X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Fng_TPTP%2FLAT043-1.ma;fp=matita%2Fmatita%2Fcontribs%2Fng_TPTP%2FLAT043-1.ma;h=93a02235a60326ab57effc8612d9b6c767976f0e;hb=2c01ff6094173915e7023076ea48b5804dca7778;hp=0000000000000000000000000000000000000000;hpb=a050e3f80d7ea084ce0184279af98e8251c7d2a6;p=helm.git diff --git a/matita/matita/contribs/ng_TPTP/LAT043-1.ma b/matita/matita/contribs/ng_TPTP/LAT043-1.ma new file mode 100644 index 000000000..93a02235a --- /dev/null +++ b/matita/matita/contribs/ng_TPTP/LAT043-1.ma @@ -0,0 +1,155 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT043-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT043-1 : TPTP v3.7.0. Released v2.5.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Lattice compatability from Boolean algebra *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [RW01] Rose & Wilkinson (2001), Application of Model Search *) + +(* Source : [RW01] *) + +(* Names : eqp-a2.in [RW01] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.11 v3.4.0, 0.00 v2.5.0 *) + +(* Syntax : Number of clauses : 13 ( 0 non-Horn; 13 unit; 1 RR) *) + +(* Number of atoms : 13 ( 13 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 7 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 22 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include lattice 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 *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----Distributivity (4) *) + +(* ----Invertability (5) *) + +(* ----Preceding gives us Boolean Algebra *) + +(* ----Denial of compatability *) +ntheorem prove_compatability_law: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀c:Univ. +∀complement:∀_:Univ.Univ. +∀d:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀n0:Univ. +∀n1:Univ. +∀H0:∀X:Univ.eq Univ (complement (complement X)) X. +∀H1:∀X:Univ.eq Univ (meet (complement X) X) n0. +∀H2:∀X:Univ.eq Univ (join (complement X) X) n1. +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y Z)) (join (meet X Y) (meet X Z)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H6:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H8:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H9:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H10:∀X:Univ.eq Univ (join X X) X. +∀H11:∀X:Univ.eq Univ (meet X X) X.eq Univ (complement (join c d)) (meet (complement c) (complement d))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#c ##. +#complement ##. +#d ##. +#join ##. +#meet ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *)