execution order does matter for prolog, top-down; ancestor22 can cause infinite recursion

ancestor.pl

/*
    a   
   / \ 
  b   d   
  |
  c
  |
  e
*/

parent(a, b). 
parent(a, d). 
parent(b, c). 
parent(c, e). 

ancestor11(X, X). 
ancestor11(X, Y) :- parent(Z, Y), ancestor11(X, Z). 

ancestor12(X, Y) :- parent(Z, Y), ancestor12(X, Z). 
ancestor12(X, X). 
                                                               
ancestor21(X, X). 
ancestor21(X, Y) :- ancestor21(X, Z), parent(Z, Y). 

ancestor22(X, Y) :- ancestor22(X, Z), parent(Z, Y). 
ancestor22(X, X). 

ancestor31(X, Y) :- parent(X,Y).
ancestor31(X, Y) :- parent(X, Z), ancestor31(Z, Y). 

ancestor32(X, Y) :- parent(X, Z), ancestor32(Z, Y). 
ancestor32(X, Y) :- parent(X,Y).

Why do you have ancestor(X,X)? That is not correct anyway

you're right, but the point here for 21 and 22 are demonstration of the order, and possible infinite recursion