X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Fng_TPTP%2FCOL066-3.ma;fp=matita%2Fmatita%2Fcontribs%2Fng_TPTP%2FCOL066-3.ma;h=1f19300581698ee39326a19e9b16c8445feb43f6;hb=2c01ff6094173915e7023076ea48b5804dca7778;hp=0000000000000000000000000000000000000000;hpb=a050e3f80d7ea084ce0184279af98e8251c7d2a6;p=helm.git diff --git a/matita/matita/contribs/ng_TPTP/COL066-3.ma b/matita/matita/contribs/ng_TPTP/COL066-3.ma new file mode 100644 index 000000000..1f1930058 --- /dev/null +++ b/matita/matita/contribs/ng_TPTP/COL066-3.ma @@ -0,0 +1,87 @@ +include "logic/equality.ma". + +(* Inclusion of: COL066-3.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL066-3 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Find combinator equivalent to P from B, Q and W *) + +(* Version : [WM88] (equality) axioms. *) + +(* Theorem formulation : The combinator is provided and checked. *) + +(* English : Construct from B, Q and W alone a combinator that behaves as *) + +(* the combinator P does, where ((Bx)y)z = x(yz), ((Qx)y)z = *) + +(* y(xz), (Wx)y = (xy)y, (((Px)y)y)z = (xy)((xy)z) *) + +(* 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 : 0.11 v3.4.0, 0.12 v3.3.0, 0.00 v3.1.0, 0.11 v2.7.0, 0.00 v2.1.0, 0.29 v2.0.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 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 : 7 ( 6 constant; 0-2 arity) *) + +(* Number of variables : 8 ( 0 singleton) *) + +(* Maximal term depth : 10 ( 4 average) *) + +(* Comments : *) + +(* Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----This is the P equivalent *) +ntheorem prove_p_combinator: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀q:Univ. +∀w:Univ. +∀x:Univ. +∀y:Univ. +∀z:Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)). +∀H2:∀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 (apply b (apply w (apply q (apply q q)))) q) x) y) y) z) (apply (apply x y) (apply (apply x y) z))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#q ##. +#w ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *)