Consider the following premises. For all x, x is a bartender or x is not a server. For all x, x is a server if and only if x will work. For all x, x is not a bartender. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x for which x will work.
 From the fact that for all x, x is a bartender or x is not a server we can infer that for all x, if x were a server, then x is a bartender via universal rewriting. From the fact that for all x, if x were a server, then x is a bartender, and that for all x, x is not a bartender we can infer that for all x, x is not a server via universal modus tollens. Finally, from the fact that for all x, x is a server if and only if x will work, and that for all x, x is not a server we can infer that for all x, x will not work via universal biconditional elimination, which contradicts that There is at least one x for which x will work. Therefore, the answer is no.