Phylogenetic methods are used to infer the evolutionary history of species. In the Tree of Life framework, heterogeneous character data and very large species sets are considered. Supertree methods have been developped to deal with such a situation. These methods combine source topologies, inferred from separate character sets, into a larger, so-called supertree. One of the main challenges met by supertree methods is the handling of topological conflicts arising among source trees. Some methods resolve these conflicts based on a voting approach: they rely on various criteria to decide which particular resolution, among conflicting ones, is to be kept in the supertree. Other methods follow a veto approach, proposing supertrees that do not favor any resolution among several conflicting ones. Compared to voting methods, they usually propose less resolved trees but avoid the problematic, implicit weighting of non-independent information contained in source trees. This article points out some desirable mathematical properties of veto supertrees called induction and non-contradiction. It also describes PhySIC (Phylogenetic Signal with Induction and non-Contradiction), an effective supertree method outputting supertrees that verify these properties. The method is available as a web service at www.lirmm.fr/~vberry/TOL/physic.cgi . The relevance of PhySIC is illustrated on a biological case study on primates where it is compared to MRP, the most widely used voting method.