You made it say as if "Natural Law" wasn't invented by man. It is. Maybe it's more ancient/low_level/basic but still it's invented by man. Similarly institutions/goverments and constitutions are invented by man.

And as both are man-made I don't see any contradiction by one overruling another. It's just a convention we made up.

That is the problem with death penalty. It's an ultimate tool to silence inconvenient people forever.

Without death penalty if you set up someone and send them to jail (think dictator states) you risk getting exposed somewhere in the future. It introduces some back-pressure to the oppressive state.

And that is the reason why I am against death penalty. It's just a too powerful tool for dictator wannabes.