Consider the following premises. w_3. forall x_4: ~S_1(x_4). forall x_4: W(x_4) -> S_1(x_4). forall x_4: W(x_4) or P(x_4). Can we infer ~P(g) from them?
 From forall x_4: W(x_4) -> S_1(x_4), forall x_4: ~S_1(x_4) we can infer forall x_4: ~W(x_4). Finally, from forall x_4: W(x_4) or P(x_4), forall x_4: ~W(x_4) we can infer forall x_4: P(x_4), which contradicts ~P(g). Therefore, the answer is no.