An Inconsistency

This paper proves an inconsistency in the Peano arithmetic (PA). We show that for a strengthened form of the strong Goldbach conjecture and its negation, assuming either statement implies that we have a proof of that statement. In other words, the paper actually does not solve the conjecture, but it proves that it does. This contradiction is the consequence of two properties of a specific set which we use to reformulate the conjecture.