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_260,type,
sK135: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_261,type,
sK136: $i > $o ).
thf(func_def_262,type,
sK137: $i > $o ).
thf(func_def_263,type,
sK138: $o > $i > $i > $i ).
thf(func_def_266,type,
sK141: $o ).
thf(func_def_270,type,
sK145: $i > $o ).
thf(func_def_273,type,
sK148: $i > ( $i > $o ) > $i ).
thf(func_def_274,type,
sK149: $i > $o ).
thf(func_def_277,type,
sK152: $i > $i ).
thf(func_def_283,type,
sK158: $i > $i ).
thf(func_def_284,type,
sK159: $i > $i ).
thf(func_def_285,type,
sK160: $i > $i ).
thf(func_def_286,type,
sK161: $i > $i ).
thf(func_def_287,type,
sK162: $i > $i ).
thf(func_def_288,type,
sK163: $i > $i > $i > $i ).
thf(func_def_289,type,
sK164: $i > $i ).
thf(func_def_290,type,
sK165: $i > $i ).
thf(func_def_291,type,
sK166: $i > $i ).
thf(func_def_292,type,
sK167: $i > $i ).
thf(func_def_293,type,
sK168: $i > $i > $i ).
thf(func_def_294,type,
sK169: $i > $i > $i ).
thf(func_def_295,type,
sK170: $i > $i > $i > $i ).
thf(func_def_296,type,
sK171: $i > $i > $i > $i ).
thf(func_def_297,type,
sK172: $i > $i > $i > $i ).
thf(func_def_298,type,
sK173: $i > $i > $i ).
thf(func_def_299,type,
sK174: $i > $i > $i ).
thf(func_def_300,type,
sK175: $i > $i > $i ).
thf(func_def_321,type,
sK196: ( $i > $o ) > $i ).
thf(func_def_322,type,
sK197: $i > $o ).
thf(func_def_323,type,
sK198: $i > $i ).
thf(func_def_324,type,
sK199: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_325,type,
sK200: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_328,type,
sK203: $i > $o ).
thf(func_def_329,type,
sK204: $i > $o ).
thf(func_def_332,type,
sK207: $o ).
thf(func_def_335,type,
sK210: $i > $o ).
thf(func_def_341,type,
sK216: $o ).
thf(func_def_342,type,
sK217: $i > $o ).
thf(func_def_344,type,
sK219: $i > $i > $i ).
thf(func_def_345,type,
sK220: $i > $i > $i ).
thf(func_def_356,type,
sK231: $o ).
thf(func_def_359,type,
sK234: $i > $o ).
thf(func_def_362,type,
sK237: ( $i > $o ) > $i > $i ).
thf(func_def_364,type,
sK239: $i > $o ).
thf(func_def_366,type,
sK241: $i > $o ).
thf(func_def_368,type,
sK243: $i > $i ).
thf(func_def_387,type,
sK262: $i > $i > $i ).
thf(f96,axiom,
( powersetE1
= ( ! [X1: $i,X0: $i] :
( ( in @ X1 @ ( powerset @ X0 ) )
=> ( subset @ X1 @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(f99,axiom,
! [X1: $i > $o,X0: $i] :
( ( in
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ ( powerset @ X0 ) )
= sepInPowerset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(f100,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ! [X1: $i > $o,X0: $i] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(f101,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ! [X1: $i > $o,X0: $i] :
( subset
@ ( dsetconstr @ X0
@ ^ [X2: $i] : ( X1 @ X2 ) )
@ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f100]) ).
thf(f138,plain,
! [X0: $i > $o,X1: $i] :
( ( in
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
@ ( powerset @ X1 ) )
= sepInPowerset ),
inference(rectify,[],[f99]) ).
thf(f139,plain,
( ( sepInPowerset = $true )
<=> ! [X1: $i,X0: $i > $o] :
( ( in
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( powerset @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f138]) ).
thf(f178,plain,
( powersetE1
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( powerset @ X1 ) )
=> ( subset @ X0 @ X1 ) ) ) ),
inference(rectify,[],[f96]) ).
