Consider the following premises. forall x_7: T(x_7) <-> P(x_7). forall x_7: P(x_7) or ~R(x_7). exists x_7: T(x_7) or R(x_7). Can we infer forall x_7: ~P(x_7) from them?
 From forall x_7: T(x_7) <-> P(x_7) we can infer forall x_7: T(x_7) -> P(x_7). From forall x_7: P(x_7) or ~R(x_7) we can infer forall x_7: R(x_7) -> P(x_7). Finally, from forall x_7: T(x_7) -> P(x_7), forall x_7: R(x_7) -> P(x_7), exists x_7: T(x_7) or R(x_7) we can infer exists x_7: P(x_7), which contradicts forall x_7: ~P(x_7). Therefore, the answer is no.