Added problems from CASC 208

[helm.git] / helm / software / matita / contribs / ng_TPTP / CASC_2008 / COL046-1.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL046-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL046-1.ma
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@@ -0,0 +1,84 @@
+include "logic/equality.ma".
+
+(* Inclusion of: COL046-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL046-1 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Strong fixed point for B, M and S *)
+
+(*  Version  : [WM88] (equality) axioms. *)
+
+(*  English  : The strong fixed point property holds for the set  *)
+
+(*             P consisting of the combinators B, M and S, where ((Sx)y)z  *)
+
+(*             = (xz)(yz), ((Bx)y)z = x(yz), Mx = xx. *)
+
+(*  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 *)
+
+(*           : [Wos89] Wos (1989), A Challenge Problem and a Recent Workshop *)
+
+(*  Source   : [Wos89] *)
+
+(*  Names    : - [Wos89] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.33 v3.4.0, 0.50 v3.3.0, 0.57 v3.2.0, 0.64 v3.1.0, 0.67 v2.7.0, 0.55 v2.6.0, 0.17 v2.5.0, 0.25 v2.4.0, 0.00 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;   4 unit;   1 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 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :    8 (   0 singleton) *)
+
+(*             Maximal term depth    :    4 (   3 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_fixed_point:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀f:∀_:Univ.Univ.
+∀m:Univ.
+∀s:Univ.
+∀H0:∀X:Univ.eq Univ (apply m X) (apply X X).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#b ##.
+#f ##.
+#m ##.
+#s ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1,H2 ##;
+##| ##skip ##]
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)