Consider the following premises. For all x_4, x_4 will work or x_4 will go running. For all x_4, if x_4 plays tennis, then x_4 is taking a plane. For all x_4, x_4 will not work or x_4 will play tennis. For all x_4, x_4 will take a plane or x_4 will not go running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_4 for which x_4 will not take a plane.
 From the fact that for all x_4, x_4 will take a plane or x_4 will not go running we can infer that for all x_4, if x_4 goes running, then x_4 is taking a plane via universal rewriting. From the fact that for all x_4, x_4 will work or x_4 will go running, and that for all x_4, x_4 will not work or x_4 will play tennis we can infer that for all x_4, x_4 will go running or x_4 will play tennis via universal resolution. Finally, from the fact that for all x_4, if x_4 goes running, then x_4 is taking a plane, that for all x_4, if x_4 plays tennis, then x_4 is taking a plane, and that for all x_4, x_4 will go running or x_4 will play tennis we can infer that for all x_4, x_4 will take a plane via universal disjunction elimination, which contradicts that There is at least one x_4 for which x_4 will not take a plane. Therefore, the answer is no.