I was thinking about a reverse case of validity of resolution rule and had a question about it.
Basically, let me state resolution rule first.
Suppose $C_1$ and $C_2$ are clauses such that a literal $l$ belongs to $C_1$ and a complementary literal $l'$ belongs to $C_2$. Then the resolvant $C$ of $C_1$ and $C_2$ is $(C_1 \cup C_2) \setminus \{l, l'\}$
Now with this rule, we know that always $C_1 \models C$ and $C_2 \models C$.
But, is it always true that $C \models C_1$ and $C \models C_2$?