Consider the following premises. For all x_5, if x_5 goes running, then x_5 is a soldier. For all x_5, if x_5 were a soldier, then x_5 is taking a plane. There is at least one x_5 for which x_5 will go running or x_5 will sleep. For all x_5, x_5 will take a plane or x_5 will not sleep. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 will not take a plane.
 From the fact that for all x_5, if x_5 goes running, then x_5 is a soldier, and that for all x_5, if x_5 were a soldier, then x_5 is taking a plane we can infer that for all x_5, if x_5 goes running, then x_5 is taking a plane via universal transitivity. From the fact that for all x_5, x_5 will take a plane or x_5 will not sleep we can infer that for all x_5, if x_5 sleeps, then x_5 is taking a plane via universal rewriting. Finally, from the fact that for all x_5, if x_5 goes running, then x_5 is taking a plane, that for all x_5, if x_5 sleeps, then x_5 is taking a plane, and that there is at least one x_5 for which x_5 will go running or x_5 will sleep we can infer that there is at least one x_5 for which x_5 will take a plane via existential disjunction elimination, which contradicts that For all x_5, x_5 will not take a plane. Therefore, the answer is no.