Consider the following premises. For all x_2, x_2 will not take a plane or x_2 is a carpenter. There is at least one x_2 for which x_2 is a bartender or x_2 will take a plane. For all x_2, x_2 is not a bartender or x_2 will sleep. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_2 for which x_2 will sleep or x_2 is a carpenter.
 From the fact that there is at least one x_2 for which x_2 is a bartender or x_2 will take a plane, and that for all x_2, x_2 is not a bartender or x_2 will sleep we can infer that there is at least one x_2 for which x_2 will take a plane or x_2 will sleep via existential resolution. Finally, from the fact that there is at least one x_2 for which x_2 will take a plane or x_2 will sleep, and that for all x_2, x_2 will not take a plane or x_2 is a carpenter we can infer that there is at least one x_2 for which x_2 will sleep or x_2 is a carpenter via existential resolution. Therefore, the answer is yes.