Prolog program - list of Peano numbers - rule returns multiple answers

Question

I'm trying to write a Prolog program with a rule good which takes a list, where each term in the list is a Peano number. The rule should be true if and only if each element in the list is greater than the previous element.

For example, the following examples should be true:

good([]).
good([0]).
good([0,s(0)]).
good([0,s(s(0))]).
good([0,s(0),s(s(0))]).

And the following examples should be false:

good([s(0),0]).
good([0,s(0),0]).

Here is my code:

plus(X,0,X).
plus(X,s(Y),s(Z)) :- plus(X,Y,Z).

geq(X,Y) :- plus(K,Y,X).
ge(X,Y) :- geq(X,Y), not(X = Y).

good([]).
good([X]).
good([H|T]) :- good(H,T).
good(X,[H|T]) :- ge(H,X), good(T).

However, for the positive query good([0,s(0),s(s(0))]), both true and false are solutions.

What is the error?

Answer 1

Please see this answer. First getting true and then getting false after backtracking, just means that it found an answer, then at your request tried a different path, and then couldn't find any other path to reach true, so returned false.

In other words, as that answerer says,

The false response can appear inconsistent to beginning Prolog programmers and "feel" like an error or warning, but it's actually a perfectly normal Prolog response.