added tests for paramod

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO001-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO001-1.p.ma
new file mode 100644 (file)
index 0000000..9d39e84
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO001-1.p.ma
@@ -0,0 +1,66 @@
+set "baseuri" "cic:/matita/TPTP/BOO001-1".
+include "logic/equality.ma".
+(* Inclusion of: BOO001-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO001-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra (Ternary) *)
+(*  Problem  : In B3 algebra, inverse is an involution *)
+(*  Version  : [OTTER] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [OTTER] *)
+(*  Names    : tba_gg.in [OTTER] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    6 (   0 non-Horn;   6 unit;   1 RR) *)
+(*             Number of atoms       :    6 (   6 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    3 (   1 constant; 0-3 arity) *)
+(*             Number of variables   :   13 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include ternary Boolean algebra axioms  *)
+(* Inclusion of: Axioms/BOO001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Algebra (Ternary Boolean) *)
+(*  Axioms   : Ternary Boolean algebra (equality) axioms *)
+(*  Version  : [OTTER] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*           : [Win82] Winker (1982), Generation and Verification of Finite M *)
+(*  Source   : [OTTER] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    5 (   0 non-Horn;   5 unit;   0 RR) *)
+(*             Number of literals   :    5 (   5 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    2 (   0 constant; 1-3 arity) *)
+(*             Number of variables  :   13 (   2 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : These axioms appear in [Win82], in which ternary_multiply_1 is *)
+(*             shown to be independant. *)
+(*           : These axioms are also used in [Wos88], p.222. *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_inverse_is_self_cancelling:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y (inverse Y)) X.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X X Y) X.
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (multiply Y X X) X.
+\forall H4:\forall V:Univ.\forall W:Univ.\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (inverse (inverse a)) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO003-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO003-2.p.ma
new file mode 100644 (file)
index 0000000..6014b92
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO003-2.p.ma
@@ -0,0 +1,75 @@
+set "baseuri" "cic:/matita/TPTP/BOO003-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO003-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO003-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Multiplication is idempotent (X * X = X) *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [ANL] *)
+(*  Names    : prob2_part1.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.38 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    :    6 (   3 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 v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_times_a_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a a) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO003-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO003-4.p.ma
new file mode 100644 (file)
index 0000000..c8d225c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO003-4.p.ma
@@ -0,0 +1,69 @@
+set "baseuri" "cic:/matita/TPTP/BOO003-4".
+include "logic/equality.ma".
+(* Inclusion of: BOO003-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO003-4 : TPTP v3.1.1. Released v1.1.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Multiplication is idempotent (X * X = X) *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    : TA [Ver94] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.13 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    9 (   0 non-Horn;   9 unit;   1 RR) *)
+(*             Number of atoms       :    9 (   9 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    6 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   14 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Axioms   : Boolean algebra (equality) axioms *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_times_a_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H1:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H3:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a a) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO004-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO004-2.p.ma
new file mode 100644 (file)
index 0000000..dc59877
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO004-2.p.ma
@@ -0,0 +1,75 @@
+set "baseuri" "cic:/matita/TPTP/BOO004-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO004-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Addition is idempotent (X + X = X) *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [ANL] *)
+(*  Names    : prob2_part2.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.13 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    :    6 (   3 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 v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_plus_a_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a a) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO004-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO004-4.p.ma
new file mode 100644 (file)
index 0000000..05d7e37
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO004-4.p.ma
@@ -0,0 +1,69 @@
+set "baseuri" "cic:/matita/TPTP/BOO004-4".
+include "logic/equality.ma".
+(* Inclusion of: BOO004-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-4 : TPTP v3.1.1. Released v1.1.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Addition is idempotent (X + X = X) *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    : TA [Ver94] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    9 (   0 non-Horn;   9 unit;   1 RR) *)
+(*             Number of atoms       :    9 (   9 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    6 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   14 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Axioms   : Boolean algebra (equality) axioms *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_plus_a_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H1:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H3:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a a) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO005-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO005-2.p.ma
new file mode 100644 (file)
index 0000000..4e5de1b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO005-2.p.ma
@@ -0,0 +1,76 @@
+set "baseuri" "cic:/matita/TPTP/BOO005-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO005-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO005-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Addition is bounded (X + 1 = 1) *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [ANL] *)
+(*  Names    : prob3_part1.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.14 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    :    6 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   24 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.1 - Clause prove_a_plus_1_is_a fixed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO003-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO003-0 : TPTP v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_plus_1_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a multiplicative_identity) multiplicative_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO005-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO005-4.p.ma
new file mode 100644 (file)
index 0000000..2878580
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO005-4.p.ma
@@ -0,0 +1,70 @@
+set "baseuri" "cic:/matita/TPTP/BOO005-4".
+include "logic/equality.ma".
+(* Inclusion of: BOO005-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO005-4 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Addition is bounded (X + 1 = 1) *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    : TB [Ver94] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    9 (   0 non-Horn;   9 unit;   1 RR) *)
+(*             Number of atoms       :    9 (   9 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    6 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   14 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.1 - Clause prove_a_plus_1_is_a fixed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Axioms   : Boolean algebra (equality) axioms *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_plus_1_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H1:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H3:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a multiplicative_identity) multiplicative_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO006-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO006-2.p.ma
new file mode 100644 (file)
index 0000000..b745d9d
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO006-2.p.ma
@@ -0,0 +1,75 @@
+set "baseuri" "cic:/matita/TPTP/BOO006-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO006-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO006-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Multiplication is bounded (X * 0 = 0) *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [ANL] *)
+(*  Names    : prob3_part2.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.38 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    :    6 (   3 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 v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_right_identity:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a additive_identity) additive_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO006-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO006-4.p.ma
new file mode 100644 (file)
index 0000000..2988e20
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO006-4.p.ma
@@ -0,0 +1,69 @@
+set "baseuri" "cic:/matita/TPTP/BOO006-4".
+include "logic/equality.ma".
+(* Inclusion of: BOO006-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO006-4 : TPTP v3.1.1. Released v1.1.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Multiplication is bounded (X * 0 = 0) *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    : TB [Ver94] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.13 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    9 (   0 non-Horn;   9 unit;   1 RR) *)
+(*             Number of atoms       :    9 (   9 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    6 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   14 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Axioms   : Boolean algebra (equality) axioms *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_right_identity:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H1:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H3:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a additive_identity) additive_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO009-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO009-2.p.ma
new file mode 100644 (file)
index 0000000..1ed1100
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO009-2.p.ma
@@ -0,0 +1,76 @@
+set "baseuri" "cic:/matita/TPTP/BOO009-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO009-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO009-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Multiplication absorption (X * (X + Y) = X) *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [ANL] *)
+(*  Names    : prob4_part1.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.50 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    :    7 (   4 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 v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_operation:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (add a b)) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO009-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO009-4.p.ma
new file mode 100644 (file)
index 0000000..f79df59
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO009-4.p.ma
@@ -0,0 +1,70 @@
+set "baseuri" "cic:/matita/TPTP/BOO009-4".
+include "logic/equality.ma".
+(* Inclusion of: BOO009-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO009-4 : TPTP v3.1.1. Released v1.1.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Multiplication absorption (X * (X + Y) = X) *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    : TC [Ver94] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :   14 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Axioms   : Boolean algebra (equality) axioms *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_operation:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H1:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H3:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply a (add a b)) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO010-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO010-2.p.ma
new file mode 100644 (file)
index 0000000..020cba1
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO010-2.p.ma
@@ -0,0 +1,76 @@
+set "baseuri" "cic:/matita/TPTP/BOO010-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO010-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO010-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Addition absorbtion (X + (X * Y) = X) *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [ANL] *)
+(*  Names    : prob4_part2.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.38 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    :    7 (   4 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 v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_plus_ab_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (multiply a b)) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO010-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO010-4.p.ma
new file mode 100644 (file)
index 0000000..792f428
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO010-4.p.ma
@@ -0,0 +1,70 @@
+set "baseuri" "cic:/matita/TPTP/BOO010-4".
+include "logic/equality.ma".
+(* Inclusion of: BOO010-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO010-4 : TPTP v3.1.1. Released v1.1.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Addition absorbtion (X + (X * Y) = X) *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    : TC [Ver94] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0, 0.09 v2.6.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :   14 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Axioms   : Boolean algebra (equality) axioms *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_plus_ab_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H1:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H3:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add a (multiply a b)) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO011-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO011-2.p.ma
new file mode 100644 (file)
index 0000000..1108abd
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO011-2.p.ma
@@ -0,0 +1,76 @@
+set "baseuri" "cic:/matita/TPTP/BOO011-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO011-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO011-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Inverse of additive identity = Multiplicative identity *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  : The inverse of the additive identity is the multiplicative  *)
+(*             identity. *)
+(*  Refs     :  *)
+(*  Source   : [ANL] *)
+(*  Names    : prob7.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :   24 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.1 - Clause prove_inverse_of_1_is_0 fixed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO003-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO003-0 : TPTP v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_inverse_of_1_is_0:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse additive_identity) multiplicative_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO011-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO011-4.p.ma
new file mode 100644 (file)
index 0000000..5cb02f2
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO011-4.p.ma
@@ -0,0 +1,69 @@
+set "baseuri" "cic:/matita/TPTP/BOO011-4".
+include "logic/equality.ma".
+(* Inclusion of: BOO011-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO011-4 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Inverse of additive identity = Multiplicative identity *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    : TG [Ver94] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :   14 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.1 - Clause prove_inverse_of_1_is_0 fixed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Axioms   : Boolean algebra (equality) axioms *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_inverse_of_1_is_0:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H1:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H3:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse additive_identity) multiplicative_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO012-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO012-2.p.ma
new file mode 100644 (file)
index 0000000..f7eba80
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO012-2.p.ma
@@ -0,0 +1,75 @@
+set "baseuri" "cic:/matita/TPTP/BOO012-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO012-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO012-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Inverse is an involution *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [ANL] *)
+(*  Names    : prob8.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   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    :    6 (   3 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 v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_inverse_is_an_involution:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall x:Univ.
+\forall H0:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H1:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H2:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H3:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H4:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H5:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H7:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (inverse x)) x
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO012-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO012-4.p.ma
new file mode 100644 (file)
index 0000000..7e63ac0
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO012-4.p.ma
@@ -0,0 +1,69 @@
+set "baseuri" "cic:/matita/TPTP/BOO012-4".
+include "logic/equality.ma".
+(* Inclusion of: BOO012-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO012-4 : TPTP v3.1.1. Released v1.1.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Inverse is an involution *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    : TF [Ver94] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    9 (   0 non-Horn;   9 unit;   1 RR) *)
+(*             Number of atoms       :    9 (   9 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    6 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   14 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Axioms   : Boolean algebra (equality) axioms *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_inverse_is_an_involution:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall x:Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H1:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H3:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse (inverse x)) x
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO013-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO013-2.p.ma
new file mode 100644 (file)
index 0000000..d3c76c2
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO013-2.p.ma
@@ -0,0 +1,83 @@
+set "baseuri" "cic:/matita/TPTP/BOO013-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO013-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO013-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : The inverse of X is unique *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [ANL] *)
+(*  Names    : prob9.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.14 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   19 (   0 non-Horn;  19 unit;   5 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    :    8 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :   24 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.1 - Clauses b_and_multiplicative_identity and *)
+(*             c_and_multiplicative_identity fixed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO003-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO003-0 : TPTP v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_b_is_a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (multiply a c) additive_identity.
+\forall H1:eq Univ (multiply a b) additive_identity.
+\forall H2:eq Univ (add a c) multiplicative_identity.
+\forall H3:eq Univ (add a b) multiplicative_identity.
+\forall H4:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H5:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H6:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H7:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H8:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H9:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H10:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H11:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H15:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H16:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H17:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ b c
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO013-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO013-4.p.ma
new file mode 100644 (file)
index 0000000..d8f58f5
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO013-4.p.ma
@@ -0,0 +1,72 @@
+set "baseuri" "cic:/matita/TPTP/BOO013-4".
+include "logic/equality.ma".
+(* Inclusion of: BOO013-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO013-4 : TPTP v3.1.1. Released v1.1.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : The inverse of X is unique *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    : TE [Ver94] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   11 (   0 non-Horn;  11 unit;   3 RR) *)
+(*             Number of atoms       :   11 (  11 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   :   14 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Axioms   : Boolean algebra (equality) axioms *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_a_inverse_is_b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (multiply a b) additive_identity.
+\forall H1:eq Univ (add a b) multiplicative_identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H3:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H4:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H5:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ b (inverse a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO016-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO016-2.p.ma
new file mode 100644 (file)
index 0000000..acca295
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO016-2.p.ma
@@ -0,0 +1,78 @@
+set "baseuri" "cic:/matita/TPTP/BOO016-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO016-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO016-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Relating product and sum (X * Y = Z -> X + Z = X) *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.38 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   16 (   0 non-Horn;  16 unit;   2 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 (   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 v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_sum:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:eq Univ (multiply x y) z.
+\forall H1:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H2:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H3:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H4:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H5:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H7:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H8:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (add x z) x
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO017-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO017-2.p.ma
new file mode 100644 (file)
index 0000000..2563236
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO017-2.p.ma
@@ -0,0 +1,78 @@
+set "baseuri" "cic:/matita/TPTP/BOO017-2".
+include "logic/equality.ma".
+(* Inclusion of: BOO017-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO017-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Relating sum and product (X + Y = Z -> X * Z = X) *)
+(*  Version  : [ANL] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     :  *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.50 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   16 (   0 non-Horn;  16 unit;   2 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 (   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 v3.1.1. 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 literals   :   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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_sum:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:eq Univ (add x y) z.
+\forall H1:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H2:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H3:\forall X:Univ.eq Univ (multiply multiplicative_identity X) X.
+\forall H4:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H5:\forall X:Univ.eq Univ (multiply (inverse X) X) additive_identity.
+\forall H6:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H7:\forall X:Univ.eq Univ (add (inverse X) X) multiplicative_identity.
+\forall H8:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (multiply X Y) Z) (multiply (add X Z) (add Y Z)).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply x z) x
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO018-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO018-4.p.ma
new file mode 100644 (file)
index 0000000..78be716
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO018-4.p.ma
@@ -0,0 +1,69 @@
+set "baseuri" "cic:/matita/TPTP/BOO018-4".
+include "logic/equality.ma".
+(* Inclusion of: BOO018-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO018-4 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Inverse of multiplicative identity = Additive identity *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    : TG [Ver94] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :   14 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.1 - Clause prove_inverse_of_1_is_0 fixed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include boolean algebra axioms for equality formulation  *)
+(* Inclusion of: Axioms/BOO004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Axioms   : Boolean algebra (equality) axioms *)
+(*  Version  : [Ver94] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Ver94] Veroff (1994), Problem Set *)
+(*  Source   : [Ver94] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_inverse_of_1_is_0:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiplicative_identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+\forall H1:\forall X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X multiplicative_identity) X.
+\forall H3:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (inverse multiplicative_identity) additive_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO034-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO034-1.p.ma
new file mode 100644 (file)
index 0000000..722b41f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO034-1.p.ma
@@ -0,0 +1,75 @@
+set "baseuri" "cic:/matita/TPTP/BOO034-1".
+include "logic/equality.ma".
+(* Inclusion of: BOO034-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO034-1 : TPTP v3.1.1. 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   : 0.21 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Algebra (Ternary Boolean) *)
+(*  Axioms   : Ternary Boolean algebra (equality) axioms *)
+(*  Version  : [OTTER] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*           : [Win82] Winker (1982), Generation and Verification of Finite M *)
+(*  Source   : [OTTER] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    5 (   0 non-Horn;   5 unit;   0 RR) *)
+(*             Number of literals   :    5 (   5 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    2 (   0 constant; 1-3 arity) *)
+(*             Number of variables  :   13 (   2 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : These axioms appear in [Win82], in which ternary_multiply_1 is *)
+(*             shown to be independant. *)
+(*           : These axioms are also used in [Wos88], p.222. *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Denial of single axiom: *)
+theorem prove_single_axiom:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall d:Univ.
+\forall e:Univ.
+\forall f:Univ.
+\forall g:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X Y (inverse Y)) X.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (inverse Y) Y X) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X X Y) X.
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (multiply Y X X) X.
+\forall H4:\forall V:Univ.\forall W:Univ.\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply V W X) Y (multiply V W Z)) (multiply V W (multiply X Y Z)).eq Univ (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
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO069-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO069-1.p.ma
new file mode 100644 (file)
index 0000000..4b73d0b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO069-1.p.ma
@@ -0,0 +1,38 @@
+set "baseuri" "cic:/matita/TPTP/BOO069-1".
+include "logic/equality.ma".
+(* Inclusion of: BOO069-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO069-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Boolean Algebra (Ternary) *)
+(*  Problem  : Ternary Boolean Algebra Single axiom is complete, part 3 *)
+(*  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   : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 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; 0-3 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of BOO035-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_tba_axioms_3:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.\forall D:Univ.\forall E:Univ.\forall F:Univ.\forall G:Univ.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.eq Univ (multiply a b (inverse b)) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO071-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO071-1.p.ma
new file mode 100644 (file)
index 0000000..9e14205
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO071-1.p.ma
@@ -0,0 +1,38 @@
+set "baseuri" "cic:/matita/TPTP/BOO071-1".
+include "logic/equality.ma".
+(* Inclusion of: BOO071-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO071-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Boolean Algebra (Ternary) *)
+(*  Problem  : Ternary Boolean Algebra Single axiom is complete, part 5 *)
+(*  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   : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 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; 0-3 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of BOO035-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_tba_axioms_5:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.\forall D:Univ.\forall E:Univ.\forall F:Univ.\forall G:Univ.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.eq Univ (multiply (inverse b) b a) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/BOO075-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/BOO075-1.p.ma
new file mode 100644 (file)
index 0000000..0ac678c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/BOO075-1.p.ma
@@ -0,0 +1,37 @@
+set "baseuri" "cic:/matita/TPTP/BOO075-1".
+include "logic/equality.ma".
+(* Inclusion of: BOO075-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : BOO075-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Boolean Algebra *)
+(*  Problem  : Sh-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   : 0.00 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 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   1 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of BOO039-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_meredith_2_basis_1:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall nand:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (nand (nand A (nand (nand B A) A)) (nand B (nand C A))) B.eq Univ (nand (nand a a) (nand b a)) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL004-3.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL004-3.p.ma
new file mode 100644 (file)
index 0000000..fd5a875
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL004-3.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/COL004-3".
+include "logic/equality.ma".
+(* Inclusion of: COL004-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL004-3 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to U from S and K. *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combination is provided and checked. *)
+(*  English  : Construct from S and K alone a combinator that behaves as the  *)
+(*             combinator U does, where ((Sx)y)z = (xz)(yz), (Kx)y = x,  *)
+(*             (Ux)y = y((xx)y). *)
+(*  Refs     : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.21 v3.1.0, 0.22 v2.7.0, 0.27 v2.6.0, 0.17 v2.5.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 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    :    5 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   1 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the U equivalent *)
+theorem prove_u_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall k:Univ.
+\forall s:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply k X) Y) X.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).eq Univ (apply (apply (apply (apply s (apply k (apply s (apply (apply s k) k)))) (apply (apply s (apply (apply s k) k)) (apply (apply s k) k))) x) y) (apply y (apply (apply x x) y))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL007-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL007-1.p.ma
new file mode 100644 (file)
index 0000000..dd75603
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL007-1.p.ma
@@ -0,0 +1,44 @@
+set "baseuri" "cic:/matita/TPTP/COL007-1".
+include "logic/equality.ma".
+(* Inclusion of: COL007-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL007-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for L *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinator L, where (Lx)y = x(yy). *)
+(*  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   : 0.00 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    :    3 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall combinator:Univ.
+\forall l:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL008-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL008-1.p.ma
new file mode 100644 (file)
index 0000000..0d67b7e
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL008-1.p.ma
@@ -0,0 +1,48 @@
+set "baseuri" "cic:/matita/TPTP/COL008-1".
+include "logic/equality.ma".
+(* Inclusion of: COL008-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL008-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for M and B *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators M and B, where ((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 *)
+(*           : [MW88]  McCune & Wos (1988), Some Fixed Point Problems in Comb *)
+(*           : [Wos93] Wos (1993), The Kernel Strategy and Its Use for the St *)
+(*  Source   : [MW88] *)
+(*  Names    : - [MW88] *)
+(*           : Question 13 [Wos93] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall combinator:Univ.
+\forall m:Univ.
+\forall H0:\forall X:Univ.eq Univ (apply m X) (apply X X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL010-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL010-1.p.ma
new file mode 100644 (file)
index 0000000..615defe
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL010-1.p.ma
@@ -0,0 +1,47 @@
+set "baseuri" "cic:/matita/TPTP/COL010-1".
+include "logic/equality.ma".
+(* Inclusion of: COL010-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL010-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for B and S2 *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators B and S2, where ((Bx)y)z = x(yz),  *)
+(*             ((S2x)y)z = (xz)(yy). *)
+(*  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   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall combinator:Univ.
+\forall s2:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply s2 X) Y) Z) (apply (apply X Z) (apply Y Y)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL012-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL012-1.p.ma
new file mode 100644 (file)
index 0000000..8c6a371
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL012-1.p.ma
@@ -0,0 +1,44 @@
+set "baseuri" "cic:/matita/TPTP/COL012-1".
