-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / COL002-5.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/COL002-5.ma b/helm/software/matita/contribs/ng_TPTP/COL002-5.ma
new file mode 100644 (file)
index 0000000..c026dd8
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+++ b/helm/software/matita/contribs/ng_TPTP/COL002-5.ma
@@ -0,0 +1,86 @@
+include "logic/equality.ma".
+
+(* Inclusion of: COL002-5.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL002-5 : TPTP v3.2.0. Bugfixed v3.1.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Weak fixed point for S, B, C, and I *)
+
+(*  Version  : [WM88] (equality) axioms. *)
+
+(*             Theorem formulation : The fixed point is provided and checked. *)
+
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+
+(*             of the combinators S, B, C, and I, where ((Sx)y)z = (xz)(yz),  *)
+
+(*             ((Bx)y)z = x(yz), ((Cx)y)z = (xz)y, and Ix = x. *)
+
+(*  Refs     : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.43 v3.1.0 *)
+
+(*  Syntax   : Number of clauses     :    6 (   0 non-Horn;   6 unit;   1 RR) *)
+
+(*             Number of atoms       :    6 (   6 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    7 (   5 constant; 0-2 arity) *)
+
+(*             Number of variables   :   11 (   0 singleton) *)
+
+(*             Maximal term depth    :    6 (   3 average) *)
+
+(*  Comments : This is the one found in proof 3 of C1.1 in [WM88]. *)
+
+(*  Bugfixes : Fixed clauses weak_fixed_point and prove_weak_fixed_point. *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_weak_fixed_point:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀c:Univ.
+∀fixed_pt:Univ.
+∀i:Univ.
+∀s:Univ.
+∀weak_fixed_point:∀_:Univ.Univ.
+∀H0:∀X:Univ.eq Univ (weak_fixed_point X) (apply (apply (apply s (apply c (apply b X))) (apply s (apply c (apply b X)))) (apply s (apply c (apply b X)))).
+∀H1:∀X:Univ.eq Univ (apply i X) X.
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y).
+∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).
+∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (weak_fixed_point fixed_pt) (apply fixed_pt (weak_fixed_point fixed_pt))
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#apply.
+#b.
+#c.
+#fixed_pt.
+#i.
+#s.
+#weak_fixed_point.
+#H0.
+#H1.
+#H2.
+#H3.
+#H4.
+nauto by H0,H1,H2,H3,H4;
+nqed.
+
+(* -------------------------------------------------------------------------- *)