Prolog solution(ish) to 6th grade logic puzzle

puzzle.pl

diff_known(X, Diff, Y):- Y is X + Diff.
abs_diff(X, Diff, Y):- Y is X + Diff ; Y is X - Diff.

older(X, Y):- X > Y.

drop_lie(Facts, Index, Truths):- nth0(Index, Facts, _, Truths).

% Prints program dropping a configuration of lies
print_program(L1, L2, L3):-
  % Valid program:
  drop_lie([
    "Synnove is 22",
    "diff_known(Synnove, 2, Lindis)",
    "diff_known(Synnove, -1, Kristine)"
  ], L1, Synnove_truths),
  drop_lie([
    "Kristine is 25",
    "(older(Lindis, Synnove); older(Lindis, Kristine))",
    "abs_diff(Kristine, 3, Lindis)"
  ], L2, Lindis_truths),
  drop_lie([
    "Synnove is 23",
    "older(Synnove, Kristine)",
    "diff_known(Lindis, 3, Synnove)"
  ], L3, Kristine_truths),
  append(Synnove_truths, Lindis_truths, X),
  append(X, Kristine_truths, Truths),
  atomic_list_concat(Truths, ',\n\t', Y),
  atom_string(Y, Z),
  format('solve(Synnove, Lindis, Kristine):-\n\t~w .', [Z]).

% print_program(0, 0, 2).
% This prints the program which omits the lies we know are lies:
% solve(Synnove, Lindis, Kristine):-
%   diff_known(Synnove, 2, Lindis),
%   diff_known(Synnove, -1, Kristine),
%   (older(Lindis, Synnove); older(Lindis, Kristine)),
%   abs_diff(Kristine, 3, Lindis),
%   Synnove is 23,
%   older(Synnove, Kristine) .

% However, we need to reorder the facts so that the initialization of Synnove to 23
% is at the top, in order for Prolog to be able to figure out the rest of the
% clauses.
solve(Synnove, Lindis, Kristine):-
  Synnove is 23,
  diff_known(Synnove, 2, Lindis),
  diff_known(Synnove, -1, Kristine),
  (older(Lindis, Synnove); older(Lindis, Kristine)),
  abs_diff(Kristine, 3, Lindis),
  older(Synnove, Kristine) .