%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU599^1 : 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 : n014.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 08:30:15 AM UTC 2026
% Result : Theorem 0.74s 0.37s
% Output : Refutation 0.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 15 unt; 0 typ; 4 def)
% Number of atoms : 1886 ( 500 equ; 0 cnn)
% Maximal formula atoms : 117 ( 47 avg)
% Number of connectives : 960 ( 29 ~; 21 |; 351 &; 90 @)
% ( 5 <=>; 464 =>; 0 <=; 0 <~>)
% Maximal formula depth : 122 ( 23 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 : 254 ( 251 usr; 133 con; 0-4 aty)
% Number of variables : 34 ( 0 sgn 26 !; 8 ?; 34 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_3,type,
setextAx: $o ).
thf(func_def_5,type,
emptysetAx: $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_7,type,
setadjoinAx: $o ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_9,type,
powersetAx: $o ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_11,type,
setunionAx: $o ).
thf(func_def_13,type,
omega0Ax: $o ).
thf(func_def_14,type,
omegaSAx: $o ).
thf(func_def_15,type,
omegaIndAx: $o ).
thf(func_def_16,type,
replAx: $o ).
thf(func_def_17,type,
foundationAx: $o ).
thf(func_def_18,type,
wellorderingAx: $o ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_20,type,
descrp: $o ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_22,type,
dsetconstrI: $o ).
thf(func_def_23,type,
dsetconstrEL: $o ).
thf(func_def_24,type,
dsetconstrER: $o ).
thf(func_def_25,type,
exuE1: $o ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_27,type,
prop2setE: $o ).
thf(func_def_28,type,
emptysetE: $o ).
thf(func_def_29,type,
emptysetimpfalse: $o ).
thf(func_def_30,type,
notinemptyset: $o ).
thf(func_def_31,type,
exuE3e: $o ).
thf(func_def_32,type,
setext: $o ).
thf(func_def_33,type,
emptyI: $o ).
thf(func_def_34,type,
noeltsimpempty: $o ).
thf(func_def_35,type,
setbeta: $o ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_37,type,
nonemptyE1: $o ).
thf(func_def_38,type,
nonemptyI: $o ).
thf(func_def_39,type,
nonemptyI1: $o ).
thf(func_def_40,type,
setadjoinIL: $o ).
thf(func_def_41,type,
emptyinunitempty: $o ).
thf(func_def_42,type,
setadjoinIR: $o ).
thf(func_def_43,type,
setadjoinE: $o ).
thf(func_def_44,type,
setadjoinOr: $o ).
thf(func_def_45,type,
setoftrueEq: $o ).
thf(func_def_46,type,
powersetI: $o ).
thf(func_def_47,type,
emptyinPowerset: $o ).
thf(func_def_48,type,
emptyInPowerset: $o ).
thf(func_def_49,type,
powersetE: $o ).
thf(func_def_50,type,
setunionI: $o ).
thf(func_def_51,type,
setunionE: $o ).
thf(func_def_52,type,
subPowSU: $o ).
thf(func_def_53,type,
exuE2: $o ).
thf(func_def_54,type,
nonemptyImpWitness: $o ).
thf(func_def_55,type,
uniqinunit: $o ).
thf(func_def_56,type,
notinsingleton: $o ).
thf(func_def_57,type,
eqinunit: $o ).
thf(func_def_58,type,
singletonsswitch: $o ).
thf(func_def_59,type,
upairsetE: $o ).
thf(func_def_60,type,
upairsetIL: $o ).
thf(func_def_61,type,
upairsetIR: $o ).
thf(func_def_62,type,
emptyE1: $o ).
thf(func_def_63,type,
vacuousDall: $o ).
thf(func_def_64,type,
quantDeMorgan1: $o ).
thf(func_def_65,type,
quantDeMorgan2: $o ).
thf(func_def_66,type,
quantDeMorgan3: $o ).
thf(func_def_67,type,
quantDeMorgan4: $o ).
thf(func_def_68,type,
prop2setI: $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_70,type,
prop2set2propI: $o ).
thf(func_def_71,type,
notdexE: $o ).
thf(func_def_72,type,
notdallE: $o ).
thf(func_def_73,type,
exuI1: $o ).
thf(func_def_74,type,
exuI3: $o ).
thf(func_def_75,type,
exuI2: $o ).
thf(func_def_76,type,
inCongP: $o ).
thf(func_def_77,type,
in__Cong: $o ).
thf(func_def_78,type,
exuE3u: $o ).
