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[helm.git] / matita / tests / TPTP / Veloci / LCL164-1.p.ma

diff --git a/matita/tests/TPTP/Veloci/LCL164-1.p.ma b/matita/tests/TPTP/Veloci/LCL164-1.p.ma
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+
+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.
+(* -------------------------------------------------------------------------- *)