TSTP Solution File: NUM139-1 by Prover9---1109a
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Prover9---1109a
% Problem : NUM139-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : tptp2X_and_run_prover9 %d %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 13:25:24 EDT 2022
% Result : Unsatisfiable 1.58s 1.89s
% Output : Refutation 1.58s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM139-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13 % Command : tptp2X_and_run_prover9 %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 07:05:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.84/1.14 ============================== Prover9 ===============================
% 0.84/1.14 Prover9 (32) version 2009-11A, November 2009.
% 0.84/1.14 Process 16579 was started by sandbox on n023.cluster.edu,
% 0.84/1.14 Thu Jul 7 07:05:12 2022
% 0.84/1.14 The command was "/export/starexec/sandbox/solver/bin/prover9 -t 300 -f /tmp/Prover9_16426_n023.cluster.edu".
% 0.84/1.14 ============================== end of head ===========================
% 0.84/1.14
% 0.84/1.14 ============================== INPUT =================================
% 0.84/1.14
% 0.84/1.14 % Reading from file /tmp/Prover9_16426_n023.cluster.edu
% 0.84/1.14
% 0.84/1.14 set(prolog_style_variables).
% 0.84/1.14 set(auto2).
% 0.84/1.14 % set(auto2) -> set(auto).
% 0.84/1.14 % set(auto) -> set(auto_inference).
% 0.84/1.14 % set(auto) -> set(auto_setup).
% 0.84/1.14 % set(auto_setup) -> set(predicate_elim).
% 0.84/1.14 % set(auto_setup) -> assign(eq_defs, unfold).
% 0.84/1.14 % set(auto) -> set(auto_limits).
% 0.84/1.14 % set(auto_limits) -> assign(max_weight, "100.000").
% 0.84/1.14 % set(auto_limits) -> assign(sos_limit, 20000).
% 0.84/1.14 % set(auto) -> set(auto_denials).
% 0.84/1.14 % set(auto) -> set(auto_process).
% 0.84/1.14 % set(auto2) -> assign(new_constants, 1).
% 0.84/1.14 % set(auto2) -> assign(fold_denial_max, 3).
% 0.84/1.14 % set(auto2) -> assign(max_weight, "200.000").
% 0.84/1.14 % set(auto2) -> assign(max_hours, 1).
% 0.84/1.14 % assign(max_hours, 1) -> assign(max_seconds, 3600).
% 0.84/1.14 % set(auto2) -> assign(max_seconds, 0).
% 0.84/1.14 % set(auto2) -> assign(max_minutes, 5).
% 0.84/1.14 % assign(max_minutes, 5) -> assign(max_seconds, 300).
% 0.84/1.14 % set(auto2) -> set(sort_initial_sos).
% 0.84/1.14 % set(auto2) -> assign(sos_limit, -1).
% 0.84/1.14 % set(auto2) -> assign(lrs_ticks, 3000).
% 0.84/1.14 % set(auto2) -> assign(max_megs, 400).
% 0.84/1.14 % set(auto2) -> assign(stats, some).
% 0.84/1.14 % set(auto2) -> clear(echo_input).
% 0.84/1.14 % set(auto2) -> set(quiet).
% 0.84/1.14 % set(auto2) -> clear(print_initial_clauses).
% 0.84/1.14 % set(auto2) -> clear(print_given).
% 0.84/1.14 assign(lrs_ticks,-1).
% 0.84/1.14 assign(sos_limit,10000).
% 0.84/1.14 assign(order,kbo).
% 0.84/1.14 set(lex_order_vars).
% 0.84/1.14 clear(print_given).
% 0.84/1.14
% 0.84/1.14 % formulas(sos). % not echoed (160 formulas)
% 0.84/1.14
% 0.84/1.14 ============================== end of input ==========================
% 0.84/1.14
% 0.84/1.14 % From the command line: assign(max_seconds, 300).
% 0.84/1.14
% 0.84/1.14 ============================== PROCESS NON-CLAUSAL FORMULAS ==========
% 0.84/1.14
% 0.84/1.14 % Formulas that are not ordinary clauses:
% 0.84/1.14
% 0.84/1.14 ============================== end of process non-clausal formulas ===
% 0.84/1.14
% 0.84/1.14 ============================== PROCESS INITIAL CLAUSES ===============
% 0.84/1.14
% 0.84/1.14 ============================== PREDICATE ELIMINATION =================
% 0.84/1.14 1 -member(null_class,A) | -subclass(image(successor_relation,A),A) | inductive(A) # label(inductive3) # label(axiom). [assumption].
