Consider the following premises. forall z_1: Q(z_1) or ~U(z_1). forall z_1: ~Q(z_1). forall z_1: S(z_1) -> U(z_1). Can we infer forall z_1: ~S(z_1) from them? If possible, name the inference rules being used at each step.
 From forall z_1: Q(z_1) or ~U(z_1) we can infer forall z_1: U(z_1) -> Q(z_1) via universal rewriting. From forall z_1: U(z_1) -> Q(z_1), forall z_1: ~Q(z_1) we can infer forall z_1: ~U(z_1) via universal modus tollens. Finally, from forall z_1: S(z_1) -> U(z_1), forall z_1: ~U(z_1) we can infer forall z_1: ~S(z_1) via universal modus tollens. Therefore, the answer is yes.