Consider the following premises. S(d) <-> w_2. forall x_8: P_8(x_8) <-> S(x_8). forall x_8: ~P_8(x_8). Can we infer ~w_2 from them?
 From forall x_8: P_8(x_8) <-> S(x_8), forall x_8: ~P_8(x_8) we can infer forall x_8: ~S(x_8). From forall x_8: ~S(x_8) we can infer ~S(d). Finally, from S(d) <-> w_2, ~S(d) we can infer ~w_2. Therefore, the answer is yes.