Consider the following premises. ~t. t or ~U(a_12). forall x_12: U(x_12) <-> S_12(x_12). Can we infer S_12(a_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: U(x_12) <-> S_12(x_12) we can infer U(a_12) <-> S_12(a_12) via universal instantiation. From t or ~U(a_12) we can infer U(a_12) -> t via rewriting. From U(a_12) -> t, ~t we can infer ~U(a_12) via modus tollens. Finally, from U(a_12) <-> S_12(a_12), ~U(a_12) we can infer ~S_12(a_12) via biconditional elimination, which contradicts S_12(a_12). Therefore, the answer is no.