thf(func_def_79,type,
exu__Cong: $o ).
thf(func_def_80,type,
emptyset__Cong: $o ).
thf(func_def_81,type,
setadjoin__Cong: $o ).
thf(func_def_82,type,
powerset__Cong: $o ).
thf(func_def_83,type,
setunion__Cong: $o ).
thf(func_def_84,type,
omega__Cong: $o ).
thf(func_def_85,type,
exuEu: $o ).
thf(func_def_86,type,
descr__Cong: $o ).
thf(func_def_87,type,
dsetconstr__Cong: $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_91,type,
subsetI1: $o ).
thf(func_def_92,type,
eqimpsubset2: $o ).
thf(func_def_93,type,
eqimpsubset1: $o ).
thf(func_def_94,type,
subsetI2: $o ).
thf(func_def_95,type,
emptysetsubset: $o ).
thf(func_def_96,type,
subsetE: $o ).
thf(func_def_97,type,
subsetE2: $o ).
thf(func_def_98,type,
notsubsetI: $o ).
thf(func_def_99,type,
notequalI1: $o ).
thf(func_def_100,type,
notequalI2: $o ).
thf(func_def_101,type,
subsetRefl: $o ).
thf(func_def_102,type,
subsetTrans: $o ).
thf(func_def_103,type,
setadjoinSub: $o ).
thf(func_def_104,type,
setadjoinSub2: $o ).
thf(func_def_105,type,
subset2powerset: $o ).
thf(func_def_106,type,
setextsub: $o ).
thf(func_def_107,type,
subsetemptysetimpeq: $o ).
thf(func_def_108,type,
powersetI1: $o ).
thf(func_def_109,type,
powersetE1: $o ).
thf(func_def_110,type,
inPowerset: $o ).
thf(func_def_111,type,
powersetsubset: $o ).
thf(func_def_112,type,
sepInPowerset: $o ).
thf(func_def_113,type,
sepSubset: $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_115,type,
binunionIL: $o ).
thf(func_def_116,type,
upairset2IR: $o ).
thf(func_def_117,type,
binunionIR: $o ).
thf(func_def_118,type,
binunionEcases: $o ).
thf(func_def_119,type,
binunionE: $o ).
thf(func_def_120,type,
binunionLsub: $o ).
thf(func_def_121,type,
binunionRsub: $o ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_123,type,
binintersectI: $o ).
thf(func_def_124,type,
binintersectSubset5: $o ).
thf(func_def_125,type,
binintersectEL: $o ).
thf(func_def_126,type,
binintersectLsub: $o ).
thf(func_def_127,type,
binintersectSubset2: $o ).
thf(func_def_128,type,
binintersectSubset3: $o ).
thf(func_def_129,type,
binintersectER: $o ).
thf(func_def_130,type,
disjointsetsI1: $o ).
thf(func_def_131,type,
binintersectRsub: $o ).
thf(func_def_132,type,
binintersectSubset4: $o ).
thf(func_def_135,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_136,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_137,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_138,type,
vAND: $o > $o > $o ).
thf(func_def_139,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_140,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_141,type,
vIMP: $o > $o > $o ).
thf(func_def_142,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_143,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_144,type,
vNOT: $o > $o ).
thf(func_def_145,type,
sP0: $i > $i > $o ).
thf(func_def_146,type,
sP1: $i > $o ).
thf(func_def_147,type,
sP2: $o ).
thf(func_def_150,type,
sK5: $i > $i > $i ).
thf(func_def_153,type,
sK8: $i > $o ).
thf(func_def_160,type,
sK15: ( $i > $o ) > $i > $i ).
thf(func_def_162,type,
sK17: $i > $o ).
thf(func_def_165,type,
sK20: $o ).
thf(func_def_171,type,
sK26: $i > $o ).
thf(func_def_172,type,
sK27: $i > $o ).
thf(func_def_173,type,
sK28: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_174,type,
sK29: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_175,type,
sK30: $i > $i ).
thf(func_def_186,type,
sK41: $i > $o ).
thf(func_def_188,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_193,type,
sK48: $i > $i ).
thf(func_def_194,type,
sK49: $i > $i ).
thf(func_def_195,type,
sK50: $i > $i ).
thf(func_def_196,type,
sK51: $i > $i ).
thf(func_def_197,type,
sK52: $i > $i ).
thf(func_def_198,type,
sK53: $i > $i > $i > $i ).
thf(func_def_199,type,
sK54: $i > $i ).
thf(func_def_200,type,
sK55: $i > $i ).
