Postgres 13

By using db<>fiddle, you agree to license everything you submit by Creative Commons CC0.

create table mytable (
	id serial primary key,
	custom_barcode int,
	system_barcode int,
	check (custom_barcode <> system_barcode),
	exclude using gist((array[custom_barcode, system_barcode]) with &&)
);

CREATE TABLE


insert into mytable (custom_barcode, system_barcode) values (1, 1);

ERROR:  new row for relation "mytable" violates check constraint "mytable_check"
DETAIL:  Failing row contains (1, 1, 1).


insert into mytable (custom_barcode, system_barcode) values (2, 3);

INSERT 0 1


insert into mytable (custom_barcode, system_barcode) values (4, 2);

ERROR:  conflicting key value violates exclusion constraint "mytable_array_excl"
DETAIL:  Key ((ARRAY[custom_barcode, system_barcode]))=({4,2}) conflicts with existing key ((ARRAY[custom_barcode, system_barcode]))=({2,3}).