Consider the following premises. For all x_4, x_4 will not listen to a song. For all x_4, x_4 will climb a mountain or x_4 will listen to a song. There is at least one x_4 for which x_4 is an office clerk. For all x_4, x_4 will not climb a mountain or x_4 is a janitor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 is an office clerk and x_4 is a janitor.
 From the fact that for all x_4, x_4 will climb a mountain or x_4 will listen to a song, and that for all x_4, x_4 will not climb a mountain or x_4 is a janitor we can infer that for all x_4, x_4 will listen to a song or x_4 is a janitor via universal resolution. From the fact that for all x_4, x_4 will listen to a song or x_4 is a janitor, and that for all x_4, x_4 will not listen to a song we can infer that for all x_4, x_4 is a janitor via universal disjunctive syllogism. Finally, from the fact that there is at least one x_4 for which x_4 is an office clerk, and that for all x_4, x_4 is a janitor we can infer that there is at least one x_4 for which x_4 is an office clerk and x_4 is a janitor via existential conjunction. Therefore, the answer is yes.