Consider the following premises. For all x_10, if x_10 goes running, then x_10 is making tea. For all x_10, if x_10 makes tea, then x_10 is running. Barbara is not making tea. Can we infer the following from them? If we can, name the inference rule being used: Barbara is running.
 From the fact that for all x_10, if x_10 makes tea, then x_10 is running, and that for all x_10, if x_10 goes running, then x_10 is making tea we can infer that for all x_10, x_10 will make tea if and only if x_10 will go running via universal biconditional introduction. From the fact that for all x_10, x_10 will make tea if and only if x_10 will go running we can infer that for all x_10, if x_10 goes running, then x_10 is making tea via universal biconditional elimination. From the fact that for all x_10, if x_10 goes running, then x_10 is making tea we can infer that if Barbara goes running, then Barbara is making tea via universal instantiation. Finally, from the fact that if Barbara goes running, then Barbara is making tea, and that Barbara is not making tea we can infer that Barbara is not running via modus tollens, which contradicts that Barbara is running. Therefore, the answer is no.