(* -------------------------------------------------------------------------- *)
-(* File : RNG021-7 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : RNG021-7 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Ring Theory (Alternative) *)
(* Status : Unsatisfiable *)
-(* Rating : 0.14 v3.2.0, 0.21 v3.1.0, 0.33 v2.7.0, 0.45 v2.6.0, 0.33 v2.5.0, 0.25 v2.4.0, 0.67 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.88 v2.0.0 *)
+(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.14 v3.2.0, 0.21 v3.1.0, 0.33 v2.7.0, 0.45 v2.6.0, 0.33 v2.5.0, 0.25 v2.4.0, 0.67 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.88 v2.0.0 *)
(* Syntax : Number of clauses : 23 ( 0 non-Horn; 23 unit; 1 RR) *)
(* -------------------------------------------------------------------------- *)
-(* File : RNG003-0 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : RNG003-0 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Ring Theory (Alternative) *)
(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *)
-(* Number of literals : 15 ( 15 equality) *)
+(* Number of atoms : 15 ( 15 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* ----The next 7 clause are extra lemmas which Stevens found useful *)
ntheorem prove_linearised_form3:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀add:∀_:Univ.∀_:Univ.Univ.
∀additive_identity:Univ.
∀additive_inverse:∀_:Univ.Univ.
∀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 (associator (add u v) x y) (add (associator u x y) (associator v x y))
+∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator (add u v) x y) (add (associator u x y) (associator v x y)))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#add.
-#additive_identity.
-#additive_inverse.
-#associator.
-#commutator.
-#multiply.
-#u.
-#v.
-#x.
-#y.
-#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;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#additive_identity ##.
+#additive_inverse ##.
+#associator ##.
+#commutator ##.
+#multiply ##.
+#u ##.
+#v ##.
+#x ##.
+#y ##.
+#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 ##;
+ntry (nassumption) ##;
nqed.
(* -------------------------------------------------------------------------- *)