From 2b649ad5e3d7413b795fe86bdf7fe6a5c0b9c194 Mon Sep 17 00:00:00 2001 From: denes Date: Mon, 22 Jun 2009 17:03:32 +0000 Subject: [PATCH] Added problems from CASC 208 --- .../contribs/ng_TPTP/CASC_2008/BOO007-2.ma | 145 ++++++++++ .../contribs/ng_TPTP/CASC_2008/BOO007-4.ma | 133 +++++++++ .../contribs/ng_TPTP/CASC_2008/BOO031-1.ma | 107 ++++++++ .../contribs/ng_TPTP/CASC_2008/BOO034-1.ma | 143 ++++++++++ .../contribs/ng_TPTP/CASC_2008/BOO072-1.ma | 68 +++++ .../contribs/ng_TPTP/CASC_2008/BOO073-1.ma | 70 +++++ .../contribs/ng_TPTP/CASC_2008/BOO076-1.ma | 67 +++++ .../contribs/ng_TPTP/CASC_2008/COL003-1.ma | 110 ++++++++ .../contribs/ng_TPTP/CASC_2008/COL003-12.ma | 83 ++++++ .../contribs/ng_TPTP/CASC_2008/COL003-20.ma | 79 ++++++ .../contribs/ng_TPTP/CASC_2008/COL006-6.ma | 77 ++++++ .../contribs/ng_TPTP/CASC_2008/COL011-1.ma | 80 ++++++ .../contribs/ng_TPTP/CASC_2008/COL037-1.ma | 84 ++++++ .../contribs/ng_TPTP/CASC_2008/COL038-1.ma | 84 ++++++ 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diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO007-2.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO007-2.ma new file mode 100644 index 000000000..70cf42bba --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO007-2.ma @@ -0,0 +1,145 @@ +include "logic/equality.ma". + +(* Inclusion of: BOO007-2.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO007-2 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Boolean Algebra *) + +(* Problem : Product is associative ( (X * Y) * Z = X * (Y * Z) ) *) + +(* Version : [ANL] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ver92] Veroff (1992), Email to G. Sutcliffe *) + +(* Source : [Ver92] *) + +(* Names : associativity [Ver92] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.21 v3.2.0, 0.14 v3.1.0, 0.00 v2.7.0, 0.18 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1, 0.44 v2.2.0, 0.57 v2.1.0, 0.75 v2.0.0 *) + +(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 1 RR) *) + +(* Number of atoms : 15 ( 15 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 8 ( 5 constant; 0-2 arity) *) + +(* Number of variables : 24 ( 0 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include boolean algebra axioms for equality formulation *) + +(* Inclusion of: Axioms/BOO003-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO003-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Boolean Algebra *) + +(* Axioms : Boolean algebra (equality) axioms *) + +(* Version : [ANL] (equality) axioms. *) + +(* English : *) + +(* Refs : *) + +(* Source : [ANL] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 14 ( 0 non-Horn; 14 unit; 0 RR) *) + +(* Number of atoms : 14 ( 14 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 : 24 ( 0 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_associativity: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀b:Univ. +∀c:Univ. +∀inverse:∀_:Univ.Univ. +∀multiplicative_identity:Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.eq Univ (add additive_identity X) X. +∀H1:∀X:Univ.eq Univ (add X additive_identity) X. +∀H2:∀X:Univ.eq Univ (multiply multiplicative_identity X) X. +∀H3:∀X:Univ.eq Univ (multiply X multiplicative_identity) X. +∀H4:∀X:Univ.eq Univ (multiply (inverse X) X) additive_identity. +∀H5:∀X:Univ.eq Univ (multiply X (inverse X)) additive_identity. +∀H6:∀X:Univ.eq Univ (add (inverse X) X) multiplicative_identity. +∀H7:∀X:Univ.eq Univ (add X (inverse X)) multiplicative_identity. +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). +∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)). +∀H12:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). +∀H13:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#c ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO007-4.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO007-4.ma new file mode 100644 index 000000000..36ecd6386 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO007-4.ma @@ -0,0 +1,133 @@ +include "logic/equality.ma". + +(* Inclusion of: BOO007-4.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO007-4 : TPTP v3.7.0. Released v1.1.0. *) + +(* Domain : Boolean Algebra *) + +(* Problem : Product is associative ( (X * Y) * Z = X * (Y * Z) ) *) + +(* Version : [Ver94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ver94] Veroff (1994), Problem Set *) + +(* Source : [Ver94] *) + +(* Names : TD [Ver94] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.14 v3.2.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.09 v2.6.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.62 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 : 8 ( 5 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 v3.7.0. 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 atoms : 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 : *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_associativity: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀b:Univ. +∀c:Univ. +∀inverse:∀_:Univ.Univ. +∀multiplicative_identity:Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.eq Univ (multiply X (inverse X)) additive_identity. +∀H1:∀X:Univ.eq Univ (add X (inverse X)) multiplicative_identity. +∀H2:∀X:Univ.eq Univ (multiply X multiplicative_identity) X. +∀H3:∀X:Univ.eq Univ (add X additive_identity) X. +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)). +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#b ##. +#c ##. +#inverse ##. +#multiplicative_identity ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO031-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO031-1.ma new file mode 100644 index 000000000..1dff3e286 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO031-1.ma @@ -0,0 +1,107 @@ +include "logic/equality.ma". + +(* Inclusion of: BOO031-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO031-1 : TPTP v3.7.0. Released v2.2.0. *) + +(* Domain : Boolean Algebra *) + +(* Problem : Dual BA 3-basis, proof of distributivity. *) + +(* Version : [MP96] (equality) axioms : Especial. *) + +(* English : This is part of a proof of the existence of a self-dual *) + +(* 3-basis for Boolean algebra by majority reduction. *) + +(* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *) + +(* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *) + +(* Source : [McC98] *) + +(* Names : DUAL-BA-8-a [MP96] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.29 v3.2.0, 0.21 v3.1.0, 0.22 v2.7.0, 0.09 v2.6.0, 0.17 v2.5.0, 0.00 v2.4.0, 0.00 v2.2.1 *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 1 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 8 ( 5 constant; 0-2 arity) *) + +(* Number of variables : 27 ( 8 singleton) *) + +(* Maximal term depth : 4 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Self-dual distributivity: *) + +(* ----3 properties of Boolean algebra and the corresponding duals. *) + +(* ----Existence of 0 and 1. *) + +(* ----Associativity of the 2 operations. *) + +(* ----Denial of conclusion: *) +ntheorem prove_multiply_add_property: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀c:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀n0:Univ. +∀n1:Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). +∀H2:∀X:Univ.eq Univ (multiply X (inverse X)) n0. +∀H3:∀X:Univ.eq Univ (add X (inverse X)) n1. +∀H4:∀X:Univ.∀Y:Univ.eq Univ (add (multiply X (inverse X)) Y) Y. +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply (add X Y) (add Y Z)) Y) Y. +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (add X Z))) X. +∀H7:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X (inverse X)) Y) Y. +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add (multiply X Y) (multiply Y Z)) Y) Y. +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y (multiply X Z))) X. +∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (multiply X Y) (add (multiply Y Z) (multiply Z X))) (multiply (add X Y) (multiply (add Y Z) (add Z X))).eq Univ (multiply a (add b c)) (add (multiply b a) (multiply c a))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#inverse ##. +#multiply ##. +#n0 ##. +#n1 ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO034-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO034-1.ma new file mode 100644 index 000000000..c0898be50 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO034-1.ma @@ -0,0 +1,143 @@ +include "logic/equality.ma". + +(* Inclusion of: BOO034-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO034-1 : TPTP v3.7.0. Released v2.2.0. *) + +(* Domain : Boolean Algebra (Ternary) *) + +(* Problem : Ternary Boolean Algebra Single axiom is sound. *) + +(* Version : [MP96] (equality) axioms. *) + +(* English : We show that that an equation (which turns out to be a single *) + +(* axiom for TBA) can be derived from the axioms of TBA. *) + +(* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *) + +(* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *) + +(* Source : [McC98] *) + +(* Names : TBA-1-a [MP96] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.44 v3.4.0, 0.50 v3.3.0, 0.29 v3.2.0, 0.21 v3.1.0, 0.11 v2.7.0, 0.27 v2.6.0, 0.33 v2.5.0, 0.00 v2.2.1 *) + +(* 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 : 9 ( 7 constant; 0-3 arity) *) + +(* Number of variables : 13 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include ternary Boolean algebra axioms *) + +(* Inclusion of: Axioms/BOO001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO001-0 : TPTP v3.7.0. 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 atoms : 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. *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----Denial of single axiom: *) +ntheorem prove_single_axiom: + (∀Univ:Type.∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀d:Univ. +∀e:Univ. +∀f:Univ. +∀g:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y (inverse Y)) X. +∀H1:∀X:Univ.∀Y:Univ.eq Univ (multiply (inverse Y) Y X) X. +∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply X X Y) X. +∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply Y X X) X. +∀H4:∀V:Univ.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (multiply (multiply a (inverse a) b) (inverse (multiply (multiply c d e) f (multiply c d g))) (multiply d (multiply g f e) c)) b) +. +#Univ ##. +#V ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#e ##. +#f ##. +#g ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO072-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO072-1.ma new file mode 100644 index 000000000..1a692e7fa --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO072-1.ma @@ -0,0 +1,68 @@ +include "logic/equality.ma". + +(* Inclusion of: BOO072-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO072-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Boolean Algebra *) + +(* Problem : DN-1 is a single axiom for Boolean algebra, part 1 *) + +(* Version : [EF+02] axioms. *) + +(* English : *) + +(* Refs : [EF+02] Ernst et al. (2002), More First-order Test Problems in *) + +(* : [MV+02] McCune et al. (2002), Short Single Axioms for Boolean *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.07 v3.1.0, 0.00 v2.7.0, 0.09 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 4 ( 2 singleton) *) + +(* Maximal term depth : 9 ( 4 average) *) + +(* Comments : A UEQ part of BOO038-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem huntinton_1: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀inverse:∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add b a) (add a b)) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#add ##. +#b ##. +#inverse ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO073-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO073-1.ma new file mode 100644 index 000000000..071d386a2 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO073-1.ma @@ -0,0 +1,70 @@ +include "logic/equality.ma". + +(* Inclusion of: BOO073-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO073-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Boolean Algebra *) + +(* Problem : DN-1 is a single axiom for Boolean algebra, part 2 *) + +(* Version : [EF+02] axioms. *) + +(* English : *) + +(* Refs : [EF+02] Ernst et al. (2002), More First-order Test Problems in *) + +(* : [MV+02] McCune et al. (2002), Short Single Axioms for Boolean *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 4 ( 2 singleton) *) + +(* Maximal term depth : 9 ( 4 average) *) + +(* Comments : A UEQ part of BOO038-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem huntinton_2: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀c:Univ. +∀inverse:∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (add (inverse (add (inverse (add A B)) C)) (inverse (add A (inverse (add (inverse C) (inverse (add C D)))))))) C.eq Univ (add (add a b) c) (add a (add b c))) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a ##. +#add ##. +#b ##. +#c ##. +#inverse ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO076-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO076-1.ma new file mode 100644 index 000000000..c8f012207 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/BOO076-1.ma @@ -0,0 +1,67 @@ +include "logic/equality.ma". + +(* Inclusion of: BOO076-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : BOO076-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Boolean Algebra *) + +(* Problem : Sh-1 is a single axiom for Boolean algebra, part 2 *) + +(* Version : [EF+02] axioms. *) + +(* English : *) + +(* Refs : [EF+02] Ernst et al. (2002), More First-order Test Problems in *) + +(* : [MV+02] McCune et al. (2002), Short Single Axioms for Boolean *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.67 v3.4.0, 0.88 v3.3.0, 0.71 v3.1.0, 0.78 v2.7.0, 0.91 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 3 ( 1 singleton) *) + +(* Maximal term depth : 5 ( 4 average) *) + +(* Comments : A UEQ part of BOO039-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_meredith_2_basis_2: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀nand:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand a (nand b (nand a c))) (nand (nand (nand c b) b) a)) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#a ##. +#b ##. +#c ##. +#nand ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL003-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL003-1.ma new file mode 100644 index 000000000..61442e2e0 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL003-1.ma @@ -0,0 +1,110 @@ +include "logic/equality.ma". + +(* Inclusion of: COL003-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL003-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for B and W *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators B and W alone, where ((Bx)y)z *) + +(* = x(yz) and (Wx)y = (xy)y. *) + +(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *) + +(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *) + +(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* : [Ove90] Overbeek (1990), ATP competition announced at CADE-10 *) + +(* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *) + +(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *) + +(* : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal *) + +(* : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11 *) + +(* : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in *) + +(* Source : [WM88] *) + +(* Names : C2 [WM88] *) + +(* : Problem 2 [WM88] *) + +(* : Test Problem 17 [Wos88] *) + +(* : Sages and Combinatory Logic [Wos88] *) + +(* : CADE-11 Competition Eq-8 [Ove90] *) + +(* : CL2 [LW92] *) + +(* : THEOREM EQ-8 [LM93] *) + +(* : Question 3 [Wos93] *) + +(* : Question 5 [Wos93] *) + +(* : PROBLEM 8 [Zha93] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.67 v3.4.0, 0.75 v3.3.0, 0.71 v3.2.0, 0.79 v3.1.0, 0.78 v2.7.0, 0.73 v2.6.0, 0.67 v2.5.0, 0.25 v2.4.0, 0.33 v2.3.0, 0.67 v2.2.1, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *) + +(* Number of atoms : 3 ( 3 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_strong_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀f:∀_:Univ.Univ. +∀w:Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#w ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL003-12.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL003-12.ma new file mode 100644 index 000000000..339ea482b --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL003-12.ma @@ -0,0 +1,83 @@ +include "logic/equality.ma". + +(* Inclusion of: COL003-12.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL003-12 : TPTP v3.7.0. Released v2.1.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for B and W *) + +(* Version : [WM88] (equality) axioms. *) + +(* Theorem formulation : The fixed point is provided and checked. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators B and W alone, where ((Bx)y)z *) + +(* = x(yz) and (Wx)y = (xy)y. *) + +(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *) + +(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *) + +(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *) + +(* Source : [TPTP] *) + +(* Names : J sage [MW87] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.07 v3.1.0, 0.22 v2.7.0, 0.18 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1, 0.25 v2.2.0, 0.40 v2.1.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 2 RR) *) + +(* Number of atoms : 4 ( 4 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 5 ( 0 singleton) *) + +(* Maximal term depth : 5 ( 3 average) *) + +(* Comments : Found by Statman. *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_strong_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀fixed_pt:Univ. +∀strong_fixed_point:Univ. +∀w:Univ. +∀H0:eq Univ strong_fixed_point (apply (apply b (apply w w)) (apply (apply b w) (apply (apply b b) b))). +∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#strong_fixed_point ##. +#w ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL003-20.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL003-20.ma new file mode 100644 index 000000000..45e13d68b --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL003-20.ma @@ -0,0 +1,79 @@ +include "logic/equality.ma". + +(* Inclusion of: COL003-20.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL003-20 : TPTP v3.7.0. Released v2.1.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for B and W *) + +(* Version : [WM88] (equality) axioms. *) + +(* Theorem formulation : The fixed point is provided and checked. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators B and W alone, where ((Bx)y)z *) + +(* = x(yz) and (Wx)y = (xy)y. *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.21 v3.1.0, 0.22 v2.7.0, 0.36 v2.6.0, 0.33 v2.5.0, 0.00 v2.2.1, 0.62 v2.2.0, 0.80 v2.1.