-(exists x (P(x)&D(x)-> (all y (P(y)->D(y)))))-> -(exists x P(x)).


For sics:

( (Ax (p(x) | ~p(x))) & (Ay (d(y) | ~d(y))) ) ->
(~(Ex ((p(x) & d(x)) -> (Ay (p(y)->d(y))))) -> ~(Ex p(x))).


For gandalf:

(define bezem 
  '(
    (frm (-> (& (all x (v (p x) (- (p x))))  
	        (all y (v (d y) (- (d y)))) )
	     (->
	         (- (exist x (->  (& (p x) (d x))
			          (all y (-> (p y) (d y))) )))
		 (- (exist x (p x))) )))))




relies on the decidability of atomic formulas, I forgot to mention that.
I am thinking of a slight variation wh