Consider the following premises. forall x_15: P_15(x_15) or Q_15(x_15). exists x_15: U(x_15) -> S_3(x_15). forall x_15: Q_9(x_15) -> S_3(x_15). forall x_15: U(x_15) or Q_9(x_15). forall x_15: Q_15(x_15) -> S(x_15). forall x_15: P_15(x_15) -> S(x_15). Can we infer forall x_15: ~S(x_15) from them? If possible, name the inference rules being used at each step.
That contradicts the premises. Therefore the answer is no.