+include "logic/equality.ma".
+(* Inclusion of: COL012-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL012-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for U *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinator U, where (Ux)y = y((xx)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   : 0.00 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    :    3 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall combinator:Univ.
+\forall u:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply u X) Y) (apply Y (apply (apply X X) Y)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL013-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL013-1.p.ma
new file mode 100644 (file)
index 0000000..c3dd0be
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL013-1.p.ma
@@ -0,0 +1,47 @@
+set "baseuri" "cic:/matita/TPTP/COL013-1".
+include "logic/equality.ma".
+(* Inclusion of: COL013-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL013-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for S and L *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators S and L, where ((Sx)y)z = (xz)(yz), (Lx)y  *)
+(*             = x(yy). *)
+(*  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   : 0.00 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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    6 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall combinator:Univ.
+\forall l:Univ.
+\forall s:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL014-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL014-1.p.ma
new file mode 100644 (file)
index 0000000..0b1b928
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL014-1.p.ma
@@ -0,0 +1,47 @@
+set "baseuri" "cic:/matita/TPTP/COL014-1".
+include "logic/equality.ma".
+(* Inclusion of: COL014-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL014-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for L and O *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators L and O, where (Lx)y = x(yy), (Ox)y  *)
+(*             = y(xy). *)
+(*  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   : 0.00 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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall combinator:Univ.
+\forall l:Univ.
+\forall o:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)).
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL015-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL015-1.p.ma
new file mode 100644 (file)
index 0000000..11ce88f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL015-1.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL015-1".
+include "logic/equality.ma".
+(* Inclusion of: COL015-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL015-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for Q and M *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators Q and M, where Mx = xx, ((Qx)y)z = y(xz). *)
+(*  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   : 0.00 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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall combinator:Univ.
+\forall m:Univ.
+\forall q:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)).
+\forall H1:\forall X:Univ.eq Univ (apply m X) (apply X X).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL016-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL016-1.p.ma
new file mode 100644 (file)
index 0000000..536efc4
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL016-1.p.ma
@@ -0,0 +1,49 @@
+set "baseuri" "cic:/matita/TPTP/COL016-1".
+include "logic/equality.ma".
+(* Inclusion of: COL016-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL016-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for B, M and L *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators B, M and L, where ((Bx)y)z = x(yz), (Lx)y  *)
+(*             = x(yy), 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 *)
+(*           : [MW88]  McCune & Wos (1988), Some Fixed Point Problems in Comb *)
+(*  Source   : [MW88] *)
+(*  Names    : - [MW88] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall combinator:Univ.
+\forall l:Univ.
+\forall m:Univ.
+\forall H0:\forall X:Univ.eq Univ (apply m X) (apply X X).
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL017-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL017-1.p.ma
new file mode 100644 (file)
index 0000000..475f914
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL017-1.p.ma
@@ -0,0 +1,49 @@
+set "baseuri" "cic:/matita/TPTP/COL017-1".
+include "logic/equality.ma".
+(* Inclusion of: COL017-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL017-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for B, M, and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators B, M, and T, where ((Bx)y)z = x(yz),  *)
+(*             Mx = xx, (Tx)y = yx. *)
+(*  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   : 0.00 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall combinator:Univ.
+\forall m:Univ.
+\forall t:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.eq Univ (apply m X) (apply X X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL018-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL018-1.p.ma
new file mode 100644 (file)
index 0000000..1881d33
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL018-1.p.ma
@@ -0,0 +1,49 @@
+set "baseuri" "cic:/matita/TPTP/COL018-1".
+include "logic/equality.ma".
+(* Inclusion of: COL018-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL018-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for W, Q, and L *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators W, Q, and L, where (Lx)y = x(yy), (Wx)y  *)
+(*             = (xy)y, ((Qx)y)z = y(xz). *)
+(*  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   : 0.00 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall combinator:Univ.
+\forall l:Univ.
+\forall q:Univ.
+\forall w:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply q X) Y) Z) (apply Y (apply X Z)).
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply l X) Y) (apply X (apply Y Y)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL021-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL021-1.p.ma
new file mode 100644 (file)
index 0000000..2332e16
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL021-1.p.ma
@@ -0,0 +1,49 @@
+set "baseuri" "cic:/matita/TPTP/COL021-1".
+include "logic/equality.ma".
+(* Inclusion of: COL021-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL021-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for B, M, and V *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak 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   : 0.00 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall combinator:Univ.
+\forall m:Univ.
+\forall v:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply v X) Y) Z) (apply (apply Z X) Y).
+\forall H1:\forall X:Univ.eq Univ (apply m X) (apply X X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL022-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL022-1.p.ma
new file mode 100644 (file)
index 0000000..4f68c0a
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL022-1.p.ma
@@ -0,0 +1,49 @@
+set "baseuri" "cic:/matita/TPTP/COL022-1".
+include "logic/equality.ma".
+(* Inclusion of: COL022-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL022-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for B, O, and M *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators B, O, and M, where ((Bx)y)z = x(yz),  *)
+(*             Mx = xx, (Ox)y = y(xy). *)
+(*  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   : 0.00 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall combinator:Univ.
+\forall m:Univ.
+\forall o:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply o X) Y) (apply Y (apply X Y)).
+\forall H1:\forall X:Univ.eq Univ (apply m X) (apply X X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL024-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL024-1.p.ma
new file mode 100644 (file)
index 0000000..d729fed
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL024-1.p.ma
@@ -0,0 +1,49 @@
+set "baseuri" "cic:/matita/TPTP/COL024-1".
+include "logic/equality.ma".
+(* Inclusion of: COL024-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL024-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for B, M, and C *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators B, M, and C, where ((Bx)y)z = x(yz),  *)
+(*             Mx = xx, ((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   : 0.00 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall combinator:Univ.
+\forall m:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply c X) Y) Z) (apply (apply X Z) Y).
+\forall H1:\forall X:Univ.eq Univ (apply m X) (apply X X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL025-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL025-1.p.ma
new file mode 100644 (file)
index 0000000..2446698
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL025-1.p.ma
@@ -0,0 +1,48 @@
+set "baseuri" "cic:/matita/TPTP/COL025-1".
+include "logic/equality.ma".
+(* Inclusion of: COL025-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL025-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for B and W *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak fixed point property holds for the set P consisting  *)
+(*             of the combinators B and W, where ((Bx)y)z = x(yz), (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 *)
+(*           : [MW88]  McCune & Wos (1988), Some Fixed Point Problems in Comb *)
+(*  Source   : [MW88] *)
+(*  Names    : stage1.in & stage2.in [OTTER] *)
+(*           : - [MW88] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    6 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall combinator:Univ.
+\forall w:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL045-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL045-1.p.ma
new file mode 100644 (file)
index 0000000..46f9219
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL045-1.p.ma
@@ -0,0 +1,49 @@
+set "baseuri" "cic:/matita/TPTP/COL045-1".
+include "logic/equality.ma".
+(* Inclusion of: COL045-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL045-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for B, M and S *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak 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   : 0.00 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall combinator:Univ.
+\forall m:Univ.
+\forall s:Univ.
+\forall H0:\forall X:Univ.eq Univ (apply m X) (apply X X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply s X) Y) Z) (apply (apply X Z) (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL048-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL048-1.p.ma
new file mode 100644 (file)
index 0000000..6b3e51f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL048-1.p.ma
@@ -0,0 +1,49 @@
+set "baseuri" "cic:/matita/TPTP/COL048-1".
+include "logic/equality.ma".
+(* Inclusion of: COL048-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL048-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Weak fixed point for B, W, and M *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*  English  : The weak 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 *)
+(*           : [MW88]  McCune & Wos (1988), Some Fixed Point Problems in Comb *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_fixed_point:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall combinator:Univ.
+\forall m:Univ.
+\forall w:Univ.
+\forall H0:\forall X:Univ.eq Univ (apply m X) (apply X X).
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply w X) Y) (apply (apply X Y) Y).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).\exist Y:Univ.eq Univ Y (apply combinator Y)
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL050-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL050-1.p.ma
new file mode 100644 (file)
index 0000000..b3cd44d
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL050-1.p.ma
@@ -0,0 +1,56 @@
+set "baseuri" "cic:/matita/TPTP/COL050-1".
+include "logic/equality.ma".
+(* Inclusion of: COL050-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL050-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : The Significance of the Mockingbird *)
+(*  Version  : Especial. *)
+(*  English  : There exists a mocking bird. For all birds x and y, there  *)
+(*             exists a bird z that composes x with y for all birds w. Prove  *)
+(*             that every bird is fond of at least one other bird. *)
+(*  Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+(*  Source   : [ANL] *)
+(*  Names    : bird1.ver1.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ---- There exists a mocking bird (Mock). *)
+(* ----    TEx FAy [response(x,y) = response(y,y)]. *)
+(* ----    response(Mock,y) = response(y,y). *)
+(* ---- For all birds x and y, there exists a bird z that composes *)
+(* ---- x with y for all birds w. *)
+(* ----    FAx FAy TEz FAw [response(z,w) = response(x,response(y,w))] *)
+(* ----    response(comp(x,y),w) = response(x,response(y,w)).  *)
+(* ---- Hypothesis: Every bird is fond of at least one other bird. *)
+(* ----    -FAx TEy [response(x,y) = y]. *)
+(* ----    TEx FAy -[response(x,y) = y]. *)
+(* ----    Letting A = x, *)
+(* ----    -[response(A,y) = y]. *)
+theorem prove_all_fond_of_another:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall compose:\forall _:Univ.\forall _:Univ.Univ.
+\forall mocking_bird:Univ.
+\forall response:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall W:Univ.\forall X:Univ.\forall Y:Univ.eq Univ (response (compose X Y) W) (response X (response Y W)).
+\forall H1:\forall Y:Univ.eq Univ (response mocking_bird Y) (response Y Y).\exist Y:Univ.eq Univ (response a Y) Y
+.
+intros.
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL058-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL058-2.p.ma
new file mode 100644 (file)
index 0000000..7065d7f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL058-2.p.ma
@@ -0,0 +1,42 @@
+set "baseuri" "cic:/matita/TPTP/COL058-2".
+include "logic/equality.ma".
+(* Inclusion of: COL058-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL058-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : If there's a lark, then there's an egocentric bird. *)
+(*  Version  : Especial. *)
+(*             Theorem formulation : The egocentric bird is provided and  *)
+(*             checked. *)
+(*  English  : Suppose we are given a forest that contains a lark, and  *)
+(*             we are not given any other information. Prove that at least  *)
+(*             one bird in the forest must be egocentric. *)
+(*  Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+(*           : [GO86]  Glickfield & Overbeek (1986), A Foray into Combinatory *)
+(*  Source   : [GO86] *)
+(*  Names    : - [GO86] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.00 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    :    2 (   1 constant; 0-2 arity) *)
+(*             Number of variables   :    2 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   5 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ---- There exists a lark  *)
+(* ---- Hypothesis: This bird is egocentric  *)
+theorem prove_the_bird_exists:
+ \forall Univ:Set.
+\forall lark:Univ.
+\forall response:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X1:Univ.\forall X2:Univ.eq Univ (response (response lark X1) X2) (response X1 (response X2 X2)).eq Univ (response (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark))) (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark)))) (response (response lark (response (response lark (response lark lark)) (response lark (response lark lark)))) (response lark (response lark lark)))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL058-3.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL058-3.p.ma
new file mode 100644 (file)
index 0000000..e36faea
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL058-3.p.ma
@@ -0,0 +1,42 @@
+set "baseuri" "cic:/matita/TPTP/COL058-3".
+include "logic/equality.ma".
+(* Inclusion of: COL058-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL058-3 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : If there's a lark, then there's an egocentric bird. *)
+(*  Version  : Especial. *)
+(*             Theorem formulation : The egocentric bird is provided and  *)
+(*             checked. *)
+(*  English  : Suppose we are given a forest that conrtains a lark, and  *)
+(*             we are not given any other information. Prove that at least  *)
+(*             one bird in the forest must be egocentric. *)
+(*  Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+(*           : [GO86]  Glickfield & Overbeek (1986), A Foray into Combinatory *)
+(*  Source   : [GO86] *)
+(*  Names    : - [GO86] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.00 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    :    2 (   1 constant; 0-2 arity) *)
+(*             Number of variables   :    2 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   4 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ---- There exists a lark  *)
+(* ---- Hypothesis: This bird is egocentric  *)
+theorem prove_the_bird_exists:
+ \forall Univ:Set.
+\forall lark:Univ.
+\forall response:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X1:Univ.\forall X2:Univ.eq Univ (response (response lark X1) X2) (response X1 (response X2 X2)).eq Univ (response (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark))) (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark)))) (response (response (response lark lark) (response lark (response lark lark))) (response lark (response lark lark)))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL060-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL060-2.p.ma
new file mode 100644 (file)
index 0000000..359d087
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL060-2.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL060-2".
+include "logic/equality.ma".
+(* Inclusion of: COL060-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL060-2 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to Q from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.29 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the q equivalent *)
+theorem prove_q_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t b)) (apply (apply b b) t)) x) y) z) (apply y (apply x z))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL060-3.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL060-3.p.ma
new file mode 100644 (file)
index 0000000..d3788ff
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL060-3.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL060-3".
+include "logic/equality.ma".
+(* Inclusion of: COL060-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL060-3 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to Q from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.29 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the q equivalent *)
+theorem prove_q_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t b)) b)) t) x) y) z) (apply y (apply x z))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL061-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL061-2.p.ma
new file mode 100644 (file)
index 0000000..404a5f6
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL061-2.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL061-2".
+include "logic/equality.ma".
+(* Inclusion of: COL061-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL061-2 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to Q1 from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.29 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the Q1 equivalent *)
+theorem prove_q1_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) b)) x) y) z) (apply x (apply z y))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL061-3.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL061-3.p.ma
new file mode 100644 (file)
index 0000000..6b50157
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL061-3.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL061-3".
+include "logic/equality.ma".
+(* Inclusion of: COL061-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL061-3 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to Q1 from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.29 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the Q1 equivalent *)
+theorem prove_q1_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) b) x) y) z) (apply x (apply z y))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL062-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL062-2.p.ma
new file mode 100644 (file)
index 0000000..c6b265c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL062-2.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL062-2".
+include "logic/equality.ma".
+(* Inclusion of: COL062-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL062-2 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to C from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  English  : Construct from B and T alone a combinator that behaves as the  *)
+(*             combinator C does, where ((Bx)y)z = x(yz), (Tx)y = yx,  *)
+(*             ((Cx)y)z = (xz)y *)
+(*  Refs     : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+(*           : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to  *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.29 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the C equivalent *)
+theorem prove_c_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) t)) x) y) z) (apply (apply x z) y)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL062-3.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL062-3.p.ma
new file mode 100644 (file)
index 0000000..441838a
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL062-3.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL062-3".
+include "logic/equality.ma".
+(* Inclusion of: COL062-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL062-3 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to C from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  English  : Construct from B and T alone a combinator that behaves as the  *)
+(*             combinator C does, where ((Bx)y)z = x(yz), (Tx)y = yx,  *)
+(*             ((Cx)y)z = (xz)y *)
+(*  Refs     : [WM88]  Wos & McCune (1988), Challenge Problems Focusing on Eq *)
+(*           : [WW+90] Wos et al. (1990), Automated Reasoning Contributes to  *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.43 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :   11 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the C equivalent *)
+theorem prove_c_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) t) x) y) z) (apply (apply x z) y)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL063-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL063-2.p.ma
new file mode 100644 (file)
index 0000000..3731bf6
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL063-2.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL063-2".
+include "logic/equality.ma".
+(* Inclusion of: COL063-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL063-2 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to F from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.00 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    8 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the F equivalent *)
+theorem prove_f_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z y) x)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL063-3.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL063-3.p.ma
new file mode 100644 (file)
index 0000000..c1976c2
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL063-3.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL063-3".
+include "logic/equality.ma".
+(* Inclusion of: COL063-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL063-3 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to F from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.29 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the F equivalent *)
+theorem prove_f_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) b)) (apply (apply b b) t)) x) y) z) (apply (apply z y) x)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL063-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL063-4.p.ma
new file mode 100644 (file)
index 0000000..36b5094
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL063-4.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL063-4".
+include "logic/equality.ma".
+(* Inclusion of: COL063-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL063-4 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to F from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.43 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the F equivalent *)
+theorem prove_f_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t t)) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z y) x)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL063-5.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL063-5.p.ma
new file mode 100644 (file)
index 0000000..37a0a46
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL063-5.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL063-5".
+include "logic/equality.ma".
+(* Inclusion of: COL063-5.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL063-5 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to F from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.43 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the F equivalent *)
+theorem prove_f_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t t)) (apply (apply b b) b))) t) x) y) z) (apply (apply z y) x)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL063-6.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL063-6.p.ma
new file mode 100644 (file)
index 0000000..e363b5d
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL063-6.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL063-6".
+include "logic/equality.ma".
+(* Inclusion of: COL063-6.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL063-6 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to F from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.43 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :   11 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the F equivalent *)
+theorem prove_f_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply (apply b (apply t t)) b)) b)) t) x) y) z) (apply (apply z y) x)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL064-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL064-2.p.ma
new file mode 100644 (file)
index 0000000..7c3d328
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL064-2.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL064-2".
+include "logic/equality.ma".
+(* Inclusion of: COL064-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL064-2 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to V from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.57 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the V equivalent *)
+theorem prove_v_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b b) t))) x) y) z) (apply (apply z x) y)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL064-3.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL064-3.p.ma
new file mode 100644 (file)
index 0000000..8654fb4
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL064-3.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL064-3".
+include "logic/equality.ma".
+(* Inclusion of: COL064-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL064-3 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to V from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.43 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :   11 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the V equivalent *)
+theorem prove_v_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b b) t)) x) y) z) (apply (apply z x) y)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL064-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL064-4.p.ma
new file mode 100644 (file)
index 0000000..e4af943
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL064-4.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL064-4".
+include "logic/equality.ma".
+(* Inclusion of: COL064-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL064-4 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to V from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.57 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the V equivalent *)
+theorem prove_v_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) b)) t)) x) y) z) (apply (apply z x) y)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL064-5.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL064-5.p.ma
new file mode 100644 (file)
index 0000000..79cff67
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL064-5.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL064-5".
+include "logic/equality.ma".
+(* Inclusion of: COL064-5.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL064-5 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to V from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.57 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :   11 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the V equivalent *)
+theorem prove_v_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) b))) t) x) y) z) (apply (apply z x) y)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL064-6.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL064-6.p.ma
new file mode 100644 (file)
index 0000000..d913d56
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL064-6.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL064-6".
+include "logic/equality.ma".
+(* Inclusion of: COL064-6.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL064-6 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to V from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.43 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :   13 (   5 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the V equivalent *)
+theorem prove_v_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) b)) t) x) y) z) (apply (apply z x) y)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL064-7.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL064-7.p.ma
new file mode 100644 (file)
index 0000000..b6e9324
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL064-7.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL064-7".
+include "logic/equality.ma".
+(* Inclusion of: COL064-7.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL064-7 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to V from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.71 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the V equivalent *)
+theorem prove_v_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b b) (apply (apply b t) t))) x) y) z) (apply (apply z x) y)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL064-8.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL064-8.p.ma
new file mode 100644 (file)
index 0000000..132e4da
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL064-8.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL064-8".
+include "logic/equality.ma".
+(* Inclusion of: COL064-8.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL064-8 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to V from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.71 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :   11 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the V equivalent *)
+theorem prove_v_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply (apply b (apply t (apply (apply b b) t))) b)) (apply (apply b t) t)) x) y) z) (apply (apply z x) y)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL064-9.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL064-9.p.ma
new file mode 100644 (file)
index 0000000..5169c5b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL064-9.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL064-9".
+include "logic/equality.ma".
+(* Inclusion of: COL064-9.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL064-9 : TPTP v3.1.1. Bugfixed v1.2.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Find combinator equivalent to V from B and T *)
+(*  Version  : [WM88] (equality) axioms. *)
+(*             Theorem formulation : The combinator is provided and checked. *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.71 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 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    9 (   4 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v1.2.0 : Redundant [fgh]_substitution axioms removed. *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is the V equivalent *)
+theorem prove_v_combinator:
+ \forall Univ:Set.
+\forall apply:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall t:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall z:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (apply (apply t X) Y) (apply Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (apply (apply (apply b X) Y) Z) (apply X (apply Y Z)).eq Univ (apply (apply (apply (apply (apply b (apply t (apply (apply b b) t))) (apply (apply b (apply (apply b b) t)) t)) x) y) z) (apply (apply z x) y)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL083-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL083-1.p.ma
new file mode 100644 (file)
index 0000000..0002bc8
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL083-1.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL083-1".
+include "logic/equality.ma".
+(* Inclusion of: COL083-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL083-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Compatible Birds, part 1 *)
+(*  Version  : Especial. *)
+(*  English  :  *)
+(*  Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    6 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : A UEQ part of COL054-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_birds_are_compatible_1:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall compose:\forall _:Univ.\forall _:Univ.Univ.
