Static compaction methods aim at finding unnecessary test patterns to reduce the size of the test set as a post-process of test generation. Techniques based on partial maximum satisfiability are often used to track many hard problems in various domains, including artificial intelligence, computational biology, data mining, and machine learning. We observe that part of the test patterns generated by the commercial Automatic Test Pattern Generation (ATPG) tool is redundant, and the relationship between test patterns and faults, as a significant information, can effectively induce the test patterns reduction process. Considering a test pattern can detect one or more faults, we map the problem of static test compaction to a partial maximum satisfiability problem. Experiments on ISCAS89, ISCAS85, and ITC99 benchmarks show that this approach can reduce the initial test set size generated by TetraMAX18 while maintaining fault coverage.