% 0.84/1.14 2 -inductive(A) | member(null_class,A) # label(inductive1) # label(axiom). [assumption].
% 0.84/1.14 3 -inductive(A) | subclass(image(successor_relation,A),A) # label(inductive2) # label(axiom). [assumption].
% 0.84/1.14 4 inductive(omega) # label(omega_is_inductive1) # label(axiom). [assumption].
% 0.84/1.14 Derived: member(null_class,omega). [resolve(4,a,2,a)].
% 0.84/1.14 Derived: subclass(image(successor_relation,omega),omega). [resolve(4,a,3,a)].
% 0.84/1.14 5 -inductive(A) | subclass(omega,A) # label(omega_is_inductive2) # label(axiom). [assumption].
% 0.84/1.14 Derived: subclass(omega,A) | -member(null_class,A) | -subclass(image(successor_relation,A),A). [resolve(5,a,1,c)].
% 0.84/1.14 Derived: subclass(omega,omega). [resolve(5,a,4,a)].
% 0.84/1.14 6 -subclass(compose(A,inverse(A)),identity_relation) | single_valued_class(A) # label(single_valued_class2) # label(axiom). [assumption].
% 0.84/1.14 7 -single_valued_class(A) | subclass(compose(A,inverse(A)),identity_relation) # label(single_valued_class1) # label(axiom). [assumption].
% 0.84/1.14 8 -function(inverse(A)) | -function(A) | one_to_one(A) # label(one_to_one3) # label(axiom). [assumption].
% 0.84/1.14 9 -one_to_one(A) | function(A) # label(one_to_one1) # label(axiom). [assumption].
% 0.84/1.14 10 -one_to_one(A) | function(inverse(A)) # label(one_to_one2) # label(axiom). [assumption].
% 0.84/1.14 11 -function(A) | domain_of(domain_of(B)) != domain_of(A) | -subclass(range_of(A),domain_of(domain_of(C))) | compatible(A,B,C) # label(compatible4) # label(axiom). [assumption].
% 0.84/1.14 12 -compatible(A,B,C) | function(A) # label(compatible1) # label(axiom). [assumption].
% 0.84/1.14 13 -compatible(A,B,C) | domain_of(domain_of(B)) = domain_of(A) # label(compatible2) # label(axiom). [assumption].
% 0.84/1.14 14 -compatible(A,B,C) | subclass(range_of(A),domain_of(domain_of(C))) # label(compatible3) # label(axiom). [assumption].
% 0.84/1.14 15 -homomorphism(A,B,C) | compatible(A,B,C) # label(homomorphism3) # label(axiom). [assumption].
% 0.84/1.14 Derived: -homomorphism(A,B,C) | function(A). [resolve(15,b,12,a)].
% 0.84/1.14 Derived: -homomorphism(A,B,C) | domain_of(domain_of(B)) = domain_of(A). [resolve(15,b,13,a)].
% 0.84/1.14 Derived: -homomorphism(A,B,C) | subclass(range_of(A),domain_of(domain_of(C))). [resolve(15,b,14,a)].
% 0.84/1.14 16 -operation(A) | -operation(B) | -compatible(C,A,B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | homomorphism(C,A,B) # label(homomorphism5) # label(axiom). [assumption].
% 0.84/1.14 Derived: -operation(A) | -operation(B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | homomorphism(C,A,B) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(B))). [resolve(16,c,11,d)].
% 0.84/1.14 17 -operation(A) | -operation(B) | -compatible(C,A,B) | apply(B,ordered_pair(apply(C,not_homomorphism1(C,A,B)),apply(C,not_homomorphism2(C,A,B)))) != apply(C,apply(A,ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)))) | homomorphism(C,A,B) # label(homomorphism6) # label(axiom). [assumption].
% 0.84/1.14 Derived: -operation(A) | -operation(B) | apply(B,ordered_pair(apply(C,not_homomorphism1(C,A,B)),apply(C,not_homomorphism2(C,A,B)))) != apply(C,apply(A,ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)))) | homomorphism(C,A,B) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(B))). [resolve(17,c,11,d)].
% 0.84/1.14 18 -operation(A) | -operation(B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | homomorphism(C,A,B) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(B))). [resolve(16,c,11,d)].
% 0.84/1.14 19 -homomorphism(A,B,C) | operation(B) # label(homomorphism1) # label(axiom). [assumption].
