(* -------------------------------------------------------------------------- *)
-(* File : LCL163-1 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : LCL163-1 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Logic Calculi (Wajsberg Algebra) *)
(* Status : Unsatisfiable *)
-(* Rating : 0.14 v3.1.0, 0.11 v2.7.0, 0.09 v2.6.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.44 v2.2.0, 0.43 v2.1.0, 0.75 v2.0.0 *)
+(* Rating : 0.00 v3.4.0, 0.12 v3.3.0, 0.14 v3.1.0, 0.11 v2.7.0, 0.09 v2.6.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.44 v2.2.0, 0.43 v2.1.0, 0.75 v2.0.0 *)
(* Syntax : Number of clauses : 14 ( 0 non-Horn; 14 unit; 2 RR) *)
(* -------------------------------------------------------------------------- *)
-(* File : LCL002-0 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : LCL002-0 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Logic Calculi (Wajsberg Algebras) *)
(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *)
-(* Number of literals : 8 ( 8 equality) *)
+(* Number of atoms : 8 ( 8 equality) *)
(* Maximal clause size : 1 ( 1 average) *)
(* ----Include the definition of implies in terms of xor and and_star *)
ntheorem prove_wajsberg_axiom:
- ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀and_star:∀_:Univ.∀_:Univ.Univ.
∀falsehood:Univ.
∀implies:∀_:Univ.∀_:Univ.Univ.
∀H9:∀X:Univ.eq Univ (and_star X truth) X.
∀H10:∀X:Univ.eq Univ (xor X X) falsehood.
∀H11:∀X:Univ.eq Univ (xor X falsehood) X.
-∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies x y) y) (implies (implies y x) x)
+∀H12:∀X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies x y) y) (implies (implies y x) x))
.
-#Univ.
-#X.
-#Y.
-#Z.
-#and_star.
-#falsehood.
-#implies.
-#not.
-#truth.
-#x.
-#xor.
-#y.
-#H0.
-#H1.
-#H2.
-#H3.
-#H4.
-#H5.
-#H6.
-#H7.
-#H8.
-#H9.
-#H10.
-#H11.
-#H12.
-nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12;
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#and_star ##.
+#falsehood ##.
+#implies ##.
+#not ##.
+#truth ##.
+#x ##.
+#xor ##.
+#y ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12 ##;
+ntry (nassumption) ##;
nqed.
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