A Method for Constructing Minimally Unsatisfiable CNFs

Ivor Spence[1] has developed an ingenious method for easily generating unsatisfiable 3-cnfs that turn out to be rather difficult for ATPs (automated theorem provers). In this paper, we generalize his construction to cnfs of arbitrary clause length and then show that the unsatisfiable cnfs generated are, usually, “minimally unsatisfiable,” that is, the removal of even one clause results in a satisfiable cnf. We first review Spence’s method in a more general setting and then illustrate this minimality property.