Consider the following premises. forall x_2: P_1(x_2) and S_2(x_2). Can we infer ~P_1(a_2) from them?
 From forall x_2: P_1(x_2) and S_2(x_2) we can infer P_1(a_2) and S_2(a_2). Finally, from P_1(a_2) and S_2(a_2) we can infer P_1(a_2), which contradicts ~P_1(a_2). Therefore, the answer is no.