Consider the following premises. For all x_9, x_9 will not read a book. For all x_9, if x_9 listens to a song, then x_9 is excited. For all x_9, if x_9 were excited, then x_9 is listening to a song. There is at least one x_9 for which if x_9 listens to a song, then x_9 is reading a book. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is excited.
 From the fact that for all x_9, if x_9 listens to a song, then x_9 is excited, and that for all x_9, if x_9 were excited, then x_9 is listening to a song we can infer that for all x_9, x_9 will listen to a song if and only if x_9 is excited via universal biconditional introduction. From the fact that there is at least one x_9 for which if x_9 listens to a song, then x_9 is reading a book, and that for all x_9, x_9 will not read a book we can infer that there is at least one x_9 for which x_9 will not listen to a song via existential modus tollens. Finally, from the fact that for all x_9, x_9 will listen to a song if and only if x_9 is excited, and that there is at least one x_9 for which x_9 will not listen to a song we can infer that there is at least one x_9 for which x_9 is not excited via existential biconditional elimination, which contradicts that For all x_9, x_9 is excited. Therefore, the answer is no.