Consider the following premises. For all x_9, if x_9 plays a game, then x_9 is sleeping. There is at least one x_9 for which if x_9 sleeps, then x_9 is playing a game. For all x_9, x_9 will play a game or x_9 will read a book. For all x_9, x_9 will not sleep. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will not read a book.
 From the fact that there is at least one x_9 for which if x_9 sleeps, then x_9 is playing a game, and that for all x_9, if x_9 plays a game, then x_9 is sleeping we can infer that there is at least one x_9 for which x_9 will sleep if and only if x_9 will play a game via existential biconditional introduction. From the fact that there is at least one x_9 for which x_9 will sleep if and only if x_9 will play a game, and that for all x_9, x_9 will not sleep we can infer that there is at least one x_9 for which x_9 will not play a game via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will play a game or x_9 will read a book, and that there is at least one x_9 for which x_9 will not play a game we can infer that there is at least one x_9 for which x_9 will read a book via existential disjunctive syllogism, which contradicts that For all x_9, x_9 will not read a book. Therefore, the answer is no.