+\forall mocking_bird:Univ.
+\forall response:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (response (compose A B) C) (response A (response B C)).
+\forall H1:\forall A:Univ.eq Univ (response mocking_bird A) (response A A).\exist A:Univ.\exist B:Univ.eq Univ (response a A) B
+.
+intros.
+exists[
+2:
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL084-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL084-1.p.ma
new file mode 100644 (file)
index 0000000..e590c85
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL084-1.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/COL084-1".
+include "logic/equality.ma".
+(* Inclusion of: COL084-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL084-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Compatible Birds, part 2 *)
+(*  Version  : Especial. *)
+(*  English  :  *)
+(*  Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    6 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : A UEQ part of COL054-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_birds_are_compatible_2:
+ \forall Univ:Set.
+\forall b:Univ.
+\forall compose:\forall _:Univ.\forall _:Univ.Univ.
+\forall mocking_bird:Univ.
+\forall response:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (response (compose A B) C) (response A (response B C)).
+\forall H1:\forall A:Univ.eq Univ (response mocking_bird A) (response A A).\exist A:Univ.\exist B:Univ.eq Univ (response b B) A
+.
+intros.
+exists[
+2:
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL085-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL085-1.p.ma
new file mode 100644 (file)
index 0000000..fa64095
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL085-1.p.ma
@@ -0,0 +1,44 @@
+set "baseuri" "cic:/matita/TPTP/COL085-1".
+include "logic/equality.ma".
+(* Inclusion of: COL085-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL085-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Happy Birds, part 1 *)
+(*  Version  : Especial. *)
+(*  English  :  *)
+(*  Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  Syntax   : Number of clauses     :    2 (   0 non-Horn;   2 unit;   2 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 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    2 (   2 singleton) *)
+(*             Maximal term depth    :    2 (   2 average) *)
+(*  Comments : A UEQ part of COL055-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_happiness_1:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall response:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (response a b) b.\exist A:Univ.\exist B:Univ.eq Univ (response a A) B
+.
+intros.
+exists[
+2:
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/COL086-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/COL086-1.p.ma
new file mode 100644 (file)
index 0000000..29f5443
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/COL086-1.p.ma
@@ -0,0 +1,44 @@
+set "baseuri" "cic:/matita/TPTP/COL086-1".
+include "logic/equality.ma".
+(* Inclusion of: COL086-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : COL086-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Combinatory Logic *)
+(*  Problem  : Happy Birds, part 2 *)
+(*  Version  : Especial. *)
+(*  English  :  *)
+(*  Refs     : [Smu85] Smullyan (1978), To Mock a Mocking Bird and Other Logi *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  Syntax   : Number of clauses     :    2 (   0 non-Horn;   2 unit;   2 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 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    2 (   2 singleton) *)
+(*             Maximal term depth    :    2 (   2 average) *)
+(*  Comments : A UEQ part of COL055-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_happiness_2:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall response:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (response a b) b.\exist A:Univ.\exist B:Univ.eq Univ (response a B) A
+.
+intros.
+exists[
+2:
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+|
+skip]
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP001-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP001-2.p.ma
new file mode 100644 (file)
index 0000000..da11b63
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP001-2.p.ma
@@ -0,0 +1,86 @@
+set "baseuri" "cic:/matita/TPTP/GRP001-2".
+include "logic/equality.ma".
+(* Inclusion of: GRP001-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP001-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : X^2 = identity => commutativity *)
+(*  Version  : [MOW76] (equality) axioms : Augmented. *)
+(*  English  : If the square of every element is the identity, the system  *)
+(*             is commutative. *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [LO85]  Lusk & Overbeek (1985), Reasoning about Equality *)
+(*           : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
+(*  Source   : [ANL] *)
+(*  Names    : GP1 [MOW76] *)
+(*           : Problem 1 [LO85] *)
+(*           : GT1 [LW92] *)
+(*           : xsquared.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    8 (   0 non-Horn;   8 unit;   2 RR) *)
+(*             Number of atoms       :    8 (   8 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    6 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include equality group theory axioms  *)
+(* Inclusion of: Axioms/GRP004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Redundant two axioms *)
+theorem prove_b_times_a_is_c:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (multiply a b) c.
+\forall H1:\forall X:Univ.eq Univ (multiply X X) identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X (inverse X)) identity.
+\forall H3:\forall X:Univ.eq Univ (multiply X identity) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H5:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H6:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply b a) c
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP001-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP001-4.p.ma
new file mode 100644 (file)
index 0000000..34825a3
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP001-4.p.ma
@@ -0,0 +1,47 @@
+set "baseuri" "cic:/matita/TPTP/GRP001-4".
+include "logic/equality.ma".
+(* Inclusion of: GRP001-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP001-4 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : X^2 = identity => commutativity *)
+(*  Version  : [Wos65] (equality) axioms : Incomplete. *)
+(*  English  : If the square of every element is the identity, the system  *)
+(*             is commutative. *)
+(*  Refs     : [Wos65] Wos (1965), Unpublished Note *)
+(*           : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au *)
+(*  Source   : [Pel86] *)
+(*  Names    : Pelletier 65 [Pel86] *)
+(*           : x2_quant.in [OTTER] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   2 RR) *)
+(*             Number of atoms       :    5 (   5 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    5 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : [Pel86] says "... problems, published I think, by Larry Wos  *)
+(*             (but I cannot locate where)." *)
+(* -------------------------------------------------------------------------- *)
+(* ----The operation '*' is associative  *)
+(* ----There exists an identity element 'e' defined below. *)
+theorem prove_b_times_a_is_c:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (multiply a b) c.
+\forall H1:\forall X:Univ.eq Univ (multiply X X) identity.
+\forall H2:\forall X:Univ.eq Univ (multiply identity X) X.
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b a) c
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP010-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP010-4.p.ma
new file mode 100644 (file)
index 0000000..f792d14
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP010-4.p.ma
@@ -0,0 +1,45 @@
+set "baseuri" "cic:/matita/TPTP/GRP010-4".
+include "logic/equality.ma".
+(* Inclusion of: GRP010-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP010-4 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Inverse is a symmetric relationship *)
+(*  Version  : [Wos65] (equality) axioms : Incomplete. *)
+(*  English  : If a is an inverse of b then b is an inverse of a. *)
+(*  Refs     : [Wos65] Wos (1965), Unpublished Note *)
+(*           : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au *)
+(*  Source   : [Pel86] *)
+(*  Names    : Pelletier 64 [Pel86] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.13 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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : [Pel86] says "... problems, published I think, by Larry Wos *)
+(*             (but I cannot locate where)." *)
+(* -------------------------------------------------------------------------- *)
+(* ----The operation '*' is associative  *)
+(* ----There exists an identity element 'e' defined below. *)
+theorem prove_b_times_c_is_e:
+ \forall Univ:Set.
+\forall b:Univ.
+\forall c:Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (multiply c b) identity.
+\forall H1:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H2:\forall X:Univ.eq Univ (multiply identity X) X.
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b c) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP011-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP011-4.p.ma
new file mode 100644 (file)
index 0000000..eeee302
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP011-4.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/GRP011-4".
+include "logic/equality.ma".
+(* Inclusion of: GRP011-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP011-4 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Left cancellation *)
+(*  Version  : [Wos65] (equality) axioms : Incomplete. *)
+(*  English  :  *)
+(*  Refs     : [Wos65] Wos (1965), Unpublished Note *)
+(*           : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au *)
+(*  Source   : [Pel86] *)
+(*  Names    : Pelletier 63 [Pel86] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   2 RR) *)
+(*             Number of atoms       :    5 (   5 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    6 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : [Pel86] says "... problems, published I think, by Larry Wos *)
+(*             (but I cannot locate where)." *)
+(* -------------------------------------------------------------------------- *)
+(* ----The operation '*' is associative  *)
+(* ----There exists an identity element  *)
+theorem prove_left_cancellation:
+ \forall Univ:Set.
+\forall b:Univ.
+\forall c:Univ.
+\forall d:Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (multiply b c) (multiply d c).
+\forall H1:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H2:\forall X:Univ.eq Univ (multiply identity X) X.
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ b d
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP012-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP012-4.p.ma
new file mode 100644 (file)
index 0000000..87fbe74
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP012-4.p.ma
@@ -0,0 +1,78 @@
+set "baseuri" "cic:/matita/TPTP/GRP012-4".
+include "logic/equality.ma".
+(* Inclusion of: GRP012-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP012-4 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Inverse of products = Product of inverses *)
+(*  Version  : [MOW76] (equality) axioms : Augmented. *)
+(*  English  : The inverse of products equals the product of the inverse,  *)
+(*             in opposite order *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*  Source   : [ANL] *)
+(*  Names    : - [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : In Lemmas.eq.clauses of [ANL] *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include equality group theory axioms  *)
+(* Inclusion of: Axioms/GRP004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Redundant two axioms *)
+theorem prove_inverse_of_product_is_product_of_inverses:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) identity.
+\forall H1:\forall X:Univ.eq Univ (multiply X identity) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H3:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H4:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse (multiply a b)) (multiply (inverse b) (inverse a))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP022-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP022-2.p.ma
new file mode 100644 (file)
index 0000000..7e34e0e
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP022-2.p.ma
@@ -0,0 +1,78 @@
+set "baseuri" "cic:/matita/TPTP/GRP022-2".
+include "logic/equality.ma".
+(* Inclusion of: GRP022-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP022-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Inverse is an involution *)
+(*  Version  : [MOW76] (equality) axioms : Augmented. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [LO85]  Lusk & Overbeek (1985), Reasoning about Equality *)
+(*  Source   : [TPTP] *)
+(*  Names    : Established lemma [MOW76] *)
+(*           : Problem 2 [LO85] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    6 (   0 non-Horn;   6 unit;   1 RR) *)
+(*             Number of atoms       :    6 (   6 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include equality group theory axioms  *)
+(* Inclusion of: Axioms/GRP004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Redundant two axioms *)
+theorem prove_inverse_of_inverse_is_original:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) identity.
+\forall H1:\forall X:Univ.eq Univ (multiply X identity) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H3:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H4:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse (inverse a)) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP023-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP023-2.p.ma
new file mode 100644 (file)
index 0000000..9c85e53
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP023-2.p.ma
@@ -0,0 +1,75 @@
+set "baseuri" "cic:/matita/TPTP/GRP023-2".
+include "logic/equality.ma".
+(* Inclusion of: GRP023-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP023-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : The inverse of the identity is the identity *)
+(*  Version  : [MOW76] (equality) axioms : Augmented. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*  Source   : [TPTP] *)
+(*  Names    : Established lemma [MOW76] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    6 (   0 non-Horn;   6 unit;   1 RR) *)
+(*             Number of atoms       :    6 (   6 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include equality group theory axioms  *)
+(* Inclusion of: Axioms/GRP004-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Redundant two axioms *)
+theorem prove_inverse_of_id_is_id:
+ \forall Univ:Set.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X (inverse X)) identity.
+\forall H1:\forall X:Univ.eq Univ (multiply X identity) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H3:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H4:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (inverse identity) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP115-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP115-1.p.ma
new file mode 100644 (file)
index 0000000..d580276
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP115-1.p.ma
@@ -0,0 +1,36 @@
+set "baseuri" "cic:/matita/TPTP/GRP115-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP115-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP115-1 : TPTP v3.1.1. Released v1.2.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Derive order 3 from a single axiom for groups order 3 *)
+(*  Version  : [Wos96] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Wos96] Wos (1996), The Automation of Reasoning: An Experiment  *)
+(*  Source   : [OTTER] *)
+(*  Names    : groups.exp3.in part 1 [OTTER] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.14 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    :    3 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_order3:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a (multiply a a)) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP116-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP116-1.p.ma
new file mode 100644 (file)
index 0000000..34bc0c1
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP116-1.p.ma
@@ -0,0 +1,36 @@
+set "baseuri" "cic:/matita/TPTP/GRP116-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP116-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP116-1 : TPTP v3.1.1. Released v1.2.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Derive left identity from a single axiom for groups order 3 *)
+(*  Version  : [Wos96] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Wos96] Wos (1996), The Automation of Reasoning: An Experiment  *)
+(*  Source   : [OTTER] *)
+(*  Names    : groups.exp3.in part 2 [OTTER] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.14 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    :    3 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_order3:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply identity a) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP117-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP117-1.p.ma
new file mode 100644 (file)
index 0000000..8c7bfcc
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP117-1.p.ma
@@ -0,0 +1,36 @@
+set "baseuri" "cic:/matita/TPTP/GRP117-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP117-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP117-1 : TPTP v3.1.1. Released v1.2.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Derive right identity from a single axiom for groups order 3 *)
+(*  Version  : [Wos96] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Wos96] Wos (1996), The Automation of Reasoning: An Experiment  *)
+(*  Source   : [OTTER] *)
+(*  Names    : groups.exp3.in part 3 [OTTER] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.14 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    :    3 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_order3:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply a identity) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP118-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP118-1.p.ma
new file mode 100644 (file)
index 0000000..478e1d3
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP118-1.p.ma
@@ -0,0 +1,38 @@
+set "baseuri" "cic:/matita/TPTP/GRP118-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP118-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP118-1 : TPTP v3.1.1. Released v1.2.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Derive associativity from a single axiom for groups order 3 *)
+(*  Version  : [Wos96] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Wos96] Wos (1996), The Automation of Reasoning: An Experiment  *)
+(*  Source   : [OTTER] *)
+(*  Names    : groups.exp3.in part 4 [OTTER] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.14 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_order3:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall identity:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (multiply (multiply X (multiply (multiply X Y) Z)) (multiply identity (multiply Z Z)))) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP136-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP136-1.p.ma
new file mode 100644 (file)
index 0000000..0af6b7b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP136-1.p.ma
@@ -0,0 +1,119 @@
+set "baseuri" "cic:/matita/TPTP/GRP136-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP136-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP136-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove anti-symmetry axiom using the LUB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original anti-symmetry axiom from the  *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_antisyma [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 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    :    3 (   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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_antisyma:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (least_upper_bound a b) a.
+\forall H1:eq Univ (least_upper_bound a b) b.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ a b
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP137-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP137-1.p.ma
new file mode 100644 (file)
index 0000000..d4509fe
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP137-1.p.ma
@@ -0,0 +1,119 @@
+set "baseuri" "cic:/matita/TPTP/GRP137-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP137-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP137-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove anti-symmetry axiom using the GLB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original anti-symmetry axiom from the *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_antisymb [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 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    :    3 (   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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_antisymb:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (greatest_lower_bound a b) b.
+\forall H1:eq Univ (greatest_lower_bound a b) a.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ a b
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP139-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP139-1.p.ma
new file mode 100644 (file)
index 0000000..a495736
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP139-1.p.ma
@@ -0,0 +1,122 @@
+set "baseuri" "cic:/matita/TPTP/GRP139-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP139-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP139-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove greatest lower-bound axiom using the GLB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original axiom of anti-symmetry from *)
+(*             the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_glb1b [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_glb1b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (greatest_lower_bound b c) c.
+\forall H1:eq Univ (greatest_lower_bound a c) c.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) c) c
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP141-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP141-1.p.ma
new file mode 100644 (file)
index 0000000..8aceda0
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP141-1.p.ma
@@ -0,0 +1,122 @@
+set "baseuri" "cic:/matita/TPTP/GRP141-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP141-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP141-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove greatest lower-bound axiom using a transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original greatest lower-bound axiom *)
+(*             from the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_glb1d [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.14 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_glb1d:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (least_upper_bound b c) b.
+\forall H1:eq Univ (least_upper_bound a c) a.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) c) c
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP142-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP142-1.p.ma
new file mode 100644 (file)
index 0000000..c06356f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP142-1.p.ma
@@ -0,0 +1,117 @@
+set "baseuri" "cic:/matita/TPTP/GRP142-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP142-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP142-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove greatest lower-bound axiom using the LUB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original greatest lower-bound axiom *)
+(*             from the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_glb2a [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    7 (   3 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 *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_glb2a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) a) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP143-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP143-1.p.ma
new file mode 100644 (file)
index 0000000..33a901d
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP143-1.p.ma
@@ -0,0 +1,117 @@
+set "baseuri" "cic:/matita/TPTP/GRP143-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP143-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP143-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove greatest lower-bound axiom using the GLB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original greatest lower-bound axiom *)
+(*             from the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_glb2b [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    7 (   3 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 *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_glb2b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) a) (greatest_lower_bound a b)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP144-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP144-1.p.ma
new file mode 100644 (file)
index 0000000..5a0a95a
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP144-1.p.ma
@@ -0,0 +1,117 @@
+set "baseuri" "cic:/matita/TPTP/GRP144-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP144-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP144-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove greatest lower-bound axiom using the LUB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original greatest lower-bound axiom *)
+(*             from the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_glb3a [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    7 (   3 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 *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_glb3a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (greatest_lower_bound a b) b) b
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP145-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP145-1.p.ma
new file mode 100644 (file)
index 0000000..3c53d6a
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP145-1.p.ma
@@ -0,0 +1,117 @@
+set "baseuri" "cic:/matita/TPTP/GRP145-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP145-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP145-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove greatest lower-bound axiom using the GLB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original greatest lower-bound axiom *)
+(*             from the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_glb3b [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    7 (   3 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 *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_glb3b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (greatest_lower_bound a b) b) (greatest_lower_bound a b)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP146-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP146-1.p.ma
new file mode 100644 (file)
index 0000000..868dc50
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP146-1.p.ma
@@ -0,0 +1,122 @@
+set "baseuri" "cic:/matita/TPTP/GRP146-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP146-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP146-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove least upper-bound axiom using the LUB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original least upper-bound axiom from *)
+(*             the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_lub1a [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_lub1a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (least_upper_bound b c) c.
+\forall H1:eq Univ (least_upper_bound a c) c.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound a b) c) c
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP149-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP149-1.p.ma
new file mode 100644 (file)
index 0000000..6ebe28f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP149-1.p.ma
@@ -0,0 +1,122 @@
+set "baseuri" "cic:/matita/TPTP/GRP149-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP149-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP149-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove least upper-bound axiom using a transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original least upper-bound axiom from *)
+(*             the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_lub1d [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.14 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_lub1d:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (greatest_lower_bound b c) b.
+\forall H1:eq Univ (greatest_lower_bound a c) a.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (least_upper_bound a b) c) c
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP150-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP150-1.p.ma
new file mode 100644 (file)
index 0000000..a5be66a
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP150-1.p.ma
@@ -0,0 +1,117 @@
+set "baseuri" "cic:/matita/TPTP/GRP150-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP150-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP150-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove least upper-bound axiom using the LUB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original least upper-bound axiom from *)
+(*             the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_lub2a [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    7 (   3 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 *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_lub2a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a (least_upper_bound a b)) (least_upper_bound a b)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP151-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP151-1.p.ma
new file mode 100644 (file)
index 0000000..7080776
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP151-1.p.ma
@@ -0,0 +1,117 @@
+set "baseuri" "cic:/matita/TPTP/GRP151-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP151-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP151-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove least upper-bound axiom using the GLB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original least upper-bound axiom from *)
+(*             the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_lub2b [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    7 (   3 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 *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_lub2b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a (least_upper_bound a b)) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP152-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP152-1.p.ma
new file mode 100644 (file)
index 0000000..3ed9231
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP152-1.p.ma
@@ -0,0 +1,117 @@
+set "baseuri" "cic:/matita/TPTP/GRP152-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP152-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP152-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove least upper-bound axiom using the LUB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original least upper-bound axiom from *)
+(*             the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_lub3a [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    7 (   3 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 *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_lub3a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP153-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP153-1.p.ma
new file mode 100644 (file)
index 0000000..b046855
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP153-1.p.ma
@@ -0,0 +1,117 @@
+set "baseuri" "cic:/matita/TPTP/GRP153-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP153-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP153-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove least upper-bound axiom using the GLB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original least upper-bound axiom from *)
+(*             the equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_lub3b [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    7 (   3 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 *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_lub3b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP154-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP154-1.p.ma
new file mode 100644 (file)
index 0000000..7e7269b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP154-1.p.ma
@@ -0,0 +1,121 @@
+set "baseuri" "cic:/matita/TPTP/GRP154-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP154-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP154-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove monotonicity axiom using the LUB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original mononicity axiom from the *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_mono1a [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_mono1a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (least_upper_bound a b) b.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H7:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H8:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H14:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a c) (multiply b c)) (multiply b c)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP155-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP155-1.p.ma
new file mode 100644 (file)
index 0000000..e11fa9e
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP155-1.p.ma
@@ -0,0 +1,119 @@
+set "baseuri" "cic:/matita/TPTP/GRP155-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP155-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP155-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove monotonicity axiom using the GLB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original monotonicity axiom from the *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_mono1b [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_mono1b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (greatest_lower_bound a b) a.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H7:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H8:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H14:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b c)) (multiply a c)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP156-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP156-1.p.ma
new file mode 100644 (file)
index 0000000..29cb5dd
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP156-1.p.ma
@@ -0,0 +1,121 @@
+set "baseuri" "cic:/matita/TPTP/GRP156-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP156-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP156-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove monotonicity axiom using a transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original monotonicity axiom from the *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_mono1c [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_mono1c:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (least_upper_bound a b) b.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H7:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H8:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H14:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply a c) (multiply b c)) (multiply a c)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP157-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP157-1.p.ma
new file mode 100644 (file)
index 0000000..65a2082
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP157-1.p.ma
@@ -0,0 +1,119 @@
+set "baseuri" "cic:/matita/TPTP/GRP157-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP157-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP157-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove monotonicity axiom using the LUB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original monotonicity axiom from the *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_mono2a [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_mono2a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (least_upper_bound a b) b.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H7:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H8:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H14:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply c a) (multiply c b)) (multiply c b)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP158-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP158-1.p.ma
new file mode 100644 (file)
index 0000000..bf25675
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP158-1.p.ma
@@ -0,0 +1,119 @@
+set "baseuri" "cic:/matita/TPTP/GRP158-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP158-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP158-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove monotonicity axiom using the GLB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original monotonicity axiom from the *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_mono2b [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_mono2b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (greatest_lower_bound a b) a.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H7:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H8:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H14:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply c a) (multiply c b)) (multiply c a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP159-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP159-1.p.ma
new file mode 100644 (file)
index 0000000..0acd9c3
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP159-1.p.ma
@@ -0,0 +1,119 @@
+set "baseuri" "cic:/matita/TPTP/GRP159-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP159-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP159-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove monotonicity axiom using a transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original monotonicity axiom from the *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_mono2c [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.14 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    :    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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_mono2c:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (greatest_lower_bound a b) a.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H7:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H8:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H14:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply c a) (multiply c b)) (multiply c b)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP160-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP160-1.p.ma
new file mode 100644 (file)
index 0000000..f5a6847
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP160-1.p.ma
@@ -0,0 +1,116 @@
+set "baseuri" "cic:/matita/TPTP/GRP160-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP160-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP160-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove reflexivity axiom using the LUB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original reflexivity axiom from the *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_refla [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    6 (   2 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 *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_refla:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a a) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP161-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP161-1.p.ma
new file mode 100644 (file)
index 0000000..dc8c068
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP161-1.p.ma
@@ -0,0 +1,116 @@
+set "baseuri" "cic:/matita/TPTP/GRP161-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP161-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP161-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove reflexivity axiom using the GLB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original reflexivity axiom from the *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_reflb [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    6 (   2 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 *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_reflb:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a a) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP162-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP162-1.p.ma
new file mode 100644 (file)
index 0000000..c192776
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP162-1.p.ma
@@ -0,0 +1,120 @@
+set "baseuri" "cic:/matita/TPTP/GRP162-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP162-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP162-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove transitivity axiom using the LUB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original transitivity axiom from the *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_transa [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_transa:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (least_upper_bound b c) c.
