Consider the following premises. q <-> q_15. q_15 or ~W_1(h). forall x_12: W_1(x_12) <-> S_12(x_12). ~q. Can we infer ~S_12(h) from them? If possible, name the inference rules being used at each step.
 From q <-> q_15, ~q we can infer ~q_15 via biconditional elimination. From forall x_12: W_1(x_12) <-> S_12(x_12) we can infer W_1(h) <-> S_12(h) via universal instantiation. From q_15 or ~W_1(h) we can infer W_1(h) -> q_15 via rewriting. From W_1(h) -> q_15, ~q_15 we can infer ~W_1(h) via modus tollens. Finally, from W_1(h) <-> S_12(h), ~W_1(h) we can infer ~S_12(h) via biconditional elimination. Therefore, the answer is yes.