Consider the following premises. For all x_1, x_1 will play squash. For all x_1, if x_1 were excited, then x_1 is sleeping. There is at least one x_1 for which if x_1 were excited, then x_1 is not playing squash. For all x_1, if x_1 sleeps, then x_1 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, x_1 will sleep.
 From the fact that for all x_1, if x_1 were excited, then x_1 is sleeping, and that for all x_1, if x_1 sleeps, then x_1 is excited we can infer that for all x_1, x_1 is excited if and only if x_1 will sleep via universal biconditional introduction. From the fact that there is at least one x_1 for which if x_1 were excited, then x_1 is not playing squash, and that for all x_1, x_1 will play squash we can infer that there is at least one x_1 for which x_1 is not excited via existential modus tollens. Finally, from the fact that for all x_1, x_1 is excited if and only if x_1 will sleep, and that there is at least one x_1 for which x_1 is not excited we can infer that there is at least one x_1 for which x_1 will not sleep via existential biconditional elimination, which contradicts that For all x_1, x_1 will sleep. Therefore, the answer is no.