Consider the following premises. For all x_8, if x_8 works, then x_8 is driving a car. For all x_8, if x_8 drinks water, then x_8 is working. For all x_8, x_8 will write a letter or x_8 will drive a car. For all x_8, if x_8 drives a car, then x_8 is working. There is at least one x_8 for which x_8 will not write a letter or x_8 will drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_8 for which x_8 will work.
 From the fact that for all x_8, x_8 will write a letter or x_8 will drive a car, and that there is at least one x_8 for which x_8 will not write a letter or x_8 will drink water we can infer that there is at least one x_8 for which x_8 will drive a car or x_8 will drink water via existential resolution. From the fact that for all x_8, if x_8 drives a car, then x_8 is working, and that for all x_8, if x_8 works, then x_8 is driving a car we can infer that for all x_8, x_8 will drive a car if and only if x_8 will work via universal biconditional introduction. From the fact that for all x_8, x_8 will drive a car if and only if x_8 will work we can infer that for all x_8, if x_8 drives a car, then x_8 is working via universal biconditional elimination. Finally, from the fact that for all x_8, if x_8 drives a car, then x_8 is working, that for all x_8, if x_8 drinks water, then x_8 is working, and that there is at least one x_8 for which x_8 will drive a car or x_8 will drink water we can infer that there is at least one x_8 for which x_8 will work via existential disjunction elimination. Therefore, the answer is yes.