:- use_module(library(lists)).

knows(P1, P2) :- knows(P1, P2, []) .

knows(P1, P2, V) :-
    knows_l1(P1, P2),
    \+ memberchk((P1, P2), V) .

knows(P1, P2, V) :-
    knows_l1(P1, OtherPerson),
    \+ memberchk((P1, OtherPerson), V),
    knows(OtherPerson, P2, [(P1, OtherPerson) | V]) .

1.0 :: knows_l1(0, 2) .
1.0 :: knows_l1(0, 3) .
1.0 :: knows_l1(0, 4) .
1.0 :: knows_l1(1, 0) .
1.0 :: knows_l1(1, 2) .
1.0 :: knows_l1(1, 3) .
1.0 :: knows_l1(1, 4) .
1.0 :: knows_l1(2, 0) .
1.0 :: knows_l1(2, 1) .
1.0 :: knows_l1(2, 3) .
1.0 :: knows_l1(2, 4) .
1.0 :: knows_l1(3, 0) .
1.0 :: knows_l1(3, 1) .
1.0 :: knows_l1(3, 2) .
1.0 :: knows_l1(3, 4) .
1.0 :: knows_l1(4, 0) .
1.0 :: knows_l1(4, 1) .
1.0 :: knows_l1(4, 2) .
1.0 :: knows_l1(4, 3) .

query(knows(0, 1)) .