X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FCOL071-1.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FCOL071-1.ma;h=6a0ff4c1d0409ff9c55d1cfc57c14f7d900ea457;hb=11e495dda047bcdfa4267c06cad2d074fcffe3e3;hp=0000000000000000000000000000000000000000;hpb=b7587a7dd68463086e8a6b7c14f10c1dc33f64ba;p=helm.git diff --git a/helm/software/matita/contribs/ng_TPTP/COL071-1.ma b/helm/software/matita/contribs/ng_TPTP/COL071-1.ma new file mode 100644 index 000000000..6a0ff4c1d --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/COL071-1.ma @@ -0,0 +1,78 @@ +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. + +(* -------------------------------------------------------------------------- *)