Consider the following premises. forall x_11: P_11(x_11) <-> Q_11(x_11). forall x_11: P_3(x_11). forall x_11: P_7(x_11) -> P_11(x_11). forall x_11: P_7(x_11) or Q_11(x_11). Can we infer ~P_3(a_2) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.