Consider the following premises. For all x_9, x_9 will not take a plane. For all x_9, x_9 will cook or x_9 is a poet. For all x_9, if x_9 were a poet, then x_9 is not playing tennis. For all x_9, x_9 will take a plane or x_9 will play tennis. There is at least one x_9 for which x_9 will not cook or x_9 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_9, x_9 will not climb a mountain.
 From the fact that for all x_9, x_9 will take a plane or x_9 will play tennis, and that for all x_9, x_9 will not take a plane we can infer that for all x_9, x_9 will play tennis via universal disjunctive syllogism. From the fact that for all x_9, x_9 will cook or x_9 is a poet, and that there is at least one x_9 for which x_9 will not cook or x_9 will climb a mountain we can infer that there is at least one x_9 for which x_9 is a poet or x_9 will climb a mountain via existential resolution. From the fact that for all x_9, if x_9 were a poet, then x_9 is not playing tennis, and that for all x_9, x_9 will play tennis we can infer that for all x_9, x_9 is not a poet via universal modus tollens. Finally, from the fact that there is at least one x_9 for which x_9 is a poet or x_9 will climb a mountain, and that for all x_9, x_9 is not a poet we can infer that there is at least one x_9 for which x_9 will climb a mountain via existential disjunctive syllogism, which contradicts that For all x_9, x_9 will not climb a mountain. Therefore, the answer is no.