How to choose between UC and PL when using the DPLL algorithm? We know DPLL algorithm is backtracking + unit propagation + pure
literal rule.

I have an example. There is one example to solve following Satisfiability problem with DPLL. if assign of "0" to variables is prior to assign "1" to variables, Which of Unit Clause (UC) or Pure Literal (PL) is used to solve this specific example?


  $\{\lnot A \lor B \lor C\}, \{A \lor \lnot B \lor C\}, \{A \lor B \lor \lnot C\}, \{A \lor B \lor C\}$


Olympiad Solution is: PL and UC.

Our Solution is just UC.

Who can satisfy me why Olympiad solution is correct ?!

Unit propagation is not possible as there are no unit clauses.

Pure literal rule is not applicable as there is no literals that occur
only positively or only negatively.

Update:
I think in node (3) we can user PL or UC. Isn't it?
If you use the original specification of the DPLL algorithm, in which the unit rule is applied to a fixed point and then the pure literal rule, then only the unit rule is needed to reach a satisfying assignment.  If the rule order is reversed then the pure literal rule is used to eliminate the final unsatisfied clause.

DPLL is a complete and sound algorithm for deciding Boolean satisfiability even if the pure literal rule is removed.  In practice, pure literals are typically removed only during the preprocessing of a SAT instance, where the formula is simplified as much as possible before beginning recursive search.  This is because detecting pure literals during search is computationally expensive enough to more than offset any expected runtime gains.