We present sharpened lower bounds on the size of cut free proofs for first-order logic. Prior lower bounds for eliminating cuts from a proof established superexponential lower bounds as a stack of exponentials, with the height of the stack proportional to the maximum depth d of the formulas in the original proof. Our results remove the constant of proportionality, giving an exponential stack of height equal to d-O(1). The proof method is based on more efficiently expressing the Gentzen—Solovay cut formulas as low depth formulas.
"Sharpened lower bounds for cut elimination." J. Symbolic Logic 77 (2) 656 - 668, June 2012. https://doi.org/10.2178/jsl/1333566644