Consider the following premises. For all x_8, if x_8 reads a book, then x_8 is not sleeping. For all x_8, x_8 will not work or x_8 will take a plane. For all x_8, x_8 will work or x_8 will read a book. For all x_8, x_8 will sleep. There is at least one x_8 for which if x_8 plays a game, then x_8 is not taking a plane. 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, if x_8 reads a book, then x_8 is not sleeping, and that for all x_8, x_8 will sleep we can infer that for all x_8, x_8 will not read a book via universal modus tollens. From the fact that for all x_8, x_8 will work or x_8 will read a book, and that for all x_8, x_8 will not work or x_8 will take a plane we can infer that for all x_8, x_8 will read a book or x_8 will take a plane via universal resolution. From the fact that for all x_8, x_8 will read a book or x_8 will take a plane, and that for all x_8, x_8 will not read a book we can infer that for all x_8, x_8 will take a plane via universal disjunctive syllogism. 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 taking a plane, and that for all x_8, x_8 will take a plane 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.