Improvement

[BertLisser]

-- Permutations have the property that if x is a permutation of y and
-- y is a permutation of z, then x is a permutation of z.
prop4d :: [Int] -> [Int] -> [Int] -> Bool
prop4d x y z
    | isPermutation x y && isPermutation y z && not (isPermutation x z) = False
    | otherwise = True

better

prop4d x y z =  isPermutation x y && isPermutation y z && isPermutation x z

-- Derangements have the property that if x is a derangement of y and y is
-- a derangement of z and x not equal to z, then x is a derangement of z.
prop5d :: [Int] -> [Int] -> [Int] -> Bool
prop5d x y z
    | isDerangement x y && isDerangement y z && not (isDerangement x z) && x /= z = False
    | otherwise = True

Counter example
x=[1,2,3,4] y=[4,3,1,2] y=[3,1,2,4] z= [1,2,4,3] x=[1,2,3,4] z=[1,2,4,3]