thf(f179,plain,
( ( powersetE1 = $true )
<=> ! [X1: $i,X0: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ),
inference(fool_elimination,[],[f178]) ).
thf(f237,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ! [X0: $i > $o,X1: $i] :
( subset
@ ( dsetconstr @ X1
@ ^ [X2: $i] : ( X0 @ X2 ) )
@ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f101]) ).
thf(f238,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ! [X1: $i,X0: $i > $o] :
( $true
= ( subset
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f237]) ).
thf(f369,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
<=> ( powersetE1 = $true ) ),
inference(ennf_transformation,[],[f179]) ).
thf(f377,plain,
( ? [X0: $i > $o,X1: $i] :
( $true
!= ( subset
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ X1 ) )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f238]) ).
thf(f378,plain,
( ( setadjoinSub2 = $true )
& ( omegaIndAx = $true )
& ( nonemptyE1 = $true )
& ( powersetAx = $true )
& ( eqimpsubset2 = $true )
& ( exu__Cong = $true )
& ( foundationAx = $true )
& ( vacuousDall = $true )
& ( exuI1 = $true )
& ( powersetsubset = $true )
& ( notdexE = $true )
& ( setadjoinSub = $true )
& ( replAx = $true )
& ( prop2set2propI = $true )
& ( omega0Ax = $true )
& ( subset2powerset = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( prop2setE = $true )
& ( subsetE = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( inPowerset = $true )
& ( dsetconstrER = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( in__Cong = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan4 = $true )
& ( powersetI1 = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( upairsetIR = $true )
& ( emptyI = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinIL = $true )
& ( uniqinunit = $true )
& ( omegaSAx = $true )
& ( emptyset__Cong = $true )
& ( emptysetAx = $true )
& ( subsetTrans = $true )
& ( setadjoin__Cong = $true )
& ( setext = $true )
& ( powersetE1 = $true )
& ( setextsub = $true )
& ( powersetE = $true )
& ( setextAx = $true )
& ( emptysetimpfalse = $true )
& ( setunionAx = $true )
& ( notsubsetI = $true )
& ( setadjoinOr = $true )
& ( dsetconstrEL = $true )
& ( upairsetE = $true )
& ( wellorderingAx = $true )
& ( exuE3e = $true )
& ( setadjoinIR = $true )
& ( nonemptyImpWitness = $true )
& ( upairsetIL = $true )
& ( subsetI2 = $true )
& ( subPowSU = $true )
& ( notequalI2 = $true )
& ( descrp = $true )
& ( sepInPowerset = $true )
& ( powersetI = $true )
& ( noeltsimpempty = $true )
& ( emptysetsubset = $true )
& ( subsetemptysetimpeq = $true )
& ( eqinunit = $true )
& ( powerset__Cong = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( singletonsswitch = $true )
& ( setunionE = $true )
& ( exuEu = $true )
& ( setbeta = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyI = $true )
& ( exuI3 = $true )
& ( eqimpsubset1 = $true )
& ? [X0: $i > $o,X1: $i] :
( $true
!= ( subset
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ X1 ) )
& ( emptyE1 = $true )
& ( emptyInPowerset = $true )
& ( setadjoinAx = $true )
& ( exuI2 = $true )
& ( setoftrueEq = $true )
& ( setunionI = $true )
& ( subsetRefl = $true )
& ( setadjoinE = $true )
& ( prop2setI = $true )
& ( notdallE = $true )
& ( exuE3u = $true )
& ( exuE1 = $true )
& ( subsetE2 = $true )
& ( notequalI1 = $true )
& ( notinsingleton = $true )
& ( dsetconstrI = $true )
& ( exuE2 = $true ) ),
inference(flattening,[],[f377]) ).
thf(f505,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ? [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
= $true )
& ( ( subset @ X0 @ X1 )
!= $true ) ) ) ),
inference(nnf_transformation,[],[f369]) ).
thf(f506,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ? [X2: $i,X3: $i] :
( ( $true
= ( in @ X2 @ ( powerset @ X3 ) ) )
& ( $true
!= ( subset @ X2 @ X3 ) ) ) ) ),
inference(rectify,[],[f505]) ).
