Consider the following premises. For all x_4, if x_4 goes running, then x_4 is a scientist. There is at least one x_4 for which x_4 is a musician. For all x_4, x_4 will sleep or x_4 will go running. For all x_4, if x_4 sleeps, then x_4 is a scientist. Can we infer the following from them? If we can, name the inference rule being used: Some scientists are musicians.
 From the fact that for all x_4, if x_4 sleeps, then x_4 is a scientist, that for all x_4, if x_4 goes running, then x_4 is a scientist, and that for all x_4, x_4 will sleep or x_4 will go running we can infer that for all x_4, x_4 is a scientist via universal disjunction elimination. Finally, from the fact that for all x_4, x_4 is a scientist, and that there is at least one x_4 for which x_4 is a musician we can infer that some scientists are musicians via existential conjunction. Therefore, the answer is yes.