X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=matita%2Fmatita%2Fcontribs%2Fng_TPTP%2FGRP185-4.ma;fp=matita%2Fmatita%2Fcontribs%2Fng_TPTP%2FGRP185-4.ma;h=630bfb3ed7c9d063e521dac2a0dbd5b6e706c0f7;hb=2c01ff6094173915e7023076ea48b5804dca7778;hp=0000000000000000000000000000000000000000;hpb=a050e3f80d7ea084ce0184279af98e8251c7d2a6;p=helm.git diff --git a/matita/matita/contribs/ng_TPTP/GRP185-4.ma b/matita/matita/contribs/ng_TPTP/GRP185-4.ma new file mode 100644 index 000000000..630bfb3ed --- /dev/null +++ b/matita/matita/contribs/ng_TPTP/GRP185-4.ma @@ -0,0 +1,231 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP185-4.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP185-4 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Application of monotonicity and distributivity *) + +(* Version : [Fuc94] (equality) axioms : Augmented. *) + +(* Theorem formulation : Using a dual definition of =<. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : p22b [Sch95] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.25 v3.3.0, 0.21 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0, 0.67 v2.5.0, 0.75 v2.4.0, 0.67 v2.2.1, 0.67 v2.2.0, 0.57 v2.1.0, 0.43 v2.0.0 *) + +(* Syntax : Number of clauses : 19 ( 0 non-Horn; 19 unit; 2 RR) *) + +(* Number of atoms : 19 ( 19 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 7 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 36 ( 2 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a > b *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Group Theory *) + +(* Axioms : Group theory (equality) axioms *) + +(* Version : [MOW76] (equality) axioms : *) + +(* Reduced > Complete. *) + +(* English : *) + +(* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [ANL] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 0 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 : 3 ( 1 constant; 0-2 arity) *) + +(* Number of variables : 5 ( 0 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : [MOW76] also contains redundant right_identity and *) + +(* right_inverse axioms. *) + +(* : These axioms are also used in [Wos88] p.186, also with *) + +(* right_identity and right_inverse. *) + +(* -------------------------------------------------------------------------- *) + +(* ----For any x and y in the group x*y is also in the group. No clause *) + +(* ----is needed here since this is an instance of reflexivity *) + +(* ----There exists an identity element *) + +(* ----For any x in the group, there exists an element y such that x*y = y*x *) + +(* ----= identity. *) + +(* ----The operation '*' is associative *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_p22b: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)). +∀H1:∀X:Univ.eq Univ (inverse (inverse X)) X. +∀H2:eq Univ (inverse identity) identity. +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H8:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H9:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H10:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H13:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (least_upper_bound (multiply a b) identity)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *)