Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / COL042-8.ma

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+include "logic/equality.ma".
+
+(* Inclusion of: COL042-8.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL042-8 : TPTP v3.7.0. Released v2.1.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Strong fixed point for B and W1 *)
+
+(*  Version  : [WM88] (equality) axioms. *)
+
+(*             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 W1, where ((Bx)y)z  *)
+
+(*             = x(yz), (W1x)y = (yx)x. *)
+
+(*  Refs     : [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   : 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.1.0, 0.11 v2.7.0, 0.18 v2.6.0, 0.00 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.50 v2.2.0, 0.80 v2.1.0 *)
+
+(*  Syntax   : Number of clauses     :    4 (   0 non-Horn;   4 unit;   2 RR) *)
+
+(*             Number of atoms       :    4 (   4 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    5 (   4 constant; 0-2 arity) *)
+
+(*             Number of variables   :    5 (   0 singleton) *)
+
+(*             Maximal term depth    :    7 (   3 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_strong_fixed_point:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀fixed_pt:Univ.
+∀strong_fixed_point:Univ.
+∀w1:Univ.
+∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply w1 w1)) (apply (apply b (apply b w1)) b))) b).
+∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w1 X) Y) (apply (apply Y X) X).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt)))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#b ##.
+#fixed_pt ##.
+#strong_fixed_point ##.
+#w1 ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+nauto by H0,H1,H2 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)