Consider the following premises. forall x_3: S_4(x_3) -> T(x_3). forall x_3: U(x_3) -> S_4(x_3). ~T(j_4). T(j_4) <-> U(j_4). Can we infer U(j_4) from them? If possible, name the inference rules being used at each step.
 From forall x_3: U(x_3) -> S_4(x_3), forall x_3: S_4(x_3) -> T(x_3) we can infer forall x_3: U(x_3) -> T(x_3) via universal transitivity. From forall x_3: U(x_3) -> T(x_3) we can infer U(j_4) -> T(j_4) via universal instantiation. From T(j_4) <-> U(j_4) we can infer T(j_4) -> U(j_4) via biconditional elimination. From U(j_4) -> T(j_4), T(j_4) -> U(j_4) we can infer U(j_4) <-> T(j_4) via biconditional introduction. Finally, from U(j_4) <-> T(j_4), ~T(j_4) we can infer ~U(j_4) via biconditional elimination, which contradicts U(j_4). Therefore, the answer is no.