"I do solemnly swear (or affirm) that I will faithfully execute the Office of President of the United States, and will, to the best of my Ability, preserve, protect and defend the Constitution of the United States.

The entire Oath is in two parts:

(1) "Faithfully execute the Office of President of the United States," and

(2) "Will to the best of my ability, preserve, protect and defend the Constitution of the United States."

Whether Linocln violated part (1) or not is of no consequence because we know it is impossible to determine if he did or did not violate part (2). Why?

Because the "best of" Lincoln's ability wsa then and remains today - an unknown.