:- use_module(library(lists), [member/2]).

starpalindrome(Commands) :-
	collect_stars(Commands,Stars),
	( Stars == [] ->
	    true
	;
	    check_palindrome(Stars)
	).

check_palindrome(Stars) :-
	setof((X,Y),symmetry_point(Stars,X,Y),SymmetryPoints),
	member((X,Y),SymmetryPoints),
	\+ some_star_has_no_symmetric_star(Stars,X,Y).

some_star_has_no_symmetric_star(Stars,X,Y) :-
	member(star(A,B),Stars),
	\+ has_symmetric_star(A,B,Stars,X,Y).

has_symmetric_star(A,B,Stars,X,Y) :-
	member(star(C,D),Stars),
	X is A + C,
	Y is B + D.

symmetry_point(Stars,X,Y) :-
	member(star(X1,Y1),Stars),
	member(star(X2,Y2),Stars),
	X is X1 + X2,
	Y is Y1 + Y2.