Consider the following premises. For all x_7, if x_7 sleeps, then x_7 is excited. For all x_7, x_7 will climb a mountain if and only if x_7 will sleep. For all x_7, x_7 will climb a mountain or x_7 is a poet. For all x_7, if x_7 were a poet, then x_7 is sleeping. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 is excited.
 From the fact that for all x_7, x_7 will climb a mountain if and only if x_7 will sleep we can infer that for all x_7, if x_7 climbs a mountain, then x_7 is sleeping via universal biconditional elimination. From the fact that for all x_7, if x_7 climbs a mountain, then x_7 is sleeping, that for all x_7, if x_7 were a poet, then x_7 is sleeping, and that for all x_7, x_7 will climb a mountain or x_7 is a poet we can infer that for all x_7, x_7 will sleep via universal disjunction elimination. Finally, from the fact that for all x_7, if x_7 sleeps, then x_7 is excited, and that for all x_7, x_7 will sleep we can infer that for all x_7, x_7 is excited via universal modus ponens. Therefore, the answer is yes.