"Sorry, but they were excluded from only ONE tree before they sinned. They were free to eat of the life tree."
Yeah, but which one was more appealing to man at the time?
The ability to learn through science, relationships, to ponder who God is, where He came from, whether He created the universe or did some finches do it on some island, or, the latter, to live long in oblivious joy? Man chose the former. Thus, because of satan's pushing towards carnality. the woman would become pregnant and have great birth pains.
Not so...
Genesis 3
1. Now the serpent was more crafty than any of the wild animals the LORD God had made. He said to the woman, "Did God really say, `You must not eat from any tree in the garden'?"
2. The woman said to the serpent, "We may eat fruit from the trees in the garden,
3. but God did say, `You must not eat fruit from the tree that is in the middle of the garden, and you must not touch it, or you will die.'"
4. "You will not surely die," the serpent said to the woman.
5. "For God knows that when you eat of it your eyes will be opened, and you will be like God, knowing good and evil."
Satan tempted her with 'being like GOD'. That is sure NOT 'carnality'!
Satan can only do this - "Did God really say..." - create doubt. Everything we do, against GOD, is because of doubt.
What is unbelief, but doubt.