Consider the following premises. For all x_2, x_2 will go running or x_2 is a lawyer. For all x_2, x_2 is not a lawyer. For all x_2, x_2 will not go running or x_2 will play a game. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 will not play a game.
 From the fact that for all x_2, x_2 will go running or x_2 is a lawyer, and that for all x_2, x_2 will not go running or x_2 will play a game we can infer that for all x_2, x_2 is a lawyer or x_2 will play a game via universal resolution. Finally, from the fact that for all x_2, x_2 is a lawyer or x_2 will play a game, and that for all x_2, x_2 is not a lawyer we can infer that for all x_2, x_2 will play a game via universal disjunctive syllogism, which contradicts that There is at least one x_2 for which x_2 will not play a game. Therefore, the answer is no.