exists_shorter(Word, List) :-
    member(Another, List),
    length(Another,L1),
    length(Word,L2),
    L1 < L2.

/* shortest word */
shortest(List, Word) :-
    member(Word, List),
    not(exists_shorter(Word,List)).

/* If two words have common latter */
has_common_letter([First|_], Word2) :- member(First, Word2).
has_common_letter([_|Tail1], Word2) :- has_common_letter(Tail1, Word2).

/* If exists Word2 that has no common letters with Word1 */
bad_word(Word1, List) :-
    member(Word2, List),
    not(has_common_letter(Word1,Word2)).

filter_words(List, [H|T], [H|T2]) :- not(bad_word(H,List)), !, filter_words(List, T, T2).
filter_words(List, [_|T], T2) :- filter_words(List,T,T2).
filter_words(_,[],[]).

filter_pretty(List, Result) :- filter_words(List,List,Result).

gee(List,Res) :- filter_pretty(List,Filtered), shortest(Filtered, Res).