Take a look at https://en.wikipedia.org/wiki/Boolean_satisfiability_problem#Schaefer's_dichotomy_theorem https://en.wikipedia.org/wiki/Boolean_satisfiability_pr

Take a look at https://en.wikipedia.org/wiki/Boolean_satisfiability_problem#Schaefer's_dichotomy_theorem https://en.wikipedia.org/wiki/Boolean_satisfiability_problem... (based on Schaefer's "The complexity of satisfiability problems"). Horn clause satisfiability problems (HORN SAT) fall in P-c.