X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Ftests%2FTPTP%2FVeloci%2FGRP001-2.p.ma;fp=matita%2Ftests%2FTPTP%2FVeloci%2FGRP001-2.p.ma;h=07a012a4a143b45fef45fee861dc8f1a3141b426;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/tests/TPTP/Veloci/GRP001-2.p.ma b/matita/tests/TPTP/Veloci/GRP001-2.p.ma new file mode 100644 index 000000000..07a012a4a --- /dev/null +++ b/matita/tests/TPTP/Veloci/GRP001-2.p.ma @@ -0,0 +1,86 @@ + +include "logic/equality.ma". +(* Inclusion of: GRP001-2.p *) +(* -------------------------------------------------------------------------- *) +(* File : GRP001-2 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Group Theory *) +(* Problem : X^2 = identity => commutativity *) +(* Version : [MOW76] (equality) axioms : Augmented. *) +(* English : If the square of every element is the identity, the system *) +(* is commutative. *) +(* Refs : [MOW76] McCharen et al. (1976), Problems and Experiments for a *) +(* : [LO85] Lusk & Overbeek (1985), Reasoning about Equality *) +(* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *) +(* Source : [ANL] *) +(* Names : GP1 [MOW76] *) +(* : Problem 1 [LO85] *) +(* : GT1 [LW92] *) +(* : xsquared.ver2.in [ANL] *) +(* 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 : 8 ( 0 non-Horn; 8 unit; 2 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 : 6 ( 4 constant; 0-2 arity) *) +(* Number of variables : 8 ( 0 singleton) *) +(* Maximal term depth : 3 ( 2 average) *) +(* Comments : *) +(* -------------------------------------------------------------------------- *) +(* ----Include equality group theory axioms *) +(* Inclusion of: Axioms/GRP004-0.ax *) +(* -------------------------------------------------------------------------- *) +(* File : GRP004-0 : TPTP v3.1.1. 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 literals : 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 *) +(* -------------------------------------------------------------------------- *) +(* -------------------------------------------------------------------------- *) +(* ----Redundant two axioms *) +theorem prove_b_times_a_is_c: + \forall Univ:Set. +\forall a:Univ. +\forall b:Univ. +\forall c:Univ. +\forall identity:Univ. +\forall inverse:\forall _:Univ.Univ. +\forall multiply:\forall _:Univ.\forall _:Univ.Univ. +\forall H0:eq Univ (multiply a b) c. +\forall H1:\forall X:Univ.eq Univ (multiply X X) identity. +\forall H2:\forall X:Univ.eq Univ (multiply X (inverse X)) identity. +\forall H3:\forall X:Univ.eq Univ (multiply X identity) X. +\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +\forall H5:\forall X:Univ.eq Univ (multiply (inverse X) X) identity. +\forall H6:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply b a) c +. +intros. +autobatch paramodulation timeout=100; +try assumption. +print proofterm. +qed. +(* -------------------------------------------------------------------------- *)