Consider the following premises. For all x_2, if x_2 were a janitor, then x_2 is climbing a mountain. For all x_2, x_2 will climb a mountain or x_2 will not make tea. For all x_2, x_2 is a janitor or x_2 will make tea. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 will not climb a mountain.
 From the fact that for all x_2, x_2 will climb a mountain or x_2 will not make tea we can infer that for all x_2, if x_2 makes tea, then x_2 is climbing a mountain via universal rewriting. Finally, from the fact that for all x_2, if x_2 were a janitor, then x_2 is climbing a mountain, that for all x_2, if x_2 makes tea, then x_2 is climbing a mountain, and that for all x_2, x_2 is a janitor or x_2 will make tea we can infer that for all x_2, x_2 will climb a mountain via universal disjunction elimination, which contradicts that There is at least one x_2 for which x_2 will not climb a mountain. Therefore, the answer is no.