Consider the following premises. For all x_6, if x_6 were a writer, then x_6 is not listening to a song. For all x_6, if x_6 were an office clerk, then x_6 is listening to a song. For all x_6, x_6 is not happy. For all x_6, x_6 is happy or x_6 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_6 for which x_6 is a writer.
 From the fact that for all x_6, x_6 is happy or x_6 is an office clerk, and that for all x_6, x_6 is not happy we can infer that for all x_6, x_6 is an office clerk via universal disjunctive syllogism. From the fact that for all x_6, if x_6 were an office clerk, then x_6 is listening to a song, and that for all x_6, x_6 is an office clerk we can infer that for all x_6, x_6 will listen to a song via universal modus ponens. Finally, from the fact that for all x_6, if x_6 were a writer, then x_6 is not listening to a song, and that for all x_6, x_6 will listen to a song we can infer that for all x_6, x_6 is not a writer via universal modus tollens, which contradicts that There is at least one x_6 for which x_6 is a writer. Therefore, the answer is no.