thf(func_def_201,type,
sK56: $i > $i ).
thf(func_def_202,type,
sK57: $i > $i ).
thf(func_def_203,type,
sK58: $i > $i > $i ).
thf(func_def_204,type,
sK59: $i > $i > $i > $i ).
thf(func_def_205,type,
sK60: $i > $i > $i > $i ).
thf(func_def_206,type,
sK61: $i > $i > $i > $i ).
thf(func_def_207,type,
sK62: $i > $i > $i ).
thf(func_def_208,type,
sK63: $i > $i > $i ).
thf(func_def_209,type,
sK64: $i > $i > $i ).
thf(func_def_210,type,
sK65: $i > $i > $i ).
thf(func_def_214,type,
sK69: $i > $o ).
thf(func_def_216,type,
sK71: ( $i > $o ) > $i ).
thf(func_def_217,type,
sK72: $i > $o ).
thf(func_def_220,type,
sK75: $i > $i > $i ).
thf(func_def_221,type,
sK76: ( $i > $o ) > $i > $i ).
thf(func_def_223,type,
sK78: $i > $o ).
thf(func_def_225,type,
sK80: $o ).
thf(func_def_229,type,
sK84: $i > $o ).
thf(func_def_231,type,
sK86: $i > ( $i > $o ) > $i ).
thf(func_def_234,type,
sK89: $i > $i > $i ).
thf(func_def_235,type,
sK90: $i > $i > $i ).
thf(func_def_243,type,
sK98: ( $i > $o ) > $i > $i ).
thf(func_def_245,type,
sK100: $i > $o ).
thf(func_def_256,type,
sK111: $i > $o ).
thf(func_def_261,type,
sK116: $i > $o ).
thf(func_def_266,type,
sK121: $o ).
thf(func_def_281,type,
sK136: $i > $o ).
thf(func_def_282,type,
sK137: $i > $i ).
thf(func_def_283,type,
sK138: ( $i > $o ) > $i ).
thf(func_def_287,type,
sK142: $o ).
thf(func_def_289,type,
sK144: $i > $i ).
thf(func_def_298,type,
sK153: $i > $o ).
thf(func_def_299,type,
sK154: $i > $o ).
thf(func_def_300,type,
sK155: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_301,type,
sK156: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_304,type,
sK159: $i > $i ).
thf(func_def_306,type,
sK161: $i > $i ).
thf(func_def_308,type,
sK163: $i > ( $i > $o ) > $i ).
thf(func_def_309,type,
sK164: $i > $o ).
thf(func_def_321,type,
sK176: ( $i > $o ) > $i ).
thf(func_def_322,type,
sK177: $i > $o ).
thf(func_def_323,type,
sK178: $i > $i ).
thf(func_def_340,type,
sK195: $o ).
thf(func_def_354,type,
sK209: $i > $i > $i ).
thf(func_def_356,type,
sK211: $i > $i > $i ).
thf(func_def_361,type,
sK216: $i > $o ).
thf(func_def_366,type,
sK221: $i > $o ).
thf(func_def_370,type,
sK225: ( $i > $i > $o ) > $i > $i ).
thf(func_def_371,type,
sK226: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_372,type,
sK227: ( $i > $i > $o ) > $i > $i ).
thf(func_def_374,type,
sK229: $i > $i > $o ).
thf(func_def_375,type,
sK230: $i > $i ).
thf(func_def_376,type,
sK231: $i > $i ).
thf(func_def_377,type,
sK232: $i > $o ).
thf(func_def_380,type,
sK235: $i > $o ).
thf(func_def_381,type,
sK236: $i > $o ).
thf(func_def_386,type,
sK241: $i > $o ).
thf(func_def_390,type,
sK245: $i > $i ).
thf(func_def_392,type,
sK247: $i > $i > $i ).
thf(func_def_396,type,
sK251: $i > $i ).
thf(func_def_397,type,
sK252: $i > $o ).
thf(func_def_399,type,
sK254: ( $i > $o ) > $i ).
thf(func_def_400,type,
sK255: ( $i > $o ) > $i ).
thf(func_def_409,type,
sK264: $o > $i > $i > $i ).
thf(func_def_412,type,
sK267: $o ).
thf(func_def_416,type,
sK271: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_417,type,
sK272: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_418,type,
sK273: $i > $o ).
thf(func_def_419,type,
sK274: $i > $o ).
thf(func_def_423,type,
sK278: $o ).
thf(func_def_432,type,
sK287: $i > $o ).
thf(func_def_435,type,
sK290: $i > $i > $i ).
