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KB Term:  Term intersection
English Word: 

  lessThan

Sigma KEE - lessThan
lessThan

appearance as argument number 1
-------------------------


(documentation lessThan ChineseLanguage "(lessThan ?NUMBER1 ?NUMBER2) 是真的 以防 ?NUMBER1 的 Quantity 比 ?NUMBER2 的 Quantity 要少。") Merge.kif 1904-1905
(documentation lessThan EnglishLanguage "(lessThan ?NUMBER1 ?NUMBER2) is true just in case the Quantity ?NUMBER1 is less than the Quantity ?NUMBER2.") Merge.kif 1902-1903
(domain lessThan 1 Quantity) Merge.kif 1900-1900 The number 1 argument of less than is an instance of quantity
(domain lessThan 2 Quantity) Merge.kif 1901-1901 The number 2 argument of less than is an instance of quantity
(instance lessThan BinaryPredicate) Merge.kif 1895-1895 less than is an instance of binary predicate
(instance lessThan IrreflexiveRelation) Merge.kif 1897-1897 less than is an instance of irreflexive relation
(instance lessThan RelationExtendedToQuantities) Merge.kif 1898-1898 less than is an instance of relation extended to quantities
(instance lessThan TransitiveRelation) Merge.kif 1896-1896 less than is an instance of transitive relation
(trichotomizingOn lessThan RealNumber) Merge.kif 1899-1899 less than is trichotomizing on real number

appearance as argument number 2
-------------------------


(format ChineseLanguage lessThan "%1 %n 是 lessThan %2") chinese_format.kif 141-141
(format EnglishLanguage lessThan "%1 is %n less than %2") english_format.kif 97-97
(inverse greaterThan lessThan) Merge.kif 1915-1915 greater than is an inverse of less than
(termFormat ChineseLanguage lessThan "少于") chinese_format.kif 142-142 "少于" is the printable form of less than in ChineseLanguage
(termFormat EnglishLanguage lessThan "less than") domainEnglishFormat.kif 6109-6109 "less than" is the printable form of less than in english language

antecedent
-------------------------


(<=>
    (and
        (instance ?LD LiquidDrop)
        (approximateDiameter ?LD
            (MeasureFn ?S Micrometer))
        (lessThan 500 ?S))
    (instance ?LD Droplet))
Geography.kif 6874-6880 A self connected object is an instance of liquid drop and the approximate diameter of the self connected object is a real number micrometer(s) and 500 is less than the real number if and only if the self connected object is an instance of droplet
(<=>
    (exists (?Stock ?StockPrice ?StrikePrice)
        (and
            (instance ?Option CallOption)
            (underlier ?Option ?Stock)
            (price ?Stock ?StockPrice ?Time)
            (strikePrice ?Option ?StrikePrice)
            (lessThan ?StockPrice ?StrikePrice)))
    (outOfTheMoney ?Option ?Time))
FinancialOntology.kif 2965-2973 There exist a financial instrument, the financial instrumentPrice and another currency measure such that an agreement is an instance of call option and the financial instrument is an underlier of the agreement and the financial instrument price the financial instrumentPrice for an agent and the other currency measure is a strike price of the agreement and the financial instrumentPrice is less than the other currency measure if and only if the agent is an out of the money of the agreement
(<=>
    (exists (?Stock ?StockPrice ?StrikePrice)
        (and
            (instance ?Option CallOption)
            (underlier ?Option ?Stock)
            (price ?Stock ?StockPrice ?Time)
            (strikePrice ?Option ?StrikePrice)
            (lessThan ?StrikePrice ?StockPrice)))
    (inTheMoney ?Option ?Time))
FinancialOntology.kif 2922-2930 There exist a financial instrument, the financial instrumentPrice and another currency measure such that an agreement is an instance of call option and the financial instrument is an underlier of the agreement and the financial instrument price the financial instrumentPrice for an agent and the other currency measure is a strike price of the agreement and the other currency measure is less than the financial instrumentPrice if and only if the agent is an in the money of the agreement
(<=>
    (exists (?Stock ?StockPrice ?StrikePrice)
        (and
            (instance ?Option PutOption)
            (underlier ?Option ?Stock)
            (price ?Stock ?StockPrice ?Time)
            (strikePrice ?Option ?StrikePrice)
            (lessThan ?StockPrice ?StrikePrice)))
    (inTheMoney ?Option ?Time))
FinancialOntology.kif 2932-2940 There exist a financial instrument, the financial instrumentPrice and another currency measure such that an agreement is an instance of put option and the financial instrument is an underlier of the agreement and the financial instrument price the financial instrumentPrice for an agent and the other currency measure is a strike price of the agreement and the financial instrumentPrice is less than the other currency measure if and only if the agent is an in the money of the agreement
(<=>
    (exists (?Stock ?StockPrice ?StrikePrice)
        (and
            (instance ?Option PutOption)
            (underlier ?Option ?Stock)
            (price ?Stock ?StockPrice ?Time)
            (strikePrice ?Option ?StrikePrice)
            (lessThan ?StrikePrice ?StockPrice)))
    (outOfTheMoney ?Option ?Time))
FinancialOntology.kif 2975-2983 There exist a financial instrument, the financial instrumentPrice and another currency measure such that an agreement is an instance of put option and the financial instrument is an underlier of the agreement and the financial instrument price the financial instrumentPrice for an agent and the other currency measure is a strike price of the agreement and the other currency measure is less than the financial instrumentPrice if and only if the agent is an out of the money of the agreement
(=>
    (and
        (currentAccountBalance ?Account ?Date
            (MeasureFn ?Balance UnitedStatesDollar))
        (lessThan ?Balance 0)
        (equal ?Overdraft
            (SubtractionFn 0 ?Balance)))
    (overdraft ?Account
        (MeasureFn ?Overdraft UnitedStatesDollar) ?Date))
FinancialOntology.kif 733-738
(=>
    (and
        (instance ?Account ?FinancialAccount)
        (minimumBalance ?Account UsingAnAccount ?Balance)
        (currentAccountBalance ?Account ?Date ?Amount)
        (lessThan ?Amount ?Balance))
    (exists (?Penalty)
        (and
            (instance ?Penalty Penalty)
            (date ?Penalty ?Date)
            (destination ?Penalty
                (CurrencyFn ?Account)))))
FinancialOntology.kif 658-668
(=>
    (and
        (instance ?Account LiabilityAccount)
        (minimumPayment ?Account ?MinPayment MonthDuration)
        (exists (?Payment ?Month)
            (and
                (instance ?Month Month)
                (destination ?Payment
                    (CurrencyFn ?Account))
                (paymentsPerPeriod ?Account ?Amount ?Month)
                (lessThan ?Amount ?MinPayment))))
    (exists (?Penalty)
        (and
            (instance ?Penalty Penalty)
            (destination ?Penalty
                (CurrencyFn ?Account)))))
FinancialOntology.kif 712-725
(=>
    (and
        (instance ?H Human)
        (holdsDuring ?T1
            (age ?H
                (MeasureFn ?N YearDuration)))
        (greaterThan ?N 12)
        (lessThan ?N 20))
    (holdsDuring ?T1
        (instance ?H Teenager)))
Mid-level-ontology.kif 492-498
(=>
    (and
        (instance ?H Human)
        (holdsDuring ?T1
            (age ?H
                (MeasureFn ?N YearDuration)))
        (lessThan ?N 18))
    (holdsDuring ?T1
        (instance ?H HumanYouth)))
Mid-level-ontology.kif 419-424
(=>
    (and
        (instance ?SUBSTANCE ?TYPE)
        (boilingPoint ?TYPE
            (MeasureFn ?TEMP1 ?MEASURE))
        (meltingPoint ?TYPE
            (MeasureFn ?TEMP2 ?MEASURE))
        (instance ?MEASURE UnitOfTemperature)
        (holdsDuring ?TIME
            (measure ?SUBSTANCE
                (MeasureFn ?TEMP3 ?MEASURE)))
        (greaterThan ?TEMP3 ?TEMP2)
        (lessThan ?TEMP3 ?TEMP1))
    (or
        (holdsDuring ?TIME
            (attribute ?SUBSTANCE Liquid))
        (exists (?MELT)
            (and
                (overlapsTemporally
                    (WhenFn ?MELT) ?TIME)
                (instance ?MELT Melting)
                (patient ?BOIL ?SUBSTANCE)))))
Merge.kif 13854-13869
(=>
    (and
        (instance ?SUBSTANCE ?TYPE)
        (meltingPoint ?TYPE
            (MeasureFn ?TEMP1 ?MEASURE))
        (holdsDuring ?TIME
            (measure ?SUBSTANCE
                (MeasureFn ?TEMP2 ?MEASURE)))
        (instance ?MEASURE UnitOfTemperature)
        (lessThan ?TEMP2 ?TEMP1))
    (or
        (holdsDuring ?TIME
            (attribute ?SUBSTANCE Solid))
        (exists (?FREEZE)
            (and
                (overlapsTemporally
                    (WhenFn ?FREEZE) ?TIME)
                (instance ?FREEZE Freezing)
                (patient ?FREEZE ?SUBSTANCE)))))
Merge.kif 13871-13884
(=>
    (and
        (instance ?WATERWAY Waterway)
        (depth ?OBJ ?WATERWAY
            (MeasureFn ?DEPTH ?UNIT))
        (instance ?UNIT UnitOfLength)
        (lessThan ?DRAFT ?DEPTH))
    (navigableForDraft ?WATERWAY
        (MeasureFn ?DRAFT ?UNIT)))
Transportation.kif 2608-2614
(=>
    (and
        (instance ?X ?Y)
        (subclass ?Y PureSubstance)
        (boilingPoint ?Y
            (MeasureFn ?BOIL KelvinDegree))
        (meltingPoint ?Y
            (MeasureFn ?MELT KelvinDegree))
        (measure ?X
            (MeasureFn ?TEMP KelvinDegree))
        (greaterThan ?TEMP ?MELT)
        (lessThan ?TEMP ?BOIL))
    (attribute ?X Liquid))
Merge.kif 13798-13807
(=>
    (and
        (instance ?X ?Y)
        (subclass ?Y PureSubstance)
        (meltingPoint ?Y
            (MeasureFn ?MELT KelvinDegree))
        (barometricPressure ?X
            (MeasureFn ?PRES InchMercury))
        (greaterThan ?PRES 29.92)
        (measure ?X
            (MeasureFn ?TEMP KelvinDegree))
        (lessThan ?TEMP ?MELT))
    (attribute ?X Solid))
Merge.kif 13809-13818
(=>
    (and
        (processList @ROW)
        (inList ?Process1
            (ListFn @ROW))
        (inList ?Process2
            (ListFn @ROW))
        (equal
            (ListOrderFn
                (ListFn @ROW) ?Number1) ?Process1)
        (equal
            (ListOrderFn
                (ListFn @ROW) ?Number2) ?Process2)
        (lessThan ?Number1 ?Number2))
    (earlier
        (WhenFn ?Process1)
        (WhenFn ?Process2)))
QoSontology.kif 690-698
(=>
    (and
        (productPrice ?ENT ?PRICE1 ?AGENT)
        (publishedPrice ?ENT ?PRICE2 ?AGENT ?PS)
        (validFor ?PS ?CUSTCLASS)
        (instance ?ITEM ?ENT)
        (instance ?B Buying)
        (immediateInstance ?CUST ?CUSTCLASS)
        (agent ?B ?CUST)
        (origin ?B ?AGENT)
        (lessThan ?PRICE2 ?PRICE1))
    (modalAttribute
        (transactionAmount ?B ?PRICE1) Likely))
Catalog.kif 415-427

