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: For all x, if x takes a plane, then x is climbing a mountain. For all x, x is a carpenter if and only if x will go running. For all x, x will not go running. For all x, if x goes running, then x is a carpenter. There is at least one x for which if x climbs a mountain, then x is a carpenter.
There is at least one x for which if x takes a plane, then x is a carpenter can be inferred via the existential transitivity rule. For all x, if x were a carpenter, then x is running can be inferred via the universal biconditional elimination rule. For all x, if x goes running, then x is a carpenter can be inferred via the universal biconditional elimination rule. For all x, x is not a carpenter can be inferred via the universal biconditional elimination rule.