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