thf(f507,plain,
( ( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ( powersetE1 != $true ) )
& ( ( powersetE1 = $true )
| ( ( $true
= ( in @ sK77 @ ( powerset @ sK78 ) ) )
& ( $true
!= ( subset @ sK77 @ sK78 ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK77,sK78]),skolemize(X2,sK77),skolemize(X3,sK78)],[f506]) ).
thf(f650,plain,
( ( ( sepInPowerset = $true )
| ? [X1: $i,X0: $i > $o] :
( ( in
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( powerset @ X1 ) )
!= $true ) )
& ( ! [X1: $i,X0: $i > $o] :
( ( in
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
@ ( powerset @ X1 ) )
= $true )
| ( sepInPowerset != $true ) ) ),
inference(nnf_transformation,[],[f139]) ).
thf(f651,plain,
( ( ( sepInPowerset = $true )
| ? [X0: $i,X1: $i > $o] :
( $true
!= ( in
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) )
@ ( powerset @ X0 ) ) ) )
& ( ! [X2: $i,X3: $i > $o] :
( $true
= ( in
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X3 @ Y0 ) )
@ ( powerset @ X2 ) ) )
| ( sepInPowerset != $true ) ) ),
inference(rectify,[],[f650]) ).
thf(f652,plain,
( ( ( sepInPowerset = $true )
| ( $true
!= ( in
@ ( dsetconstr @ sK209
@ ^ [Y0: $i] : ( sK210 @ Y0 ) )
@ ( powerset @ sK209 ) ) ) )
& ( ! [X2: $i,X3: $i > $o] :
( $true
= ( in
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X3 @ Y0 ) )
@ ( powerset @ X2 ) ) )
| ( sepInPowerset != $true ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK209,sK210]),skolemize(X0,sK209),skolemize(X1,sK210)],[f651]) ).
thf(f684,plain,
( ( setadjoinSub2 = $true )
& ( omegaIndAx = $true )
& ( nonemptyE1 = $true )
& ( powersetAx = $true )
& ( eqimpsubset2 = $true )
& ( exu__Cong = $true )
& ( foundationAx = $true )
& ( vacuousDall = $true )
& ( exuI1 = $true )
& ( powersetsubset = $true )
& ( notdexE = $true )
& ( setadjoinSub = $true )
& ( replAx = $true )
& ( prop2set2propI = $true )
& ( omega0Ax = $true )
& ( subset2powerset = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( prop2setE = $true )
& ( subsetE = $true )
& ( emptysetE = $true )
& ( descr__Cong = $true )
& ( inPowerset = $true )
& ( dsetconstrER = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( in__Cong = $true )
& ( emptyinunitempty = $true )
& ( quantDeMorgan4 = $true )
& ( powersetI1 = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( upairsetIR = $true )
& ( emptyI = $true )
& ( dsetconstr__Cong = $true )
& ( setadjoinIL = $true )
& ( uniqinunit = $true )
& ( omegaSAx = $true )
& ( emptyset__Cong = $true )
& ( emptysetAx = $true )
& ( subsetTrans = $true )
& ( setadjoin__Cong = $true )
& ( setext = $true )
& ( powersetE1 = $true )
& ( setextsub = $true )
& ( powersetE = $true )
& ( setextAx = $true )
& ( emptysetimpfalse = $true )
& ( setunionAx = $true )
& ( notsubsetI = $true )
& ( setadjoinOr = $true )
& ( dsetconstrEL = $true )
& ( upairsetE = $true )
& ( wellorderingAx = $true )
& ( exuE3e = $true )
& ( setadjoinIR = $true )
& ( nonemptyImpWitness = $true )
& ( upairsetIL = $true )
& ( subsetI2 = $true )
& ( subPowSU = $true )
& ( notequalI2 = $true )
& ( descrp = $true )
& ( sepInPowerset = $true )
& ( powersetI = $true )
