unit clause

A unit clause is any clause that contains only a single literal:

$$\neg Q,(P\vee Q),(\neg P\vee \neg R\vee S),(\neg P\vee Q\vee \neg S),(\neg P\vee \neg Q),R,(Q\vee R\vee S)$$

We have no choice in the assignment of unit clauses:

$$Q:=\perp ,R:=\top$$

We can now eliminate these literals:

$$\cancel{\neg Q},(P\vee Q),(\neg P\vee \neg R\vee S),(\neg P\vee Q\vee \neg S),\cancel{(\neg P\vee \neg Q)},\cancel{R},\cancel{(Q\vee R\vee S)}$$

Furthermore, we can simplify the remaining clauses:

$$P,(\neg P\vee S),(\neg P\vee \neg S)$$

We may find this leads to further assignments, repeating the process, we find:

$$\begin{array}{c}P=\top \\ \cancel{P},(\neg P\vee S),(\neg P\vee \neg S)\\ S,\neg S\end{array}$$