X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Ftests%2FTPTP%2FVeloci%2FBOO001-1.p.ma;fp=matita%2Ftests%2FTPTP%2FVeloci%2FBOO001-1.p.ma;h=3cb2beeda60a55ed1559d1c1439069db083b745e;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/tests/TPTP/Veloci/BOO001-1.p.ma b/matita/tests/TPTP/Veloci/BOO001-1.p.ma new file mode 100644 index 000000000..3cb2beeda --- /dev/null +++ b/matita/tests/TPTP/Veloci/BOO001-1.p.ma @@ -0,0 +1,66 @@ + +include "logic/equality.ma". +(* Inclusion of: BOO001-1.p *) +(* -------------------------------------------------------------------------- *) +(* File : BOO001-1 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Boolean Algebra (Ternary) *) +(* Problem : In B3 algebra, inverse is an involution *) +(* Version : [OTTER] (equality) axioms. *) +(* English : *) +(* Refs : *) +(* Source : [OTTER] *) +(* Names : tba_gg.in [OTTER] *) +(* Status : Unsatisfiable *) +(* Rating : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.25 v2.0.0 *) +(* Syntax : Number of clauses : 6 ( 0 non-Horn; 6 unit; 1 RR) *) +(* Number of atoms : 6 ( 6 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 3 ( 1 constant; 0-3 arity) *) +(* Number of variables : 13 ( 2 singleton) *) +(* Maximal term depth : 3 ( 2 average) *) +(* Comments : *) +(* -------------------------------------------------------------------------- *) +(* ----Include ternary Boolean algebra axioms *) +(* Inclusion of: Axioms/BOO001-0.ax *) +(* -------------------------------------------------------------------------- *) +(* File : BOO001-0 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Algebra (Ternary Boolean) *) +(* Axioms : Ternary Boolean algebra (equality) axioms *) +(* Version : [OTTER] (equality) axioms. *) +(* English : *) +(* Refs : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) +(* : [Win82] Winker (1982), Generation and Verification of Finite M *) +(* Source : [OTTER] *) +(* Names : *) +(* Status : *) +(* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 0 RR) *) +(* Number of literals : 5 ( 5 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 2 ( 0 constant; 1-3 arity) *) +(* Number of variables : 13 ( 2 singleton) *) +(* Maximal term depth : 3 ( 2 average) *) +(* Comments : These axioms appear in [Win82], in which ternary_multiply_1 is *) +(* shown to be independant. *) +(* : These axioms are also used in [Wos88], p.222. *) +(* -------------------------------------------------------------------------- *) +(* -------------------------------------------------------------------------- *) +(* -------------------------------------------------------------------------- *) +theorem prove_inverse_is_self_cancelling: + \forall Univ:Set. +\forall a:Univ. +\forall inverse:\forall _:Univ.Univ. +\forall multiply:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ. +\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y (inverse Y)) X. +\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (inverse Y) Y X) X. +\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X X Y) X. +\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (multiply Y X X) X. +\forall H4:\forall V:Univ.\forall W:Univ.\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (inverse (inverse a)) a +. +intros. +autobatch paramodulation timeout=100; +try assumption. +print proofterm. +qed. +(* -------------------------------------------------------------------------- *)