X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;ds=inline;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FGRP473-1.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FGRP473-1.ma;h=ecdd2d0bb7fad253c8ced24c7b90827f27ac16aa;hb=11e495dda047bcdfa4267c06cad2d074fcffe3e3;hp=0000000000000000000000000000000000000000;hpb=b7587a7dd68463086e8a6b7c14f10c1dc33f64ba;p=helm.git diff --git a/helm/software/matita/contribs/ng_TPTP/GRP473-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP473-1.ma new file mode 100644 index 000000000..ecdd2d0bb --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/GRP473-1.ma @@ -0,0 +1,69 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP473-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP473-1 : TPTP v3.2.0. Released v2.6.0. *) + +(* Domain : Group Theory *) + +(* Problem : Axiom for group theory, in division and inverse, part 2 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.07 v3.1.0, 0.11 v2.7.0, 0.18 v2.6.0 *) + +(* 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 : 5 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 5 ( 3 average) *) + +(* Comments : A UEQ part of GRP072-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_2: + ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. +∀a2:Univ. +∀b2:Univ. +∀divide:∀_:Univ.∀_:Univ.Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (divide (inverse (divide A B)) (divide (divide C D) A)) (divide D C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2 +. +#Univ. +#A. +#B. +#C. +#D. +#a2. +#b2. +#divide. +#inverse. +#multiply. +#H0. +#H1. +nauto by H0,H1; +nqed. + +(* -------------------------------------------------------------------------- *)