Science and Education Publishing American Journal of Modeling and Optimization 2 1 2014 03 18 Polynomial Simulation and Refutation of Complex Formulas of Resolution over Linear Equations in Propositional Proof System 34 38 EN Vishwa Nath Maurya Professor & Principal, Shekhawati Engineering College, Rajasthan Technical University, India Avadhesh Kumar Maurya AJMO2014215 10.12691/ajmo-2-1-5 2014 03 10 2014 03 15 2014 03 18 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).