X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FCASC_2008%2FBOO007-4.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2Fng_TPTP%2FCASC_2008%2FBOO007-4.ma;h=36ecd6386730739577b2f3d0f081b024b383b83d;hb=2b649ad5e3d7413b795fe86bdf7fe6a5c0b9c194;hp=0000000000000000000000000000000000000000;hpb=02e8b3eb9d2a8a3bb3942c41b47b6ac048efd5be;p=helm.git diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO007-4.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO007-4.ma new file mode 100644 index 000000000..36ecd6386 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO007-4.ma @@ -0,0 +1,133 @@ +include "logic/equality.ma". + +(* Inclusion of: BOO007-4.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO007-4 : TPTP v3.7.0. Released v1.1.0. *) + +(* Domain : Boolean Algebra *) + +(* Problem : Product is associative ( (X * Y) * Z = X * (Y * Z) ) *) + +(* Version : [Ver94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ver94] Veroff (1994), Problem Set *) + +(* Source : [Ver94] *) + +(* Names : TD [Ver94] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.14 v3.2.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.09 v2.6.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.62 v2.0.0 *) + +(* Syntax : Number of clauses : 9 ( 0 non-Horn; 9 unit; 1 RR) *) + +(* Number of atoms : 9 ( 9 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 8 ( 5 constant; 0-2 arity) *) + +(* Number of variables : 14 ( 0 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include boolean algebra axioms for equality formulation *) + +(* Inclusion of: Axioms/BOO004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO004-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Boolean Algebra *) + +(* Axioms : Boolean algebra (equality) axioms *) + +(* Version : [Ver94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ver94] Veroff (1994), Problem Set *) + +(* Source : [Ver94] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *) + +(* Number of atoms : 8 ( 8 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 : 14 ( 0 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_associativity: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀b:Univ. +∀c:Univ. +∀inverse:∀_:Univ.Univ. +∀multiplicative_identity:Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.eq Univ (multiply X (inverse X)) additive_identity. +∀H1:∀X:Univ.eq Univ (add X (inverse X)) multiplicative_identity. +∀H2:∀X:Univ.eq Univ (multiply X multiplicative_identity) X. +∀H3:∀X:Univ.eq Univ (add X additive_identity) X. +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#c ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *)