Is there an algorithm for reducing CNFs further
CNF minimization is hard; see https://cstheory.stackexchange.com/q/9839/5038.  It is certainly NP-hard, and there is a sense in which it is &quot;even harder&quot;.
One way to get some intuition why it is hard is that if the CNF is not satisfiable, then its reduced form is &quot;False&quot;, whereas if it is satisfiable, its reduced form is something else.  So, if you had an efficient way to find a reduced form, that would immediately give you a way to tell whether the CNF is satisfiable -- a task that we know is NP-hard.
See https://cstheory.stackexchange.com/q/9839/5038 and https://en.wikipedia.org/wiki/Logic_optimization#Circuit_minimization_in_Boolean_algebra for some points into the literature on algorithms for this task.