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forall (forall)

The universal quantifier of predicate logic.

Ontology

SUMO / STRUCTURAL-ONTOLOGY

Class(es)

taarkika prachaalaka
is instance of
  forall  

Coordinate term(s)

<=>  =>  and  entails  exists  not  or 

Type restrictions

forall(sUchI, sUtra)

Related WordNet synsets

See more related synsets on a separate page.

Axioms (114)

Agar rel1 is an inverse of rel2, to sab-kuch inst1,inst2 ke lie hai, ki: rel1(inst1,inst2) holds agar hai rel2(inst2,inst1) holds.
(=>
      (inverse ?REL1 ?REL2)
      (forall
            (?INST1 ?INST2)
            (<=>
                  (holds ?REL1 ?INST1 ?INST2)
                  (holds ?REL2 ?INST2 ?INST1))))

subclass is a subclass of class agar hai
(<=>
      (subclass ?SUBCLASS ?CLASS)
      (and
            (instance ?SUBCLASS SetOrClass)
            (instance ?CLASS SetOrClass)
            (forall
                  (?INST)
                  (=>
                        (instance ?INST ?SUBCLASS)
                        (instance ?INST ?CLASS)))))

Agar thing1 is equal to thing2, to sab-kuch attr ke lie hai, ki: thing1 has an attribute attr agar hai thing2 has an attribute attr.
(=>
      (equal ?THING1 ?THING2)
      (forall
            (?ATTR)
            (<=>
                  (property ?THING1 ?ATTR)
                  (property ?THING2 ?ATTR))))

Agar attr1 is equal to attr2, to sab-kuch thing ke lie hai, ki: thing has an attribute attr1 agar hai thing has an attribute attr2.
(=>
      (equal ?ATTR1 ?ATTR2)
      (forall
            (?THING)
            (<=>
                  (property ?THING ?ATTR1)
                  (property ?THING ?ATTR2))))

Agar thing1 is equal to thing2, to sab-kuch class ke lie hai, ki: thing1 is an instance of class agar hai thing2 is an instance of class.
(=>
      (equal ?THING1 ?THING2)
      (forall
            (?CLASS)
            (<=>
                  (instance ?THING1 ?CLASS)
                  (instance ?THING2 ?CLASS))))

Agar class1 is equal to class2, to sab-kuch thing ke lie hai, ki: thing is an instance of class1 agar hai thing is an instance of class2.
(=>
      (equal ?CLASS1 ?CLASS2)
      (forall
            (?THING)
            (<=>
                  (instance ?THING ?CLASS1)
                  (instance ?THING ?CLASS2))))

Agar rel1 is equal to rel2, to sab-kuch ke lie hai, ki: rel1() holds agar hai rel2() holds.
(=>
      (equal ?REL1 ?REL2)
      (forall
            (@ROW)
            (<=>
                  (holds ?REL1 @ROW)
                  (holds ?REL2 @ROW))))

(=>
      (equal ?LIST1 ?LIST2)
      (=>
            (and
                  (equal
                        ?LIST1
                        (ListFn @ROW1))
                  (equal
                        ?LIST2
                        (ListFn @ROW2)))
            (forall
                  (?NUMBER)
                  (equal
                        (ListOrderFn
                              (ListFn @ROW1)
                              ?NUMBER)
                        (ListOrderFn
                              (ListFn @ROW2)
                              ?NUMBER)))))

class1 asansavat class2 se hai agar hai
(<=>
      (disjoint ?CLASS1 ?CLASS2)
      (and
            (instance ?CLASS1 SetOrClass)
            (instance ?CLASS2 SetOrClass)
            (forall
                  (?INST)
                  (not
                        (and
                              (instance ?INST ?CLASS1)
                              (instance ?INST ?CLASS2))))))

(=>
      (contraryAttribute @ROW)
      (forall
            (?ATTR1 ?ATTR2)
            (=>
                  (and
                        (equal
                              ?ATTR1
                              (ListOrderFn
                                    (ListFn @ROW)
                                    ?NUMBER1))
                        (equal
                              ?ATTR2
                              (ListOrderFn
                                    (ListFn @ROW)
                                    ?NUMBER2))
                        (not
                              (equal ?NUMBER1 ?NUMBER2)))
                  (=>
                        (property ?OBJ ?ATTR1)
                        (not
                              (property ?OBJ ?ATTR2))))))

(=>
      (exhaustiveAttribute ?CLASS @ROW)
      (forall
            (?OBJ)
            (=>
                  (instance ?ATTR1 ?CLASS)
                  (exists
                        (?ATTR2)
                        (and
                              (inList
                                    ?ATTR2
                                    (ListFn @ROW))
                              (equal ?ATTR1 ?ATTR2))))))

(=>
      (subAttribute ?ATTR1 ?ATTR2)
      (forall
            (?OBJ)
            (=>
                  (property ?OBJ ?ATTR1)
                  (property ?OBJ ?ATTR2))))

(=>
      (piece ?SUBSTANCE1 ?SUBSTANCE2)
      (forall
            (?CLASS)
            (=>
                  (instance ?SUBSTANCE1 ?CLASS)
                  (instance ?SUBSTANCE2 ?CLASS))))

(=>
      (instance ?ATOM Atom)
      (forall
            (?NUCLEUS1 ?NUCLEUS2)
            (=>
                  (and
                        (component ?NUCLEUS1 ?ATOM)
                        (component ?NUCLEUS2 ?ATOM)
                        (instance ?NUCLEUS1 AtomicNucleus)
                        (instance ?NUCLEUS2 AtomicNucleus))
                  (equal ?NUCLEUS1 ?NUCLEUS2))))

coll1 is a proper sub-collection of coll2 agar hai
(<=>
      (subCollection ?COLL1 ?COLL2)
      (and
            (instance ?COLL1 Collection)
            (instance ?COLL2 Collection)
            (forall
                  (?MEMBER)
                  (=>
                        (member ?MEMBER ?COLL1)
                        (member ?MEMBER ?COLL2)))))

