English: Two example runs of the Davis-Putnam procedure.

Left: The formula ${\displaystyle (a\lor b\lor c)\land (b\lor \lnot c\lor \lnot f)\land (\lnot b\lor e)}$ is satisfiable: starting from the given formula (top row), resolving each possible clause pair on the variable ${\displaystyle b}$ yields the middle row, then resolving each pair on ${\displaystyle c}$ yields the bottom row ${\displaystyle a\lor e\lor \lnot f}$. Since no further resolution steps are possible, the algorithm stops; since the empty clause couldn't be derived, the result is "satisfiable". In fact, instantiating e.g. ${\displaystyle a=b=e={\textit {true}}}$ will make the original formula ${\displaystyle {\textit {true}}}$.

Right: The formula ${\displaystyle (a\lor b)\land (a\lor \lnot b)\land (\lnot a\lor c)\land (\lnot a\lor \lnot c)}$ is unsatisfiable: starting from the given formula (top row), resolving all pairs on ${\displaystyle b}$, then on ${\displaystyle a}$, then on ${\displaystyle c}$ yields the 2nd, 3rd, and 4th row from above, respectively. Since the latter is the empty clause, the algorithm halts with result "unsatisfiable". In fact, each row is a consequence of the row above it, and the bottom row denotes ${\displaystyle {\textit {false}}}$, which certainly cannot be satisfied.