X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FCOL063-4.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FCOL063-4.ma;h=66775e4f6a3d451c8546160b164fd6f1b47755c8;hb=11e495dda047bcdfa4267c06cad2d074fcffe3e3;hp=0000000000000000000000000000000000000000;hpb=b7587a7dd68463086e8a6b7c14f10c1dc33f64ba;p=helm.git diff --git a/helm/software/matita/contribs/ng_TPTP/COL063-4.ma b/helm/software/matita/contribs/ng_TPTP/COL063-4.ma new file mode 100644 index 000000000..66775e4f6 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/COL063-4.ma @@ -0,0 +1,82 @@ +include "logic/equality.ma". + +(* Inclusion of: COL063-4.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL063-4 : TPTP v3.2.0. Bugfixed v1.2.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Find combinator equivalent to F from B and T *) + +(* Version : [WM88] (equality) axioms. *) + +(* Theorem formulation : The combinator is provided and checked. *) + +(* English : Construct from B and T alone a combinator that behaves as the *) + +(* combinator F does, where ((Bx)y)z = x(yz), (Tx)y = yx, *) + +(* ((Fx)y)z = (zy)x. *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.43 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 : 6 ( 5 constant; 0-2 arity) *) + +(* Number of variables : 5 ( 0 singleton) *) + +(* Maximal term depth : 9 ( 4 average) *) + +(* Comments : *) + +(* Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----This is the F equivalent *) +ntheorem prove_f_combinator: + ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀t:Univ. +∀x:Univ. +∀y:Univ. +∀z:Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z y) x) +. +#Univ. +#X. +#Y. +#Z. +#apply. +#b. +#t. +#x. +#y. +#z. +#H0. +#H1. +nauto by H0,H1; +nqed. + +(* -------------------------------------------------------------------------- *)