The explicitly-correlated coupled-cluster method CCSD(T)(R12) is extended to include F12 geminal basis functions that decay exponentially with the interelectronic distance and reproduce the form of the average Coulomb hole more accurately than linear-r(12). Equations derived using the Ansatz 2 strong orthogonality projector are presented. The convergence of the correlation energy with orbital basis set for the new CCSD(T)(F12) method is studied and found to be rapid, 98% of the basis set limit correlation energy is typically recovered using triple-zeta orbital basis sets. The performance for reaction enthalpies is assessed via a test set of 15 reactions involving 23 molecules. The title statement is found to hold equally true for total and relative correlation energies.