+\forall H1:eq Univ (least_upper_bound a b) b.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound a c) c
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP163-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP163-1.p.ma
new file mode 100644 (file)
index 0000000..0da9490
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP163-1.p.ma
@@ -0,0 +1,120 @@
+set "baseuri" "cic:/matita/TPTP/GRP163-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP163-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP163-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Prove transitivity axiom using the GLB transformation *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : This problem proves the original transitivity axiom from *)
+(*             equational axiomatization. *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : ax_transb [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_ax_transb:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (greatest_lower_bound b c) b.
+\forall H1:eq Univ (greatest_lower_bound a b) a.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound a c) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP168-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP168-1.p.ma
new file mode 100644 (file)
index 0000000..82f45ad
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP168-1.p.ma
@@ -0,0 +1,123 @@
+set "baseuri" "cic:/matita/TPTP/GRP168-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP168-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP168-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Inner group automorphisms are order preserving *)
+(*  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    : p01a [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.1.0, 0.14 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    :    8 (   4 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 > c *)
+(*           : ORDERING LPO greatest_lower_bound > least_upper_bound >  *)
+(*             inverse > product > identity > a > b > c *)
+(*           : [Dah95] says "Not difficult by monotony. Sometimes useful  *)
+(*             for transforming inequalities." *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p01a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (least_upper_bound a b) b.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H7:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H8:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H14:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply b c))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP168-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP168-2.p.ma
new file mode 100644 (file)
index 0000000..bba04f4
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP168-2.p.ma
@@ -0,0 +1,121 @@
+set "baseuri" "cic:/matita/TPTP/GRP168-2".
+include "logic/equality.ma".
+(* Inclusion of: GRP168-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP168-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Inner group automorphisms are order preserving *)
+(*  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    : p01b [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.1.0, 0.14 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    :    8 (   4 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 > 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p01b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (greatest_lower_bound a b) a.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H7:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H8:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H14:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound (multiply (inverse c) (multiply a c)) (multiply (inverse c) (multiply b c))) (multiply (inverse c) (multiply a c))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP173-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP173-1.p.ma
new file mode 100644 (file)
index 0000000..19233ea
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP173-1.p.ma
@@ -0,0 +1,122 @@
+set "baseuri" "cic:/matita/TPTP/GRP173-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP173-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP173-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Each subgroup of negative elements is trivial *)
+(*  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    : p05a [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.14 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 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    :    3 (   2 average) *)
+(*  Comments : ORDERING LPO greatest_lower_bound > least_upper_bound > *)
+(*             inverse > product > identity > a *)
+(*           : ORDERING LPO inverse > product > greatest_lower_bound >  *)
+(*             least_upper_bound > identity > a *)
+(*           : [Dah95] says "The proof is not difficult but combines group *)
+(*             theory, lattice theory and monotonicity." *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p05a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (least_upper_bound identity (inverse a)) identity.
+\forall H1:eq Univ (least_upper_bound identity a) identity.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ identity a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP174-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP174-1.p.ma
new file mode 100644 (file)
index 0000000..cd9b1ec
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP174-1.p.ma
@@ -0,0 +1,119 @@
+set "baseuri" "cic:/matita/TPTP/GRP174-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP174-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP174-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Each subgroup of positive elements is trivial *)
+(*  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    : p05b [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.14 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   18 (   0 non-Horn;  18 unit;   3 RR) *)
+(*             Number of atoms       :   18 (  18 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    :    3 (   2 average) *)
+(*  Comments : ORDERING LPO greatest_lower_bound > least_upper_bound > *)
+(*             inverse > product > identity > a *)
+(*           : 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p05b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (greatest_lower_bound identity (inverse a)) (inverse a).
+\forall H1:eq Univ (greatest_lower_bound identity a) a.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H8:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H9:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H15:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H16:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ identity a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP176-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP176-1.p.ma
new file mode 100644 (file)
index 0000000..5b04b0b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP176-1.p.ma
@@ -0,0 +1,125 @@
+set "baseuri" "cic:/matita/TPTP/GRP176-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP176-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP176-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : General form of distributivity *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    9 (   5 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 > c > d *)
+(*           : ORDERING LPO greatest_lower_bound > least_upper_bound >  *)
+(*             inverse > product > identity > a > b > c > d *)
+(*           : This is a standardized version of the problem that appears in *)
+(*             [Sch95]. *)
+(*           : [Dah95] says "Easy from equational axioms, More difficult from *)
+(*             monotonicity. The assumtion is a consequence of group theory." *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p07:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall d:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d)))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP176-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP176-2.p.ma
new file mode 100644 (file)
index 0000000..3f38130
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP176-2.p.ma
@@ -0,0 +1,121 @@
+set "baseuri" "cic:/matita/TPTP/GRP176-2".
+include "logic/equality.ma".
+(* Inclusion of: GRP176-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP176-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : General form of 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    : p07 [Sch95] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   17 (   0 non-Horn;  17 unit;   1 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    :    9 (   5 constant; 0-2 arity) *)
+(*             Number of variables   :   35 (   2 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments : ORDERING LPO inverse > product > greatest_lower_bound > *)
+(*             least_upper_bound > identity > a > b > c > d *)
+(*           : ORDERING LPO greatest_lower_bound > least_upper_bound >  *)
+(*             inverse > product > identity > a > b > c > d *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p07:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall d:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H7:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H8:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H14:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply c (multiply (least_upper_bound a b) d)) (least_upper_bound (multiply c (multiply a d)) (multiply c (multiply b d)))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP182-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP182-1.p.ma
new file mode 100644 (file)
index 0000000..8641d99
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP182-1.p.ma
@@ -0,0 +1,127 @@
+set "baseuri" "cic:/matita/TPTP/GRP182-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP182-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP182-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Positive part of the negative part is identity *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    6 (   2 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 *)
+(*           : ORDERING LPO greatest_lower_bound > least_upper_bound >  *)
+(*             inverse > product > identity > a *)
+(*           : This is a standardized version of the problem that appears in *)
+(*             [Sch95]. *)
+(*           : The theorem clause has been modified according to instructions *)
+(*             in [Dah95]. *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is Schulz's clause *)
+(* input_clause(prove_p17a,negated_conjecture, *)
+(*     [--equal(least_upper_bound(identity,least_upper_bound(a,identity)), *)
+(* least_upper_bound(a,identity))]). *)
+(* ----This is Dahn's clause *)
+theorem prove_p17a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (greatest_lower_bound a identity)) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP182-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP182-2.p.ma
new file mode 100644 (file)
index 0000000..1f93eda
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP182-2.p.ma
@@ -0,0 +1,128 @@
+set "baseuri" "cic:/matita/TPTP/GRP182-2".
+include "logic/equality.ma".
+(* Inclusion of: GRP182-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP182-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Positive part of the negative part is identity *)
+(*  Version  : [Fuc94] (equality) axioms : Augmented. *)
+(*  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    : p17a [Sch95] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    3 (   2 average) *)
+(*  Comments : ORDERING LPO inverse > product > greatest_lower_bound > *)
+(*             least_upper_bound > identity > a *)
+(*           : ORDERING LPO greatest_lower_bound > least_upper_bound >  *)
+(*             inverse > product > identity > a *)
+(*           : The theorem clause has been modified according to instructions *)
+(*             in [Dah95]. *)
+(*  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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----This is Schulz's clause *)
+(* input_clause(prove_p17a,negated_conjecture, *)
+(*     [--equal(least_upper_bound(identity,least_upper_bound(a,identity)), *)
+(* least_upper_bound(a,identity))]). *)
+(* ----This is Dahn's clause *)
+theorem prove_p17a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)).
+\forall H1:\forall X:Univ.eq Univ (inverse (inverse X)) X.
+\forall H2:eq Univ (inverse identity) identity.
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H9:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H10:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H15:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H16:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H17:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound identity (greatest_lower_bound a identity)) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP182-3.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP182-3.p.ma
new file mode 100644 (file)
index 0000000..558e029
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP182-3.p.ma
@@ -0,0 +1,120 @@
+set "baseuri" "cic:/matita/TPTP/GRP182-3".
+include "logic/equality.ma".
+(* Inclusion of: GRP182-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP182-3 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Positive part of the negative part is identity *)
+(*  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   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    6 (   2 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 *)
+(*           : ORDERING LPO greatest_lower_bound > least_upper_bound >  *)
+(*             inverse > product > 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p17b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (least_upper_bound a identity)) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP182-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP182-4.p.ma
new file mode 100644 (file)
index 0000000..43b2414
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP182-4.p.ma
@@ -0,0 +1,121 @@
+set "baseuri" "cic:/matita/TPTP/GRP182-4".
+include "logic/equality.ma".
+(* Inclusion of: GRP182-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP182-4 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Positive part of the negative part is identity *)
+(*  Version  : [Fuc94] (equality) axioms : Augmented. *)
+(*             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    : p17b [Sch95] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    3 (   2 average) *)
+(*  Comments : ORDERING LPO inverse > product > greatest_lower_bound > *)
+(*             least_upper_bound > identity > a *)
+(*           : ORDERING LPO greatest_lower_bound > least_upper_bound >  *)
+(*             inverse > product > 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p17b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)).
+\forall H1:\forall X:Univ.eq Univ (inverse (inverse X)) X.
+\forall H2:eq Univ (inverse identity) identity.
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H9:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H10:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H15:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H16:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H17:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound identity (least_upper_bound a identity)) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP186-3.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP186-3.p.ma
new file mode 100644 (file)
index 0000000..615fcd9
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP186-3.p.ma
@@ -0,0 +1,119 @@
+set "baseuri" "cic:/matita/TPTP/GRP186-3".
+include "logic/equality.ma".
+(* Inclusion of: GRP186-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP186-3 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Application of distributivity and group theory *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*             Theorem formulation : Switched from GLB to LUB. *)
+(*  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   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.14 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p23x:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (least_upper_bound (inverse a) b))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP186-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP186-4.p.ma
new file mode 100644 (file)
index 0000000..b24baeb
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP186-4.p.ma
@@ -0,0 +1,120 @@
+set "baseuri" "cic:/matita/TPTP/GRP186-4".
+include "logic/equality.ma".
+(* Inclusion of: GRP186-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP186-4 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Application of distributivity and group theory *)
+(*  Version  : [Fuc94] (equality) axioms : Augmented. *)
+(*             Theorem formulation : Switched from GLB to LUB. *)
+(*  English  :  *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : p23x [Sch95] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.14 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p23x:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)).
+\forall H1:\forall X:Univ.eq Univ (inverse (inverse X)) X.
+\forall H2:eq Univ (inverse identity) identity.
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H9:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H10:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H15:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H16:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H17:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound (multiply a b) identity) (multiply a (least_upper_bound (inverse a) b))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP188-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP188-1.p.ma
new file mode 100644 (file)
index 0000000..d22324e
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP188-1.p.ma
@@ -0,0 +1,118 @@
+set "baseuri" "cic:/matita/TPTP/GRP188-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP188-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP188-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Consequence of lattice 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   : 0.00 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    :    7 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   33 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : ORDERING LPO greatest_lower_bound > least_upper_bound > *)
+(*             inverse > product > 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p38a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP188-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP188-2.p.ma
new file mode 100644 (file)
index 0000000..b9a448f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP188-2.p.ma
@@ -0,0 +1,119 @@
+set "baseuri" "cic:/matita/TPTP/GRP188-2".
+include "logic/equality.ma".
+(* Inclusion of: GRP188-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP188-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Consequence of lattice 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    : p38a [Sch95] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    3 (   2 average) *)
+(*  Comments : ORDERING LPO greatest_lower_bound > least_upper_bound > *)
+(*             inverse > product > 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p38a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)).
+\forall H1:\forall X:Univ.eq Univ (inverse (inverse X)) X.
+\forall H2:eq Univ (inverse identity) identity.
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H9:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H10:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H15:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H16:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H17:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (least_upper_bound b (least_upper_bound a b)) (least_upper_bound a b)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP189-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP189-1.p.ma
new file mode 100644 (file)
index 0000000..d87f2d1
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP189-1.p.ma
@@ -0,0 +1,118 @@
+set "baseuri" "cic:/matita/TPTP/GRP189-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP189-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP189-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Consequence of lattice 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   : 0.00 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    :    7 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   33 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : ORDERING LPO greatest_lower_bound > least_upper_bound > *)
+(*             inverse > product > 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p38b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H6:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H7:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H13:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H14:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP189-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP189-2.p.ma
new file mode 100644 (file)
index 0000000..190ce11
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP189-2.p.ma
@@ -0,0 +1,119 @@
+set "baseuri" "cic:/matita/TPTP/GRP189-2".
+include "logic/equality.ma".
+(* Inclusion of: GRP189-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP189-2 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Consequence of lattice 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    : p38b [Sch95] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    3 (   2 average) *)
+(*  Comments : ORDERING LPO greatest_lower_bound > least_upper_bound > *)
+(*             inverse > product > 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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p38b:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (inverse (multiply X Y)) (multiply (inverse Y) (inverse X)).
+\forall H1:\forall X:Univ.eq Univ (inverse (inverse X)) X.
+\forall H2:eq Univ (inverse identity) identity.
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H9:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H10:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H14:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H15:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H16:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H17:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (greatest_lower_bound b (least_upper_bound a b)) b
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP192-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP192-1.p.ma
new file mode 100644 (file)
index 0000000..9a4fcec
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP192-1.p.ma
@@ -0,0 +1,118 @@
+set "baseuri" "cic:/matita/TPTP/GRP192-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP192-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP192-1 : TPTP v3.1.1. Bugfixed v1.2.1. *)
+(*  Domain   : Group Theory (Lattice Ordered) *)
+(*  Problem  : Even elements implies trivial group *)
+(*  Version  : [Fuc94] (equality) axioms. *)
+(*  English  : The assumption all(X,1 =< X) even implies that the group is  *)
+(*             trivial, i.e., all(X, X = 1). *)
+(*  Refs     : [Fuc94] Fuchs (1994), The Application of Goal-Orientated Heuri *)
+(*           : [Sch95] Schulz (1995), Explanation Based Learning for Distribu *)
+(*  Source   : [Sch95] *)
+(*  Names    : p40a [Sch95]  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.33 v2.2.0, 0.43 v2.1.0, 0.14 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   17 (   0 non-Horn;  17 unit;   1 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   :   34 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   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 v3.1.1. Released v1.0.0. *)
+(*  Domain   : Group Theory *)
+(*  Axioms   : Group theory (equality) axioms *)
+(*  Version  : [MOW76] (equality) axioms :  *)
+(*             Reduced > Complete. *)
+(*  English  :  *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    3 (   0 non-Horn;   3 unit;   0 RR) *)
+(*             Number of literals   :    3 (   3 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    3 (   1 constant; 0-2 arity) *)
+(*             Number of variables  :    5 (   0 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : [MOW76] also contains redundant right_identity and *)
+(*             right_inverse axioms. *)
+(*           : These axioms are also used in [Wos88] p.186, also with *)
+(*             right_identity and right_inverse. *)
+(* -------------------------------------------------------------------------- *)
+(* ----For any x and y in the group x*y is also in the group. No clause  *)
+(* ----is needed here since this is an instance of reflexivity  *)
+(* ----There exists an identity element  *)
+(* ----For any x in the group, there exists an element y such that x*y = y*x  *)
+(* ----= identity. *)
+(* ----The operation '*' is associative  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Lattice ordered group (equality) axioms *)
+(* Inclusion of: Axioms/GRP004-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP004-2 : TPTP v3.1.1. 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 literals   :   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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_p40a:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall greatest_lower_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall least_upper_bound:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (least_upper_bound identity X) X.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (greatest_lower_bound Y Z) X) (greatest_lower_bound (multiply Y X) (multiply Z X)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (least_upper_bound Y Z) X) (least_upper_bound (multiply Y X) (multiply Z X)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (greatest_lower_bound Y Z)) (greatest_lower_bound (multiply X Y) (multiply X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (least_upper_bound Y Z)) (least_upper_bound (multiply X Y) (multiply X Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X (least_upper_bound X Y)) X.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X (greatest_lower_bound X Y)) X.
+\forall H7:\forall X:Univ.eq Univ (greatest_lower_bound X X) X.
+\forall H8:\forall X:Univ.eq Univ (least_upper_bound X X) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (least_upper_bound X (least_upper_bound Y Z)) (least_upper_bound (least_upper_bound X Y) Z).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (greatest_lower_bound X (greatest_lower_bound Y Z)) (greatest_lower_bound (greatest_lower_bound X Y) Z).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (least_upper_bound X Y) (least_upper_bound Y X).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (greatest_lower_bound X Y) (greatest_lower_bound Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H14:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H15:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP206-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP206-1.p.ma
new file mode 100644 (file)
index 0000000..b19e797
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP206-1.p.ma
@@ -0,0 +1,53 @@
+set "baseuri" "cic:/matita/TPTP/GRP206-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP206-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP206-1 : TPTP v3.1.1. Released v2.3.0. *)
+(*  Domain   : Group Theory (Loops) *)
+(*  Problem  : In Loops, Moufang-4 => Moufang-1. *)
+(*  Version  : [MP96] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Wos96] Wos (1996), OTTER and the Moufang Identity Problem *)
+(*  Source   : [Wos96] *)
+(*  Names    : - [Wos96] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.3.0 *)
+(*  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    :    9 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :   15 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments : *)
+(* -------------------------------------------------------------------------- *)
+(* ----Loop axioms: *)
+(* ----Moufang-4 *)
+(* ----Denial of Moufang-1 *)
+theorem prove_moufang1:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall identity:Univ.
+\forall left_division:\forall _:Univ.\forall _:Univ.Univ.
+\forall left_inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall right_division:\forall _:Univ.\forall _:Univ.Univ.
+\forall right_inverse:\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (multiply (multiply Y Z) X)) (multiply (multiply X Y) (multiply Z X)).
+\forall H1:\forall X:Univ.eq Univ (multiply (left_inverse X) X) identity.
+\forall H2:\forall X:Univ.eq Univ (multiply X (right_inverse X)) identity.
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (right_division (multiply X Y) Y) X.
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (right_division X Y) Y) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (left_division X (multiply X Y)) Y.
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (left_division X Y)) Y.
+\forall H7:\forall X:Univ.eq Univ (multiply X identity) X.
