Consider the following premises. For all x_1, if x_1 were bored, then x_1 is fast. For all x_1, x_1 is not fast. There is at least one x_1 for which x_1 is bored or x_1 will work. Can we infer the following from them? If we can, name the inference rule being used: For all x_1, x_1 will not work.
 From the fact that for all x_1, if x_1 were bored, then x_1 is fast, and that for all x_1, x_1 is not fast we can infer that for all x_1, x_1 is not bored via universal modus tollens. Finally, from the fact that there is at least one x_1 for which x_1 is bored or x_1 will work, and that for all x_1, x_1 is not bored we can infer that there is at least one x_1 for which x_1 will work via existential disjunctive syllogism, which contradicts that For all x_1, x_1 will not work. Therefore, the answer is no.