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