Consider the following premises. There is at least one x_5 for which x_5 will not make tea or x_5 is a lawyer. For all x_5, x_5 is a police officer or x_5 will make tea. For all x_5, x_5 is not a police officer or x_5 is a bartender. For all x_5, if x_5 were a bartender, then x_5 is a carpenter. For all x_5, if x_5 were a lawyer, then x_5 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_5 for which x_5 is a carpenter.
 From the fact that for all x_5, x_5 is a police officer or x_5 will make tea, and that for all x_5, x_5 is not a police officer or x_5 is a bartender we can infer that for all x_5, x_5 will make tea or x_5 is a bartender via universal resolution. From the fact that for all x_5, x_5 will make tea or x_5 is a bartender, and that there is at least one x_5 for which x_5 will not make tea or x_5 is a lawyer we can infer that there is at least one x_5 for which x_5 is a bartender or x_5 is a lawyer via existential resolution. Finally, from the fact that for all x_5, if x_5 were a bartender, then x_5 is a carpenter, that for all x_5, if x_5 were a lawyer, then x_5 is a carpenter, and that there is at least one x_5 for which x_5 is a bartender or x_5 is a lawyer we can infer that there is at least one x_5 for which x_5 is a carpenter via existential disjunction elimination. Therefore, the answer is yes.