X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Ftests%2FTPTP%2FVeloci%2FBOO003-4.p.ma;fp=matita%2Ftests%2FTPTP%2FVeloci%2FBOO003-4.p.ma;h=a3761dfa7ad2bcd6f0429a383e12af6ca70457df;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1 diff --git a/matita/tests/TPTP/Veloci/BOO003-4.p.ma b/matita/tests/TPTP/Veloci/BOO003-4.p.ma new file mode 100644 index 000000000..a3761dfa7 --- /dev/null +++ b/matita/tests/TPTP/Veloci/BOO003-4.p.ma @@ -0,0 +1,69 @@ + +include "logic/equality.ma". +(* Inclusion of: BOO003-4.p *) +(* -------------------------------------------------------------------------- *) +(* File : BOO003-4 : TPTP v3.1.1. Released v1.1.0. *) +(* Domain : Boolean Algebra *) +(* Problem : Multiplication is idempotent (X * X = X) *) +(* Version : [Ver94] (equality) axioms. *) +(* English : *) +(* Refs : [Ver94] Veroff (1994), Problem Set *) +(* Source : [Ver94] *) +(* Names : TA [Ver94] *) +(* Status : Unsatisfiable *) +(* Rating : 0.00 v2.1.0, 0.13 v2.0.0 *) +(* Syntax : Number of clauses : 9 ( 0 non-Horn; 9 unit; 1 RR) *) +(* Number of atoms : 9 ( 9 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 6 ( 3 constant; 0-2 arity) *) +(* Number of variables : 14 ( 0 singleton) *) +(* Maximal term depth : 3 ( 2 average) *) +(* Comments : *) +(* -------------------------------------------------------------------------- *) +(* ----Include boolean algebra axioms for equality formulation *) +(* Inclusion of: Axioms/BOO004-0.ax *) +(* -------------------------------------------------------------------------- *) +(* File : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *) +(* Domain : Boolean Algebra *) +(* Axioms : Boolean algebra (equality) axioms *) +(* Version : [Ver94] (equality) axioms. *) +(* English : *) +(* Refs : [Ver94] Veroff (1994), Problem Set *) +(* Source : [Ver94] *) +(* Names : *) +(* Status : *) +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *) +(* Number of literals : 8 ( 8 equality) *) +(* Maximal clause size : 1 ( 1 average) *) +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) +(* Number of functors : 5 ( 2 constant; 0-2 arity) *) +(* Number of variables : 14 ( 0 singleton) *) +(* Maximal term depth : 3 ( 2 average) *) +(* Comments : *) +(* -------------------------------------------------------------------------- *) +(* -------------------------------------------------------------------------- *) +(* -------------------------------------------------------------------------- *) +theorem prove_a_times_a_is_a: + \forall Univ:Set. +\forall a:Univ. +\forall add:\forall _:Univ.\forall _:Univ.Univ. +\forall additive_identity:Univ. +\forall inverse:\forall _:Univ.Univ. +\forall multiplicative_identity:Univ. +\forall multiply:\forall _:Univ.\forall _:Univ.Univ. +\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity. +\forall H1:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity. +\forall H2:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X. +\forall H3:\forall X:Univ.eq Univ (add X additive_identity) X. +\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). +\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X). +\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a a) a +. +intros. +autobatch paramodulation timeout=100; +try assumption. +print proofterm. +qed. +(* -------------------------------------------------------------------------- *)