X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=sidebyside;f=matita%2Fmatita%2Fcontribs%2Fng_TPTP%2FLDA007-3.ma;fp=matita%2Fmatita%2Fcontribs%2Fng_TPTP%2FLDA007-3.ma;h=d65e2fd7711847ae5c23212b977b156936bc1c85;hb=2c01ff6094173915e7023076ea48b5804dca7778;hp=0000000000000000000000000000000000000000;hpb=a050e3f80d7ea084ce0184279af98e8251c7d2a6;p=helm.git diff --git a/matita/matita/contribs/ng_TPTP/LDA007-3.ma b/matita/matita/contribs/ng_TPTP/LDA007-3.ma new file mode 100644 index 000000000..d65e2fd77 --- /dev/null +++ b/matita/matita/contribs/ng_TPTP/LDA007-3.ma @@ -0,0 +1,93 @@ +include "logic/equality.ma". + +(* Inclusion of: LDA007-3.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : LDA007-3 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : LD-Algebras (Embedding algebras) *) + +(* Problem : Let g = cr(t). Show that t(tsg) = tt(ts)(tg) *) + +(* Version : [Jec93] axioms : Incomplete > Reduced & Augmented > Incomplete. *) + +(* English : *) + +(* Refs : [Jec93] Jech (1993), LD-Algebras *) + +(* Source : [Jec93] *) + +(* Names : Problem 8 [Jec93] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 v2.0.0 *) + +(* Syntax : Number of clauses : 7 ( 0 non-Horn; 7 unit; 6 RR) *) + +(* Number of atoms : 7 ( 7 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 9 ( 8 constant; 0-2 arity) *) + +(* Number of variables : 3 ( 0 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Embedding algebra axioms *) + +(* include('Axioms/LDA001-0.ax'). *) + +(* -------------------------------------------------------------------------- *) + +(* ----t(tsk) = tt(ts)(tk), where k=crit(t) *) +ntheorem prove_equation: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀f:∀_:Univ.∀_:Univ.Univ. +∀k:Univ. +∀s:Univ. +∀t:Univ. +∀tk:Univ. +∀ts:Univ. +∀tsk:Univ. +∀tt:Univ. +∀tt_ts:Univ. +∀H0:eq Univ tsk (f ts k). +∀H1:eq Univ tk (f t k). +∀H2:eq Univ tt_ts (f tt ts). +∀H3:eq Univ ts (f t s). +∀H4:eq Univ tt (f t t). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f t tsk) (f tt_ts tk)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#f ##. +#k ##. +#s ##. +#t ##. +#tk ##. +#ts ##. +#tsk ##. +#tt ##. +#tt_ts ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +nauto by H0,H1,H2,H3,H4,H5 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *)