Consider the following premises. For all y_4, y_4 is a soldier or y_4 is a lawyer. For all y_4, y_4 is not a soldier or y_4 will play a game. For all y_4, y_4 is not a lawyer. Can we infer the following from them? If we can, name the inference rule being used: There is at least one y_4 for which y_4 will not play a game.
 From the fact that for all y_4, y_4 is a soldier or y_4 is a lawyer, and that for all y_4, y_4 is not a soldier or y_4 will play a game we can infer that for all y_4, y_4 is a lawyer or y_4 will play a game via universal resolution. Finally, from the fact that for all y_4, y_4 is a lawyer or y_4 will play a game, and that for all y_4, y_4 is not a lawyer we can infer that for all y_4, y_4 will play a game via universal disjunctive syllogism, which contradicts that There is at least one y_4 for which y_4 will not play a game. Therefore, the answer is no.