Consider the following premises. For all x_14, if x_14 listens to a song, then x_14 is an artist. For all x_14, if x_14 were a politician, then x_14 is working. For all x_14, if x_14 were an artist, then x_14 is listening to a song. For all x_14, x_14 is not a politician. For all x_14, if x_14 works, then x_14 is a politician. There is at least one x_14 for which x_14 is an artist if and only if x_14 will work. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 will listen to a song.
 From the fact that for all x_14, if x_14 were a politician, then x_14 is working, and that for all x_14, if x_14 works, then x_14 is a politician we can infer that for all x_14, x_14 is a politician if and only if x_14 will work via universal biconditional introduction. From the fact that for all x_14, x_14 is a politician if and only if x_14 will work, and that for all x_14, x_14 is not a politician we can infer that for all x_14, x_14 will not work via universal biconditional elimination. From the fact that for all x_14, if x_14 were an artist, then x_14 is listening to a song, and that for all x_14, if x_14 listens to a song, then x_14 is an artist we can infer that for all x_14, x_14 is an artist if and only if x_14 will listen to a song via universal biconditional introduction. From the fact that there is at least one x_14 for which x_14 is an artist if and only if x_14 will work, and that for all x_14, x_14 will not work we can infer that there is at least one x_14 for which x_14 is not an artist via existential biconditional elimination. Finally, from the fact that for all x_14, x_14 is an artist if and only if x_14 will listen to a song, and that there is at least one x_14 for which x_14 is not an artist we can infer that there is at least one x_14 for which x_14 will not listen to a song via existential biconditional elimination, which contradicts that For all x_14, x_14 will listen to a song. Therefore, the answer is no.