Consider the following premises. There is at least one x_8 for which x_8 is a server if and only if x_8 is a janitor. For all x_8, x_8 is a server and x_8 will sleep. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 is not a janitor.
 From the fact that there is at least one x_8 for which x_8 is a server if and only if x_8 is a janitor we can infer that there is at least one x_8 for which if x_8 were a server, then x_8 is a janitor via existential biconditional elimination. From the fact that for all x_8, x_8 is a server and x_8 will sleep we can infer that for all x_8, x_8 is a server via universal simplification. Finally, from the fact that there is at least one x_8 for which if x_8 were a server, then x_8 is a janitor, and that for all x_8, x_8 is a server we can infer that there is at least one x_8 for which x_8 is a janitor via existential modus ponens, which contradicts that For all x_8, x_8 is not a janitor. Therefore, the answer is no.