"the description of class" is equal to attr agar hai sab-kuch inst ke lie hai, ki: inst is an instance of class agar hai inst has an attribute attr.
(<=>
      (equal
            (AbstractionFn ?CLASS)
            ?ATTR)
      (forall
            (?INST)
            (<=>
                  (instance ?INST ?CLASS)
                  (property ?INST ?ATTR))))

rel is an instance of eka mUlyaadeya sambandha agar hai sab-kuch ,item1,item2 ke lie hai, ki: agar rel(,item1) holds aur rel(,item2) holds, to item1 is equal to item2.
(<=>
      (instance ?REL SingleValuedRelation)
      (forall
            (@ROW ?ITEM1 ?ITEM2)
            (=>
                  (and
                        (holds ?REL @ROW ?ITEM1)
                        (holds ?REL @ROW ?ITEM2))
                  (equal ?ITEM1 ?ITEM2))))

rel is an instance of pUrNa mUlyaadeya sambandha agar hai yah kuch valence nahin, ki rel is an instance of sambandha aur rel ke valence konaanke bahanen hai aur
(<=>
      (instance ?REL TotalValuedRelation)
      (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)
                              (holds ?REL @ROW ?ITEM))))))

Agar rel is an instance of anaatmavaachaka sambandha, to sab-kuch inst ke lie hai, ki: rel(inst,inst) doesn't hold.
(=>
      (instance ?REL IrreflexiveRelation)
      (forall
            (?INST)
            (not
                  (holds ?REL ?INST ?INST))))

(=>
      (instance ?REL SymmetricRelation)
      (forall
            (?INST1 ?INST2)
            (=>
                  (holds ?REL ?INST1 ?INST2)
                  (holds ?REL ?INST2 ?INST1))))

(=>
      (instance ?REL AntisymmetricRelation)
      (forall
            (?INST1 ?INST2)
            (=>
                  (and
                        (holds ?REL ?INST1 ?INST2)
                        (holds ?REL ?INST2 ?INST1))
                  (equal ?INST1 ?INST2))))

Agar rel is an instance of , to sab-kuch inst1,inst2 ke lie hai, ki: rel(inst1,inst2) holds yaa inst1 is equal to inst2 yaa rel(inst2,inst1) holds.
(=>
      (instance ?REL TrichotomizingRelation)
      (forall
            (?INST1 ?INST2)
            (or
                  (holds ?REL ?INST1 ?INST2)
                  (equal ?INST1 ?INST2)
                  (holds ?REL ?INST2 ?INST1))))

(=>
      (instance ?REL TransitiveRelation)
      (forall
            (?INST1 ?INST2 ?INST3)
            (=>
                  (and
                        (holds ?REL ?INST1 ?INST2)
                        (holds ?REL ?INST2 ?INST3))
                  (holds ?REL ?INST1 ?INST3))))

(=>
      (instance ?REL IntransitiveRelation)
      (forall
            (?INST1 ?INST2 ?INST3)
            (=>
                  (and
                        (holds ?REL ?INST1 ?INST2)
                        (holds ?REL ?INST2 ?INST3))
                  (not
                        (holds ?REL ?INST1 ?INST3)))))

Agar rel is an instance of pUrna anukrama sambandha, to sab-kuch inst1,inst2 ke lie hai, ki: rel(inst1,inst2) holds yaa rel(inst2,inst1) holds.
(=>
      (instance ?REL TotalOrderingRelation)
      (forall
            (?INST1 ?INST2)
            (or
                  (holds ?REL ?INST1 ?INST2)
                  (holds ?REL ?INST2 ?INST1))))

(=>
      (instance ?LIST List)
      (exists
            (?NUMBER1)
            (exists
                  (?ITEM1)
                  (and
                        (not
                              (equal
                                    (ListOrderFn ?LIST ?NUMBER1)
                                    ?ITEM1))
                        (forall
                              (?NUMBER2)
                              (=>
                                    (and
                                          (instance ?NUMBER2 PositiveInteger)
                                          (lessThan ?NUMBER2 ?NUMBER1))
                                    (exists
                                          (?ITEM2)
                                          (equal
                                                (ListOrderFn ?LIST ?NUMBER2)
                                                ?ITEM2))))))))

list is an instance of asaadhaaraNa sUchI agar hai sab-kuch number1,number2 ke lie hai, ki: agar "number1th element of list" is equal to "number2th element of list", to number1 is equal to number2.
(<=>
      (instance ?LIST UniqueList)
      (forall
            (?NUMBER1 ?NUMBER2)
            (=>
                  (equal
                        (ListOrderFn ?LIST ?NUMBER1)
                        (ListOrderFn ?LIST ?NUMBER2))
                  (equal ?NUMBER1 ?NUMBER2))))

(=>
      (exhaustiveDecomposition ?CLASS @ROW)
      (forall
            (?OBJ)
            (=>
                  (instance ?OBJ ?CLASS)
                  (exists
                        (?ITEM)
                        (and
                              (inList
                                    ?ITEM
                                    (ListFn @ROW))
                              (instance ?OBJ ?ITEM))))))

(=>
      (disjointDecomposition ?CLASS @ROW)
      (forall
            (?ITEM)
            (=>
                  (inList
                        ?ITEM
                        (ListFn @ROW))
                  (subclass ?ITEM ?CLASS))))

(=>
      (disjointDecomposition ?CLASS @ROW)
      (forall
            (?ITEM1 ?ITEM2)
            (=>
                  (and
                        (inList
                              ?ITEM1
                              (ListFn @ROW))
                        (inList
                              ?ITEM2
                              (ListFn @ROW))
                        (not
                              (equal ?ITEM1 ?ITEM2)))
                  (disjoint ?ITEM1 ?ITEM2))))

Agar list1 is an instance of sUchI aur list2 is an instance of sUchI aur sab-kuch number ke lie hai, ki: "numberth element of list1" is equal to "numberth element of list2", to list1 is equal to list2.
(=>
      (and
            (instance ?LIST1 List)
            (instance ?LIST2 List)
            (forall
                  (?NUMBER)
                  (equal
                        (ListOrderFn ?LIST1 ?NUMBER)
                        (ListOrderFn ?LIST2 ?NUMBER))))
      (equal ?LIST1 ?LIST2))

