Consider the following premises. For all x_13, x_13 is an office clerk or x_13 is a writer. There is at least one x_13 for which x_13 will play squash. For all x_13, if x_13 were an office clerk, then x_13 is not playing squash. For all x_13, x_13 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, either x_13 will climb a mountain or x_13 is a writer are not true.
 From the fact that for all x_13, if x_13 were an office clerk, then x_13 is not playing squash, and that there is at least one x_13 for which x_13 will play squash we can infer that there is at least one x_13 for which x_13 is not an office clerk via existential modus tollens. From the fact that for all x_13, x_13 is an office clerk or x_13 is a writer, and that there is at least one x_13 for which x_13 is not an office clerk we can infer that there is at least one x_13 for which x_13 is a writer via existential disjunctive syllogism. Finally, from the fact that for all x_13, x_13 will climb a mountain, and that there is at least one x_13 for which x_13 is a writer we can infer that there is at least one x_13 for which x_13 will climb a mountain and x_13 is a writer via existential conjunction, which contradicts that For all x_13, either x_13 will climb a mountain or x_13 is a writer are not true. Therefore, the answer is no.