Consider the following premises. For all x_5, x_5 will climb a mountain. For all x_5, x_5 is a lawyer or x_5 will play squash. There is at least one x_5 for which if x_5 plays squash, then x_5 is not climbing a mountain. For all x_5, x_5 is not a lawyer or x_5 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: For all x_5, x_5 is not an office clerk.
 From the fact that there is at least one x_5 for which if x_5 plays squash, then x_5 is not climbing a mountain, and that for all x_5, x_5 will climb a mountain we can infer that there is at least one x_5 for which x_5 will not play squash via existential modus tollens. From the fact that for all x_5, x_5 is a lawyer or x_5 will play squash, and that for all x_5, x_5 is not a lawyer or x_5 is an office clerk we can infer that for all x_5, x_5 will play squash or x_5 is an office clerk via universal resolution. Finally, from the fact that for all x_5, x_5 will play squash or x_5 is an office clerk, and that there is at least one x_5 for which x_5 will not play squash we can infer that there is at least one x_5 for which x_5 is an office clerk via existential disjunctive syllogism, which contradicts that For all x_5, x_5 is not an office clerk. Therefore, the answer is no.