consequent
-------------------------


(<=>
    (and
        (instance ?REL TotalValuedRelation)
        (instance ?REL Predicate))
    (exists (?VALENCE)
        (and
            (instance ?REL Relation)
            (valence ?REL ?VALENCE)
            (=>
                (forall (?NUMBER ?ELEMENT ?CLASS)
                    (=>
                        (and
                            (lessThan ?NUMBER ?VALENCE)
                            (domain ?REL ?NUMBER ?CLASS)
                            (equal ?ELEMENT
                                (ListOrderFn
                                    (ListFn @ROW) ?NUMBER)))
                        (instance ?ELEMENT ?CLASS)))
                (exists (?ITEM)
                    (?REL @ROW ?ITEM))))))
Merge.kif 2331-2348 A relation is an instance of total valued relation and the relation is an instance of predicate if and only if there exists a positive integer such that the relation is an instance of relation and the relation %&has the positive integer argument(s) and
(<=>
    (equal
        (DeathsPerThousandLiveBirthsFn ?AREA
            (YearFn ?YEAR)) ?REALNUMBER)
    (and
        (equal ?BIRTHCOUNT
            (CardinalityFn
                (KappaFn ?BIRTH
                    (and
                        (instance ?BIRTH Birth)
                        (experiencer ?BIRTH ?INFANT)
                        (instance ?INFANT Human)
                        (during
                            (WhenFn ?BIRTH)
                            (YearFn ?YEAR))
                        (equal
                            (WhereFn ?BIRTH
                                (WhenFn ?BIRTH)) ?AREA)))))
        (equal
            (DivisionFn ?BIRTHCOUNT 1000) ?THOUSANDSOFBIRTHS)
        (equal ?INFANTDEATHCOUNT
            (CardinalityFn
                (KappaFn ?DEATH
                    (and
                        (instance ?DEATH Death)
                        (experiencer ?DEATH ?INFANT)
                        (instance ?INFANT Human)
                        (age ?INFANT
                            (MeasureFn ?AGE YearDuration))
                        (lessThan ?AGE 1)
                        (during
                            (WhenFn ?DEATH)
                            (YearFn ?YEAR))
                        (equal
                            (WhereFn ?DEATH
                                (WhenFn ?DEATH)) ?AREA)))))
        (equal
            (DivisionFn ?INFANTDEATHCOUNT ?THOUSANDSOFBIRTHS) ?REALNUMBER)))
People.kif 253-277 The deaths per thousand live births of a geopolitical area and the year an integer is equal to a real number if and only if another integer is equal to the number of instances in the class described by a symbolic string and the other integer and 1000 is equal to a quantity and a third integer is equal to the number of instances in the class described by another symbolic string and the third integer and the quantity is equal to the real number
(<=>
    (instance ?NUMBER NegativeRealNumber)
    (and
        (lessThan ?NUMBER 0)
        (instance ?NUMBER RealNumber)))
Merge.kif 2020-2024 A quantity is an instance of negative real number if and only if the quantity is less than 0 and the quantity is an instance of real number
(<=>
    (lessThanOrEqualTo ?NUMBER1 ?NUMBER2)
    (or
        (equal ?NUMBER1 ?NUMBER2)
        (lessThan ?NUMBER1 ?NUMBER2)))
Merge.kif 1934-1938 A quantity is less than or equal to another quantity if and only if the quantity is equal to the other quantity or the quantity is less than the other quantity
(=>
    (and
        (attribute ?P CollegeFreshman)
        (occupiesPosition ?H ?P ?ORG))
    (exists (?T)
        (and
            (holdsDuring ?T
                (student ?H ?ORG))
            (lessThan ?T
                (MeasureFn 1 YearDuration)))))
Mid-level-ontology.kif 16311-16319
(=>
    (and
        (attribute ?P CollegeJunior)
        (occupiesPosition ?H ?P ?ORG))
    (exists (?T)
        (and
            (holdsDuring ?T
                (student ?H ?ORG))
            (greaterThanOrEqualTo ?T
                (MeasureFn 2 YearDuration))
            (lessThan ?T
                (MeasureFn 3 YearDuration)))))
Mid-level-ontology.kif 16325-16336
(=>
    (and
