For certain UNSAT formulas the solver still says there is one solution. The simplest UNSAT formula, where this happens is just the following two line DIMACS file
p cnf 0 0
0
but also if you have two conflicting unit clauses the same issue occurs, i.e.,
p cnf 1 2
1 0
-1 0
I think this is corner case though, where the formula becomes UNSAT during parsing, since for larger UNSAT formulas which really require search, I have not seen this issue.
For certain UNSAT formulas the solver still says there is one solution. The simplest UNSAT formula, where this happens is just the following two line DIMACS file
p cnf 0 0
0
but also if you have two conflicting unit clauses the same issue occurs, i.e.,
p cnf 1 2
1 0
-1 0
I think this is corner case though, where the formula becomes UNSAT during parsing, since for larger UNSAT formulas which really require search, I have not seen this issue.