thf(func_def_441,type,
sK296: $i > $o ).
thf(func_def_444,type,
sK299: $i > ( $i > $o ) > $i ).
thf(func_def_446,type,
sK301: $i > $o ).
thf(func_def_449,type,
sK304: $i > $i ).
thf(func_def_450,type,
sK305: $i > $i > $i ).
thf(func_def_456,type,
sK311: $i > ( $i > $o ) > $i ).
thf(func_def_457,type,
sK312: $i > $o ).
thf(f116,axiom,
( binintersectRsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(f118,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( subset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(f119,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( subset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f118]) ).
thf(f218,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( subset @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[],[f119]) ).
thf(f219,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ! [X0: $i,X1: $i] :
( ( ( binintersect @ X0 @ X1 )
= X0 )
=> ( ( subset @ X0 @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f218]) ).
thf(f244,plain,
( binintersectRsub
= ( ! [X0: $i,X1: $i] : ( subset @ ( binintersect @ X0 @ X1 ) @ X1 ) ) ),
inference(rectify,[],[f116]) ).
thf(f245,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
<=> ( binintersectRsub = $true ) ),
inference(fool_elimination,[],[f244]) ).
thf(f390,plain,
( ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( ( binintersect @ X0 @ X1 )
= X0 ) )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[],[f219]) ).
thf(f391,plain,
( ( subsetTrans = $true )
& ( binintersectSubset3 = $true )
& ( powersetE = $true )
& ( setbeta = $true )
& ( subsetRefl = $true )
& ( binintersectRsub = $true )
& ( foundationAx = $true )
& ( omega0Ax = $true )
& ( upairset2IR = $true )
& ( binintersectEL = $true )
& ( nonemptyI = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( powersetE1 = $true )
& ( powerset__Cong = $true )
& ( setadjoinSub2 = $true )
& ( setunionAx = $true )
& ( emptyinunitempty = $true )
& ( descr__Cong = $true )
& ( binunionIR = $true )
& ( nonemptyI1 = $true )
& ( binunionRsub = $true )
& ( exuE2 = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( sepInPowerset = $true )
& ( setext = $true )
& ( notsubsetI = $true )
& ( notequalI2 = $true )
& ( emptyset__Cong = $true )
& ( omegaIndAx = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectSubset2 = $true )
& ( setunion__Cong = $true )
& ( setunionE = $true )
& ( setoftrueEq = $true )
& ( omegaSAx = $true )
& ( notdexE = $true )
& ( omega__Cong = $true )
& ( setadjoinAx = $true )
& ( emptysetsubset = $true )
& ( setextsub = $true )
& ( upairsetIL = $true )
& ( subsetE = $true )
& ( upairsetIR = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( sepSubset = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( binintersectSubset5 = $true )
& ( binunionE = $true )
& ( vacuousDall = $true )
& ( binintersectI = $true )
& ( exuE3u = $true )
& ( subPowSU = $true )
& ( powersetI = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( eqimpsubset2 = $true )
& ( binunionLsub = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionEcases = $true )
& ( disjointsetsI1 = $true )
& ( exu__Cong = $true )
& ( powersetsubset = $true )
& ( emptyinPowerset = $true )
& ( subsetI2 = $true )
& ( setadjoinSub = $true )
& ( dsetconstrI = $true )
& ( binintersectLsub = $true )
& ( dsetconstr__Cong = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan1 = $true )
& ( singletonsswitch = $true )
& ( setunionI = $true )
& ( exuI1 = $true )
& ( dsetconstrEL = $true )
& ( emptyI = $true )
& ( emptyE1 = $true )
& ( binintersectSubset4 = $true )
& ? [X0: $i,X1: $i] :
( ( ( subset @ X0 @ X1 )
!= $true )
& ( ( binintersect @ X0 @ X1 )
= X0 ) )
& ( setadjoinIR = $true )
& ( uniqinunit = $true )
& ( eqimpsubset1 = $true )
& ( binintersectER = $true )
& ( prop2set2propI = $true )
& ( emptysetE = $true )
& ( exuE1 = $true )
& ( binunionIL = $true )
& ( exuI2 = $true )
& ( subsetI1 = $true )
& ( inCongP = $true )
& ( nonemptyImpWitness = $true )
& ( inPowerset = $true )
& ( descrp = $true )
& ( exuI3 = $true )
& ( prop2setE = $true )
& ( notinsingleton = $true )
& ( setadjoin__Cong = $true )
& ( emptysetimpfalse = $true )
& ( nonemptyE1 = $true )
& ( in__Cong = $true )
& ( noeltsimpempty = $true )
& ( exuEu = $true )
& ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( wellorderingAx = $true )
& ( subsetE2 = $true )
& ( upairsetE = $true )
& ( subset2powerset = $true )
& ( quantDeMorgan3 = $true )
& ( prop2setI = $true )
& ( notequalI1 = $true )
& ( setadjoinIL = $true ) ),
inference(flattening,[],[f390]) ).
