Consider the following premises. For all z, z will play tennis. For all z, if z were a scientist, then z is a politician. For all z, if z were a politician, then z is not playing tennis. There is at least one z for which if z were a politician, then z is a scientist. Can we infer the following from them? There is at least one z for which z is not a scientist.
 From the fact that there is at least one z for which if z were a politician, then z is a scientist, and that for all z, if z were a scientist, then z is a politician we can infer that there is at least one z for which z is a politician if and only if z is a scientist. From the fact that for all z, if z were a politician, then z is not playing tennis, and that for all z, z will play tennis we can infer that for all z, z is not a politician. Finally, from the fact that there is at least one z for which z is a politician if and only if z is a scientist, and that for all z, z is not a politician we can infer that there is at least one z for which z is not a scientist. Therefore, the answer is yes.