+\forall H8:\forall X:Univ.eq Univ (multiply identity X) X.eq Univ (multiply (multiply a (multiply b c)) a) (multiply (multiply a b) (multiply c a))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP454-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP454-1.p.ma
new file mode 100644 (file)
index 0000000..12dc8c9
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP454-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP454-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP454-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP454-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    8 (   2 average) *)
+(*  Comments : A UEQ part of GRP066-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP455-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP455-1.p.ma
new file mode 100644 (file)
index 0000000..dfc9a81
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP455-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP455-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP455-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP455-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in division and identity, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    8 (   2 average) *)
+(*  Comments : A UEQ part of GRP066-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A (divide B (divide (divide (divide A A) A) C)))) C) B.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP456-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP456-1.p.ma
new file mode 100644 (file)
index 0000000..5b46051
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP456-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP456-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP456-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP456-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in division and identity, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    8 (   3 average) *)
+(*  Comments : A UEQ part of GRP066-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (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))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP457-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP457-1.p.ma
new file mode 100644 (file)
index 0000000..b8bc438
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP457-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP457-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP457-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP457-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   2 average) *)
+(*  Comments : A UEQ part of GRP067-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP458-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP458-1.p.ma
new file mode 100644 (file)
index 0000000..716d8e2
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP458-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP458-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP458-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP458-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in division and identity, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   2 average) *)
+(*  Comments : A UEQ part of GRP067-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP459-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP459-1.p.ma
new file mode 100644 (file)
index 0000000..6b31ac4
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP459-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP459-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP459-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP459-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in division and identity, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP067-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A A) (divide A (divide B (divide (divide identity A) C)))) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP460-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP460-1.p.ma
new file mode 100644 (file)
index 0000000..908ea3c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP460-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP460-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP460-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP460-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP068-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide A (divide (divide (divide identity B) C) (divide (divide (divide A A) A) C))) B.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP463-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP463-1.p.ma
new file mode 100644 (file)
index 0000000..76d7098
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP463-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP463-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP463-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP463-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP069-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide A (divide (divide (divide (divide A A) B) C) (divide (divide identity A) C))) B.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP467-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP467-1.p.ma
new file mode 100644 (file)
index 0000000..c4cb419
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP467-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP467-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP467-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP467-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in division and inverse, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    6 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments : A UEQ part of GRP070-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.\forall D:Univ.eq Univ (divide (divide A A) (divide B (divide (divide C (divide D B)) (inverse D)))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP481-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP481-1.p.ma
new file mode 100644 (file)
index 0000000..c4c633a
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP481-1.p.ma
@@ -0,0 +1,42 @@
+set "baseuri" "cic:/matita/TPTP/GRP481-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP481-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP481-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Neu86] Neumann (1986), Yet Another Single Law for Groups *)
+(*           : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   2 average) *)
+(*  Comments : A UEQ part of GRP075-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.\forall D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP484-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP484-1.p.ma
new file mode 100644 (file)
index 0000000..8a6ef3a
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP484-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP484-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP484-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP484-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP076-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP485-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP485-1.p.ma
new file mode 100644 (file)
index 0000000..b2c04b8
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP485-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP485-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP485-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP485-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP076-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP486-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP486-1.p.ma
new file mode 100644 (file)
index 0000000..5d40fea
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP486-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP486-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP486-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP486-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments : A UEQ part of GRP076-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide A B) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP487-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP487-1.p.ma
new file mode 100644 (file)
index 0000000..3004ed9
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP487-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP487-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP487-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP487-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   2 average) *)
+(*  Comments : A UEQ part of GRP077-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide A (double_divide (double_divide (double_divide identity (double_divide (double_divide A identity) (double_divide B C))) B) identity)) C.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP488-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP488-1.p.ma
new file mode 100644 (file)
index 0000000..7447347
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP488-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP488-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP488-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP488-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   2 average) *)
+(*  Comments : A UEQ part of GRP077-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide A (double_divide (double_divide (double_divide identity (double_divide (double_divide A identity) (double_divide B C))) B) identity)) C.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP490-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP490-1.p.ma
new file mode 100644 (file)
index 0000000..2ff23a7
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP490-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP490-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP490-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP490-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP078-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP491-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP491-1.p.ma
new file mode 100644 (file)
index 0000000..836a3ad
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP491-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP491-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP491-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP491-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP078-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP492-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP492-1.p.ma
new file mode 100644 (file)
index 0000000..89c4207
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP492-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP492-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP492-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP492-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments : A UEQ part of GRP078-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP493-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP493-1.p.ma
new file mode 100644 (file)
index 0000000..63a8d59
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP493-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP493-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP493-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP493-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP079-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP494-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP494-1.p.ma
new file mode 100644 (file)
index 0000000..6bbae9c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP494-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP494-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP494-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP494-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP079-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP495-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP495-1.p.ma
new file mode 100644 (file)
index 0000000..4dec7d5
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP495-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP495-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP495-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP495-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP079-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide (double_divide (double_divide B C) (double_divide identity identity)) (double_divide A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP496-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP496-1.p.ma
new file mode 100644 (file)
index 0000000..1df419c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP496-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP496-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP496-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP496-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP080-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP497-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP497-1.p.ma
new file mode 100644 (file)
index 0000000..ded973f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP497-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP497-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP497-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP497-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP080-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP498-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP498-1.p.ma
new file mode 100644 (file)
index 0000000..626cd74
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP498-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP498-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP498-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP498-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory *)
+(*  Problem  : Axiom for group theory, in double division and identity, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP080-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity (double_divide A (double_divide B identity))) (double_divide (double_divide B (double_divide C A)) identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP509-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP509-1.p.ma
new file mode 100644 (file)
index 0000000..586e03a
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP509-1.p.ma
@@ -0,0 +1,38 @@
+set "baseuri" "cic:/matita/TPTP/GRP509-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP509-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP509-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in product and inverse, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [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   : 0.00 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    :    4 (   3 average) *)
+(*  Comments : A UEQ part of GRP085-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall b1:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP510-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP510-1.p.ma
new file mode 100644 (file)
index 0000000..11bd0b2
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP510-1.p.ma
@@ -0,0 +1,38 @@
+set "baseuri" "cic:/matita/TPTP/GRP510-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP510-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP510-1 : TPTP v3.1.1. 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     : [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   : 0.00 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    :    4 (   2 average) *)
+(*  Comments : A UEQ part of GRP085-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP511-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP511-1.p.ma
new file mode 100644 (file)
index 0000000..71dae36
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP511-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP511-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP511-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP511-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in product and inverse, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [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   : 0.00 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    :    4 (   3 average) *)
+(*  Comments : A UEQ part of GRP085-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP512-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP512-1.p.ma
new file mode 100644 (file)
index 0000000..23121a3
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP512-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP512-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP512-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP512-1 : TPTP v3.1.1. 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     : [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   : 0.00 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   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments : A UEQ part of GRP085-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply (multiply (multiply A B) C) (inverse (multiply A C))) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP513-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP513-1.p.ma
new file mode 100644 (file)
index 0000000..81534b3
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP513-1.p.ma
@@ -0,0 +1,37 @@
+set "baseuri" "cic:/matita/TPTP/GRP513-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP513-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP513-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in product and inverse, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 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   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   3 average) *)
+(*  Comments : A UEQ part of GRP086-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall b1:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP514-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP514-1.p.ma
new file mode 100644 (file)
index 0000000..70ac86f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP514-1.p.ma
@@ -0,0 +1,37 @@
+set "baseuri" "cic:/matita/TPTP/GRP514-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP514-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP514-1 : TPTP v3.1.1. 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     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   3 average) *)
+(*  Comments : A UEQ part of GRP086-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP515-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP515-1.p.ma
new file mode 100644 (file)
index 0000000..fc49b20
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP515-1.p.ma
@@ -0,0 +1,38 @@
+set "baseuri" "cic:/matita/TPTP/GRP515-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP515-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP515-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in product 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   : 0.00 v3.1.0, 0.11 v2.7.0, 0.00 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    :    5 (   3 average) *)
+(*  Comments : A UEQ part of GRP086-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP516-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP516-1.p.ma
new file mode 100644 (file)
index 0000000..da70834
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP516-1.p.ma
@@ -0,0 +1,38 @@
+set "baseuri" "cic:/matita/TPTP/GRP516-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP516-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP516-1 : TPTP v3.1.1. 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     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP086-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply B C) (inverse (multiply A C)))) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP517-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP517-1.p.ma
new file mode 100644 (file)
index 0000000..bbbb368
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP517-1.p.ma
@@ -0,0 +1,37 @@
+set "baseuri" "cic:/matita/TPTP/GRP517-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP517-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP517-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in product and inverse, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    6 (   3 average) *)
+(*  Comments : A UEQ part of GRP087-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall b1:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP518-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP518-1.p.ma
new file mode 100644 (file)
index 0000000..0209207
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP518-1.p.ma
@@ -0,0 +1,37 @@
+set "baseuri" "cic:/matita/TPTP/GRP518-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP518-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP518-1 : TPTP v3.1.1. 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     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    6 (   3 average) *)
+(*  Comments : A UEQ part of GRP087-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP520-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP520-1.p.ma
new file mode 100644 (file)
index 0000000..c5fd793
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP520-1.p.ma
@@ -0,0 +1,38 @@
+set "baseuri" "cic:/matita/TPTP/GRP520-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP520-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP520-1 : TPTP v3.1.1. 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     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments : A UEQ part of GRP087-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (multiply A (multiply (multiply (inverse (multiply A B)) C) B)) C.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP541-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP541-1.p.ma
new file mode 100644 (file)
index 0000000..3fa88b8
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP541-1.p.ma
@@ -0,0 +1,42 @@
+set "baseuri" "cic:/matita/TPTP/GRP541-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP541-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP541-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP093-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall b1:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP542-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP542-1.p.ma
new file mode 100644 (file)
index 0000000..21eb32d
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP542-1.p.ma
@@ -0,0 +1,42 @@
+set "baseuri" "cic:/matita/TPTP/GRP542-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP542-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP542-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP093-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP543-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP543-1.p.ma
new file mode 100644 (file)
index 0000000..2a772c9
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP543-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP543-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP543-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP543-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP093-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP544-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP544-1.p.ma
new file mode 100644 (file)
index 0000000..38a6ac6
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP544-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP544-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP544-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP544-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP093-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide (divide (divide A B) C) A)) C) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP545-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP545-1.p.ma
new file mode 100644 (file)
index 0000000..6d3230b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP545-1.p.ma
@@ -0,0 +1,42 @@
+set "baseuri" "cic:/matita/TPTP/GRP545-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP545-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP545-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments : A UEQ part of GRP094-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall b1:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP546-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP546-1.p.ma
new file mode 100644 (file)
index 0000000..c08fc15
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP546-1.p.ma
@@ -0,0 +1,42 @@
+set "baseuri" "cic:/matita/TPTP/GRP546-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP546-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP546-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments : A UEQ part of GRP094-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP547-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP547-1.p.ma
new file mode 100644 (file)
index 0000000..44086b1
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP547-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP547-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP547-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP547-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments : A UEQ part of GRP094-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP548-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP548-1.p.ma
new file mode 100644 (file)
index 0000000..ab4ad4c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP548-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP548-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP548-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP548-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments : A UEQ part of GRP094-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity (divide A B)) (divide (divide B C) A)) C.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP549-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP549-1.p.ma
new file mode 100644 (file)
index 0000000..efcfc9f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP549-1.p.ma
@@ -0,0 +1,42 @@
+set "baseuri" "cic:/matita/TPTP/GRP549-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP549-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP549-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP095-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall b1:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP550-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP550-1.p.ma
new file mode 100644 (file)
index 0000000..d02e348
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP550-1.p.ma
@@ -0,0 +1,42 @@
+set "baseuri" "cic:/matita/TPTP/GRP550-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP550-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP550-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP095-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP551-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP551-1.p.ma
new file mode 100644 (file)
index 0000000..ca26318
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP551-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP551-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP551-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP551-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP095-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP552-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP552-1.p.ma
new file mode 100644 (file)
index 0000000..bb79a3b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP552-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP552-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP552-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP552-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and identity, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP095-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (divide A A).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (divide identity A).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (divide identity B)).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide identity A) (divide (divide (divide B A) C) B)) C.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP556-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP556-1.p.ma
new file mode 100644 (file)
index 0000000..77f2537
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP556-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP556-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP556-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP556-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and inverse, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments : A UEQ part of GRP096-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide A (inverse (divide B (divide A C)))) C) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP558-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP558-1.p.ma
new file mode 100644 (file)
index 0000000..a2cc53b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP558-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP558-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP558-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP558-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and inverse, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   3 average) *)
+(*  Comments : A UEQ part of GRP097-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP560-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP560-1.p.ma
new file mode 100644 (file)
index 0000000..d683744
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP560-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP560-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP560-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP560-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and inverse, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP097-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide A (inverse (divide (divide B C) (divide A C)))) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP561-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP561-1.p.ma
new file mode 100644 (file)
index 0000000..e64a752
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP561-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP561-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP561-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP561-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and inverse, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0, 0.09 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   3 average) *)
+(*  Comments : A UEQ part of GRP098-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall b1:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP562-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP562-1.p.ma
new file mode 100644 (file)
index 0000000..6b5ac4a
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP562-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP562-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP562-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP562-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and inverse, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   3 average) *)
+(*  Comments : A UEQ part of GRP098-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP564-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP564-1.p.ma
new file mode 100644 (file)
index 0000000..467c25c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP564-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP564-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP564-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP564-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in division and inverse, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments : A UEQ part of GRP098-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (divide A (inverse B)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (divide (divide (divide A (inverse B)) C) (divide A C)) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP565-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP565-1.p.ma
new file mode 100644 (file)
index 0000000..190874f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP565-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP565-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP565-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP565-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP099-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP566-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP566-1.p.ma
new file mode 100644 (file)
index 0000000..dd2e955
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP566-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP566-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP566-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP566-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP099-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP567-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP567-1.p.ma
new file mode 100644 (file)
index 0000000..d914e6b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP567-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP567-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP567-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP567-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.14 v3.1.0, 0.11 v2.7.0, 0.09 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments : A UEQ part of GRP099-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP568-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP568-1.p.ma
new file mode 100644 (file)
index 0000000..cfddf66
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP568-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP568-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP568-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP568-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.14 v3.1.0, 0.11 v2.7.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP099-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide identity C))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP569-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP569-1.p.ma
new file mode 100644 (file)
index 0000000..e919cd3
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP569-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP569-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP569-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP569-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP100-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP570-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP570-1.p.ma
new file mode 100644 (file)
index 0000000..5d1418c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP570-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP570-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP570-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP570-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP100-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP572-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP572-1.p.ma
new file mode 100644 (file)
index 0000000..14f0155
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP572-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP572-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP572-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP572-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP100-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide A C)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP573-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP573-1.p.ma
new file mode 100644 (file)
index 0000000..53f1956
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP573-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP573-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP573-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP573-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP101-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP574-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP574-1.p.ma
new file mode 100644 (file)
index 0000000..bccea60
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP574-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP574-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP574-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP574-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP101-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP576-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP576-1.p.ma
new file mode 100644 (file)
index 0000000..4cbe988
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP576-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP576-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP576-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP576-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP101-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide B (double_divide C A)) (double_divide C identity))) (double_divide identity identity)) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP577-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP577-1.p.ma
new file mode 100644 (file)
index 0000000..3bab0d3
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP577-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP577-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP577-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP577-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP102-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP578-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP578-1.p.ma
new file mode 100644 (file)
index 0000000..1e4e99e
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP578-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP578-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP578-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP578-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP102-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP580-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP580-1.p.ma
new file mode 100644 (file)
index 0000000..b05d411
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP580-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP580-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP580-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP580-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP102-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP581-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP581-1.p.ma
new file mode 100644 (file)
index 0000000..a85c49c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP581-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP581-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP581-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP581-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP103-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply (inverse a1) a1) identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP582-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP582-1.p.ma
new file mode 100644 (file)
index 0000000..3ece06e
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP582-1.p.ma
@@ -0,0 +1,41 @@
+set "baseuri" "cic:/matita/TPTP/GRP582-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP582-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP582-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.6.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP103-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply identity a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP583-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP583-1.p.ma
new file mode 100644 (file)
index 0000000..134e789
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP583-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP583-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP583-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP583-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments : A UEQ part of GRP103-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP584-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP584-1.p.ma
new file mode 100644 (file)
index 0000000..24ddd7e
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP584-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/GRP584-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP584-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP584-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments : A UEQ part of GRP103-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A (double_divide (double_divide identity B) (double_divide C (double_divide B A)))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP586-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP586-1.p.ma
new file mode 100644 (file)
index 0000000..f91a424
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP586-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP586-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP586-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP586-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP104-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP588-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP588-1.p.ma
new file mode 100644 (file)
index 0000000..f27de51
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP588-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP588-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP588-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP588-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP104-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide A (inverse (double_divide (inverse (double_divide (double_divide A B) (inverse C))) B))) C.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP590-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP590-1.p.ma
new file mode 100644 (file)
index 0000000..881af35
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP590-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP590-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP590-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP590-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP105-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP592-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP592-1.p.ma
new file mode 100644 (file)
index 0000000..8508efd
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP592-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP592-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP592-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP592-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP105-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse C))))) B) C.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP595-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP595-1.p.ma
new file mode 100644 (file)
index 0000000..b30ce39
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP595-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP595-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP595-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP595-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 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   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP106-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP596-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP596-1.p.ma
new file mode 100644 (file)
index 0000000..8d358e3
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP596-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP596-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP596-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP596-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP106-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide C B)))))) C.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP597-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP597-1.p.ma
new file mode 100644 (file)
index 0000000..03160a5
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP597-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP597-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP597-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP597-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP107-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall b1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP598-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP598-1.p.ma
new file mode 100644 (file)
index 0000000..d0e3599
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP598-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP598-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP598-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP598-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP107-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP599-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP599-1.p.ma
new file mode 100644 (file)
index 0000000..9ccd994
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP599-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP599-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP599-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP599-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 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   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP107-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP600-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP600-1.p.ma
new file mode 100644 (file)
index 0000000..de36114
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP600-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP600-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP600-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP600-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP107-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide A B) (inverse (double_divide A (inverse (double_divide (inverse C) B))))) C.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP602-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP602-1.p.ma
new file mode 100644 (file)
index 0000000..4e19411
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP602-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP602-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP602-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP602-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    8 (   3 average) *)
+(*  Comments : A UEQ part of GRP108-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP603-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP603-1.p.ma
new file mode 100644 (file)
index 0000000..9d72d69
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP603-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP603-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP603-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP603-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 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   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    8 (   3 average) *)
+(*  Comments : A UEQ part of GRP108-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP604-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP604-1.p.ma
new file mode 100644 (file)
index 0000000..4693754
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP604-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP604-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP604-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP604-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    8 (   3 average) *)
+(*  Comments : A UEQ part of GRP108-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (inverse (double_divide A (inverse (double_divide B (double_divide A C))))) C)) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP605-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP605-1.p.ma
new file mode 100644 (file)
index 0000000..7a6ff41
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP605-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP605-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP605-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP605-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP109-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall b1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP606-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP606-1.p.ma
new file mode 100644 (file)
index 0000000..a317d5a
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP606-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP606-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP606-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP606-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP109-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP608-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP608-1.p.ma
new file mode 100644 (file)
index 0000000..d64555f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP608-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP608-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP608-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP608-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP109-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide A (inverse (double_divide (inverse B) (double_divide A C))))) C) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP612-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP612-1.p.ma
new file mode 100644 (file)
index 0000000..61b2a80
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP612-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP612-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP612-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP612-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP110-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (inverse (double_divide (inverse (double_divide (inverse (double_divide A B)) C)) (double_divide A C))) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP613-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP613-1.p.ma
new file mode 100644 (file)
index 0000000..290d935
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP613-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP613-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP613-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP613-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 1 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP111-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_1:
+ \forall Univ:Set.
+\forall a1:Univ.
+\forall b1:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (inverse a1) a1) (multiply (inverse b1) b1)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP614-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP614-1.p.ma
new file mode 100644 (file)
index 0000000..d1a988c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP614-1.p.ma
@@ -0,0 +1,39 @@
+set "baseuri" "cic:/matita/TPTP/GRP614-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP614-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP614-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 2 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP111-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall b2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP615-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP615-1.p.ma
new file mode 100644 (file)
index 0000000..e1cc77b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP615-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP615-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP615-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP615-1 : TPTP v3.1.1. Released v2.6.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 3 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 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   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP111-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_3:
+ \forall Univ:Set.
+\forall a3:Univ.
+\forall b3:Univ.
+\forall c3:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/GRP616-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/GRP616-1.p.ma
new file mode 100644 (file)
index 0000000..c68f5a3
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/GRP616-1.p.ma
@@ -0,0 +1,40 @@
+set "baseuri" "cic:/matita/TPTP/GRP616-1".
+include "logic/equality.ma".
+(* Inclusion of: GRP616-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : GRP616-1 : TPTP v3.1.1. Bugfixed v2.7.0. *)
+(*  Domain   : Group Theory (Abelian) *)
+(*  Problem  : Axiom for Abelian group theory, in double div and inv, part 4 *)
+(*  Version  : [McC93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.7.0 *)
+(*  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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    5 (   0 singleton) *)
+(*             Maximal term depth    :    7 (   3 average) *)
+(*  Comments : A UEQ part of GRP111-1 *)
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_4:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+\forall H1:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (inverse (double_divide (inverse (double_divide A (inverse B))) C)) (double_divide A C)) B.eq Univ (multiply a b) (multiply b a)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LAT008-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LAT008-1.p.ma
new file mode 100644 (file)
index 0000000..e1f6f58
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LAT008-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/LAT008-1".
