It doesn't say they were forbidden to eat from the tree of life, true. That doesn't let you assume that they must have.
If they already had eaten from the TOL, why was god so concerned that they would eat from it after eating from the first tree, so concerned that he set up some kind of motion-detecting laser gun to guard it?
Also, do you imagine that eating from the TOL just once gives the supposed immortality, or do you think regular consumption is necessary? If the latter, it is hardly immortality if it is dependent upon the mortality of a tree.
Oh, and to get back on topic, goodness in humanity is innate and has nothing to do with any religion. That should be a no-brainer to everyone.
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