Consider the following premises. For all x_10, x_10 will not drive a car or x_10 is a soldier. For all x_10, x_10 will drive a car or x_10 is a police officer. For all x_10, if x_10 were a police officer, then x_10 is running. For all x_10, if x_10 goes running, then x_10 is a police officer. For all x_10, x_10 will drink water if and only if x_10 will go running. For all x_10, x_10 will not drink water. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_10 for which x_10 is not a soldier.
 From the fact that for all x_10, x_10 will drink water if and only if x_10 will go running, and that for all x_10, x_10 will not drink water we can infer that for all x_10, x_10 will not go running via universal biconditional elimination. From the fact that for all x_10, x_10 will drive a car or x_10 is a police officer, and that for all x_10, x_10 will not drive a car or x_10 is a soldier we can infer that for all x_10, x_10 is a police officer or x_10 is a soldier via universal resolution. From the fact that for all x_10, if x_10 goes running, then x_10 is a police officer, and that for all x_10, if x_10 were a police officer, then x_10 is running we can infer that for all x_10, x_10 will go running if and only if x_10 is a police officer via universal biconditional introduction. From the fact that for all x_10, x_10 will go running if and only if x_10 is a police officer, and that for all x_10, x_10 will not go running we can infer that for all x_10, x_10 is not a police officer via universal biconditional elimination. Finally, from the fact that for all x_10, x_10 is a police officer or x_10 is a soldier, and that for all x_10, x_10 is not a police officer we can infer that for all x_10, x_10 is a soldier via universal disjunctive syllogism, which contradicts that There is at least one x_10 for which x_10 is not a soldier. Therefore, the answer is no.