Here's a counterexample.

Sequence is [1, 2, 3, 4, 6, 6, 7, 8, 9, 10] so m = 5 and d = 6

  diff = 5-6 = -1
  xor = 5^6 = 3

  1-2 = -1
  1^2 = 3

  5-6 = -1
  5^6 = 3

  9-10 = -1
  9^10 = 3

So three different combinations, within N, that obey the two constraints