Consider the following premises. For all z, if z goes running, then z is driving a car. For all z, z will drive a car if and only if z is curious. For all z, z is curious if and only if z will go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one z for which if is not true that z will drive a car if and only if z is curious.
 From the fact that for all z, z is curious if and only if z will go running we can infer that for all z, if z were curious, then z is running via universal biconditional elimination. From the fact that for all z, z will drive a car if and only if z is curious we can infer that for all z, if z drives a car, then z is curious via universal biconditional elimination. From the fact that for all z, if z were curious, then z is running, and that for all z, if z goes running, then z is driving a car we can infer that for all z, if z were curious, then z is driving a car via universal transitivity. Finally, from the fact that for all z, if z drives a car, then z is curious, and that for all z, if z were curious, then z is driving a car we can infer that for all z, z will drive a car if and only if z is curious via universal biconditional introduction, which contradicts that There is at least one z for which if is not true that z will drive a car if and only if z is curious. Therefore, the answer is no.