X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FLAT002-1.ma;fp=matita%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FLAT002-1.ma;h=a68c8d44b263f3c3f2b4b8c8d11007d8b7a8c632;hb=2c01ff6094173915e7023076ea48b5804dca7778;hp=0000000000000000000000000000000000000000;hpb=a050e3f80d7ea084ce0184279af98e8251c7d2a6;p=helm.git diff --git a/matita/matita/contribs/TPTP/HEQ/LAT002-1.ma b/matita/matita/contribs/TPTP/HEQ/LAT002-1.ma new file mode 100644 index 000000000..a68c8d44b --- /dev/null +++ b/matita/matita/contribs/TPTP/HEQ/LAT002-1.ma @@ -0,0 +1,220 @@ +set "baseuri" "cic:/matita/TPTP/LAT002-1". +include "logic/equality.ma". + +(* Inclusion of: LAT002-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT002-1 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : If X' = U v V and Y' = U ^ V, then U' exists *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : The theorem states that there is a complement of "a" in a *) + +(* modular lattice with 0 and 1. *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [GO+69] Guard et al. (1969), Semi-Automated Mathematics *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* Source : [McC88] *) + +(* Names : L1b [McC88] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.43 v3.1.0, 0.78 v2.7.0, 0.83 v2.6.0, 0.71 v2.5.0, 1.00 v2.4.0, 0.83 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 19 ( 0 non-Horn; 15 unit; 6 RR) *) + +(* Number of atoms : 24 ( 18 equality) *) + +(* Maximal clause size : 3 ( 1 average) *) + +(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 8 ( 6 constant; 0-2 arity) *) + +(* Number of variables : 30 ( 5 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include lattice axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.2.0. 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 literals : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include modular lattice axioms *) + +(* Inclusion of: Axioms/LAT001-1.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-1 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory modularity (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 : 5 ( 0 non-Horn; 4 unit; 0 RR) *) + +(* Number of literals : 6 ( 6 equality) *) + +(* Maximal clause size : 2 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 7 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires LAT001-0.ax *) + +(* : These axioms, with 4 extra redundant axioms about 0 & 1, are *) + +(* used in [Wos88] p.217. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include 1 and 0 in the lattice *) + +(* ----Require the lattice to be modular *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include definition of complement *) + +(* Inclusion of: Axioms/LAT001-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-2 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory complement (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 0 unit; 3 RR) *) + +(* Number of literals : 7 ( 4 equality) *) + +(* Maximal clause size : 3 ( 2 average) *) + +(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 2 ( 1 average) *) + +(* Comments : Requires LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Definition of complement *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +theorem prove_complememt_exists: + ∀Univ:Set.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (join X Y) n1.∀_:eq Univ (meet X Y) n0.complement X Y.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet X Z) X.eq Univ (meet Z (join X Y)) (join X (meet Y Z)).∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.∃W:Univ.complement a W +. +intros. +exists[ +2: +autobatch depth=5 width=5 size=20 timeout=10; +try assumption. +| +skip] +print proofterm. +qed. + +(* -------------------------------------------------------------------------- *)