Consider the following premises. For all x_9, x_9 will drive a car if and only if x_9 is a mechanic. For all x_9, if x_9 drives a car, then x_9 is not a sailor. For all x_9, x_9 is a sailor. There is at least one x_9 for which if x_9 were a mechanic, then x_9 is listening to a song. For all x_9, if x_9 listens to a song, then x_9 is a mechanic. 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 will not listen to a song.
 From the fact that there is at least one x_9 for which if x_9 were a mechanic, then x_9 is listening to a song, and that for all x_9, if x_9 listens to a song, then x_9 is a mechanic we can infer that there is at least one x_9 for which x_9 is a mechanic if and only if x_9 will listen to a song via existential biconditional introduction. From the fact that for all x_9, if x_9 drives a car, then x_9 is not a sailor, and that for all x_9, x_9 is a sailor we can infer that for all x_9, x_9 will not drive a car via universal modus tollens. From the fact that for all x_9, x_9 will drive a car if and only if x_9 is a mechanic, and that for all x_9, x_9 will not drive a car we can infer that for all x_9, x_9 is not a mechanic via universal biconditional elimination. Finally, from the fact that there is at least one x_9 for which x_9 is a mechanic if and only if x_9 will listen to a song, and that for all x_9, x_9 is not a mechanic we can infer that there is at least one x_9 for which x_9 will not listen to a song via existential biconditional elimination. Therefore, the answer is yes.