Consider the following premises. For all x_2, x_2 will not make tea. For all x_2, x_2 is not an artist or x_2 is a mechanic. There is at least one x_2 for which x_2 is an artist or x_2 will make tea. Can we infer the following from them? If we can, name the inference rule being used: For all x_2, x_2 is not a mechanic.
 From the fact that there is at least one x_2 for which x_2 is an artist or x_2 will make tea, and that for all x_2, x_2 is not an artist or x_2 is a mechanic we can infer that there is at least one x_2 for which x_2 will make tea or x_2 is a mechanic via existential resolution. Finally, from the fact that there is at least one x_2 for which x_2 will make tea or x_2 is a mechanic, and that for all x_2, x_2 will not make tea we can infer that there is at least one x_2 for which x_2 is a mechanic via existential disjunctive syllogism, which contradicts that For all x_2, x_2 is not a mechanic. Therefore, the answer is no.