Consider the following premises. P_1(a_1). forall x_1: W(x_1). Can we infer forall x_1: ~(W(x_1) and P_1(x_1)) from them?
 From P_1(a_1) we can infer exists x_1: P_1(x_1). Finally, from forall x_1: W(x_1), exists x_1: P_1(x_1) we can infer exists x_1: W(x_1) and P_1(x_1), which contradicts forall x_1: ~(W(x_1) and P_1(x_1)). Therefore, the answer is no.