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 2 RR) *) + +(* Number of atoms : 4 ( 4 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 5 ( 0 singleton) *) + +(* Maximal term depth : 5 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_strong_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀fixed_pt:Univ. +∀strong_fixed_point:Univ. +∀w:Univ. +∀H0:eq Univ strong_fixed_point (apply (apply b (apply w w)) (apply (apply b (apply b w)) (apply (apply b b) b))). +∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#strong_fixed_point ##. +#w ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL006-6.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL006-6.ma new file mode 100644 index 000000000..2b0c454bc --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL006-6.ma @@ -0,0 +1,77 @@ +include "logic/equality.ma". + +(* Inclusion of: COL006-6.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL006-6 : TPTP v3.7.0. Released v2.1.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for S and K *) + +(* Version : [WM88] (equality) axioms. *) + +(* Theorem formulation : The fixed point is provided and checked. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators S and K alone, where *) + +(* ((Sx)y)z = (xz)(yz), (Kx)y = x. *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.44 v3.4.0, 0.38 v3.3.0, 0.64 v3.1.0, 0.78 v2.7.0, 0.73 v2.6.0, 0.50 v2.5.0, 0.75 v2.4.0, 0.67 v2.2.1, 0.88 v2.2.0, 0.80 v2.1.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 2 RR) *) + +(* Number of atoms : 4 ( 4 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 5 ( 1 singleton) *) + +(* Maximal term depth : 8 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_strong_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀fixed_pt:Univ. +∀k:Univ. +∀s:Univ. +∀strong_fixed_point:Univ. +∀H0:eq Univ strong_fixed_point (apply (apply s (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k)))) (apply (apply s (apply (apply s (apply k s)) k)) (apply k (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))))). +∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply k X) Y) X. +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#fixed_pt ##. +#k ##. +#s ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL011-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL011-1.ma new file mode 100644 index 000000000..c4559798d --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL011-1.ma @@ -0,0 +1,80 @@ +include "logic/equality.ma". + +(* Inclusion of: COL011-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL011-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Weak fixed point for O and Q1 *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : The weak fixed point property holds for the set P consisting *) + +(* of the combinators O and Q1, where (Ox)y = y(xy), ((Q1x)y)z *) + +(* = x(zy). *) + +(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *) + +(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *) + +(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb *) + +(* Source : [MW88] *) + +(* Names : - [MW88] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.36 v3.1.0, 0.67 v2.7.0, 0.36 v2.6.0, 0.33 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.14 v2.1.0, 0.62 v2.0.0 *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *) + +(* Number of atoms : 3 ( 3 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀combinator:Univ. +∀o:Univ. +∀q1:Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply q1 X) Y) Z) (apply X (apply Z Y)). +∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)).∃Y:Univ.eq Univ Y (apply combinator Y)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#combinator ##. +#o ##. +#q1 ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL037-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL037-1.ma new file mode 100644 index 000000000..e4df1f20b --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL037-1.ma @@ -0,0 +1,84 @@ +include "logic/equality.ma". + +(* Inclusion of: COL037-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL037-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for B, S, and C *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators B, S, and C, where ((Sx)y)z *) + +(* = (xz)(yz), ((Bx)y)z = x(yz), ((Cx)y)z = (xz)y. *) + +(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *) + +(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *) + +(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb *) + +(* Source : [MW88] *) + +(* Names : - [MW88] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.29 v3.1.0, 0.44 v2.7.0, 0.36 v2.6.0, 0.33 v2.5.0, 0.25 v2.4.0, 0.33 v2.3.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.14 v2.1.0, 0.88 v2.0.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR) *) + +(* Number of atoms : 4 ( 4 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 10 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 4 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀c:Univ. +∀f:∀_:Univ.Univ. +∀s:Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#c ##. +#f ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL038-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL038-1.ma new file mode 100644 index 000000000..5eabab97a --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL038-1.ma @@ -0,0 +1,84 @@ +include "logic/equality.ma". + +(* Inclusion of: COL038-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL038-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for B, M, and V *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators B, M, and V, where ((Bx)y)z *) + +(* = x(yz), Mx = xx, ((Vx)y)z = (zx)y. *) + +(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *) + +(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *) + +(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [MW88] McCune & Wos (1988), Some Fixed Point Problems in Comb *) + +(* Source : [MW88] *) + +(* Names : - [MW88] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.50 v3.3.0, 0.57 v3.2.0, 0.64 v3.1.0, 0.78 v2.7.0, 0.64 v2.6.0, 0.17 v2.5.0, 0.50 v2.4.0, 0.00 v2.2.1, 0.56 v2.2.0, 0.43 v2.1.0, 0.88 v2.0.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR) *) + +(* Number of atoms : 4 ( 4 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 8 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀f:∀_:Univ.Univ. +∀m:Univ. +∀v:Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply v X) Y) Z) (apply (apply Z X) Y). +∀H1:∀X:Univ.eq Univ (apply m X) (apply X X). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#m ##. +#v ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL043-3.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL043-3.ma new file mode 100644 index 000000000..86fe64607 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL043-3.ma @@ -0,0 +1,81 @@ +include "logic/equality.ma". + +(* Inclusion of: COL043-3.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL043-3 : TPTP v3.7.0. Bugfixed v2.3.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for B and H *) + +(* Version : [WM88] (equality) axioms. *) + +(* Theorem formulation : The fixed point is provided and checked. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators B and H, where ((Bx)y)z *) + +(* = x(yz), ((Hx)y)z = ((xy)z)y. *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *) + +(* Source : [TPTP] *) + +(* Names : - [Wos93] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.67 v3.4.0, 0.75 v3.3.0, 0.79 v3.2.0, 0.71 v3.1.0, 0.78 v2.7.0, 1.00 v2.6.0, 0.83 v2.5.0, 0.75 v2.4.0, 0.67 v2.3.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 2 RR) *) + +(* Number of atoms : 4 ( 4 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 11 ( 4 average) *) + +(* Comments : *) + +(* Bugfixes : v2.3.0 - Clause strong_fixed_point fixed. *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_strong_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀fixed_pt:Univ. +∀h:Univ. +∀strong_fixed_point:Univ. +∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply h (apply (apply b (apply (apply b h) (apply b b))) (apply h (apply (apply b h) (apply b b))))) h)) b)) b). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply h X) Y) Z) (apply (apply (apply X Y) Z) Y). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#h ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL044-8.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL044-8.ma new file mode 100644 index 000000000..baf4c5c62 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL044-8.ma @@ -0,0 +1,79 @@ +include "logic/equality.ma". + +(* Inclusion of: COL044-8.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL044-8 : TPTP v3.7.0. Released v2.1.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for B and N *) + +(* Version : [WM88] (equality) axioms. *) + +(* Theorem formulation : The fixed point is provided and checked. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators B and N, where ((Bx)y)z *) + +(* = x(yz), ((Nx)y)z = ((xz)y)z. *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.67 v3.4.0, 0.75 v3.3.0, 0.79 v3.2.0, 0.71 v3.1.0, 0.78 v2.7.0, 1.00 v2.6.0, 0.67 v2.5.0, 0.50 v2.4.0, 0.67 v2.2.1, 0.88 v2.2.0, 0.80 v2.1.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 2 RR) *) + +(* Number of atoms : 4 ( 4 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 12 ( 4 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_strong_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀fixed_pt:Univ. +∀n:Univ. +∀strong_fixed_point:Univ. +∀H0:eq Univ strong_fixed_point (apply (apply b (apply (apply b (apply (apply n (apply n (apply (apply b (apply b b)) (apply n (apply (apply b b) n))))) n)) b)) b). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply n X) Y) Z) (apply (apply (apply X Z) Y) Z). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply strong_fixed_point fixed_pt) (apply fixed_pt (apply strong_fixed_point fixed_pt))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#fixed_pt ##. +#n ##. +#strong_fixed_point ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL046-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL046-1.ma new file mode 100644 index 000000000..91a275fb2 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL046-1.ma @@ -0,0 +1,84 @@ +include "logic/equality.ma". + +(* Inclusion of: COL046-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL046-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for B, M and S *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators B, M and S, where ((Sx)y)z *) + +(* = (xz)(yz), ((Bx)y)z = x(yz), Mx = xx. *) + +(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *) + +(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *) + +(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [Wos89] Wos (1989), A Challenge Problem and a Recent Workshop *) + +(* Source : [Wos89] *) + +(* Names : - [Wos89] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.50 v3.3.0, 0.57 v3.2.0, 0.64 v3.1.0, 0.67 v2.7.0, 0.55 v2.6.0, 0.17 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR) *) + +(* Number of atoms : 4 ( 4 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 8 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀f:∀_:Univ.Univ. +∀m:Univ. +∀s:Univ. +∀H0:∀X:Univ.eq Univ (apply m X) (apply X X). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#m ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL049-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL049-1.ma new file mode 100644 index 000000000..120d93770 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL049-1.ma @@ -0,0 +1,104 @@ +include "logic/equality.ma". + +(* Inclusion of: COL049-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL049-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for B, W, and M *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators B, W, and M, where ((Bx)y)z *) + +(* = x(yz), (Wx)y = (xy)y, Mx = xx. *) + +(* Refs : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *) + +(* : [MW87] McCune & Wos (1987), A Case Study in Automated Theorem *) + +(* : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [Ove90] Overbeek (1990), ATP competition announced at CADE-10 *) + +(* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *) + +(* : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *) + +(* : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal *) + +(* : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11 *) + +(* : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in *) + +(* Source : [Ove90] *) + +(* Names : Problem 2 [WM88] *) + +(* : CADE-11 Competition Eq-6 [Ove90] *) + +(* : CL1 [LW92] *) + +(* : THEOREM EQ-6 [LM93] *) + +(* : Question 2 [Wos93] *) + +(* : PROBLEM 6 [Zha93] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.29 v3.1.0, 0.44 v2.7.0, 0.27 v2.6.0, 0.17 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.14 v2.1.0, 0.62 v2.0.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR) *) + +(* Number of atoms : 4 ( 4 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 7 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_strong_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀f:∀_:Univ.Univ. +∀m:Univ. +∀w:Univ. +∀H0:∀X:Univ.eq Univ (apply m X) (apply X X). +∀H1:∀X:Univ.∀Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#m ##. +#w ##. +#H0 ##. +#H1 ##. +#H2 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL057-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL057-1.ma new file mode 100644 index 000000000..2cb813814 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL057-1.ma @@ -0,0 +1,84 @@ +include "logic/equality.ma". + +(* Inclusion of: COL057-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL057-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Strong fixed point for S, B, C, and I *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : The strong fixed point property holds for the set *) + +(* P consisting of the combinators S, B, C, and I, where *) + +(* ((Sx)y)z = (xz)(yz), ((Bx)y)z = x(yz), ((Cx)y)z = (xz)y, and *) + +(* Ix = x. *) + +(* Refs : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *) + +(* Source : [LW92] *) + +(* Names : CL5 [LW92] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.36 v3.1.0, 0.56 v2.7.0, 0.27 v2.6.0, 0.17 v2.5.0, 0.00 v2.1.0, 0.25 v2.0.0 *) + +(* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 1 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 : 11 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_strong_fixed_point: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀c:Univ. +∀f:∀_:Univ.Univ. +∀i:Univ. +∀s:Univ. +∀H0:∀X:Univ.eq Univ (apply i X) X. +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).∃Y:Univ.eq Univ (apply Y (f Y)) (apply (f Y) (apply Y (f Y)))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#c ##. +#f ##. +#i ##. +#s ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2,H3 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL060-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL060-1.ma new file mode 100644 index 000000000..179591d91 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL060-1.ma @@ -0,0 +1,80 @@ +include "logic/equality.ma". + +(* Inclusion of: COL060-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL060-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Find combinator equivalent to Q from B and T *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : Construct from B and T alone a combinator that behaves as the *) + +(* combinator Q does, where ((Bx)y)z = x(yz), (Tx)y = yx, *) + +(* ((Qx)y)z = y(xz). *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to *) + +(* Source : [WW+90] *) + +(* Names : CL-1 [WW+90] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.62 v2.0.0 *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *) + +(* Number of atoms : 3 ( 3 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 5 ( 4 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_q_combinator: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀f:∀_:Univ.Univ. +∀g:∀_:Univ.Univ. +∀h:∀_:Univ.Univ. +∀t:Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (g X) (apply (f X) (h X)))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL061-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL061-1.ma new file mode 100644 index 000000000..988e17796 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL061-1.ma @@ -0,0 +1,80 @@ +include "logic/equality.ma". + +(* Inclusion of: COL061-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL061-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Find combinator equivalent to Q1 from B and T *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : Construct from B and T alone a combinator that behaves as the *) + +(* combinator Q1 does, where ((Bx)y)z = x(yz), (Tx)y = yx, *) + +(* ((Q1x)y)z = x(zy). *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to *) + +(* Source : [WW+90] *) + +(* Names : CL-2 [WW+90] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.75 v2.0.0 *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *) + +(* Number of atoms : 3 ( 3 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 5 ( 4 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_q1_combinator: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀f:∀_:Univ.Univ. +∀g:∀_:Univ.Univ. +∀h:∀_:Univ.Univ. +∀t:Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (f X) (apply (h X) (g X)))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL063-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL063-1.ma new file mode 100644 index 000000000..b10d59347 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL063-1.ma @@ -0,0 +1,80 @@ +include "logic/equality.ma". + +(* Inclusion of: COL063-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL063-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Find combinator equivalent to F from B and T *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : Construct from B and T alone a combinator that behaves as the *) + +(* combinator F does, where ((Bx)y)z = x(yz), (Tx)y = yx, *) + +(* ((Fx)y)z = (zy)x. *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to *) + +(* Source : [WW+90] *) + +(* Names : CL-4 [WW+90] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.44 v3.4.0, 0.50 v3.1.0, 0.44 v2.7.0, 0.36 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1, 0.44 v2.2.0, 0.57 v2.1.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *) + +(* Number of atoms : 3 ( 3 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 5 ( 4 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_f_combinator: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀f:∀_:Univ.Univ. +∀g:∀_:Univ.Univ. +∀h:∀_:Univ.Univ. +∀t:Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (apply (h X) (g X)) (f X))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL064-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL064-1.ma new file mode 100644 index 000000000..ca08a7631 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL064-1.ma @@ -0,0 +1,80 @@ +include "logic/equality.ma". + +(* Inclusion of: COL064-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL064-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Find combinator equivalent to V from B and T *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : Construct from B and T alone a combinator that behaves as the *) + +(* combinator V does, where ((Bx)y)z = x(yz), (Tx)y = yx, *) + +(* ((Vx)y)z = (zx)y. *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to *) + +(* Source : [WW+90] *) + +(* Names : CL-5 [WW+90] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.50 v3.3.0, 0.64 v3.1.0, 0.44 v2.7.0, 0.45 v2.6.0, 0.17 v2.5.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.78 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *) + +(* Number of atoms : 3 ( 3 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 5 ( 4 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_v_combinator: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀f:∀_:Univ.Univ. +∀g:∀_:Univ.Univ. +∀h:∀_:Univ.Univ. +∀t:Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply X (f X)) (g X)) (h X)) (apply (apply (h X) (f X)) (g X))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL065-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL065-1.ma new file mode 100644 index 000000000..13f4a8168 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/COL065-1.ma @@ -0,0 +1,82 @@ +include "logic/equality.ma". + +(* Inclusion of: COL065-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : COL065-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Combinatory Logic *) + +(* Problem : Find combinator equivalent to G from B and T *) + +(* Version : [WM88] (equality) axioms. *) + +(* English : Construct from B and T alone a combinator that behaves as the *) + +(* combinator G does, where ((Bx)y)z = x(yz), (Tx)y = yx, *) + +(* (((Gx)y)z)w = (xw)(yz) *) + +(* Refs : [WM88] Wos & McCune (1988), Challenge Problems Focusing on Eq *) + +(* : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to *) + +(* Source : [WW+90] *) + +(* Names : CL-6 [WW+90] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.62 v3.3.0, 0.64 v3.2.0, 0.71 v3.1.0, 0.56 v2.7.0, 0.45 v2.6.0, 0.33 v2.5.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *) + +(* Number of atoms : 3 ( 3 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 7 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 6 ( 4 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_g_combinator: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀apply:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀f:∀_:Univ.Univ. +∀g:∀_:Univ.Univ. +∀h:∀_:Univ.Univ. +∀i:∀_:Univ.Univ. +∀t:Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).∃X:Univ.eq Univ (apply (apply (apply (apply X (f X)) (g X)) (h X)) (i X)) (apply (apply (f X) (i X)) (apply (g X) (h X)))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#apply ##. +#b ##. +#f ##. +#g ##. +#h ##. +#i ##. +#t ##. +#H0 ##. +#H1 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP014-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP014-1.ma new file mode 100644 index 000000000..a3a196e75 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP014-1.ma @@ -0,0 +1,82 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP014-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP014-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Group Theory *) + +(* Problem : Product is associative in this group theory *) + +(* Version : [Ove90] (equality) axioms : Incomplete. *) + +(* English : The group theory specified by the axiom given implies the *) + +(* associativity of multiply. *) + +(* Refs : [Ove90] Overbeek (1990), ATP competition announced at CADE-10 *) + +(* : [Ove93] Overbeek (1993), The CADE-11 Competitions: A Personal *) + +(* : [LM93] Lusk & McCune (1993), Uniform Strategies: The CADE-11 *) + +(* : [Zha93] Zhang (1993), Automated Proofs of Equality Problems in *) + +(* Source : [Ove90] *) + +(* Names : CADE-11 Competition Eq-4 [Ove90] *) + +(* : THEOREM EQ-4 [LM93] *) + +(* : PROBLEM 4 [Zha93] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.07 v3.2.0, 0.14 v3.1.0, 0.11 v2.7.0, 0.18 v2.6.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.50 v2.0.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 4 ( 0 singleton) *) + +(* Maximal term depth : 9 ( 4 average) *) + +(* Comments : The group_axiom is in fact a single axiom for group theory *) + +(* [LM93]. *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_associativity: + (∀Univ:Type.∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀W:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (inverse (multiply (multiply (inverse (multiply (inverse Y) (multiply (inverse X) W))) Z) (inverse (multiply Y Z))))) W.eq Univ (multiply a (multiply b c)) (multiply (multiply a b) c)) +. +#Univ ##. +#W ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP024-5.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP024-5.ma new file mode 100644 index 000000000..a4368daa2 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP024-5.ma @@ -0,0 +1,161 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP024-5.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP024-5 : TPTP v3.7.0. Released v2.2.0. *) + +(* Domain : Group Theory *) + +(* Problem : Levi commutator problem. *) + +(* Version : [McC98] (equality) axioms. *) + +(* English : In group theory, if the commutator [x,y] is associative, *) + +(* then x*[y,z] = [y,z]*x. *) + +(* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *) + +(* : [ML92] McCune & Lusk (1992), A Challenging Theorem of Levi *) + +(* : [Kur56] Kurosh (1956), The Theory of Groups *) + +(* Source : [McC98] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.57 v3.2.0, 0.50 v3.1.0, 0.44 v2.7.0, 0.64 v2.6.0, 0.33 v2.5.0, 0.00 v2.4.0, 0.33 v2.3.0, 0.67 v2.2.1 *) + +(* 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 : 7 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 10 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----Definition of commutator: *) + +(* ----Theorem: commutator is associative implies x*[y,z] = [y,z]*x. *) + +(* ----Hypothesis: *) + +(* ----Denial of conclusion: *) +ntheorem prove_center: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀commutator:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (commutator (commutator X Y) Z) (commutator X (commutator Y Z)). +∀H1:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (multiply (inverse X) (multiply (inverse Y) (multiply X Y))). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H3:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H4:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a (commutator b c)) (multiply (commutator b c) a)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#commutator ##. +#identity ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +nauto by H0,H1,H2,H3,H4 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP114-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP114-1.ma new file mode 100644 index 000000000..4d919c928 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP114-1.ma @@ -0,0 +1,193 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP114-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP114-1 : TPTP v3.7.0. Released v1.2.0. *) + +(* Domain : Group Theory *) + +(* Problem : Product of positive and negative parts of X equals X *) + +(* Version : [MOW76] (equality) axioms : Augmented. *) + +(* English : Prove that for each element X in a group, X is equal to the *) + +(* product of its positive part (the union with the identity) *) + +(* and its negative part (the intersection with the identity). *) + +(* Refs : [Wos94] Wos (1994), Challenge in Group Theory *) + +(* Source : [Wos94] *) + +(* Names : - [Wos94] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.25 v3.3.0, 0.29 v3.1.0, 0.22 v2.7.0, 0.36 v2.6.0, 0.17 v2.5.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.44 v2.2.0, 0.57 v2.1.0, 0.86 v2.0.0 *) + +(* Syntax : Number of clauses : 21 ( 0 non-Horn; 21 unit; 2 RR) *) + +(* Number of atoms : 21 ( 21 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 8 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 38 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : I know some of the axioms are redundant, and have put comments *) + +(* to that effect. However, I don't know how to make a complete *) + +(* standard axiomatisation for the union and intersection axioms. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include the axioms for named groups *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----This axiom is a lemma *) + +(* ----This axiom is a lemma *) + +(* ----This axiom is a lemma *) +ntheorem prove_product: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀identity:Univ. +∀intersection:∀_:Univ.∀_:Univ.Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀negative_part:∀_:Univ.Univ. +∀positive_part:∀_:Univ.Univ. +∀union:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.eq Univ (negative_part X) (intersection X identity). +∀H1:∀X:Univ.eq Univ (positive_part X) (union X identity). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (intersection Y Z) X) (intersection (multiply Y X) (multiply Z X)). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (union Y Z) X) (union (multiply Y X) (multiply Z X)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (intersection Y Z)) (intersection (multiply X Y) (multiply X Z)). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (union Y Z)) (union (multiply X Y) (multiply X Z)). +∀H6:∀X:Univ.∀Y:Univ.eq Univ (intersection (union X Y) Y) Y. +∀H7:∀X:Univ.∀Y:Univ.eq Univ (union (intersection X Y) Y) Y. +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (union X (union Y Z)) (union (union X Y) Z). +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (intersection X (intersection Y Z)) (intersection (intersection X Y) Z). +∀H10:∀X:Univ.∀Y:Univ.eq Univ (union X Y) (union Y X). +∀H11:∀X:Univ.∀Y:Univ.eq Univ (intersection X Y) (intersection Y X). +∀H12:∀X:Univ.eq Univ (union X X) X. +∀H13:∀X:Univ.eq Univ (intersection X X) X. +∀H14:∀X:Univ.∀Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)). +∀H15:∀X:Univ.eq Univ (inverse (inverse X)) X. +∀H16:eq Univ (inverse identity) identity. +∀H17:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H18:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H19:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (positive_part a) (negative_part a)) a) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#identity ##. +#intersection ##. +#inverse ##. +#multiply ##. +#negative_part ##. +#positive_part ##. +#union ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP164-2.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP164-2.ma new file mode 100644 index 000000000..1fd78a85c --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP164-2.ma @@ -0,0 +1,227 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP164-2.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP164-2 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : The lattice of each LOG is distributive *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* Theorem formulation : Dual. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : distrun [Sch95] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.89 v3.4.0, 0.88 v3.3.0, 0.93 v3.1.0, 0.89 v2.7.0, 0.91 v2.6.0, 0.83 v2.5.0, 0.75 v2.4.0, 0.67 v2.2.1, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 16 ( 0 non-Horn; 16 unit; 1 RR) *) + +(* Number of atoms : 16 ( 16 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 8 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 33 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a > b > c *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_distrun: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H5:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H6:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H7:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H10:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound b c)) (least_upper_bound (greatest_lower_bound a b) (greatest_lower_bound a c))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP167-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP167-1.ma new file mode 100644 index 000000000..3392a52f7 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP167-1.ma @@ -0,0 +1,253 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP167-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP167-1 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Product of positive and negative parts *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : Each element in a lattice ordered group can be stated as a *) + +(* product of it's positive and it's negative part. *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* : [Dah95] Dahn (1995), Email to G. Sutcliffe *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.21 v3.1.0, 0.11 v2.7.0, 0.18 v2.6.0, 0.17 v2.5.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.86 v2.0.0 *) + +(* Syntax : Number of clauses : 20 ( 0 non-Horn; 20 unit; 1 RR) *) + +(* Number of atoms : 20 ( 20 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 8 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 41 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > greatest_lower_bound > *) + +(* least_upper_bound > product > negative_part > positive_part > *) + +(* identity > a *) + +(* : This is a standardized version of the problem that appears in *) + +(* [Sch95]. *) + +(* : [Dah95] says "This is crucial for reducing some problems *) + +(* on arbitrary elements to problems on positive elements. The *) + +(* proof is relatively difficult. It is non-obvious to humans *) + +(* since the standard tactics (unfold definitions - use *) + +(* distributivity - simplify) is not useful." *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_lat4: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀negative_part:∀_:Univ.Univ. +∀positive_part:∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (least_upper_bound Y Z)) (least_upper_bound (greatest_lower_bound X Y) (greatest_lower_bound X Z)). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (least_upper_bound X Y) (least_upper_bound X Z)). +∀H2:∀X:Univ.eq Univ (negative_part X) (greatest_lower_bound X identity). +∀H3:∀X:Univ.eq Univ (positive_part X) (least_upper_bound X identity). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H8:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H9:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H10:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H11:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H14:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H15:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H17:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H18:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a (multiply (positive_part a) (negative_part a))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#negative_part ##. +#positive_part ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP178-2.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP178-2.ma new file mode 100644 index 000000000..af1321db2 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP178-2.ma @@ -0,0 +1,239 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP178-2.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP178-2 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : A consequence of monotonicity *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* Theorem formulation : Dual. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : p09b [Sch95] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.21 v3.2.0, 0.14 v3.1.0, 0.22 v2.7.0, 0.45 v2.6.0, 0.33 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 0.43 v2.0.0 *) + +(* Syntax : Number of clauses : 20 ( 0 non-Horn; 20 unit; 5 RR) *) + +(* Number of atoms : 20 ( 20 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 8 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 33 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a > b > c *) + +(* : ORDERING LPO greatest_lower_bound > least_upper_bound > *) + +(* inverse > product > identity > a > b > c *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_p09b: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:eq Univ (greatest_lower_bound a b) identity. +∀H1:eq Univ (greatest_lower_bound identity c) identity. +∀H2:eq Univ (greatest_lower_bound identity b) identity. +∀H3:eq Univ (greatest_lower_bound identity a) identity. +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H8:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H9:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H10:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H11:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H14:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H15:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H17:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H18:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (multiply b c)) (greatest_lower_bound a c)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP181-4.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP181-4.ma new file mode 100644 index 000000000..345781c4f --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP181-4.ma @@ -0,0 +1,243 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP181-4.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP181-4 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Distributivity of a lattice *) + +(* Version : [Fuc94] (equality) axioms : Augmented. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : p12x [Sch95] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.25 v3.3.0, 0.43 v3.1.0, 0.44 v2.7.0, 0.36 v2.6.0, 0.00 v2.2.1, 0.56 v2.2.0, 0.57 v2.1.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 23 ( 0 non-Horn; 23 unit; 4 RR) *) + +(* Number of atoms : 23 ( 23 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 8 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 40 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a > b > c *) + +(* : ORDERING LPO greatest_lower_bound > least_upper_bound > *) + +(* inverse > product > identity > a > b > c *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_p12x: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (inverse (least_upper_bound X Y)) (greatest_lower_bound (inverse X) (inverse Y)). +∀H1:∀X:Univ.∀Y:Univ.eq Univ (inverse (greatest_lower_bound X Y)) (least_upper_bound (inverse X) (inverse Y)). +∀H2:eq Univ (least_upper_bound a c) (least_upper_bound b c). +∀H3:eq Univ (greatest_lower_bound a c) (greatest_lower_bound b c). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)). +∀H5:∀X:Univ.eq Univ (inverse (inverse X)) X. +∀H6:eq Univ (inverse identity) identity. +∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H12:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H13:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H14:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H16:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H17:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H18:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H19:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H20:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H21:∀X:Univ.eq Univ (multiply identity X) X.eq Univ a b) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP183-4.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP183-4.ma new file mode 100644 index 000000000..e17ff2973 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP183-4.ma @@ -0,0 +1,229 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP183-4.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP183-4 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Orthogonal elements form a subgroup with orthogonal parts *) + +(* Version : [Fuc94] (equality) axioms : Augmented. *) + +(* Theorem formulation : Variant. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : p20x [Sch95] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.45 v2.6.0, 0.50 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 0.86 v2.0.0 *) + +(* Syntax : Number of clauses : 19 ( 0 non-Horn; 19 unit; 2 RR) *) + +(* Number of atoms : 19 ( 19 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 36 ( 2 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_20x: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)). +∀H1:∀X:Univ.eq Univ (inverse (inverse X)) X. +∀H2:eq Univ (inverse identity) identity. +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H8:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H9:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H10:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H13:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound a identity) (least_upper_bound (inverse a) identity)) identity) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP184-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP184-1.ma new file mode 100644 index 000000000..2a6adbab5 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP184-1.ma @@ -0,0 +1,229 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP184-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP184-1 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Orthogonal elements commute and form a subgroup *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : For each X {Y: X orth Y} is a subgroup. X orthogonal to Y *) + +(* implies that X and Y commute. Moreover, pp(a) orthogonal to *) + +(* np(a). *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.29 v3.1.0, 0.00 v2.7.0, 0.36 v2.6.0, 0.33 v2.5.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 0.86 v2.0.0 *) + +(* Syntax : Number of clauses : 16 ( 0 non-Horn; 16 unit; 1 RR) *) + +(* Number of atoms : 16 ( 16 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 33 ( 2 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a *) + +(* : This is a standardized version of the problem that appears in *) + +(* [Sch95]. *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_p21: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H5:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H6:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H7:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H10:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) (multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP184-3.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP184-3.ma new file mode 100644 index 000000000..6049e68b8 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP184-3.ma @@ -0,0 +1,225 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP184-3.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP184-3 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Orthogonal elements commute and form a subgroup *) + +(* Version : [Fuc94] (equality) axioms : Augmented. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.25 v3.3.0, 0.21 v3.1.0, 0.00 v2.7.0, 0.45 v2.6.0, 0.33 v2.5.0, 0.00 v2.4.0, 0.00 v2.2.1, 0.67 v2.2.0, 0.71 v2.1.0, 0.86 v2.0.0 *) + +(* Syntax : Number of clauses : 16 ( 0 non-Horn; 16 unit; 1 RR) *) + +(* Number of atoms : 16 ( 16 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 33 ( 2 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a *) + +(* : This is a standardized version of the problem that appears in *) + +(* [Sch95]. *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_p21x: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H5:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H6:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H7:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H10:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (least_upper_bound a identity) (inverse (greatest_lower_bound a identity))) (multiply (inverse (greatest_lower_bound a identity)) (least_upper_bound a identity))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP185-2.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP185-2.ma new file mode 100644 index 000000000..3d3bf9ed5 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP185-2.ma @@ -0,0 +1,229 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP185-2.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP185-2 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Application of monotonicity and distributivity *) + +(* Version : [Fuc94] (equality) axioms : Augmented. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : p22a [Sch95] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.12 v3.3.0, 0.21 v3.2.0, 0.07 v3.1.0, 0.11 v2.7.0, 0.27 v2.6.0, 0.17 v2.5.0, 0.25 v2.4.0, 0.67 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.29 v2.0.0 *) + +(* Syntax : Number of clauses : 19 ( 0 non-Horn; 19 unit; 2 RR) *) + +(* Number of atoms : 19 ( 19 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 7 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 36 ( 2 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a > b *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_p22a: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)). +∀H1:∀X:Univ.eq Univ (inverse (inverse X)) X. +∀H2:eq Univ (inverse identity) identity. +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H8:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H9:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H10:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H13:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP185-3.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP185-3.ma new file mode 100644 index 000000000..224eb23d3 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP185-3.ma @@ -0,0 +1,229 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP185-3.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP185-3 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Application of monotonicity and distributivity *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* Theorem formulation : Using a dual definition of =<. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.25 v3.3.0, 0.21 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0, 0.67 v2.5.0, 0.75 v2.4.0, 0.33 v2.2.1, 0.56 v2.2.0, 0.43 v2.1.0, 0.43 v2.0.0 *) + +(* Syntax : Number of clauses : 16 ( 0 non-Horn; 16 unit; 1 RR) *) + +(* Number of atoms : 16 ( 16 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 7 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 33 ( 2 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a > b *) + +(* : This is a standardized version of the problem that appears in *) + +(* [Sch95]. *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_p22b: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H5:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H6:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H7:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H10:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (least_upper_bound (multiply a b) identity) (multiply (least_upper_bound a identity) (least_upper_bound b identity))) (least_upper_bound (multiply a b) identity)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP186-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP186-1.ma new file mode 100644 index 000000000..ffca86da1 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP186-1.ma @@ -0,0 +1,229 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP186-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP186-1 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Application of distributivity and group theory *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.44 v3.4.0, 0.62 v3.3.0, 0.57 v3.1.0, 0.44 v2.7.0, 0.55 v2.6.0, 0.50 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.78 v2.2.0, 0.86 v2.1.0, 0.86 v2.0.0 *) + +(* Syntax : Number of clauses : 16 ( 0 non-Horn; 16 unit; 1 RR) *) + +(* Number of atoms : 16 ( 16 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 7 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 33 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a > b *) + +(* : This is a standardized version of the problem that appears in *) + +(* [Sch95]. *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_p23: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H5:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H6:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H7:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H10:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H11:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H13:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H14:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (inverse (greatest_lower_bound a (inverse b))))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP186-2.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP186-2.ma new file mode 100644 index 000000000..4eb6eba58 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP186-2.ma @@ -0,0 +1,231 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP186-2.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP186-2 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Application of distributivity and group theory *) + +(* Version : [Fuc94] (equality) axioms : Augmented. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : p23 [Sch95] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.36 v3.1.0, 0.33 v2.7.0, 0.55 v2.6.0, 0.50 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.78 v2.2.0, 0.86 v2.1.0, 0.86 v2.0.0 *) + +(* Syntax : Number of clauses : 19 ( 0 non-Horn; 19 unit; 2 RR) *) + +(* Number of atoms : 19 ( 19 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 7 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 36 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a > b *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_p23: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)). +∀H1:∀X:Univ.eq Univ (inverse (inverse X)) X. +∀H2:eq Univ (inverse identity) identity. +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H8:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H9:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H10:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H12:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H13:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H14:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H15:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H16:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H17:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (inverse (greatest_lower_bound a (inverse b))))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP187-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP187-1.ma new file mode 100644 index 000000000..cb55cb8d7 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP187-1.ma @@ -0,0 +1,229 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP187-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP187-1 : TPTP v3.7.0. Bugfixed v1.2.1. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Problem : Orthogonal elements commute *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* : [Dah95] Dahn (1995), Email to G. Sutcliffe *) + +(* Source : [Sch95] *) + +(* Names : p33 [Sch95] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.62 v3.3.0, 0.64 v3.1.0, 0.56 v2.7.0, 0.55 v2.6.0, 0.50 v2.5.0, 0.75 v2.4.0, 0.67 v2.2.1, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 17 ( 0 non-Horn; 17 unit; 2 RR) *) + +(* Number of atoms : 17 ( 17 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 7 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 33 ( 2 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : ORDERING LPO inverse > product > greatest_lower_bound > *) + +(* least_upper_bound > identity > a > b *) + +(* : [Dah95] says "Non-obvious. Usually proved using lat4." *) + +(* Bugfixes : v1.2.1 - Duplicate axioms in GRP004-2.ax removed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include equality group theory axioms *) + +(* Inclusion of: Axioms/GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-0 : TPTP v3.7.0. 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 atoms : 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 *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include Lattice ordered group (equality) axioms *) + +(* Inclusion of: Axioms/GRP004-2.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP004-2 : TPTP v3.7.0. Bugfixed v1.2.0. *) + +(* Domain : Group Theory (Lattice Ordered) *) + +(* Axioms : Lattice ordered group (equality) axioms *) + +(* Version : [Fuc94] (equality) axioms. *) + +(* English : *) + +(* Refs : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *) + +(* : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *) + +(* Source : [Sch95] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 0 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 3 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 28 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : Requires GRP004-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* ----Specification of the least upper bound and greatest lower bound *) + +(* ----Monotony of multiply *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_p33: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀greatest_lower_bound:∀_:Univ.∀_:Univ.Univ. +∀identity:Univ. +∀inverse:∀_:Univ.Univ. +∀least_upper_bound:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:eq Univ (greatest_lower_bound (least_upper_bound a (inverse a)) (least_upper_bound b (inverse b))) identity. +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X. +∀H7:∀X:Univ.eq Univ (greatest_lower_bound X X) X. +∀H8:∀X:Univ.eq Univ (least_upper_bound X X) X. +∀H9:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z). +∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z). +∀H11:∀X:Univ.∀Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X). +∀H12:∀X:Univ.∀Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X). +∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)). +∀H14:∀X:Univ.eq Univ (multiply (inverse X) X) identity. +∀H15:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a b) (multiply b a)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#greatest_lower_bound ##. +#identity ##. +#inverse ##. +#least_upper_bound ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP200-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP200-1.ma new file mode 100644 index 000000000..3eff1ff3d --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP200-1.ma @@ -0,0 +1,103 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP200-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP200-1 : TPTP v3.7.0. Released v2.2.0. *) + +(* Domain : Group Theory (Loops) *) + +(* Problem : In Loops, Moufang-1 => Moufang-2. *) + +(* Version : [MP96] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *) + +(* : [Wos96] Wos (1996), OTTER and the Moufang Identity Problem *) + +(* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *) + +(* Source : [McC98] *) + +(* Names : MFL-1 [MP96] *) + +(* : - [Wos96] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.29 v3.1.0, 0.33 v2.7.0, 0.27 v2.6.0, 0.00 v2.2.1 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 9 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 15 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Loop axioms: *) + +(* ----Moufang-1: *) + +(* ----Denial of Moufang-2: *) +ntheorem prove_moufang2: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀identity:Univ. +∀left_division:∀_:Univ.∀_:Univ.Univ. +∀left_inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀right_division:∀_:Univ.∀_:Univ.Univ. +∀right_inverse:∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply X (multiply Y Z)) X) (multiply (multiply X Y) (multiply Z X)). +∀H1:∀X:Univ.eq Univ (multiply (left_inverse X) X) identity. +∀H2:∀X:Univ.eq Univ (multiply X (right_inverse X)) identity. +∀H3:∀X:Univ.∀Y:Univ.eq Univ (right_division (multiply X Y) Y) X. +∀H4:∀X:Univ.∀Y:Univ.eq Univ (multiply (right_division X Y) Y) X. +∀H5:∀X:Univ.∀Y:Univ.eq Univ (left_division X (multiply X Y)) Y. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X (left_division X Y)) Y. +∀H7:∀X:Univ.eq Univ (multiply X identity) X. +∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply (multiply a b) c) b) (multiply a (multiply b (multiply c b)))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#left_division ##. +#left_inverse ##. +#multiply ##. +#right_division ##. +#right_inverse ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP202-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP202-1.ma new file mode 100644 index 000000000..6ce77c9ba --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP202-1.ma @@ -0,0 +1,103 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP202-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP202-1 : TPTP v3.7.0. Released v2.2.0. *) + +(* Domain : Group Theory (Loops) *) + +(* Problem : In Loops, Moufang-3 => Moufang-1. *) + +(* Version : [MP96] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *) + +(* : [Wos96] Wos (1996), OTTER and the Moufang Identity Problem *) + +(* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *) + +(* Source : [McC98] *) + +(* Names : MFL-3 [MP96] *) + +(* : - [Wos96] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.38 v3.3.0, 0.43 v3.1.0, 0.44 v2.7.0, 0.36 v2.6.0, 0.00 v2.2.1 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 9 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 15 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Loop axioms: *) + +(* ----Moufang-3 *) + +(* ----Denial of Moufang-1 *) +ntheorem prove_moufang1: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀identity:Univ. +∀left_division:∀_:Univ.