You want a hash of hash, not an array of array. Hashes are great for detecting and/or eliminating duplicates.

my %hosts;

while (<IN_FILE>) {
   chomp;
   my ($ip, @aliases) = split(/\s+/, $_);

   foreach my $alias (@aliases) {
      $hosts{$ip}{$alias} = 1;
   }
}

foreach my $ip (sort keys %hosts) {
   my @aliases = sort keys %{$hosts{$ip}};
   print OUT_FILE ("$ip ", join(' ', @aliases), "\n");
}
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