& ( noeltsimpempty = $true )
& ( emptysetsubset = $true )
& ( subsetemptysetimpeq = $true )
& ( eqinunit = $true )
& ( powerset__Cong = $true )
& ( inCongP = $true )
& ( notinemptyset = $true )
& ( singletonsswitch = $true )
& ( setunionE = $true )
& ( exuEu = $true )
& ( setbeta = $true )
& ( subsetI1 = $true )
& ( quantDeMorgan1 = $true )
& ( nonemptyI = $true )
& ( exuI3 = $true )
& ( eqimpsubset1 = $true )
& ( ( subset
@ ( dsetconstr @ sK242
@ ^ [Y0: $i] : ( sK241 @ Y0 ) )
@ sK242 )
!= $true )
& ( emptyE1 = $true )
& ( emptyInPowerset = $true )
& ( setadjoinAx = $true )
& ( exuI2 = $true )
& ( setoftrueEq = $true )
& ( setunionI = $true )
& ( subsetRefl = $true )
& ( setadjoinE = $true )
& ( prop2setI = $true )
& ( notdallE = $true )
& ( exuE3u = $true )
& ( exuE1 = $true )
& ( subsetE2 = $true )
& ( notequalI1 = $true )
& ( notinsingleton = $true )
& ( dsetconstrI = $true )
& ( exuE2 = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK241,sK242]),skolemize(X0,sK241),skolemize(X1,sK242)],[f378]) ).
thf(f830,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true )
| ( powersetE1 != $true ) ),
inference(cnf_transformation,[],[f507]) ).
thf(f1037,plain,
! [X2: $i,X3: $i > $o] :
( ( $true
= ( in
@ ( dsetconstr @ X2
@ ^ [Y0: $i] : ( X3 @ Y0 ) )
@ ( powerset @ X2 ) ) )
| ( sepInPowerset != $true ) ),
inference(cnf_transformation,[],[f652]) ).
thf(f1102,plain,
( ( subset
@ ( dsetconstr @ sK242
@ ^ [Y0: $i] : ( sK241 @ Y0 ) )
@ sK242 )
!= $true ),
inference(cnf_transformation,[],[f684]) ).
thf(f1120,plain,
sepInPowerset = $true,
inference(cnf_transformation,[],[f684]) ).
thf(f1139,plain,
powersetE1 = $true,
inference(cnf_transformation,[],[f684]) ).
thf(f1314,plain,
! [X2: $i,X3: $i > $o] :
( ( sepInPowerset != $true )
| ( $true
= ( in @ ( dsetconstr @ X2 @ X3 ) @ ( powerset @ X2 ) ) ) ),
inference(beta-eta_normalization,[],[f1037]) ).
thf(f1337,plain,
( ( subset @ ( dsetconstr @ sK242 @ sK241 ) @ sK242 )
!= $true ),
inference(beta-eta_normalization,[],[f1102]) ).
thf(f1820,definition,
( spl268_105
<=> ( sepInPowerset = $true ) ),
introduced(definition,[new_symbols(definition,[spl268_105])],[avatar_definition]) ).
thf(f1823,plain,
spl268_105,
inference(avatar_split_clause,[],[f1120,f1820]) ).
thf(f2111,definition,
( spl268_169
<=> ( powersetE1 = $true ) ),
introduced(definition,[new_symbols(definition,[spl268_169])],[avatar_definition]) ).
thf(f2913,definition,
( spl268_340
<=> ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) ) ),
introduced(definition,[new_symbols(definition,[spl268_340])],[avatar_definition]) ).
thf(f2914,plain,
( ! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( powerset @ X1 ) )
!= $true )
| ( ( subset @ X0 @ X1 )
= $true ) )
| ~ spl268_340 ),
inference(avatar_component_clause,[],[f2913]) ).
thf(f2915,plain,
( spl268_340
| ~ spl268_169 ),
inference(avatar_split_clause,[],[f830,f2111,f2913]) ).
thf(f2967,definition,
( spl268_351
<=> ! [X2: $i,X3: $i > $o] :
( $true
= ( in @ ( dsetconstr @ X2 @ X3 ) @ ( powerset @ X2 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl268_351])],[avatar_definition]) ).
