  The radical solution of polynomials with rational coefficients is a famous
solved problem. This paper found that it is a $\mathbb{NP}$ problem.
Furthermore, this paper found that arbitrary $ \mathscr{P} \in \mathbb{P}$
shall have a one-way running graph $G$, and have a corresponding $\mathscr{Q}
\in \mathbb{NP}$ which have a two-way running graph $G'$, $G$ and $G'$ is
isomorphic, i.e., $G'$ is combined by $G$ and its reverse $G^{-1}$. When
$\mathscr{P}$ is an algorithm for solving polynomials, $G^{-1}$ is the radical
formula. According to Galois' Theory, a general radical formula does not exist.
Therefore, there exists an $\mathbb{NP}$, which does not have a general,
deterministic and polynomial time-complexity algorithm, i.e., $\mathbb{P} \neq
\mathbb{NP}$. Moreover, this paper pointed out that this theorem actually is an
impossible trinity.
