Consider the following premises. exists x_8: P_8(x_8) or W(x_8). forall x_8: P_2(x_8) or ~W(x_8). forall x_8: ~P_8(x_8). Can we infer forall x_8: ~P_8(x_8) from them?
That is one of the premises. Therefore, the answer is yes.