Consider the following premises. For all x_6, x_6 will not drive a car. For all x_6, x_6 is sad or x_6 is a bartender. For all x_6, x_6 is not a bartender or x_6 will work. There is at least one x_6 for which x_6 is not sad or x_6 will drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will not work.
 From the fact that for all x_6, x_6 is sad or x_6 is a bartender, and that there is at least one x_6 for which x_6 is not sad or x_6 will drive a car we can infer that there is at least one x_6 for which x_6 is a bartender or x_6 will drive a car via existential resolution. From the fact that there is at least one x_6 for which x_6 is a bartender or x_6 will drive a car, and that for all x_6, x_6 is not a bartender or x_6 will work we can infer that there is at least one x_6 for which x_6 will drive a car or x_6 will work via existential resolution. Finally, from the fact that there is at least one x_6 for which x_6 will drive a car or x_6 will work, and that for all x_6, x_6 will not drive a car we can infer that there is at least one x_6 for which x_6 will work via existential disjunctive syllogism, which contradicts that For all x_6, x_6 will not work. Therefore, the answer is no.