The semantics of decision problems are always essentially independent of the
underlying representation. Thus the space of input data (under appropriate
indexing) is closed
under action of the symmetrical group $S_n$ (for a specific data-size)
and the input-output relation is closed under the action of $S_n$.
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We develop and study the complexity of propositional proof systems of varying strength extending resolution by allowing it to operate with disjunctions of linear equations instead of clauses. We demonstrate polynomial-size refutations for hard tautologies like the pigeonhole principle, Tseitin graph tautologies and the clique-coloring tautologies in these proof systems. ... more >>>