∀_:Univ.Univ. +∀left_inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀right_division:∀_:Univ.∀_:Univ.Univ. +∀right_inverse:∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (multiply (multiply X Y) X) Z) (multiply X (multiply Y (multiply X Z))). +∀H1:∀X:Univ.eq Univ (multiply (left_inverse X) X) identity. +∀H2:∀X:Univ.eq Univ (multiply X (right_inverse X)) identity. +∀H3:∀X:Univ.∀Y:Univ.eq Univ (right_division (multiply X Y) Y) X. +∀H4:∀X:Univ.∀Y:Univ.eq Univ (multiply (right_division X Y) Y) X. +∀H5:∀X:Univ.∀Y:Univ.eq Univ (left_division X (multiply X Y)) Y. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply X (left_division X Y)) Y. +∀H7:∀X:Univ.eq Univ (multiply X identity) X. +∀H8:∀X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply a (multiply b c)) a) (multiply (multiply a b) (multiply c a))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#identity ##. +#left_division ##. +#left_inverse ##. +#multiply ##. +#right_division ##. +#right_inverse ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP404-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP404-1.ma new file mode 100644 index 000000000..e0afa803c --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP404-1.ma @@ -0,0 +1,67 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP404-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP404-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Group Theory *) + +(* Problem : Axiom for group theory, in product & inverse, part 2 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [Kun92] Kunen (1992), Single Axioms for Groups *) + +(* : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.29 v3.2.0, 0.21 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 3 ( 0 singleton) *) + +(* Maximal term depth : 8 ( 4 average) *) + +(* Comments : A UEQ part of GRP049-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_2: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. +∀a2:Univ. +∀b2:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (inverse (multiply B (multiply (inverse B) B)))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP405-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP405-1.ma new file mode 100644 index 000000000..4cb99b329 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP405-1.ma @@ -0,0 +1,69 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP405-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP405-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Group Theory *) + +(* Problem : Axiom for group theory, in product & inverse, part 3 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [Kun92] Kunen (1992), Single Axioms for Groups *) + +(* : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.29 v3.2.0, 0.21 v3.1.0, 0.33 v2.7.0, 0.27 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 3 ( 0 singleton) *) + +(* Maximal term depth : 8 ( 4 average) *) + +(* Comments : A UEQ part of GRP049-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_3: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. +∀a3:Univ. +∀b3:Univ. +∀c3:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A (inverse (multiply (inverse (multiply (inverse (multiply A B)) C)) (inverse (multiply B (multiply (inverse B) B)))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP422-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP422-1.ma new file mode 100644 index 000000000..3713e152d --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP422-1.ma @@ -0,0 +1,67 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP422-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP422-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Group Theory *) + +(* Problem : Axiom for group theory, in product & inverse, part 2 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [Kun92] Kunen (1992), Single Axioms for Groups *) + +(* : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.29 v3.1.0, 0.44 v2.7.0, 0.27 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 3 ( 0 singleton) *) + +(* Maximal term depth : 11 ( 4 average) *) + +(* Comments : A UEQ part of GRP055-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_2: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. +∀a2:Univ. +∀b2:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (multiply (inverse C) (inverse (multiply (inverse C) C))))))) (multiply A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP423-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP423-1.ma new file mode 100644 index 000000000..1ca22cf52 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP423-1.ma @@ -0,0 +1,69 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP423-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP423-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Group Theory *) + +(* Problem : Axiom for group theory, in product & inverse, part 3 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [Kun92] Kunen (1992), Single Axioms for Groups *) + +(* : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.36 v3.1.0, 0.22 v2.7.0, 0.36 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 3 ( 0 singleton) *) + +(* Maximal term depth : 11 ( 4 average) *) + +(* Comments : A UEQ part of GRP055-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_3: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. +∀a3:Univ. +∀b3:Univ. +∀c3:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (inverse (multiply (inverse (multiply A (inverse (multiply (inverse B) (multiply (inverse C) (inverse (multiply (inverse C) C))))))) (multiply A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP444-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP444-1.ma new file mode 100644 index 000000000..c9913c566 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP444-1.ma @@ -0,0 +1,68 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP444-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP444-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Group Theory *) + +(* Problem : Axiom for group theory, in product & inverse, part 3 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.21 v3.1.0, 0.22 v2.7.0, 0.27 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 4 ( 0 singleton) *) + +(* Maximal term depth : 8 ( 4 average) *) + +(* Comments : A UEQ part of GRP062-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_3: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. +∀a3:Univ. +∀b3:Univ. +∀c3:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (inverse (multiply A (multiply B (multiply (multiply C (inverse C)) (inverse (multiply D (multiply A B))))))) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP452-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP452-1.ma new file mode 100644 index 000000000..048248031 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP452-1.ma @@ -0,0 +1,71 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP452-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP452-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Group Theory *) + +(* Problem : Axiom for group theory, in division, part 2 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.21 v3.2.0, 0.14 v3.1.0, 0.11 v2.7.0, 0.18 v2.6.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR) *) + +(* Number of atoms : 4 ( 4 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 : 8 ( 0 singleton) *) + +(* Maximal term depth : 8 ( 3 average) *) + +(* Comments : A UEQ part of GRP065-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_2: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. +∀a2:Univ. +∀b2:Univ. +∀divide:∀_:Univ.∀_:Univ.Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#a2 ##. +#b2 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP453-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP453-1.ma new file mode 100644 index 000000000..cf6d44071 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP453-1.ma @@ -0,0 +1,73 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP453-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP453-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Group Theory *) + +(* Problem : Axiom for group theory, in division, part 3 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.21 v3.1.0, 0.11 v2.7.0, 0.27 v2.6.0 *) + +(* Syntax : Number of clauses : 4 ( 0 non-Horn; 4 unit; 1 RR) *) + +(* Number of atoms : 4 ( 4 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 : 8 ( 0 singleton) *) + +(* Maximal term depth : 8 ( 3 average) *) + +(* Comments : A UEQ part of GRP065-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_3: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ. +∀a3:Univ. +∀b3:Univ. +∀c3:Univ. +∀divide:∀_:Univ.∀_:Univ.Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A). +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)). +∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +nauto by H0,H1,H2 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP471-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP471-1.ma new file mode 100644 index 000000000..b9c4e7a84 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP471-1.ma @@ -0,0 +1,72 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP471-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP471-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Group Theory *) + +(* Problem : Axiom for group theory, in division and inverse, part 3 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.29 v3.2.0, 0.21 v3.1.0, 0.11 v2.7.0, 0.18 v2.6.0 *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *) + +(* Number of atoms : 3 ( 3 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 : 6 ( 0 singleton) *) + +(* Maximal term depth : 6 ( 3 average) *) + +(* Comments : A UEQ part of GRP071-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_3: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. +∀a3:Univ. +∀b3:Univ. +∀c3:Univ. +∀divide:∀_:Univ.∀_:Univ.Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide A (divide B (divide C D)))) (divide (divide D C) A)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP477-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP477-1.ma new file mode 100644 index 000000000..73efaed82 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP477-1.ma @@ -0,0 +1,72 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP477-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP477-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Group Theory *) + +(* Problem : Axiom for group theory, in division and inverse, part 3 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.25 v3.3.0, 0.21 v3.1.0, 0.00 v2.7.0, 0.27 v2.6.0 *) + +(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *) + +(* Number of atoms : 3 ( 3 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 : 6 ( 0 singleton) *) + +(* Maximal term depth : 6 ( 3 average) *) + +(* Comments : A UEQ part of GRP073-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_3: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ. +∀a3:Univ. +∀b3:Univ. +∀c3:Univ. +∀divide:∀_:Univ.∀_:Univ.Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (divide A (inverse B)). +∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (divide (inverse (divide (divide (divide A B) C) (divide D C))) (divide B A)) D.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#a3 ##. +#b3 ##. +#c3 ##. +#divide ##. +#inverse ##. +#multiply ##. +#H0 ##. +#H1 ##. +nauto by H0,H1 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP506-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP506-1.ma new file mode 100644 index 000000000..260c455b0 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP506-1.ma @@ -0,0 +1,72 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP506-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP506-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Group Theory (Abelian) *) + +(* Problem : Axiom for Abelian group theory, in product and inverse, part 2 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [Neu81] Neumann (1981), Another Single Law for Groups *) + +(* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *) + +(* : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.67 v3.4.0, 0.75 v3.3.0, 0.71 v3.2.0, 0.64 v3.1.0, 0.67 v2.7.0, 0.73 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 10 ( 4 average) *) + +(* Comments : A UEQ part of GRP084-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_2: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. +∀a2:Univ. +∀b2:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply (multiply (inverse b2) b2) a2) a2) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a2 ##. +#b2 ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP508-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP508-1.ma new file mode 100644 index 000000000..b2f9b979e --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/GRP508-1.ma @@ -0,0 +1,74 @@ +include "logic/equality.ma". + +(* Inclusion of: GRP508-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : GRP508-1 : TPTP v3.7.0. Bugfixed v2.7.0. *) + +(* Domain : Group Theory (Abelian) *) + +(* Problem : Axiom for Abelian group theory, in product and inverse, part 4 *) + +(* Version : [McC93] (equality) axioms. *) + +(* English : *) + +(* Refs : [Neu81] Neumann (1981), Another Single Law for Groups *) + +(* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *) + +(* : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.62 v3.3.0, 0.64 v3.2.0, 0.57 v3.1.0, 0.56 v2.7.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 0 singleton) *) + +(* Maximal term depth : 10 ( 4 average) *) + +(* Comments : A UEQ part of GRP084-1 *) + +(* Bugfixes : v2.7.0 - Grounded conjecture *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_these_axioms_4: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. +∀a:Univ. +∀b:Univ. +∀inverse:∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply a b) (multiply b a)) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a ##. +#b ##. +#inverse ##. +#multiply ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT080-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT080-1.ma new file mode 100644 index 000000000..5c01e5d41 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT080-1.ma @@ -0,0 +1,69 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT080-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT080-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Axiom for lattice theory, part 1 *) + +(* Version : [MP96] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *) + +(* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.50 v3.3.0, 0.36 v3.1.0, 0.11 v2.7.0, 0.55 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 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 : 7 ( 1 singleton) *) + +(* Maximal term depth : 12 ( 4 average) *) + +(* Comments : A UEQ part of LAT015-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_normal_axioms_1: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. +∀a:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a a) a) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT087-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT087-1.ma new file mode 100644 index 000000000..4e2fb6447 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT087-1.ma @@ -0,0 +1,71 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT087-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT087-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Axiom for lattice theory, part 8 *) + +(* Version : [MP96] (equality) axioms. *) + +(* English : *) + +(* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *) + +(* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.67 v3.4.0, 0.62 v3.3.0, 0.43 v3.1.0, 0.22 v2.7.0, 0.55 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 7 ( 1 singleton) *) + +(* Maximal term depth : 12 ( 4 average) *) + +(* Comments : A UEQ part of LAT015-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_normal_axioms_8: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ. +∀a:Univ. +∀b:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (join a (meet a b)) a) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#G ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT093-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT093-1.ma new file mode 100644 index 000000000..107f2fbc3 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT093-1.ma @@ -0,0 +1,70 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT093-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT093-1 : TPTP v3.7.0. Released v2.6.0. *) + +(* Domain : Lattice Theory (Weakly Associative Lattices) *) + +(* Problem : Axiom for weakly associative lattices (WAL), part 2 *) + +(* Version : [MP96] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC98] McCune (1998), Email to G. Sutcliffe *) + +(* : [MP96] McCune & Padmanabhan (1996), Automated Deduction in Eq *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.50 v3.3.0, 0.43 v3.1.0, 0.22 v2.7.0, 0.45 v2.6.0 *) + +(* Syntax : Number of clauses : 2 ( 0 non-Horn; 2 unit; 1 RR) *) + +(* Number of atoms : 2 ( 2 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 6 ( 1 singleton) *) + +(* Maximal term depth : 11 ( 4 average) *) + +(* Comments : A UEQ part of LAT030-1 *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_wal_axioms_2: + (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ. +∀a:Univ. +∀b:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet B D) (meet E B)) B)) (meet (join (meet B (meet (meet (join B D) (join E B)) B)) (meet F (join B (meet (meet (join B D) (join E B)) B)))) (join A (join (join (meet B D) (meet E B)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet b a) (meet a b)) +. +#Univ ##. +#A ##. +#B ##. +#C ##. +#D ##. +#E ##. +#F ##. +#a ##. +#b ##. +#join ##. +#meet ##. +#H0 ##. +nauto by H0 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT138-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT138-1.ma new file mode 100644 index 000000000..5da2b4ace --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT138-1.ma @@ -0,0 +1,135 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT138-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT138-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H7 implies H6 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.89 v3.4.0, 0.88 v3.3.0, 1.00 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 19 ( 2 singleton) *) + +(* Maximal term depth : 7 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H6: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (meet X Z))) (meet X (join Y (meet X (join (meet X Y) (meet Z (join X Y)))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT140-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT140-1.ma new file mode 100644 index 000000000..d087e5072 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT140-1.ma @@ -0,0 +1,135 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT140-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT140-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H21 implies H2 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.89 v3.4.0, 1.00 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 19 ( 2 singleton) *) + +(* Maximal term depth : 7 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H2: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (meet X Y) (meet X Z)) (meet X (join (meet Y (join X (meet Y Z))) (meet Z (join X Y)))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet c (join (meet a (join b c)) (meet b c)))))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT146-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT146-1.ma new file mode 100644 index 000000000..554cafcd5 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT146-1.ma @@ -0,0 +1,138 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT146-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT146-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H34 implies H28 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.62 v3.3.0, 0.79 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 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 : 20 ( 2 singleton) *) + +(* Maximal term depth : 7 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H28: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀d:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (meet Z U))) (meet X (join Y (meet Z (join Y (meet U (join Y Z)))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (meet c d)))) (meet a (join b (meet c (meet d (join a (meet b d))))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT148-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT148-1.ma new file mode 100644 index 000000000..c44c3a5a4 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT148-1.ma @@ -0,0 +1,136 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT148-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT148-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H34 implies H7 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.50 v3.3.0, 0.71 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 20 ( 2 singleton) *) + +(* Maximal term depth : 7 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H7: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (meet Z U))) (meet X (join Y (meet Z (join Y (meet U (join Y Z)))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet a (join (meet a b) (meet c (join a b))))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT152-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT152-1.ma new file mode 100644 index 000000000..b175d6f7f --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT152-1.ma @@ -0,0 +1,136 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT152-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT152-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H40 implies H6 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.78 v3.4.0, 0.62 v3.3.0, 0.86 v3.2.0, 0.79 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 20 ( 2 singleton) *) + +(* Maximal term depth : 7 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H6: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (meet Z (join X U)))) (meet X (join Y (meet Z (join U (meet Z (join X Y)))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT156-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT156-1.ma new file mode 100644 index 000000000..f27036d53 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT156-1.ma @@ -0,0 +1,136 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT156-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT156-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H49 implies H6 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.38 v3.3.0, 0.71 v3.2.0, 0.64 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 20 ( 2 singleton) *) + +(* Maximal term depth : 6 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H6: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (meet Z (join X U)))) (meet X (join Y (join (meet X Z) (meet Z (join Y U))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT159-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT159-1.ma new file mode 100644 index 000000000..b58b6decf --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT159-1.ma @@ -0,0 +1,136 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT159-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT159-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H50 implies H7 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.78 v3.4.0, 0.62 v3.3.0, 0.86 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 20 ( 2 singleton) *) + +(* Maximal term depth : 7 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H7: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (meet Z (join X U)))) (meet X (join Y (meet Z (join X (meet Z (join Y U)))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join b (meet a (join (meet a b) (meet c (join a b))))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT164-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT164-1.ma new file mode 100644 index 000000000..c6e42e5c9 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT164-1.ma @@ -0,0 +1,136 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT164-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT164-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H76 implies H6 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.78 v3.4.0, 0.75 v3.3.0, 0.93 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 20 ( 2 singleton) *) + +(* Maximal term depth : 6 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H6: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (meet Z (join Y U)))) (meet X (join Y (meet Z (join U (meet X Y))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a c))) (meet a (join (meet a (join b (meet a c))) (meet c (join a b))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT165-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT165-1.ma new file mode 100644 index 000000000..9968ae823 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT165-1.ma @@ -0,0 +1,138 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT165-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT165-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H76 implies H77 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.89 v3.4.0, 0.75 v3.3.0, 0.86 v3.2.0, 0.93 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 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 : 20 ( 2 singleton) *) + +(* Maximal term depth : 7 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H77: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀d:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (meet Z (join Y U)))) (meet X (join Y (meet Z (join U (meet X Y))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join b d)))) (meet a (join b (meet c (join d (meet a (meet b c))))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT166-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT166-1.ma new file mode 100644 index 000000000..7c9530702 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT166-1.ma @@ -0,0 +1,138 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT166-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT166-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H77 implies H78 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.89 v3.4.0, 0.88 v3.3.0, 0.93 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 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 : 20 ( 2 singleton) *) + +(* Maximal term depth : 7 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H78: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀d:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (meet Z (join Y U)))) (meet X (join Y (meet Z (join U (meet X (meet Y Z)))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join b d)))) (meet a (join b (meet c (join d (meet b (join a d))))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT169-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT169-1.ma new file mode 100644 index 000000000..1ea707b51 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT169-1.ma @@ -0,0 +1,135 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT169-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT169-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H21_dual implies H58 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.78 v3.4.0, 0.75 v3.3.0, 0.86 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 19 ( 2 singleton) *) + +(* Maximal term depth : 6 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H58: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (join X Y) (join X Z)) (join X (meet (join Y (meet X (join Y Z))) (join Z (meet X Y)))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b)))))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT170-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT170-1.ma new file mode 100644 index 000000000..375ca372f --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT170-1.ma @@ -0,0 +1,136 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT170-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT170-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H49_dual implies H58 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.67 v3.4.0, 0.62 v3.3.0, 0.79 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 5 ( 3 constant; 0-2 arity) *) + +(* Number of variables : 20 ( 2 singleton) *) + +(* Maximal term depth : 6 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H58: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (join Z (meet X U)))) (join X (meet Y (meet (join X Z) (join Z (meet Y U))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b)))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT173-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT173-1.ma new file mode 100644 index 000000000..4fe6e9e7e --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT173-1.ma @@ -0,0 +1,138 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT173-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT173-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H76_dual implies H40 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.89 v3.4.0, 0.88 v3.3.0, 0.93 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 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 : 20 ( 2 singleton) *) + +(* Maximal term depth : 7 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H40: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀d:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (join Z (meet Y U)))) (join X (meet Y (join Z (meet U (join X Y))))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet c (join a d)))) (meet a (join b (meet c (join d (meet c (join a b))))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT175-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT175-1.ma new file mode 100644 index 000000000..680afdd07 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/LAT175-1.ma @@ -0,0 +1,138 @@ +include "logic/equality.ma". + +(* Inclusion of: LAT175-1.p *) + +(* ------------------------------------------------------------------------------ *) + +(* File : LAT175-1 : TPTP v3.7.0. Released v3.1.0. *) + +(* Domain : Lattice Theory *) + +(* Problem : Huntington equation H79_dual implies H32 *) + +(* Version : [McC05] (equality) axioms : Especial. *) + +(* English : *) + +(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *) + +(* Source : [McC05] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.89 v3.4.0, 0.88 v3.3.0, 0.93 v3.1.0 *) + +(* Syntax : Number of clauses : 10 ( 0 non-Horn; 10 unit; 1 RR) *) + +(* Number of atoms : 10 ( 10 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 : 20 ( 2 singleton) *) + +(* Maximal term depth : 6 ( 3 average) *) + +(* Comments : *) + +(* ------------------------------------------------------------------------------ *) + +(* ----Include Lattice theory (equality) axioms *) + +(* Inclusion of: Axioms/LAT001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : LAT001-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Lattice Theory *) + +(* Axioms : Lattice theory (equality) axioms *) + +(* Version : [McC88] (equality) axioms. *) + +(* English : *) + +(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *) + +(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *) + +(* : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* Source : [McC88] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 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 : 2 ( 0 constant; 2-2 arity) *) + +(* Number of variables : 16 ( 2 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----The following 8 clauses characterise lattices *) + +(* -------------------------------------------------------------------------- *) + +(* ------------------------------------------------------------------------------ *) +ntheorem prove_H32: + (∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀b:Univ. +∀c:Univ. +∀d:Univ. +∀join:∀_:Univ.∀_:Univ.Univ. +∀meet:∀_:Univ.∀_:Univ.Univ. +∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (join Z (meet X U)))) (join X (meet (join X (meet Y (join X Z))) (join Z U))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X. +∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X. +∀H7:∀X:Univ.eq Univ (join X X) X. +∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b (meet a (meet c d)))) (meet a (join b (meet c (join (meet a d) (meet b d)))))) +. +#Univ ##. +#U ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#b ##. +#c ##. +#d ##. +#join ##. +#meet ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8 ##; +ntry (nassumption) ##; +nqed. + +(* ------------------------------------------------------------------------------ *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/Makefile b/helm/software/matita/contribs/ng_TPTP/CASC_2008/Makefile new file mode 100644 index 000000000..147cb03fd --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/Makefile @@ -0,0 +1,15 @@ +BIN=../../../ +DIR=$(shell basename $$PWD) + +$(DIR) all: + $(BIN)matitac +$(DIR).opt opt all.opt: + $(BIN)matitac.opt +clean: + $(BIN)matitaclean +clean.opt: + $(BIN)matitaclean.opt +depend: + $(BIN)matitadep +depend.opt: + $(BIN)matitadep.opt diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG009-7.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG009-7.ma new file mode 100644 index 000000000..4a79566da --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG009-7.ma @@ -0,0 +1,157 @@ +include "logic/equality.ma". + +(* Inclusion of: RNG009-7.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG009-7 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory *) + +(* Problem : If X*X*X = X then the ring is commutative *) + +(* Version : [LW91] (equality) axioms. *) + +(* English : Given a ring in which for all x, x * x * x = x, prove that *) + +(* for all x and y, x * y = y * x. *) + +(* Refs : [LO85] Lusk & Overbeek (1985), Reasoning about Equality *) + +(* : [LW91] Lusk & Wos (1991), Benchmark Problems in Which Equalit *) + +(* Source : [LW91] *) + +(* Names : Problem 6 [LO85] *) + +(* : RT2 [LW91] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.62 v3.3.0, 0.50 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0, 0.17 v2.5.0, 0.25 v2.4.0, 0.00 v2.2.1, 0.56 v2.2.0, 0.71 v2.1.0, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 2 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 7 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 19 ( 0 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include ring theory axioms *) + +(* Inclusion of: Axioms/RNG005-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG005-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory *) + +(* Axioms : Ring theory (equality) axioms *) + +(* Version : [LW92] (equality) axioms. *) + +(* English : *) + +(* Refs : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *) + +(* Source : [LW92] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 9 ( 0 non-Horn; 9 unit; 0 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 : 4 ( 1 constant; 0-2 arity) *) + +(* Number of variables : 18 ( 0 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : These axioms are used in [Wos88] p.203. *) + +(* -------------------------------------------------------------------------- *) + +(* ----There exists an additive identity element *) + +(* ----Existence of left additive additive_inverse *) + +(* ----Associativity for addition *) + +(* ----Commutativity for addition *) + +(* ----Associativity for multiplication *) + +(* ----Distributive property of product over sum *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_commutativity: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀additive_inverse:∀_:Univ.Univ. +∀b:Univ. +∀c:Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:eq Univ (multiply a b) c. +∀H1:∀X:Univ.eq Univ (multiply X (multiply X X)) X. +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply Y Z)) (multiply (multiply X Y) Z). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). +∀H7:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. +∀H8:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. +∀H9:∀X:Univ.eq Univ (add X additive_identity) X. +∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#b ##. +#c ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG019-6.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG019-6.ma new file mode 100644 index 000000000..0e713d970 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG019-6.ma @@ -0,0 +1,177 @@ +include "logic/equality.ma". + +(* Inclusion of: RNG019-6.