I think I'm getting close.

Snake-in-the-Box/snake.lp

@@ -0,0 +1,52 @@
+
+%% Instance
+
+% The total number of bits, as individual labels.
+% Enough has changed that I'm not 100% certain this phase is necessary.
+bits(a, b, c).
+
+bit(A) :- bits(A, B, C).
+bit(B) :- bits(A, B, C).
+bit(C) :- bits(A, B, C).
+
+% Generate all possible vertices.
+vertex(T, U, V) :- bits(A, B, C), value(T), value(U), value(V).
+
+% Assignments are binary.
+value(0 ; 1).
+
+% Define adjacency
+adjacent((T, U, V) , (W, X, Y)) :- vertex(T, U, V), vertex(W, X, Y),
+																	 T < W, U == X, V == Y.
+adjacent((T, U, V) , (W, X, Y)) :- vertex(T, U, V), vertex(W, X, Y),
+																	 T == W, U < X, V == Y.
+adjacent((T, U, V) , (W, X, Y)) :- vertex(T, U ,V), vertex(W, X, Y),
+																	 T == W, U =  X, V < Y.
+
+%% Defining Paths
+
+% Define an eventual starting, ending point.
+{ first(X, Y, Z) } :- vertex(X, Y, Z).
+ {  last(X, Y, Z) } :- vertex(X, Y, Z).
+
+% Exactly one first/last assignment.
+:- #count{ X, Y, Z : first(X, Y, Z) } != 1.
+:- #count{ X, Y, Z :  last(X, Y, Z) } != 1.
+
+% The start and aren not the same assignment
+:- first(T, U, V), last(X, Y, Z), T != X, U != Y, V != Z.
+
+% Every Pair is a candidate for the path.
+{ path((T, U, V) , (W, X, Y)) } :- adjacent((T, U, V) , (W, X, Y)).
+
+% Define reachabilty.
+
+% Define path.
+
+% Define additional problem parameters (e.g., adjacency).
+
+% Locate the longest such path.
+% #maximize
+
+% Display
+% #show pred/arity.