Consider the following premises. There is at least one x_16 for which x_16 is not a cashier or x_16 is a lawyer. For all x_16, x_16 is a cashier or x_16 will play squash. For all x_16, if x_16 plays squash, then x_16 is drinking water. For all x_16, x_16 will drink water or x_16 is not a lawyer. 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 will drink water or x_16 will listen to a song.
 From the fact that for all x_16, x_16 is a cashier or x_16 will play squash, and that there is at least one x_16 for which x_16 is not a cashier or x_16 is a lawyer we can infer that there is at least one x_16 for which x_16 will play squash or x_16 is a lawyer via existential resolution. From the fact that for all x_16, x_16 will drink water or x_16 is not a lawyer we can infer that for all x_16, if x_16 were a lawyer, then x_16 is drinking water via universal rewriting. From the fact that for all x_16, if x_16 plays squash, then x_16 is drinking water, that for all x_16, if x_16 were a lawyer, then x_16 is drinking water, and that there is at least one x_16 for which x_16 will play squash or x_16 is a lawyer we can infer that there is at least one x_16 for which x_16 will drink water via existential disjunction elimination. Finally, from the fact that there is at least one x_16 for which x_16 will drink water we can infer that there is at least one x_16 for which x_16 will drink water or x_16 will listen to a song via existential addition. Therefore, the answer is yes.