Consider the following premises. There is at least one x_13 for which if x_13 were an office clerk, then x_13 is listening to a song. For all x_13, if x_13 were a taxi driver, then x_13 is an office clerk. For all x_13, if x_13 listens to a song, then x_13 is reading a book. For all x_13, x_13 is not a taxi driver. For all x_13, if x_13 reads a book, then x_13 is a taxi driver. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 will listen to a song.
 From the fact that for all x_13, if x_13 listens to a song, then x_13 is reading a book, and that for all x_13, if x_13 reads a book, then x_13 is a taxi driver we can infer that for all x_13, if x_13 listens to a song, then x_13 is a taxi driver via universal transitivity. From the fact that for all x_13, if x_13 were a taxi driver, then x_13 is an office clerk, and that there is at least one x_13 for which if x_13 were an office clerk, then x_13 is listening to a song we can infer that there is at least one x_13 for which if x_13 were a taxi driver, then x_13 is listening to a song via existential transitivity. From the fact that for all x_13, if x_13 listens to a song, then x_13 is a taxi driver, and that there is at least one x_13 for which if x_13 were a taxi driver, then x_13 is listening to a song we can infer that there is at least one x_13 for which x_13 will listen to a song if and only if x_13 is a taxi driver via existential biconditional introduction. From the fact that there is at least one x_13 for which x_13 will listen to a song if and only if x_13 is a taxi driver we can infer that there is at least one x_13 for which if x_13 listens to a song, then x_13 is a taxi driver via existential biconditional elimination. Finally, from the fact that there is at least one x_13 for which if x_13 listens to a song, then x_13 is a taxi driver, and that for all x_13, x_13 is not a taxi driver we can infer that there is at least one x_13 for which x_13 will not listen to a song via existential modus tollens, which contradicts that For all x_13, x_13 will listen to a song. Therefore, the answer is no.