Consider the following premises. There is at least one x_3 for which if x_3 makes tea, then x_3 is not running. For all x_3, x_3 will make tea if and only if x_3 is rich. For all x_3, x_3 will go running. Can we infer the following from them? If we can, name the inference rule being used: For all x_3, x_3 is rich.
 From the fact that there is at least one x_3 for which if x_3 makes tea, then x_3 is not running, and that for all x_3, x_3 will go running we can infer that there is at least one x_3 for which x_3 will not make tea via existential modus tollens. Finally, from the fact that for all x_3, x_3 will make tea if and only if x_3 is rich, and that there is at least one x_3 for which x_3 will not make tea we can infer that there is at least one x_3 for which x_3 is not rich via existential biconditional elimination, which contradicts that For all x_3, x_3 is rich. Therefore, the answer is no.