Consider the following premises. For all x_6, x_6 will not work. There is at least one x_6 for which if x_6 were a scientist, then x_6 is climbing a mountain. For all x_6, if x_6 plays tennis, then x_6 is a scientist. For all x_6, x_6 will work or x_6 will play tennis. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not climb a mountain.
 From the fact that for all x_6, if x_6 plays tennis, then x_6 is a scientist, and that there is at least one x_6 for which if x_6 were a scientist, then x_6 is climbing a mountain we can infer that there is at least one x_6 for which if x_6 plays tennis, then x_6 is climbing a mountain via existential transitivity. From the fact that for all x_6, x_6 will work or x_6 will play tennis, and that for all x_6, x_6 will not work we can infer that for all x_6, x_6 will play tennis via universal disjunctive syllogism. Finally, from the fact that there is at least one x_6 for which if x_6 plays tennis, then x_6 is climbing a mountain, and that for all x_6, x_6 will play tennis we can infer that there is at least one x_6 for which x_6 will climb a mountain via existential modus ponens, which contradicts that For all x_6, x_6 will not climb a mountain. Therefore, the answer is no.