Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / LCL140-1.ma

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+include "logic/equality.ma".
+
+(* Inclusion of: LCL140-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LCL140-1 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+
+(*  Problem  : A lemma in Wajsberg algebras *)
+
+(*  Version  : [Bon91] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(*  Source   : [Bon91] *)
+
+(*  Names    : Lemma 9 [Bon91] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   1 RR) *)
+
+(*             Number of atoms       :    5 (   5 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    4 (   2 constant; 0-2 arity) *)
+
+(*             Number of variables   :    8 (   0 singleton) *)
+
+(*             Maximal term depth    :    4 (   2 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 :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_wajsberg_lemma:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀implies:∀_:Univ.∀_:Univ.Univ.
+∀not:∀_:Univ.Univ.
+∀truth:Univ.
+∀x:Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+∀H1:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+∀H3:∀X:Univ.eq Univ (implies truth X) X.eq Univ (not (not x)) x)
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#implies ##.
+#not ##.
+#truth ##.
+#x ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+nauto by H0,H1,H2,H3 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)