Separation of P and NP

There have been many attempts to solve the P versus NP problem. However, with a new proof method, already used in arXiv:2104.14316, P not equal NP can be proved. A time limit is set for an arbitrary Turing machine and an input word is rejected on a timeout. The time limit goes toward infinity. Due to the halting problem, whether a word is accepted can only be determined at runtime. It can be shown by Rice's theorem, if a finite set of words are to be checked, they all have to be tested by brute force.