Agar "list kii lambaaaii" is equal to number1, to sab-kuch number2 ke lie hai, ki: yah kuch item nahin, ki "number2th element of list" is equal to item agar hai number2 is less than or equal to number1.
(=>
      (equal
            (ListLengthFn ?LIST)
            ?NUMBER1)
      (forall
            (?NUMBER2)
            (<=>
                  (exists
                        (?ITEM)
                        (equal
                              (ListOrderFn ?LIST ?NUMBER2)
                              ?ITEM))
                  (lessThanOrEqualTo ?NUMBER2 ?NUMBER1))))

(=>
      (valence ?REL ?NUMBER)
      (forall
            (@ROW)
            (=>
                  (holds ?REL @ROW)
                  (equal
                        (ListLengthFn
                              (ListFn @ROW))
                        ?NUMBER))))

list3 is equal to "the list composed of list1 and list2" agar hai sab-kuch number1,number2 ke lie hai, ki: agar number1 is less than or equal to "list1 kii lambaaaii" aur number2 is less than or equal to "list2 kii lambaaaii" aur number1 is an instance of dhanaatmaka pUrNaanka aur number2 is an instance of dhanaatmaka pUrNaanka, to "number1th element of list3" is equal to "number1th element of list1" aur ""("list1 kii lambaaaii"+number2)"th element of list3" is equal to "number2th element of list2".
(<=>
      (equal
            ?LIST3
            (ListConcatenateFn ?LIST1 ?LIST2))
      (forall
            (?NUMBER1 ?NUMBER2)
            (=>
                  (and
                        (lessThanOrEqualTo
                              ?NUMBER1
                              (ListLengthFn ?LIST1))
                        (lessThanOrEqualTo
                              ?NUMBER2
                              (ListLengthFn ?LIST2))
                        (instance ?NUMBER1 PositiveInteger)
                        (instance ?NUMBER2 PositiveInteger))
                  (and
                        (equal
                              (ListOrderFn ?LIST3 ?NUMBER1)
                              (ListOrderFn ?LIST1 ?NUMBER1))
                        (equal
                              (ListOrderFn
                                    ?LIST3
                                    (AdditionFn
                                          (ListLengthFn ?LIST1)
                                          ?NUMBER2))
                              (ListOrderFn ?LIST2 ?NUMBER2))))))

(=>
      (subList ?LIST1 ?LIST2)
      (forall
            (?ITEM)
            (=>
                  (inList ?ITEM ?LIST1)
                  (inList ?ITEM ?LIST2))))

(=>
      (subList ?LIST1 ?LIST2)
      (exists
            (?NUMBER3)
            (forall
                  (?ITEM)
                  (=>
                        (inList ?ITEM ?LIST1)
                        (exists
                              (?NUMBER1 ?NUMBER2)
                              (and
                                    (equal
                                          (ListOrderFn ?LIST1 ?NUMBER1)
                                          ?ITEM)
                                    (equal
                                          (ListOrderFn ?LIST2 ?NUMBER2)
                                          ?ITEM)
                                    (equal
                                          ?NUMBER2
                                          (AdditionFn ?NUMBER1 ?NUMBER3))))))))

(=>
      (initialList ?LIST1 ?LIST2)
      (forall
            (?NUMBER1 ?NUMBER2)
            (=>
                  (and
                        (equal
                              (ListLengthFn ?LIST1)
                              ?NUMBER1)
                        (lessThanOrEqualTo ?NUMBER2 ?NUMBER1))
                  (equal
                        (ListOrderFn ?LIST1 ?NUMBER2)
                        (ListOrderFn ?LIST2 ?NUMBER2)))))

(=>
      (instance ?FUN OneToOneFunction)
      (forall
            (?ARG1 ?ARG2)
            (=>
                  (and
                        (domain ?FUN 1 ?CLASS)
                        (instance ?ARG1 ?CLASS)
                        (instance ?ARG2 ?CLASS)
                        (not
                              (equal ?ARG1 ?ARG2)))
                  (not
                        (equal
                              (AssignmentFn ?FUN ?ARG1)
                              (AssignmentFn ?FUN ?ARG2))))))

(=>
      (instance ?FUNCTION AssociativeFunction)
      (forall
            (?INST1 ?INST2 ?INST3)
            (=>
                  (and
                        (domain ?FUNCTION 1 ?CLASS)
                        (instance ?INST1 ?CLASS)
                        (instance ?INST2 ?CLASS)
                        (instance ?INST3 ?CLASS))
                  (equal
                        (AssignmentFn
                              ?FUNCTION
                              ?INST1
                              (AssignmentFn ?FUNCTION ?INST2 ?INST3))
                        (AssignmentFn
                              ?FUNCTION
                              (AssignmentFn ?FUNCTION ?INST1 ?INST2)
                              ?INST3)))))

(=>
      (instance ?FUNCTION CommutativeFunction)
      (forall
            (?INST1 ?INST2)
            (=>
                  (and
                        (domain ?FUNCTION 1 ?CLASS)
                        (instance ?INST1 ?CLASS)
                        (instance ?INST2 ?CLASS))
                  (equal
                        (AssignmentFn ?FUNCTION ?INST1 ?INST2)
                        (AssignmentFn ?FUNCTION ?INST2 ?INST1)))))

(=>
      (and
            (closedOn ?FUNCTION ?CLASS)
            (instance ?FUNCTION UnaryFunction))
      (forall
            (?INST)
            (=>
                  (instance ?INST ?CLASS)
                  (instance
                        (AssignmentFn ?FUNCTION ?INST)
                        ?CLASS))))

(=>
      (and
            (closedOn ?FUNCTION ?CLASS)
            (instance ?FUNCTION BinaryFunction))
      (forall
            (?INST1 ?INST2)
            (=>
                  (and
                        (instance ?INST1 ?CLASS)
                        (instance ?INST2 ?CLASS))
                  (instance
                        (AssignmentFn ?FUNCTION ?INST1 ?INST2)
                        ?CLASS))))

