Consider the following premises. forall y_4: S_1(y_4) <-> Q(y_4). q <-> q_11. Q(a_7) -> q. ~q_11. Can we infer S_1(a_7) from them? If possible, name the inference rules being used at each step.
 From q <-> q_11, ~q_11 we can infer ~q via biconditional elimination. From forall y_4: S_1(y_4) <-> Q(y_4) we can infer S_1(a_7) <-> Q(a_7) via universal instantiation. From Q(a_7) -> q, ~q we can infer ~Q(a_7) via modus tollens. Finally, from S_1(a_7) <-> Q(a_7), ~Q(a_7) we can infer ~S_1(a_7) via biconditional elimination, which contradicts S_1(a_7). Therefore, the answer is no.