I didn't get your code block to work, but I am able to format/3 to a file correctly. I think perhaps the problem is with your switches, but

#+begin_src prolog :results output
format('hello~n',[]).
#+end_src

doesn't output anything.

For writing to a file, my switches are:

#+begin_src prolog :results file :file counts.csv
...

and a link to the output file appears as expected.

My setup:

• GNU Emacs 27.1 (build 1, x86_64-apple-darwin18.7.0, NS appkit-1671.60 Version 10.14.6 (Build 18G95)) of 2020-08-12

• Org mode version 9.3 (release_9.3 @ /Applications/Emacs.app/Contents/Resources/lisp/org/)

• SWI-Prolog (threaded, 64 bits, version 8.0.3)

• /Applications/Emacs.app/Contents/Resources/site-lisp/ob-prolog.el

I hope this is some help.

I tried to run as well and it gives no output
I'm using:

1. Emacs GNU Emacs 27.1 (build 1, x86_64-w64-mingw32) of 2020-08-21
2. Org mode version 9.3 (release_9.3 @ c:/Emacs/x86_64/share/emacs/27.1/lisp/org/)
3. SWI-Prolog (threaded, 64 bits, version 8.2.4)

I believe it might there be something wrong with the lisp on ob-prolog

I'm having the same issues as described in #21 and in #18

I'm trying it with swi and gnu-prolog, when (setq org-babel-prolog-command "swipl") the following block:

#+begin_src prolog
write('hello').
#+end_src

produces no output. There's a message "Code block produced no output.", and indeed, there's none whatsoever;

To get that to work with SWI-prolog you need to specify it as a goal. So either:

#+begin_src prolog :results output
:-write('hello').
#+end_src

or

#+begin_src prolog :results output :goal a 
a:-write('hello').
#+end_src

should both work and will produce the output:

#+RESULTS:
: hello

And in general if you want to run a program which doesn't produce any output e.g. with the write/2 predicate, then you need to run it in session mode. For example a simple factorial predicate might be run as:

#+BEGIN_SRC prolog :results output :session :goal fact(7,F)
fact(0,1).
fact(N,F):-
    N #> 0,
    F #> 0,
    N1 #= N-1,
    F #= N*F1,
    fact(N1,F1).
#+END_SRC

It will produce the result:

#+RESULTS:
: F = 5040.