Consider the following premises. There is at least one x_6 for which x_6 will not make tea. For all x_6, if x_6 goes running, then x_6 is climbing a mountain. For all x_6, x_6 will make tea if and only if x_6 will climb a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_6, x_6 will go running.
 From the fact that for all x_6, x_6 will make tea if and only if x_6 will climb a mountain, and that there is at least one x_6 for which x_6 will not make tea we can infer that there is at least one x_6 for which x_6 will not climb a mountain via existential biconditional elimination. Finally, from the fact that for all x_6, if x_6 goes running, then x_6 is climbing a mountain, and that there is at least one x_6 for which x_6 will not climb a mountain we can infer that there is at least one x_6 for which x_6 will not go running via existential modus tollens, which contradicts that For all x_6, x_6 will go running. Therefore, the answer is no.