parent(ojciec, syn1).
parent(matka, corka1).
parent(matka, corka2).
parent(matka, syn1).
parent(dziadek, matka).
man(ojciec).
man(dziadek).
man(syn1).
woman(matka).
woman(corka1).
woman(corka2).

ismother(X) :-
	woman(X), parent(X, _).

isfather(X) :-
	man(X), parent(X, _).

isson(X) :-
	man(X), parent(_, X).

aresisters(X, Y) :-
	woman(X), woman(Y), X \= Y, parent(Z, X), parent(Z, Y).

isgrandpaof(X, Y) :-
	man(X), parent(X, Z), parent(Z, Y).

aresiblings(X, Y) :-
	X \= Y, parent(Z, X), parent(Z, Y).



on(b1, b4).
on(b4, b3).

above(X, Y) :- on(X, Y).

above(X, Y) :-
	on(X, Z),
	above(Z, Y).


onleft(eggtimer, pencil).
onleft(butterfly, eggtimer).
onleft(fish, butterfly).
ontop(pencil, bicycle).
ontop(butterfly, camera).

moreleftedfrom(X, Y) :- onleft(X, Y).

moreleftedfrom(X, Y) :-
	onleft(X, Z),
	moreleftedfrom(Z, Y).

morerightedfrom(X, Y) :- moreleftedfrom(Y, X).

higherthan(X, Y) :- ontop(X, Y).

higherthan(X, Y) :-
	ontop(X, Z),
	higherthan(Z, Y).

belowthan(X, Y) :- higherthan(Y, X).

higher(X, Y) :-
	higherthan(Z, Y),
	(moreleftedfrom(X, Z); morerightedfrom(X, Z)).


le(1,5).
le(1,7).
le(5,35).
le(7,35).
le(7,14).


wiekszyod(X,Y) :- le(X,Y).

wiekszyod(X, Y) :-
	le(X, Z),
	wiekszyod(Z, Y).

maksymalny(X) :-
	\+ le(X,A),
	le(B,X).

najw(X) :-
	maksymalny(X),
	le(Y, X),
	((le(Y,Z), (\+ najw(Z))); true).

minimalny(X) :-
	\+ le(A,X),
	le(X,B).

divisible(X,Y) :- X mod Y =:= 0.
divisible(X,Y) :- sqrt(X) >= Y+2, divisible(X, Y+2).

isPrime(X) :- X =:= 2; X =:= 3; (X > 3, X mod 2 =:= 1, \+ divisible(X, 3)).


prime(LO, HI, N) :-
	between(LO, HI, N),
	isPrime(N).