Consider the following premises. For all x_2, x_2 will cook or x_2 will go running. There is at least one x_2 for which x_2 will not go running or x_2 will work. For all x_2, x_2 will not cook or x_2 is an artist. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 is an artist or x_2 will work.
 From the fact that for all x_2, x_2 will cook or x_2 will go running, and that for all x_2, x_2 will not cook or x_2 is an artist we can infer that for all x_2, x_2 will go running or x_2 is an artist via universal resolution. Finally, from the fact that for all x_2, x_2 will go running or x_2 is an artist, and that there is at least one x_2 for which x_2 will not go running or x_2 will work we can infer that there is at least one x_2 for which x_2 is an artist or x_2 will work via existential resolution. Therefore, the answer is yes.