thf(f583,plain,
( ( subsetTrans = $true )
& ( binintersectSubset3 = $true )
& ( powersetE = $true )
& ( setbeta = $true )
& ( subsetRefl = $true )
& ( binintersectRsub = $true )
& ( foundationAx = $true )
& ( omega0Ax = $true )
& ( upairset2IR = $true )
& ( binintersectEL = $true )
& ( nonemptyI = $true )
& ( exuE3e = $true )
& ( emptysetAx = $true )
& ( powersetE1 = $true )
& ( powerset__Cong = $true )
& ( setadjoinSub2 = $true )
& ( setunionAx = $true )
& ( emptyinunitempty = $true )
& ( descr__Cong = $true )
& ( binunionIR = $true )
& ( nonemptyI1 = $true )
& ( binunionRsub = $true )
& ( exuE2 = $true )
& ( replAx = $true )
& ( powersetAx = $true )
& ( sepInPowerset = $true )
& ( setext = $true )
& ( notsubsetI = $true )
& ( notequalI2 = $true )
& ( emptyset__Cong = $true )
& ( omegaIndAx = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan4 = $true )
& ( binintersectSubset2 = $true )
& ( setunion__Cong = $true )
& ( setunionE = $true )
& ( setoftrueEq = $true )
& ( omegaSAx = $true )
& ( notdexE = $true )
& ( omega__Cong = $true )
& ( setadjoinAx = $true )
& ( emptysetsubset = $true )
& ( setextsub = $true )
& ( upairsetIL = $true )
& ( subsetE = $true )
& ( upairsetIR = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( sepSubset = $true )
& ( setextAx = $true )
& ( notinemptyset = $true )
& ( binintersectSubset5 = $true )
& ( binunionE = $true )
& ( vacuousDall = $true )
& ( binintersectI = $true )
& ( exuE3u = $true )
& ( subPowSU = $true )
& ( powersetI = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( eqimpsubset2 = $true )
& ( binunionLsub = $true )
& ( subsetemptysetimpeq = $true )
& ( binunionEcases = $true )
& ( disjointsetsI1 = $true )
& ( exu__Cong = $true )
& ( powersetsubset = $true )
& ( emptyinPowerset = $true )
& ( subsetI2 = $true )
& ( setadjoinSub = $true )
& ( dsetconstrI = $true )
& ( binintersectLsub = $true )
& ( dsetconstr__Cong = $true )
& ( powersetI1 = $true )
& ( quantDeMorgan1 = $true )
& ( singletonsswitch = $true )
& ( setunionI = $true )
& ( exuI1 = $true )
& ( dsetconstrEL = $true )
& ( emptyI = $true )
& ( emptyE1 = $true )
& ( binintersectSubset4 = $true )
& ( ( subset @ sK87 @ sK88 )
!= $true )
& ( sK87
= ( binintersect @ sK87 @ sK88 ) )
& ( setadjoinIR = $true )
& ( uniqinunit = $true )
& ( eqimpsubset1 = $true )
& ( binintersectER = $true )
& ( prop2set2propI = $true )
& ( emptysetE = $true )
& ( exuE1 = $true )
& ( binunionIL = $true )
& ( exuI2 = $true )
& ( subsetI1 = $true )
& ( inCongP = $true )
& ( nonemptyImpWitness = $true )
& ( inPowerset = $true )
& ( descrp = $true )
& ( exuI3 = $true )
& ( prop2setE = $true )
& ( notinsingleton = $true )
& ( setadjoin__Cong = $true )
& ( emptysetimpfalse = $true )
& ( nonemptyE1 = $true )
& ( in__Cong = $true )
& ( noeltsimpempty = $true )
& ( exuEu = $true )
& ( eqinunit = $true )
& ( dsetconstrER = $true )
& ( wellorderingAx = $true )
& ( subsetE2 = $true )
& ( upairsetE = $true )
& ( subset2powerset = $true )
& ( quantDeMorgan3 = $true )
& ( prop2setI = $true )
& ( notequalI1 = $true )
& ( setadjoinIL = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK87,sK88]),skolemize(X0,sK87),skolemize(X1,sK88)],[f391]) ).
