Consider the following premises. For all z, z will not go running. For all z, z will sleep if and only if z will go running. For all z, if z works, then z is sleeping. There is at least one z for which z will work if and only if z will drink water. Can we infer the following from them? There is at least one z for which z will not drink water.
 From the fact that for all z, z will sleep if and only if z will go running, and that for all z, z will not go running we can infer that for all z, z will not sleep. From the fact that for all z, if z works, then z is sleeping, and that for all z, z will not sleep we can infer that for all z, z will not work. Finally, from the fact that there is at least one z for which z will work if and only if z will drink water, and that for all z, z will not work we can infer that there is at least one z for which z will not drink water. Therefore, the answer is yes.