X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Ftests%2FTPTP%2FVeloci%2FGRP011-4.p.ma;fp=matita%2Ftests%2FTPTP%2FVeloci%2FGRP011-4.p.ma;h=a935ade1c04848d2057d4dd9afca3de735356068;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/tests/TPTP/Veloci/GRP011-4.p.ma b/matita/tests/TPTP/Veloci/GRP011-4.p.ma new file mode 100644 index 000000000..a935ade1c --- /dev/null +++ b/matita/tests/TPTP/Veloci/GRP011-4.p.ma @@ -0,0 +1,46 @@ + +include "logic/equality.ma". +(* Inclusion of: GRP011-4.p *) +(* -------------------------------------------------------------------------- *) +(* File : GRP011-4 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Group Theory *) +(* Problem : Left cancellation *) +(* Version : [Wos65] (equality) axioms : Incomplete. *) +(* English : *) +(* Refs : [Wos65] Wos (1965), Unpublished Note *) +(* : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au *) +(* Source : [Pel86] *) +(* Names : Pelletier 63 [Pel86] *) +(* Status : Unsatisfiable *) +(* Rating : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *) +(* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 2 RR) *) +(* Number of atoms : 5 ( 5 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 : 5 ( 0 singleton) *) +(* Maximal term depth : 3 ( 2 average) *) +(* Comments : [Pel86] says "... problems, published I think, by Larry Wos *) +(* (but I cannot locate where)." *) +(* -------------------------------------------------------------------------- *) +(* ----The operation '*' is associative *) +(* ----There exists an identity element *) +theorem prove_left_cancellation: + \forall Univ:Set. +\forall b:Univ. +\forall c:Univ. +\forall d:Univ. +\forall identity:Univ. +\forall inverse:\forall _:Univ.Univ. +\forall multiply:\forall _:Univ.\forall _:Univ.Univ. +\forall H0:eq Univ (multiply b c) (multiply d c). +\forall H1:\forall X:Univ.eq Univ (multiply (inverse X) X) identity. +\forall H2:\forall X:Univ.eq Univ (multiply identity X) X. +\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ b d +. +intros. +autobatch paramodulation timeout=100; +try assumption. +print proofterm. +qed. +(* -------------------------------------------------------------------------- *)