Examples of Hard Tautologies in the Propositional Calculus
We present examples of hard tautologies in propositional calculus by encoding instances of the assertions made by Ramsey's theorem. We provide evidence that these tautologies are indeed hard by
 1. showing that there are no short proofs for these tautologies in certain restricted classes of proof systems;
 2. relating a proof of these tautologies to the problem of determining the diagonal Ramsey numbers for graphs.