Consider the following premises. forall x_13: T(x_13) or S_13(x_13). T(a) <-> s_3. S_13(a) <-> s_3. Can we infer ~s_3 from them? If possible, name the inference rules being used at each step.
 From forall x_13: T(x_13) or S_13(x_13) we can infer T(a) or S_13(a) via universal instantiation. From T(a) <-> s_3 we can infer T(a) -> s_3 via biconditional elimination. From S_13(a) <-> s_3 we can infer S_13(a) -> s_3 via biconditional elimination. Finally, from T(a) -> s_3, S_13(a) -> s_3, T(a) or S_13(a) we can infer s_3 via disjunction elimination, which contradicts ~s_3. Therefore, the answer is no.