(* -------------------------------------------------------------------------- *)
-(* File : GRP002-3 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : GRP002-3 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Group Theory *)
(* Status : Unsatisfiable *)
-(* Rating : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.25 v2.0.0 *)
+(* Rating : 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.25 v2.0.0 *)
(* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 1 RR) *)
(* -------------------------------------------------------------------------- *)
-(* File : GRP004-0 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : GRP004-0 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Group Theory *)
(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *)
-(* Number of literals : 3 ( 3 equality) *)
+(* Number of atoms : 3 ( 3 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* ----Definition of the commutator *)
ntheorem prove_commutator:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀b:Univ.
∀commutator:∀_:Univ.∀_:Univ.Univ.
∀H1:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (multiply X (multiply Y (multiply (inverse X) (inverse Y)))).
∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
∀H3:∀X:Univ.eq Univ (multiply (inverse X) X) identity.
-∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (commutator (commutator a b) b) identity
+∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (commutator (commutator a b) b) identity)
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#b.
-#commutator.
-#identity.
-#inverse.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-nauto by H0,H1,H2,H3,H4;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#commutator ##.
+#identity ##.
+#inverse ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+nauto by H0,H1,H2,H3,H4 ##;
+ntry (nassumption) ##;
nqed.
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