Consider the following premises. For all x_6, x_6 is a janitor or x_6 will not play a game. For all x_6, if x_6 were a janitor, then x_6 is climbing a mountain. For all x_6, if x_6 drinks water, then x_6 is a janitor. For all x_6, x_6 will drink water or x_6 will play a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will not climb a mountain.
 From the fact that for all x_6, x_6 is a janitor or x_6 will not play a game we can infer that for all x_6, if x_6 plays a game, then x_6 is a janitor via universal rewriting. From the fact that for all x_6, if x_6 drinks water, then x_6 is a janitor, that for all x_6, if x_6 plays a game, then x_6 is a janitor, and that for all x_6, x_6 will drink water or x_6 will play a game we can infer that for all x_6, x_6 is a janitor via universal disjunction elimination. Finally, from the fact that for all x_6, if x_6 were a janitor, then x_6 is climbing a mountain, and that for all x_6, x_6 is a janitor we can infer that for all x_6, x_6 will climb a mountain via universal modus ponens, which contradicts that There is at least one x_6 for which x_6 will not climb a mountain. Therefore, the answer is no.