-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / COL017-1.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/COL017-1.ma b/helm/software/matita/contribs/ng_TPTP/COL017-1.ma
new file mode 100644 (file)
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+++ b/helm/software/matita/contribs/ng_TPTP/COL017-1.ma
@@ -0,0 +1,84 @@
+include "logic/equality.ma".
+
+(* Inclusion of: COL017-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL017-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Weak fixed point for B, M, and T *)
+
+(*  Version  : [WM88] (equality) axioms. *)
+
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+
+(*             of the combinators B, M, and T, where ((Bx)y)z = x(yz),  *)
+
+(*             Mx = xx, (Tx)y = yx. *)
+
+(*  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   : 0.00 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 (   4 constant; 0-2 arity) *)
+
+(*             Number of variables   :    7 (   0 singleton) *)
+
+(*             Maximal term depth    :    4 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_fixed_point:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀combinator:Univ.
+∀m:Univ.
+∀t:Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+∀H1:∀X:Univ.eq Univ (apply m X) (apply X X).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ Y (apply combinator Y)
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#apply.
+#b.
+#combinator.
+#m.
+#t.
+#H0.
+#H1.
+#H2.
+napply ex_intro[
+nid2:
+nauto by H0,H1,H2;
+nid|
+skip]
+nqed.
+
+(* -------------------------------------------------------------------------- *)