Consider the following premises. forall z_3: P(z_3) -> P_3(z_3). forall z_3: P_3(z_3) or ~P(z_3). forall z_3: P_3(z_3) -> P(z_3). exists z_3: ~P(z_3). Can we infer forall z_3: P_3(z_3) from them?
 From forall z_3: P_3(z_3) or ~P(z_3) we can infer forall z_3: P(z_3) -> P_3(z_3). From forall z_3: P(z_3) -> P_3(z_3), forall z_3: P_3(z_3) -> P(z_3) we can infer forall z_3: P(z_3) <-> P_3(z_3). From forall z_3: P(z_3) <-> P_3(z_3) we can infer forall z_3: P_3(z_3) -> P(z_3). From forall z_3: P(z_3) -> P_3(z_3), forall z_3: P_3(z_3) -> P(z_3) we can infer forall z_3: P(z_3) <-> P_3(z_3). Finally, from forall z_3: P(z_3) <-> P_3(z_3), exists z_3: ~P(z_3) we can infer exists z_3: ~P_3(z_3), which contradicts forall z_3: P_3(z_3). Therefore, the answer is no.