oddeven.out

max expr size  =    5
  |- on ineqs  =    4
  |- on conds  =    4
max  #-tests   =  500
min  #-tests   =   25  (to consider p ==> q true)
max  #-vars    =    2  (for inequational and conditional laws)

_ :: Bool  (holes: Bool)
_ :: Int  (holes: Int)
0 :: Int
1 :: Int
2 :: Int
False :: Bool
True :: Bool
odd :: Int -> Bool
even :: Int -> Bool
mod :: Int -> Int -> Int
(==) :: Int -> Int -> Bool
(==) :: Bool -> Bool -> Bool

           (p == p) == True
        (p == True) == p
           (x == x) == True
           (x == y) == (y == x)
    odd (x `mod` 2) == odd x
   even (x `mod` 2) == even x
   (False == odd x) == even x
  (False == even x) == odd x
  (odd x == even x) == False
   (2 == x `mod` 2) == False
   (0 == x `mod` 2) == even x
   (1 == x `mod` 2) == odd x
  (even x == odd y) == (odd x == even y)
 (even x == even y) == (odd x == odd y)
          x `mod` 1 == 0
(x `mod` 2) `mod` 2 == x `mod` 2

        p ==> True
    False ==> p
   x == 0 ==> even x
   x == 1 ==> odd x
   x == 2 ==> even x
x `mod` 2 <=  2
        0 <=  x `mod` 2
x `mod` 2 <=  1

 odd x ==>           x `mod` x == 0
 odd x ==>           0 `mod` x == 0
 odd x ==>           x `mod` 2 == 1
 odd y ==> (x `mod` y) `mod` y == x `mod` y
even x ==>           x `mod` 2 == 0