Definition: A minimal 3CNF formula is an unsatisfiable 3CNF formula with minimum clauses connected by conjunctions, where each clause is disjunction of 3 literals, that is if any of it's clauses is removed from the formula, then the 3CNF formula becomes satisfiable.
For some natural number n, where n is the number of atomic variables, what is the set of all minimal 3CNF formulas? Is it finite? If it is finite then what is it's cardinality, i.e. how many different minimal 3CNF formulas is possible?
In a minimal k-cnf formula, there should be 2k different k literals clauses exactly, so in a minimal 3CNF formula, there should be 23=8 different 3 literals clauses exactly.
That's what I think anyway, but correct me if I am wrong.
Note that for k-cnf formula n≥k, so in 3CNF formula n≥3.