MAYBE 2.2 virg x y virg y x * x y * y x * x * y z * * x y z virg x virg y z virg virg x y z virg x virg y z virg virg x y z virg x virg y z virg x y * x * y z * * x y z virg x y virg y x * x * y z * x y * x y * y x exists f neg forall neg f substf forall f s . 1 ron s shift convs sequent virg convf or f g a b sequent virg convf g a b substf substf f s t ron s t sequent a virg convf or f g b virg virg convf f convf g b convs sequent a convf and f g convs sequent a convf f substf forall f s substf f . 1 ron s shift sequent virg convf neg f a b virg convf f b sequent convf neg f b virg convf f b convs sequent a convf and f g sequent a convf f substf or f g s substf f s substf neg f s substf f s convs sequent a convf and f g convs sequent a convf g substf exists f s exists substf f . 1 ron s shift sequent virg convf and f g a b virg convf g virg convf f a ron . x s t substt x t convs sequent convf or f g b * convs sequent convf f b convs sequent convf g b sequent virg convf and f g a b virg convf f a imp f g or neg f g sequent a virg convf or f g b virg convf f convf g sequent virg convf neg f a b sequent a virg convf f b sequent a convf neg f virg convf f a 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 convf or f g b convs sequent convf g b sequent a convf or f g sequent a virg convf f convf g sequent virg convf and f g a b sequent virg convf g virg convf f a b substf exists f s substf f . 1 ron s shift convs sequent virg convf or f g a b * convs sequent virg convf f a b convs sequent virg convf g a b substf neg f s neg substf f s substf and f g s substf g s substf exists f s ron s shift convs sequent a convf and f g * convs sequent a convf f convs sequent a convf g ron ron s t u ron t u sequent a convf or f g virg convf f convf g substt substt x s t substt x ron s t substf and f g s and substf f s substf g s imp f g neg f convs sequent a virg convf and f g b convs sequent a virg convf f b ron . x s t ron s t convs sequent virg convf or f g a b virg convf g a substf or f g s or substf f s substf g s convs sequent a convf and f g sequent a convf g convs sequent virg convf or f g a b convs sequent virg convf f a b substf imp f g s imp substf f s substf g s convs sequent convf or f g b convs sequent convf f b convs sequent convf or f g b sequent convf g b sequent a virg convf neg f b virg convf f a substt ef x y substt x y sequent convf and f g b virg convf f convf g substf forall f s ron s shift sequent a virg convf or f g b sequent a virg virg convf f convf g b convs sequent virg convf or f g a b convs sequent virg convf g a b substf imp f g s substf g s substf substf f s t substf f ron s t convs sequent virg convf or f g a b virg convf f a ron . x s t . substt x t ron s t convs sequent a virg convf and f g b convs sequent a virg convf g b substt substt x s t ron s t convs sequent a virg convf and f g b virg convf g b sequent a virg convf neg f b sequent virg convf f a b convs sequent virg convf or f g a b sequent virg convf f a b ron ron s t u ron s ron t u sequent convf neg f b sequent emptyfset virg convf f b substf imp f g s substf f s convs sequent a virg convf and f g b virg convf f b exists f neg f substf exists f s . 1 ron s shift substf Pe x y substt x y substf or f g s substf g s convs sequent convf or f g b sequent convf f b convs sequent a virg convf and f g b sequent a virg convf f b sequent convf and f g b sequent virg convf f convf g b substf and f g s substf f s sequent a convf neg f sequent virg convf f a emptyfset convs sequent a virg convf and f g b sequent a virg convf g b * * convs sequent virg f a virg g b convs sequent a b _1 * convs sequent a b _1 * * convs sequent virg f a b convs sequent a b _1 * convs sequent a b _1 * * convs sequent emptyfset emptyfset convs sequent a b _1 * convs sequent emptyfset emptyfset _1 * * convs sequent a virg f b convs sequent a b _1 * convs sequent a b _1 * * convs sequent emptyfset b convs sequent a b _1 * convs sequent emptyfset b _1 * * a a _1 * a _1 * * emptysset a _1 * a _1 * * convs sequent a emptyfset convs sequent a b _1 * convs sequent a emptyfset _1 * * convs sequent virg f a b convs sequent a emptyfset _1 * convs sequent a emptyfset _1 virg virg a a _1 virg a _1 virg virg emptyfset a _1 virg a _1 * * convs sequent emptyfset b convs sequent a virg f b _1 * convs sequent emptyfset b _1 substf and f g s substf f s substf or f g s substf g s substf and f g s substf g s substf imp f g s substf f s substf exists f s substf f . 