Consider the following premises. For all x_8, if x_8 were a doctor, then x_8 is excited. For all x_8, if x_8 goes running, then x_8 is excited. For all x_8, x_8 will drink water and x_8 is an electrician. For all x_8, x_8 will go running or x_8 is a doctor. 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 either x_8 will drink water or x_8 is excited are not true.
 From the fact that for all x_8, if x_8 goes running, then x_8 is excited, that for all x_8, if x_8 were a doctor, then x_8 is excited, and that for all x_8, x_8 will go running or x_8 is a doctor we can infer that for all x_8, x_8 is excited via universal disjunction elimination. From the fact that for all x_8, x_8 will drink water and x_8 is an electrician we can infer that for all x_8, x_8 will drink water via universal simplification. Finally, from the fact that for all x_8, x_8 will drink water, and that for all x_8, x_8 is excited we can infer that for all x_8, x_8 will drink water and x_8 is excited via universal conjunction, which contradicts that There is at least one x_8 for which either x_8 will drink water or x_8 is excited are not true. Therefore, the answer is no.