haskell-te: 068fb20e5aa3fd4679b2bac6df80ae6c8d948b13

     1: ;; a + 0 = a
     2: (assert-not (forall ((a Nat))
     3:   (= (plus a constructorZ)
     4:      a)))
     5: 
     6: ;; a * 0 = 0
     7: (assert-not (forall ((a Nat))
     8:   (= (times a constructorZ)
     9:      constructorZ)))
    10: 
    11: ;; a + b = b + a
    12: (assert-not (forall ((a Nat) (b Nat))
    13:   (= (plus a b)
    14:      (plus b a))))
    15: 
    16: ;; (a + b) + c = a + (b + c)
    17: (assert-not (forall ((a Nat) (b Nat) (c Nat))
    18:   (= (plus (plus a b) c)
    19:      (plus a (plus b c)))))
    20: 
    21: ;; (a * b) + (c * b) = (a + c) * b
    22: (assert-not (forall ((a Nat) (b Nat) (c Nat))
    23:   (= (plus (times a b) (times c b))
    24:      (times (plus a c) b))))
    25: 
    26: ;; a + (S b) = S (a + b)
    27: (assert-not (forall ((a Nat) (b Nat))
    28:   (= (plus a (constructorS b))
    29:      (constructorS (plus a b)))))
    30: 
    31: ;; a * (S b) = a + (a * b)
    32: (assert-not (forall ((a Nat) (b Nat))
    33:   (= (times a (constructorS b))
    34:      (plus a (times a b)))))
    35: 
    36: ;; a * b = b * a
    37: (assert-not (forall ((a Nat) (b Nat))
    38:   (= (times a b)
    39:      (times b a))))
    40: 
    41: ;; (a * b) * c = a * (b * c)
    42: (assert-not (forall ((a Nat) (b Nat) (c Nat))
    43:   (= (times (times a b) c)
    44:      (times a (times b c)))))
    45: 
    46: ;; (a * b) + (a * c) = (b + c) * a
    47: (assert-not (forall ((a Nat) (b Nat) (c Nat))
    48:   (= (plus (times a b) (times a c))
    49:      (times (plus b c) a))))
    50: 
    51: ;; (S m) + n = m + (S n)
    52: (assert-not (forall ((n Nat) (m Nat))
    53:   (= (plus (constructorS m) n)
    54:      (plus m (constructorS n)))))
    55: 
    56: ;; x + (y + z) = y + (x + z)
    57: (assert-not (forall ((x Nat) (y Nat) (z Nat))
    58:   (= (plus x (plus y z))
    59:      (plus y (plus x z)))))