Consider the following premises. For all y, if y were a police officer, then y is a janitor. For all y, if y climbs a mountain, then y is a police officer. For all y, y will play a game or y is not a janitor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y for which the fact that y climbs a mountain does not imply that y is playing a game.
 From the fact that for all y, y will play a game or y is not a janitor we can infer that for all y, if y were a janitor, then y is playing a game via universal rewriting. From the fact that for all y, if y climbs a mountain, then y is a police officer, and that for all y, if y were a police officer, then y is a janitor we can infer that for all y, if y climbs a mountain, then y is a janitor via universal transitivity. Finally, from the fact that for all y, if y climbs a mountain, then y is a janitor, and that for all y, if y were a janitor, then y is playing a game we can infer that for all y, if y climbs a mountain, then y is playing a game via universal transitivity, which contradicts that There is at least one y for which the fact that y climbs a mountain does not imply that y is playing a game. Therefore, the answer is no.