Consider the following premises. For all x_8, x_8 will go running if and only if x_8 is an artist. For all x_8, if x_8 were excited, then x_8 is working. There is at least one x_8 for which if x_8 were an artist, then x_8 is excited. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which if x_8 goes running, then x_8 is working.
 From the fact that for all x_8, x_8 will go running if and only if x_8 is an artist we can infer that for all x_8, if x_8 goes running, then x_8 is an artist via universal biconditional elimination. From the fact that for all x_8, if x_8 goes running, then x_8 is an artist, and that there is at least one x_8 for which if x_8 were an artist, then x_8 is excited we can infer that there is at least one x_8 for which if x_8 goes running, then x_8 is excited via existential transitivity. Finally, from the fact that there is at least one x_8 for which if x_8 goes running, then x_8 is excited, and that for all x_8, if x_8 were excited, then x_8 is working we can infer that there is at least one x_8 for which if x_8 goes running, then x_8 is working via existential transitivity. Therefore, the answer is yes.