-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / COL056-1.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/COL056-1.ma b/helm/software/matita/contribs/ng_TPTP/COL056-1.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: COL056-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : COL056-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Combinatory Logic *)
+
+(*  Problem  : Normal Birds *)
+
+(*  Version  : Especial. *)
+
+(*  English  : For all birds x and y, there exists a bird z that composes  *)
+
+(*             x with y for all birds w. Prove that if there exists a happy  *)
+
+(*             bird then there exists a normal bird. *)
+
+(*  Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+
+(*  Source   : [ANL] *)
+
+(*  Names    : bird8.ver1.in [ANL] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.07 v3.1.0, 0.00 v2.7.0, 0.09 v2.6.0, 0.17 v2.5.0, 0.00 v2.0.0 *)
+
+(*  Syntax   : Number of clauses     :    4 (   0 non-Horn;   4 unit;   3 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 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :    5 (   1 singleton) *)
+
+(*             Maximal term depth    :    3 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----For all birds x and y, there exists a bird z that composes x with  *)
+
+(* ----y for all birds w. *)
+
+(* ----   FAx FAy TEz FAw [response(z,w) = response(x,response(y,w))]. *)
+
+(* ----   response(comp(x,y),w) = response(x,response(y,w)).  *)
+
+(* ----Hypothesis: If there exists a happy bird then there exists a normal  *)
+
+(* ----bird. *)
+
+(* ----Finding clause (using xy to replace response(x,y)): *)
+
+(* ----   -[ If TEx TEy TEz (xy = z) and (xz = y) *)
+
+(* ----      then TEw TEv (wv = v) ]. *)
+
+(* ----   -[ FAx FAy FAz -((xy = z) and (xz = y)) | TEw TEv (wv = v) ] *)
+
+(* ----   TEx TEy TEz [(xy = z) and (xz = y)] and FAw FAv -(wv = v). *)
+
+(* ----   (AB = C) and (AC = B) and -(wv = v). *)
+ntheorem prove_there_exists_a_happy_bird:
+ ∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.
+∀a:Univ.
+∀b:Univ.
+∀c:Univ.
+∀compose:∀_:Univ.∀_:Univ.Univ.
+∀response:∀_:Univ.∀_:Univ.Univ.
+∀H0:eq Univ (response a c) b.
+∀H1:eq Univ (response a b) c.
+∀H2:∀W:Univ.∀X:Univ.∀Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).∃V:Univ.∃W:Univ.eq Univ (response W V) V
+.
+#Univ.
+#V.
+#W.
+#X.
+#Y.
+#a.
+#b.
+#c.
+#compose.
+#response.
+#H0.
+#H1.
+#H2.
+napply ex_intro[
+nid2:
+napply ex_intro[
+nid2:
+nauto by H0,H1,H2;
+nid|
+skip]
+nid|
+skip]
+nqed.
+
+(* -------------------------------------------------------------------------- *)