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%%% Sam Lloyd's puzzle with 16 cells and 15 tiles
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%%% Coded by DFP, June 2010,
%%% as required for the by ASP competition 2009
%%% http://dtai.cs.kuleuven.be/events/ASP-competition/Benchmarks/15Puzzle.shtml
%%% by Lengning Liu, Miroslaw Truszczynski, and Martin Gebser
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%%%%% 1   2   3   4   (Y)
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% 1 % 0   1   2   3
% 2 % 4   5   6   7
% 3 % 8   9  10  11
% 4 %12  13  14  15
%(X)%%%%%%%%%%%%%%%%%%

tile(N)  :- interval(N,0,15). %%% entry(N). %%%

        direction(n).
direction(w).   
        direction(s).
                   direction(e).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Action Theory
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

fluent(at(N),0,15) :- tile(N).
action(move(D)) :- direction(D).

%%%%%%%%

executable(move(n), [at(0) geq 4]).
executable(move(s), [at(0) leq 11]).
executable(move(e), [at(0) neq 3,at(0) neq 7,at(0) neq 11,at(0) neq 15]).
executable(move(w), [at(0) neq 0,at(0) neq 4,at(0) neq 8,at(0) neq 12]).

%%%%%%%%%

causes(move(n), at(0) eq at(0)^(-1) - 4, []).
causes(move(s), at(0) eq at(0)^(-1) + 4, []).
causes(move(w), at(0) eq at(0)^(-1) - 1, []).
causes(move(e), at(0) eq at(0)^(-1) + 1, []).

%%%%%%%%%

causes(move(n), at(N) eq at(0)^(-1),[at(N) eq at(0)-4]) :-
       tile(N), N > 0.
causes(move(s), at(N) eq at(0)^(-1),[at(N) eq at(0)+4]) :-
       tile(N), N > 0.
causes(move(e), at(N) eq at(0)^(-1),[at(N) eq at(0)+1]) :-
       tile(N), N > 0.
causes(move(w), at(N) eq at(0)^(-1),[at(N) eq at(0)-1]) :-
      tile(N), N > 0.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%% Expected Goal

goal(at(N) eq N) :- tile(N).

%%%%% Initial state, retrieved from ASP competition input

initially(at(N) eq 4*(X-1) + Y-1 )      :- in0(X,Y,N).


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%%%% Instance  10 moves                            %%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%in0(1,1,1).  in0(1,2,2).  in0(1,3,3).  in0(1,4,7).
%in0(2,1,8).  in0(2,2,4).  in0(2,3,5).  in0(2,4,6).
%in0(3,1,9).  in0(3,2,10).  in0(3,3,0). in0(3,4,11).
%in0(4,1,12). in0(4,2,13). in0(4,3,14). in0(4,4,15).

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Instance  20 moves                            %%%%%%
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

in0(1,1,1).  in0(1,2,2).  in0(1,3,7).  in0(1,4,6).
in0(2,1,8).  in0(2,2,4).  in0(2,3,3).  in0(2,4,11).
in0(3,1,0).  in0(3,2,10).  in0(3,3,5). in0(3,4,15).
in0(4,1,9). in0(4,2,12). in0(4,3,13). in0(4,4,14).


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Instance  .init1 -> 35 moves                  %%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%%%in0(1,1,4).
%%%in0(1,2,0).
%%%in0(1,3,3).
%%%in0(1,4,6).
%%%in0(2,1,12).
%%%in0(2,2,1).
%%%in0(2,3,11).
%%%in0(2,4,7).
%%%in0(3,1,9).
%%%in0(3,2,5).
%%%in0(3,3,10).
%%%in0(3,4,15).
%%%in0(4,1,13).
%%%in0(4,2,8).
%%%in0(4,3,14).
%%%in0(4,4,2).
%%%
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