Consider the following premises. forall x_25: P_25(x_25). forall x_18: P_18(x_18). forall x_25: P_25(x_25) <-> R_2(x_25). Can we infer ~P_18(a_18) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.