Consider the following premises. forall x_6: P_6(x_6) or T(x_6). forall x_6: ~P_6(x_6) or U(x_6). forall x_6: U(x_6) -> P(x_6). forall x_6: T(x_6) -> P(x_6). Can we infer ~P(e) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) or T(x_6), forall x_6: ~P_6(x_6) or U(x_6) we can infer forall x_6: T(x_6) or U(x_6) via universal resolution. Finally, from forall x_6: T(x_6) -> P(x_6), forall x_6: U(x_6) -> P(x_6), forall x_6: T(x_6) or U(x_6) we can infer forall x_6: P(x_6) via universal disjunction elimination, which contradicts ~P(e). Therefore, the answer is no.