Consider the following premises. For all x_9, if x_9 sleeps, then x_9 is climbing a mountain. There is at least one x_9 for which x_9 is a poet. For all x_9, x_9 will not climb a mountain. For all x_9, x_9 will sleep if and only if x_9 is a poet. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is a server.
 From the fact that there is at least one x_9 for which x_9 is a poet we can infer that there is at least one x_9 for which x_9 is a poet or x_9 is a server via existential addition. From the fact that for all x_9, if x_9 sleeps, then x_9 is climbing a mountain, and that for all x_9, x_9 will not climb a mountain we can infer that for all x_9, x_9 will not sleep via universal modus tollens. From the fact that for all x_9, x_9 will sleep if and only if x_9 is a poet, and that for all x_9, x_9 will not sleep we can infer that for all x_9, x_9 is not a poet via universal biconditional elimination. Finally, from the fact that there is at least one x_9 for which x_9 is a poet or x_9 is a server, and that for all x_9, x_9 is not a poet we can infer that there is at least one x_9 for which x_9 is a server via existential disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.