TSTP Solution File: SET018-4 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET018-4 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n021.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 : 300s
% DateTime : Thu Aug 31 14:32:11 EDT 2023
% Result : Unsatisfiable 45.07s 45.22s
% Output : CNFRefutation 45.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 92
% Syntax : Number of formulae : 157 ( 39 unt; 76 typ; 0 def)
% Number of atoms : 141 ( 72 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 95 ( 35 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 122 ( 66 >; 56 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-5 aty)
% Number of functors : 63 ( 63 usr; 10 con; 0-5 aty)
% Number of variables : 79 ( 18 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
member: ( $i * $i ) > $o ).
tff(decl_23,type,
little_set: $i > $o ).
tff(decl_24,type,
f1: ( $i * $i ) > $i ).
tff(decl_25,type,
non_ordered_pair: ( $i * $i ) > $i ).
tff(decl_26,type,
singleton_set: $i > $i ).
tff(decl_27,type,
ordered_pair: ( $i * $i ) > $i ).
tff(decl_28,type,
ordered_pair_predicate: $i > $o ).
tff(decl_29,type,
f2: $i > $i ).
tff(decl_30,type,
f3: $i > $i ).
tff(decl_31,type,
first: $i > $i ).
tff(decl_32,type,
f4: ( $i * $i ) > $i ).
tff(decl_33,type,
f5: ( $i * $i ) > $i ).
tff(decl_34,type,
second: $i > $i ).
tff(decl_35,type,
f6: ( $i * $i ) > $i ).
tff(decl_36,type,
f7: ( $i * $i ) > $i ).
tff(decl_37,type,
estin: $i ).
tff(decl_38,type,
intersection: ( $i * $i ) > $i ).
tff(decl_39,type,
complement: $i > $i ).
tff(decl_40,type,
union: ( $i * $i ) > $i ).
tff(decl_41,type,
domain_of: $i > $i ).
tff(decl_42,type,
f8: ( $i * $i ) > $i ).
tff(decl_43,type,
cross_product: ( $i * $i ) > $i ).
tff(decl_44,type,
converse: $i > $i ).
tff(decl_45,type,
rotate_right: $i > $i ).
tff(decl_46,type,
f9: ( $i * $i ) > $i ).
tff(decl_47,type,
f10: ( $i * $i ) > $i ).
tff(decl_48,type,
f11: ( $i * $i ) > $i ).
tff(decl_49,type,
flip_range_of: $i > $i ).
tff(decl_50,type,
f12: ( $i * $i ) > $i ).
tff(decl_51,type,
f13: ( $i * $i ) > $i ).
tff(decl_52,type,
f14: ( $i * $i ) > $i ).
tff(decl_53,type,
successor: $i > $i ).
tff(decl_54,type,
empty_set: $i ).
tff(decl_55,type,
universal_set: $i ).
tff(decl_56,type,
infinity: $i ).
tff(decl_57,type,
sigma: $i > $i ).
tff(decl_58,type,
f16: ( $i * $i ) > $i ).
tff(decl_59,type,
subset: ( $i * $i ) > $o ).
tff(decl_60,type,
f17: ( $i * $i ) > $i ).
tff(decl_61,type,
proper_subset: ( $i * $i ) > $o ).
tff(decl_62,type,
powerset: $i > $i ).
tff(decl_63,type,
relation: $i > $o ).
tff(decl_64,type,
f18: $i > $i ).
tff(decl_65,type,
single_valued_set: $i > $o ).
tff(decl_66,type,
f19: $i > $i ).
tff(decl_67,type,
f20: $i > $i ).
tff(decl_68,type,
f21: $i > $i ).
tff(decl_69,type,
function: $i > $o ).
tff(decl_70,type,
image: ( $i * $i ) > $i ).
tff(decl_71,type,
f22: ( $i * $i * $i ) > $i ).
tff(decl_72,type,
disjoint: ( $i * $i ) > $o ).
tff(decl_73,type,
f23: ( $i * $i ) > $i ).
tff(decl_74,type,
f24: $i > $i ).
tff(decl_75,type,
f25: $i ).
tff(decl_76,type,
f26: $i > $i ).
tff(decl_77,type,
range_of: $i > $i ).
tff(decl_78,type,
f27: ( $i * $i ) > $i ).
tff(decl_79,type,
identity_relation: $i ).
tff(decl_80,type,
restrict: ( $i * $i ) > $i ).
