Consider the following premises. There is at least one x_13 for which x_13 will drink water or x_13 will write a letter. For all x_13, if x_13 writes a letter, then x_13 is driving a car. For all x_13, if x_13 drinks water, then x_13 is driving a car. For all x_13, x_13 is rich or x_13 will not drive a car. Can we infer the following from them? If we can, name the inference rule being used: For all x_13, x_13 is not rich.
 From the fact that for all x_13, if x_13 drinks water, then x_13 is driving a car, that for all x_13, if x_13 writes a letter, then x_13 is driving a car, and that there is at least one x_13 for which x_13 will drink water or x_13 will write a letter we can infer that there is at least one x_13 for which x_13 will drive a car via existential disjunction elimination. From the fact that for all x_13, x_13 is rich or x_13 will not drive a car we can infer that for all x_13, if x_13 drives a car, then x_13 is rich via universal rewriting. Finally, from the fact that for all x_13, if x_13 drives a car, then x_13 is rich, and that there is at least one x_13 for which x_13 will drive a car we can infer that there is at least one x_13 for which x_13 is rich via existential modus ponens, which contradicts that For all x_13, x_13 is not rich. Therefore, the answer is no.