Consider the following premises. forall x_10: ~P_5(x_10). exists x_10: P_5(x_10) <-> P_10(x_10). forall x_10: P_10(x_10) or ~P(x_10). Can we infer forall x_10: P(x_10) from them?
 From forall x_10: P_10(x_10) or ~P(x_10) we can infer forall x_10: P(x_10) -> P_10(x_10). From exists x_10: P_5(x_10) <-> P_10(x_10), forall x_10: ~P_5(x_10) we can infer exists x_10: ~P_10(x_10). Finally, from forall x_10: P(x_10) -> P_10(x_10), exists x_10: ~P_10(x_10) we can infer exists x_10: ~P(x_10), which contradicts forall x_10: P(x_10). Therefore, the answer is no.