Consider the following premises. For all x_9, x_9 will go running if and only if x_9 is a musician. For all x_9, if x_9 were a lawyer, then x_9 is running. For all x_9, if x_9 goes running, then x_9 is a lawyer. There is at least one x_9 for which x_9 is not a musician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 is not a lawyer.
 From the fact that for all x_9, if x_9 goes running, then x_9 is a lawyer, and that for all x_9, if x_9 were a lawyer, then x_9 is running we can infer that for all x_9, x_9 will go running if and only if x_9 is a lawyer via universal biconditional introduction. From the fact that for all x_9, x_9 will go running if and only if x_9 is a musician, and that there is at least one x_9 for which x_9 is not a musician we can infer that there is at least one x_9 for which x_9 will not go running via existential biconditional elimination. Finally, from the fact that for all x_9, x_9 will go running if and only if x_9 is a lawyer, and that there is at least one x_9 for which x_9 will not go running we can infer that there is at least one x_9 for which x_9 is not a lawyer via existential biconditional elimination. Therefore, the answer is yes.