Consider the following premises. For all x_8, if x_8 takes a plane, then x_8 is running. For all x_8, x_8 will go running if and only if x_8 will work. For all x_8, x_8 will take a plane or x_8 will work. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which neither x_8 will go running nor x_8 is a janitor.
 From the fact that for all x_8, x_8 will go running if and only if x_8 will work we can infer that for all x_8, if x_8 works, then x_8 is running via universal biconditional elimination. From the fact that for all x_8, if x_8 takes a plane, then x_8 is running, that for all x_8, if x_8 works, then x_8 is running, and that for all x_8, x_8 will take a plane or x_8 will work we can infer that for all x_8, x_8 will go running via universal disjunction elimination. Finally, from the fact that for all x_8, x_8 will go running we can infer that for all x_8, x_8 will go running or x_8 is a janitor via universal addition, which contradicts that There is at least one x_8 for which neither x_8 will go running nor x_8 is a janitor. Therefore, the answer is no.