Consider the following premises. For all x_8, x_8 is an office clerk. For all x_8, x_8 will not work or x_8 is fast. For all x_8, x_8 will work or x_8 is a mechanic. For all x_8, if x_8 were a mechanic, then x_8 is not an office clerk. There is at least one x_8 for which if x_8 were curious, then x_8 is not fast. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 is not curious.
 From the fact that for all x_8, if x_8 were a mechanic, then x_8 is not an office clerk, and that for all x_8, x_8 is an office clerk we can infer that for all x_8, x_8 is not a mechanic via universal modus tollens. From the fact that for all x_8, x_8 will work or x_8 is a mechanic, and that for all x_8, x_8 will not work or x_8 is fast we can infer that for all x_8, x_8 is a mechanic or x_8 is fast via universal resolution. From the fact that for all x_8, x_8 is a mechanic or x_8 is fast, and that for all x_8, x_8 is not a mechanic we can infer that for all x_8, x_8 is fast via universal disjunctive syllogism. Finally, from the fact that there is at least one x_8 for which if x_8 were curious, then x_8 is not fast, and that for all x_8, x_8 is fast we can infer that there is at least one x_8 for which x_8 is not curious via existential modus tollens. Therefore, the answer is yes.