Consider the following premises. For all x_8, x_8 is sad if and only if x_8 will take a plane. There is at least one x_8 for which x_8 will take a plane or x_8 will not go running. For all x_8, x_8 is not sad. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, x_8 will go running.
 From the fact that for all x_8, x_8 is sad if and only if x_8 will take a plane, and that for all x_8, x_8 is not sad we can infer that for all x_8, x_8 will not take a plane via universal biconditional elimination. From the fact that there is at least one x_8 for which x_8 will take a plane or x_8 will not go running we can infer that there is at least one x_8 for which if x_8 goes running, then x_8 is taking a plane via existential rewriting. Finally, from the fact that there is at least one x_8 for which if x_8 goes running, then x_8 is taking a plane, and that for all x_8, x_8 will not take a plane we can infer that there is at least one x_8 for which x_8 will not go running via existential modus tollens, which contradicts that For all x_8, x_8 will go running. Therefore, the answer is no.