Well the problem with peace is that once peace comes someone will want to disrupt that peace to create chaos. They may do this unknowingly or they may do this for fun it could happen either way. They may create disorder to see what it looks like without peace, or because they feel it is better to have different opinions in the world.
Another problem with the statement that we are proving wrong is, it depends on what your definition of peace is. The dictionary says that peace is a nonwarring, normal state of the world, and it also says that peace is a state of serenity. I would imagine that if you were in a state of complete serenity that you would be happy but that's just what I think. So I would say that peace itself is possible but not peace with complete and total happiness. It would be a situation like in Logan's Run. If you haven't seen it yet, rent it its a great movie. It is a perfect society after a war but there's still a few people that want to stur up trouble. Everyone in the movie is happy almost all of the time and at the end *everyone* ends up with perfect peace, harmony, happiness, and all the other good and nice emotions you can think of.
As such I think that world peace with happiness is possible but highly unlikely.