Consider the following premises. P_17(e) -> p. forall x_17: P_17(x_17) or ~T(x_17). p_3 <-> p. p_3 or T(e). Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From forall x_17: P_17(x_17) or ~T(x_17) we can infer forall x_17: T(x_17) -> P_17(x_17) via universal rewriting. From forall x_17: T(x_17) -> P_17(x_17) we can infer T(e) -> P_17(e) via universal instantiation. From T(e) -> P_17(e), P_17(e) -> p we can infer T(e) -> p via transitivity. From p_3 <-> p we can infer p_3 -> p via biconditional elimination. Finally, from p_3 -> p, T(e) -> p, p_3 or T(e) we can infer p via disjunction elimination, which contradicts ~p. Therefore, the answer is no.