--- /dev/null
+include "logic/equality.ma".
+
+(* Inclusion of: RNG026-7.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : RNG026-7 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Ring Theory (Alternative) *)
+
+(* Problem : Teichmuller Identity *)
+
+(* Version : [Ste87] (equality) axioms : Augmented. *)
+
+(* English : *)
+
+(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.50 v3.1.0, 0.33 v2.7.0, 0.64 v2.6.0, 0.50 v2.5.0, 0.25 v2.4.0, 0.67 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 23 ( 0 non-Horn; 23 unit; 1 RR) *)
+
+(* Number of atoms : 23 ( 23 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 10 ( 5 constant; 0-3 arity) *)
+
+(* Number of variables : 45 ( 2 singleton) *)
+
+(* Maximal term depth : 7 ( 3 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include nonassociative ring axioms *)
+
+(* Inclusion of: Axioms/RNG003-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : RNG003-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Ring Theory (Alternative) *)
+
+(* Axioms : Alternative ring theory (equality) axioms *)
+
+(* Version : [Ste87] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
+
+(* Source : [Ste87] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *)
+
+(* Number of literals : 15 ( 15 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 6 ( 1 constant; 0-3 arity) *)
+
+(* Number of variables : 27 ( 2 singleton) *)
+
+(* Maximal term depth : 5 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----There exists an additive identity element *)
+
+(* ----Multiplicative zero *)
+
+(* ----Existence of left additive additive_inverse *)
+
+(* ----Inverse of additive_inverse of X is X *)
+
+(* ----Distributive property of product over sum *)
+
+(* ----Commutativity for addition *)
+
+(* ----Associativity for addition *)
+
+(* ----Right alternative law *)
+
+(* ----Left alternative law *)
+
+(* ----Associator *)
+
+(* ----Commutator *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----The next 7 clause are extra lemmas which Stevens found useful *)
+ntheorem prove_teichmuller_identity:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀add:∀_:Univ.∀_:Univ.Univ.
+∀additive_identity:Univ.
+∀additive_inverse:∀_:Univ.Univ.
+∀associator:∀_:Univ.∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀c:Univ.
+∀commutator:∀_:Univ.∀_:Univ.Univ.
+∀d:Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) (additive_inverse Z)) (add (additive_inverse (multiply X Z)) (additive_inverse (multiply Y Z))).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (additive_inverse X) (add Y Z)) (add (additive_inverse (multiply X Y)) (additive_inverse (multiply X Z))).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X (additive_inverse Y)) Z) (add (multiply X Z) (additive_inverse (multiply Y Z))).
+∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
+∀H4:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
+∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).
+∀H7:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
+∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))).
+∀H9:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)).
+∀H10:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)).
+∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
+∀H12:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).
+∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+∀H15:∀X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+∀H16:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
+∀H17:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+∀H20:∀X:Univ.eq Univ (add X additive_identity) X.
+∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d)))) additive_identity
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#a.
+#add.
+#additive_identity.
+#additive_inverse.
+#associator.
+#b.
+#c.
+#commutator.
+#d.
+#multiply.
+#H0.
+#H1.
+#H2.
+#H3.
+#H4.
+#H5.
+#H6.
+#H7.
+#H8.
+#H9.
+#H10.
+#H11.
+#H12.
+#H13.
+#H14.
+#H15.
+#H16.
+#H17.
+#H18.
+#H19.
+#H20.
+#H21.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21;
+nqed.
+
+(* -------------------------------------------------------------------------- *)
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