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 z, z will climb a mountain if and only if z will go running. For all z, if z climbs a mountain, then z is running. There is at least one z for which z will not go running.
There is at least one z for which z will not climb a mountain can be inferred via the existential modus tollens rule. For all z, if z climbs a mountain, then z is running can be inferred via the universal biconditional elimination rule. For all z, if z goes running, then z is climbing a mountain can be inferred via the universal biconditional elimination rule. There is at least one z for which z will not climb a mountain can be inferred via the existential biconditional elimination rule.