Consider the following premises. For all x_4, x_4 will not drink water. For all x_4, x_4 is not bored or x_4 will play a game. For all x_4, x_4 will drink water or x_4 is bored. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 will sleep or x_4 will play a game.
 From the fact that for all x_4, x_4 will drink water or x_4 is bored, and that for all x_4, x_4 will not drink water we can infer that for all x_4, x_4 is bored via universal disjunctive syllogism. From the fact that for all x_4, x_4 is bored we can infer that for all x_4, x_4 is bored or x_4 will sleep via universal addition. Finally, from the fact that for all x_4, x_4 is bored or x_4 will sleep, and that for all x_4, x_4 is not bored or x_4 will play a game we can infer that for all x_4, x_4 will sleep or x_4 will play a game via universal resolution. Therefore, the answer is yes.