So.. Please tell me where my logic breaks down...

1) Adam and Eve have kids.

2) Adam and Eve commit the first sin.

3) All the sons and daughters of them are cursed.

4) Cain goes to somewhere east of eden and marries Lilith.

5) Lilith is from another tribe.. Not named by god, but there is other humans on the planet.

6) We presume Cain and Lilith had kids.

7) It's safe to say that other people in the tribe also had kids.

8) Therefore, it's possible that women who didn't have kids with Cain gave birth to people who didn't have original sin.

9) This may mean that Jesus dying on the cross for original sin was invalid because it's possible that no one left alive had it.