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)))))