        (attribute ?P CollegeSenior)
        (occupiesPosition ?H ?P ?ORG))
    (exists (?T)
        (and
            (holdsDuring ?T
                (student ?H ?ORG))
            (greaterThanOrEqualTo ?T
                (MeasureFn 3 YearDuration))
            (lessThan ?T
                (MeasureFn 4 YearDuration)))))
Mid-level-ontology.kif 16342-16353
(=>
    (and
        (attribute ?P CollegeSophomore)
        (occupiesPosition ?H ?P ?ORG))
    (exists (?T)
        (and
            (holdsDuring ?T
                (student ?H ?ORG))
            (greaterThanOrEqualTo ?T
                (MeasureFn 1 YearDuration))
            (lessThan ?T
                (MeasureFn 2 YearDuration)))))
Mid-level-ontology.kif 16359-16370
(=>
    (and
        (conditionalProbability
            (attribute ?X ComfortFood)
            (attribute ?X HeartHealthyFood) ?NUMBER1)
        (conditionalProbability
            (attribute ?X ComfortFood)
            (not
                (attribute ?X HeartHealthyFood)) ?NUMBER2))
    (lessThan ?NUMBER1 ?NUMBER2))
Dining.kif 1102-1110
(=>
    (and
        (dayPhone ?Number ?Agent)
        (instance ?Day Day))
    (exists (?Phone)
        (and
            (phoneNumber ?Number ?Phone)
            (holdsDuring
                (HourFn ?Number ?Day)
                (possesses ?Agent ?Phone))
            (lessThan ?Number 18))))
FinancialOntology.kif 3583-3591
(=>
    (and
        (decreasesLikelihood ?FORMULA1 ?FORMULA2)
        (equal
            (ProbabilityFn ?FORMULA2) ?NUMBER1)
        (conditionalProbability ?FORMULA1 ?FORMULA2 ?NUMBER2))
    (lessThan ?NUMBER2 ?NUMBER1))
Merge.kif 2800-2805
(=>
    (and
        (defaultMeasure ?OBJECT
            (MeasureFn ?Q ?UNIT))
        (instance ?UNIT CompositeUnitOfMeasure))
    (modalAttribute
        (exists (?INST ?QUANTITY)
            (and
                (instance ?INST ?OBJECT)
                (measure ?INST
                    (MeasureFn ?QUANTITY ?UNIT))
                (lessThan ?QUANTITY
                    (MultiplicationFn ?Q .5)))) Unlikely))
Mid-level-ontology.kif 11171-11180
(=>
    (and
        (defaultMinimumMeasure ?OBJECT
            (MeasureFn ?Q ?UNIT))
        (instance ?UNIT CompositeUnitOfMeasure))
    (modalAttribute
        (exists (?INST ?QUANTITY)
            (and
                (instance ?INST ?OBJECT)
                (measure ?INST
                    (MeasureFn ?QUANTITY ?UNIT))
                (lessThan ?QUANTITY ?Q))) Unlikely))
Mid-level-ontology.kif 11102-11111
(=>
    (and
        (defaultMinimumMeasure ?OBJECT
            (MeasureFn ?Q ?UNIT1))
        (subclass ?UNITCLASS NonCompositeUnitOfMeasure)
        (instance ?UNIT1 ?UNITCLASS))
    (modalAttribute
        (exists (?INST ?QUANTITY ?UNIT2)
            (and
                (instance ?INST ?OBJECT)
                (measure ?INST
                    (MeasureFn ?QUANTITY ?UNIT2))
                (instance ?UNIT2 ?UNITCLASS)
                (lessThan
                    (MeasureFn ?QUANTITY ?UNIT2)
                    (MeasureFn ?Q ?UNIT1)))) Unlikely))
Mid-level-ontology.kif 11112-11123
(=>
    (and
        (defaultMinimumSphereRadius ?OBJECT ?R)
        (instance ?INST ?OBJECT)
        (attribute ?INST Sphere))
    (modalAttribute
        (and
            (sphereRadius ?INST ?RADIUS)
            (lessThan ?RADIUS ?R)) Unlikely))
Mid-level-ontology.kif 11069-11077
(=>
    (and
        (instance ?A AcuteAngle)
        (angularMeasure ?A
            (MeasureFn ?N AngularDegree)))
    (lessThan ?N 90))
Mid-level-ontology.kif 5181-5185
(=>
    (and
        (instance ?AGENT Agent)
        (potentialCustomer ?CUST ?AGENT)
        (modalAttribute
            (and
                (instance ?R Reserving)
                (destination ?R ?AGENT)) Necessity)
        (conditionalProbability
            (exists (?RES1)
                (and
                    (instance ?RES1 Reservation)
                    (reservingEntity ?CUST ?RES1)
                    (fulfillingEntity ?AGENT ?RES1)))
            (customer ?CUST ?AGENT) ?NUM1)
        (conditionalProbability
            (not
                (exists (?RES2)
                    (and
                        (instance ?RES2 Reservation)
