Consider the following premises. For all x_6, if x_6 were a server, then x_6 is sleeping. For all x_6, if x_6 works, then x_6 is not a janitor. For all x_6, x_6 is a janitor. For all x_6, x_6 will work or x_6 is a server. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will not sleep.
 From the fact that for all x_6, if x_6 works, then x_6 is not a janitor, and that for all x_6, x_6 is a janitor we can infer that for all x_6, x_6 will not work via universal modus tollens. From the fact that for all x_6, x_6 will work or x_6 is a server, and that for all x_6, x_6 will not work we can infer that for all x_6, x_6 is a server via universal disjunctive syllogism. Finally, from the fact that for all x_6, if x_6 were a server, then x_6 is sleeping, and that for all x_6, x_6 is a server we can infer that for all x_6, x_6 will sleep via universal modus ponens, which contradicts that There is at least one x_6 for which x_6 will not sleep. Therefore, the answer is no.