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, x is excited or x is a soldier. For all x, x is excited if and only if x is a lawyer. There is at least one x for which x is not a lawyer.
For all x, if x were excited, then x is a lawyer can be inferred via the universal biconditional elimination rule. For all x, if x were a lawyer, then x is excited can be inferred via the universal biconditional elimination rule. There is at least one x for which x is not excited can be inferred via the existential biconditional elimination rule.