Consider the following premises. For all x_11, x_11 will drink water and x_11 will climb a mountain. There is at least one x_11 for which x_11 will not work or x_11 is happy. For all x_11, x_11 will work or x_11 will play a game. For all x_11, if x_11 plays a game, then x_11 is not drinking water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which x_11 is happy.
 From the fact that for all x_11, x_11 will work or x_11 will play a game, and that there is at least one x_11 for which x_11 will not work or x_11 is happy we can infer that there is at least one x_11 for which x_11 will play a game or x_11 is happy via existential resolution. From the fact that for all x_11, x_11 will drink water and x_11 will climb a mountain we can infer that for all x_11, x_11 will drink water via universal simplification. From the fact that for all x_11, if x_11 plays a game, then x_11 is not drinking water, and that for all x_11, x_11 will drink water we can infer that for all x_11, x_11 will not play a game via universal modus tollens. Finally, from the fact that there is at least one x_11 for which x_11 will play a game or x_11 is happy, and that for all x_11, x_11 will not play a game we can infer that there is at least one x_11 for which x_11 is happy via existential disjunctive syllogism. Therefore, the answer is yes.