Consider the following premises. u_4. forall x_11: P(x_11) <-> S_11(x_11). ~S_11(a_11). Can we infer ~P(a_11) and u_4 from them? If possible, name the inference rules being used at each step.
 From forall x_11: P(x_11) <-> S_11(x_11) we can infer P(a_11) <-> S_11(a_11) via universal instantiation. From P(a_11) <-> S_11(a_11), ~S_11(a_11) we can infer ~P(a_11) via biconditional elimination. Finally, from ~P(a_11), u_4 we can infer ~P(a_11) and u_4 via conjunction. Therefore, the answer is yes.