forms

((FORALL ?x ?y)
  ((EXISTS ?z) (P ?x ?y ?z)))

((FORALL ?u ?v ?w ?x ?y ?z)
  (=> (AND (P ?x ?y ?u) (P ?y ?z ?v))
      (IFF (P ?x ?v ?w) (P ?u ?z ?w))))

((EXISTS ?x)
  (AND ((FORALL ?y) (P ?x ?y ?y))
       ((FORALL ?y) ((EXISTS ?z) (P ?z ?y ?x)))))