Consider the following premises. For all x_15, x_15 is an artist or x_15 will listen to a song. For all x_15, x_15 will not cook. For all x_15, if x_15 were an artist, then x_15 is not an office clerk. There is at least one x_15 for which x_15 is a writer if and only if x_15 will listen to a song. For all x_15, x_15 will cook or x_15 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_15 for which x_15 is a writer.
 From the fact that for all x_15, x_15 will cook or x_15 is an office clerk, and that for all x_15, x_15 will not cook we can infer that for all x_15, x_15 is an office clerk via universal disjunctive syllogism. From the fact that for all x_15, if x_15 were an artist, then x_15 is not an office clerk, and that for all x_15, x_15 is an office clerk we can infer that for all x_15, x_15 is not an artist via universal modus tollens. From the fact that there is at least one x_15 for which x_15 is a writer if and only if x_15 will listen to a song we can infer that there is at least one x_15 for which if x_15 listens to a song, then x_15 is a writer via existential biconditional elimination. From the fact that for all x_15, x_15 is an artist or x_15 will listen to a song, and that for all x_15, x_15 is not an artist we can infer that for all x_15, x_15 will listen to a song via universal disjunctive syllogism. Finally, from the fact that there is at least one x_15 for which if x_15 listens to a song, then x_15 is a writer, and that for all x_15, x_15 will listen to a song we can infer that there is at least one x_15 for which x_15 is a writer via existential modus ponens. Therefore, the answer is yes.