The wall and the man

There is this wall; the one thing that is true about this wall is that it cannot be climbed. There is this man; the one thing that is true about this man is that he can climb any wall. What would happen when the man attempted to climb the wall? It is a paradox as both cannot be true at the same time. If the man climbs the wall then the wall is climbable. If the man cannot climb the wall then the man cannot climb any wall.

My personal answer to this paradox is that they both cannot exist in the same universe. If the man goes into the universe of the wall then he cannot climb it. If the wall enters the universe of the man then he can climb it.

What if it is in the same universe can it exist? An answer is maybe, if the rules changed depending on creation. Such as in our universe something can be made and sold as unbeatable yet beaten later on. If this is the case both would be true but one would become false. It could be chosen on when they was created.

If one were true and the other false which one would win? The wall, if it did indeed like being wrote down came first, then the man should have attempted to climb it before being named the man who can climb any wall. Therefore the man is true and the wall is false. But the wall is not a living object and therefore unless given that title in error. The man could have failed and said he climbed it, therefore making the man false and the wall true.

What do you think?