Consider the following premises. forall x_15: Q(x_15) -> P(x_15). forall x_15: ~P(x_15). forall x_15: P_15(x_15) <-> P(x_15). exists x_15: Q(x_15) or P_15(x_15). Can we infer exists x_15: T_2(x_15) from them?
 From forall x_15: P_15(x_15) <-> P(x_15) we can infer forall x_15: P_15(x_15) -> P(x_15). From forall x_15: Q(x_15) -> P(x_15), forall x_15: P_15(x_15) -> P(x_15), exists x_15: Q(x_15) or P_15(x_15) we can infer exists x_15: P(x_15). From exists x_15: P(x_15) we can infer exists x_15: P(x_15) or T_2(x_15). Finally, from exists x_15: P(x_15) or T_2(x_15), forall x_15: ~P(x_15) we can infer exists x_15: T_2(x_15). Therefore, the answer is yes.