(* -------------------------------------------------------------------------- *)
-(* File : ROB032-1 : TPTP v3.2.0. Released v3.1.0. *)
+(* File : ROB032-1 : TPTP v3.7.0. Released v3.1.0. *)
(* Domain : Robbins Algebra *)
(* -------------------------------------------------------------------------- *)
-(* File : ROB001-0 : TPTP v3.2.0. Released v1.0.0. *)
+(* File : ROB001-0 : TPTP v3.7.0. Released v1.0.0. *)
(* Domain : Robbins algebra *)
(* 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) *)
(* -------------------------------------------------------------------------- *)
ntheorem prove_absorbtion:
- ∀Univ:Type.∀C:Univ.∀D:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
+ (∀Univ:Type.∀C:Univ.∀D:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
∀add:∀_:Univ.∀_:Univ.Univ.
∀negate:∀_:Univ.Univ.
∀H0:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
-∀H2:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃C:Univ.∃D:Univ.eq Univ (add C D) D
+∀H2:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃C:Univ.∃D:Univ.eq Univ (add C D) D)
.
-#Univ.
-#C.
-#D.
-#X.
-#Y.
-#Z.
-#add.
-#negate.
-#H0.
-#H1.
-#H2.
-napply ex_intro[
-nid2:
-napply ex_intro[
-nid2:
-nauto by H0,H1,H2;
-nid|
-skip]
-nid|
-skip]
+#Univ ##.
+#C ##.
+#D ##.
+#X ##.
+#Y ##.
+#Z ##.
+#add ##.
+#negate ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1,H2 ##;
+##| ##skip ##]
+##| ##skip ##]
+ntry (nassumption) ##;
nqed.
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