(=>
      (reflexiveOn ?RELATION ?CLASS)
      (forall
            (?INST)
            (=>
                  (instance ?INST ?CLASS)
                  (holds ?RELATION ?INST ?INST))))

(=>
      (irreflexiveOn ?RELATION ?CLASS)
      (forall
            (?INST)
            (=>
                  (instance ?INST ?CLASS)
                  (not
                        (holds ?RELATION ?INST ?INST)))))

(=>
      (trichotomizingOn ?RELATION ?CLASS)
      (forall
            (?INST1 ?INST2)
            (=>
                  (and
                        (instance ?INST1 ?CLASS)
                        (instance ?INST2 ?CLASS))
                  (or
                        (holds ?RELATION ?INST1 ?INST2)
                        (holds ?RELATION ?INST2 ?INST1)
                        (equal ?INST1 ?INST2)))))

(=>
      (distributes ?FUNCTION1 ?FUNCTION2)
      (forall
            (?INST1 ?INST2 ?INST3)
            (=>
                  (and
                        (domain ?FUNCTION1 1 ?CLASS1)
                        (instance ?INST1 ?CLASS1)
                        (instance ?INST2 ?CLASS1)
                        (instance ?INST3 ?CLASS1)
                        (domain ?FUNCTION2 1 ?CLASS2)
                        (instance ?INST1 ?CLASS2)
                        (instance ?INST2 ?CLASS2)
                        (instance ?INST3 ?CLASS2))
                  (equal
                        (AssignmentFn
                              ?FUNCTION1
                              ?INST1
                              (AssignmentFn ?FUNCTION2 ?INST2 ?INST3))
                        (AssignmentFn
                              ?FUNCTION2
                              (AssignmentFn ?FUNCTION1 ?INST1 ?INST2)
                              (AssignmentFn ?FUNCTION1 ?INST1 ?INST3))))))

(=>
      (causesSubclass ?PROC1 ?PROC2)
      (forall
            (?INST2)
            (=>
                  (instance ?INST2 ?PROC2)
                  (exists
                        (?INST1)
                        (and
                              (instance ?INST1 ?PROC1)
                              (causes ?INST1 ?INST2))))))

(=>
      (copy ?OBJ1 ?OBJ2)
      (forall
            (?ATTR)
            (=>
                  (attribute ?OBJ1 ?ATTR)
                  (attribute ?OBJ2 ?ATTR))))

(=>
      (located ?OBJ ?REGION)
      (forall
            (?SUBOBJ)
            (=>
                  (part ?SUBOBJ ?OBJ)
                  (located ?SUBOBJ ?REGION))))

(=>
      (possesses ?PERSON ?OBJ)
      (exists
            (?TYPE)
            (and
                  (holdsRight ?PERSON ?TYPE)
                  (forall
                        (?PROCESS)
                        (=>
                              (instance ?PROCESS ?TYPE)
                              (patient ?PROCESS ?OBJ))))))

Agar proc1 inhibits proc2, to sab-kuch time,place ke lie hai, ki: "yah kuch proc1 inst1 nahin, ki inst1 is located at place during time" decreases likelihood of "yah kuch proc2 inst2 nahin, ki inst2 is located at place during time".
(=>
      (inhibits ?PROC1 ?PROC2)
      (forall
            (?TIME ?PLACE)
            (decreasesLikelihood
                  (holdsDuring
                        ?TIME
                        (exists
                              (?INST1)
                              (and
                                    (instance ?INST1 ?PROC1)
                                    (located ?INST1 ?PLACE))))
                  (holdsDuring
                        ?TIME
                        (exists
                              (?INST2)
                              (and
                                    (instance ?INST2 ?PROC2)
                                    (located ?INST2 ?PLACE)))))))

(=>
      (prevents ?PROC1 ?PROC2)
      (forall
            (?TIME ?PLACE)
            (=>
                  (holdsDuring
                        ?TIME
                        (exists
                              (?INST1)
                              (and
                                    (instance ?INST1 ?PROC1)
                                    (located ?INST1 ?PLACE))))
                  (not
                        (holdsDuring
                              ?TIME
                              (exists
                                    (?INST2)
                                    (and
                                          (instance ?INST2 ?PROC2)
                                          (located ?INST2 ?PLACE))))))))

class1 subsumes the content of class2 agar hai sab-kuch obj2,info ke lie hai, ki: agar obj2 is an instance of class2 aur obj2 contains information info, to yah kuch class1 obj1 nahin, ki obj1 contains information info.
(<=>
      (subsumesContentClass ?CLASS1 ?CLASS2)
      (forall
            (?OBJ2 ?INFO)
            (=>
                  (and
                        (instance ?OBJ2 ?CLASS2)
                        (containsInformation ?OBJ2 ?INFO))
                  (exists
                        (?OBJ1)
                        (and
                              (instance ?OBJ1 ?CLASS1)
                              (containsInformation ?OBJ1 ?INFO))))))

obj1 subsumes the content of obj2 agar hai sab-kuch info ke lie hai, ki: agar obj2 contains information info, to obj1 contains information info.
(<=>
      (subsumesContentInstance ?OBJ1 ?OBJ2)
      (forall
            (?INFO)
            (=>
                  (containsInformation ?OBJ2 ?INFO)
                  (containsInformation ?OBJ1 ?INFO))))

(=>
      (subProposition ?PROP1 ?PROP2)
      (forall
            (?OBJ1 ?OBJ2)
            (=>
                  (and
                        (containsInformation ?OBJ1 ?PROP1)
                        (containsInformation ?OBJ2 ?PROP2))
                  (subsumesContentInstance ?OBJ2 ?OBJ1))))

(=>
      (equal
            (GreatestCommonDivisorFn @ROW)
            ?NUMBER)
      (forall
            (?ELEMENT)
            (=>
                  (inList
                        ?ELEMENT
                        (ListFn @ROW))
                  (equal
                        (RemainderFn ?ELEMENT ?NUMBER)
                        0))))

