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