Prologue: When is false also a solution?

Hello,

Sometimes Prolog gives me false and sometimes it doesn't. I had learned it this way: "If it's not defined, then it's false for Prolog." But then I have this case:

 p(a,b). p(a,c). p(d,e). p(d,f). p(g,f). q(h). q(i). q(j). r(h, a). r(i, d). r(j, g). s(X,Y,Z):- q(X), r(X, Y), p(Y, Z).

The query for this is ?- s(X,Y,f). If you replace X with h, you get ?-r(h,Y),p(Y,f). If I now replace Y with a, I would have expected it to return false because p(a,f) is undefined, but it "fails" and keeps searching. The solutions are X=i, Y=d and X=j, Y=g. If you enter ?- p(a,f) as the query, you get false.

Another example where false comes out:

 append ( [] , L , L ) . append ( [H|T1] , L2 , [H|T3]) :- append (T1,L2 ,T3)

With the query ?-append(X,X,[ ]). Solutions are X=[ ];false.

In both examples, I intuitively figured out the correct solutions. I'd just like to know the difference.

Thank you very much in advance:))