(=>
      (equal
            (GreatestCommonDivisorFn @ROW)
            ?NUMBER)
      (not
            (exists
                  (?GREATER)
                  (and
                        (greaterThan ?GREATER ?NUMBER)
                        (forall
                              (?ELEMENT)
                              (=>
                                    (inList
                                          ?ELEMENT
                                          (ListFn @ROW))
                                    (equal
                                          (RemainderFn ?ELEMENT ?GREATER)
                                          0)))))))

(=>
      (equal
            (LeastCommonMultipleFn @ROW)
            ?NUMBER)
      (forall
            (?ELEMENT)
            (=>
                  (inList
                        ?ELEMENT
                        (ListFn @ROW))
                  (equal
                        (RemainderFn ?NUMBER ?ELEMENT)
                        0))))

(=>
      (equal
            (LeastCommonMultipleFn @ROW)
            ?NUMBER)
      (not
            (exists
                  (?LESS)
                  (and
                        (lessThan ?LESS ?NUMBER)
                        (forall
                              (?ELEMENT)
                              (=>
                                    (inList
                                          ?ELEMENT
                                          (ListFn @ROW))
                                    (equal
                                          (RemainderFn ?LESS ?ELEMENT)
                                          0)))))))

(=>
      (instance ?PRIME PrimeNumber)
      (forall
            (?NUMBER)
            (=>
                  (equal
                        (RemainderFn ?PRIME ?NUMBER)
                        0)
                  (or
                        (equal ?NUMBER 1)
                        (equal ?NUMBER ?PRIME)))))

(=>
      (identityElement ?FUNCTION ?ID)
      (forall
            (?INST)
            (=>
                  (and
                        (domain ?FUNCTION 1 ?CLASS)
                        (instance ?INST ?CLASS))
                  (equal
                        (AssignmentFn ?FUNCTION ?ID ?INST)
                        ?INST))))

(=>
      (subset ?SUBSET ?SET)
      (forall
            (?ELEMENT)
            (=>
                  (element ?ELEMENT ?SUBSET)
                  (element ?ELEMENT ?SET))))

Agar sab-kuch element ke lie hai, ki: element is an element of set1 agar hai element is an element of set2, to set1 is equal to set2.
(=>
      (forall
            (?ELEMENT)
            (<=>
                  (element ?ELEMENT ?SET1)
                  (element ?ELEMENT ?SET2)))
      (equal ?SET1 ?SET2))

(=>
      (instance ?SUPERCLASS PairwiseDisjointClass)
      (forall
            (?CLASS1 ?CLASS2)
            (=>
                  (and
                        (instance ?CLASS1 ?SUPERCLASS)
                        (instance ?CLASS2 ?SUPERCLASS))
                  (or
                        (equal ?CLASS1 ?CLASS2)
                        (disjoint ?CLASS1 ?CLASS2)))))

(=>
      (instance ?CLASS MutuallyDisjointClass)
      (forall
            (?INST1 ?INST2)
            (=>
                  (and
                        (instance ?INST1 ?CLASS)
                        (instance ?INST2 ?INST1))
                  (exists
                        (?INST3)
                        (and
                              (instance ?INST3 ?CLASS)
                              (not
                                    (instance ?INST2 ?INST3)))))))

(=>
      (and
            (equal
                  (PathWeightFn ?PATH)
                  ?SUM)
            (subGraph ?SUBPATH ?PATH)
            (graphPart ?ARC1 ?PATH)
            (arcWeight ?ARC1 ?NUMBER1)
            (forall
                  (?ARC2)
                  (=>
                        (graphPart ?ARC2 ?PATH)
                        (or
                              (graphPart ?ARC2 ?SUBPATH)
                              (equal ?ARC2 ?ARC1)))))
      (equal
            ?SUM
            (AdditionFn
                  (PathWeightFn ?SUBPATH)
                  ?NUMBER1)))

(=>
      (and
            (equal
                  (PathWeightFn ?PATH)
                  ?SUM)
            (graphPart ?ARC1 ?PATH)
            (graphPart ?ARC2 ?PATH)
            (arcWeight ?ARC1 ?NUMBER1)
            (arcWeight ?ARC2 ?NUMBER2)
            (forall
                  (?ARC3)
                  (=>
                        (graphPart ?ARC3 ?PATH)
                        (or
                              (equal ?ARC3 ?ARC1)
                              (equal ?ARC3 ?ARC2)))))
      (equal
            (PathWeightFn ?PATH)
            (AdditionFn ?NUMBER1 ?NUMBER2)))

(=>
      (and
            (equal
                  (MinimalWeightedPathFn ?NODE1 ?NODE2)
                  ?PATH)
            (equal
                  (PathWeightFn ?PATH)
                  ?NUMBER))
      (forall
            (?PATH2)
            (=>
                  (and
                        (instance
                              ?PATH2
                              (GraphPathFn ?NODE1 ?NODE2))
                        (equal
                              (PathWeightFn ?PATH2)
                              ?NUMBER2))
                  (greaterThanOrEqualTo ?NUMBER2 ?NUMBER1))))

(=>
      (and
            (equal
                  (MaximalWeightedPathFn ?NODE1 ?NODE2)
                  ?PATH)
            (equal
                  (PathWeightFn ?PATH)
                  ?NUMBER))
      (forall
            (?PATH2)
            (=>
                  (and
                        (instance
                              ?PATH2
                              (GraphPathFn ?NODE1 ?NODE2))
                        (equal
                              (PathWeightFn ?PATH2)
                              ?NUMBER2))
                  (lessThanOrEqualTo ?NUMBER2 ?NUMBER1))))

(=>
      (equal
            (MinimalCutSetFn ?GRAPH)
            ?PATHCLASS)
      (exists
            (?NUMBER)
            (forall
                  (?PATH)
                  (=>
                        (instance ?PATH ?PATHCLASS)
                        (pathLength ?PATH ?NUMBER)))))

