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: forall x: ~P_1(x). exists x: P_1(x) <-> S(x). forall x: S(x) -> P_1(x).
forall x: ~S(x) can be inferred via the universal modus tollens rule. exists x: P_1(x) -> S(x) can be inferred via the existential biconditional elimination rule. exists x: S(x) -> P_1(x) can be inferred via the existential biconditional elimination rule. exists x: ~S(x) can be inferred via the existential biconditional elimination rule.