Consider the following premises. For all x_6, if x_6 were curious, then x_6 is not an office clerk. For all x_6, x_6 is curious or x_6 will cook. For all x_6, if x_6 were a janitor, then x_6 is not cooking. For all x_6, x_6 is an office clerk. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_6 for which x_6 is a janitor.
 From the fact that for all x_6, if x_6 were curious, then x_6 is not an office clerk, and that for all x_6, x_6 is an office clerk we can infer that for all x_6, x_6 is not curious via universal modus tollens. From the fact that for all x_6, x_6 is curious or x_6 will cook, and that for all x_6, x_6 is not curious we can infer that for all x_6, x_6 will cook via universal disjunctive syllogism. Finally, from the fact that for all x_6, if x_6 were a janitor, then x_6 is not cooking, and that for all x_6, x_6 will cook we can infer that for all x_6, x_6 is not a janitor via universal modus tollens, which contradicts that There is at least one x_6 for which x_6 is a janitor. Therefore, the answer is no.