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) _ :: Int 0 :: Int 1 :: Int id :: Int -> Int abs :: Int -> Int negate :: Int -> Int (+) :: Int -> Int -> Int (*) :: Int -> Int -> Int id x == x negate (negate x) == x x + 0 == x x * 1 == x x * 0 == 0 abs (abs x) == abs x abs (negate x) == abs x x + negate x == 0 x + y == y + x x * y == y * x abs (x * x) == x * x x * negate y == negate (x * y) x <= abs x 0 <= abs x x <= x * x x <= x + 1 0 <= x * x negate x <= abs x negate (abs x) <= x negate (abs x) <= 0 abs x <= x * x negate (abs x) <= negate x