thf(f654,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ? [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[],[f245]) ).
thf(f655,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ? [X2: $i,X3: $i] :
( $true
!= ( subset @ ( binintersect @ X2 @ X3 ) @ X3 ) ) ) ),
inference(rectify,[],[f654]) ).
thf(f656,plain,
( ( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
| ( binintersectRsub != $true ) )
& ( ( binintersectRsub = $true )
| ( $true
!= ( subset @ ( binintersect @ sK149 @ sK150 ) @ sK150 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK149,sK150]),skolemize(X2,sK149),skolemize(X3,sK150)],[f655]) ).
thf(f1005,plain,
( sK87
= ( binintersect @ sK87 @ sK88 ) ),
inference(cnf_transformation,[],[f583]) ).
thf(f1006,plain,
( ( subset @ sK87 @ sK88 )
!= $true ),
inference(cnf_transformation,[],[f583]) ).
thf(f1083,plain,
binintersectRsub = $true,
inference(cnf_transformation,[],[f583]) ).
thf(f1176,plain,
! [X0: $i,X1: $i] :
( ( binintersectRsub != $true )
| ( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true ) ),
inference(cnf_transformation,[],[f656]) ).
thf(f1773,definition,
( spl314_49
<=> ( ( subset @ sK87 @ sK88 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl314_49])],[avatar_definition]) ).
thf(f1775,plain,
( ( ( subset @ sK87 @ sK88 )
!= $true )
| spl314_49 ),
inference(avatar_component_clause,[],[f1773]) ).
thf(f1776,plain,
~ spl314_49,
inference(avatar_split_clause,[],[f1006,f1773]) ).
thf(f2253,definition,
( spl314_157
<=> ( sK87
= ( binintersect @ sK87 @ sK88 ) ) ),
introduced(definition,[new_symbols(definition,[spl314_157])],[avatar_definition]) ).
thf(f2255,plain,
( ( sK87
= ( binintersect @ sK87 @ sK88 ) )
| ~ spl314_157 ),
inference(avatar_component_clause,[],[f2253]) ).
thf(f2256,plain,
spl314_157,
inference(avatar_split_clause,[],[f1005,f2253]) ).
thf(f3450,definition,
( spl314_410
<=> ( binintersectRsub = $true ) ),
introduced(definition,[new_symbols(definition,[spl314_410])],[avatar_definition]) ).
thf(f3453,plain,
spl314_410,
inference(avatar_split_clause,[],[f1083,f3450]) ).
thf(f4106,definition,
( spl314_546
<=> ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl314_546])],[avatar_definition]) ).
thf(f4107,plain,
( ! [X0: $i,X1: $i] :
( ( subset @ ( binintersect @ X0 @ X1 ) @ X1 )
= $true )
| ~ spl314_546 ),
inference(avatar_component_clause,[],[f4106]) ).
thf(f4108,plain,
( ~ spl314_410
| spl314_546 ),
inference(avatar_split_clause,[],[f1176,f4106,f3450]) ).
thf(f4273,plain,
( ( ( subset @ sK87 @ sK88 )
= $true )
| ~ spl314_157
| ~ spl314_546 ),
inference(superposition,[],[f4107,f2255]) ).
thf(f4276,plain,
( $false
| spl314_49
| ~ spl314_157
| ~ spl314_546 ),
inference(forward_subsumption_resolution,[],[f4273,f1775]) ).
thf(f4277,plain,
( spl314_49
| ~ spl314_157
| ~ spl314_546 ),
inference(avatar_contradiction_clause,[],[f4276]) ).
cnf(s30,plain,
~ spl314_49,
inference(sat_conversion,[],[f1776]) ).
cnf(s112,plain,
spl314_157,
inference(sat_conversion,[],[f2256]) ).
cnf(s386,plain,
spl314_410,
inference(sat_conversion,[],[f3453]) ).
cnf(s558,plain,
( ~ spl314_410
| spl314_546 ),
inference(sat_conversion,[],[f4108]) ).
cnf(s561,plain,
( spl314_49
| ~ spl314_157
| ~ spl314_546 ),
inference(sat_conversion,[],[f4277]) ).
cnf(s574,plain,
spl314_546,
inference(rat,[],[s558,s386]) ).
cnf(s663,plain,
spl314_49,
inference(rat,[],[s561,s574,s112]) ).
cnf(s694,plain,
$false,
inference(rat,[],[s30,s663]) ).
