Consider the following premises. For all x_16, x_16 is a musician. For all x_16, if x_16 were a politician, then x_16 is an office clerk. There is at least one x_16 for which x_16 is rich or x_16 is a carpenter. For all x_16, x_16 is not an office clerk. For all x_16, if x_16 were rich, then x_16 is a politician. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_16 for which x_16 is a carpenter.
 From the fact that for all x_16, if x_16 were rich, then x_16 is a politician, and that for all x_16, if x_16 were a politician, then x_16 is an office clerk we can infer that for all x_16, if x_16 were rich, then x_16 is an office clerk via universal transitivity. From the fact that for all x_16, if x_16 were rich, then x_16 is an office clerk, and that for all x_16, x_16 is not an office clerk we can infer that for all x_16, x_16 is not rich via universal modus tollens. Finally, from the fact that there is at least one x_16 for which x_16 is rich or x_16 is a carpenter, and that for all x_16, x_16 is not rich we can infer that there is at least one x_16 for which x_16 is a carpenter via existential disjunctive syllogism. Therefore, the answer is yes.