Consider the following premises. For all x_8, x_8 is a writer. For all x_8, x_8 is a nurse and x_8 is poor. There is at least one x_8 for which if x_8 plays a game, then x_8 is not a nurse. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will play a game.
 From the fact that for all x_8, x_8 is a nurse and x_8 is poor we can infer that for all x_8, x_8 is a nurse via universal simplification. From the fact that for all x_8, x_8 is a nurse, and that for all x_8, x_8 is a writer we can infer that for all x_8, x_8 is a nurse and x_8 is a writer via universal conjunction. From the fact that for all x_8, x_8 is a nurse and x_8 is a writer we can infer that for all x_8, x_8 is a nurse via universal simplification. Finally, from the fact that there is at least one x_8 for which if x_8 plays a game, then x_8 is not a nurse, and that for all x_8, x_8 is a nurse we can infer that there is at least one x_8 for which x_8 will not play a game via existential modus tollens, which contradicts that For all x_8, x_8 will play a game. Therefore, the answer is no.