Consider the following premises. forall x_12: ~P_12(x_12). U(e_1) <-> p. forall x_12: T(x_12) <-> U(x_12). forall x_12: P_12(x_12) <-> T(x_12). Can we infer p from them?
 From forall x_12: P_12(x_12) <-> T(x_12), forall x_12: ~P_12(x_12) we can infer forall x_12: ~T(x_12). From forall x_12: T(x_12) <-> U(x_12), forall x_12: ~T(x_12) we can infer forall x_12: ~U(x_12). From forall x_12: ~U(x_12) we can infer ~U(e_1). Finally, from U(e_1) <-> p, ~U(e_1) we can infer ~p, which contradicts p. Therefore, the answer is no.