Consider the following premises. For all x_4, if x_4 drives a car, then x_4 is sleeping. For all x_4, x_4 will take a plane or x_4 will drive a car. There is at least one x_4 for which x_4 will take a plane if and only if x_4 will sleep. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 will not sleep.
 From the fact that there is at least one x_4 for which x_4 will take a plane if and only if x_4 will sleep we can infer that there is at least one x_4 for which if x_4 takes a plane, then x_4 is sleeping via existential biconditional elimination. Finally, from the fact that there is at least one x_4 for which if x_4 takes a plane, then x_4 is sleeping, that for all x_4, if x_4 drives a car, then x_4 is sleeping, and that for all x_4, x_4 will take a plane or x_4 will drive a car we can infer that there is at least one x_4 for which x_4 will sleep via existential disjunction elimination, which contradicts that For all x_4, x_4 will not sleep. Therefore, the answer is no.