Consider the following premises. For all x_6, if x_6 were a bartender, then x_6 is a poet. There is at least one x_6 for which if x_6 were a poet, then x_6 is running. For all x_6, if x_6 works, then x_6 is a bartender. For all x_6, x_6 will work. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 will go running.
 From the fact that for all x_6, if x_6 works, then x_6 is a bartender, and that for all x_6, if x_6 were a bartender, then x_6 is a poet we can infer that for all x_6, if x_6 works, then x_6 is a poet via universal transitivity. From the fact that for all x_6, if x_6 works, then x_6 is a poet, and that there is at least one x_6 for which if x_6 were a poet, then x_6 is running we can infer that there is at least one x_6 for which if x_6 works, then x_6 is running via existential transitivity. Finally, from the fact that there is at least one x_6 for which if x_6 works, then x_6 is running, and that for all x_6, x_6 will work we can infer that there is at least one x_6 for which x_6 will go running via existential modus ponens. Therefore, the answer is yes.