There's an issue with PHP 7.1.4 and including "wp-include/version.php" when $wp_version is declared global (as is done in Core_Command::download() and Core_Command::update()) in that it doesn't seem to get set (though I haven't been able to find anything about this behaviour elsewhere, which is odd).

This is the cause of the "Make sure files are cleaned up" test failing (#6). A simple fix is to use Core_Command::get_wp_details() instead.

Another issue is the mysql extension being removed in PHP 7 (although it is possible to pecl install it in PHP 7.0 at least), which is only catered for in WordPress >= 3.9 (see trac changeset [27257]).

So upping the versions used to WP >= 3.9 (except for one, as a BC check) fixes that and gets all the tests (bar the BC one) running for PHP >= 7. See gitlost#3. I'll open a PR.