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 is a mechanic or z is not a scientist. For all z, if z were a mechanic, then z is a scientist. There is at least one z for which z will work if and only if z is a scientist.
For all z, if z were a scientist, then z is a mechanic can be inferred via the universal rewriting rule. There is at least one z for which if z works, then z is a scientist can be inferred via the existential biconditional elimination rule. There is at least one z for which if z were a scientist, then z is working can be inferred via the existential biconditional elimination rule.