Consider the following premises. There is at least one x_3 for which if x_3 were a mechanic, then x_3 is listening to a song. For all x_3, x_3 will not listen to a song. For all x_3, x_3 is a mechanic if and only if x_3 is a server. For all x_3, if x_3 listens to a song, then x_3 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_3 for which x_3 is not a server.
 From the fact that there is at least one x_3 for which if x_3 were a mechanic, then x_3 is listening to a song, and that for all x_3, if x_3 listens to a song, then x_3 is a mechanic we can infer that there is at least one x_3 for which x_3 is a mechanic if and only if x_3 will listen to a song via existential biconditional introduction. From the fact that there is at least one x_3 for which x_3 is a mechanic if and only if x_3 will listen to a song, and that for all x_3, x_3 will not listen to a song we can infer that there is at least one x_3 for which x_3 is not a mechanic via existential biconditional elimination. Finally, from the fact that for all x_3, x_3 is a mechanic if and only if x_3 is a server, and that there is at least one x_3 for which x_3 is not a mechanic we can infer that there is at least one x_3 for which x_3 is not a server via existential biconditional elimination. Therefore, the answer is yes.