% 0.84/1.14 20 -homomorphism(A,B,C) | operation(C) # label(homomorphism2) # label(axiom). [assumption].
% 0.84/1.14 21 -homomorphism(A,B,C) | -member(ordered_pair(D,E),domain_of(B)) | apply(C,ordered_pair(apply(A,D),apply(A,E))) = apply(A,apply(B,ordered_pair(D,E))) # label(homomorphism4) # label(axiom). [assumption].
% 0.84/1.14 22 -homomorphism(A,B,C) | function(A). [resolve(15,b,12,a)].
% 0.84/1.14 23 -homomorphism(A,B,C) | domain_of(domain_of(B)) = domain_of(A). [resolve(15,b,13,a)].
% 0.84/1.14 24 -homomorphism(A,B,C) | subclass(range_of(A),domain_of(domain_of(C))). [resolve(15,b,14,a)].
% 0.84/1.14 Derived: -operation(A) | -operation(B) | member(ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)),domain_of(A)) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(B))) | -member(ordered_pair(D,E),domain_of(A)) | apply(B,ordered_pair(apply(C,D),apply(C,E))) = apply(C,apply(A,ordered_pair(D,E))). [resolve(18,d,21,a)].
% 0.84/1.14 25 -operation(A) | -operation(B) | apply(B,ordered_pair(apply(C,not_homomorphism1(C,A,B)),apply(C,not_homomorphism2(C,A,B)))) != apply(C,apply(A,ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)))) | homomorphism(C,A,B) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(B))). [resolve(17,c,11,d)].
% 0.84/1.14 Derived: -operation(A) | -operation(B) | apply(B,ordered_pair(apply(C,not_homomorphism1(C,A,B)),apply(C,not_homomorphism2(C,A,B)))) != apply(C,apply(A,ordered_pair(not_homomorphism1(C,A,B),not_homomorphism2(C,A,B)))) | -function(C) | domain_of(domain_of(A)) != domain_of(C) | -subclass(range_of(C),domain_of(domain_of(B))) | -member(ordered_pair(D,E),domain_of(A)) | apply(B,ordered_pair(apply(C,D),apply(C,E))) = apply(C,apply(A,ordered_pair(D,E))). [resolve(25,d,21,a)].
% 0.84/1.14 26 -function(A) | -subclass(range_of(A),B) | maps(A,domain_of(A),B) # label(maps4) # label(axiom). [assumption].
% 0.84/1.14 27 -maps(A,B,C) | function(A) # label(maps1) # label(axiom). [assumption].
% 0.84/1.14 28 -maps(A,B,C) | domain_of(A) = B # label(maps2) # label(axiom). [assumption].
% 0.84/1.14 29 -maps(A,B,C) | subclass(range_of(A),C) # label(maps3) # label(axiom). [assumption].
% 0.88/1.18 Derived: -function(A) | -subclass(range_of(A),B) | domain_of(A) = domain_of(A). [resolve(26,c,28,a)].
% 0.88/1.18 30 -subclass(restrict(A,B,B),complement(identity_relation)) | irreflexive(A,B) # label(irreflexive2) # label(axiom). [assumption].
% 0.88/1.18 31 -irreflexive(A,B) | subclass(restrict(A,B,B),complement(identity_relation)) # label(irreflexive1) # label(axiom). [assumption].
% 0.88/1.18 32 -subclass(cross_product(A,A),union(identity_relation,symmetrization_of(B))) | connected(B,A) # label(connected2) # label(axiom). [assumption].
% 0.88/1.18 33 -connected(A,B) | subclass(cross_product(B,B),union(identity_relation,symmetrization_of(A))) # label(connected1) # label(axiom). [assumption].
% 0.88/1.18 34 -well_ordering(A,B) | connected(A,B) # label(well_ordering1) # label(axiom). [assumption].
% 0.88/1.18 Derived: -well_ordering(A,B) | subclass(cross_product(B,B),union(identity_relation,symmetrization_of(A))). [resolve(34,b,33,a)].
% 0.88/1.18 35 -connected(A,B) | not_well_ordering(A,B) != null_class | well_ordering(A,B) # label(well_ordering6) # label(axiom). [assumption].
% 0.88/1.18 Derived: not_well_ordering(A,B) != null_class | well_ordering(A,B) | -subclass(cross_product(B,B),union(identity_relation,symmetrization_of(A))). [resolve(35,a,32,b)].
