Consider the following premises. There is at least one x_6 for which if x_6 were bored, then x_6 is reading a book. For all x_6, if x_6 were excited, then x_6 is bored. For all x_6, if x_6 reads a book, then x_6 is listening to a song. For all x_6, x_6 will not listen to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 is excited.
 From the fact that for all x_6, if x_6 reads a book, then x_6 is listening to a song, and that for all x_6, x_6 will not listen to a song we can infer that for all x_6, x_6 will not read a book via universal modus tollens. From the fact that for all x_6, if x_6 were excited, then x_6 is bored, and that there is at least one x_6 for which if x_6 were bored, then x_6 is reading a book we can infer that there is at least one x_6 for which if x_6 were excited, then x_6 is reading a book via existential transitivity. Finally, from the fact that there is at least one x_6 for which if x_6 were excited, then x_6 is reading a book, and that for all x_6, x_6 will not read a book we can infer that there is at least one x_6 for which x_6 is not excited via existential modus tollens, which contradicts that For all x_6, x_6 is excited. Therefore, the answer is no.