Consider the following premises. u_4 <-> s_3. forall x_12: R_12(x_12) <-> S_12(x_12). s_3 <-> S_12(a_4). ~R_12(a_4). Can we infer u_4 from them? If possible, name the inference rules being used at each step.
 From forall x_12: R_12(x_12) <-> S_12(x_12) we can infer R_12(a_4) <-> S_12(a_4) via universal instantiation. From R_12(a_4) <-> S_12(a_4), ~R_12(a_4) we can infer ~S_12(a_4) via biconditional elimination. From s_3 <-> S_12(a_4), ~S_12(a_4) we can infer ~s_3 via biconditional elimination. Finally, from u_4 <-> s_3, ~s_3 we can infer ~u_4 via biconditional elimination, which contradicts u_4. Therefore, the answer is no.