/* 

  The Fifth Trial (Smullyan) puzzle in Picat.

  From Martin Chlond Integer Programming Puzzles:
  http://www.chlond.demon.co.uk/puzzles/puzzles3.html, puzzle nr. 7.
  Description  : The Fifth Trial
  Source       : Smullyan, R., (1991), The Lady or The Tiger, Oxford University Press

  This model was inspired by the XPress Mosel model created by Martin Chlond.
  http://www.chlond.demon.co.uk/puzzles/sol3s7.html


  This program was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.

go =>
  Door = 2,
  Prize = 2,	% 1 = Lady, 2 = Tiger

  D = 1..Door,
  P = 1..Prize,

  % x(i,j) = 1 if door i hides prize j, else 0
  X = new_array(Door,Prize),
  X :: 0..1,

  % t(i) = 1 if statement on door i is true, else 0
  T = new_list(Door),
  T :: 0..1,

  % each door hides 1 prize
  foreach(I in D)
    sum([X[I,J] : J in P]) #= 1
  end,

  % if door i hides prize i then statement i is true else false
  foreach(I in D) 
     X[I,I] = T[I]
  end,
  
  % if statement on door 1 is true [i.e. x[1,1]+x[2,1]>=2] then set t[1] = 1, else t[1] = 0
  X[1,1]+X[2,1]-T[1] #<= 0,
  X[1,1]+X[2,1]-T[1] #>= 0,

  % if statement on door 2 is true then set t[2] = 1, else t[2] = 0
  X[1,1] #= T[2],

  Vars = X.vars ++ T,
  solve(Vars),

  println(x=X),
  println(t=T),
  fail,
  
  nl.