We prove in this paper that there is a language $L_d$ accepted by some nondeterministic Turing machines but not by any ${\rm co}\mathcal{NP}$-machines (defined later). We further show that $L_d$ is in $\mathcal{NP}$, thus proving that $\mathcal{NP}\neq{\rm co}\mathcal{NP}$. The techniques used in this paper are lazy-diagonalization and the novel new technique developed in author's recent work \cite{Lin21}. As a by-product, we reach the important result \cite{Lin21} that $\mathcal{P}\neq\mathcal{NP}$ once again, which is clear from the above outcome and the well-known fact that $\mathcal{P}={\rm co}\mathcal{P}$. Then, we show that the complexity class ${\rm co}\mathcal{NP}$ has intermediate languages. Other direct consequences are also summarized.

翻译：本文证明存在一种语言$L_d$，它能被某些非确定性图灵机接受，但无法被任何${\rm co}\mathcal{NP}$机（定义见后文）接受。我们进一步证明$L_d$属于$\mathcal{NP}$类，从而证实$\mathcal{NP}\neq{\rm co}\mathcal{NP}$。本文采用的技术包括惰性对角化方法以及作者近期工作\cite{Lin21}中提出的创新技术。作为推论，我们再次得到了\cite{Lin21}中的重要结论$\mathcal{P}\neq\mathcal{NP}$，这从上述结果与$\mathcal{P}={\rm co}\mathcal{P}$的已知事实可直接推得。此外，我们证明了复杂度类${\rm co}\mathcal{NP}$存在中间语言。文中亦总结了其他直接推论。