Consider the following premises. For all x_4, x_4 will play a game. For all x_4, x_4 will not climb a mountain. There is at least one x_4 for which x_4 will not play a game or x_4 is a scientist. Can we infer the following from them? If we can, name the inference rule being used: For all x_4, x_4 is not a scientist.
 From the fact that for all x_4, x_4 will play a game we can infer that for all x_4, x_4 will play a game or x_4 will climb a mountain via universal addition. From the fact that for all x_4, x_4 will play a game or x_4 will climb a mountain, and that there is at least one x_4 for which x_4 will not play a game or x_4 is a scientist we can infer that there is at least one x_4 for which x_4 will climb a mountain or x_4 is a scientist via existential resolution. Finally, from the fact that there is at least one x_4 for which x_4 will climb a mountain or x_4 is a scientist, and that for all x_4, x_4 will not climb a mountain we can infer that there is at least one x_4 for which x_4 is a scientist via existential disjunctive syllogism, which contradicts that For all x_4, x_4 is not a scientist. Therefore, the answer is no.