How can this be settled?

There are only three possibilities:

1. Either man can surrender his claim, letting the other win.
2. They can compromise their differences.
3. They can continue the conflict.

There are no other possibilities.

To solve the problem there are three distinct steps to be taken:

1. Learn the facts.
2. Make a decision.
3. Gain acceptance of the decision.

How are these things to be accomplished?

A peaceful decision can be reached and supported.  A violent decision can be reached and supported.  Or no decision can be accepted.

What is important to recognize is that the fewer the conflicts we have, and the shorter they are in duration, the more we can maximize human well-being.