Consider the following premises. There is at least one x_9 for which x_9 will make tea or x_9 will listen to a song. For all x_9, if x_9 listens to a song, then x_9 is a musician. For all x_9, if x_9 makes tea, then x_9 is a musician. For all x_9, if x_9 were a writer, then x_9 is not a musician. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 is a writer.
 From the fact that for all x_9, if x_9 makes tea, then x_9 is a musician, that for all x_9, if x_9 listens to a song, then x_9 is a musician, and that there is at least one x_9 for which x_9 will make tea or x_9 will listen to a song we can infer that there is at least one x_9 for which x_9 is a musician via existential disjunction elimination. Finally, from the fact that for all x_9, if x_9 were a writer, then x_9 is not a musician, and that there is at least one x_9 for which x_9 is a musician we can infer that there is at least one x_9 for which x_9 is not a writer via existential modus tollens, which contradicts that For all x_9, x_9 is a writer. Therefore, the answer is no.