thf(f2968,plain,
( ! [X2: $i,X3: $i > $o] :
( $true
= ( in @ ( dsetconstr @ X2 @ X3 ) @ ( powerset @ X2 ) ) )
| ~ spl268_351 ),
inference(avatar_component_clause,[],[f2967]) ).
thf(f2969,plain,
( ~ spl268_105
| spl268_351 ),
inference(avatar_split_clause,[],[f1314,f2967,f1820]) ).
thf(f3201,plain,
spl268_169,
inference(avatar_split_clause,[],[f1139,f2111]) ).
thf(f3230,definition,
( spl268_405
<=> ( ( subset @ ( dsetconstr @ sK242 @ sK241 ) @ sK242 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl268_405])],[avatar_definition]) ).
thf(f3232,plain,
( ( ( subset @ ( dsetconstr @ sK242 @ sK241 ) @ sK242 )
!= $true )
| spl268_405 ),
inference(avatar_component_clause,[],[f3230]) ).
thf(f3233,plain,
~ spl268_405,
inference(avatar_split_clause,[],[f1337,f3230]) ).
thf(f3777,plain,
( ! [X0: $i,X1: $i > $o] :
( ( $true
= ( subset @ ( dsetconstr @ X0 @ X1 ) @ X0 ) )
| ( $true != $true ) )
| ~ spl268_340
| ~ spl268_351 ),
inference(superposition,[],[f2914,f2968]) ).
thf(f3780,plain,
( ! [X0: $i,X1: $i > $o] :
( $true
= ( subset @ ( dsetconstr @ X0 @ X1 ) @ X0 ) )
| ~ spl268_340
| ~ spl268_351 ),
inference(trivial_inequality_removal,[],[f3777]) ).
thf(f5087,plain,
( ( $true != $true )
| ~ spl268_340
| ~ spl268_351
| spl268_405 ),
inference(superposition,[],[f3232,f3780]) ).
thf(f5097,plain,
( $false
| ~ spl268_340
| ~ spl268_351
| spl268_405 ),
inference(trivial_inequality_removal,[],[f5087]) ).
thf(f5098,plain,
( ~ spl268_340
| ~ spl268_351
| spl268_405 ),
inference(avatar_contradiction_clause,[],[f5097]) ).
cnf(s69,plain,
spl268_105,
inference(sat_conversion,[],[f1823]) ).
cnf(s304,plain,
( ~ spl268_169
| spl268_340 ),
inference(sat_conversion,[],[f2915]) ).
cnf(s317,plain,
( ~ spl268_105
| spl268_351 ),
inference(sat_conversion,[],[f2969]) ).
cnf(s385,plain,
spl268_169,
inference(sat_conversion,[],[f3201]) ).
cnf(s393,plain,
~ spl268_405,
inference(sat_conversion,[],[f3233]) ).
cnf(s532,plain,
( ~ spl268_340
| ~ spl268_351
| spl268_405 ),
inference(sat_conversion,[],[f5098]) ).
cnf(s553,plain,
spl268_340,
inference(rat,[],[s304,s385]) ).
cnf(s554,plain,
~ spl268_351,
inference(rat,[],[s532,s393,s553]) ).
cnf(s555,plain,
~ spl268_105,
inference(rat,[],[s317,s554]) ).
cnf(s638,plain,
$false,
inference(rat,[],[s69,s555]) ).
thf(f5101,plain,
$false,
inference(avatar_sat_refutation,[],[s638]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU581^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n018.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 13:54:27 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running higher-order theorem proving
% 0.07/0.25 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
% 0.23/0.36 % (111098)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.23/0.36 % (111116)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=3347146098: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)
% 0.23/0.36 % (111119)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.23/0.36 % (111119)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
% 0.23/0.36 % (111112)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3059978686:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.23/0.36 % (111113)lrs+10_16_si=on:nwc=1.5:random_seed=1808066217:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.23/0.36 % (111115)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=355599105:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.23/0.36 % (111118)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2845449259:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.23/0.36 % (111119)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=590539148:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.23/0.36 % (111117)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1435674999:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.23/0.36 % (111115)Instruction limit reached!
