P systems with proteins on membranes are a class of bio-inspired computing models, where the execution of each rule completes in exactly one time unit. However, in living cells, the execution time of biochemical reactions is difficult to know precisely because of various uncontrollable factors. In this work, we present a time-free uniform solution to SAT problem by P systems with proteins on membranes in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules, and the P systems are constructed from the sizes of instances.