Consider the following premises. ~q_6. S_12(a_12) -> q_6. q_6 -> S_12(a_12). forall x_12: W_2(x_12) -> S_12(x_12). Can we infer ~W_2(a_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: W_2(x_12) -> S_12(x_12) we can infer W_2(a_12) -> S_12(a_12) via universal instantiation. From S_12(a_12) -> q_6, q_6 -> S_12(a_12) we can infer S_12(a_12) <-> q_6 via biconditional introduction. From S_12(a_12) <-> q_6, ~q_6 we can infer ~S_12(a_12) via biconditional elimination. Finally, from W_2(a_12) -> S_12(a_12), ~S_12(a_12) we can infer ~W_2(a_12) via modus tollens. Therefore, the answer is yes.