+
+include "logic/equality.ma".
+(* Inclusion of: LCL132-1.p *)
+(* -------------------------------------------------------------------------- *)
+(* File : LCL132-1 : TPTP v3.1.1. 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 1 [Bon91] *)
+(* Status : Unsatisfiable *)
+(* Rating : 0.00 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 v3.1.1. 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 : *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_lemma:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x x) truth
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)