Consider the following premises. For all x_8, x_8 is a janitor or x_8 will work. For all x_8, if x_8 works, then x_8 is running. For all x_8, x_8 will go running if and only if x_8 is a janitor. There is at least one x_8 for which x_8 is an artist. Can we infer the following from them? If we can, name the inference rule being used: For all x_8, either x_8 will go running or x_8 is an artist are not true.
 From the fact that for all x_8, x_8 will go running if and only if x_8 is a janitor we can infer that for all x_8, if x_8 were a janitor, then x_8 is running via universal biconditional elimination. From the fact that for all x_8, if x_8 were a janitor, 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 is a janitor 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, and that there is at least one x_8 for which x_8 is an artist we can infer that there is at least one x_8 for which x_8 will go running and x_8 is an artist via existential conjunction, which contradicts that For all x_8, either x_8 will go running or x_8 is an artist are not true. Therefore, the answer is no.