max expr size = 4 |- on ineqs = 3 |- on conds = 3 max #-tests = 500 min #-tests = 25 (to consider p ==> q true) max #-vars = 2 (for inequational and conditional laws) _ :: Bool False :: Bool True :: Bool not :: Bool -> Bool (&&) :: Bool -> Bool -> Bool (||) :: Bool -> Bool -> Bool (==) :: Bool -> Bool -> Bool (p && p) == p (p || p) == p not (not p) == p (p && True) == p (p || False) == p (p == p) == True (p == True) == p (p && False) == False (p || True) == True (p && not p) == False (p || not p) == True (p == False) == not p (p && q) == (q && p) (p || q) == (q || p) (p == not q) == not (p == q) p ==> True False ==> p p ==> p || q p && q ==> p p && q ==> p == q