/* ************************************************ */
     /*                                                  */
     /*   delete_one/3                                   */
     /*      Arg 1:                                      */
     /*      Arg 2:  List                                */
     /*      Arg 3:  List                                */
     /*   Summary: true if Arg 3 is Arg 2 with an        */
     /*            instance of Arg 1 deleted.            */
     /*   Author: P J Hancox                             */
     /*   Date:   28 October 1994                        */
     /*                                                  */
     /* ************************************************ */

     % 1 terminating condition
     delete_one(Elem, [Elem|Tail], Tail).
     % 2 recursive
     delete_one(Elem, [Head|Tail1], [Head|Tail2]) :-
          \+ (Elem = Head),
          delete_one(Elem, Tail1, Tail2).

This requires the addition of one test. Note that this solution doesn't have recourse to extra-logical extensions of Prolog, such as the cut.