(=>
      (and
            (instance ?REL RelationExtendedToQuantities)
            (instance ?REL TernaryRelation)
            (instance ?NUMBER1 RealNumber)
            (instance ?NUMBER2 RealNumber)
            (holds ?REL ?NUMBER1 ?NUMBER2 ?VALUE))
      (forall
            (?UNIT)
            (=>
                  (instance ?UNIT UnitOfMeasure)
                  (holds
                        ?REL
                        (MeasureFn ?NUMBER1 ?UNIT)
                        (MeasureFn ?NUMBER2 ?UNIT)
                        (MeasureFn ?VALUE ?UNIT)))))

(=>
      (and
            (instance ?REL RelationExtendedToQuantities)
            (instance ?REL BinaryRelation)
            (instance ?NUMBER1 RealNumber)
            (instance ?NUMBER2 RealNumber)
            (holds ?REL ?NUMBER1 ?NUMBER2))
      (forall
            (?UNIT)
            (=>
                  (instance ?UNIT UnitOfMeasure)
                  (holds
                        ?REL
                        (MeasureFn ?NUMBER1 ?UNIT)
                        (MeasureFn ?NUMBER2 ?UNIT)))))

(=>
      (larger ?OBJ1 ?OBJ2)
      (forall
            (?QUANT1 ?QUANT2)
            (=>
                  (and
                        (measure
                              ?OBJ1
                              (MeasureFn ?QUANT1 LengthMeasure))
                        (measure
                              ?OBJ2
                              (MeasureFn ?QUANT2 LengthMeasure)))
                  (greaterThan ?QUANT1 ?QUANT2))))

(=>
      (frequency ?PROC ?TIME1)
      (forall
            (?TIME2)
            (=>
                  (duration ?TIME2 ?TIME1)
                  (exists
                        (?POSITION)
                        (and
                              (temporalPart ?POSITION ?TIME2)
                              (holdsDuring
                                    ?POSITION
                                    (exists
                                          (?INST)
                                          (instance ?INST ?PROC))))))))

(=>
      (equal
            (BeginFn ?INTERVAL)
            ?POINT)
      (forall
            (?OTHERPOINT)
            (=>
                  (and
                        (temporalPart ?OTHERPOINT ?INTERVAL)
                        (not
                              (equal ?OTHERPOINT ?POINT)))
                  (before ?POINT ?OTHERPOINT))))

(=>
      (equal
            (EndFn ?INTERVAL)
            ?POINT)
      (forall
            (?OTHERPOINT)
            (=>
                  (and
                        (temporalPart ?OTHERPOINT ?INTERVAL)
                        (not
                              (equal ?OTHERPOINT ?POINT)))
                  (before ?OTHERPOINT ?POINT))))

(=>
      (instance ?OBJ Object)
      (exists
            (?TIME1 ?TIME2)
            (and
                  (instance ?TIME1 TimePoint)
                  (instance ?TIME2 TimePoint)
                  (before ?TIME1 ?TIME2)
                  (forall
                        (?TIME)
                        (=>
                              (and
                                    (beforeOrEqual ?TIME1 ?TIME)
                                    (beforeOrEqual ?TIME ?TIME2))
                              (time ?OBJ ?TIME))))))

(=>
      (result ?PROC ?OBJ)
      (forall
            (?TIME)
            (=>
                  (before
                        ?TIME
                        (BeginFn
                              (WhenFn ?PROC)))
                  (not
                        (time ?OBJ ?TIME)))))

Agar "interval between point1 and point2" is equal to interval, to sab-kuch point ke lie hai, ki: point is between or at point1 and point2 agar hai point is a part of interval.
(=>
      (equal
            (TimeIntervalFn ?POINT1 ?POINT2)
            ?INTERVAL)
      (forall
            (?POINT)
            (<=>
                  (temporallyBetweenOrEqual ?POINT1 ?POINT ?POINT2)
                  (temporalPart ?POINT ?INTERVAL))))

(=>
      (equal
            (TemporalCompositionFn ?INTERVAL ?INTERVAL-TYPE)
            ?CLASS)
      (forall
            (?TIME1 ?TIME2)
            (=>
                  (and
                        (instance ?TIME1 ?INTERVAL-TYPE)
                        (instance ?TIME2 ?CLASS))
                  (exists
                        (?DURATION)
                        (and
                              (duration ?TIME1 ?DURATION)
                              (duration ?TIME2 ?DURATION))))))

(=>
      (equal
            (TemporalCompositionFn ?INTERVAL ?INTERVAL-TYPE)
            ?CLASS)
      (forall
            (?TIME1 ?TIME2)
            (=>
                  (and
                        (instance ?TIME1 ?CLASS)
                        (instance ?TIME2 ?CLASS)
                        (not
                              (equal ?TIME1 ?TIME2)))
                  (or
                        (meetsTemporally ?TIME1 ?TIME2)
                        (meetsTemporally ?TIME2 ?TIME1)
                        (earlier ?TIME1 ?TIME2)
                        (earlier ?TIME2 ?TIME1)))))

(=>
      (equal
            (TemporalCompositionFn ?INTERVAL ?INTERVAL-TYPE)
            ?CLASS)
      (forall
            (?TIME1)
            (=>
                  (and
                        (instance ?TIME1 ?CLASS)
                        (not
                              (finishes ?TIME1 ?INTERVAL)))
                  (exists
                        (?TIME2)
                        (and
                              (instance ?TIME2 ?CLASS)
                              (meetsTemporally ?TIME1 ?TIME2))))))

(=>
      (equal
            (TemporalCompositionFn ?INTERVAL ?INTERVAL-TYPE)
            ?CLASS)
      (forall
            (?TIME1)
            (=>
                  (and
                        (instance ?TIME1 ?CLASS)
                        (not
                              (starts ?TIME1 ?INTERVAL)))
                  (exists
                        (?TIME2)
                        (and
                              (instance ?TIME2 ?CLASS)
                              (meetsTemporally ?TIME2 ?TIME1))))))

