Consider the following premises. S_12(a_12) -> p_3. forall x_12: S(x_12) -> S_12(x_12). ~S_12(a_12). p_3 -> S(a_12). Can we infer ~p_3 from them?
 From forall x_12: S(x_12) -> S_12(x_12) we can infer S(a_12) -> S_12(a_12). From p_3 -> S(a_12), S(a_12) -> S_12(a_12) we can infer p_3 -> S_12(a_12). From p_3 -> S_12(a_12), S_12(a_12) -> p_3 we can infer p_3 <-> S_12(a_12). Finally, from p_3 <-> S_12(a_12), ~S_12(a_12) we can infer ~p_3. Therefore, the answer is yes.