X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Ftests%2FTPTP%2FVeloci%2FLCL154-1.p.ma;fp=matita%2Ftests%2FTPTP%2FVeloci%2FLCL154-1.p.ma;h=1d4c41b30fb612cbc9acd5ed05c558693e687858;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/tests/TPTP/Veloci/LCL154-1.p.ma b/matita/tests/TPTP/Veloci/LCL154-1.p.ma new file mode 100644 index 000000000..1d4c41b30 --- /dev/null +++ b/matita/tests/TPTP/Veloci/LCL154-1.p.ma @@ -0,0 +1,136 @@ + +include "logic/equality.ma". +(* Inclusion of: LCL154-1.p *) +(* -------------------------------------------------------------------------- *) +(* File : LCL154-1 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Logic Calculi (Wajsberg Algebra) *) +(* Problem : The 2nd alternative Wajsberg algebra axiom *) +(* Version : [Bon91] (equality) axioms. *) +(* English : *) +(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *) +(* : [AB90] Anantharaman & Bonacina (1990), An Application of the *) +(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *) +(* Source : [Bon91] *) +(* Names : W' axiom 2 [Bon91] *) +(* Status : Unsatisfiable *) +(* Rating : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 v2.0.0 *) +(* Syntax : Number of clauses : 17 ( 0 non-Horn; 17 unit; 2 RR) *) +(* Number of atoms : 17 ( 17 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 9 ( 3 constant; 0-2 arity) *) +(* Number of variables : 33 ( 0 singleton) *) +(* Maximal term depth : 4 ( 2 average) *) +(* Comments : *) +(* -------------------------------------------------------------------------- *) +(* ----Include Wajsberg algebra axioms *) +(* Inclusion of: Axioms/LCL001-0.ax *) +(* -------------------------------------------------------------------------- *) +(* File : LCL001-0 : TPTP v3.1.1. 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 and and or definitions *) +(* Inclusion of: Axioms/LCL001-2.ax *) +(* -------------------------------------------------------------------------- *) +(* File : LCL001-2 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Logic Calculi (Wajsberg Algebras) *) +(* Axioms : Wajsberg algebra AND and OR definitions *) +(* Version : [AB90] (equality) axioms. *) +(* English : *) +(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *) +(* : [AB90] Anantharaman & Bonacina (1990), An Application of the *) +(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *) +(* Source : [Bon91] *) +(* Names : *) +(* Status : *) +(* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 0 RR) *) +(* Number of literals : 6 ( 6 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 4 ( 0 constant; 1-2 arity) *) +(* Number of variables : 14 ( 0 singleton) *) +(* Maximal term depth : 4 ( 3 average) *) +(* Comments : Requires LCL001-0.ax *) +(* -------------------------------------------------------------------------- *) +(* ----Definitions of or and and, which are AC *) +(* -------------------------------------------------------------------------- *) +(* ----Include Alternative Wajsberg algebra definitions *) +(* Inclusion of: Axioms/LCL002-1.ax *) +(* -------------------------------------------------------------------------- *) +(* File : LCL002-1 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Logic Calculi (Wajsberg Algebras) *) +(* Axioms : Alternative Wajsberg algebra definitions *) +(* Version : [AB90] (equality) axioms. *) +(* English : *) +(* Refs : [FRT84] Font et al. (1984), Wajsberg Algebras *) +(* : [AB90] Anantharaman & Bonacina (1990), An Application of the *) +(* : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *) +(* Source : [Bon91] *) +(* Names : *) +(* Status : *) +(* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 1 RR) *) +(* Number of literals : 6 ( 6 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 7 ( 2 constant; 0-2 arity) *) +(* Number of variables : 11 ( 0 singleton) *) +(* Maximal term depth : 4 ( 2 average) *) +(* Comments : Requires LCL001-0.ax LCL001-2.ax *) +(* -------------------------------------------------------------------------- *) +(* ----Definitions of and_star and xor, where and_star is AC and xor is C *) +(* ---I guess the next two can be derived from the AC of and *) +(* ----Definition of false in terms of truth *) +(* -------------------------------------------------------------------------- *) +(* -------------------------------------------------------------------------- *) +theorem prove_alternative_wajsberg_axiom: + \forall Univ:Set. +\forall myand:\forall _:Univ.\forall _:Univ.Univ. +\forall and_star:\forall _:Univ.\forall _:Univ.Univ. +\forall falsehood:Univ. +\forall implies:\forall _:Univ.\forall _:Univ.Univ. +\forall not:\forall _:Univ.Univ. +\forall or:\forall _:Univ.\forall _:Univ.Univ. +\forall truth:Univ. +\forall x:Univ. +\forall xor:\forall _:Univ.\forall _:Univ.Univ. +\forall H0:eq Univ (not truth) falsehood. +\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (and_star Y X). +\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)). +\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (not (or (not X) (not Y))). +\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (xor Y X). +\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (or (myand X (not Y)) (myand (not X) Y)). +\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (myand Y X). +\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (myand (myand X Y) Z) (myand X (myand Y Z)). +\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (not (or (not X) (not Y))). +\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (or Y X). +\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (or (or X Y) Z) (or X (or Y Z)). +\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (implies (not X) Y). +\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth. +\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X). +\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth. +\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (xor x falsehood) x +. +intros. +autobatch paramodulation timeout=100; +try assumption. +print proofterm. +qed. +(* -------------------------------------------------------------------------- *)