substt ef x y ef substt x y substf Pe x y Pe substt x y substf neg f s neg substf f s substf and f g s and substf f s substf g s substf or f g s or substf f s substf g s substf imp f g s imp substf f s substf g s substf forall f s forall substf f . 1 ron s shift substf exists f s exists substf f . 1 ron s shift substt x id x substf f id f substt substt x s t substt x ron s t substf substf f s t substf f ron s t substt 1 . x s x ron id s s ron shift . x s s ron ron s t u ron s ron t u ron . x s t . substt x t ron s t ron s id s . 1 shift id . substt 1 s ron shift s s virg emptyfset a a virg a a a * emptysset a a * a a a neg neg f f and f f f or f f f imp f g or neg f g exists f neg forall neg f sequent virg convf neg f a b sequent a virg convf f b sequent convf neg f b sequent emptyfset virg convf f b sequent a virg convf neg f b sequent virg convf f a b sequent a convf neg f sequent virg convf f a emptyfset sequent virg convf and f g a b sequent virg convf g virg convf f a b sequent convf and f g b sequent virg convf f convf g b sequent a virg convf or f g b sequent a virg virg convf f convf g b sequent a convf or f g sequent a virg convf f convf g convs sequent a virg convf and f g b * convs sequent a virg convf f b convs sequent a virg convf g b convs sequent a convf and f g * convs sequent a convf f convs sequent a convf g convs sequent virg convf or f g a b * convs sequent virg convf f a b convs sequent virg convf g a b convs sequent convf or f g b * convs sequent convf f b convs sequent convf g b convs sequent virg convf f a virg convf f b emptysset convs sequent virg convf f a convf f emptysset convs sequent convf f virg convf f b emptysset convs sequent convf f convf f emptysset * convs sequent virg f a virg g b convs sequent a b convs sequent a b * convs sequent virg f a b convs sequent a b convs sequent a b * convs sequent a virg f b convs sequent a b convs sequent a b * convs sequent virg f a b convs sequent a emptyfset convs sequent a emptyfset * convs sequent emptyfset b convs sequent a virg f b convs sequent emptyfset b * convs sequent emptyfset b convs sequent a b convs sequent emptyfset b * convs sequent a emptyfset convs sequent a b convs sequent a emptyfset * convs sequent emptyfset emptyfset convs sequent a b convs sequent emptyfset emptyfset substt 2 ef 1 substf 2 Pe 1 neg 1 and 2 or 2 imp 2 forall 1 . 2 1 0 ron 2 shift 0 exists 1 id 0 virg 2 AC emptyfset 0 * 2 AC emptysset 0 sequent 2 convf 1 convs 1 FULL ./TRS/CimeAC/sequent_modulo.trs