-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / LCL109-6.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/LCL109-6.ma b/helm/software/matita/contribs/ng_TPTP/LCL109-6.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: LCL109-6.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LCL109-6 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+
+(*  Problem  : A ntheorem in the lattice structure of Wajsberg algebras *)
+
+(*  Version  : [Bon91] (equality) axioms : Augmented. *)
+
+(*             Theorem formulation : Alternative Wajsberg algebras lattice  *)
+
+(*             structure. *)
+
+(*  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    : Lattice structure ntheorem 8 [Bon91] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.14 v3.1.0, 0.11 v2.7.0, 0.09 v2.6.0, 0.17 v2.5.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 0.88 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 v3.2.0. 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  *)
+ntheorem prove_wajsberg_mv_4:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀and_star:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀falsehood:Univ.
+∀implies:∀_:Univ.∀_:Univ.Univ.
+∀not:∀_:Univ.Univ.
+∀truth:Univ.
+∀xor:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies X Y) (xor truth (and_star X (xor truth Y))).
+∀H1:eq Univ (not truth) falsehood.
+∀H2:∀X:Univ.∀Y:Univ.eq Univ (and_star X Y) (and_star Y X).
+∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)).
+∀H4:∀X:Univ.∀Y:Univ.eq Univ (xor X Y) (xor Y X).
+∀H5:∀X:Univ.∀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).
+∀H6:∀X:Univ.∀Y:Univ.eq Univ (xor X (xor truth Y)) (xor (xor X truth) Y).
+∀H7:∀X:Univ.eq Univ (and_star (xor truth X) X) falsehood.
+∀H8:∀X:Univ.eq Univ (and_star X falsehood) falsehood.
+∀H9:∀X:Univ.eq Univ (and_star X truth) X.
+∀H10:∀X:Univ.eq Univ (xor X X) falsehood.
+∀H11:∀X:Univ.eq Univ (xor X falsehood) X.
+∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies (implies a b) (implies b a)) (implies b a)) truth
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#a.
+#and_star.
+#b.
+#falsehood.
+#implies.
+#not.
+#truth.
+#xor.
+#H0.
+#H1.
+#H2.
+#H3.
+#H4.
+#H5.
+#H6.
+#H7.
+#H8.
+#H9.
+#H10.
+#H11.
+#H12.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12;
+nqed.
+
+(* -------------------------------------------------------------------------- *)