X-Git-Url: http://matita.cs.unibo.it/gitweb/?a=blobdiff_plain;f=helm%2Fsoftware%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FROB006-3.ma;fp=helm%2Fsoftware%2Fmatita%2Fcontribs%2FTPTP%2FHEQ%2FROB006-3.ma;h=6e579be8b5c11ec313a7326e35e9bf3ec13eb00e;hb=36326bac6e833046698176f50fdbb4517f6705a5;hp=0000000000000000000000000000000000000000;hpb=0910d4f494486273e3a22fbfbb2290b48f5786b7;p=helm.git diff --git a/helm/software/matita/contribs/TPTP/HEQ/ROB006-3.ma b/helm/software/matita/contribs/TPTP/HEQ/ROB006-3.ma new file mode 100644 index 000000000..6e579be8b --- /dev/null +++ b/helm/software/matita/contribs/TPTP/HEQ/ROB006-3.ma @@ -0,0 +1,164 @@ +set "baseuri" "cic:/matita/TPTP/ROB006-3". +include "logic/equality.ma". + +(* Inclusion of: ROB006-3.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : ROB006-3 : TPTP v3.2.0. Released v1.0.0. *) + +(* Domain : Robbins Algebra *) + +(* Problem : c + d=d => Boolean *) + +(* Version : [Win90] (equality) axioms : Augmented. *) + +(* Theorem formulation : Denies Huntington's axiom. *) + +(* English : If there are elements c and d such that c+d=d, then the *) + +(* algebra is Boolean. *) + +(* Refs : [HMT71] Henkin et al. (1971), Cylindrical Algebras *) + +(* : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *) + +(* : [Wos92] Wos (1992), An Opportunity to Test Your Skills, and th *) + +(* Source : [Wos92] *) + +(* Names : Theorem 1.1 [Win90] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.86 v3.1.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 13 ( 0 non-Horn; 8 unit; 8 RR) *) + +(* Number of atoms : 19 ( 14 equality) *) + +(* Maximal clause size : 3 ( 1 average) *) + +(* Number of predicates : 2 ( 0 propositional; 1-2 arity) *) + +(* Number of functors : 9 ( 5 constant; 0-2 arity) *) + +(* Number of variables : 19 ( 0 singleton) *) + +(* Maximal term depth : 8 ( 3 average) *) + +(* Comments : Commutativity, associativity, and Huntington's axiom *) + +(* axiomatize Boolean algebra. *) + +(* : The extra lemmas are suggested by Winker (1990). *) + +(* -------------------------------------------------------------------------- *) + +(* ----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 Robbins algebra numbers *) + +(* 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 *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following are extra lemmas *) + +(* ----Hypothesis of the theorem *) +theorem prove_huntingtons_axiom: + ∀Univ:Set.∀V:Univ.∀V2:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀add:∀_:Univ.∀_:Univ.Univ.∀b:Univ.∀c:Univ.∀d:Univ.∀multiply:∀_:Univ.∀_:Univ.Univ.∀negate:∀_:Univ.Univ.∀one:Univ.∀positive_integer:∀_:Univ.Prop.∀successor:∀_:Univ.Univ.∀H0:eq Univ (add c d) d.∀H1:∀X:Univ.∀Y:Univ.∀_:eq Univ (negate (add (negate Y) (negate (add X (negate Y))))) X.eq Univ (add Y (multiply (successor (successor one)) (add X (negate (add X (negate Y)))))) (add Y (multiply (successor one) (add X (negate (add X (negate Y)))))).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (negate (add X (negate Y))) (negate Y).eq Univ (add Y (multiply (successor (successor one)) (add X (negate (add X (negate Y)))))) (add Y (multiply (successor one) (add X (negate (add X (negate Y)))))).∀H3:∀V2:Univ.∀X:Univ.∀Y:Univ.∀_:eq Univ (negate (add X Y)) (negate Y).∀_:positive_integer V2.eq Univ (negate (add Y (multiply V2 (add X (negate (add X (negate Y))))))) (negate Y).∀H4:∀X:Univ.eq Univ (add X X) X.∀H5:∀X:Univ.∀_:positive_integer X.positive_integer (successor X).∀H6:positive_integer one.∀H7:∀V:Univ.∀X:Univ.∀_:positive_integer X.eq Univ (multiply (successor V) X) (add X (multiply V X)).∀H8:∀X:Univ.eq Univ (multiply one X) X.∀H9:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).∀H11:∀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 +. +intros. +autobatch paramodulation timeout=600; +try assumption. +print proofterm. +qed. + +(* -------------------------------------------------------------------------- *)