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, if z works, then z is a soldier. There is at least one z for which z is sad if and only if z is a scientist. For all z, if z were a soldier, then z is sad.
For all z, if z works, then z is sad can be inferred via the universal transitivity rule. There is at least one z for which if z were sad, 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 sad can be inferred via the existential biconditional elimination rule.