Consider the following premises. There is at least one x_11 for which if x_11 goes running, then x_11 is a doctor. For all x_11, if x_11 were a doctor, then x_11 is an office clerk. For all x_11, if x_11 were a janitor, then x_11 is running. For all x_11, x_11 is a doctor or x_11 is not an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_11 for which if x_11 were a janitor, then x_11 is an office clerk.
 From the fact that for all x_11, if x_11 were a janitor, then x_11 is running, and that there is at least one x_11 for which if x_11 goes running, then x_11 is a doctor we can infer that there is at least one x_11 for which if x_11 were a janitor, then x_11 is a doctor via existential transitivity. From the fact that for all x_11, x_11 is a doctor or x_11 is not an office clerk we can infer that for all x_11, if x_11 were an office clerk, then x_11 is a doctor via universal rewriting. From the fact that for all x_11, if x_11 were a doctor, then x_11 is an office clerk, and that for all x_11, if x_11 were an office clerk, then x_11 is a doctor we can infer that for all x_11, x_11 is a doctor if and only if x_11 is an office clerk via universal biconditional introduction. From the fact that for all x_11, x_11 is a doctor if and only if x_11 is an office clerk we can infer that for all x_11, if x_11 were a doctor, then x_11 is an office clerk via universal biconditional elimination. Finally, from the fact that there is at least one x_11 for which if x_11 were a janitor, then x_11 is a doctor, and that for all x_11, if x_11 were a doctor, then x_11 is an office clerk we can infer that there is at least one x_11 for which if x_11 were a janitor, then x_11 is an office clerk via existential transitivity. Therefore, the answer is yes.