data

6
whale: big black water animal
penguin: black white ice beak
piano: keyboard black white wire
jackboot: leather heel black
train: rail wheel black
rose: red green thorn
4
whale penguin piano jackboot train
penguin piano
jackboot rose
piano train

rec.erl

#!/usr/bin/env escript

-module(rec).
-export([main/1]).

recombine(_, []) -> nil;
recombine([], Common) -> Common;
recombine([Head|Tail], Common) -> recombine(Tail, [X || X <- Head, Y <- Common, X == Y]).
recombine([]) -> nil;
recombine([Head|Tail]) -> recombine(Tail, Head).

remove_newline(S) -> lists:sublist(S, 1, length(S) - 1).

read_n_lines(_, Lines, 0) -> Lines;
read_n_lines(File, Lines, N) ->
read_n_lines(File, [remove_newline(io:get_line(File, nil)) | Lines], N - 1).

print_solutions(Defs, Comb) ->
  M = [Props || Term1 <- Comb, {Term, Props} <- Defs, Term1 == Term],
  R = recombine(M),
  io:fwrite("Intersection: ~p~n", [R]).

main([FileName]) ->
  {ok, File} = file:open(FileName, [read]),

  TermDefs = read_n_lines(File, [], list_to_integer(remove_newline(io:get_line(File, nil)))),
  Defs0 = [string:tokens(Def, ":") || Def <- TermDefs],
  Defs = [{list_to_atom(H1), [list_to_atom(S) || S <- string:tokens(H2, " ")]} || [H1|[H2|_]] <- Defs0],
  

  TermCombs = read_n_lines(File, [], list_to_integer(remove_newline(io:get_line(File, nil)))),
  Combs = [[list_to_atom(S) || S <- string:tokens(Comb, " ")] || Comb <- TermCombs],
  
  [print_solutions(Defs, Comb) || Comb <- Combs].

result

Intersection: [black]
Intersection: nil
Intersection: [black,white]
Intersection: [black]