[Avshalom]

Now I immediately turned to library(clpfd). Something along the lines of:

  Names = [rudolph, dancer...
  Vars = [Rudolph, Dancer...
  Vars ins 1..9,
  all_different(Vars),
  Rudolph #> Dancer,
  ...
  ...
  pairs_keys_values(P,Vars,Names),
  keysort(P,S),
  write(S).

[tbensky]

I like the clpfd approach too:

:- use_module(library(clpfd)).

go(L) :- L = [Vixen, Rudolph, Prancer, Dasher, Comet, Dancer, Donder, Blitzen, Cupid], L ins 1..9,

        % Vixen should be behind Rudolph, Prancer and Dasher,
        maplist(#>(Vixen),[Rudolph,Prancer,Dasher]),
        
        %  Vixen should be in front of Dancer and Comet.
        maplist(#<(Vixen),[Dancer,Comet]),

        % Dancer should be behind Donder, Blitzen and Rudolph. 
        maplist(#>(Dancer),[Donder,Blitzen,Rudolph]),
        
        % Comet should be behind Cupid, Prancer and Rudolph.
        maplist(#>(Comet),[Cupid,Prancer,Rudolph]),

        % Donder should be behind Comet, Vixen, Dasher, Prancer and Cupid. 
        maplist(#>(Donder),[Comet, Vixen, Dasher, Prancer,Cupid]),

        % Cupid should be in front of Comet, Blitzen, Vixen, Dancer and Rudolph
        maplist(#<(Cupid),[Comet, Blitzen, Vixen, Dancer,Rudolph]),

        % Prancer should be in front of Blitzen, Donder and Cupid.
        maplist(#<(Prancer),[Blitzen,Donder,Cupid]),

        % Blitzen should be behind Cupid 
        Blitzen #> Cupid,

        % but in front of Dancer, Vixen and Donder.
        maplist(#<(Blitzen),[Dancer,Vixen,Donder]),

        % Rudolph should be behind Prancer
        Rudolph #> Prancer,
        
        % but in front of Dasher, Dancer and Donder.
        maplist(#<(Rudolph),[Dasher,Dancer,Donder]),

        % Finally, Dasher should be behind Prancer
        Dasher #> Prancer,

        % but in front of Blitzen, Dancer and Vixen.
        maplist(#<(Dasher),[Blitzen,Dancer,Vixen]).