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[helm.git] / matitaB / matita / contribs / TPTP / HEQ / LCL147-1.ma

diff --git a/matitaB/matita/contribs/TPTP/HEQ/LCL147-1.ma b/matitaB/matita/contribs/TPTP/HEQ/LCL147-1.ma
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+set "baseuri" "cic:/matita/TPTP/LCL147-1".
+include "logic/equality.ma".
+
+(* Inclusion of: LCL147-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LCL147-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+
+(*  Problem  : A theorem in the lattice structure of 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    : Lattice structure theorem 6 [Bon91] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.71 v3.1.0, 1.00 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    9 (   0 non-Horn;   7 unit;   3 RR) *)
+
+(*             Number of atoms       :   11 (   9 equality) *)
+
+(*             Maximal clause size   :    2 (   1 average) *)
+
+(*             Number of predicates  :    2 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    8 (   4 constant; 0-2 arity) *)
+
+(*             Number of variables   :   16 (   0 singleton) *)
+
+(*             Maximal term depth    :    4 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Wajsberg algebra axioms  *)
+
+(* Inclusion of: Axioms/LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LCL001-0 : TPTP v3.2.0. 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 literals   :    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 lattice structure axioms  *)
+
+(* Inclusion of: Axioms/LCL001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LCL001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+
+(*  Axioms   : Wajsberg algebra lattice structure definitions *)
+
+(*  Version  : [Bon91] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+
+(*  Source   : [Bon91] *)
+
+(*  Names    :  *)
+
+(*  Status   :  *)
+
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   2 unit;   2 RR) *)
+
+(*             Number of literals   :    6 (   4 equality) *)
+
+(*             Maximal clause size  :    2 (   2 average) *)
+
+(*             Number of predicates :    2 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors   :    5 (   1 constant; 0-2 arity) *)
+
+(*             Number of variables  :    8 (   0 singleton) *)
+
+(*             Maximal term depth   :    4 (   2 average) *)
+
+(*  Comments : Requires LCL001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definitions of big_V and big_hat  *)
+
+(* ----Definition of partial order  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_theorem:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀big_V:∀_:Univ.∀_:Univ.Univ.∀big_hat:∀_:Univ.∀_:Univ.Univ.∀implies:∀_:Univ.∀_:Univ.Univ.∀not:∀_:Univ.Univ.∀ordered:∀_:Univ.∀_:Univ.Prop.∀truth:Univ.∀x:Univ.∀y:Univ.∀z:Univ.∀H0:∀X:Univ.∀Y:Univ.∀_:eq Univ (implies X Y) truth.ordered X Y.∀H1:∀X:Univ.∀Y:Univ.∀_:ordered X Y.eq Univ (implies X Y) truth.∀H2:∀X:Univ.∀Y:Univ.eq Univ (big_hat X Y) (not (big_V (not X) (not Y))).∀H3:∀X:Univ.∀Y:Univ.eq Univ (big_V X Y) (implies (implies X Y) Y).∀H4:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.∀H5:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.∀H7:∀X:Univ.eq Univ (implies truth X) X.eq Univ (implies (big_V x y) z) (big_hat (implies x z) (implies y z))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)