X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Fng_TPTP%2FLAT106-1.ma;fp=matita%2Fmatita%2Fcontribs%2Fng_TPTP%2FLAT106-1.ma;h=288bd831be9346764eea369e911bde87660936b5;hb=2c01ff6094173915e7023076ea48b5804dca7778;hp=0000000000000000000000000000000000000000;hpb=a050e3f80d7ea084ce0184279af98e8251c7d2a6;p=helm.git diff --git a/matita/matita/contribs/ng_TPTP/LAT106-1.ma b/matita/matita/contribs/ng_TPTP/LAT106-1.ma new file mode 100644 index 000000000..288bd831b --- /dev/null +++ b/matita/matita/contribs/ng_TPTP/LAT106-1.ma @@ -0,0 +1,137 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT106-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT106-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H3 is independent of H22 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : Show that Huntington equation H22 does not imply Huntington *) + +(* equation H3 in lattice theory. *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Satisfiable *) + +(* Rating : 0.33 v3.3.0, 0.67 v3.2.0, 1.00 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 19 ( 2 singleton) *) + +(* Maximal term depth : 8 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *) + +(* Number of atoms : 8 ( 8 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H3: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (meet X Y) (meet X Z)) (meet X (join (meet Y (join Z (meet X Y))) (meet Z (join X Y)))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join b (meet a (join c (meet a b)))))))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *)