-- Three Dining Cryptographers in SMCDEL

VARS  0,     -- the NSA paid
      1,2,3, -- cryptographer i paid
      4,5,6  -- shared bits/coins

-- exactly one cryptographer or the NSA paid
LAW  AND ( OR (0,1,2,3), ~(0&1), ~(0&2), ~(0&3), ~(1&2), ~(1&3), ~(2&3) )

OBS  alice: 1, 4,5
     bob  : 2, 4,  6
     carol: 3,   5,6

VALID?  (alice,bob,carol) comknow that (OR (0,1,2,3))

VALID?  alice knows whether 1

VALID?
  [?! XOR (1, 4, 5)] -- After everyone announces the
  [?! XOR (2, 4, 6)] -- XOR of whether they paid and
  [?! XOR (3, 5, 6)] -- the coins they see ...
  AND (
    -- if the NSA paid this is common knowledge:
    0 -> (alice,bob,carol) comknow that 0,
    -- if one of the agents paid, the others don't know that:
    1 -> AND (~ bob   knows that 1, ~ carol knows that 1),
    2 -> AND (~ alice knows that 2, ~ carol knows that 2),
    3 -> AND (~ alice knows that 3, ~ bob   knows that 3)
  )