Consider the following premises. forall x: Q(x) -> ~P(x). r <-> Q(a). forall x: P(x). Can we infer ~r from them? If possible, name the inference rules being used at each step.
 From forall x: Q(x) -> ~P(x), forall x: P(x) we can infer forall x: ~Q(x) via universal modus tollens. From forall x: ~Q(x) we can infer ~Q(a) via universal instantiation. Finally, from r <-> Q(a), ~Q(a) we can infer ~r via biconditional elimination. Therefore, the answer is yes.