+include "logic/equality.ma".
+(* Inclusion of: LAT008-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT008-1 : TPTP v3.1.1. Released v2.2.0. *)
+(*  Domain   : Lattice Theory (Distributive lattices) *)
+(*  Problem  : Sholander's basis for distributive lattices, part 5 (of 6). *)
+(*  Version  : [MP96] (equality) axioms. *)
+(*  English  : This is part of the proof that Sholanders 2-basis for *)
+(*             distributive lattices is correct. Here we prove the absorption  *)
+(*             law  x v (x ^ y) = x. *)
+(*  Refs     : [McC98] McCune (1998), Email to G. Sutcliffe *)
+(*           : [MP96]  McCune & Padmanabhan (1996), Automated Deduction in Eq *)
+(*  Source   : [McC98] *)
+(*  Names    : LT-3-f [MP96] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1 *)
+(*  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   :    5 (   1 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments : *)
+(* -------------------------------------------------------------------------- *)
+(* ----Sholander's 2-basis for distributive lattices: *)
+(* ----Denial of the conclusion: *)
+theorem prove_absorbtion_dual:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall join:\forall _:Univ.\forall _:Univ.Univ.
+\forall meet:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet X (join Y Z)) (join (meet Z X) (meet Y X)).
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join a (meet a b)) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LAT033-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LAT033-1.p.ma
new file mode 100644 (file)
index 0000000..de8d777
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LAT033-1.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/LAT033-1".
+include "logic/equality.ma".
+(* Inclusion of: LAT033-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT033-1 : TPTP v3.1.1. Bugfixed v2.5.0. *)
+(*  Domain   : Lattice Theory *)
+(*  Problem  : Idempotency of join *)
+(*  Version  : [McC88] (equality) axioms. *)
+(*  English  : *)
+(*  Refs     : [DeN00] DeNivelle (2000), Email to G. Sutcliffe *)
+(*             [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+(*  Source   : [DeN00] *)
+(*  Names    : idemp_of_join [DeN00] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.5.0 *)
+(*  Syntax   : Number of clauses     :    7 (   0 non-Horn;   7 unit;   1 RR) *)
+(*             Number of atoms       :    7 (   7 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   :   14 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v2.5.0 - Used axioms without the conjecture *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include lattice theory axioms *)
+(* include('Axioms/LAT001-0.ax'). *)
+(* -------------------------------------------------------------------------- *)
+theorem idempotence_of_join:
+ \forall Univ:Set.
+\forall join:\forall _:Univ.\forall _:Univ.Univ.
+\forall meet:\forall _:Univ.\forall _:Univ.Univ.
+\forall xx:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (join X Y) (join Y X).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (meet X Y) (meet Y X).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (join X (meet X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join xx xx) xx
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LAT034-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LAT034-1.p.ma
new file mode 100644 (file)
index 0000000..098aff3
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LAT034-1.p.ma
@@ -0,0 +1,46 @@
+set "baseuri" "cic:/matita/TPTP/LAT034-1".
+include "logic/equality.ma".
+(* Inclusion of: LAT034-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT034-1 : TPTP v3.1.1. Bugfixed v2.5.0. *)
+(*  Domain   : Lattice Theory *)
+(*  Problem  : Idempotency of meet *)
+(*  Version  : [McC88] (equality) axioms. *)
+(*  English  : *)
+(*  Refs     : [DeN00] DeNivelle (2000), Email to G. Sutcliffe *)
+(*             [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+(*  Source   : [DeN00] *)
+(*  Names    : idemp_of_meet [DeN00] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.5.0 *)
+(*  Syntax   : Number of clauses     :    7 (   0 non-Horn;   7 unit;   1 RR) *)
+(*             Number of atoms       :    7 (   7 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   :   14 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(*  Bugfixes : v2.5.0 - Used axioms without the conjecture *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include lattice theory axioms *)
+(* include('Axioms/LAT001-0.ax'). *)
+(* -------------------------------------------------------------------------- *)
+theorem idempotence_of_meet:
+ \forall Univ:Set.
+\forall join:\forall _:Univ.\forall _:Univ.Univ.
+\forall meet:\forall _:Univ.\forall _:Univ.Univ.
+\forall xx:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (join X Y) (join Y X).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (meet X Y) (meet Y X).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (join X (meet X Y)) X.
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (meet xx xx) xx
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LAT039-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LAT039-1.p.ma
new file mode 100644 (file)
index 0000000..d9727fe
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LAT039-1.p.ma
@@ -0,0 +1,77 @@
+set "baseuri" "cic:/matita/TPTP/LAT039-1".
+include "logic/equality.ma".
+(* Inclusion of: LAT039-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT039-1 : TPTP v3.1.1. Released v2.4.0. *)
+(*  Domain   : Lattice Theory *)
+(*  Problem  : Every distributive lattice is modular *)
+(*  Version  : [McC88] (equality) axioms. *)
+(*             Theorem formulation : Modularity is expressed by:  *)
+(*             x <= y -> x v (y & z) = y & (x v z) *)
+(*  English  : *)
+(*  Refs     : [DeN00] DeNivelle (2000), Email to G. Sutcliffe *)
+(*             [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+(*  Source   : [DeN00] *)
+(*  Names    : lattice-mod-2 [DeN00] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.4.0 *)
+(*  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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   22 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include lattice theory axioms *)
+(* Inclusion of: Axioms/LAT001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT001-0 : TPTP v3.1.1. 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 literals   :    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  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem rhs:
+ \forall Univ:Set.
+\forall join:\forall _:Univ.\forall _:Univ.Univ.
+\forall meet:\forall _:Univ.\forall _:Univ.Univ.
+\forall xx:Univ.
+\forall yy:Univ.
+\forall zz:Univ.
+\forall H0:eq Univ (join xx yy) yy.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet X (join Y Z)) (join (meet X Y) (meet X Z)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join X (meet Y Z)) (meet (join X Y) (join X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (join X Y) (join Y X).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (meet X Y) (meet Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (join X (meet X Y)) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.
+\forall H9:\forall X:Univ.eq Univ (join X X) X.
+\forall H10:\forall X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet yy (join xx zz))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LAT039-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/LAT039-2.p.ma
new file mode 100644 (file)
index 0000000..17b66a7
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LAT039-2.p.ma
@@ -0,0 +1,76 @@
+set "baseuri" "cic:/matita/TPTP/LAT039-2".
+include "logic/equality.ma".
+(* Inclusion of: LAT039-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT039-2 : TPTP v3.1.1. Released v2.4.0. *)
+(*  Domain   : Lattice Theory *)
+(*  Problem  : Every distributive lattice is modular *)
+(*  Version  : [McC88] (equality) axioms. *)
+(*  English  : Theorem formulation : Modularity is expressed by:  *)
+(*             x <= y -> x v (y & z) = (x v y) & (x v z) *)
+(*  Refs     : [DeN00] DeNivelle (2000), Email to G. Sutcliffe *)
+(*             [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+(*  Source   : [DeN00] *)
+(*  Names    : lattice-mod-3 [DeN00] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.4.0 *)
+(*  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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   22 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include lattice theory axioms *)
+(* Inclusion of: Axioms/LAT001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT001-0 : TPTP v3.1.1. 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 literals   :    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  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem rhs:
+ \forall Univ:Set.
+\forall join:\forall _:Univ.\forall _:Univ.Univ.
+\forall meet:\forall _:Univ.\forall _:Univ.Univ.
+\forall xx:Univ.
+\forall yy:Univ.
+\forall zz:Univ.
+\forall H0:eq Univ (join xx yy) yy.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet X (join Y Z)) (join (meet X Y) (meet X Z)).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join X (meet Y Z)) (meet (join X Y) (join X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (join X Y) (join Y X).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (meet X Y) (meet Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (join X (meet X Y)) X.
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.
+\forall H9:\forall X:Univ.eq Univ (join X X) X.
+\forall H10:\forall X:Univ.eq Univ (meet X X) X.eq Univ (join xx (meet yy zz)) (meet (join xx yy) (join xx zz))
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LAT040-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LAT040-1.p.ma
new file mode 100644 (file)
index 0000000..b377525
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LAT040-1.p.ma
@@ -0,0 +1,77 @@
+set "baseuri" "cic:/matita/TPTP/LAT040-1".
+include "logic/equality.ma".
+(* Inclusion of: LAT040-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT040-1 : TPTP v3.1.1. Released v2.4.0. *)
+(*  Domain   : Lattice Theory *)
+(*  Problem  : Another simplification rule for distributive lattices *)
+(*  Version  : [McC88] (equality) axioms. *)
+(*  English  : In every distributive lattice the simplification rule holds: *)
+(*             forall x, y, z: (x v y = x v z, x & y = x & z -> y = z ). *)
+(*  Refs     : [DeN00] DeNivelle (2000), Email to G. Sutcliffe *)
+(*             [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+(*  Source   : [DeN00] *)
+(*  Names    : lattice-simpl [DeN00] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.4.0 *)
+(*  Syntax   : Number of clauses     :   13 (   0 non-Horn;  13 unit;   3 RR) *)
+(*             Number of atoms       :   13 (  13 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   :   22 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include lattice theory axioms *)
+(* Inclusion of: Axioms/LAT001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT001-0 : TPTP v3.1.1. 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 literals   :    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  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem rhs:
+ \forall Univ:Set.
+\forall join:\forall _:Univ.\forall _:Univ.Univ.
+\forall meet:\forall _:Univ.\forall _:Univ.Univ.
+\forall xx:Univ.
+\forall yy:Univ.
+\forall zz:Univ.
+\forall H0:eq Univ (meet xx yy) (meet xx zz).
+\forall H1:eq Univ (join xx yy) (join xx zz).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet X (join Y Z)) (join (meet X Y) (meet X Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join X (meet Y Z)) (meet (join X Y) (join X Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (join X Y) (join Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (meet X Y) (meet Y X).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (join X (meet X Y)) X.
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.
+\forall H10:\forall X:Univ.eq Univ (join X X) X.
+\forall H11:\forall X:Univ.eq Univ (meet X X) X.eq Univ yy zz
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LAT045-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LAT045-1.p.ma
new file mode 100644 (file)
index 0000000..6c05f2e
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LAT045-1.p.ma
@@ -0,0 +1,84 @@
+set "baseuri" "cic:/matita/TPTP/LAT045-1".
+include "logic/equality.ma".
+(* Inclusion of: LAT045-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT045-1 : TPTP v3.1.1. Released v2.5.0. *)
+(*  Domain   : Lattice Theory *)
+(*  Problem  : Lattice orthomodular law from modular lattice *)
+(*  Version  : [McC88] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [McC88] McCune (1988), Challenge Equality Problems in Lattice  *)
+(*           : [RW01]  Rose & Wilkinson (2001), Application of Model Search *)
+(*  Source   : [RW01] *)
+(*  Names    : eqp-f.in [RW01] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.5.0 *)
+(*  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    :    7 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :   26 (   2 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include lattice axioms  *)
+(* Inclusion of: Axioms/LAT001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LAT001-0 : TPTP v3.1.1. 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 literals   :    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  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Compatibility (6) *)
+(* ----Invertability (5) *)
+(* ----Modular law (7) *)
+(* ----Denial of orthomodular law (8) *)
+theorem prove_orthomodular_law:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall complement:\forall _:Univ.Univ.
+\forall join:\forall _:Univ.\forall _:Univ.Univ.
+\forall meet:\forall _:Univ.\forall _:Univ.Univ.
+\forall n0:Univ.
+\forall n1:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join X (meet Y (join X Z))) (meet (join X Y) (join X Z)).
+\forall H1:\forall X:Univ.eq Univ (complement (complement X)) X.
+\forall H2:\forall X:Univ.eq Univ (meet (complement X) X) n0.
+\forall H3:\forall X:Univ.eq Univ (join (complement X) X) n1.
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (complement (meet X Y)) (join (complement X) (complement Y)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (complement (join X Y)) (meet (complement X) (complement Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (join X Y) (join Y X).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (meet X Y) (meet Y X).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (join X (meet X Y)) X.
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.
+\forall H12:\forall X:Univ.eq Univ (join X X) X.
+\forall H13:\forall X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement a) (join a b))) (join a b)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL110-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL110-2.p.ma
new file mode 100644 (file)
index 0000000..d9a5f5c
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL110-2.p.ma
@@ -0,0 +1,71 @@
+set "baseuri" "cic:/matita/TPTP/LCL110-2".
+include "logic/equality.ma".
+(* Inclusion of: LCL110-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL110-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Many valued sentential) *)
+(*  Problem  : MV-24 depends on the Meredith system *)
+(*  Version  : [LW92] axioms. *)
+(*             Theorem formulation : Wajsberg algebra formulation *)
+(*  English  : An axiomatisation of the many valued sentential calculus  *)
+(*             is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg presented  *)
+(*             an equality axiomatisation. Show that MV-24 depends on the  *)
+(*             Wajsberg axiomatisation. *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*           : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
+(*  Source   : [LW92] *)
+(*  Names    : MV1.1 [LW92] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_mv_24:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not (not x)) x) truth
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL112-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL112-2.p.ma
new file mode 100644 (file)
index 0000000..76e8e97
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL112-2.p.ma
@@ -0,0 +1,72 @@
+set "baseuri" "cic:/matita/TPTP/LCL112-2".
+include "logic/equality.ma".
+(* Inclusion of: LCL112-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL112-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Many valued sentential) *)
+(*  Problem  : MV-29 depends on the Meredith system *)
+(*  Version  : [McC92] axioms. *)
+(*             Theorem formulation : Wajsberg algebra formulation *)
+(*  English  : An axiomatisation of the many valued sentential calculus  *)
+(*             is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg presented  *)
+(*             an equality axiomatisation. Show that MV-29 depends on the  *)
+(*             Wajsberg axiomatisation. *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*           : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
+(*           : [McC92] McCune (1992), Email to G. Sutcliffe *)
+(*  Source   : [McC92] *)
+(*  Names    : MV1.2 [LW92] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_mv_29:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (not (not x))) truth
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL113-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL113-2.p.ma
new file mode 100644 (file)
index 0000000..6727632
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL113-2.p.ma
@@ -0,0 +1,71 @@
+set "baseuri" "cic:/matita/TPTP/LCL113-2".
+include "logic/equality.ma".
+(* Inclusion of: LCL113-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL113-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Many valued sentential) *)
+(*  Problem  : MV-33 depends on the Meredith system *)
+(*  Version  : [TPTP] axioms. *)
+(*             Theorem formulation : Wajsberg algebra formulation *)
+(*  English  : An axiomatisation of the many valued sentential calculus  *)
+(*             is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg presented  *)
+(*             an equality axiomatisation. Show that MV-33 depends on the  *)
+(*             Wajsberg axiomatisation. *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_mv_33:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies (not x) y) (implies (not y) x)) truth
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL114-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL114-2.p.ma
new file mode 100644 (file)
index 0000000..a92adbd
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL114-2.p.ma
@@ -0,0 +1,72 @@
+set "baseuri" "cic:/matita/TPTP/LCL114-2".
+include "logic/equality.ma".
+(* Inclusion of: LCL114-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL114-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Many valued sentential) *)
+(*  Problem  : MV-36 depends on the Meredith system *)
+(*  Version  : [LW92] axioms. *)
+(*             Theorem formulation : Wajsberg algebra formulation *)
+(*  English  : An axiomatisation of the many valued sentential calculus  *)
+(*             is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg presented  *)
+(*             an equality axiomatisation. Show that MV-36 depends on the  *)
+(*             Wajsberg axiomatisation. *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*           : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
+(*  Source   : [LW92] *)
+(*  Names    : MV3 [LW92] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_mv_36:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (implies x y) (implies (not y) (not x))) truth
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL115-2.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL115-2.p.ma
new file mode 100644 (file)
index 0000000..38a627d
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL115-2.p.ma
@@ -0,0 +1,71 @@
+set "baseuri" "cic:/matita/TPTP/LCL115-2".
+include "logic/equality.ma".
+(* Inclusion of: LCL115-2.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL115-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Many valued sentential) *)
+(*  Problem  : MV-39 depends on the Meredith system *)
+(*  Version  : [TPTP] axioms. *)
+(*             Theorem formulation : Wajsberg algebra formulation *)
+(*  English  : An axiomatisation of the many valued sentential calculus  *)
+(*             is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg presented  *)
+(*             an equality axiomatisation. Show that MV-39 depends on the  *)
+(*             Wajsberg axiomatisation. *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_mv_39:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not (implies a b)) (not b)) truth
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL132-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL132-1.p.ma
new file mode 100644 (file)
index 0000000..07a4b25
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL132-1.p.ma
@@ -0,0 +1,66 @@
+set "baseuri" "cic:/matita/TPTP/LCL132-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL132-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL132-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : A lemma in Wajsberg algebras *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : Lemma 1 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_lemma:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x x) truth
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL133-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL133-1.p.ma
new file mode 100644 (file)
index 0000000..56c0f69
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL133-1.p.ma
@@ -0,0 +1,68 @@
+set "baseuri" "cic:/matita/TPTP/LCL133-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL133-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL133-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : A lemma in Wajsberg algebras *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : Lemma 2 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   10 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_lemma:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies X Y) (implies Y X).
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H4:\forall X:Univ.eq Univ (implies truth X) X.eq Univ x y
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL134-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL134-1.p.ma
new file mode 100644 (file)
index 0000000..cd72ff7
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL134-1.p.ma
@@ -0,0 +1,66 @@
+set "baseuri" "cic:/matita/TPTP/LCL134-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL134-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL134-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : A lemma in Wajsberg algebras *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : Lemma 3 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_lemma:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x truth) truth
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL135-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL135-1.p.ma
new file mode 100644 (file)
index 0000000..828dfc8
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL135-1.p.ma
@@ -0,0 +1,71 @@
+set "baseuri" "cic:/matita/TPTP/LCL135-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL135-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL135-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : A lemma in Wajsberg algebras *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  : An axiomatisation of the many valued sentential calculus  *)
+(*             is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg provided  *)
+(*             a different axiomatisation. Show that MV-1 depends on the  *)
+(*             Wajsberg system. *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [Bon91] *)
+(*  Names    : Lemma 4 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_lemma:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (implies y x)) truth
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL139-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL139-1.p.ma
new file mode 100644 (file)
index 0000000..addf036
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL139-1.p.ma
@@ -0,0 +1,66 @@
+set "baseuri" "cic:/matita/TPTP/LCL139-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL139-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL139-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : A lemma in Wajsberg algebras *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : Lemma 8 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_lemma:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies x (not truth)) (not x)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL140-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL140-1.p.ma
new file mode 100644 (file)
index 0000000..47e7f8f
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL140-1.p.ma
@@ -0,0 +1,66 @@
+set "baseuri" "cic:/matita/TPTP/LCL140-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL140-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL140-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : A lemma in Wajsberg algebras *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : Lemma 9 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_lemma:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (not (not x)) x
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL141-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL141-1.p.ma
new file mode 100644 (file)
index 0000000..8e45dc5
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL141-1.p.ma
@@ -0,0 +1,71 @@
+set "baseuri" "cic:/matita/TPTP/LCL141-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL141-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL141-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : A lemma in Wajsberg algebras *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  : An axiomatisation of the many valued sentential calculus  *)
+(*             is {MV-1,MV-2,MV-3,MV-5} by Meredith. Wajsberg provided  *)
+(*             a different axiomatisation. Show that MV-5 depends on the  *)
+(*             Wajsberg system. *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [Bon91] *)
+(*  Names    : Lemma 10 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_wajsberg_lemma:
+ \forall Univ:Set.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H3:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (implies (not x) (not y)) (implies y x)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL153-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL153-1.p.ma
new file mode 100644 (file)
index 0000000..e09864d
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL153-1.p.ma
@@ -0,0 +1,136 @@
+set "baseuri" "cic:/matita/TPTP/LCL153-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL153-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL153-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : The 1st alternative Wajsberg algebra axiom *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : W' axiom 1 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 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    :    9 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   33 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra and and or definitions  *)
+(* Inclusion of: Axioms/LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra AND and OR definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   0 RR) *)
+(*             Number of literals   :    6 (   6 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    4 (   0 constant; 1-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   3 average) *)
+(*  Comments : Requires LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of or and and, which are AC  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Alternative Wajsberg algebra definitions  *)
+(* Inclusion of: Axioms/LCL002-1.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL002-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Alternative Wajsberg algebra definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   1 RR) *)
+(*             Number of literals   :    6 (   6 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  :   11 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments : Requires LCL001-0.ax LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of and_star and xor, where and_star is AC and xor is C  *)
+(* ---I guess the next two can be derived from the AC of and *)
+(* ----Definition of false in terms of truth  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_alternative_wajsberg_axiom:
+ \forall Univ:Set.
+\forall myand:\forall _:Univ.\forall _:Univ.Univ.
+\forall and_star:\forall _:Univ.\forall _:Univ.Univ.
