% Hamiltonian path, adapted from Eyelet's input/hamiltonian-path.pl.
%
% The graph is the same six-vertex undirected graph.  Eyelog spells the finite
% vertex set directly and derives every path that visits each vertex exactly
% once.

memoize(adjacent, 2).

edge(v1, v2).
edge(v1, v3).
edge(v1, v5).
edge(v1, v6).
edge(v2, v3).
edge(v2, v4).
edge(v2, v6).
edge(v3, v4).
edge(v3, v6).
edge(v4, v5).
edge(v4, v6).

adjacent(V, U) :- edge(V, U).
adjacent(V, U) :- edge(U, V).

vertex(v1).
vertex(v2).
vertex(v3).
vertex(v4).
vertex(v5).
vertex(v6).

hamiltonian_path([A, B, C, D, E, F]) :-
  vertex(A),
  vertex(B), adjacent(A, B), not_member(B, [A]),
  vertex(C), adjacent(B, C), not_member(C, [A, B]),
  vertex(D), adjacent(C, D), not_member(D, [A, B, C]),
  vertex(E), adjacent(D, E), not_member(E, [A, B, C, D]),
  vertex(F), adjacent(E, F), not_member(F, [A, B, C, D, E]).

triple(graph, hasHamiltonianPath, true) :-
  hamiltonian_path(_Path).

triple(graph, hamiltonianPath, Path) :-
  hamiltonian_path(Path).