Consider the following premises. For all x_5, x_5 is not a writer. For all x_5, if x_5 were rich, then x_5 is listening to a song. For all x_5, x_5 is a writer. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will listen to a song.
 From the fact that for all x_5, x_5 is a writer we can infer that for all x_5, x_5 is a writer or x_5 is rich via universal addition. From the fact that for all x_5, x_5 is a writer or x_5 is rich, and that for all x_5, x_5 is not a writer we can infer that for all x_5, x_5 is rich via universal disjunctive syllogism. Finally, from the fact that for all x_5, if x_5 were rich, then x_5 is listening to a song, and that for all x_5, x_5 is rich we can infer that for all x_5, x_5 will listen to a song via universal modus ponens. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.