Consider the following premises. For all x_7, x_7 is not an electrician or x_7 will cook. For all x_7, x_7 is an electrician. For all x_7, x_7 will cook if and only if x_7 will climb a mountain. There is at least one x_7 for which if x_7 were a politician, then x_7 is climbing a mountain. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will not climb a mountain.
 From the fact that for all x_7, x_7 will cook if and only if x_7 will climb a mountain we can infer that for all x_7, if x_7 cooks, then x_7 is climbing a mountain via universal biconditional elimination. From the fact that for all x_7, x_7 is an electrician we can infer that for all x_7, x_7 is an electrician or x_7 is a politician via universal addition. From the fact that for all x_7, x_7 is an electrician or x_7 is a politician, and that for all x_7, x_7 is not an electrician or x_7 will cook we can infer that for all x_7, x_7 is a politician or x_7 will cook via universal resolution. Finally, from the fact that there is at least one x_7 for which if x_7 were a politician, then x_7 is climbing a mountain, that for all x_7, if x_7 cooks, then x_7 is climbing a mountain, and that for all x_7, x_7 is a politician or x_7 will cook we can infer that there is at least one x_7 for which x_7 will climb a mountain via existential disjunction elimination, which contradicts that For all x_7, x_7 will not climb a mountain. Therefore, the answer is no.