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG019-6 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Problem : First part of the linearised form of the associator *) + +(* Version : [Ste87] (equality) axioms. *) + +(* English : The associator can be expressed in another form called *) + +(* a linearised form. There are three clauses to be proved *) + +(* to establish the equivalence of the two forms. *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [Ste87] *) + +(* Names : c24 [Ste87] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.22 v3.4.0, 0.38 v3.3.0, 0.14 v3.2.0, 0.21 v3.1.0, 0.11 v2.7.0, 0.18 v2.6.0, 0.33 v2.5.0, 0.25 v2.4.0, 0.67 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.50 v2.0.0 *) + +(* Syntax : Number of clauses : 16 ( 0 non-Horn; 16 unit; 1 RR) *) + +(* Number of atoms : 16 ( 16 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 10 ( 5 constant; 0-3 arity) *) + +(* Number of variables : 27 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include nonassociative ring axioms *) + +(* Inclusion of: Axioms/RNG003-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG003-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Axioms : Alternative ring theory (equality) axioms *) + +(* Version : [Ste87] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [Ste87] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *) + +(* Number of atoms : 15 ( 15 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 1 constant; 0-3 arity) *) + +(* Number of variables : 27 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----There exists an additive identity element *) + +(* ----Multiplicative zero *) + +(* ----Existence of left additive additive_inverse *) + +(* ----Inverse of additive_inverse of X is X *) + +(* ----Distributive property of product over sum *) + +(* ----Commutativity for addition *) + +(* ----Associativity for addition *) + +(* ----Right alternative law *) + +(* ----Left alternative law *) + +(* ----Associator *) + +(* ----Commutator *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_linearised_form1: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀additive_inverse:∀_:Univ.Univ. +∀associator:∀_:Univ.∀_:Univ.∀_:Univ.Univ. +∀commutator:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀u:Univ. +∀v:Univ. +∀x:Univ. +∀y:Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))). +∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H8:∀X:Univ.eq Univ (additive_inverse (additive_inverse X)) X. +∀H9:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. +∀H10:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. +∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. +∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. +∀H13:∀X:Univ.eq Univ (add X additive_identity) X. +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y (add u v)) (add (associator x y u) (associator x y v))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#u ##. +#v ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG019-7.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG019-7.ma new file mode 100644 index 000000000..c2877ffd3 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG019-7.ma @@ -0,0 +1,193 @@ +include "logic/equality.ma". + +(* Inclusion of: RNG019-7.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG019-7 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Problem : First part of the linearised form of the associator *) + +(* Version : [Ste87] (equality) axioms : Augmented. *) + +(* English : The associator can be expressed in another form called *) + +(* a linearised form. There are three clauses to be proved *) + +(* to establish the equivalence of the two forms. *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.14 v3.2.0, 0.21 v3.1.0, 0.22 v2.7.0, 0.27 v2.6.0, 0.33 v2.5.0, 0.25 v2.4.0, 0.67 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.50 v2.0.0 *) + +(* Syntax : Number of clauses : 23 ( 0 non-Horn; 23 unit; 1 RR) *) + +(* Number of atoms : 23 ( 23 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 10 ( 5 constant; 0-3 arity) *) + +(* Number of variables : 45 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include nonassociative ring axioms *) + +(* Inclusion of: Axioms/RNG003-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG003-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Axioms : Alternative ring theory (equality) axioms *) + +(* Version : [Ste87] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [Ste87] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *) + +(* Number of atoms : 15 ( 15 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 1 constant; 0-3 arity) *) + +(* Number of variables : 27 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----There exists an additive identity element *) + +(* ----Multiplicative zero *) + +(* ----Existence of left additive additive_inverse *) + +(* ----Inverse of additive_inverse of X is X *) + +(* ----Distributive property of product over sum *) + +(* ----Commutativity for addition *) + +(* ----Associativity for addition *) + +(* ----Right alternative law *) + +(* ----Left alternative law *) + +(* ----Associator *) + +(* ----Commutator *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----The next 7 clause are extra lemmas which Stevens found useful *) +ntheorem prove_linearised_form1: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀additive_inverse:∀_:Univ.Univ. +∀associator:∀_:Univ.∀_:Univ.∀_:Univ.Univ. +∀commutator:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀u:Univ. +∀v:Univ. +∀x:Univ. +∀y:Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) (additive_inverse Z)) (add (additive_inverse (multiply X Z)) (additive_inverse (multiply Y Z))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (additive_inverse X) (add Y Z)) (add (additive_inverse (multiply X Y)) (additive_inverse (multiply X Z))). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X (additive_inverse Y)) Z) (add (multiply X Z) (additive_inverse (multiply Y Z))). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)). +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))). +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))). +∀H9:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)). +∀H10:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)). +∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). +∀H12:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X). +∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H15:∀X:Univ.eq Univ (additive_inverse (additive_inverse X)) X. +∀H16:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. +∀H17:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. +∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. +∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. +∀H20:∀X:Univ.eq Univ (add X additive_identity) X. +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y (add u v)) (add (associator x y u) (associator x y v))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#u ##. +#v ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG020-6.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG020-6.ma new file mode 100644 index 000000000..3edeb6d91 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG020-6.ma @@ -0,0 +1,177 @@ +include "logic/equality.ma". + +(* Inclusion of: RNG020-6.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG020-6 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Problem : Second part of the linearised form of the associator *) + +(* Version : [Ste87] (equality) axioms. *) + +(* English : The associator can be expressed in another form called *) + +(* a linearised form. There are three clauses to be proved *) + +(* to establish the equivalence of the two forms. *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [Ste87] *) + +(* Names : c25 [Ste87] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.33 v3.4.0, 0.38 v3.3.0, 0.21 v3.2.0, 0.29 v3.1.0, 0.33 v2.7.0, 0.36 v2.6.0, 0.33 v2.5.0, 0.25 v2.4.0, 0.67 v2.2.1, 0.78 v2.2.0, 0.71 v2.1.0, 0.88 v2.0.0 *) + +(* Syntax : Number of clauses : 16 ( 0 non-Horn; 16 unit; 1 RR) *) + +(* Number of atoms : 16 ( 16 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 10 ( 5 constant; 0-3 arity) *) + +(* Number of variables : 27 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include nonassociative ring axioms *) + +(* Inclusion of: Axioms/RNG003-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG003-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Axioms : Alternative ring theory (equality) axioms *) + +(* Version : [Ste87] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [Ste87] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *) + +(* Number of atoms : 15 ( 15 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 1 constant; 0-3 arity) *) + +(* Number of variables : 27 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----There exists an additive identity element *) + +(* ----Multiplicative zero *) + +(* ----Existence of left additive additive_inverse *) + +(* ----Inverse of additive_inverse of X is X *) + +(* ----Distributive property of product over sum *) + +(* ----Commutativity for addition *) + +(* ----Associativity for addition *) + +(* ----Right alternative law *) + +(* ----Left alternative law *) + +(* ----Associator *) + +(* ----Commutator *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_linearised_form2: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀additive_inverse:∀_:Univ.Univ. +∀associator:∀_:Univ.∀_:Univ.∀_:Univ.Univ. +∀commutator:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀u:Univ. +∀v:Univ. +∀x:Univ. +∀y:Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))). +∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H8:∀X:Univ.eq Univ (additive_inverse (additive_inverse X)) X. +∀H9:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. +∀H10:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. +∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. +∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. +∀H13:∀X:Univ.eq Univ (add X additive_identity) X. +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (add u v) y) (add (associator x u y) (associator x v y))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#u ##. +#v ##. +#x ##. +#y ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG026-6.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG026-6.ma new file mode 100644 index 000000000..71b1fb979 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG026-6.ma @@ -0,0 +1,173 @@ +include "logic/equality.ma". + +(* Inclusion of: RNG026-6.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG026-6 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Problem : Teichmuller Identity *) + +(* Version : [Ste87] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [Ste87] *) + +(* Names : Teichmuller Identity [Ste87] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.56 v3.4.0, 0.62 v3.3.0, 0.50 v3.2.0, 0.57 v3.1.0, 0.33 v2.7.0, 0.64 v2.6.0, 0.50 v2.5.0, 0.25 v2.4.0, 0.67 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 0.88 v2.0.0 *) + +(* Syntax : Number of clauses : 16 ( 0 non-Horn; 16 unit; 1 RR) *) + +(* Number of atoms : 16 ( 16 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 10 ( 5 constant; 0-3 arity) *) + +(* Number of variables : 27 ( 2 singleton) *) + +(* Maximal term depth : 7 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include nonassociative ring axioms *) + +(* Inclusion of: Axioms/RNG003-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG003-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Axioms : Alternative ring theory (equality) axioms *) + +(* Version : [Ste87] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [Ste87] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *) + +(* Number of atoms : 15 ( 15 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 1 constant; 0-3 arity) *) + +(* Number of variables : 27 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----There exists an additive identity element *) + +(* ----Multiplicative zero *) + +(* ----Existence of left additive additive_inverse *) + +(* ----Inverse of additive_inverse of X is X *) + +(* ----Distributive property of product over sum *) + +(* ----Commutativity for addition *) + +(* ----Associativity for addition *) + +(* ----Right alternative law *) + +(* ----Left alternative law *) + +(* ----Associator *) + +(* ----Commutator *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_teichmuller_identity: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀additive_inverse:∀_:Univ.Univ. +∀associator:∀_:Univ.∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀c:Univ. +∀commutator:∀_:Univ.∀_:Univ.Univ. +∀d:Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))). +∀H2:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H8:∀X:Univ.eq Univ (additive_inverse (additive_inverse X)) X. +∀H9:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. +∀H10:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. +∀H11:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. +∀H12:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. +∀H13:∀X:Univ.eq Univ (add X additive_identity) X. +∀H14:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (add (add (associator (multiply a b) c d) (associator a b (multiply c d))) (additive_inverse (add (add (associator a (multiply b c) d) (multiply a (associator b c d))) (multiply (associator a b c) d)))) additive_identity) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#b ##. +#c ##. +#commutator ##. +#d ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG027-7.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG027-7.ma new file mode 100644 index 000000000..09463d1b7 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG027-7.ma @@ -0,0 +1,191 @@ +include "logic/equality.ma". + +(* Inclusion of: RNG027-7.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG027-7 : TPTP v3.7.0. Bugfixed v2.3.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Problem : Right Moufang identity *) + +(* Version : [Ste87] (equality) axioms : Augmented. *) + +(* Theorem formulation : In terms of associators *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.78 v3.4.0, 0.75 v3.3.0, 0.86 v3.1.0, 0.89 v2.7.0, 0.91 v2.6.0, 0.83 v2.5.0, 0.75 v2.4.0, 0.67 v2.3.0 *) + +(* Syntax : Number of clauses : 23 ( 0 non-Horn; 23 unit; 1 RR) *) + +(* Number of atoms : 23 ( 23 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 9 ( 4 constant; 0-3 arity) *) + +(* Number of variables : 45 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 3 average) *) + +(* Comments : *) + +(* Bugfixes : v2.3.0 - Clause prove_right_moufang fixed. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include nonassociative ring axioms *) + +(* Inclusion of: Axioms/RNG003-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG003-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Axioms : Alternative ring theory (equality) axioms *) + +(* Version : [Ste87] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [Ste87] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *) + +(* Number of atoms : 15 ( 15 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 1 constant; 0-3 arity) *) + +(* Number of variables : 27 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----There exists an additive identity element *) + +(* ----Multiplicative zero *) + +(* ----Existence of left additive additive_inverse *) + +(* ----Inverse of additive_inverse of X is X *) + +(* ----Distributive property of product over sum *) + +(* ----Commutativity for addition *) + +(* ----Associativity for addition *) + +(* ----Right alternative law *) + +(* ----Left alternative law *) + +(* ----Associator *) + +(* ----Commutator *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----The next 7 clause are extra lemmas which Stevens found useful *) +ntheorem prove_right_moufang: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀additive_inverse:∀_:Univ.Univ. +∀associator:∀_:Univ.∀_:Univ.∀_:Univ.Univ. +∀commutator:∀_:Univ.∀_:Univ.Univ. +∀cx:Univ. +∀cy:Univ. +∀cz:Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) (additive_inverse Z)) (add (additive_inverse (multiply X Z)) (additive_inverse (multiply Y Z))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (additive_inverse X) (add Y Z)) (add (additive_inverse (multiply X Y)) (additive_inverse (multiply X Z))). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X (additive_inverse Y)) Z) (add (multiply X Z) (additive_inverse (multiply Y Z))). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)). +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))). +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))). +∀H9:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)). +∀H10:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)). +∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). +∀H12:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X). +∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H15:∀X:Univ.eq Univ (additive_inverse (additive_inverse X)) X. +∀H16:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. +∀H17:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. +∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. +∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. +∀H20:∀X:Univ.eq Univ (add X additive_identity) X. +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply cz (multiply cx (multiply cy cx))) (multiply (multiply (multiply cz cx) cy) cx)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#cx ##. +#cy ##. +#cz ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG028-9.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG028-9.ma new file mode 100644 index 000000000..d61a3734a --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG028-9.ma @@ -0,0 +1,189 @@ +include "logic/equality.ma". + +(* Inclusion of: RNG028-9.