Consider the following premises. forall x: W(x). forall x_20: P_3(x_20) and S_20(x_20). Can we infer ~P_3(a_20) from them? If possible, name the inference rules being used at each step.
 From forall x_20: P_3(x_20) and S_20(x_20) we can infer P_3(a_20) and S_20(a_20) via universal instantiation. Finally, from P_3(a_20) and S_20(a_20) we can infer P_3(a_20) via simplification, which contradicts ~P_3(a_20). Therefore, the answer is no.