All-optical three-input logic minterms are generated at 42 Gbit/s with a Sagnac interferometer by using cross-phase modulation in a semiconductor optical amplifier. To the best of the author's knowledge, this is the first time that high-speed logic operations with more than two inputs have been experimentally demonstrated in a Sagnac interferometer. Correct and clear temporal waveforms are successfully observed. Bit error ratios and optical signal-to-noise ratios are measured to demonstrate the effectiveness of the method. As the basic units of combinational logic operations, logic minterms are promising candidates to construct reconfigurable and programmable logic functions.