Consider the following premises. For all x_10, if x_10 were a doctor, then x_10 is a mechanic. For all x_10, x_10 is not a musician or x_10 is a doctor. For all x_10, x_10 will drink water if and only if x_10 will play a game. For all x_10, if x_10 plays a game, then x_10 is not a mechanic. For all x_10, x_10 is a musician or x_10 will climb a mountain. For all x_10, if x_10 climbs a mountain, then x_10 is a mechanic. Can we infer the following from them? If we can, name the inference rule being used: For all x_10, x_10 will not drink water.
 From the fact that for all x_10, x_10 is a musician or x_10 will climb a mountain, and that for all x_10, x_10 is not a musician or x_10 is a doctor we can infer that for all x_10, x_10 will climb a mountain or x_10 is a doctor via universal resolution. From the fact that for all x_10, if x_10 climbs a mountain, then x_10 is a mechanic, that for all x_10, if x_10 were a doctor, then x_10 is a mechanic, and that for all x_10, x_10 will climb a mountain or x_10 is a doctor we can infer that for all x_10, x_10 is a mechanic via universal disjunction elimination. From the fact that for all x_10, if x_10 plays a game, then x_10 is not a mechanic, and that for all x_10, x_10 is a mechanic we can infer that for all x_10, x_10 will not play a game via universal modus tollens. Finally, from the fact that for all x_10, x_10 will drink water if and only if x_10 will play a game, and that for all x_10, x_10 will not play a game we can infer that for all x_10, x_10 will not drink water via universal biconditional elimination. Therefore, the answer is yes.