% 0.88/1.18 36 -connected(A,B) | subclass(not_well_ordering(A,B),B) | well_ordering(A,B) # label(well_ordering7) # label(axiom). [assumption].
% 0.88/1.18 Derived: subclass(not_well_ordering(A,B),B) | well_ordering(A,B) | -subclass(cross_product(B,B),union(identity_relation,symmetrization_of(A))). [resolve(36,a,32,b)].
% 0.88/1.18 37 -member(A,not_well_ordering(B,C)) | segment(B,not_well_ordering(B,C),A) != null_class | -connected(B,C) | well_ordering(B,C) # label(well_ordering8) # label(axiom). [assumption].
% 0.88/1.18 Derived: -member(A,not_well_ordering(B,C)) | segment(B,not_well_ordering(B,C),A) != null_class | well_ordering(B,C) | -subclass(cross_product(C,C),union(identity_relation,symmetrization_of(B))). [resolve(37,c,32,b)].
% 0.88/1.18 38 -subclass(compose(restrict(A,B,B),restrict(A,B,B)),restrict(A,B,B)) | transitive(A,B) # label(transitive2) # label(axiom). [assumption].
% 0.88/1.18 39 -transitive(A,B) | subclass(compose(restrict(A,B,B),restrict(A,B,B)),restrict(A,B,B)) # label(transitive1) # label(axiom). [assumption].
% 0.88/1.18 40 restrict(intersection(A,inverse(A)),B,B) != null_class | asymmetric(A,B) # label(asymmetric2) # label(axiom). [assumption].
% 0.88/1.18 41 -asymmetric(A,B) | restrict(intersection(A,inverse(A)),B,B) = null_class # label(asymmetric1) # label(axiom). [assumption].
% 0.88/1.18 42 -subclass(A,B) | -subclass(domain_of(restrict(C,B,A)),A) | section(C,A,B) # label(section3) # label(axiom). [assumption].
% 0.88/1.18 43 -section(A,B,C) | subclass(B,C) # label(section1) # label(axiom). [assumption].
% 0.88/1.18 44 -section(A,B,C) | subclass(domain_of(restrict(A,C,B)),B) # label(section2) # label(axiom). [assumption].
% 0.88/1.18
% 0.88/1.18 ============================== end predicate elimination =============
% 0.88/1.18
% 0.88/1.18 Auto_denials: (non-Horn, no changes).
% 0.88/1.18
% 0.88/1.18 Term ordering decisions:
% 0.88/1.18 Function symbol KB weights: universal_class=1. null_class=1. element_relation=1. identity_relation=1. omega=1. ordinal_numbers=1. successor_relation=1. union_of_range_map=1. application_function=1. composition_function=1. domain_relation=1. rest_relation=1. subset_relation=1. choice=1. kind_1_ordinals=1. add_relation=1. limit_ordinals=1. singleton_relation=1. x=1. z=1. ordered_pair=1. cross_product=1. apply=1. intersection=1. compose=1. image=1. union=1. unordered_pair=1. not_subclass_element=1. not_well_ordering=1. least=1. ordinal_add=1. ordinal_multiply=1. symmetric_difference=1. domain_of=1. complement=1. singleton=1. inverse=1. range_of=1. rest_of=1. sum_class=1. recursion_equation_functions=1. symmetrization_of=1. flip=1. compose_class=1. first=1. rotate=1. second=1. successor=1. diagonalise=1. integer_of=1. power_class=1. regular=1. single_valued1=1. single_valued2=1. cantor=1. single_valued3=1. restrict=1. not_homomorphism1=1. not_homomorphism2=1. segment=1. domain=1. recursion=1. range=1.
% 0.88/1.18
% 0.88/1.18 ============================== end of process initial clauses ========
% 0.88/1.18
% 0.88/1.18 ============================== CLAUSES FOR SEARCH ====================
% 1.58/1.89
% 1.58/1.89 ============================== end of clauses for search =============
% 1.58/1.89
% 1.58/1.89 ============================== SEARCH ================================
% 1.58/1.89
% 1.58/1.89 % Starting search at 0.06 seconds.
% 1.58/1.89
% 1.58/1.89 Low Water (keep): wt=72.000, iters=4484
% 1.58/1.89
% 1.58/1.89 Low Water (keep): wt=55.000, iters=4433
% 1.58/1.89
% 1.58/1.89 Low Water (keep): wt=34.000, iters=4288
% 1.58/1.89
% 1.58/1.89 NOTE: Back_subsumption disabled, ratio of kept to back_subsumed is 137 (0.00 of 0.63 sec).
% 1.58/1.89
% 1.58/1.89 ============================== PROOF =================================
% 1.58/1.89 % SZS status Unsatisfiable
% 1.58/1.89 % SZS output start Refutation
% 1.58/1.89
% 1.58/1.89 % Proof 1 at 0.76 (+ 0.02) seconds.
% 1.58/1.89 % Length of proof is 18.
% 1.58/1.89 % Level of proof is 7.
% 1.58/1.89 % Maximum clause weight is 31.000.
% 1.58/1.89 % Given clauses 564.
% 1.58/1.89
% 1.58/1.89 46 member(not_subclass_element(A,B),A) | subclass(A,B) # label(not_subclass_members1) # label(axiom). [assumption].
% 1.58/1.89 74 -member(A,intersection(B,C)) | member(A,C) # label(intersection2) # label(axiom). [assumption].
% 1.58/1.89 82 intersection(A,cross_product(B,C)) = restrict(A,B,C) # label(restriction1) # label(axiom). [assumption].
% 1.58/1.89 83 restrict(A,B,C) = intersection(A,cross_product(B,C)). [copy(82),flip(a)].
% 1.58/1.89 100 domain_of(flip(cross_product(A,universal_class))) = inverse(A) # label(inverse) # label(axiom). [assumption].
% 1.58/1.89 101 inverse(A) = domain_of(flip(cross_product(A,universal_class))). [copy(100),flip(a)].
% 1.58/1.89 102 domain_of(inverse(A)) = range_of(A) # label(range_of) # label(axiom). [assumption].
% 1.58/1.89 103 range_of(A) = domain_of(domain_of(flip(cross_product(A,universal_class)))). [copy(102),rewrite([101(1)]),flip(a)].
% 1.58/1.89 108 range_of(restrict(A,B,universal_class)) = image(A,B) # label(image) # label(axiom). [assumption].
% 1.58/1.89 109 image(A,B) = domain_of(domain_of(flip(cross_product(intersection(A,cross_product(B,universal_class)),universal_class)))). [copy(108),rewrite([83(2),103(4)]),flip(a)].
% 1.58/1.89 122 complement(image(element_relation,complement(A))) = power_class(A) # label(power_class_definition) # label(axiom). [assumption].
% 1.58/1.89 123 power_class(A) = complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(A),universal_class)),universal_class))))). [copy(122),rewrite([109(3)]),flip(a)].
% 1.58/1.89 239 -member(not_subclass_element(intersection(power_class(x),z),x),z) # label(prove_complete_induction3_1) # label(negated_conjecture). [assumption].
% 1.58/1.89 240 -member(not_subclass_element(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z),x),z). [copy(239),rewrite([123(2)])].
% 1.58/1.89 241 -subclass(intersection(power_class(x),z),x) # label(prove_complete_induction3_2) # label(negated_conjecture). [assumption].
% 1.58/1.89 242 -subclass(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z),x). [copy(241),rewrite([123(2)])].
% 1.58/1.89 396 member(not_subclass_element(intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z),x),intersection(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(x),universal_class)),universal_class))))),z)). [resolve(242,a,46,b)].
% 1.58/1.89 6637 $F. [resolve(396,a,74,a),unit_del(a,240)].
% 1.58/1.89
% 1.58/1.89 % SZS output end Refutation
% 1.58/1.89 ============================== end of proof ==========================
% 1.58/1.89
% 1.58/1.89 ============================== STATISTICS ============================
% 1.58/1.89
% 1.58/1.89 Given=564. Generated=8669. Kept=6506. proofs=1.
% 1.58/1.89 Usable=551. Sos=5909. Demods=35. Limbo=1, Disabled=221. Hints=0.
% 1.58/1.89 Megabytes=12.87.
% 1.58/1.89 User_CPU=0.76, System_CPU=0.02, Wall_clock=1.
% 1.58/1.89
% 1.58/1.89 ============================== end of statistics =====================
% 1.58/1.89
% 1.58/1.89 ============================== end of search =========================
% 1.58/1.89
% 1.58/1.89 THEOREM PROVED
% 1.58/1.89 % SZS status Unsatisfiable
% 1.58/1.89
% 1.58/1.89 Exiting with 1 proof.
% 1.58/1.89
% 1.58/1.89 Process 16579 exit (max_proofs) Thu Jul 7 07:05:13 2022
% 1.58/1.89 Prover9 interrupted
%------------------------------------------------------------------------------