Consider the following premises. For all x_6, x_6 will drink water or x_6 is a writer. For all x_6, x_6 is happy or x_6 is not a writer. For all x_6, if x_6 drinks water, then x_6 is happy. For all x_6, if x_6 were a janitor, then x_6 is not happy. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is a janitor.
 From the fact that for all x_6, x_6 is happy or x_6 is not a writer we can infer that for all x_6, if x_6 were a writer, then x_6 is happy via universal rewriting. From the fact that for all x_6, if x_6 drinks water, then x_6 is happy, that for all x_6, if x_6 were a writer, then x_6 is happy, and that for all x_6, x_6 will drink water or x_6 is a writer we can infer that for all x_6, x_6 is happy via universal disjunction elimination. Finally, from the fact that for all x_6, if x_6 were a janitor, then x_6 is not happy, and that for all x_6, x_6 is happy we can infer that for all x_6, x_6 is not a janitor via universal modus tollens, which contradicts that There is at least one x_6 for which x_6 is a janitor. Therefore, the answer is no.