Model the following puzzle using a propositional formula. The models of

the formula should represent solutions.

Consider three Calabrian companies Ellebi, Emmedi, Ennegi. The towns

Rossano, Lamezia, Vibo each have one company seat, and each company

has only one seat. We also know that one company produces cement, one

produces caciocavallo, and one produces soppressata; each company only

produces one of the three. Furthermore, it is known that:

$($a$)$ Ellebi does not produce cement.

$($b$)$ Ennegi does not have its seat at Rossano.

$($c$)$ The company at Lamezia does not produce soppressata.

$($d$)$ Emmedi produes caciocavallo.

$($e$)$ The company producing cement is not at Vibo.