(=>
      (equal
            (TemporalCompositionFn ?INTERVAL ?INTERVAL-TYPE)
            ?CLASS)
      (forall
            (?TIME)
            (=>
                  (and
                        (instance ?TIME TimePoint)
                        (temporalPart ?TIME ?INTERVAL))
                  (exists
                        (?INSTANCE)
                        (and
                              (instance ?INSTANCE ?CLASS)
                              (temporalPart ?TIME ?INSTANCE))))))

obj is an instance of aatmasambaddha vastu agar hai sab-kuch part1,part2 ke lie hai, ki: agar obj is equal to "the union of the parts of part1 and part2", to part1 is connected to part2.
(<=>
      (instance ?OBJ SelfConnectedObject)
      (forall
            (?PART1 ?PART2)
            (=>
                  (equal
                        ?OBJ
                        (MereologicalSumFn ?PART1 ?PART2))
                  (connected ?PART1 ?PART2))))

(=>
      (surface ?OBJ1 ?OBJ2)
      (forall
            (?OBJ3)
            (=>
                  (superficialPart ?OBJ3 ?OBJ2)
                  (part ?OBJ3 ?OBJ1))))

(=>
      (interiorPart ?OBJ1 ?OBJ2)
      (forall
            (?PART)
            (=>
                  (superficialPart ?PART ?OBJ2)
                  (not
                        (overlapsSpatially ?OBJ1 ?PART)))))

Agar obj3 is equal to "the union of the parts of obj1 and obj2", to sab-kuch part ke lie hai, ki: part is a part of obj3 agar hai part is a part of obj1 yaa part is a part of obj2.
(=>
      (equal
            ?OBJ3
            (MereologicalSumFn ?OBJ1 ?OBJ2))
      (forall
            (?PART)
            (<=>
                  (part ?PART ?OBJ3)
                  (or
                        (part ?PART ?OBJ1)
                        (part ?PART ?OBJ2)))))

Agar obj3 is equal to "the intersection of the parts of obj1 and obj2", to sab-kuch part ke lie hai, ki: part is a part of obj3 agar hai part is a part of obj1 aur part is a part of obj2.
(=>
      (equal
            ?OBJ3
            (MereologicalProductFn ?OBJ1 ?OBJ2))
      (forall
            (?PART)
            (<=>
                  (part ?PART ?OBJ3)
                  (and
                        (part ?PART ?OBJ1)
                        (part ?PART ?OBJ2)))))

Agar obj3 is equal to "the difference between the parts of obj1 and obj2", to sab-kuch part ke lie hai, ki: part is a part of obj3 agar hai part is a part of obj1 aur part is not a part of obj2.
(=>
      (equal
            ?OBJ3
            (MereologicalDifferenceFn ?OBJ1 ?OBJ2))
      (forall
            (?PART)
            (<=>
                  (part ?PART ?OBJ3)
                  (and
                        (part ?PART ?OBJ1)
                        (not
                              (part ?PART ?OBJ2))))))

(=>
      (and
            (hole ?HOLE1 ?OBJ)
            (hole ?HOLE2 ?OBJ))
      (forall
            (?HOLE3)
            (=>
                  (part
                        ?HOLE3
                        (MereologicalSumFn ?HOLE1 ?HOLE2))
                  (hole ?HOLE3 ?OBJ))))

Agar obj1 is equal to "the host of the hole hole", to sab-kuch obj2 ke lie hai, ki: obj2 overlaps with obj1 agar hai yah kuch obj3 nahin, ki hole obj3 men chidra hai aur obj2 overlaps with obj3.
(=>
      (equal
            ?OBJ1
            (PrincipalHostFn ?HOLE))
      (forall
            (?OBJ2)
            (<=>
                  (overlapsSpatially ?OBJ2 ?OBJ1)
                  (exists
                        (?OBJ3)
                        (and
                              (hole ?HOLE ?OBJ3)
                              (overlapsSpatially ?OBJ2 ?OBJ3))))))

(=>
      (completelyFills ?OBJ1 ?HOLE)
      (forall
            (?OBJ2)
            (=>
                  (connected ?OBJ2 ?HOLE)
                  (connected ?OBJ2 ?OBJ1))))

Agar obj1 is equal to "the surface of the hole hole", to sab-kuch obj2 ke lie hai, ki: obj2 overlaps with obj1 agar hai yah kuch obj3 nahin, ki obj3 is a superficial part of "the host of the hole hole" aur hole meets obj3 aur obj2 overlaps with obj3.
(=>
      (equal
            ?OBJ1
            (SkinFn ?HOLE))
      (forall
            (?OBJ2)
            (<=>
                  (overlapsSpatially ?OBJ2 ?OBJ1)
                  (exists
                        (?OBJ3)
                        (and
                              (superficialPart
                                    ?OBJ3
                                    (PrincipalHostFn ?HOLE))
                              (meetsSpatially ?HOLE ?OBJ3)
                              (overlapsSpatially ?OBJ2 ?OBJ3))))))

(=>
      (subProcess ?SUBPROC ?PROC)
      (forall
            (?REGION)
            (=>
                  (located ?PROC ?REGION)
                  (located ?SUBPROC ?REGION))))

(=>
      (and
            (path ?PROCESS ?PATH1)
            (origin ?PROCESS ?SOURCE)
            (destination ?PROCESS ?DEST)
            (length ?PATH1 ?MEASURE1)
            (not
                  (exists
                        (?PATH2 ?MEASURE2)
                        (and
                              (path ?PROCESS ?PATH2)
                              (origin ?PROCESS ?ORIGIN)
                              (destination ?PROCESS ?DEST)
                              (length ?PATH2 ?MEASURE2)
                              (lessThan ?MEASURE2 ?MEASURE1)))))
      (forall
            (?OBJ)
            (=>
                  (part ?OBJ ?PATH1)
                  (between ?SOURCE ?OBJ ?DEST))))

(=>
      (and
            (instance ?KEEP Keeping)
            (patient ?KEEP ?OBJ))
      (exists
            (?PLACE)
            (forall
                  (?TIME)
                  (=>
                        (temporalPart
                              ?TIME
                              (WhenFn ?KEEP))
                        (holdsDuring
                              ?TIME
                              (located ?OBJ ?PLACE))))))

(=>
      (instance ?COOPERATE Cooperation)
      (exists
            (?PURP)
            (forall
                  (?AGENT)
                  (=>
                        (agent ?COOPERATE ?AGENT)
                        (hasPurposeForAgent ?COOPERATE ?PURP ?AGENT)))))

