(* -------------------------------------------------------------------------- *)
-(* File : BOO022-1 : TPTP v3.2.0. Released v2.2.0. *)
+(* File : BOO022-1 : TPTP v3.7.0. Released v2.2.0. *)
(* Domain : Boolean Algebra *)
(* Status : Unsatisfiable *)
-(* Rating : 0.14 v3.2.0, 0.07 v3.1.0, 0.22 v2.7.0, 0.00 v2.2.1 *)
+(* Rating : 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.2.0, 0.07 v3.1.0, 0.22 v2.7.0, 0.00 v2.2.1 *)
(* Syntax : Number of clauses : 7 ( 0 non-Horn; 7 unit; 1 RR) *)
(* ----Denial of conclusion: *)
ntheorem prove_associativity_of_multiply:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀a:Univ.
∀add:∀_:Univ.∀_:Univ.Univ.
∀b:Univ.
∀H2:∀X:Univ.∀Y:Univ.eq Univ (add (multiply X Y) Y) Y.
∀H3:∀X:Univ.eq Univ (add X (inverse X)) n1.
∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)).
-∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c))
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c)))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#a.
-#add.
-#b.
-#c.
-#inverse.
-#multiply.
-#n0.
-#n1.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-nauto by H0,H1,H2,H3,H4,H5;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#b ##.
+#c ##.
+#inverse ##.
+#multiply ##.
+#n0 ##.
+#n1 ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+nauto by H0,H1,H2,H3,H4,H5 ##;
+ntry (nassumption) ##;
nqed.
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