Consider the following premises. For all x_14, if x_14 were excited, then x_14 is a writer. There is at least one x_14 for which if x_14 were a writer, then x_14 is running. For all x_14, x_14 will not play a game. For all x_14, x_14 is excited if and only if x_14 will play a game. For all x_14, x_14 will go running if and only if x_14 is excited. Can we infer the following from them? If we can, name the inference rule being used: For all x_14, x_14 will go running.
 From the fact that for all x_14, x_14 will go running if and only if x_14 is excited we can infer that for all x_14, if x_14 goes running, then x_14 is excited via universal biconditional elimination. From the fact that for all x_14, if x_14 were excited, then x_14 is a writer, and that there is at least one x_14 for which if x_14 were a writer, then x_14 is running we can infer that there is at least one x_14 for which if x_14 were excited, then x_14 is running via existential transitivity. From the fact that for all x_14, x_14 is excited if and only if x_14 will play a game, and that for all x_14, x_14 will not play a game we can infer that for all x_14, x_14 is not excited via universal biconditional elimination. From the fact that there is at least one x_14 for which if x_14 were excited, then x_14 is running, and that for all x_14, if x_14 goes running, then x_14 is excited we can infer that there is at least one x_14 for which x_14 is excited if and only if x_14 will go running via existential biconditional introduction. Finally, from the fact that there is at least one x_14 for which x_14 is excited if and only if x_14 will go running, and that for all x_14, x_14 is not excited we can infer that there is at least one x_14 for which x_14 will not go running via existential biconditional elimination, which contradicts that For all x_14, x_14 will go running. Therefore, the answer is no.