Consider the following premises. ~Q(f). forall y: Q(y) -> P(y). forall y: P(y) <-> Q(y). Can we infer ~P(f) from them?
 From forall y: P(y) <-> Q(y) we can infer forall y: P(y) -> Q(y). From forall y: Q(y) -> P(y), forall y: P(y) -> Q(y) we can infer forall y: Q(y) <-> P(y). From forall y: Q(y) <-> P(y) we can infer Q(f) <-> P(f). Finally, from Q(f) <-> P(f), ~Q(f) we can infer ~P(f). Therefore, the answer is yes.