% 0.23/0.36 % (111115)------------------------------
% 0.23/0.36 % (111115)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111115)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111115)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111115)Termination reason: Instruction limit
% 0.23/0.36 % (111115)Termination phase: shuffling
% 0.23/0.36 % (111115)Time elapsed: 0.002 s
% 0.23/0.36 % (111115)Peak memory usage: 10 MB
% 0.23/0.36 % (111115)Instructions burned: 4 (million)
% 0.23/0.36 % (111113)Instruction limit reached!
% 0.23/0.36 % (111113)------------------------------
% 0.23/0.36 % (111113)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111113)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111113)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111113)Termination reason: Instruction limit
% 0.23/0.36 % (111113)Termination phase: shuffling
% 0.23/0.36 % (111113)Time elapsed: 0.009 s
% 0.23/0.36 % (111113)Peak memory usage: 10 MB
% 0.23/0.36 % (111113)Instructions burned: 20 (million)
% 0.23/0.36 % (111117)Instruction limit reached!
% 0.23/0.36 % (111117)------------------------------
% 0.23/0.36 % (111117)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111117)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111117)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111117)Termination reason: Instruction limit
% 0.23/0.36 % (111117)Termination phase: Preprocessing 3
% 0.23/0.36 % (111117)Time elapsed: 0.013 s
% 0.23/0.36 % (111117)Peak memory usage: 11 MB
% 0.23/0.36 % (111117)Instructions burned: 25 (million)
% 0.23/0.36 % (111133)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1268312201:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.36 % (111133)Instruction limit reached!
% 0.23/0.36 % (111133)------------------------------
% 0.23/0.36 % (111133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111133)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111133)Termination reason: Instruction limit
% 0.23/0.36 % (111133)Termination phase: shuffling
% 0.23/0.36 % (111133)Time elapsed: 0.002 s
% 0.23/0.36 % (111133)Peak memory usage: 10 MB
% 0.23/0.36 % (111133)Instructions burned: 4 (million)
% 0.23/0.36 % (111137)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1502259331:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.23/0.36 % (111138)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.36 % (111137)Instruction limit reached!
% 0.23/0.36 % (111137)------------------------------
% 0.23/0.36 % (111137)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111137)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111137)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111137)Termination reason: Instruction limit
% 0.23/0.36 % (111137)Termination phase: shuffling
% 0.23/0.36 % (111137)Time elapsed: 0.003 s
% 0.23/0.36 % (111137)Peak memory usage: 10 MB
% 0.23/0.36 % (111137)Instructions burned: 6 (million)
% 0.23/0.36 % (111138)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1665469263:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.23/0.36 % (111118)Instruction limit reached!
% 0.23/0.36 % (111118)------------------------------
% 0.23/0.36 % (111118)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111118)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111118)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111118)Termination reason: Instruction limit
% 0.23/0.36 % (111118)Termination phase: Saturation
% 0.23/0.36 % (111118)Time elapsed: 0.036 s
% 0.23/0.36 % (111118)Peak memory usage: 13 MB
% 0.23/0.36 % (111118)Instructions burned: 77 (million)
% 0.23/0.36 % (111138)Instruction limit reached!
% 0.23/0.36 % (111138)------------------------------
% 0.23/0.36 % (111138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111138)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111138)Termination reason: Instruction limit
% 0.23/0.36 % (111138)Termination phase: shuffling
% 0.23/0.36 % (111138)Time elapsed: 0.004 s
% 0.23/0.36 % (111138)Peak memory usage: 10 MB
% 0.23/0.36 % (111138)Instructions burned: 9 (million)
% 0.23/0.36 % (111112)Instruction limit reached!
