What can be inferred from the following premises in a single inference step (ignoring inferences that add new predicates or constants)? Name the inference rule being used: There is at least one x_9 for which x_9 is not a mechanic. For all x_9, if x_9 works, then x_9 is playing tennis. For all x_9, x_9 is a mechanic if and only if x_9 will play tennis. For all x_9, if x_9 climbs a mountain, then x_9 is working.
For all x_9, if x_9 climbs a mountain, then x_9 is playing tennis can be inferred via the universal transitivity rule. For all x_9, if x_9 were a mechanic, then x_9 is playing tennis can be inferred via the universal biconditional elimination rule. For all x_9, if x_9 plays tennis, then x_9 is a mechanic can be inferred via the universal biconditional elimination rule. There is at least one x_9 for which x_9 will not play tennis can be inferred via the existential biconditional elimination rule.