thf(f4278,plain,
$false,
inference(avatar_sat_refutation,[],[s694]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU599^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.19 % Computer : n014.cluster.edu
% 0.11/0.19 % Model : x86_64 x86_64
% 0.11/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.19 % Memory : 8046.5625MB
% 0.11/0.19 % OS : Linux 6.8.0-71-generic
% 0.11/0.19 % CPULimit : 300
% 0.11/0.19 % WCLimit : 300
% 0.11/0.19 % DateTime : Tue Sep 29 13:56:15 UTC 2026
% 0.11/0.19 % CPUTime :
% 0.11/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 Running higher-order theorem proving
% 0.11/0.25 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
% 0.74/0.37 % (2702598)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.74/0.37 % (2702608)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3723504857:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.74/0.37 % (2702609)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.74/0.37 % (2702609)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
% 0.74/0.37 % (2702604)lrs+10_16_si=on:nwc=1.5:random_seed=3015690945:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.74/0.37 % (2702603)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=897160958:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.74/0.37 % (2702605)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1101656485:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.74/0.37 % (2702607)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1289126004:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.74/0.37 % (2702606)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=95239314: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)
% 0.74/0.37 % (2702609)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=1658091702:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.74/0.37 % (2702605)Instruction limit reached!
% 0.74/0.37 % (2702605)------------------------------
% 0.74/0.37 % (2702605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702605)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702605)Termination reason: Instruction limit
% 0.74/0.37 % (2702605)Termination phase: shuffling
% 0.74/0.37 % (2702605)Time elapsed: 0.002 s
% 0.74/0.37 % (2702605)Peak memory usage: 10 MB
% 0.74/0.37 % (2702605)Instructions burned: 4 (million)
% 0.74/0.37 % (2702604)Instruction limit reached!
% 0.74/0.37 % (2702604)------------------------------
% 0.74/0.37 % (2702604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702604)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702604)Termination reason: Instruction limit
% 0.74/0.37 % (2702604)Termination phase: Property scanning
% 0.74/0.37 % (2702604)Time elapsed: 0.008 s
% 0.74/0.37 % (2702604)Peak memory usage: 10 MB
% 0.74/0.37 % (2702604)Instructions burned: 19 (million)
% 0.74/0.37 % (2702608)Instruction limit reached!
% 0.74/0.37 % (2702608)------------------------------
% 0.74/0.37 % (2702608)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702608)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702608)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702608)Termination reason: Instruction limit
% 0.74/0.37 % (2702608)Termination phase: Saturation
% 0.74/0.37 % (2702608)Time elapsed: 0.019 s
% 0.74/0.37 % (2702608)Peak memory usage: 13 MB
% 0.74/0.37 % (2702608)Instructions burned: 78 (million)
% 0.74/0.37 % (2702607)Instruction limit reached!
% 0.74/0.37 % (2702607)------------------------------
% 0.74/0.37 % (2702607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702607)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702607)Termination reason: Instruction limit
% 0.74/0.37 % (2702607)Termination phase: Preprocessing 3
% 0.74/0.37 % (2702607)Time elapsed: 0.012 s
% 0.74/0.37 % (2702607)Peak memory usage: 11 MB
% 0.74/0.37 % (2702607)Instructions burned: 24 (million)
% 0.74/0.37 % (2702619)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.37 % (2702617)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=135517079:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.37 % (2702619)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2501473539:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.74/0.37 % (2702617)Instruction limit reached!
% 0.74/0.37 % (2702617)------------------------------
% 0.74/0.37 % (2702617)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702617)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702617)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702617)Termination reason: Instruction limit
% 0.74/0.37 % (2702617)Termination phase: shuffling
% 0.74/0.37 % (2702617)Time elapsed: 0.002 s
% 0.74/0.37 % (2702617)Peak memory usage: 10 MB
% 0.74/0.37 % (2702617)Instructions burned: 4 (million)
% 0.74/0.37 % (2702619)Instruction limit reached!
% 0.74/0.37 % (2702619)------------------------------
% 0.74/0.37 % (2702619)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702619)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702619)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702619)Termination reason: Instruction limit
% 0.74/0.37 % (2702619)Termination phase: shuffling
% 0.74/0.37 % (2702619)Time elapsed: 0.002 s
% 0.74/0.37 % (2702619)Peak memory usage: 10 MB
% 0.74/0.37 % (2702619)Instructions burned: 8 (million)
% 0.74/0.37 % (2702618)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1265979301:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.74/0.37 % (2702620)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1155837761:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.74/0.37 % (2702618)Instruction limit reached!
