Consider the following premises. There is at least one x_2 for which if x_2 climbs a mountain, then x_2 is running. For all x_2, if x_2 writes a letter, then x_2 is climbing a mountain. For all x_2, if x_2 were an artist, then x_2 is writing a letter. Can we infer the following from them? There is at least one x_2 for which if x_2 were an artist, then x_2 is running.
 From the fact that for all x_2, if x_2 writes a letter, then x_2 is climbing a mountain, and that there is at least one x_2 for which if x_2 climbs a mountain, then x_2 is running we can infer that there is at least one x_2 for which if x_2 writes a letter, then x_2 is running. Finally, from the fact that for all x_2, if x_2 were an artist, then x_2 is writing a letter, and that there is at least one x_2 for which if x_2 writes a letter, then x_2 is running we can infer that there is at least one x_2 for which if x_2 were an artist, then x_2 is running. Therefore, the answer is yes.