Consider the following premises. For all x_6, if x_6 plays a game, then x_6 is climbing a mountain. For all x_6, x_6 will not play tennis. For all x_6, x_6 will play tennis or x_6 will play a game. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will climb a mountain or x_6 is a soldier.
 From the fact that for all x_6, x_6 will play tennis or x_6 will play a game, and that for all x_6, x_6 will not play tennis we can infer that for all x_6, x_6 will play a game via universal disjunctive syllogism. From the fact that for all x_6, if x_6 plays a game, then x_6 is climbing a mountain, and that for all x_6, x_6 will play a game we can infer that for all x_6, x_6 will climb a mountain via universal modus ponens. Finally, from the fact that for all x_6, x_6 will climb a mountain we can infer that for all x_6, x_6 will climb a mountain or x_6 is a soldier via universal addition. Therefore, the answer is yes.