Consider the predicate $($relation$)$ symbols G$,$ U$,$ H$,$ L with arities $1,$

$1,1,2,$ respectively, and a universe in which these predicates have the following meaning

G$($u$)$ : $$u is a ghost$$

U$($u$)$ : $$u is unhappy$$

H$($u$)$ : $$u is a house in the village$$

L$($u$,$v$)$ : $$u lives in v$.$

Consider also the following statements, where tim is a constant.

$\backslash$beta $0$ : $$tim is a ghost.$$

$\backslash$beta $1$ : $$No ghost is happy.$$

$\backslash$beta $2$ : $$There is a house in this village where only ghosts live.$$

$\backslash$beta $3$ : $$There is an unhappy resident in this village.$$

$\backslash$beta $4$ : $$tim is happy.$$