Consider the following premises. For all x_5, x_5 will work or x_5 will not make tea. For all x_5, if x_5 works, then x_5 is an office clerk. For all x_5, x_5 is not an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 will make tea.
 From the fact that for all x_5, if x_5 works, then x_5 is an office clerk, and that for all x_5, x_5 is not an office clerk we can infer that for all x_5, x_5 will not work via universal modus tollens. From the fact that for all x_5, x_5 will work or x_5 will not make tea we can infer that for all x_5, if x_5 makes tea, then x_5 is working via universal rewriting. Finally, from the fact that for all x_5, if x_5 makes tea, then x_5 is working, and that for all x_5, x_5 will not work we can infer that for all x_5, x_5 will not make tea via universal modus tollens, which contradicts that There is at least one x_5 for which x_5 will make tea. Therefore, the answer is no.