X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FROB004-1.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FROB004-1.ma;h=981a05054078ae13dacf8730f48f703dd0b2656e;hb=11e495dda047bcdfa4267c06cad2d074fcffe3e3;hp=0000000000000000000000000000000000000000;hpb=b7587a7dd68463086e8a6b7c14f10c1dc33f64ba;p=helm.git diff --git a/helm/software/matita/contribs/ng_TPTP/ROB004-1.ma b/helm/software/matita/contribs/ng_TPTP/ROB004-1.ma new file mode 100644 index 000000000..981a05054 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/ROB004-1.ma @@ -0,0 +1,132 @@ +include "logic/equality.ma". + +(* Inclusion of: ROB004-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : ROB004-1 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Robbins Algebra *) + +(* Problem : c = -d, c + d=d, and c + c=c => Boolean *) + +(* Version : [Win90] (equality) axioms. *) + +(* English : If there exist c, d such that c = -d, c+d=d, and c+c=c, then *) + +(* the algebra is Boolean. *) + +(* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *) + +(* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *) + +(* Source : [Win90] *) + +(* Names : Lemma 2.3 [Win90] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 v2.0.0 *) + +(* Syntax : Number of clauses : 7 ( 0 non-Horn; 7 unit; 4 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 : 6 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 7 ( 0 singleton) *) + +(* Maximal term depth : 6 ( 2 average) *) + +(* Comments : Commutativity, associativity, and Huntington's axiom *) + +(* axiomatize Boolean algebra. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include axioms for Robbins algebra *) + +(* Inclusion of: Axioms/ROB001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : ROB001-0 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Robbins algebra *) + +(* Axioms : Robbins algebra axioms *) + +(* Version : [Win90] (equality) axioms. *) + +(* English : *) + +(* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *) + +(* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *) + +(* Source : [OTTER] *) + +(* Names : Lemma 2.2 [Win90] *) + +(* Status : *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 RR) *) + +(* Number of literals : 3 ( 3 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 2 ( 0 constant; 1-2 arity) *) + +(* Number of variables : 7 ( 0 singleton) *) + +(* Maximal term depth : 6 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_huntingtons_axiom: + ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀c:Univ. +∀d:Univ. +∀negate:∀_:Univ.Univ. +∀H0:eq Univ (add c c) c. +∀H1:eq Univ (add c d) d. +∀H2:eq Univ (negate d) c. +∀H3:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add (negate (add a (negate b))) (negate (add (negate a) (negate b)))) b +. +#Univ. +#X. +#Y. +#Z. +#a. +#add. +#b. +#c. +#d. +#negate. +#H0. +#H1. +#H2. +#H3. +#H4. +#H5. +nauto by H0,H1,H2,H3,H4,H5; +nqed. + +(* -------------------------------------------------------------------------- *)