Consider the following premises. There is at least one z for which z will not play a game. For all z, z is a police officer if and only if z will play a game. For all z, if z were a police officer, then z is a janitor. For all z, if z were a janitor, then z is a police officer. Can we infer the following from them? For all z, z is a janitor.
 From the fact that for all z, if z were a janitor, then z is a police officer, and that for all z, if z were a police officer, then z is a janitor we can infer that for all z, z is a janitor if and only if z is a police officer. From the fact that for all z, z is a police officer if and only if z will play a game, and that there is at least one z for which z will not play a game we can infer that there is at least one z for which z is not a police officer. Finally, from the fact that for all z, z is a janitor if and only if z is a police officer, and that there is at least one z for which z is not a police officer we can infer that there is at least one z for which z is not a janitor, which contradicts that For all z, z is a janitor. Therefore, the answer is no.