Consider the following premises. For all x_8, if x_8 reads a book, then x_8 is not a nurse. For all x_8, x_8 is a nurse. For all x_8, if x_8 listens to a song, then x_8 is taking a plane. There is at least one x_8 for which if x_8 takes a plane, then x_8 is reading a book. For all x_8, if x_8 reads a book, then x_8 is listening to a song. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will listen to a song.
 From the fact that for all x_8, if x_8 listens to a song, then x_8 is taking a plane, and that there is at least one x_8 for which if x_8 takes a plane, then x_8 is reading a book we can infer that there is at least one x_8 for which if x_8 listens to a song, then x_8 is reading a book via existential transitivity. From the fact that for all x_8, if x_8 reads a book, then x_8 is not a nurse, and that for all x_8, x_8 is a nurse we can infer that for all x_8, x_8 will not read a book via universal modus tollens. From the fact that there is at least one x_8 for which if x_8 listens to a song, then x_8 is reading a book, and that for all x_8, if x_8 reads a book, then x_8 is listening to a song we can infer that there is at least one x_8 for which x_8 will listen to a song if and only if x_8 will read a book via existential biconditional introduction. Finally, from the fact that there is at least one x_8 for which x_8 will listen to a song if and only if x_8 will read a book, and that for all x_8, x_8 will not read a book we can infer that there is at least one x_8 for which x_8 will not listen to a song via existential biconditional elimination, which contradicts that For all x_8, x_8 will listen to a song. Therefore, the answer is no.