--- /dev/null
+include "logic/equality.ma".
+
+(* Inclusion of: LCL153-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL153-1 : TPTP v3.7.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebra) *)
+
+(* Problem : The 1st alternative Wajsberg algebra axiom *)
+
+(* 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 : W' axiom 1 [Bon91] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 v2.0.0 *)
+
+(* Syntax : Number of clauses : 17 ( 0 non-Horn; 17 unit; 2 RR) *)
+
+(* Number of atoms : 17 ( 17 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 9 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 33 ( 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 : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include Alternative Wajsberg algebra definitions *)
+
+(* Inclusion of: Axioms/LCL002-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LCL002-1 : TPTP v3.7.0. Released v1.0.0. *)
+
+(* Domain : Logic Calculi (Wajsberg Algebras) *)
+
+(* Axioms : Alternative Wajsberg algebra 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; 1 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 : 7 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 11 ( 0 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : Requires LCL001-0.ax LCL001-2.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definitions of and_star and xor, where and_star is AC and xor is C *)
+
+(* ---I guess the next two can be derived from the AC of and *)
+
+(* ----Definition of false in terms of truth *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_alternative_wajsberg_axiom:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀myand:∀_:Univ.∀_:Univ.Univ.
+∀and_star:∀_:Univ.∀_:Univ.Univ.
+∀falsehood:Univ.
+∀implies:∀_:Univ.∀_:Univ.Univ.
+∀not:∀_:Univ.Univ.
+∀or:∀_:Univ.∀_:Univ.Univ.
+∀truth:Univ.
+∀x:Univ.
+∀xor:∀_:Univ.∀_:Univ.Univ.
+∀H0:eq Univ (not truth) falsehood.
+∀H1:∀X:Univ.∀Y:Univ.eq Univ (and_star X Y) (and_star Y X).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)).
+∀H3:∀X:Univ.∀Y:Univ.eq Univ (and_star X Y) (not (or (not X) (not Y))).
+∀H4:∀X:Univ.∀Y:Univ.eq Univ (xor X Y) (xor Y X).
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (xor X Y) (or (myand X (not Y)) (myand (not X) Y)).
+∀H6:∀X:Univ.∀Y:Univ.eq Univ (myand X Y) (myand Y X).
+∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (myand (myand X Y) Z) (myand X (myand Y Z)).
+∀H8:∀X:Univ.∀Y:Univ.eq Univ (myand X Y) (not (or (not X) (not Y))).
+∀H9:∀X:Univ.∀Y:Univ.eq Univ (or X Y) (or Y X).
+∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (or (or X Y) Z) (or X (or Y Z)).
+∀H11:∀X:Univ.∀Y:Univ.eq Univ (or X Y) (implies (not X) Y).
+∀H12:∀X:Univ.∀Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+∀H13:∀X:Univ.∀Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+∀H15:∀X:Univ.eq Univ (implies truth X) X.eq Univ (not x) (xor x truth))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#myand ##.
+#and_star ##.
+#falsehood ##.
+#implies ##.
+#not ##.
+#or ##.
+#truth ##.
+#x ##.
+#xor ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+#H14 ##.
+#H15 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)
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