Consider the following premises. For all x_23, if x_23 drives a car, then x_23 is drinking water. For all x_23, x_23 will play squash if and only if x_23 is an office clerk. For all x_23, x_23 will play squash if and only if x_23 will drink water. For all x_23, x_23 will not work. There is at least one x_23 for which x_23 is an office clerk if and only if x_23 will work. Can we infer the following from them? If we can, name the inference rule being used: For all x_23, x_23 will drive a car.
 From the fact that there is at least one x_23 for which x_23 is an office clerk if and only if x_23 will work, and that for all x_23, x_23 will not work we can infer that there is at least one x_23 for which x_23 is not an office clerk via existential biconditional elimination. From the fact that for all x_23, x_23 will play squash if and only if x_23 is an office clerk, and that there is at least one x_23 for which x_23 is not an office clerk we can infer that there is at least one x_23 for which x_23 will not play squash via existential biconditional elimination. From the fact that for all x_23, x_23 will play squash if and only if x_23 will drink water, and that there is at least one x_23 for which x_23 will not play squash we can infer that there is at least one x_23 for which x_23 will not drink water via existential biconditional elimination. Finally, from the fact that for all x_23, if x_23 drives a car, then x_23 is drinking water, and that there is at least one x_23 for which x_23 will not drink water we can infer that there is at least one x_23 for which x_23 will not drive a car via existential modus tollens, which contradicts that For all x_23, x_23 will drive a car. Therefore, the answer is no.