Consider the following premises. There is at least one x_4 for which if x_4 goes running, then x_4 is an artist. For all x_4, if x_4 works, then x_4 is running. For all x_4, if x_4 drinks water, then x_4 is an artist. For all x_4, x_4 will not make tea or x_4 will work. For all x_4, x_4 will make tea or x_4 will drink water. 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 artist.
 From the fact that for all x_4, if x_4 works, then x_4 is running, and that there is at least one x_4 for which if x_4 goes running, then x_4 is an artist we can infer that there is at least one x_4 for which if x_4 works, then x_4 is an artist via existential transitivity. From the fact that for all x_4, x_4 will make tea or x_4 will drink water, and that for all x_4, x_4 will not make tea or x_4 will work we can infer that for all x_4, x_4 will drink water or x_4 will work via universal resolution. Finally, from the fact that for all x_4, if x_4 drinks water, then x_4 is an artist, that there is at least one x_4 for which if x_4 works, then x_4 is an artist, and that for all x_4, x_4 will drink water or x_4 will work we can infer that there is at least one x_4 for which x_4 is an artist via existential disjunction elimination. Therefore, the answer is yes.