In 1930s Paul Erd?s conjectured that for any positive integer C in any infinite ?1 sequence ( x n ) there exists a subsequence x d , x 2 d , x 3 d , ? , x k d , for some positive integers k and d, such that | ? i = 1 k x i ? d | C . The conjecture has been referred to as one of the major open problems in combinatorial number theory and discrepancy theory. For the particular case of C = 1 a human proof of the conjecture exists; for C = 2 a bespoke computer program had generated sequences of length 1124 of discrepancy 2, but the status of the conjecture remained open even for such a small bound. We show that by encoding the problem into Boolean satisfiability and applying the state of the art SAT solvers, one can obtain a discrepancy 2 sequence of length 1160 and a proof of the Erd?s discrepancy conjecture for C = 2 , claiming that no discrepancy 2 sequence of length 1161, or more, exists. In the similar way, we obtain a precise bound of 127?645 on the maximal lengths of both multiplicative and completely multiplicative sequences of discrepancy 3. We also demonstrate that unrestricted discrepancy 3 sequences can be longer than 130?000.