Consider the following premises. forall x_2: ~U_4(x_2). forall x_2: P(x_2) -> U_4(x_2). P(a_5) or q. Can we infer ~q from them?
 From forall x_2: P(x_2) -> U_4(x_2), forall x_2: ~U_4(x_2) we can infer forall x_2: ~P(x_2). From forall x_2: ~P(x_2) we can infer ~P(a_5). Finally, from P(a_5) or q, ~P(a_5) we can infer q, which contradicts ~q. Therefore, the answer is no.