Consider the following premises. For all x_5, x_5 will sleep if and only if x_5 is excited. For all x_5, x_5 will not make tea. For all x_5, if x_5 sleeps, then x_5 is making tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is excited.
 From the fact that for all x_5, if x_5 sleeps, then x_5 is making tea, and that for all x_5, x_5 will not make tea we can infer that for all x_5, x_5 will not sleep via universal modus tollens. From the fact that for all x_5, x_5 will sleep if and only if x_5 is excited we can infer that for all x_5, if x_5 were excited, then x_5 is sleeping via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 were excited, then x_5 is sleeping, and that for all x_5, x_5 will not sleep we can infer that for all x_5, x_5 is not excited via universal modus tollens, which contradicts that There is at least one x_5 for which x_5 is excited. Therefore, the answer is no.