Consider the following premises. For all x, x is not a server. There is at least one x for which if x drives a car, then x is not a taxi driver. For all x, x will drive a car if and only if x will listen to a song. For all x, x is a server or x is a taxi driver. 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 not listen to a song.
 From the fact that for all x, x is a server or x is a taxi driver, and that for all x, x is not a server we can infer that for all x, x is a taxi driver via universal disjunctive syllogism. From the fact that there is at least one x for which if x drives a car, then x is not a taxi driver, and that for all x, x is a taxi driver we can infer that there is at least one x for which x will not drive a car via existential modus tollens. Finally, from the fact that for all x, x will drive a car if and only if x will listen to a song, and that there is at least one x for which x will not drive a car we can infer that there is at least one x for which x will not listen to a song via existential biconditional elimination. Therefore, the answer is yes.