Consider the following premises. For all x_15, x_15 will go running and x_15 will drive a car. For all x_15, if x_15 listens to a song, then x_15 is sleeping. For all x_15, x_15 is a soldier or x_15 will listen to a song. For all x_15, x_15 is not a soldier or x_15 is a musician. There is at least one x_15 for which if x_15 were a musician, then x_15 is sleeping. 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 will sleep and x_15 will go running.
 From the fact that for all x_15, x_15 is a soldier or x_15 will listen to a song, and that for all x_15, x_15 is not a soldier or x_15 is a musician we can infer that for all x_15, x_15 will listen to a song or x_15 is a musician via universal resolution. From the fact that for all x_15, if x_15 listens to a song, then x_15 is sleeping, that there is at least one x_15 for which if x_15 were a musician, then x_15 is sleeping, and that for all x_15, x_15 will listen to a song or x_15 is a musician we can infer that there is at least one x_15 for which x_15 will sleep via existential disjunction elimination. From the fact that for all x_15, x_15 will go running and x_15 will drive a car we can infer that for all x_15, x_15 will go running via universal simplification. Finally, from the fact that there is at least one x_15 for which x_15 will sleep, and that for all x_15, x_15 will go running we can infer that there is at least one x_15 for which x_15 will sleep and x_15 will go running via existential conjunction. Therefore, the answer is yes.