1 ron s shift substf substf f s t substf f ron s t substf neg f s substf f s substf imp f g s substf g s substf or f g s substf f s substf forall f s substf f . 1 ron s shift true 1 sequent 2 0 1 0 1 ron 2 2 1 convs 1 0 . 2 0 emptyfset 0 0 exists 1 0 and 2 1 2 1 ron 2 0 convf 1 0 substf 2 1 0 virg 2 0 * 2 0 Pe 1 0 substt 2 0 substf 2 1 2 1 forall 1 1 1 virg 2 0 imp 2 0 or 2 1 2 1 neg 1 1 1 . 2 1 2 1 ef 1 1 convs 1 0 emptysset 0 0 id 0 4 or 2 0 neg 1 0 substt 2 1 2 1 imp 2 1 2 1 sequent 2 0 and 2 0 * 2 0 shift 0 1 exists 1 1 1 substf forall f s substf f . 1 ron s shift substf or f g s substf f s substf imp f g s substf g s substf neg f s substf f s substf substf f s t substf f ron s t substf exists f s substf f . 1 ron s shift substf imp f g s substf f s substf and f g s substf g s substf or f g s substf g s substf and f g s substf f s substf Pe x y substt x y false substf forall f s ron s shift false substf or f g s or substf f s substf g s false substf neg f s neg substf f s false substf exists f s exists substf f . 1 ron s shift false exists f neg f false substf exists f s . 1 ron s shift false substf exists f s ron s shift false substf and f g s and substf f s substf g s false convs sequent virg convf or f g a b convs sequent virg convf f a b convs sequent a virg convf and f g b convs sequent a virg convf f b convs sequent convf or f g b convs sequent convf g b convs sequent a virg convf and f g b convs sequent a virg convf g b convs sequent a convf and f g convs sequent a convf g convs sequent virg convf or f g a b convs sequent virg convf g a b convs sequent a convf and f g convs sequent a convf f convs sequent convf or f g b convs sequent convf f b true 1 sequent 2 0 1 0 1 ron 2 2 1 convs 1 0 . 2 0 emptyfset 0 1 exists 1 0 and 2 1 2 1 ron 2 0 convf 1 1 1 substf 2 0 virg 2 0 * 2 0 Pe 1 0 substt 2 0 substf 2 1 forall 1 1 virg 2 1 2 0 imp 2 0 or 2 1 2 1 neg 1 1 1 . 2 1 2 1 ef 1 1 convs 1 1 0 emptysset 0 0 id 0 4 or 2 0 neg 1 0 substt 2 1 2 1 imp 2 1 sequent 2 1 2 0 and 2 0 * 2 0 shift 0 1 exists 1 1 convs sequent convf or f g b convs sequent convf f b convs sequent a convf and f g convs sequent a convf f convs sequent virg convf or f g a b convs sequent virg convf g a b convs sequent a convf and f g convs sequent a convf g convs sequent a virg convf and f g b convs sequent a virg convf g b convs sequent convf or f g b convs sequent convf g b convs sequent a virg convf and f g b convs sequent a virg convf f b convs sequent virg convf or f g a b convs sequent virg convf f a b virg x virg y z virg virg x y z virg emptyfset a a sequent a virg convf or f g b sequent a virg virg convf f convf g b sequent a virg convf neg f b sequent virg convf f a b sequent virg convf and f g a b sequent virg convf g virg convf f a b virg a a a sequent a convf neg f sequent virg convf f a emptyfset sequent virg convf neg f a b sequent a virg convf f b sequent convf neg f b sequent emptyfset virg convf f b virg x y virg y x sequent a convf or f g sequent a virg convf f convf g sequent convf and f g b sequent virg convf f convf g b convs sequent convf or f g b * convs sequent convf f b convs sequent convf g b false convs sequent convf or f g b sequent convf f b false convs sequent convf or f g b sequent convf g b false convs sequent a virg convf and f g b * convs sequent a virg convf f b convs sequent a virg convf g b false convs sequent a virg convf and f g b sequent a virg convf f b false convs sequent a virg convf and f g b virg convf f b false convs sequent a virg convf and f g b sequent a virg convf g b false convs sequent a virg convf and f g b virg convf g b false convs sequent virg convf or f g a b * convs sequent virg convf f a b convs sequent virg convf g a b false convs sequent virg convf or f g a b sequent virg convf f a b false convs sequent virg convf or f g a b virg convf f a false convs sequent virg convf or f g a b virg convf g a false convs sequent a convf and f g * convs sequent a convf f convs sequent a convf g false * x * y z * * x y z * x y * y x * x * y z * x y true convs sequent a convf and f g sequent a convf f false convs sequent a convf and f g sequent a convf g false substf substf f s t ron s t false ron . x s t ron s t substt substt x s t substt x ron s t ron ron s t u ron t u ron ron s t u ron s ron t u substt substt x s t ron s t ron . x s t substt x t substt ef x y substt x y true 1 sequent 2 0 1 0 1 ron 2 1 2 1 convs 1 0 . 