Consider the following premises. forall x_14: P_6(x_14) or ~P_14(x_14). forall x_14: P_9(x_14). forall x_14: P_14(x_14) or ~U(x_14). forall x_14: P_9(x_14) -> U(x_14). Can we infer exists x_14: ~P_6(x_14) from them? If possible, name the inference rules being used at each step.
 From forall x_14: P_14(x_14) or ~U(x_14) we can infer forall x_14: U(x_14) -> P_14(x_14) via universal rewriting. From forall x_14: P_9(x_14) -> U(x_14), forall x_14: P_9(x_14) we can infer forall x_14: U(x_14) via universal modus ponens. From forall x_14: P_6(x_14) or ~P_14(x_14) we can infer forall x_14: P_14(x_14) -> P_6(x_14) via universal rewriting. From forall x_14: U(x_14) -> P_14(x_14), forall x_14: P_14(x_14) -> P_6(x_14) we can infer forall x_14: U(x_14) -> P_6(x_14) via universal transitivity. Finally, from forall x_14: U(x_14) -> P_6(x_14), forall x_14: U(x_14) we can infer forall x_14: P_6(x_14) via universal modus ponens, which contradicts exists x_14: ~P_6(x_14). Therefore, the answer is no.