Consider the following premises. For all x_3, if x_3 were a server, then x_3 is climbing a mountain. There is at least one x_3 for which x_3 is a server or x_3 will not drive a car. For all x_3, if x_3 climbs a mountain, then x_3 is driving a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, if is not true that x_3 is a server if and only if x_3 will drive a car.
 From the fact that for all x_3, if x_3 were a server, then x_3 is climbing a mountain, and that for all x_3, if x_3 climbs a mountain, then x_3 is driving a car we can infer that for all x_3, if x_3 were a server, then x_3 is driving a car via universal transitivity. From the fact that there is at least one x_3 for which x_3 is a server or x_3 will not drive a car we can infer that there is at least one x_3 for which if x_3 drives a car, then x_3 is a server via existential rewriting. Finally, from the fact that for all x_3, if x_3 were a server, then x_3 is driving a car, and that there is at least one x_3 for which if x_3 drives a car, then x_3 is a server we can infer that there is at least one x_3 for which x_3 is a server if and only if x_3 will drive a car via existential biconditional introduction, which contradicts that For all x_3, if is not true that x_3 is a server if and only if x_3 will drive a car. Therefore, the answer is no.