didit(L) :-
	setof(P, suspect(P), L).

person(P) :-
	says(P, _, _),
	forall((says(Q,_,_), P \= Q), says(_,_, didit(Q))).
person(P) :-
	says(_, _, didit(P)).

suspect(P) :-
	person(P),
	number_liars(P, NP),
	forall((person(Q), Q \= P), (number_liars(Q, NQ), NP =< NQ)).

number_liars(P, N) :-
	liars(P, Liars),
	length(Liars, N).

liars(P, Liars) :-
	validity(P, _, Lies),
	findall(X, (member(I, Lies), says(X, I, _)), Liars0),
	sort(Liars0, Liars).

validity(P, Truths, Lies) :-
	findall(I, says(_, I, didit(P)), Truths0),
	findall(I, (says(_, I, didit(Q)), P \= Q), Lies0),
	validity(Truths0, Lies0, Truths, Lies).

validity([], [], [], []).
validity(Truths0, Lies0, Truths, Lies) :-
	(Truths0 \= []; Lies0 \= []),
	findall(I, (member(S, Truths0), says(_, I, true(S));
	member(S, Lies0), says(_, I, false(S))), Truths1),
	findall(I, (member(S, Truths0), says(_, I, false(S));
	member(S, Lies0), says(_, I, true(S))), Lies1),
	validity(Truths1, Lies1, Truths2, Lies2),
	append(Truths0, Truths2, Truths),
	append(Lies0, Lies2, Lies).