Consider the following premises. forall x_12: P(x_12) <-> S_12(x_12). ~w_4. w_4 or ~P(a_12). Can we infer S_12(a_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: P(x_12) <-> S_12(x_12) we can infer P(a_12) <-> S_12(a_12) via universal instantiation. From w_4 or ~P(a_12) we can infer P(a_12) -> w_4 via rewriting. From P(a_12) -> w_4, ~w_4 we can infer ~P(a_12) via modus tollens. Finally, from P(a_12) <-> S_12(a_12), ~P(a_12) we can infer ~S_12(a_12) via biconditional elimination, which contradicts S_12(a_12). Therefore, the answer is no.