Consider the following premises. forall x_8: S_4(x_8) or ~Q(x_8). exists x_8: W_2(x_8). forall x_8: S_4(x_8) -> ~W_2(x_8). Can we infer exists x_8: ~Q(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: S_4(x_8) -> ~W_2(x_8), exists x_8: W_2(x_8) we can infer exists x_8: ~S_4(x_8) via existential modus tollens. From forall x_8: S_4(x_8) or ~Q(x_8) we can infer forall x_8: Q(x_8) -> S_4(x_8) via universal rewriting. Finally, from forall x_8: Q(x_8) -> S_4(x_8), exists x_8: ~S_4(x_8) we can infer exists x_8: ~Q(x_8) via existential modus tollens. Therefore, the answer is yes.