Consider the following premises. For all x_9, x_9 will sleep. For all x_9, x_9 is a janitor if and only if x_9 is curious. For all x_9, x_9 is curious. 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 not a janitor.
 From the fact that for all x_9, x_9 is curious, and that for all x_9, x_9 will sleep we can infer that for all x_9, x_9 is curious and x_9 will sleep via universal conjunction. From the fact that for all x_9, x_9 is a janitor if and only if x_9 is curious we can infer that for all x_9, if x_9 were curious, then x_9 is a janitor via universal biconditional elimination. From the fact that for all x_9, x_9 is curious and x_9 will sleep we can infer that for all x_9, x_9 is curious via universal simplification. Finally, from the fact that for all x_9, if x_9 were curious, then x_9 is a janitor, and that for all x_9, x_9 is curious we can infer that for all x_9, x_9 is a janitor via universal modus ponens, which contradicts that There is at least one x_9 for which x_9 is not a janitor. Therefore, the answer is no.