tff(decl_81,type,
one_to_one_function: $i > $o ).
tff(decl_82,type,
apply: ( $i * $i ) > $i ).
tff(decl_83,type,
f28: ( $i * $i * $i ) > $i ).
tff(decl_84,type,
apply_to_two_arguments: ( $i * $i * $i ) > $i ).
tff(decl_85,type,
maps: ( $i * $i * $i ) > $o ).
tff(decl_86,type,
closed: ( $i * $i ) > $o ).
tff(decl_87,type,
compose: ( $i * $i ) > $i ).
tff(decl_88,type,
f29: ( $i * $i * $i ) > $i ).
tff(decl_89,type,
f30: ( $i * $i * $i ) > $i ).
tff(decl_90,type,
f31: ( $i * $i * $i ) > $i ).
tff(decl_91,type,
homomorphism: ( $i * $i * $i * $i * $i ) > $o ).
tff(decl_92,type,
f32: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_93,type,
f33: ( $i * $i * $i * $i * $i ) > $i ).
tff(decl_94,type,
a: $i ).
tff(decl_95,type,
b: $i ).
tff(decl_96,type,
c: $i ).
tff(decl_97,type,
d: $i ).
cnf(non_ordered_pair3,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair3) ).
cnf(ordered_pair,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',ordered_pair) ).
cnf(singleton_set,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',singleton_set) ).
cnf(non_ordered_pair4,axiom,
little_set(non_ordered_pair(X1,X2)),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair4) ).
cnf(equal_ordered_pair,hypothesis,
ordered_pair(a,b) = ordered_pair(c,d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',equal_ordered_pair) ).
cnf(d_little_set,hypothesis,
little_set(d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_little_set) ).
cnf(non_ordered_pair1,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair1) ).
cnf(prove_second_components_equal,negated_conjecture,
b != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_second_components_equal) ).
cnf(b_little_set,hypothesis,
little_set(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_little_set) ).
cnf(non_ordered_pair2,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',non_ordered_pair2) ).
cnf(empty_set,axiom,
~ member(X1,empty_set),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',empty_set) ).
cnf(extensionality2,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',extensionality2) ).
cnf(a_little_set,hypothesis,
little_set(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_little_set) ).
cnf(disjoint1,axiom,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',disjoint1) ).
cnf(disjoint2,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',disjoint2) ).
cnf(universal_set,axiom,
( member(X1,universal_set)
| ~ little_set(X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET003-0.ax',universal_set) ).
cnf(c_0_16,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X3 ),
non_ordered_pair3 ).
cnf(c_0_17,axiom,
ordered_pair(X1,X2) = non_ordered_pair(singleton_set(X1),non_ordered_pair(X1,X2)),
ordered_pair ).
cnf(c_0_18,axiom,
singleton_set(X1) = non_ordered_pair(X1,X1),
singleton_set ).
cnf(c_0_19,plain,
( member(X1,non_ordered_pair(X2,X1))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,axiom,
little_set(non_ordered_pair(X1,X2)),
non_ordered_pair4 ).
cnf(c_0_21,hypothesis,
ordered_pair(a,b) = ordered_pair(c,d),
equal_ordered_pair ).
cnf(c_0_22,plain,
ordered_pair(X1,X2) = non_ordered_pair(non_ordered_pair(X1,X1),non_ordered_pair(X1,X2)),
inference(rw,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
member(non_ordered_pair(X1,X2),non_ordered_pair(X3,non_ordered_pair(X1,X2))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,hypothesis,
non_ordered_pair(non_ordered_pair(c,c),non_ordered_pair(c,d)) = non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_22]),c_0_22]) ).
cnf(c_0_25,hypothesis,
little_set(d),
d_little_set ).
cnf(c_0_26,axiom,
( X1 = X2
| X1 = X3
| ~ member(X1,non_ordered_pair(X2,X3)) ),
non_ordered_pair1 ).
cnf(c_0_27,hypothesis,
member(non_ordered_pair(c,d),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,hypothesis,
member(d,non_ordered_pair(X1,d)),
inference(spm,[status(thm)],[c_0_19,c_0_25]) ).
cnf(c_0_29,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,a)
| non_ordered_pair(c,d) = non_ordered_pair(a,b) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_30,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,a)
| member(d,non_ordered_pair(a,b)) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_31,negated_conjecture,
b != d,
prove_second_components_equal ).
