Quasipolynomial Size Frege Proofs of Frankl's Theorem on the Trace of Finite Sets

ABSTRACT. We extend results of Bonet, Buss and Pitassi on Bondy's Theorem and of Nozaki, Arai and Arai on Boolobas's Theorem by proving that Frankl's Theorem on the trace of sets has quasipolynomial size Frege proofs. For constant values of the parameter t, we prove that Frankl's Theorem has polynomial size, constant depth proofs from instances of the pigeonhole principle.