(=>
      (and
            (instance ?WAR War)
            (agent ?WAR ?AGENT))
      (or
            (instance ?AGENT Nation)
            (and
                  (instance ?AGENT Organization)
                  (forall
                        (?MEMBER)
                        (=>
                              (member ?MEMBER ?AGENT)
                              (instance ?MEMBER Nation))))))

(=>
      (instance ?BACTERIUM Bacterium)
      (exists
            (?CELL1)
            (and
                  (component ?CELL1 ?BACTERIUM)
                  (instance ?CELL1 Cell)
                  (forall
                        (?CELL2)
                        (=>
                              (and
                                    (component ?CELL2 ?BACTERIUM)
                                    (instance ?CELL2 Cell))
                              (equal ?CELL1 ?CELL2))))))

(=>
      (instance ?VIRUS Virus)
      (exists
            (?MOL1)
            (and
                  (component ?MOL1 ?VIRUS)
                  (instance ?MOL1 Molecule)
                  (forall
                        (?MOL2)
                        (=>
                              (and
                                    (component ?MOL2 ?VIRUS)
                                    (instance ?MOL2 Molecule))
                              (equal ?MOL1 ?MOL2))))))

(=>
      (instance ?FOOD Food)
      (forall
            (?PART1)
            (=>
                  (part ?PART1 ?FOOD)
                  (exists
                        (?PART2 ?ANIMAL)
                        (and
                              (part ?PART1 ?PART2)
                              (part ?PART2 ?ANIMAL)
                              (instance ?ANIMAL Animal))))))

(=>
      (instance ?MEAT Meat)
      (forall
            (?PART)
            (=>
                  (part ?PART ?MEAT)
                  (exists
                        (?SUBPART ?TIME ?ANIMAL)
                        (and
                              (part ?SUBPART ?PART)
                              (holdsDuring
                                    ?TIME
                                    (and
                                          (instance ?ANIMAL Animal)
                                          (part ?SUBPART ?ANIMAL))))))))

(=>
      (instance ?VEG FruitOrVegetable)
      (forall
            (?PART)
            (=>
                  (part ?PART ?VEG)
                  (exists
                        (?SUBPART ?TIME ?PLANT)
                        (and
                              (part ?SUBPART ?PART)
                              (holdsDuring
                                    ?TIME
                                    (and
                                          (instance ?PLANT Plant)
                                          (part ?SUBPART ?PLANT))))))))

(=>
      (instance ?ARTIFACT StationaryArtifact)
      (exists
            (?PLACE)
            (forall
                  (?TIME)
                  (=>
                        (and
                              (beforeOrEqual
                                    ?TIME
                                    (EndFn
                                          (WhenFn ?ARTIFACT)))
                              (beforeOrEqual
                                    (BeginFn
                                          (WhenFn ?ARTIFACT))
                                    ?TIME))
                        (equal
                              (WhereFn ?ARTIFACT ?TIME)
                              ?PLACE)))))

(=>
      (instance ?MACHINE Machine)
      (forall
            (?PROC)
            (=>
                  (instrument ?PROC ?MACHINE)
                  (exists
                        (?RESOURCE ?RESULT)
                        (and
                              (resource ?PROC ?RESOURCE)
                              (result ?PROC ?RESULT))))))

(=>
      (instance ?GROUP AgeGroup)
      (forall
            (?MEMB1 ?MEMB2 ?AGE1 ?AGE2)
            (=>
                  (and
                        (member ?MEMB1 ?GROUP)
                        (member ?MEMB2 ?GROUP)
                        (age ?MEMB1 ?AGE1)
                        (age ?MEMB2 ?AGE2))
                  (equal ?AGE1 ?AGE2))))

(=>
      (instance ?GROUP FamilyGroup)
      (forall
            (?MEMB1 ?MEMB2)
            (=>
                  (and
                        (member ?MEMB1 ?GROUP)
                        (member ?MEMB2 ?GROUP))
                  (familyRelation ?MEMB1 ?MEMB2))))

(=>
      (holdsDuring
            ?TIME
            (direction ?PROC ?ATTR1))
      (forall
            (?ATTR2)
            (=>
                  (holdsDuring
                        ?TIME
                        (direction ?PROC ?ATTR2))
                  (equal ?ATTR2 ?ATTR1))))

(=>
      (holdsDuring
            ?TIME
            (faces ?PROC ?ATTR1))
      (forall
            (?ATTR2)
            (=>
                  (holdsDuring
                        ?TIME
                        (faces ?PROC ?ATTR2))
                  (equal ?ATTR2 ?ATTR1))))

Sab-kuch org ke lie hai, ki: org doesn't employ person aur person is an instance of maanava agar hai unemployed is an attribute of person.
(<=>
      (forall
            (?ORG)
            (and
                  (not
                        (employs ?ORG ?PERSON))
                  (instance ?PERSON Human)))
      (attribute ?PERSON Unemployed))

(=>
      (and
            (attribute ?OBJ Monochromatic)
            (superficialPart ?PART ?OBJ)
            (attribute ?PART ?COLOR)
            (instance ?COLOR PrimaryColor))
      (forall
            (?ELEMENT)
            (=>
                  (superficialPart ?ELEMENT ?OBJ)
                  (attribute ?ELEMENT ?COLOR))))

(=>
      (attribute ?OBJ Wet)
      (forall
            (?PART)
            (=>
                  (part ?PART ?OBJ)
                  (exists
                        (?SUBPART)
                        (and
                              (part ?SUBPART ?PART)
                              (attribute ?SUBPART Liquid))))))

entity is an instance of "the intersection of all the elements of superclass" agar hai sab-kuch class ke lie hai, ki: agar class is an instance of superclass, to entity is an instance of class.
(<=>
      (instance
            ?ENTITY
            (GeneralizedIntersectionFn ?SUPERCLASS))
      (forall
            (?CLASS)
            (=>
                  (instance ?CLASS ?SUPERCLASS)
                  (instance ?ENTITY ?CLASS))))