                        (reservingEntity ?CUST ?RES2)
                        (fulfillingEntity ?AGENT ?RES2))))
            (customer ?CUST ?AGENT) ?NUM2))
    (lessThan ?NUM2 ?NUM1))
Dining.kif 729-752
(=>
    (and
        (instance ?AIRPORT Airport)
        (attribute ?AIRPORT VeryShortRunwayAirport))
    (exists (?RUNWAY ?LENGTH)
        (and
            (instance ?RUNWAY Runway)
            (part ?RUNWAY ?AIRPORT)
            (length ?RUNWAY ?LENGTH)
            (lessThan ?LENGTH
                (MeasureFn 914 Meter)))))
Transportation.kif 1365-1374
(=>
    (and
        (instance ?AREA GeographicArea)
        (geographicSubregion
            (ElevationLowPointFn ?AREA) ?AREA)
        (elevation
            (ElevationLowPointFn ?AREA) ?ELEV1))
    (not
        (exists (?OTHER ?ELEV2)
            (and
                (geographicSubregion ?OTHER ?AREA)
                (not
                    (equal ?OTHER
                        (ElevationLowPointFn ?AREA)))
                (elevation ?OTHER ?ELEV2)
                (lessThan ?ELEV2 ?ELEV1)))))
Geography.kif 1881-1892
(=>
    (and
        (instance ?AREA GeographicArea)
        (instance ?WEATHER ClearWeather)
        (eventLocated ?WEATHER ?AREA)
        (cloudCoverFraction ?AREA ?FRACTION))
    (lessThan ?FRACTION 0.3))
Weather.kif 504-510
(=>
    (and
        (instance ?AREA GeographicArea)
        (instance ?WEATHER ClearWeather)
        (eventLocated ?WEATHER ?AREA))
    (exists (?FRACTION)
        (and
            (cloudCoverFraction ?AREA ?FRACTION)
            (lessThan ?FRACTION 0.3))))
Weather.kif 494-502
(=>
    (and
        (instance ?BOTTLE Bottle)
        (bottom ?BOTTOM ?BOTTLE)
        (top ?TOP ?BOTTLE)
        (width ?BOTTOM ?WIDTH1)
        (width ?TOP ?WIDTH2))
    (lessThan ?WIDTH2 ?WIDTH1))
Mid-level-ontology.kif 5023-5030
(=>
    (and
        (instance ?COOL Cooling)
        (patient ?COOL ?OBJ))
    (exists (?UNIT ?QUANT1 ?QUANT2)
        (and
            (instance ?UNIT TemperatureMeasure)
            (holdsDuring
                (BeginFn
                    (WhenFn ?COOL))
                (equal
                    (MeasureFn ?OBJ ?UNIT) ?QUANT1))
            (holdsDuring
                (EndFn
                    (WhenFn ?COOL))
                (equal
                    (MeasureFn ?OBJ ?UNIT) ?QUANT2))
            (lessThan ?QUANT2 ?QUANT1))))
Merge.kif 10920-10933
(=>
    (and
        (instance ?Compression DataCompression)
        (dataProcessed ?Compression ?Data)
        (holdsDuring
            (ImmediatePastFn
                (WhenFn ?Compression))
            (memorySize ?Data
                (MeasureFn ?Memory ?Measure)))
        (holdsDuring
            (ImmediateFutureFn
                (WhenFn ?Compression))
            (memorySize ?Data
                (MeasureFn ?NewMemory ?Measure))))
    (lessThan ?NewMemory ?Memory))
QoSontology.kif 1920-1928
(=>
    (and
        (instance ?D DeliveryService)
        (destination ?D ?LOC1)
        (deliveryRegion ?AGENT ?REGION)
        (conditionalProbability
            (located ?LOC1 ?REGION)
            (agent ?D ?AGENT) ?NUMBER1)
        (conditionalProbability
            (not
                (located ?LOC1 ?REGION))
            (agent ?D ?AGENT) ?NUMBER2))
    (lessThan ?NUMBER2 ?NUMBER1))
Dining.kif 511-520

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statement
-------------------------


(not
    (exists (?PATH1 ?PATH2)
        (and
            (instance ?PATH1
                (CutSetFn ?GRAPH))
            (instance ?PATH2
                (MinimalCutSetFn ?GRAPH))
            (pathLength ?PATH1 ?NUMBER1)
            (pathLength ?PATH2 ?NUMBER2)
            (lessThan ?NUMBER1 ?NUMBER2))))
Merge.kif 6230-6237 There don't exist a graph path and another graph path such that the graph path is an instance of the set of paths that partition a graph into two separate graphs and the other graph path is an instance of the set of minimal paths that partition the graph into two separate graphs and the length of the graph path is a positive integer and the length of the other graph path is another positive integer and the positive integer is less than the other positive integer


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