Consider the following premises. forall x_20: R_20(x_20) -> S_20(x_20). t <-> S_20(c_2). t_4 -> R_20(c_2). t -> t_4. Can we infer ~(R_20(c_2) <-> S_20(c_2)) from them?
 From forall x_20: R_20(x_20) -> S_20(x_20) we can infer R_20(c_2) -> S_20(c_2). From t -> t_4, t_4 -> R_20(c_2) we can infer t -> R_20(c_2). From t <-> S_20(c_2) we can infer S_20(c_2) -> t. From S_20(c_2) -> t, t -> R_20(c_2) we can infer S_20(c_2) -> R_20(c_2). 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), which contradicts ~(R_20(c_2) <-> S_20(c_2)). Therefore, the answer is no.