Consider the following premises. For all x_9, x_9 will drink water if and only if x_9 will go running. For all x_9, if x_9 goes running, then x_9 is a scientist. For all x_9, x_9 will drink water or x_9 is a scientist. For all x_9, if x_9 were a scientist, then x_9 is running. Can we infer the following from them? If we can, name the inference rule being used: There is at least one x_9 for which x_9 will not go running.
 From the fact that for all x_9, if x_9 goes running, then x_9 is a scientist, and that for all x_9, if x_9 were a scientist, then x_9 is running we can infer that for all x_9, x_9 will go running if and only if x_9 is a scientist via universal biconditional introduction. From the fact that for all x_9, x_9 will go running if and only if x_9 is a scientist we can infer that for all x_9, if x_9 were a scientist, then x_9 is running via universal biconditional elimination. From the fact that for all x_9, x_9 will drink water if and only if x_9 will go running we can infer that for all x_9, if x_9 drinks water, then x_9 is running via universal biconditional elimination. Finally, from the fact that for all x_9, if x_9 drinks water, then x_9 is running, that for all x_9, if x_9 were a scientist, then x_9 is running, and that for all x_9, x_9 will drink water or x_9 is a scientist we can infer that for all x_9, x_9 will go running via universal disjunction elimination, which contradicts that There is at least one x_9 for which x_9 will not go running. Therefore, the answer is no.