Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / LCL165-1.ma

diff --git a/matita/matita/contribs/ng_TPTP/LCL165-1.ma b/matita/matita/contribs/ng_TPTP/LCL165-1.ma
new file mode 100644 (file)
index 0000000..81396c7
--- /dev/null
+++ b/matita/matita/contribs/ng_TPTP/LCL165-1.ma
@@ -0,0 +1,191 @@
+include "logic/equality.ma".
+
+(* Inclusion of: LCL165-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LCL165-1 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+
+(*  Problem  : A ntheorem in Wajsberg algebras *)
+
+(*  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    : Third problem [Bon91] *)
+
+(*  Status   : Satisfiable *)
+
+(*  Rating   : 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.5.0, 0.67 v2.4.0, 1.00 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :   11 (   0 non-Horn;  11 unit;   1 RR) *)
+
+(*             Number of atoms       :   11 (  11 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    6 (   2 constant; 0-2 arity) *)
+
+(*             Number of variables   :   22 (   0 singleton) *)
+
+(*             Maximal term depth    :    5 (   3 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra axioms  *)
+
+(* Inclusion of: Axioms/LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LCL001-0 : TPTP v3.7.0. 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 atoms      :    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 v3.7.0. 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 atoms      :    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  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_wajsberg_ntheorem:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀myand:∀_:Univ.∀_:Univ.Univ.
+∀implies:∀_:Univ.∀_:Univ.Univ.
+∀not:∀_:Univ.Univ.
+∀or:∀_:Univ.∀_:Univ.Univ.
+∀truth:Univ.
+∀x:Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (myand X Y) (myand Y X).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand (myand X Y) Z) (myand X (myand Y Z)).
+∀H2:∀X:Univ.∀Y:Univ.eq Univ (myand X Y) (not (or (not X) (not Y))).
+∀H3:∀X:Univ.∀Y:Univ.eq Univ (or X Y) (or Y X).
+∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (or (or X Y) Z) (or X (or Y Z)).
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (or X Y) (implies (not X) Y).
+∀H6:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+∀H7:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+∀H9:∀X:Univ.eq Univ (implies truth X) X.eq Univ (not (or (myand x (or x x)) (myand x x))) (myand (not x) (or (or (not x) (not x)) (myand (not x) (not x)))))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#myand ##.
+#implies ##.
+#not ##.
+#or ##.
+#truth ##.
+#x ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)