+\forall falsehood:Univ.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall or:\forall _:Univ.\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall xor:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (not truth) falsehood.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (and_star Y X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (not (or (not X) (not Y))).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (xor Y X).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (or (myand X (not Y)) (myand (not X) Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (myand Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (myand (myand X Y) Z) (myand X (myand Y Z)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (not (or (not X) (not Y))).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (or Y X).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (or (or X Y) Z) (or X (or Y Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (implies (not X) Y).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (not x) (xor x truth)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL154-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL154-1.p.ma
new file mode 100644 (file)
index 0000000..6a7895e
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL154-1.p.ma
@@ -0,0 +1,136 @@
+set "baseuri" "cic:/matita/TPTP/LCL154-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL154-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL154-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : The 2nd alternative Wajsberg algebra axiom *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : W' axiom 2 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 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    :    9 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   33 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra and and or definitions  *)
+(* Inclusion of: Axioms/LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra AND and OR definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   0 RR) *)
+(*             Number of literals   :    6 (   6 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    4 (   0 constant; 1-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   3 average) *)
+(*  Comments : Requires LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of or and and, which are AC  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Alternative Wajsberg algebra definitions  *)
+(* Inclusion of: Axioms/LCL002-1.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL002-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Alternative Wajsberg algebra definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   1 RR) *)
+(*             Number of literals   :    6 (   6 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  :   11 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments : Requires LCL001-0.ax LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of and_star and xor, where and_star is AC and xor is C  *)
+(* ---I guess the next two can be derived from the AC of and *)
+(* ----Definition of false in terms of truth  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_alternative_wajsberg_axiom:
+ \forall Univ:Set.
+\forall myand:\forall _:Univ.\forall _:Univ.Univ.
+\forall and_star:\forall _:Univ.\forall _:Univ.Univ.
+\forall falsehood:Univ.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall or:\forall _:Univ.\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall xor:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (not truth) falsehood.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (and_star Y X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (not (or (not X) (not Y))).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (xor Y X).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (or (myand X (not Y)) (myand (not X) Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (myand Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (myand (myand X Y) Z) (myand X (myand Y Z)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (not (or (not X) (not Y))).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (or Y X).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (or (or X Y) Z) (or X (or Y Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (implies (not X) Y).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (xor x falsehood) x
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL155-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL155-1.p.ma
new file mode 100644 (file)
index 0000000..9cc3783
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL155-1.p.ma
@@ -0,0 +1,136 @@
+set "baseuri" "cic:/matita/TPTP/LCL155-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL155-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL155-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : The 3rd alternative Wajsberg algebra axiom *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : W' axiom 3 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 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    :    9 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   33 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra and and or definitions  *)
+(* Inclusion of: Axioms/LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra AND and OR definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   0 RR) *)
+(*             Number of literals   :    6 (   6 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    4 (   0 constant; 1-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   3 average) *)
+(*  Comments : Requires LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of or and and, which are AC  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Alternative Wajsberg algebra definitions  *)
+(* Inclusion of: Axioms/LCL002-1.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL002-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Alternative Wajsberg algebra definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   1 RR) *)
+(*             Number of literals   :    6 (   6 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  :   11 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments : Requires LCL001-0.ax LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of and_star and xor, where and_star is AC and xor is C  *)
+(* ---I guess the next two can be derived from the AC of and *)
+(* ----Definition of false in terms of truth  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_alternative_wajsberg_axiom:
+ \forall Univ:Set.
+\forall myand:\forall _:Univ.\forall _:Univ.Univ.
+\forall and_star:\forall _:Univ.\forall _:Univ.Univ.
+\forall falsehood:Univ.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall or:\forall _:Univ.\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall xor:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (not truth) falsehood.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (and_star Y X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (not (or (not X) (not Y))).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (xor Y X).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (or (myand X (not Y)) (myand (not X) Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (myand Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (myand (myand X Y) Z) (myand X (myand Y Z)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (not (or (not X) (not Y))).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (or Y X).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (or (or X Y) Z) (or X (or Y Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (implies (not X) Y).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (xor x x) falsehood
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL156-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL156-1.p.ma
new file mode 100644 (file)
index 0000000..a71e127
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL156-1.p.ma
@@ -0,0 +1,136 @@
+set "baseuri" "cic:/matita/TPTP/LCL156-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL156-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL156-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : The 4th alternative Wajsberg algebra axiom *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : W' axiom 4 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 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    :    9 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   33 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra and and or definitions  *)
+(* Inclusion of: Axioms/LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra AND and OR definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   0 RR) *)
+(*             Number of literals   :    6 (   6 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    4 (   0 constant; 1-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   3 average) *)
+(*  Comments : Requires LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of or and and, which are AC  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Alternative Wajsberg algebra definitions  *)
+(* Inclusion of: Axioms/LCL002-1.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL002-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Alternative Wajsberg algebra definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   1 RR) *)
+(*             Number of literals   :    6 (   6 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  :   11 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments : Requires LCL001-0.ax LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of and_star and xor, where and_star is AC and xor is C  *)
+(* ---I guess the next two can be derived from the AC of and *)
+(* ----Definition of false in terms of truth  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_alternative_wajsberg_axiom:
+ \forall Univ:Set.
+\forall myand:\forall _:Univ.\forall _:Univ.Univ.
+\forall and_star:\forall _:Univ.\forall _:Univ.Univ.
+\forall falsehood:Univ.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall or:\forall _:Univ.\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall xor:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (not truth) falsehood.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (and_star Y X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (not (or (not X) (not Y))).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (xor Y X).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (or (myand X (not Y)) (myand (not X) Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (myand Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (myand (myand X Y) Z) (myand X (myand Y Z)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (not (or (not X) (not Y))).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (or Y X).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (or (or X Y) Z) (or X (or Y Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (implies (not X) Y).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (and_star x truth) x
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL157-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL157-1.p.ma
new file mode 100644 (file)
index 0000000..04ec616
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL157-1.p.ma
@@ -0,0 +1,136 @@
+set "baseuri" "cic:/matita/TPTP/LCL157-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL157-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL157-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : The 5th alternative Wajsberg algebra axiom *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : W' axiom 5 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 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    :    9 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   33 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra and and or definitions  *)
+(* Inclusion of: Axioms/LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra AND and OR definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   0 RR) *)
+(*             Number of literals   :    6 (   6 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    4 (   0 constant; 1-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   3 average) *)
+(*  Comments : Requires LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of or and and, which are AC  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Alternative Wajsberg algebra definitions  *)
+(* Inclusion of: Axioms/LCL002-1.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL002-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Alternative Wajsberg algebra definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   1 RR) *)
+(*             Number of literals   :    6 (   6 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  :   11 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments : Requires LCL001-0.ax LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of and_star and xor, where and_star is AC and xor is C  *)
+(* ---I guess the next two can be derived from the AC of and *)
+(* ----Definition of false in terms of truth  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_alternative_wajsberg_axiom:
+ \forall Univ:Set.
+\forall myand:\forall _:Univ.\forall _:Univ.Univ.
+\forall and_star:\forall _:Univ.\forall _:Univ.Univ.
+\forall falsehood:Univ.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall or:\forall _:Univ.\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall xor:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (not truth) falsehood.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (and_star Y X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (not (or (not X) (not Y))).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (xor Y X).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (or (myand X (not Y)) (myand (not X) Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (myand Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (myand (myand X Y) Z) (myand X (myand Y Z)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (not (or (not X) (not Y))).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (or Y X).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (or (or X Y) Z) (or X (or Y Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (implies (not X) Y).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (and_star x falsehood) falsehood
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL158-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL158-1.p.ma
new file mode 100644 (file)
index 0000000..445fca8
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL158-1.p.ma
@@ -0,0 +1,136 @@
+set "baseuri" "cic:/matita/TPTP/LCL158-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL158-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL158-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : The 6th alternative Wajsberg algebra axiom *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : W' axiom 6 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 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    :    9 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   33 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*           : [MW92]  McCune & Wos (1992), Experiments in Automated Deductio *)
+(*  Source   : [MW92] *)
+(*  Names    : MV Sentential Calculus [MW92] *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    4 (   0 non-Horn;   4 unit;   0 RR) *)
+(*             Number of literals   :    4 (   4 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  :    8 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Wajsberg algebra and and or definitions  *)
+(* Inclusion of: Axioms/LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL001-2 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Wajsberg algebra AND and OR definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   0 RR) *)
+(*             Number of literals   :    6 (   6 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    4 (   0 constant; 1-2 arity) *)
+(*             Number of variables  :   14 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   3 average) *)
+(*  Comments : Requires LCL001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of or and and, which are AC  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Alternative Wajsberg algebra definitions  *)
+(* Inclusion of: Axioms/LCL002-1.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL002-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Alternative Wajsberg algebra definitions *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    6 (   0 non-Horn;   6 unit;   1 RR) *)
+(*             Number of literals   :    6 (   6 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  :   11 (   0 singleton) *)
+(*             Maximal term depth   :    4 (   2 average) *)
+(*  Comments : Requires LCL001-0.ax LCL001-2.ax *)
+(* -------------------------------------------------------------------------- *)
+(* ----Definitions of and_star and xor, where and_star is AC and xor is C  *)
+(* ---I guess the next two can be derived from the AC of and *)
+(* ----Definition of false in terms of truth  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_alternative_wajsberg_axiom:
+ \forall Univ:Set.
+\forall myand:\forall _:Univ.\forall _:Univ.Univ.
+\forall and_star:\forall _:Univ.\forall _:Univ.Univ.
+\forall falsehood:Univ.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall or:\forall _:Univ.\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall xor:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (not truth) falsehood.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (and_star Y X).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (not (or (not X) (not Y))).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (xor Y X).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (or (myand X (not Y)) (myand (not X) Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (myand Y X).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (myand (myand X Y) Z) (myand X (myand Y Z)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (myand X Y) (not (or (not X) (not Y))).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (or Y X).
+\forall H10:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (or (or X Y) Z) (or X (or Y Z)).
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (or X Y) (implies (not X) Y).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies (not X) (not Y)) (implies Y X)) truth.
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (implies (implies X Y) Y) (implies (implies Y X) X).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (implies (implies X Y) (implies (implies Y Z) (implies X Z))) truth.
+\forall H15:\forall X:Univ.eq Univ (implies truth X) X.eq Univ (and_star (xor truth x) x) falsehood
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL161-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL161-1.p.ma
new file mode 100644 (file)
index 0000000..7504ce5
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL161-1.p.ma
@@ -0,0 +1,85 @@
+set "baseuri" "cic:/matita/TPTP/LCL161-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL161-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL161-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : The 1st Wajsberg algebra axiom, from the alternative axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : W axiom 1 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   14 (   0 non-Horn;  14 unit;   2 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    :    7 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :   19 (   1 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Alternative Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL002-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL002-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Alternative Wajsberg algebra axioms *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   10 (   1 singleton) *)
+(*             Maximal term depth   :    5 (   2 average) *)
+(*  Comments : To be used in conjunction with the LAT003 alternative  *)
+(*             Wajsberg algebra definitions. *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include some Alternative Wajsberg algebra definitions  *)
+(*  include('Axioms/LCL002-1.ax'). *)
+(* ----Definition that and_star is AC and xor is C  *)
+(* ----Definition of false in terms of true  *)
+(* ----Include the definition of implies in terms of xor and and_star  *)
+theorem prove_wajsberg_axiom:
+ \forall Univ:Set.
+\forall and_star:\forall _:Univ.\forall _:Univ.Univ.
+\forall falsehood:Univ.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall xor:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies X Y) (xor truth (and_star X (xor truth Y))).
+\forall H1:eq Univ (not truth) falsehood.
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (and_star Y X).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (xor Y X).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (and_star (xor (and_star (xor truth X) Y) truth) Y) (and_star (xor (and_star (xor truth Y) X) truth) X).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (xor X (xor truth Y)) (xor (xor X truth) Y).
+\forall H7:\forall X:Univ.eq Univ (and_star (xor truth X) X) falsehood.
+\forall H8:\forall X:Univ.eq Univ (and_star X falsehood) falsehood.
+\forall H9:\forall X:Univ.eq Univ (and_star X truth) X.
+\forall H10:\forall X:Univ.eq Univ (xor X X) falsehood.
+\forall H11:\forall X:Univ.eq Univ (xor X falsehood) X.
+\forall H12:\forall X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies truth x) x
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LCL164-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LCL164-1.p.ma
new file mode 100644 (file)
index 0000000..38d3ab4
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LCL164-1.p.ma
@@ -0,0 +1,86 @@
+set "baseuri" "cic:/matita/TPTP/LCL164-1".
+include "logic/equality.ma".
+(* Inclusion of: LCL164-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL164-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebra) *)
+(*  Problem  : The 4th Wajsberg algebra axiom, from the alternative axioms *)
+(*  Version  : [Bon91] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    : W axiom 4 [Bon91] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.38 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   14 (   0 non-Horn;  14 unit;   2 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    :    8 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :   19 (   1 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Alternative Wajsberg algebra axioms  *)
+(* Inclusion of: Axioms/LCL002-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LCL002-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Logic Calculi (Wajsberg Algebras) *)
+(*  Axioms   : Alternative Wajsberg algebra axioms *)
+(*  Version  : [AB90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [FRT84] Font et al. (1984), Wajsberg Algebras *)
+(*           : [AB90]  Anantharaman & Bonacina (1990), An Application of the  *)
+(*           : [Bon91] Bonacina (1991), Problems in Lukasiewicz Logic *)
+(*  Source   : [Bon91] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+(*             Number of literals   :    8 (   8 equality) *)
+(*             Maximal clause size  :    1 (   1 average) *)
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors   :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables  :   10 (   1 singleton) *)
+(*             Maximal term depth   :    5 (   2 average) *)
+(*  Comments : To be used in conjunction with the LAT003 alternative  *)
+(*             Wajsberg algebra definitions. *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include some Alternative Wajsberg algebra definitions  *)
+(*  include('Axioms/LCL002-1.ax'). *)
+(* ----Definition that and_star is AC and xor is C  *)
+(* ----Definition of false in terms of true  *)
+(* ----Include the definition of implies in terms of xor and and_star  *)
+theorem prove_wajsberg_axiom:
+ \forall Univ:Set.
+\forall and_star:\forall _:Univ.\forall _:Univ.Univ.
+\forall falsehood:Univ.
+\forall implies:\forall _:Univ.\forall _:Univ.Univ.
+\forall not:\forall _:Univ.Univ.
+\forall truth:Univ.
+\forall x:Univ.
+\forall xor:\forall _:Univ.\forall _:Univ.Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (implies X Y) (xor truth (and_star X (xor truth Y))).
+\forall H1:eq Univ (not truth) falsehood.
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (and_star X Y) (and_star Y X).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (and_star (and_star X Y) Z) (and_star X (and_star Y Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (xor X Y) (xor Y X).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (and_star (xor (and_star (xor truth X) Y) truth) Y) (and_star (xor (and_star (xor truth Y) X) truth) X).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (xor X (xor truth Y)) (xor (xor X truth) Y).
+\forall H7:\forall X:Univ.eq Univ (and_star (xor truth X) X) falsehood.
+\forall H8:\forall X:Univ.eq Univ (and_star X falsehood) falsehood.
+\forall H9:\forall X:Univ.eq Univ (and_star X truth) X.
+\forall H10:\forall X:Univ.eq Univ (xor X X) falsehood.
+\forall H11:\forall X:Univ.eq Univ (xor X falsehood) X.
+\forall H12:\forall X:Univ.eq Univ (not X) (xor X truth).eq Univ (implies (implies (not x) (not y)) (implies y x)) truth
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LDA001-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/LDA001-1.p.ma
new file mode 100644 (file)
index 0000000..d75a6d9
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LDA001-1.p.ma
@@ -0,0 +1,43 @@
+set "baseuri" "cic:/matita/TPTP/LDA001-1".
+include "logic/equality.ma".
+(* Inclusion of: LDA001-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LDA001-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : LD-Algebras *)
+(*  Problem  : Verify 3*2*U = UUU, where U = 2*2 *)
+(*  Version  : [Jec93] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Jec93] Jech (1993), LD-Algebras *)
+(*  Source   : [Jec93] *)
+(*  Names    : Problem 1 [Jec93] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   4 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    :    5 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----A1: x(yz)=xy(xz)  *)
+(* ----3*2*U = U*U*U  *)
+theorem prove_equation:
+ \forall Univ:Set.
+\forall f:\forall _:Univ.\forall _:Univ.Univ.
+\forall n1:Univ.
+\forall n2:Univ.
+\forall n3:Univ.
+\forall u:Univ.
+\forall H0:eq Univ u (f n2 n2).
+\forall H1:eq Univ n3 (f n2 n1).
+\forall H2:eq Univ n2 (f n1 n1).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f (f n3 n2) u) (f (f u u) u)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/LDA007-3.p.ma b/helm/software/matita/tests/TPTP/Veloci/LDA007-3.p.ma
new file mode 100644 (file)
index 0000000..ea26086
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/LDA007-3.p.ma
@@ -0,0 +1,51 @@
+set "baseuri" "cic:/matita/TPTP/LDA007-3".
+include "logic/equality.ma".
+(* Inclusion of: LDA007-3.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : LDA007-3 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : LD-Algebras (Embedding algebras) *)
+(*  Problem  : Let g = cr(t). Show that t(tsg) = tt(ts)(tg)  *)
+(*  Version  : [Jec93] axioms : Incomplete > Reduced & Augmented > Incomplete. *)
+(*  English  :  *)
+(*  Refs     : [Jec93] Jech (1993), LD-Algebras *)
+(*  Source   : [Jec93] *)
+(*  Names    : Problem 8 [Jec93] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 v2.0.0 *)
+(*  Syntax   : Number of clauses     :    7 (   0 non-Horn;   7 unit;   6 RR) *)
+(*             Number of atoms       :    7 (   7 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    9 (   8 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include Embedding algebra axioms  *)
+(*  include('Axioms/LDA001-0.ax'). *)
+(* -------------------------------------------------------------------------- *)
+(* ----t(tsk) = tt(ts)(tk), where k=crit(t)  *)
+theorem prove_equation:
+ \forall Univ:Set.
+\forall f:\forall _:Univ.\forall _:Univ.Univ.
+\forall k:Univ.
+\forall s:Univ.
+\forall t:Univ.
+\forall tk:Univ.
+\forall ts:Univ.
+\forall tsk:Univ.
+\forall tt:Univ.
+\forall tt_ts:Univ.
+\forall H0:eq Univ tsk (f ts k).
+\forall H1:eq Univ tk (f t k).
+\forall H2:eq Univ tt_ts (f tt ts).
+\forall H3:eq Univ ts (f t s).
+\forall H4:eq Univ tt (f t t).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) (f X Z)).eq Univ (f t tsk) (f tt_ts tk)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/RNG007-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/RNG007-4.p.ma
new file mode 100644 (file)
index 0000000..6444719
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/RNG007-4.p.ma
@@ -0,0 +1,90 @@
+set "baseuri" "cic:/matita/TPTP/RNG007-4".
+include "logic/equality.ma".
+(* Inclusion of: RNG007-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : RNG007-4 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Ring Theory *)
+(*  Problem  : In Boolean rings, X is its own inverse *)
+(*  Version  : [Peterson & Stickel, 1981] (equality) axioms. *)
+(*             Theorem formulation : Equality. *)
+(*  English  : Given a ring in which for all x, x * x = x, prove that for  *)
+(*             all x, x + x = additive_identity *)
+(*  Refs     : [PS81]  Peterson & Stickel (1981), Complete Sets of Reductions *)
+(*  Source   : [ANL] *)
+(*  Names    : lemma.ver2.in [ANL] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   16 (   0 non-Horn;  16 unit;   2 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    :    5 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :   26 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include ring theory axioms  *)
+(* Inclusion of: Axioms/RNG002-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : RNG002-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Ring Theory *)
+(*  Axioms   : Ring theory (equality) axioms *)
+(*  Version  : [PS81] (equality) axioms : *)
+(*             Reduced & Augmented > Complete. *)
+(*  English  :  *)
+(*  Refs     : [PS81]  Peterson & Stickel (1981), Complete Sets of Reductions *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :   14 (   0 non-Horn;  14 unit;   1 RR) *)
+(*             Number of literals   :   14 (  14 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  :   25 (   2 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : Not sure if these are complete. I don't know if the reductions *)
+(*             given in [PS81] are suitable for ATP. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Existence of left identity for addition  *)
+(* ----Existence of left additive additive_inverse  *)
+(* ----Distributive property of product over sum  *)
+(* ----Inverse of identity is identity, stupid  *)
+(* ----Inverse of additive_inverse of X is X  *)
+(* ----Behavior of 0 and the multiplication operation  *)
+(* ----Inverse of (x + y) is additive_inverse(x) + additive_inverse(y)  *)
+(* ----x * additive_inverse(y) = additive_inverse (x * y)  *)
+(* ----Associativity of addition  *)
+(* ----Commutativity of addition  *)
+(* ----Associativity of product  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_inverse:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall additive_inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (multiply X X) X.
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (additive_inverse (add X Y)) (add (additive_inverse X) (additive_inverse Y)).
