Relation PAIRWISE-DISJOINT

Sets are pairwise-disjoint if and only if every set is disjoint from every other set.
Axioms:
(Undefined (Arity Pairwise-Disjoint))

(<=> (Pairwise-Disjoint @Sets)
     (Forall (?S1 ?S2)
             (=> (Item ?S1 (Listof @Sets))
                 (Item ?S2 (Listof @Sets))
                 (Or (= ?S1 ?S2) (Disjoint ?S1 ?S2)))))