Consider the following premises. For all z, if z drinks water, then z is playing tennis. There is at least one z for which if z plays tennis, then z is making tea. For all z, if z makes tea, then z is drinking water. For all z, z will not drink water. Can we infer the following from them? There is at least one z for which z will not make tea.
 From the fact that for all z, if z drinks water, then z is playing tennis, and that there is at least one z for which if z plays tennis, then z is making tea we can infer that there is at least one z for which if z drinks water, then z is making tea. From the fact that for all z, if z makes tea, then z is drinking water, and that there is at least one z for which if z drinks water, then z is making tea we can infer that there is at least one z for which z will make tea if and only if z will drink water. Finally, from the fact that there is at least one z for which z will make tea if and only if z will drink water, and that for all z, z will not drink water we can infer that there is at least one z for which z will not make tea. Therefore, the answer is yes.