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We introduce , a new proof format for unsatisfiable SAT problems, and its associated toolchain. Compared to , the format allows solvers to include more information in proofs to reduce the computational cost of subsequent elaboration to . The format is easy to parse forward and backward, and it is extensible to future proof methods. The provision of optional proof steps allows SAT solver developers to balance implementation effort against elaboration time, with little to no overhead on solver time. We benchmark our toolchain against a comparable toolchain and confirm >84% median reduction in elaboration time and >94% median decrease in peak memory usage.

Summary This is Erdős’s proof of the divergence of the sum of prime reciprocals, using the Mizar system [2], [3], as reported in “Proofs from THE BOOK” [1].