Consider the following premises. For all z_1, if z_1 goes running, then z_1 is playing tennis. For all z_1, z_1 is curious if and only if z_1 will go running. For all z_1, if z_1 drives a car, then z_1 is curious. There is at least one z_1 for which if z_1 were curious, then z_1 is driving a car. For all z_1, z_1 will not play tennis. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z_1 for which z_1 will not drive a car.
 From the fact that for all z_1, if z_1 drives a car, then z_1 is curious, and that there is at least one z_1 for which if z_1 were curious, then z_1 is driving a car we can infer that there is at least one z_1 for which z_1 will drive a car if and only if z_1 is curious via existential biconditional introduction. From the fact that for all z_1, if z_1 goes running, then z_1 is playing tennis, and that for all z_1, z_1 will not play tennis we can infer that for all z_1, z_1 will not go running via universal modus tollens. From the fact that for all z_1, z_1 is curious if and only if z_1 will go running, and that for all z_1, z_1 will not go running we can infer that for all z_1, z_1 is not curious via universal biconditional elimination. Finally, from the fact that there is at least one z_1 for which z_1 will drive a car if and only if z_1 is curious, and that for all z_1, z_1 is not curious we can infer that there is at least one z_1 for which z_1 will not drive a car via existential biconditional elimination. Therefore, the answer is yes.