How can resolution be applied to prove this statement is satisfiable

Question

Use resolution to show that the compound proposition (p ∨ q) ∧ (¬p ∨ q) ∧ (p ∨ ¬q) ∧ (¬p ∨¬q) is not satisfiable? I have solved this by taking the first two and the last two using resolution and got F However can't I take the first and last one (p ∨ q)∧ (¬p ∨¬q) and get (q v -q) = T and the middle two and also get T making the statement true?

Answer 1

As it is asked to use resolution, here is a very simple proof:

$$\begin{matrix} \text{(p ∨ q)} & & \text{(¬p ∨ q)} & & \text{(p ∨ ¬q)} & & \text{(¬p ∨¬q)}\\ \searrow &&\swarrow && \searrow && \swarrow\\ &\text{q}&&&&\text{¬q}&\\ &&\searrow &&\swarrow && \\ &&&\square&&& \end{matrix}$$

where two successive arrows like this $\searrow \ \swarrow$ mean "resolution" and $\square$ means "false".

Therefore you do not need to make a separate treatment with the first pair and then the second pair.