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