Consider the following premises. For all x_7, if x_7 were a cashier, then x_7 is not a mechanic. For all x_7, if x_7 were a cashier, then x_7 is climbing a mountain. There is at least one x_7 for which if x_7 climbs a mountain, then x_7 is a cashier. For all x_7, if x_7 goes running, then x_7 is a mechanic. For all x_7, x_7 will go running. Can we infer the following from them? If we can, name the inference rule being used: For all x_7, x_7 will climb a mountain.
 From the fact that for all x_7, if x_7 goes running, then x_7 is a mechanic, and that for all x_7, x_7 will go running we can infer that for all x_7, x_7 is a mechanic via universal modus ponens. From the fact that there is at least one x_7 for which if x_7 climbs a mountain, then x_7 is a cashier, and that for all x_7, if x_7 were a cashier, then x_7 is climbing a mountain we can infer that there is at least one x_7 for which x_7 will climb a mountain if and only if x_7 is a cashier via existential biconditional introduction. From the fact that for all x_7, if x_7 were a cashier, then x_7 is not a mechanic, and that for all x_7, x_7 is a mechanic we can infer that for all x_7, x_7 is not a cashier via universal modus tollens. Finally, from the fact that there is at least one x_7 for which x_7 will climb a mountain if and only if x_7 is a cashier, and that for all x_7, x_7 is not a cashier we can infer that there is at least one x_7 for which x_7 will not climb a mountain via existential biconditional elimination, which contradicts that For all x_7, x_7 will climb a mountain. Therefore, the answer is no.