By generating a very simple example of unsolvability in polynomial time in a well-known NP-complete problem, it is proven that the classes P and NP do not coincide in this work. A random process is built for a specific NP-complete issue that provides solutions with random numbers. The assumption that a concrete NP-complete problem belongs to the P class is demonstrated to be incompatible with the random and independent selection of a concrete solution to the problem. A polynomial method cannot find such a solution, but it can be confirmed with one if it is known. The impossibility of equivalence P = NP is demonstrated in this way.

**Author(S) Details**

**Peter Kopanov
**Faculty of Mathematics, Plovdiv University, 4000 Plovdiv, Bulgaria.

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