(* -------------------------------------------------------------------------- *)
-(* File : BOO001-1 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : BOO001-1 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Boolean Algebra (Ternary) *)
(* -------------------------------------------------------------------------- *)
-(* File : BOO001-0 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : BOO001-0 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Algebra (Ternary Boolean) *)
(* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 0 RR) *)
-(* Number of literals : 5 ( 5 equality) *)
+(* Number of atoms : 5 ( 5 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* -------------------------------------------------------------------------- *)
ntheorem prove_inverse_is_self_cancelling:
- ∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀inverse:∀_:Univ.Univ.
∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ.
∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X.
∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X.
-∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (inverse (inverse a)) a
+∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (inverse (inverse a)) a)
.
-#Univ.
-#V.
-#W.
-#X.
-#Y.
-#Z.
-#a.
-#inverse.
-#multiply.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-nauto by H0,H1,H2,H3,H4;
+#Univ ##.
+#V ##.
+#W ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#inverse ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+nauto by H0,H1,H2,H3,H4 ##;
+ntry (nassumption) ##;
nqed.
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