Consider the following premises. forall x_12: R_12(x_12) <-> S_12(x_12). q_6 -> S_12(a_12). R_12(a_12) -> q_6. Can we infer R_12(a_12) <-> S_12(a_12) from them? If possible, name the inference rules being used at each step.
We can infer R_12(a_12) <-> S_12(a_12) via the universal instantiation rule. Therefore, the answer is yes.