Consider the following premises. forall x_8: W_4(x_8) -> W_2(x_8). forall x_8: W_2(x_8) -> P(x_8). forall x_8: P(x_8) -> W_2(x_8). exists x_8: P(x_8). Can we infer forall x_8: ~W_2(x_8) from them?
 From forall x_8: P(x_8) -> W_2(x_8), forall x_8: W_2(x_8) -> P(x_8) we can infer forall x_8: P(x_8) <-> W_2(x_8). From exists x_8: P(x_8) we can infer exists x_8: P(x_8) or W_4(x_8). From forall x_8: P(x_8) <-> W_2(x_8) we can infer forall x_8: P(x_8) -> W_2(x_8). Finally, from forall x_8: P(x_8) -> W_2(x_8), forall x_8: W_4(x_8) -> W_2(x_8), exists x_8: P(x_8) or W_4(x_8) we can infer exists x_8: W_2(x_8), which contradicts forall x_8: ~W_2(x_8). Therefore, the answer is no.