+\forall H7:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+\forall H8:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+\forall H9:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+\forall H10:eq Univ (additive_inverse additive_identity) additive_identity.
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H13:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+\forall H14:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (add a a) additive_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/RNG008-4.p.ma b/helm/software/matita/tests/TPTP/Veloci/RNG008-4.p.ma
new file mode 100644 (file)
index 0000000..f3f5e75
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/RNG008-4.p.ma
@@ -0,0 +1,94 @@
+set "baseuri" "cic:/matita/TPTP/RNG008-4".
+include "logic/equality.ma".
+(* Inclusion of: RNG008-4.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : RNG008-4 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Ring Theory *)
+(*  Problem  : Boolean rings are commutative *)
+(*  Version  : [PS81] (equality) axioms. *)
+(*             Theorem formulation : Equality. *)
+(*  English  : Given a ring in which for all x, x * x = x, prove that for  *)
+(*             all x and y, x * y = y * x. *)
+(*  Refs     : [MOW76] McCharen et al. (1976), Problems and Experiments for a *)
+(*           : [PS81]  Peterson & Stickel (1981), Complete Sets of Reductions *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   17 (   0 non-Horn;  17 unit;   3 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :   26 (   2 singleton) *)
+(*             Maximal term depth    :    3 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include ring theory axioms  *)
+(* Inclusion of: Axioms/RNG002-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : RNG002-0 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Ring Theory *)
+(*  Axioms   : Ring theory (equality) axioms *)
+(*  Version  : [PS81] (equality) axioms : *)
+(*             Reduced & Augmented > Complete. *)
+(*  English  :  *)
+(*  Refs     : [PS81]  Peterson & Stickel (1981), Complete Sets of Reductions *)
+(*  Source   : [ANL] *)
+(*  Names    :  *)
+(*  Status   :  *)
+(*  Syntax   : Number of clauses    :   14 (   0 non-Horn;  14 unit;   1 RR) *)
+(*             Number of literals   :   14 (  14 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  :   25 (   2 singleton) *)
+(*             Maximal term depth   :    3 (   2 average) *)
+(*  Comments : Not sure if these are complete. I don't know if the reductions *)
+(*             given in [PS81] are suitable for ATP. *)
+(* -------------------------------------------------------------------------- *)
+(* ----Existence of left identity for addition  *)
+(* ----Existence of left additive additive_inverse  *)
+(* ----Distributive property of product over sum  *)
+(* ----Inverse of identity is identity, stupid  *)
+(* ----Inverse of additive_inverse of X is X  *)
+(* ----Behavior of 0 and the multiplication operation  *)
+(* ----Inverse of (x + y) is additive_inverse(x) + additive_inverse(y)  *)
+(* ----x * additive_inverse(y) = additive_inverse (x * y)  *)
+(* ----Associativity of addition  *)
+(* ----Commutativity of addition  *)
+(* ----Associativity of product  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_commutativity:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall additive_inverse:\forall _:Univ.Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (multiply a b) c.
+\forall H1:\forall X:Univ.eq Univ (multiply X X) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (additive_inverse (add X Y)) (add (additive_inverse X) (additive_inverse Y)).
+\forall H8:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+\forall H9:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+\forall H10:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+\forall H11:eq Univ (additive_inverse additive_identity) additive_identity.
+\forall H12:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H14:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+\forall H15:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (multiply b a) c
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/RNG011-5.p.ma b/helm/software/matita/tests/TPTP/Veloci/RNG011-5.p.ma
new file mode 100644 (file)
index 0000000..3d08d1b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/RNG011-5.p.ma
@@ -0,0 +1,83 @@
+set "baseuri" "cic:/matita/TPTP/RNG011-5".
+include "logic/equality.ma".
+(* Inclusion of: RNG011-5.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : RNG011-5 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Ring Theory *)
+(*  Problem  : In a right alternative ring (((X,X,Y)*X)*(X,X,Y)) = Add Id *)
+(*  Version  : [Ove90] (equality) axioms : *)
+(*             Incomplete > Augmented > Incomplete. *)
+(*  English  :  *)
+(*  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-10 [Ove90] *)
+(*           : THEOREM EQ-10 [LM93] *)
+(*           : PROBLEM 10 [Zha93] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.0.0 *)
+(*  Syntax   : Number of clauses     :   22 (   0 non-Horn;  22 unit;   2 RR) *)
+(*             Number of atoms       :   22 (  22 equality) *)
+(*             Maximal clause size   :    1 (   1 average) *)
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+(*             Number of functors    :    8 (   3 constant; 0-3 arity) *)
+(*             Number of variables   :   37 (   2 singleton) *)
+(*             Maximal term depth    :    5 (   2 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Commutativity of addition  *)
+(* ----Associativity of addition  *)
+(* ----Additive identity  *)
+(* ----Additive inverse  *)
+(* ----Inverse of identity is identity, stupid  *)
+(* ----Axiom of Overbeek  *)
+(* ----Inverse of (x + y) is additive_inverse(x) + additive_inverse(y),  *)
+(* ----Inverse of additive_inverse of X is X  *)
+(* ----Behavior of 0 and the multiplication operation  *)
+(* ----Axiom of Overbeek  *)
+(* ----x * additive_inverse(y) = additive_inverse (x * y),  *)
+(* ----Distributive property of product over sum  *)
+(* ----Right alternative law  *)
+(* ----Associator  *)
+(* ----Commutator  *)
+(* ----Middle associator identity  *)
+theorem prove_equality:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall additive_inverse:\forall _:Univ.Univ.
+\forall associator:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall commutator:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply (associator X X Y) X) (associator X X Y)) additive_identity.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H5:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).
+\forall H9:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+\forall H10:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+\forall H11:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (additive_inverse (add X Y)) (add (additive_inverse X) (additive_inverse Y)).
+\forall H13:\forall X:Univ.\forall Y:Univ.eq Univ (add X (add (additive_inverse X) Y)) Y.
+\forall H14:eq Univ (additive_inverse additive_identity) additive_identity.
+\forall H15:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+\forall H16:\forall X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
+\forall H17:\forall X:Univ.eq Univ (add additive_identity X) X.
+\forall H18:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H19:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H20:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (multiply (multiply (associator a a b) a) (associator a a b)) additive_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/RNG023-6.p.ma b/helm/software/matita/tests/TPTP/Veloci/RNG023-6.p.ma
new file mode 100644 (file)
index 0000000..d3f15e9
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/RNG023-6.p.ma
@@ -0,0 +1,91 @@
+set "baseuri" "cic:/matita/TPTP/RNG023-6".
+include "logic/equality.ma".
+(* Inclusion of: RNG023-6.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : RNG023-6 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Ring Theory (Alternative) *)
+(*  Problem  : Left alternative *)
+(*  Version  : [Ste87] (equality) axioms. *)
+(*             Theorem formulation : In terms of associators *)
+(*  English  :  *)
+(*  Refs     : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
+(*           : [Ste92] Stevens (1992), Unpublished Note *)
+(*  Source   : [Ste92] *)
+(*  Names    : - [Ste87] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.13 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 (   3 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 v3.1.1. 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 literals   :   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  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_left_alternative:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall additive_inverse:\forall _:Univ.Univ.
+\forall associator:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall commutator:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))).
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).
+\forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H8:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+\forall H9:\forall X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
+\forall H10:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+\forall H11:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+\forall H12:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+\forall H13:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H14:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x x y) additive_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/RNG023-7.p.ma b/helm/software/matita/tests/TPTP/Veloci/RNG023-7.p.ma
new file mode 100644 (file)
index 0000000..e5f87cd
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/RNG023-7.p.ma
@@ -0,0 +1,99 @@
+set "baseuri" "cic:/matita/TPTP/RNG023-7".
+include "logic/equality.ma".
+(* Inclusion of: RNG023-7.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : RNG023-7 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Ring Theory (Alternative) *)
+(*  Problem  : Left alternative *)
+(*  Version  : [Ste87] (equality) axioms : Augmented. *)
+(*             Theorem formulation : In terms of associators *)
+(*  English  :  *)
+(*  Refs     : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
+(*           : [Ste92] Stevens (1992), Unpublished Note *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.13 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    :    8 (   3 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 v3.1.1. 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 literals   :   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  *)
+theorem prove_left_alternative:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall additive_inverse:\forall _:Univ.Univ.
+\forall associator:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall commutator:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) (additive_inverse Z)) (add (additive_inverse (multiply X Z)) (additive_inverse (multiply Y Z))).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (additive_inverse X) (add Y Z)) (add (additive_inverse (multiply X Y)) (additive_inverse (multiply X Z))).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X (additive_inverse Y)) Z) (add (multiply X Z) (additive_inverse (multiply Y Z))).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H15:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+\forall H16:\forall X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
+\forall H17:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+\forall H18:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+\forall H19:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+\forall H20:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H21:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x x y) additive_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/RNG024-6.p.ma b/helm/software/matita/tests/TPTP/Veloci/RNG024-6.p.ma
new file mode 100644 (file)
index 0000000..806f1bd
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/RNG024-6.p.ma
@@ -0,0 +1,91 @@
+set "baseuri" "cic:/matita/TPTP/RNG024-6".
+include "logic/equality.ma".
+(* Inclusion of: RNG024-6.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : RNG024-6 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Ring Theory (Alternative) *)
+(*  Problem  : Right alternative *)
+(*  Version  : [Ste87] (equality) axioms. *)
+(*             Theorem formulation : In terms of associators *)
+(*  English  :  *)
+(*  Refs     : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
+(*           : [Ste92] Stevens (1992), Unpublished Note *)
+(*  Source   : [Ste92] *)
+(*  Names    : - [Ste87] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.1.0, 0.13 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 (   3 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 v3.1.1. 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 literals   :   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  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_right_alternative:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall additive_inverse:\forall _:Univ.Univ.
+\forall associator:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall commutator:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))).
+\forall H2:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)).
+\forall H4:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).
+\forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H8:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+\forall H9:\forall X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
+\forall H10:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+\forall H11:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+\forall H12:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+\forall H13:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H14:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y y) additive_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/RNG024-7.p.ma b/helm/software/matita/tests/TPTP/Veloci/RNG024-7.p.ma
new file mode 100644 (file)
index 0000000..4b53591
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/RNG024-7.p.ma
@@ -0,0 +1,99 @@
+set "baseuri" "cic:/matita/TPTP/RNG024-7".
+include "logic/equality.ma".
+(* Inclusion of: RNG024-7.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : RNG024-7 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Ring Theory (Alternative) *)
+(*  Problem  : Right alternative *)
+(*  Version  : [Ste87] (equality) axioms : Augmented. *)
+(*             Theorem formulation : In terms of associators *)
+(*  English  :  *)
+(*  Refs     : [Ste87] Stevens (1987), Some Experiments in Nonassociative Rin *)
+(*           : [Ste92] Stevens (1992), Unpublished Note *)
+(*  Source   : [TPTP] *)
+(*  Names    :  *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.00 v2.1.0, 0.13 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    :    8 (   3 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 v3.1.1. 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 literals   :   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  *)
+theorem prove_right_alternative:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall additive_identity:Univ.
+\forall additive_inverse:\forall _:Univ.Univ.
+\forall associator:\forall _:Univ.\forall _:Univ.\forall _:Univ.Univ.
+\forall commutator:\forall _:Univ.\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall x:Univ.
+\forall y:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) (additive_inverse Z)) (add (additive_inverse (multiply X Z)) (additive_inverse (multiply Y Z))).
+\forall H1:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (additive_inverse X) (add Y Z)) (add (additive_inverse (multiply X Y)) (additive_inverse (multiply X Z))).
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X (additive_inverse Y)) Z) (add (multiply X Z) (additive_inverse (multiply Y Z))).
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y (additive_inverse Z))) (add (multiply X Y) (additive_inverse (multiply X Z))).
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (multiply X (additive_inverse Y)) (additive_inverse (multiply X Y)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) Y) (additive_inverse (multiply X Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (additive_inverse X) (additive_inverse Y)) (multiply X Y).
+\forall H7:\forall X:Univ.\forall Y:Univ.eq Univ (commutator X Y) (add (multiply Y X) (additive_inverse (multiply X Y))).
+\forall H8:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (associator X Y Z) (add (multiply (multiply X Y) Z) (additive_inverse (multiply X (multiply Y Z)))).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X X) Y) (multiply X (multiply X Y)).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (multiply (multiply X Y) Y) (multiply X (multiply Y Y)).
+\forall H11:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add X (add Y Z)) (add (add X Y) Z).
+\forall H12:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).
+\forall H13:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (add X Y) Z) (add (multiply X Z) (multiply Y Z)).
+\forall H14:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+\forall H15:\forall X:Univ.eq Univ (additive_inverse (additive_inverse X)) X.
+\forall H16:\forall X:Univ.eq Univ (add X (additive_inverse X)) additive_identity.
+\forall H17:\forall X:Univ.eq Univ (add (additive_inverse X) X) additive_identity.
+\forall H18:\forall X:Univ.eq Univ (multiply X additive_identity) additive_identity.
+\forall H19:\forall X:Univ.eq Univ (multiply additive_identity X) additive_identity.
+\forall H20:\forall X:Univ.eq Univ (add X additive_identity) X.
+\forall H21:\forall X:Univ.eq Univ (add additive_identity X) X.eq Univ (associator x y y) additive_identity
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/ROB002-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/ROB002-1.p.ma
new file mode 100644 (file)
index 0000000..26ad559
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/ROB002-1.p.ma
@@ -0,0 +1,66 @@
+set "baseuri" "cic:/matita/TPTP/ROB002-1".
+include "logic/equality.ma".
+(* Inclusion of: ROB002-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : ROB002-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Robbins Algebra *)
+(*  Problem  : --X = X => Boolean *)
+(*  Version  : [Win90] (equality) axioms. *)
+(*  English  : If --X = X then the algebra is Boolean. *)
+(*  Refs     : [HMT71] Henkin et al. (1971), Cylindrical Algebras *)
+(*           : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+(*  Source   : [Win90] *)
+(*  Names    : Lemma 2.1 [Win90] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.11 v2.2.0, 0.14 v2.1.0, 0.13 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    :    4 (   2 constant; 0-2 arity) *)
+(*             Number of variables   :    8 (   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 v3.1.1. 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 literals   :    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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_huntingtons_axiom:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall negate:\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.eq Univ (negate (negate X)) X.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H3:\forall X:Univ.\forall 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
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/ROB009-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/ROB009-1.p.ma
new file mode 100644 (file)
index 0000000..5820893
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/ROB009-1.p.ma
@@ -0,0 +1,65 @@
+set "baseuri" "cic:/matita/TPTP/ROB009-1".
+include "logic/equality.ma".
+(* Inclusion of: ROB009-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : ROB009-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Robbins Algebra *)
+(*  Problem  : If -(a + -(b + c)) = -(b + -(a + c)) then a = b *)
+(*  Version  : [Win90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+(*  Source   : [Win90] *)
+(*  Names    : Lemma 3.2 [Win90] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v2.2.1, 0.22 v2.2.0, 0.14 v2.1.0, 0.50 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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include axioms for Robbins algebra  *)
+(* Inclusion of: Axioms/ROB001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : ROB001-0 : TPTP v3.1.1. 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 literals   :    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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_result:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall negate:\forall _:Univ.Univ.
+\forall H0:eq Univ (negate (add a (negate (add b c)))) (negate (add b (negate (add a c)))).
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ a b
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/ROB010-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/ROB010-1.p.ma
new file mode 100644 (file)
index 0000000..95c6389
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/ROB010-1.p.ma
@@ -0,0 +1,67 @@
+set "baseuri" "cic:/matita/TPTP/ROB010-1".
+include "logic/equality.ma".
+(* Inclusion of: ROB010-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : ROB010-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Robbins Algebra *)
+(*  Problem  : If -(a + -b) = c then -(c + -(b + a)) = a *)
+(*  Version  : [Win90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+(*           : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
+(*  Source   : [Win90] *)
+(*  Names    : Lemma 3.3 [Win90] *)
+(*           : RA2 [LW92] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include axioms for Robbins algebra  *)
+(* Inclusion of: Axioms/ROB001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : ROB001-0 : TPTP v3.1.1. 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 literals   :    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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_result:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall negate:\forall _:Univ.Univ.
+\forall H0:eq Univ (negate (add a (negate b))) c.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add b a)))) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/ROB013-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/ROB013-1.p.ma
new file mode 100644 (file)
index 0000000..6817807
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/ROB013-1.p.ma
@@ -0,0 +1,65 @@
+set "baseuri" "cic:/matita/TPTP/ROB013-1".
+include "logic/equality.ma".
+(* Inclusion of: ROB013-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : ROB013-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Robbins Algebra *)
+(*  Problem  : If -(a + b) = c then -(c + -(-b + a)) = a *)
+(*  Version  : [Win90] (equality) axioms. *)
+(*  English  :  *)
+(*  Refs     : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+(*  Source   : [Win90] *)
+(*  Names    : Lemma 3.5 [Win90] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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    :    5 (   3 constant; 0-2 arity) *)
+(*             Number of variables   :    7 (   0 singleton) *)
+(*             Maximal term depth    :    6 (   3 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include axioms for Robbins algebra  *)
+(* Inclusion of: Axioms/ROB001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : ROB001-0 : TPTP v3.1.1. 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 literals   :    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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_result:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall negate:\forall _:Univ.Univ.
+\forall H0:eq Univ (negate (add a b)) c.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).eq Univ (negate (add c (negate (add (negate b) a)))) a
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/ROB030-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/ROB030-1.p.ma
new file mode 100644 (file)
index 0000000..4dc584b
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/ROB030-1.p.ma
@@ -0,0 +1,75 @@
+set "baseuri" "cic:/matita/TPTP/ROB030-1".
+include "logic/equality.ma".
+(* Inclusion of: ROB030-1.p *)
+(* ------------------------------------------------------------------------------ *)
+(*  File     : ROB030-1 : TPTP v3.1.1. Released v3.1.0. *)
+(*  Domain   : Robbins Algebra *)
+(*  Problem  : Exists absorbed element => Exists absorbed within negation element *)
+(*  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     : [Win90] Winker (1990), Robbins Algebra: Conditions that make a *)
+(*           : [Loe04] Loechner (2004), Email to Geoff Sutcliffe *)
+(*  Source   : [Loe04] *)
+(*  Names    : (1) [Loe04] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 v3.1.0 *)
+(*  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   :    9 (   1 singleton) *)
+(*             Maximal term depth    :    6 (   2 average) *)
+(*  Comments :  *)
+(* ------------------------------------------------------------------------------ *)
+(* ----Include axioms for Robbins algebra  *)
+(* Inclusion of: Axioms/ROB001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : ROB001-0 : TPTP v3.1.1. 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 literals   :    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 :  *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ------------------------------------------------------------------------------ *)
+theorem prove_absorption_within_negation:
+ \forall Univ:Set.
+\forall add:\forall _:Univ.\forall _:Univ.Univ.
+\forall c:Univ.
+\forall d:Univ.
+\forall negate:\forall _:Univ.Univ.
+\forall H0:eq Univ (add c d) d.
+\forall H1:\forall X:Univ.\forall Y:Univ.eq Univ (negate (add (negate (add X Y)) (negate (add X (negate Y))))) X.
+\forall H2:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (add (add X Y) Z) (add X (add Y Z)).
+\forall H3:\forall X:Univ.\forall Y:Univ.eq Univ (add X Y) (add Y X).\exist A:Univ.\exist B:Univ.eq Univ (negate (add A B)) (negate B)
+.
+intros.
+exists[
+2:
+exists[
+2:
+auto paramodulation timeout=600.
+try assumption.
+|
+skip]
+|
+skip]
+print proofterm.
+qed.
+(* ------------------------------------------------------------------------------ *)

diff --git a/helm/software/matita/tests/TPTP/Veloci/SYN083-1.p.ma b/helm/software/matita/tests/TPTP/Veloci/SYN083-1.p.ma
new file mode 100644 (file)
index 0000000..46a9329
--- /dev/null
+++ b/helm/software/matita/tests/TPTP/Veloci/SYN083-1.p.ma
@@ -0,0 +1,38 @@
+set "baseuri" "cic:/matita/TPTP/SYN083-1".
+include "logic/equality.ma".
+(* Inclusion of: SYN083-1.p *)
+(* -------------------------------------------------------------------------- *)
+(*  File     : SYN083-1 : TPTP v3.1.1. Released v1.0.0. *)
+(*  Domain   : Syntactic *)
+(*  Problem  : Pelletier Problem 61 *)
+(*  Version  : Especial. *)
+(*  English  :  *)
+(*  Refs     : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au *)
+(*  Source   : [Pel86] *)
+(*  Names    : Pelletier 61 [Pel86] *)
+(*  Status   : Unsatisfiable *)
+(*  Rating   : 0.00 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 (   4 constant; 0-2 arity) *)
+(*             Number of variables   :    3 (   0 singleton) *)
+(*             Maximal term depth    :    4 (   4 average) *)
+(*  Comments :  *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_this:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall c:Univ.
+\forall d:Univ.
+\forall f:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (f X (f Y Z)) (f (f X Y) Z).eq Univ (f a (f b (f c d))) (f (f (f a b) c) d)
+.
+intros.
+auto paramodulation timeout=600.
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)