X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FROB014-1.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FROB014-1.ma;h=c26539236c4bedba659d9e0157a7248c76a7a0c1;hb=36326bac6e833046698176f50fdbb4517f6705a5;hp=0000000000000000000000000000000000000000;hpb=0910d4f494486273e3a22fbfbb2290b48f5786b7;p=helm.git diff --git a/helm/software/matita/contribs/TPTP/HEQ/ROB014-1.ma b/helm/software/matita/contribs/TPTP/HEQ/ROB014-1.ma new file mode 100644 index 000000000..c26539236 --- /dev/null +++ b/helm/software/matita/contribs/TPTP/HEQ/ROB014-1.ma @@ -0,0 +1,148 @@ +set "baseuri" "cic:/matita/TPTP/ROB014-1". +include "logic/equality.ma". + +(* Inclusion of: ROB014-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : ROB014-1 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Robbins Algebra *) + +(* Problem : If -(-e + -(d + -e)) = d then -(e + k(d + -(d + -e))) = -e, k=1 *) + +(* Version : [Win90] (equality) axioms. *) + +(* English : This is the base step of an induction proof. *) + +(* Refs : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *) + +(* Source : [Win90] *) + +(* Names : Lemma 3.6 [Win90] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.71 v3.1.0, 0.78 v2.7.0, 0.67 v2.6.0, 0.86 v2.5.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 9 ( 0 non-Horn; 7 unit; 4 RR) *) + +(* Number of atoms : 11 ( 7 equality) *) + +(* Maximal clause size : 2 ( 1 average) *) + +(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *) + +(* Number of functors : 7 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 11 ( 0 singleton) *) + +(* Maximal term depth : 8 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----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 : *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include axioms for numbers in Robbins algebras *) + +(* Inclusion of: Axioms/ROB001-1.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : ROB001-1 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Robbins Algebra *) + +(* Axioms : Robbins algebra numbers axioms *) + +(* Version : [Win90] (equality) axioms. *) + +(* English : *) + +(* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *) + +(* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *) + +(* Source : [Win90] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 2 unit; 2 RR) *) + +(* Number of literals : 6 ( 2 equality) *) + +(* Maximal clause size : 2 ( 2 average) *) + +(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *) + +(* Number of functors : 4 ( 1 constant; 0-2 arity) *) + +(* Number of variables : 4 ( 0 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires ROB001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +theorem prove_base_step: + ∀Univ:Set.∀V:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀d:Univ.∀e:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀negate:∀_:Univ.Univ.∀one:Univ.∀positive_integer:∀_:Univ.Prop.∀successor:∀_:Univ.Univ.∀H0:eq Univ (negate (add (negate e) (negate (add d (negate e))))) d.∀H1:∀X:Univ.∀_:positive_integer X.positive_integer (successor X).∀H2:positive_integer one.∀H3:∀V:Univ.∀X:Univ.∀_:positive_integer X.eq Univ (multiply (successor V) X) (add X (multiply V X)).∀H4:∀X:Univ.eq Univ (multiply one X) X.∀H5:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add e (multiply one (add d (negate (add d (negate e))))))) (negate e) +. +intros. +autobatch paramodulation timeout=600; +try assumption. +print proofterm. +qed. + +(* -------------------------------------------------------------------------- *)