Consider the following premises. t. ~s. forall x_17: Q_17(x_17) -> S(x_17). forall x_17: S(x_17) -> Q_17(x_17). S(g_2) <-> s. Can we infer ~Q_17(g_2) and t from them? If possible, name the inference rules being used at each step.
 From forall x_17: S(x_17) -> Q_17(x_17), forall x_17: Q_17(x_17) -> S(x_17) we can infer forall x_17: S(x_17) <-> Q_17(x_17) via universal biconditional introduction. From forall x_17: S(x_17) <-> Q_17(x_17) we can infer S(g_2) <-> Q_17(g_2) via universal instantiation. From S(g_2) <-> s, ~s we can infer ~S(g_2) via biconditional elimination. From S(g_2) <-> Q_17(g_2), ~S(g_2) we can infer ~Q_17(g_2) via biconditional elimination. Finally, from ~Q_17(g_2), t we can infer ~Q_17(g_2) and t via conjunction. Therefore, the answer is yes.