# Clarification on “clause learning” in DPLL algorithm

I am struggling to understand the idea of conflict-driven clause learning, in particular, I can not understand why the clause we ‘learned’ is a substantially new (i.e. the clause database does not already contain it, neither any subset of it). Here is what Knuth in his book says:

I can understand why the clause database has no subset of $$c’$$ that contains $$\overline{l’}$$ (because $$\overline{l’}$$ would have been forced (i.e. unit-propagated) at level lower than $$d$$), but what contradicts to the existence of clause, let’s say, $$\overline{b_1}\lor\overline{b_2}$$?