X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Ftests%2FTPTP%2FVeloci%2FLCL164-1.p.ma;fp=matita%2Ftests%2FTPTP%2FVeloci%2FLCL164-1.p.ma;h=e5bc4b5135858837b5fdb10b127f325c342a57a4;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/tests/TPTP/Veloci/LCL164-1.p.ma b/matita/tests/TPTP/Veloci/LCL164-1.p.ma new file mode 100644 index 000000000..e5bc4b513 --- /dev/null +++ b/matita/tests/TPTP/Veloci/LCL164-1.p.ma @@ -0,0 +1,86 @@ + +include "logic/equality.ma". +(* Inclusion of: LCL164-1.p *) +(* -------------------------------------------------------------------------- *) +(* File : LCL164-1 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Logic Calculi (Wajsberg Algebra) *) +(* Problem : The 4th Wajsberg algebra axiom, from the alternative axioms *) +(* 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 4 [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 : 14 ( 0 non-Horn; 14 unit; 2 RR) *) +(* Number of atoms : 14 ( 14 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 8 ( 4 constant; 0-2 arity) *) +(* Number of variables : 19 ( 1 singleton) *) +(* Maximal term depth : 5 ( 2 average) *) +(* Comments : *) +(* -------------------------------------------------------------------------- *) +(* ----Include Alternative Wajsberg algebra axioms *) +(* Inclusion of: Axioms/LCL002-0.ax *) +(* -------------------------------------------------------------------------- *) +(* File : LCL002-0 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Logic Calculi (Wajsberg Algebras) *) +(* Axioms : Alternative Wajsberg algebra axioms *) +(* 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 : 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 : 5 ( 2 constant; 0-2 arity) *) +(* Number of variables : 10 ( 1 singleton) *) +(* Maximal term depth : 5 ( 2 average) *) +(* Comments : To be used in conjunction with the LAT003 alternative *) +(* Wajsberg algebra definitions. *) +(* -------------------------------------------------------------------------- *) +(* -------------------------------------------------------------------------- *) +(* -------------------------------------------------------------------------- *) +(* ----Include some Alternative Wajsberg algebra definitions *) +(* include('Axioms/LCL002-1.ax'). *) +(* ----Definition that and_star is AC and xor is C *) +(* ----Definition of false in terms of true *) +(* ----Include the definition of implies in terms of xor and and_star *) +theorem prove_wajsberg_axiom: + \forall Univ:Set. +\forall and_star:\forall _:Univ.\forall _:Univ.Univ. +\forall falsehood:Univ. +\forall implies:\forall _:Univ.\forall _:Univ.Univ. +\forall not:\forall _:Univ.Univ. +\forall truth:Univ. +\forall x:Univ. +\forall xor:\forall _:Univ.\forall _:Univ.Univ. +\forall y:Univ. +\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies X Y) (xor truth (and_star X (xor truth Y))). +\forall H1:eq Univ (not truth) falsehood. +\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (and_star Y X). +\forall H3:\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 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 (and_star (xor (and_star (xor truth X) Y) truth) Y) (and_star (xor (and_star (xor truth Y) X) truth) X). +\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (xor X (xor truth Y)) (xor (xor X truth) Y). +\forall H7:\forall X:Univ.eq Univ (and_star (xor truth X) X) falsehood. +\forall H8:\forall X:Univ.eq Univ (and_star X falsehood) falsehood. +\forall H9:\forall X:Univ.eq Univ (and_star X truth) X. +\forall H10:\forall X:Univ.eq Univ (xor X X) falsehood. +\forall H11:\forall X:Univ.eq Univ (xor X falsehood) X. +\forall H12:\forall X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies (not x) (not y)) (implies y x)) truth +. +intros. +autobatch paramodulation timeout=100; +try assumption. +print proofterm. +qed. +(* -------------------------------------------------------------------------- *)