eng Science and Education Publishing American Journal of Modeling and Optimization 2014-03-18 2 1 34 38 10.12691/ajmo-2-1-5 AJMO2014215 article Vishwa Nath Maurya prof.drvnmaurya@gmail.com 1 Avadhesh Kumar Maurya 2 Professor & Principal, Shekhawati Engineering College, Rajasthan Technical University, India Assistant Professor, Department of Electronics & Communication Engineering Lucknow Institute of Technology, U.P. Technical University, Lucknow, India In this paper, we present that the propositional proof system R(lin) (Resolution over Linear Equations) established by Ran Raz and Iddo Tzameret is not a super system, there exists a sequence of tautologies, which require proof complexity exponential in size of tautologies. We show that there are the sequence of unsatisfiable collections of disjuncts of linear equations, which require exponential lower bounds in R(lin) and have polynomially bounded refutations by incorporating renaming inference rule to R(lin) system. Some additional properties of R(lin) have been described that many of the "hard" provable in R outstanding examples of propositional tautologies (contradictions) have polynomially bounded proofs in R(lin). http://pubs.sciepub.com/ajmo/2/1/5/ajmo-2-1-5.pdf Resolution over linear equations Resolution systems Refutation Proof complexity Hard-determinable formula Polynomial simulation