@Lusario
The system saves the information about all skills he comes into contact with whether he has trained them or not.
There is a mistake on your point.
The system doesn't automatically save skills he comes in contact with.
He do have to train them the conventional way at last to introductory levels (level 0) before they are saved on the system.
This is his whole plan with the humam bomb skill. He learned it, but didn't train, so it is not part of the system.
He went to the lower world because once he saves it on the system, he can't remove them. And if he couldn't level up it, he would be under the control of people with higher level.
But skills saved on the system on lower worlds are removed if the quest fails.
This is proved by the fact that he did learn the humam bomb skill on the main world, but it wasn't saved. He had to train it, and he did that on the lower world to be able to get rid of it, if he couldn't level up because it was incomplete, wich is exactly what happened.
Notice that the pentand can make people figure out complete skills out of incomplete parts of it, that is why he won't give up the quest.