X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FGRP548-1.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FGRP548-1.ma;h=c5c404e8c9deb6fdaf90f6d6ba11027028ff366c;hb=11e495dda047bcdfa4267c06cad2d074fcffe3e3;hp=0000000000000000000000000000000000000000;hpb=b7587a7dd68463086e8a6b7c14f10c1dc33f64ba;p=helm.git diff --git a/helm/software/matita/contribs/ng_TPTP/GRP548-1.ma b/helm/software/matita/contribs/ng_TPTP/GRP548-1.ma new file mode 100644 index 000000000..c5c404e8c --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/GRP548-1.ma @@ -0,0 +1,76 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP548-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP548-1 : TPTP v3.2.0. Bugfixed v2.7.0. *) + +(* Domain : Group Theory (Abelian) *) + +(* Problem : Axiom for Abelian group theory, in division and identity, part 4 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.00 v2.7.0 *) + +(* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 RR) *) + +(* Number of atoms : 5 ( 5 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 7 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : A UEQ part of GRP094-1 *) + +(* Bugfixes : v2.7.0 - Grounded conjecture *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_4: + ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. +∀a:Univ. +∀b:Univ. +∀divide:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.eq Univ identity (divide A A). +∀H1:∀A:Univ.eq Univ (inverse A) (divide identity A). +∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (divide identity B)). +∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply a b) (multiply b a) +. +#Univ. +#A. +#B. +#C. +#a. +#b. +#divide. +#identity. +#inverse. +#multiply. +#H0. +#H1. +#H2. +#H3. +nauto by H0,H1,H2,H3; +nqed. + +(* -------------------------------------------------------------------------- *)