Consider the following premises. forall x_7: S(x_7) <-> S_7(x_7). p_1 <-> S_7(f). ~q. p_1 <-> q. Can we infer S(f) from them? If possible, name the inference rules being used at each step.
 From p_1 <-> q, ~q we can infer ~p_1 via biconditional elimination. From forall x_7: S(x_7) <-> S_7(x_7) we can infer S(f) <-> S_7(f) via universal instantiation. From p_1 <-> S_7(f), ~p_1 we can infer ~S_7(f) via biconditional elimination. Finally, from S(f) <-> S_7(f), ~S_7(f) we can infer ~S(f) via biconditional elimination, which contradicts S(f). Therefore, the answer is no.