Consider the following premises. For all x_17, if x_17 cooks, then x_17 is playing a game. For all x_17, if x_17 plays a game, then x_17 is not playing squash. For all x_17, x_17 will play squash. There is at least one x_17 for which if x_17 were excited, then x_17 is cooking. For all x_17, if x_17 plays a game, then x_17 is excited. For all x_17, if x_17 sleeps, then x_17 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_17, x_17 will sleep.
 From the fact that for all x_17, if x_17 plays a game, then x_17 is not playing squash, and that for all x_17, x_17 will play squash we can infer that for all x_17, x_17 will not play a game via universal modus tollens. From the fact that there is at least one x_17 for which if x_17 were excited, then x_17 is cooking, and that for all x_17, if x_17 cooks, then x_17 is playing a game we can infer that there is at least one x_17 for which if x_17 were excited, then x_17 is playing a game via existential transitivity. From the fact that there is at least one x_17 for which if x_17 were excited, then x_17 is playing a game, and that for all x_17, if x_17 plays a game, then x_17 is excited we can infer that there is at least one x_17 for which x_17 is excited if and only if x_17 will play a game via existential biconditional introduction. From the fact that there is at least one x_17 for which x_17 is excited if and only if x_17 will play a game, and that for all x_17, x_17 will not play a game we can infer that there is at least one x_17 for which x_17 is not excited via existential biconditional elimination. Finally, from the fact that for all x_17, if x_17 sleeps, then x_17 is excited, and that there is at least one x_17 for which x_17 is not excited we can infer that there is at least one x_17 for which x_17 will not sleep via existential modus tollens, which contradicts that For all x_17, x_17 will sleep. Therefore, the answer is no.