Consider the following premises. forall x_12: P_4(x_12) <-> S_12(x_12). p <-> P_4(a_12). ~q_6. S_12(a_12) -> q_6. Can we infer p from them? If possible, name the inference rules being used at each step.
 From forall x_12: P_4(x_12) <-> S_12(x_12) we can infer P_4(a_12) <-> S_12(a_12) via universal instantiation. From S_12(a_12) -> q_6, ~q_6 we can infer ~S_12(a_12) via modus tollens. From P_4(a_12) <-> S_12(a_12), ~S_12(a_12) we can infer ~P_4(a_12) via biconditional elimination. Finally, from p <-> P_4(a_12), ~P_4(a_12) we can infer ~p via biconditional elimination, which contradicts p. Therefore, the answer is no.