X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matitaB%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FLCL147-1.ma;fp=matitaB%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FLCL147-1.ma;h=7e4f7d7f0591f6ae70eede34160c581ee2e533f8;hb=cacbe3c6493ddce76c4c13379ade271d8dd172e8;hp=0000000000000000000000000000000000000000;hpb=f04a064bb34aabaf91dc0c48e3b08b37ecd7b0a2;p=helm.git diff --git a/matitaB/matita/contribs/TPTP/HEQ/LCL147-1.ma b/matitaB/matita/contribs/TPTP/HEQ/LCL147-1.ma new file mode 100644 index 000000000..7e4f7d7f0 --- /dev/null +++ b/matitaB/matita/contribs/TPTP/HEQ/LCL147-1.ma @@ -0,0 +1,156 @@ +set "baseuri" "cic:/matita/TPTP/LCL147-1". +include "logic/equality.ma". + +(* Inclusion of: LCL147-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : LCL147-1 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Logic Calculi (Wajsberg Algebra) *) + +(* Problem : A theorem in the lattice structure of Wajsberg algebras *) + +(* Version : [Bon91] (equality) axioms. *) + +(* English : *) + +(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *) + +(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *) + +(* Source : [Bon91] *) + +(* Names : Lattice structure theorem 6 [Bon91] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.71 v3.1.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 3 RR) *) + +(* Number of atoms : 11 ( 9 equality) *) + +(* Maximal clause size : 2 ( 1 average) *) + +(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 8 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 16 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Wajsberg algebra axioms *) + +(* Inclusion of: Axioms/LCL001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LCL001-0 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Logic Calculi (Wajsberg Algebras) *) + +(* Axioms : Wajsberg algebra axioms *) + +(* Version : [Bon91] (equality) axioms. *) + +(* English : *) + +(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *) + +(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *) + +(* : [MW92] McCune & Wos (1992), Experiments in Automated Deductio *) + +(* Source : [MW92] *) + +(* Names : MV Sentential Calculus [MW92] *) + +(* Status : *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 0 RR) *) + +(* Number of literals : 4 ( 4 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 1 constant; 0-2 arity) *) + +(* Number of variables : 8 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Wajsberg algebra lattice structure axioms *) + +(* Inclusion of: Axioms/LCL001-1.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LCL001-1 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Logic Calculi (Wajsberg Algebras) *) + +(* Axioms : Wajsberg algebra lattice structure definitions *) + +(* Version : [Bon91] (equality) axioms. *) + +(* English : *) + +(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *) + +(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *) + +(* Source : [Bon91] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *) + +(* Number of literals : 6 ( 4 equality) *) + +(* Maximal clause size : 2 ( 2 average) *) + +(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 1 constant; 0-2 arity) *) + +(* Number of variables : 8 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : Requires LCL001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Definitions of big_V and big_hat *) + +(* ----Definition of partial order *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +theorem prove_wajsberg_theorem: + ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_V x y) z) (big_hat (implies x z) (implies y z)) +. +intros. +autobatch depth=5 width=5 size=20 timeout=10; +try assumption. +print proofterm. +qed. + +(* -------------------------------------------------------------------------- *)