Consider the following premises. S_20(a_20) -> q. forall x_20: R_20(x_20) -> S_20(x_20). q -> q_11. q_11 -> s_2. s_2 -> R_20(a_20). Can we infer ~(R_20(a_20) <-> q) from them? If possible, name the inference rules being used at each step.
 From forall x_20: R_20(x_20) -> S_20(x_20) we can infer R_20(a_20) -> S_20(a_20) via universal instantiation. From q -> q_11, q_11 -> s_2 we can infer q -> s_2 via transitivity. From R_20(a_20) -> S_20(a_20), S_20(a_20) -> q we can infer R_20(a_20) -> q via transitivity. From q -> s_2, s_2 -> R_20(a_20) we can infer q -> R_20(a_20) via transitivity. Finally, from R_20(a_20) -> q, q -> R_20(a_20) we can infer R_20(a_20) <-> q via biconditional introduction, which contradicts ~(R_20(a_20) <-> q). Therefore, the answer is no.