Consider the following premises. forall x_13: S(x_13) -> ~W_2(x_13). forall x_13: P_13(x_13). exists x_13: P_13(x_13) <-> W_2(x_13). Can we infer exists x_13: ~S(x_13) from them? If possible, name the inference rules being used at each step.
 From exists x_13: P_13(x_13) <-> W_2(x_13) we can infer exists x_13: P_13(x_13) -> W_2(x_13) via existential biconditional elimination. From exists x_13: P_13(x_13) -> W_2(x_13), forall x_13: P_13(x_13) we can infer exists x_13: W_2(x_13) via existential modus ponens. Finally, from forall x_13: S(x_13) -> ~W_2(x_13), exists x_13: W_2(x_13) we can infer exists x_13: ~S(x_13) via existential modus tollens. Therefore, the answer is yes.