Consider the following premises. For all x_17, if x_17 were an artist, then x_17 is driving a car. For all x_17, x_17 will write a letter if and only if x_17 will drive a car. There is at least one x_17 for which x_17 will play tennis or x_17 is a janitor. For all x_17, if x_17 plays tennis, then x_17 is playing squash. For all x_17, x_17 is an artist or x_17 will write a letter. For all x_17, if x_17 were a janitor, then x_17 is playing squash. Can we infer the following from them? If we can, name the inference rule being used: For all x_17, either x_17 will play squash or x_17 will drive a car are not true.
 From the fact that for all x_17, if x_17 plays tennis, then x_17 is playing squash, that for all x_17, if x_17 were a janitor, then x_17 is playing squash, and that there is at least one x_17 for which x_17 will play tennis or x_17 is a janitor we can infer that there is at least one x_17 for which x_17 will play squash via existential disjunction elimination. From the fact that for all x_17, x_17 will write a letter if and only if x_17 will drive a car we can infer that for all x_17, if x_17 writes a letter, then x_17 is driving a car via universal biconditional elimination. From the fact that for all x_17, if x_17 were an artist, then x_17 is driving a car, that for all x_17, if x_17 writes a letter, then x_17 is driving a car, and that for all x_17, x_17 is an artist or x_17 will write a letter we can infer that for all x_17, x_17 will drive a car via universal disjunction elimination. Finally, from the fact that there is at least one x_17 for which x_17 will play squash, and that for all x_17, x_17 will drive a car we can infer that there is at least one x_17 for which x_17 will play squash and x_17 will drive a car via existential conjunction, which contradicts that For all x_17, either x_17 will play squash or x_17 will drive a car are not true. Therefore, the answer is no.