-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / COL071-1.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/COL071-1.ma b/helm/software/matita/contribs/ng_TPTP/COL071-1.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: COL071-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL071-1 : TPTP v3.2.0. Released v1.2.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Strong fixed point for N and Q *)
+
+(*  Version  : [WM88] (equality) axioms. *)
+
+(*  English  : The strong fixed point property holds for the set  *)
+
+(*             P consisting of the combinators N and Q, where ((Nx)y)z  *)
+
+(*             = ((xz)y)z, ((Qx)y)z = y(xz). *)
+
+(*  Refs     : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(*           : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+
+(*           : [Zha95] Zhang (1995), Email to G. Sutcliffe *)
+
+(*  Source   : [Wos93] *)
+
+(*  Names    : Question 14 [Wos93] *)
+
+(*  Status   : Satisfiable *)
+
+(*  Rating   : 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.4.0, 1.00 v2.3.0, 0.67 v2.2.1, 0.75 v2.2.0, 1.00 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   :    7 (   0 singleton) *)
+
+(*             Maximal term depth    :    4 (   4 average) *)
+
+(*  Comments : [Zha95] provided a 4 element model of these clauses. *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_fixed_point:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀f:∀_:Univ.Univ.
+∀n: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.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#apply.
+#f.
+#n.
+#q.
+#H0.
+#H1.
+napply ex_intro[
+nid2:
+nauto by H0,H1;
+nid|
+skip]
+nqed.
+
+(* -------------------------------------------------------------------------- *)