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Two theorems about the P versus NP problem be proved in this article (1)There exists a language $L$, that the statement $L \in \textbf{P}$ isindependent of ZFC. (2) There exists a language $L \in \textbf{NP}$, for anypolynomial time deterministic Turing machine $M$, we cannot prove $L$ isdecidable on $M$.