Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / COL032-1.ma

diff --git a/matita/matita/contribs/ng_TPTP/COL032-1.ma b/matita/matita/contribs/ng_TPTP/COL032-1.ma
new file mode 100644 (file)
index 0000000..7ba259f
--- /dev/null
+++ b/matita/matita/contribs/ng_TPTP/COL032-1.ma
@@ -0,0 +1,80 @@
+include "logic/equality.ma".
+
+(* Inclusion of: COL032-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL032-1 : TPTP v3.7.0. Released v1.0.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Strong fixed point for Q and M *)
+
+(*  Version  : [WM88] (equality) axioms. *)
+
+(*  English  : The strong fixed point property holds for the set  *)
+
+(*             P consisting of the combinators Q and M, where Mx = xx,  *)
+
+(*             ((Qx)y)z = y(xz). *)
+
+(*  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 *)
+
+(*           : [MW88]  McCune & Wos (1988), Some Fixed Point Problems in Comb *)
+
+(*  Source   : [MW88] *)
+
+(*  Names    : - [MW88] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.1.0, 0.22 v2.7.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.13 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    3 (   0 non-Horn;   3 unit;   1 RR) *)
+
+(*             Number of atoms       :    3 (   3 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    4 (   2 constant; 0-2 arity) *)
+
+(*             Number of variables   :    5 (   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.
+∀f:∀_:Univ.Univ.
+∀m:Univ.
+∀q:Univ.
+∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)).
+∀H1:∀X:Univ.eq Univ (apply m X) (apply X X).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y))))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#apply ##.
+#f ##.
+#m ##.
+#q ##.
+#H0 ##.
+#H1 ##.
+napply (ex_intro ? ? ? ?) ##[
+##2:
+nauto by H0,H1 ##;
+##| ##skip ##]
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)