(* -------------------------------------------------------------------------- *)
-(* File : BOO027-1 : TPTP v3.2.0. Released v2.2.0. *)
+(* File : BOO027-1 : TPTP v3.7.0. Released v2.2.0. *)
(* Domain : Boolean Algebra *)
(* ----Denial of a property of Boolean Algebra: *)
ntheorem prove_idempotence:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀add:∀_:Univ.∀_:Univ.Univ.
∀inverse:∀_:Univ.Univ.
∀H1:∀X:Univ.∀Y:Univ.eq Univ (add (multiply X (inverse Y)) (add (multiply X Y) (multiply (inverse Y) Y))) X.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (add (multiply X (inverse X)) (add (multiply X Y) (multiply (inverse X) Y))) Y.
∀H3:∀X:Univ.eq Univ (add X (inverse X)) one.
-∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)).eq Univ (add a a) a
+∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)).eq Univ (add a a) a)
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#add.
-#inverse.
-#multiply.
-#one.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-nauto by H0,H1,H2,H3,H4;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#inverse ##.
+#multiply ##.
+#one ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+nauto by H0,H1,H2,H3,H4 ##;
+ntry (nassumption) ##;
nqed.
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