No. The First Parents disobeyed the one and only rule that they were given by God. “Thou shalt not eat...”
By that disobedience they lost their communion with the Creator. Every person born into the world has the same opportunity as did Adam and Eve - to obey or disobey.
It’s harder for us, I would say, because sin is all around us and temptation everywhere. But, we still have free will to chose.
That is what I was saying. War is not the produce of original sin. Individual choice is the produce of original sin.