cnf(c_0_32,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,a)
| d = a ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_30]),c_0_31]) ).
cnf(c_0_33,hypothesis,
( X1 = non_ordered_pair(c,c)
| X1 = non_ordered_pair(c,d)
| ~ member(X1,non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,b))) ),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
cnf(c_0_34,hypothesis,
( d = a
| member(d,non_ordered_pair(a,a)) ),
inference(spm,[status(thm)],[c_0_28,c_0_32]) ).
cnf(c_0_35,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,b)
| non_ordered_pair(c,c) = non_ordered_pair(a,b) ),
inference(spm,[status(thm)],[c_0_33,c_0_23]) ).
cnf(c_0_36,hypothesis,
d = a,
inference(spm,[status(thm)],[c_0_26,c_0_34]) ).
cnf(c_0_37,hypothesis,
( non_ordered_pair(c,c) = non_ordered_pair(a,b)
| non_ordered_pair(c,a) = non_ordered_pair(a,b) ),
inference(rw,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_38,hypothesis,
little_set(b),
b_little_set ).
cnf(c_0_39,hypothesis,
( non_ordered_pair(c,a) = non_ordered_pair(a,b)
| X1 = c
| ~ member(X1,non_ordered_pair(a,b)) ),
inference(spm,[status(thm)],[c_0_26,c_0_37]) ).
cnf(c_0_40,hypothesis,
member(b,non_ordered_pair(X1,b)),
inference(spm,[status(thm)],[c_0_19,c_0_38]) ).
cnf(c_0_41,axiom,
( member(X1,non_ordered_pair(X2,X3))
| ~ little_set(X1)
| X1 != X2 ),
non_ordered_pair2 ).
cnf(c_0_42,hypothesis,
( non_ordered_pair(c,a) = non_ordered_pair(a,b)
| b = c ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,axiom,
~ member(X1,empty_set),
empty_set ).
cnf(c_0_44,axiom,
( member(f1(X1,X2),X1)
| member(f1(X1,X2),X2)
| X1 = X2 ),
extensionality2 ).
cnf(c_0_45,plain,
( member(X1,non_ordered_pair(X1,X2))
| ~ little_set(X1) ),
inference(er,[status(thm)],[c_0_41]) ).
cnf(c_0_46,hypothesis,
little_set(a),
a_little_set ).
cnf(c_0_47,hypothesis,
( b = c
| X1 = c
| X1 = a
| ~ member(X1,non_ordered_pair(a,b)) ),
inference(spm,[status(thm)],[c_0_26,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
b != a,
inference(rw,[status(thm)],[c_0_31,c_0_36]) ).
cnf(c_0_49,axiom,
( ~ disjoint(X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X2) ),
disjoint1 ).
cnf(c_0_50,axiom,
( disjoint(X1,X2)
| member(f23(X1,X2),X1) ),
disjoint2 ).
cnf(c_0_51,axiom,
( member(X1,universal_set)
| ~ little_set(X1) ),
universal_set ).
cnf(c_0_52,plain,
( empty_set = X1
| member(f1(empty_set,X1),X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,plain,
member(non_ordered_pair(X1,X2),non_ordered_pair(non_ordered_pair(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_45,c_0_20]) ).
cnf(c_0_54,hypothesis,
member(a,non_ordered_pair(a,X1)),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,hypothesis,
b = c,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_40]),c_0_48]) ).
cnf(c_0_56,plain,
( member(f23(X1,X2),X1)
| ~ member(X3,X2)
| ~ member(X3,X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_57,hypothesis,
member(d,universal_set),
inference(spm,[status(thm)],[c_0_51,c_0_25]) ).
cnf(c_0_58,plain,
( f1(empty_set,non_ordered_pair(X1,X2)) = X1
| f1(empty_set,non_ordered_pair(X1,X2)) = X2
| non_ordered_pair(X1,X2) = empty_set ),
inference(spm,[status(thm)],[c_0_26,c_0_52]) ).
cnf(c_0_59,hypothesis,
( non_ordered_pair(c,d) = non_ordered_pair(a,a)
| non_ordered_pair(c,c) = non_ordered_pair(a,a) ),
inference(spm,[status(thm)],[c_0_33,c_0_53]) ).
cnf(c_0_60,hypothesis,
( non_ordered_pair(c,a) = non_ordered_pair(a,b)
| c = a ),
inference(spm,[status(thm)],[c_0_39,c_0_54]) ).
