Consider the following premises. t <-> S_20(c_2). t_4 -> R_20(c_2). forall x_20: R_20(x_20) -> S_20(x_20). t -> t_4. Can we infer ~(R_20(c_2) <-> S_20(c_2)) 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(c_2) -> S_20(c_2) via universal instantiation. From t -> t_4, t_4 -> R_20(c_2) we can infer t -> R_20(c_2) via transitivity. From t <-> S_20(c_2) we can infer S_20(c_2) -> t via biconditional elimination. From S_20(c_2) -> t, t -> R_20(c_2) we can infer S_20(c_2) -> R_20(c_2) via transitivity. Finally, from R_20(c_2) -> S_20(c_2), S_20(c_2) -> R_20(c_2) we can infer R_20(c_2) <-> S_20(c_2) via biconditional introduction, which contradicts ~(R_20(c_2) <-> S_20(c_2)). Therefore, the answer is no.