A sequent-style model elimination strategy and a positive refinement

We present a sequent style proof system related to the MESON procedure, which is itself based on the model elimination strategy for mechanical theorem proving. The MESON procedure is attractive because it is a problem reduction format, that is, it has a goal-subgoal structure. The sequent style system based on it shares this advantage, and also has a simple declarative semantics and soundness proof. A refinement of the sequent style system tends to produce shorter sequents and may facilitate the use of the MESON procedure with caching of solutions to subgoals to avoid repeated work on the same subgoal. In the MESON procedure, a goal is marked ‘contradicted’ and considered to be solved, if an ancestor goal is complementary to it. In the positive refinement, only the positive goals need to be checked for contradiction in this way. This means that if a list of ancestor goals is kept with each goal, it is only necessary to store the negative ancestor goals, since these are the only ones that need to be examined in testing if a positive goal is contradicted. Similar restrictions on the reduction operation of model elimination are possible.