Consider the following premises. For all x_5, if x_5 were a musician, then x_5 is listening to a song. There is at least one x_5 for which x_5 is a musician. For all x_5, if x_5 listens to a song, then x_5 is a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not listen to a song.
 From the fact that for all x_5, if x_5 listens to a song, then x_5 is a musician, and that for all x_5, if x_5 were a musician, then x_5 is listening to a song we can infer that for all x_5, x_5 will listen to a song if and only if x_5 is a musician via universal biconditional introduction. From the fact that for all x_5, x_5 will listen to a song if and only if x_5 is a musician we can infer that for all x_5, if x_5 were a musician, then x_5 is listening to a song via universal biconditional elimination. Finally, from the fact that for all x_5, if x_5 were a musician, then x_5 is listening to a song, and that there is at least one x_5 for which x_5 is a musician we can infer that there is at least one x_5 for which x_5 will listen to a song via existential modus ponens, which contradicts that For all x_5, x_5 will not listen to a song. Therefore, the answer is no.