Is the unexamined life worth not living?

All life is worth living. Even the individuals who are living so called "examined lives" have not completely examined everything. So to speak if one was to believe in that statement they would essentially be saying that they don't want to live anymore as well, because one can not truly and completely understand or examine the whole aspect of what we call life. I also believe that one's life is whatever it is to oneself. If all one knows is what one truly believes and attains happiness from this thought process, then their life is just as worth living as some one who "examined" more than them. As long as an individual is content or innocently ignorant to the world around him then who is to say that their life is not worth living. This question also nullifies the worth of our past and history in the sense that, since one can not "examine" time (the future) itself then their lives weren't worth living as well. It also dooms us in the present and many more generations to come to the same scrutiny.