% 0.74/0.37 % (2702618)------------------------------
% 0.74/0.37 % (2702618)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702618)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702618)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702618)Termination reason: Instruction limit
% 0.74/0.37 % (2702618)Termination phase: shuffling
% 0.74/0.37 % (2702618)Time elapsed: 0.004 s
% 0.74/0.37 % (2702618)Peak memory usage: 10 MB
% 0.74/0.37 % (2702618)Instructions burned: 10 (million)
% 0.74/0.37 % (2702623)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
% 0.74/0.37 % (2702623)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.74/0.37 % (2702620)Instruction limit reached!
% 0.74/0.37 % (2702620)------------------------------
% 0.74/0.37 % (2702620)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702620)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702620)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702620)Termination reason: Instruction limit
% 0.74/0.37 % (2702620)Termination phase: Property scanning
% 0.74/0.37 % (2702620)Time elapsed: 0.006 s
% 0.74/0.37 % (2702620)Peak memory usage: 10 MB
% 0.74/0.37 % (2702620)Instructions burned: 13 (million)
% 0.74/0.37 % (2702623)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2436637566:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.74/0.37 % (2702603)Instruction limit reached!
% 0.74/0.37 % (2702603)------------------------------
% 0.74/0.37 % (2702603)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702603)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702603)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702603)Termination reason: Instruction limit
% 0.74/0.37 % (2702603)Termination phase: Saturation
% 0.74/0.37 % (2702603)Time elapsed: 0.041 s
% 0.74/0.37 % (2702603)Peak memory usage: 13 MB
% 0.74/0.37 % (2702603)Instructions burned: 89 (million)
% 0.74/0.37 % (2702624)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=4263248825:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.74/0.37 % (2702623)Instruction limit reached!
% 0.74/0.37 % (2702623)------------------------------
% 0.74/0.37 % (2702623)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702623)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702623)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702623)Termination reason: Instruction limit
% 0.74/0.37 % (2702623)Termination phase: Property scanning
% 0.74/0.37 % (2702623)Time elapsed: 0.007 s
% 0.74/0.37 % (2702623)Peak memory usage: 10 MB
% 0.74/0.37 % (2702623)Instructions burned: 31 (million)
% 0.74/0.37 % (2702627)lrs+10_1_si=on:cs=on:random_seed=1550080979:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.74/0.37 % (2702629)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.74/0.37 % (2702632)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2120362838:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.74/0.37 % (2702627)Instruction limit reached!
% 0.74/0.37 % (2702627)------------------------------
% 0.74/0.37 % (2702627)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702627)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702627)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702627)Termination reason: Instruction limit
% 0.74/0.37 % (2702627)Termination phase: shuffling
% 0.74/0.37 % (2702627)Time elapsed: 0.005 s
% 0.74/0.37 % (2702627)Peak memory usage: 10 MB
% 0.74/0.37 % (2702627)Instructions burned: 10 (million)
% 0.74/0.37 % (2702629)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=872660629:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.74/0.37 % (2702629)Instruction limit reached!
% 0.74/0.37 % (2702629)------------------------------
% 0.74/0.37 % (2702629)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702629)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702629)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702629)Termination reason: Instruction limit
% 0.74/0.37 % (2702629)Termination phase: shuffling
% 0.74/0.37 % (2702629)Time elapsed: 0.003 s
% 0.74/0.37 % (2702629)Peak memory usage: 10 MB
% 0.74/0.37 % (2702629)Instructions burned: 6 (million)
% 0.74/0.37 % (2702606) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2702598-2702606"...
% 0.74/0.37 % (2702630)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=234374318:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.74/0.37 % (2702606)...printing done.
% 0.74/0.37 % (2702606)Refutation found. Thanks to Tanya!
% 0.74/0.37 % SZS status Theorem for theBenchmark
% 0.74/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.74/0.37 % (2702606)------------------------------
% 0.74/0.37 % (2702606)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.74/0.37 % (2702606)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.74/0.37 % (2702606)CaDiCaL version: 2.1.3
% 0.74/0.37 % (2702606)Termination reason: Refutation
% 0.74/0.37 % (2702606)Time elapsed: 0.063 s
% 0.74/0.37 % (2702606)Peak memory usage: 15 MB
% 0.74/0.37 % (2702606)Instructions burned: 123 (million)
% 0.74/0.37 % (2702598)Success in time 0.108 s
% 0.74/0.37 % Vampire exiting
%------------------------------------------------------------------------------