Consider the following premises. For all x_5, if x_5 goes running, then x_5 is driving a car. For all x_5, if x_5 were a sailor, then x_5 is running. For all x_5, x_5 is a sailor or x_5 will not drive a car. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which if is not true that x_5 is a sailor if and only if x_5 will drive a car.
 From the fact that for all x_5, if x_5 were a sailor, then x_5 is running, and that for all x_5, if x_5 goes running, then x_5 is driving a car we can infer that for all x_5, if x_5 were a sailor, then x_5 is driving a car via universal transitivity. From the fact that for all x_5, x_5 is a sailor or x_5 will not drive a car we can infer that for all x_5, if x_5 drives a car, then x_5 is a sailor via universal rewriting. Finally, from the fact that for all x_5, if x_5 were a sailor, then x_5 is driving a car, and that for all x_5, if x_5 drives a car, then x_5 is a sailor we can infer that for all x_5, x_5 is a sailor if and only if x_5 will drive a car via universal biconditional introduction, which contradicts that There is at least one x_5 for which if is not true that x_5 is a sailor if and only if x_5 will drive a car. Therefore, the answer is no.