Consider the following premises. forall x_6: P(x_6) -> Q_6(x_6). forall x_6: W(x_6) -> S(x_6). exists x_6: Q_6(x_6) -> W(x_6). forall x_6: ~S(x_6). Can we infer exists x_6: ~P(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P(x_6) -> Q_6(x_6), exists x_6: Q_6(x_6) -> W(x_6) we can infer exists x_6: P(x_6) -> W(x_6) via existential transitivity. From forall x_6: W(x_6) -> S(x_6), forall x_6: ~S(x_6) we can infer forall x_6: ~W(x_6) via universal modus tollens. Finally, from exists x_6: P(x_6) -> W(x_6), forall x_6: ~W(x_6) we can infer exists x_6: ~P(x_6) via existential modus tollens. Therefore, the answer is yes.