+++ /dev/null
-include "logic/equality.ma".
-
-(* Inclusion of: COL003-2.p *)
-
-(* -------------------------------------------------------------------------- *)
-
-(* File : COL003-2 : TPTP v3.2.0. Released v1.0.0. *)
-
-(* Domain : Combinatory Logic *)
-
-(* Problem : Strong fixed point for B and W *)
-
-(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
-
-(* Theorem formulation : The fixed point is provided and checked. *)
-
-(* English : The strong fixed point property holds for the set *)
-
-(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
-
-(* = x(yz) and (Wx)y = (xy)y. *)
-
-(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
-
-(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
-
-(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
-
-(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
-
-(* Source : [TPTP] *)
-
-(* Names : *)
-
-(* Status : Unsatisfiable *)
-
-(* Rating : 0.29 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0 *)
-
-(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
-
-(* Number of atoms : 5 ( 3 equality) *)
-
-(* Maximal clause size : 2 ( 1 average) *)
-
-(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
-
-(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
-
-(* Number of variables : 6 ( 0 singleton) *)
-
-(* Maximal term depth : 5 ( 3 average) *)
-
-(* Comments : This the J sage of [McCune & Wos, 1987], found by Statman. *)
-
-(* -------------------------------------------------------------------------- *)
-ntheorem prove_strong_fixed_point:
- (∀Univ:Type.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
-∀apply:∀_:Univ.∀_:Univ.Univ.
-∀b:Univ.
-∀fixed_point:∀_:Univ.Prop.
-∀fixed_pt:Univ.
-∀w:Univ.
-∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.
-∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).
-∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))))
-.
-#Univ ##.
-#Strong_fixed_point ##.
-#X ##.
-#Y ##.
-#Z ##.
-#apply ##.
-#b ##.
-#fixed_point ##.
-#fixed_pt ##.
-#w ##.
-#H0 ##.
-#H1 ##.
-#H2 ##.
-nauto by H0,H1,H2 ##;
-nqed.
-
-(* -------------------------------------------------------------------------- *)
--- /dev/null
+include "logic/equality.ma".
+
+(* Inclusion of: COL003-2.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : COL003-2 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Combinatory Logic *)
+
+(* Problem : Strong fixed point for B and W *)
+
+(* Version : [WM88] (equality) axioms : Augmented > Especial. *)
+
+(* Theorem formulation : The fixed point is provided and checked. *)
+
+(* English : The strong fixed point property holds for the set *)
+
+(* P consisting of the combinators B and W alone, where ((Bx)y)z *)
+
+(* = x(yz) and (Wx)y = (xy)y. *)
+
+(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+
+(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *)
+
+(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.29 v3.1.0, 0.33 v2.7.0, 0.17 v2.6.0, 0.29 v2.5.0, 0.20 v2.4.0, 0.33 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 4 ( 0 non-Horn; 3 unit; 2 RR) *)
+
+(* Number of atoms : 5 ( 3 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *)
+
+(* Number of functors : 4 ( 3 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 5 ( 3 average) *)
+
+(* Comments : This the J sage of [McCune & Wos, 1987], found by Statman. *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_strong_fixed_point:
+ (∀Univ:Type.∀Strong_fixed_point:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀fixed_point:∀_:Univ.Prop.
+∀fixed_pt:Univ.
+∀w:Univ.
+∀H0:∀Strong_fixed_point:Univ.∀_:eq Univ (apply Strong_fixed_point fixed_pt) (apply fixed_pt (apply Strong_fixed_point fixed_pt)).fixed_point Strong_fixed_point.
+∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).fixed_point (apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))))
+.
+#Univ ##.
+#Strong_fixed_point ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#b ##.
+#fixed_point ##.
+#fixed_pt ##.
+#w ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+nauto by H0,H1,H2 ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)