A binary function is a function with two arguments and one value. Hence, it is a relation with three arguments.
(<=> (Binary-Function ?F)
(And (Function ?F)
(Not (Empty ?F))
(Forall (?List) (=> (Member ?List ?F) (Triple ?List)))))
(Forall (?List) (=> (Member ?List ?F) (Triple ?List))) (Not (Empty ?F)) (Function ?F)
(<=> (Binary-Function ?F)
(And (Function ?F)
(Not (Empty ?F))
(Forall (?List) (=> (Member ?List ?F) (Triple ?List)))))