Consider the following premises. For all x_8, if x_8 were curious, then x_8 is an office clerk. There is at least one x_8 for which x_8 is not an office clerk. For all x_8, x_8 is curious if and only if x_8 is a carpenter. 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 a carpenter.
 From the fact that for all x_8, x_8 is curious if and only if x_8 is a carpenter we can infer that for all x_8, if x_8 were a carpenter, then x_8 is curious via universal biconditional elimination. From the fact that for all x_8, if x_8 were a carpenter, then x_8 is curious, and that for all x_8, if x_8 were curious, then x_8 is an office clerk we can infer that for all x_8, if x_8 were a carpenter, then x_8 is an office clerk via universal transitivity. Finally, from the fact that for all x_8, if x_8 were a carpenter, then x_8 is an office clerk, and that there is at least one x_8 for which x_8 is not an office clerk we can infer that there is at least one x_8 for which x_8 is not a carpenter via existential modus tollens. Therefore, the answer is yes.