Consider the following premises. forall x_6: P_6(x_6) <-> W_2(x_6). forall x_6: W(x_6) -> W_2(x_6). exists x_6: ~P_6(x_6). Can we infer forall x_6: W(x_6) from them?
 From forall x_6: P_6(x_6) <-> W_2(x_6), exists x_6: ~P_6(x_6) we can infer exists x_6: ~W_2(x_6). Finally, from forall x_6: W(x_6) -> W_2(x_6), exists x_6: ~W_2(x_6) we can infer exists x_6: ~W(x_6), which contradicts forall x_6: W(x_6). Therefore, the answer is no.