-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / COL057-1.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/COL057-1.ma b/helm/software/matita/contribs/ng_TPTP/COL057-1.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: COL057-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL057-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Strong fixed point for S, B, C, and I *)
+
+(*  Version  : [WM88] (equality) axioms. *)
+
+(*  English  : The strong 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     : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
+
+(*  Source   : [LW92] *)
+
+(*  Names    : CL5 [LW92] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.36 v3.1.0, 0.56 v2.7.0, 0.27 v2.6.0, 0.17 v2.5.0, 0.00 v2.1.0, 0.25 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   1 RR) *)
+
+(*             Number of atoms       :    5 (   5 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    6 (   4 constant; 0-2 arity) *)
+
+(*             Number of variables   :   11 (   0 singleton) *)
+
+(*             Maximal term depth    :    4 (   3 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_strong_fixed_point:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀apply:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀c:Univ.
+∀f:∀_:Univ.Univ.
+∀i:Univ.
+∀s:Univ.
+∀H0:∀X:Univ.eq Univ (apply i X) X.
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).
+∀H3:∀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.
+#c.
+#f.
+#i.
+#s.
+#H0.
+#H1.
+#H2.
+#H3.
+napply ex_intro[
+nid2:
+nauto by H0,H1,H2,H3;
+nid|
+skip]
+nqed.
+
+(* -------------------------------------------------------------------------- *)