What does a square mean in a Boolean formula
Ran's comment is correct. This isn't standard notation in proof complexity (the relevant area of TCS), though it might be standard in SAT solving (the relevant applied area). It stands for the empty disjunction.

Semantically, the empty disjunction is the same as contradiction, but the former is a clause whereas the latter is a formula (or sometimes a constant). The usual symbol for contradiction is $\bot$, read bottom.