Consider the following sentence:

$[()()][()]$

$1.$ Determine, using enumeration, whether this sentence is valid, satisfiable $($but not valid$),$ or

unsatisfiable. $(5$ points$)$

$2.$ Convert the left$-$hand and right$-$hand sides of the main implication into CNF$,$ showing each

step, and explain how the results confirm your answer to $(1).(5$ points$)$

$3.$ Prove your answer to $(2)$ using resolution. $(10$ points$)$