2 0 emptyfset 0 1 exists 1 0 and 2 1 2 1 ron 2 1 0 convf 1 1 1 substf 2 0 virg 2 0 * 2 0 Pe 1 0 substt 2 1 0 substf 2 1 forall 1 1 virg 2 1 2 0 imp 2 0 or 2 1 2 1 neg 1 1 1 . 2 1 2 1 ef 1 1 1 convs 1 1 0 emptysset 0 0 id 0 4 or 2 0 neg 1 0 substt 2 1 2 1 imp 2 1 sequent 2 1 2 0 and 2 0 * 2 0 shift 0 1 exists 1 1 substt ef x y substt x y ron . x s t substt x t substt substt x s t ron s t ron ron s t u ron s ron t u ron ron s t u ron t u substt substt x s t substt x ron s t ron . x s t ron s t virg x virg y z virg virg x y z virg emptyfset a a sequent a virg convf or f g b sequent a virg virg convf f convf g b sequent a virg convf neg f b sequent virg convf f a b sequent virg convf and f g a b sequent virg convf g virg convf f a b virg a a a sequent a convf neg f sequent virg convf f a emptyfset sequent virg convf neg f a b sequent a virg convf f b sequent convf neg f b sequent emptyfset virg convf f b virg x y virg y x sequent a convf or f g sequent a virg convf f convf g sequent convf and f g b sequent virg convf f convf g b ron . x s t . substt x t ron s t false convs sequent virg convf or f g a b sequent virg convf g a b false sequent a convf neg f sequent virg convf f a emptyfset sequent convf and f g b sequent virg convf f convf g b sequent convf neg f b sequent emptyfset virg convf f b sequent virg convf and f g a b sequent virg convf g virg convf f a b sequent a convf or f g sequent a virg convf f convf g sequent a virg convf neg f b sequent virg convf f a b sequent virg convf neg f a b sequent a virg convf f b sequent a virg convf or f g b sequent a virg virg convf f convf g b true 1 sequent 2 1 2 0 1 0 1 ron 2 1 2 1 convs 1 0 . 2 0 emptyfset 0 1 exists 1 0 and 2 1 2 2 ron 2 0 convf 1 1 1 substf 2 0 virg 2 0 * 2 0 Pe 1 0 substt 2 0 substf 2 1 forall 1 1 virg 2 1 2 0 imp 2 0 or 2 1 2 2 neg 1 1 2 . 2 1 2 1 ef 1 1 1 convs 1 1 0 emptysset 0 0 id 0 4 or 2 0 neg 1 0 substt 2 1 2 1 imp 2 1 sequent 2 1 2 0 and 2 0 * 2 0 shift 0 1 exists 1 1 sequent a virg convf or f g b sequent a virg virg convf f convf g b sequent virg convf neg f a b sequent a virg convf f b sequent a virg convf neg f b sequent virg convf f a b sequent a convf or f g sequent a virg convf f convf g sequent virg convf and f g a b sequent virg convf g virg convf f a b sequent convf neg f b sequent emptyfset virg convf f b sequent convf and f g b sequent virg convf f convf g b sequent a convf neg f sequent virg convf f a emptyfset virg x virg y z virg virg x y z virg emptyfset a a sequent a virg convf or f g b sequent a virg virg convf f convf g b sequent a virg convf neg f b sequent virg convf f a b sequent virg convf and f g a b sequent virg convf g virg convf f a b virg a a a sequent a convf neg f sequent virg convf f a emptyfset sequent virg convf neg f a b sequent a virg convf f b sequent convf neg f b sequent emptyfset virg convf f b virg x y virg y x sequent a convf or f g sequent a virg convf f convf g sequent convf and f g b sequent virg convf f convf g b sequent convf and f g b virg convf f convf g false sequent a convf or f g virg convf f convf g false sequent convf neg f b virg convf f b false sequent virg convf neg f a b virg convf f b false sequent a convf neg f virg convf f a false sequent virg convf and f g a b virg convf g virg convf f a false sequent virg convf and f g a b virg convf f a false sequent a virg convf neg f b virg convf f a false sequent a virg convf or f g b virg virg convf f convf g b false sequent a virg convf or f g b virg convf f convf g false virg x y virg y x virg x virg y z virg x y virg x virg y z virg virg x y z true substf forall f s . 1 ron s shift false exists f neg forall neg f false substf imp f g s imp substf f s substf g s false imp f g or neg f g false imp f g neg f false * * convs sequent virg f a virg g b convs sequent a b _1 * convs sequent a b _1 * * a a _1 * a _1 * * convs sequent virg f a b convs sequent a emptyfset _1 * convs sequent a emptyfset _1 * * convs sequent a virg f b convs sequent a b _1 * convs sequent a b _1 * * emptysset a _1 * a _1 * * convs sequent emptyfset b convs sequent a b _1 * convs sequent emptyfset b _1 * * convs sequent emptyfset emptyfset convs sequent a b _1 * convs sequent emptyfset emptyfset _1 * x * y z * * x y z * * convs sequent emptyfset b convs sequent a virg f b _1 * convs sequent emptyfset b _1 * * convs sequent a emptyfset convs sequent a b _1 * convs sequent a emptyfset _1 * x * y z * x y * * convs sequent virg f a b convs sequent a b _1 * convs sequent a b _1 * x y * y x true Failed! NaTT 1.7