% 0.23/0.36 % (111112)------------------------------
% 0.23/0.36 % (111112)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111112)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111112)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111112)Termination reason: Instruction limit
% 0.23/0.36 % (111112)Termination phase: Saturation
% 0.23/0.36 % (111112)Time elapsed: 0.042 s
% 0.23/0.36 % (111112)Peak memory usage: 13 MB
% 0.23/0.36 % (111112)Instructions burned: 88 (million)
% 0.23/0.36 % (111140)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=3179667614:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.23/0.36 % (111142)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
% 0.23/0.36 % (111142)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.23/0.36 % (111140)Instruction limit reached!
% 0.23/0.36 % (111140)------------------------------
% 0.23/0.36 % (111140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111140)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111140)Termination reason: Instruction limit
% 0.23/0.36 % (111140)Termination phase: Property scanning
% 0.23/0.36 % (111140)Time elapsed: 0.006 s
% 0.23/0.36 % (111140)Peak memory usage: 10 MB
% 0.23/0.36 % (111140)Instructions burned: 13 (million)
% 0.23/0.36 % (111142)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=1089616148:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.23/0.36 % (111144)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=821384433:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.23/0.36 % (111145)lrs+10_1_si=on:cs=on:random_seed=3879584718:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.23/0.36 % (111146)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.23/0.36 % (111146)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=1578004227:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.23/0.36 % (111145)Instruction limit reached!
% 0.23/0.36 % (111145)------------------------------
% 0.23/0.36 % (111145)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111145)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111145)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111145)Termination reason: Instruction limit
% 0.23/0.36 % (111145)Termination phase: shuffling
% 0.23/0.36 % (111145)Time elapsed: 0.005 s
% 0.23/0.36 % (111145)Peak memory usage: 10 MB
% 0.23/0.36 % (111145)Instructions burned: 10 (million)
% 0.23/0.36 % (111146)Instruction limit reached!
% 0.23/0.36 % (111146)------------------------------
% 0.23/0.36 % (111146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111146)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111146)Termination reason: Instruction limit
% 0.23/0.36 % (111146)Termination phase: shuffling
% 0.23/0.36 % (111146)Time elapsed: 0.001 s
% 0.23/0.36 % (111146)Peak memory usage: 10 MB
% 0.23/0.36 % (111146)Instructions burned: 2 (million)
% 0.23/0.36 % (111116) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-111098-111116"...
% 0.23/0.36 % (111116)...printing done.
% 0.23/0.36 % (111142)Instruction limit reached!
% 0.23/0.36 % (111142)------------------------------
% 0.23/0.36 % (111142)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111119)Instruction limit reached!
% 0.23/0.36 % (111119)------------------------------
% 0.23/0.36 % (111119)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111142)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111119)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111142)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111142)Termination reason: Instruction limit
% 0.23/0.36 % (111142)Termination phase: Property scanning
% 0.23/0.36 % (111119)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111142)Time elapsed: 0.015 s
% 0.23/0.36 % (111119)Termination reason: Instruction limit
% 0.23/0.36 % (111119)Termination phase: Saturation
% 0.23/0.36 % (111142)Peak memory usage: 11 MB
% 0.23/0.36 % (111119)Time elapsed: 0.067 s
% 0.23/0.36 % (111142)Instructions burned: 35 (million)
% 0.23/0.36 % (111119)Peak memory usage: 13 MB
% 0.23/0.36 % (111119)Instructions burned: 157 (million)
% 0.23/0.36 % (111148)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=2246913507:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.23/0.36 % (111116)Refutation found. Thanks to Tanya!
% 0.23/0.36 % SZS status Theorem for theBenchmark
% 0.23/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.36 % (111116)------------------------------
% 0.23/0.36 % (111116)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.36 % (111116)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.36 % (111116)CaDiCaL version: 2.1.3
% 0.23/0.36 % (111116)Termination reason: Refutation
% 0.23/0.36 % (111116)Time elapsed: 0.073 s
% 0.23/0.36 % (111116)Peak memory usage: 16 MB
% 0.23/0.36 % (111116)Instructions burned: 232 (million)
% 0.23/0.36 % (111098)Success in time 0.099 s
% 0.23/0.36 % Vampire exiting
%------------------------------------------------------------------------------