I took this problem as inspiration to write a little script to visualize matching parantheses. I probably got carried away and it is not helping on the original problem.

use strict;
use warnings;
my $tlp_p2 = "(((((((NOT(tlp_p0(0) XOR tlp_add_p0(0)) AND NOT(tlp_p0(1
+) XOR tlp_add_p0(1))) AND  NOT(tlp_p0(2) XOR tlp_add_p0(2)))";

my $level  = 0;
my $tab    = "| ";
my %action = (
        '('       => sub { print "\n", $tab x ++$level, shift },
        ')'       => sub { print "\n", $tab x $level--, shift },
        'default' => sub { print shift },
        );

( $action{$_} // $action{'default'} )->($_) for $tlp_p2 =~ /./g;
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The last line reads each character of the string $tlp_p2 individually and calls the corresponding sub from hash %action.