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG028-9 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Problem : Left Moufang identity *) + +(* Version : [Ste87] (equality) axioms : Augmented. *) + +(* Theorem formulation : Associators. *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.78 v3.4.0, 0.75 v3.3.0, 0.86 v3.1.0, 0.89 v2.7.0, 0.91 v2.6.0, 0.83 v2.5.0, 0.75 v2.4.0, 0.67 v2.2.1, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 23 ( 0 non-Horn; 23 unit; 1 RR) *) + +(* Number of atoms : 23 ( 23 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 9 ( 4 constant; 0-3 arity) *) + +(* Number of variables : 45 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include nonassociative ring axioms *) + +(* Inclusion of: Axioms/RNG003-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG003-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Axioms : Alternative ring theory (equality) axioms *) + +(* Version : [Ste87] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [Ste87] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *) + +(* Number of atoms : 15 ( 15 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 1 constant; 0-3 arity) *) + +(* Number of variables : 27 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----There exists an additive identity element *) + +(* ----Multiplicative zero *) + +(* ----Existence of left additive additive_inverse *) + +(* ----Inverse of additive_inverse of X is X *) + +(* ----Distributive property of product over sum *) + +(* ----Commutativity for addition *) + +(* ----Associativity for addition *) + +(* ----Right alternative law *) + +(* ----Left alternative law *) + +(* ----Associator *) + +(* ----Commutator *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----The next 7 clause are extra lemmas which Stevens found useful *) +ntheorem prove_left_moufang: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀additive_inverse:∀_:Univ.Univ. +∀associator:∀_:Univ.∀_:Univ.∀_:Univ.Univ. +∀commutator:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀x:Univ. +∀y:Univ. +∀z:Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) (additive_inverse Z)) (add (additive_inverse (multiply X Z)) (additive_inverse (multiply Y Z))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (additive_inverse X) (add Y Z)) (add (additive_inverse (multiply X Y)) (additive_inverse (multiply X Z))). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X (additive_inverse Y)) Z) (add (multiply X Z) (additive_inverse (multiply Y Z))). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)). +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))). +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))). +∀H9:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)). +∀H10:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)). +∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). +∀H12:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X). +∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H15:∀X:Univ.eq Univ (additive_inverse (additive_inverse X)) X. +∀H16:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. +∀H17:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. +∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. +∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. +∀H20:∀X:Univ.eq Univ (add X additive_identity) X. +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x (multiply y x) z) (multiply x (associator x y z))) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG029-7.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG029-7.ma new file mode 100644 index 000000000..faeb63fcc --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG029-7.ma @@ -0,0 +1,189 @@ +include "logic/equality.ma". + +(* Inclusion of: RNG029-7.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG029-7 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Problem : Middle Moufang identity *) + +(* Version : [Ste87] (equality) axioms : Augmented. *) + +(* Theorem formulation : In terms of associators *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [TPTP] *) + +(* Names : *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.78 v3.4.0, 0.75 v3.3.0, 0.86 v3.1.0, 0.89 v2.7.0, 0.91 v2.6.0, 0.83 v2.5.0, 0.75 v2.4.0, 0.67 v2.2.1, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 23 ( 0 non-Horn; 23 unit; 1 RR) *) + +(* Number of atoms : 23 ( 23 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 9 ( 4 constant; 0-3 arity) *) + +(* Number of variables : 45 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 3 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include nonassociative ring axioms *) + +(* Inclusion of: Axioms/RNG003-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG003-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory (Alternative) *) + +(* Axioms : Alternative ring theory (equality) axioms *) + +(* Version : [Ste87] (equality) axioms. *) + +(* English : *) + +(* Refs : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *) + +(* Source : [Ste87] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 15 ( 0 non-Horn; 15 unit; 0 RR) *) + +(* Number of atoms : 15 ( 15 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 6 ( 1 constant; 0-3 arity) *) + +(* Number of variables : 27 ( 2 singleton) *) + +(* Maximal term depth : 5 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----There exists an additive identity element *) + +(* ----Multiplicative zero *) + +(* ----Existence of left additive additive_inverse *) + +(* ----Inverse of additive_inverse of X is X *) + +(* ----Distributive property of product over sum *) + +(* ----Commutativity for addition *) + +(* ----Associativity for addition *) + +(* ----Right alternative law *) + +(* ----Left alternative law *) + +(* ----Associator *) + +(* ----Commutator *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* ----The next 7 clause are extra lemmas which Stevens found useful *) +ntheorem prove_middle_moufang: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀additive_inverse:∀_:Univ.Univ. +∀associator:∀_:Univ.∀_:Univ.∀_:Univ.Univ. +∀commutator:∀_:Univ.∀_:Univ.Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀x:Univ. +∀y:Univ. +∀z:Univ. +∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) (additive_inverse Z)) (add (additive_inverse (multiply X Z)) (additive_inverse (multiply Y Z))). +∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (additive_inverse X) (add Y Z)) (add (additive_inverse (multiply X Y)) (additive_inverse (multiply X Z))). +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X (additive_inverse Y)) Z) (add (multiply X Z) (additive_inverse (multiply Y Z))). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))). +∀H4:∀X:Univ.∀Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)). +∀H6:∀X:Univ.∀Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y). +∀H7:∀X:Univ.∀Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))). +∀H8:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))). +∀H9:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)). +∀H10:∀X:Univ.∀Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)). +∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). +∀H12:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X). +∀H13:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +∀H14:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H15:∀X:Univ.eq Univ (additive_inverse (additive_inverse X)) X. +∀H16:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. +∀H17:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. +∀H18:∀X:Univ.eq Univ (multiply X additive_identity) additive_identity. +∀H19:∀X:Univ.eq Univ (multiply additive_identity X) additive_identity. +∀H20:∀X:Univ.eq Univ (add X additive_identity) X. +∀H21:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply (multiply x y) (multiply z x)) (multiply (multiply x (multiply y z)) x)) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#associator ##. +#commutator ##. +#multiply ##. +#x ##. +#y ##. +#z ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +#H11 ##. +#H12 ##. +#H13 ##. +#H14 ##. +#H15 ##. +#H16 ##. +#H17 ##. +#H18 ##. +#H19 ##. +#H20 ##. +#H21 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13,H14,H15,H16,H17,H18,H19,H20,H21 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG035-7.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG035-7.ma new file mode 100644 index 000000000..a2fa14fee --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/RNG035-7.ma @@ -0,0 +1,153 @@ +include "logic/equality.ma". + +(* Inclusion of: RNG035-7.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG035-7 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory *) + +(* Problem : If X*X*X*X = X then the ring is commutative *) + +(* Version : [LW91] (equality) axioms. *) + +(* English : Given a ring in which for all x, x * x * x * x = x, prove *) + +(* that for all x and y, x * y = y * x. *) + +(* Refs : [LW91] Lusk & Wos (1991), Benchmark Problems in Which Equalit *) + +(* Source : [LW91] *) + +(* Names : RT3 [LW91] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.89 v3.4.0, 0.88 v3.3.0, 0.79 v3.2.0, 0.86 v3.1.0, 0.67 v2.7.0, 0.73 v2.6.0, 0.50 v2.5.0, 0.25 v2.4.0, 0.33 v2.2.1, 1.00 v2.0.0 *) + +(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 2 RR) *) + +(* Number of atoms : 12 ( 12 equality) *) + +(* Maximal clause size : 1 ( 1 average) *) + +(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *) + +(* Number of functors : 7 ( 4 constant; 0-2 arity) *) + +(* Number of variables : 19 ( 0 singleton) *) + +(* Maximal term depth : 4 ( 2 average) *) + +(* Comments : *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include ring theory axioms *) + +(* Inclusion of: Axioms/RNG005-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : RNG005-0 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Ring Theory *) + +(* Axioms : Ring theory (equality) axioms *) + +(* Version : [LW92] (equality) axioms. *) + +(* English : *) + +(* Refs : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *) + +(* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *) + +(* Source : [LW92] *) + +(* Names : *) + +(* Status : *) + +(* Syntax : Number of clauses : 9 ( 0 non-Horn; 9 unit; 0 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 : 4 ( 1 constant; 0-2 arity) *) + +(* Number of variables : 18 ( 0 singleton) *) + +(* Maximal term depth : 3 ( 2 average) *) + +(* Comments : These axioms are used in [Wos88] p.203. *) + +(* -------------------------------------------------------------------------- *) + +(* ----There exists an additive identity element *) + +(* ----Existence of left additive additive_inverse *) + +(* ----Associativity for addition *) + +(* ----Commutativity for addition *) + +(* ----Associativity for multiplication *) + +(* ----Distributive property of product over sum *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_commutativity: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀additive_identity:Univ. +∀additive_inverse:∀_:Univ.Univ. +∀b:Univ. +∀c:Univ. +∀multiply:∀_:Univ.∀_:Univ.Univ. +∀H0:eq Univ (multiply a b) c. +∀H1:∀X:Univ.eq Univ (multiply X (multiply X (multiply X X))) X. +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)). +∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)). +∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (multiply Y Z)) (multiply (multiply X Y) Z). +∀H5:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X). +∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z). +∀H7:∀X:Univ.eq Univ (add X (additive_inverse X)) additive_identity. +∀H8:∀X:Univ.eq Univ (add (additive_inverse X) X) additive_identity. +∀H9:∀X:Univ.eq Univ (add X additive_identity) X. +∀H10:∀X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#additive_identity ##. +#additive_inverse ##. +#b ##. +#c ##. +#multiply ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +#H4 ##. +#H5 ##. +#H6 ##. +#H7 ##. +#H8 ##. +#H9 ##. +#H10 ##. +nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/ROB006-1.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/ROB006-1.ma new file mode 100644 index 000000000..06e8d7c00 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/ROB006-1.ma @@ -0,0 +1,137 @@ +include "logic/equality.ma". + +(* Inclusion of: ROB006-1.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : ROB006-1 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Robbins Algebra *) + +(* Problem : Exists absorbed element => Boolean *) + +(* Version : [Win90] (equality) axioms. *) + +(* 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 *) + +(* : [LW92] Lusk & Wos (1992), Benchmark Problems in Which Equalit *) + +(* Source : [Wos92] *) + +(* Names : Theorem 1.1 [Win90] *) + +(* : RA4 [LW92] *) + +(* Status : Unsatisfiable *) + +(* Rating : 0.78 v3.4.0, 0.88 v3.3.0, 0.86 v3.1.0, 0.89 v2.7.0, 0.91 v2.6.0, 0.83 v2.5.0, 0.75 v2.4.0, 0.67 v2.3.0, 1.00 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 : 7 ( 0 singleton) *) + +(* Maximal term depth : 6 ( 3 average) *) + +(* Comments : Commutativity, associativity, and Huntington's axiom *) + +(* axiomatize Boolean algebra. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include axioms for Robbins algebra *) + +(* Inclusion of: Axioms/ROB001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : ROB001-0 : TPTP v3.7.0. 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 atoms : 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 : *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_huntingtons_axiom: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀a:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀b:Univ. +∀c:Univ. +∀d:Univ. +∀negate:∀_:Univ.Univ. +∀H0:eq Univ (add c d) d. +∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). +∀H3:∀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) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#a ##. +#add ##. +#b ##. +#c ##. +#d ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +nauto by H0,H1,H2,H3 ##; +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/ROB006-2.ma b/helm/software/matita/contribs/ng_TPTP/CASC_2008/ROB006-2.ma new file mode 100644 index 000000000..62d596e0a --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/ROB006-2.ma @@ -0,0 +1,132 @@ +include "logic/equality.ma". + +(* Inclusion of: ROB006-2.p *) + +(* -------------------------------------------------------------------------- *) + +(* File : ROB006-2 : TPTP v3.7.0. Released v1.0.0. *) + +(* Domain : Robbins Algebra *) + +(* Problem : Exists absorbed element => Exists idempotent element *) + +(* Version : [Win90] (equality) axioms. *) + +(* Theorem formulation : Denies idempotence. *) + +(* 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 : 0.78 v3.4.0, 0.88 v3.3.0, 0.86 v3.1.0, 0.89 v2.7.0, 0.91 v2.6.0, 0.83 v2.5.0, 0.75 v2.4.0, 0.67 v2.3.0, 1.00 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 : 4 ( 2 constant; 0-2 arity) *) + +(* Number of variables : 8 ( 0 singleton) *) + +(* Maximal term depth : 6 ( 2 average) *) + +(* Comments : Commutativity, associativity, and Huntington's axiom *) + +(* axiomatize Boolean algebra. *) + +(* -------------------------------------------------------------------------- *) + +(* ----Include axioms for Robbins algebra *) + +(* Inclusion of: Axioms/ROB001-0.ax *) + +(* -------------------------------------------------------------------------- *) + +(* File : ROB001-0 : TPTP v3.7.0. 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 atoms : 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 : *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) + +(* -------------------------------------------------------------------------- *) +ntheorem prove_idempotence: + (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ. +∀add:∀_:Univ.∀_:Univ.Univ. +∀c:Univ. +∀d:Univ. +∀negate:∀_:Univ.Univ. +∀H0:eq Univ (add c d) d. +∀H1:∀X:Univ.∀Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X. +∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)). +∀H3:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).∃X:Univ.eq Univ (add X X) X) +. +#Univ ##. +#X ##. +#Y ##. +#Z ##. +#add ##. +#c ##. +#d ##. +#negate ##. +#H0 ##. +#H1 ##. +#H2 ##. +#H3 ##. +napply (ex_intro ? ? ? ?) ##[ +##2: +nauto by H0,H1,H2,H3 ##; +##| ##skip ##] +ntry (nassumption) ##; +nqed. + +(* -------------------------------------------------------------------------- *) diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/depends b/helm/software/matita/contribs/ng_TPTP/CASC_2008/depends new file mode 100644 index 000000000..7f740c092 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/depends @@ -0,0 +1,81 @@ +GRP184-3.ma logic/equality.ma +COL006-6.ma logic/equality.ma +GRP444-1.ma logic/equality.ma +COL049-1.ma logic/equality.ma +GRP471-1.ma logic/equality.ma +LAT159-1.ma logic/equality.ma +COL046-1.ma logic/equality.ma +BOO034-1.ma logic/equality.ma +COL044-8.ma logic/equality.ma +LAT156-1.ma logic/equality.ma +BOO031-1.ma logic/equality.ma +GRP508-1.ma logic/equality.ma +GRP014-1.ma logic/equality.ma +LAT152-1.ma logic/equality.ma +GRP506-1.ma logic/equality.ma +GRP167-1.ma logic/equality.ma +BOO007-4.ma logic/equality.ma +COL011-1.ma logic/equality.ma +GRP186-2.ma logic/equality.ma +LAT087-1.ma logic/equality.ma +RNG019-7.ma logic/equality.ma +RNG026-6.ma logic/equality.ma +GRP185-2.ma logic/equality.ma +RNG028-9.ma logic/equality.ma +COL003-12.ma logic/equality.ma +RNG020-6.ma logic/equality.ma +LAT080-1.ma logic/equality.ma +GRP405-1.ma logic/equality.ma +COL003-20.ma logic/equality.ma +COL038-1.ma logic/equality.ma +GRP404-1.ma logic/equality.ma +COL065-1.ma logic/equality.ma +LAT148-1.ma logic/equality.ma +COL037-1.ma logic/equality.ma +LAT175-1.ma logic/equality.ma +COL064-1.ma logic/equality.ma +COL063-1.ma logic/equality.ma +LAT146-1.ma logic/equality.ma +LAT173-1.ma logic/equality.ma +COL061-1.ma logic/equality.ma +COL060-1.ma logic/equality.ma +GRP187-1.ma logic/equality.ma +LAT170-1.ma logic/equality.ma +GRP186-1.ma logic/equality.ma +COL003-1.ma logic/equality.ma +RNG019-6.ma logic/equality.ma +GRP178-2.ma logic/equality.ma +GRP184-1.ma logic/equality.ma +LAT140-1.ma logic/equality.ma +COL043-3.ma logic/equality.ma +ROB006-2.ma logic/equality.ma +GRP114-1.ma logic/equality.ma +RNG009-7.ma logic/equality.ma +RNG035-7.ma logic/equality.ma +GRP024-5.ma logic/equality.ma +BOO076-1.ma logic/equality.ma +GRP453-1.ma logic/equality.ma +GRP183-4.ma logic/equality.ma +GRP452-1.ma logic/equality.ma +LAT169-1.ma logic/equality.ma +BOO073-1.ma logic/equality.ma +COL057-1.ma logic/equality.ma +GRP423-1.ma logic/equality.ma +GRP422-1.ma logic/equality.ma +GRP181-4.ma logic/equality.ma +BOO072-1.ma logic/equality.ma +LAT166-1.ma logic/equality.ma +LAT138-1.ma logic/equality.ma +BOO007-2.ma logic/equality.ma +LAT165-1.ma logic/equality.ma +LAT164-1.ma logic/equality.ma +GRP202-1.ma logic/equality.ma +GRP200-1.ma logic/equality.ma +ROB006-1.ma logic/equality.ma +RNG029-7.ma logic/equality.ma +GRP477-1.ma logic/equality.ma +RNG027-7.ma logic/equality.ma +GRP164-2.ma logic/equality.ma +GRP185-3.ma logic/equality.ma +LAT093-1.ma logic/equality.ma +logic/equality.ma diff --git a/helm/software/matita/contribs/ng_TPTP/CASC_2008/root b/helm/software/matita/contribs/ng_TPTP/CASC_2008/root new file mode 100644 index 000000000..7f6625891 --- /dev/null +++ b/helm/software/matita/contribs/ng_TPTP/CASC_2008/root @@ -0,0 +1 @@ +baseuri=cic:/matita/ngtptp -- 2.39.2