-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / COL043-3.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/COL043-3.ma b/helm/software/matita/contribs/ng_TPTP/COL043-3.ma
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+++ b/helm/software/matita/contribs/ng_TPTP/COL043-3.ma
@@ -0,0 +1,80 @@
+include "logic/equality.ma".
+
+(* Inclusion of: COL043-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL043-3 : TPTP v3.2.0. Bugfixed v2.3.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Strong fixed point for B and H *)
+
+(*  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 H, where ((Bx)y)z  *)
+
+(*             = x(yz), ((Hx)y)z = ((xy)z)y. *)
+
+(*  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    : - [Wos93] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.79 v3.2.0, 0.71 v3.1.0, 0.78 v2.7.0, 1.00 v2.6.0, 0.83 v2.5.0, 0.75 v2.4.0, 0.67 v2.3.0 *)
+
+(*  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   :    6 (   0 singleton) *)
+
+(*             Maximal term depth    :   11 (   4 average) *)
+
+(*  Comments :  *)
+
+(*  Bugfixes : v2.3.0 - Clause strong_fixed_point fixed. *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_strong_fixed_point:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀fixed_pt:Univ.
+∀h:Univ.
+∀strong_fixed_point:Univ.
+∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply h (apply (apply b (apply (apply b h) (apply b b))) (apply h (apply (apply b h) (apply b b))))) h)) b)) b).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply h X) Y) Z) (apply (apply (apply X Y) Z) Y).
+∀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.
+#h.
+#strong_fixed_point.
+#H0.
+#H1.
+#H2.
+nauto by H0,H1,H2;
+nqed.
+
+(* -------------------------------------------------------------------------- *)