Consider the following premises. forall x_10: P(x_10). forall x_10: P_10(x_10) <-> Q_10(x_10). forall x_10: ~Q_10(x_10). forall x_10: P_10(x_10). Can we infer exists x_10: ~(P(x_10) and Q_5(x_10)) from them? If possible, name the inference rules being used at each step.
The premises are contradictory and we can infer anything from them. Therefore, the answer is yes.