Consider the following premises. For all x_5, if x_5 were an office clerk, then x_5 is poor. For all x_5, x_5 is a scientist or x_5 will make tea. For all x_5, if x_5 makes tea, then x_5 is an office clerk. There is at least one x_5 for which if x_5 were a carpenter, then x_5 is not poor. For all x_5, if x_5 were a scientist, then x_5 is poor. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_5 for which x_5 is not a carpenter.
 From the fact that for all x_5, if x_5 makes tea, then x_5 is an office clerk, and that for all x_5, if x_5 were an office clerk, then x_5 is poor we can infer that for all x_5, if x_5 makes tea, then x_5 is poor via universal transitivity. From the fact that for all x_5, if x_5 were a scientist, then x_5 is poor, that for all x_5, if x_5 makes tea, then x_5 is poor, and that for all x_5, x_5 is a scientist or x_5 will make tea we can infer that for all x_5, x_5 is poor via universal disjunction elimination. Finally, from the fact that there is at least one x_5 for which if x_5 were a carpenter, then x_5 is not poor, and that for all x_5, x_5 is poor we can infer that there is at least one x_5 for which x_5 is not a carpenter via existential modus tollens. Therefore, the answer is yes.