An oxidation polymer of a substituted phenol, obtained by oxidative polymerization of at least one compound selected from the group consisting of a compound of formula (Ia) and a compound of formula (Ib), in which the oxidation polymer has a number-average polymerization degree of 3 or more: wherein R1 to R4 each represent a hydrogen atom and the like; provided that at least one of R1 to R4 represents a substituted or unsubstituted, saturated hydrocarbon group having 10 or more carbon atoms, and R1 and/or R4 represent a hydrogen atom; wherein R11 represents a substituted or unsubstituted, saturated hydrocarbon group having 15 or more carbon atoms, and R12 is the same as R11, or when R12 is different from R11, R12 represents a substituted or unsubstituted hydrocarbon group and the like.