Consider the following premises. For all x_9, x_9 will sleep or x_9 is a cashier. For all x_9, if x_9 climbs a mountain, then x_9 is a police officer. For all x_9, x_9 is not a police officer. There is at least one x_9 for which x_9 will climb a mountain if and only if x_9 will sleep. 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 cashier.
 From the fact that for all x_9, if x_9 climbs a mountain, then x_9 is a police officer, and that for all x_9, x_9 is not a police officer we can infer that for all x_9, x_9 will not climb a mountain via universal modus tollens. From the fact that there is at least one x_9 for which x_9 will climb a mountain if and only if x_9 will sleep, and that for all x_9, x_9 will not climb a mountain we can infer that there is at least one x_9 for which x_9 will not sleep via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will sleep or x_9 is a cashier, and that there is at least one x_9 for which x_9 will not sleep we can infer that there is at least one x_9 for which x_9 is a cashier via existential disjunctive syllogism. Therefore, the answer is yes.