Professor Ulrich asks "Can a fully-automated proof of the sufficiency of Meredith's 21-character single axiom,  CCCCCpqCNrNsrtCCtpCsp / ((((p⊃q)⊃(~r⊃~s))⊃r)⊃t)⊃((t⊃p)⊃(s⊃p)), for classical logic in C and N be found that equals (or shortens) Meredith's own derivation of Syl = CCpqCCqrCpr / ((p⊃q)⊃((q⊃r)⊃(p⊃r)), Scotus = CpCNpq / p⊃(~p⊃q),  and Clavius = CCNppp / (~p⊃p)⊃p using just 41 condensed detachments? 
UPDATE: Larry Wos has (with OTTER) now discovered a proof using only 38 applications of condensed detachment.  See Automated reasoning and the discovery of missing and elegant proofs, L. Wos and G. Peiper, Rinton, Paramus, 2003, sections 3.1 through 3.3."

The question seems local to the derivation of {CCpqCCqrCpr, CpCNpq, CCNppp}.  One might ask "Can a fully-automated proof of the sufficiency of Meredith's 21-character single axiom,  CCCCCpqCNrNsrtCCtpCsp / ((((p⊃q)⊃(~r⊃~s))⊃r)⊃t)⊃((t⊃p)⊃(s⊃p)), for classical logic in C and N be found that requires less than 38 condensed detachments to get to the axioms for any distinct basis of C-N classical logic?"

It takes no more than 5 condensed detachments to get to CpCqp.