cnf(c_0_61,negated_conjecture,
c != a,
inference(rw,[status(thm)],[c_0_48,c_0_55]) ).
cnf(c_0_62,hypothesis,
( member(f23(X1,universal_set),X1)
| ~ member(d,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_63,plain,
( f1(empty_set,non_ordered_pair(X1,X1)) = X1
| non_ordered_pair(X1,X1) = empty_set ),
inference(er,[status(thm)],[inference(ef,[status(thm)],[c_0_58])]) ).
cnf(c_0_64,hypothesis,
member(a,universal_set),
inference(spm,[status(thm)],[c_0_51,c_0_46]) ).
cnf(c_0_65,hypothesis,
member(non_ordered_pair(c,c),non_ordered_pair(non_ordered_pair(a,a),non_ordered_pair(a,c))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_24]),c_0_55]) ).
cnf(c_0_66,hypothesis,
( non_ordered_pair(c,c) = non_ordered_pair(a,a)
| non_ordered_pair(c,a) = non_ordered_pair(a,a) ),
inference(rw,[status(thm)],[c_0_59,c_0_36]) ).
cnf(c_0_67,hypothesis,
non_ordered_pair(c,a) = non_ordered_pair(a,c),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_60,c_0_55]),c_0_61]) ).
cnf(c_0_68,hypothesis,
( f23(non_ordered_pair(X1,X2),universal_set) = X1
| f23(non_ordered_pair(X1,X2),universal_set) = X2
| ~ member(d,non_ordered_pair(X1,X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_62]) ).
cnf(c_0_69,plain,
( non_ordered_pair(X1,X1) = empty_set
| member(X1,non_ordered_pair(X1,X1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_63]),c_0_43]) ).
cnf(c_0_70,hypothesis,
( member(f23(X1,universal_set),X1)
| ~ member(a,X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_64]) ).
cnf(c_0_71,hypothesis,
( non_ordered_pair(c,c) = non_ordered_pair(a,a)
| non_ordered_pair(c,c) = non_ordered_pair(a,c) ),
inference(spm,[status(thm)],[c_0_26,c_0_65]) ).
cnf(c_0_72,hypothesis,
( non_ordered_pair(a,c) = non_ordered_pair(a,a)
| non_ordered_pair(c,c) = non_ordered_pair(a,a) ),
inference(rw,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_73,hypothesis,
( f23(non_ordered_pair(d,d),universal_set) = d
| non_ordered_pair(d,d) = empty_set ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_74,hypothesis,
( f23(non_ordered_pair(X1,X2),universal_set) = X1
| f23(non_ordered_pair(X1,X2),universal_set) = X2
| ~ member(a,non_ordered_pair(X1,X2)) ),
inference(spm,[status(thm)],[c_0_26,c_0_70]) ).
cnf(c_0_75,hypothesis,
non_ordered_pair(c,c) = non_ordered_pair(a,a),
inference(csr,[status(thm)],[inference(ef,[status(thm)],[c_0_71]),c_0_72]) ).
cnf(c_0_76,hypothesis,
member(a,non_ordered_pair(X1,a)),
inference(spm,[status(thm)],[c_0_19,c_0_46]) ).
cnf(c_0_77,hypothesis,
( f23(non_ordered_pair(a,a),universal_set) = a
| non_ordered_pair(a,a) = empty_set ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_73,c_0_36]),c_0_36]),c_0_36]),c_0_36]),c_0_36]) ).
cnf(c_0_78,hypothesis,
f23(non_ordered_pair(a,a),universal_set) = c,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_75]),c_0_76])]) ).
cnf(c_0_79,hypothesis,
non_ordered_pair(a,a) = empty_set,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_78]),c_0_61]) ).
cnf(c_0_80,hypothesis,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_79]),c_0_43]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET018-4 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 08:23:12 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.64 start to proof: theBenchmark
% 45.07/45.22 % Version : CSE_E---1.5
% 45.07/45.22 % Problem : theBenchmark.p
% 45.07/45.22 % Proof found
% 45.07/45.22 % SZS status Theorem for theBenchmark.p
% 45.07/45.22 % SZS output start Proof
% See solution above
% 45.07/45.23 % Total time : 44.512000 s
% 45.07/45.23 % SZS output end Proof
% 45.07/45.23 % Total time : 44.519000 s
%------------------------------------------------------------------------------