TSTP Solution File: GRP642+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : GRP642+1 : TPTP v8.1.2. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 : Wed May 31 12:12:22 EDT 2023
% Result : Theorem 0.15s 0.32s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 18
% Syntax : Number of formulae : 84 ( 17 unt; 0 def)
% Number of atoms : 311 ( 26 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 374 ( 147 ~; 156 |; 46 &)
% ( 13 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 12 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 49 (; 46 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_group_1(B)
& m1_group_2(B,A) )
=> k1_funct_1(k1_latsubgr(A),B) != k1_xboole_0 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) )
=> ( B = k1_latsubgr(A)
<=> ! [C] :
( ( v1_group_1(C)
& m1_group_2(C,A) )
=> k1_funct_1(B,C) = u1_struct_0(C) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A) )
=> ( v1_funct_1(k1_latsubgr(A))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
! [A] :
( l1_group_1(A)
=> l1_struct_0(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_group_1(A)
& l1_group_1(A) )
=> ! [B] :
( m1_group_2(B,A)
=> ( ~ v3_struct_0(B)
& v3_group_1(B)
& l1_group_1(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
v1_xboole_0(k1_xboole_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,plain,
? [A] :
( ~ v3_struct_0(A)
& v3_group_1(A)
& v4_group_1(A)
& l1_group_1(A)
& ? [B] :
( v1_group_1(B)
& m1_group_2(B,A)
& k1_funct_1(k1_latsubgr(A),B) = k1_xboole_0 ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f56,plain,
( ~ v3_struct_0(sk0_0)
& v3_group_1(sk0_0)
& v4_group_1(sk0_0)
& l1_group_1(sk0_0)
& v1_group_1(sk0_1)
& m1_group_2(sk0_1,sk0_0)
& k1_funct_1(k1_latsubgr(sk0_0),sk0_1) = k1_xboole_0 ),
inference(skolemization,[status(esa)],[f55]) ).
fof(f57,plain,
~ v3_struct_0(sk0_0),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f58,plain,
v3_group_1(sk0_0),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f59,plain,
v4_group_1(sk0_0),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f60,plain,
l1_group_1(sk0_0),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f61,plain,
v1_group_1(sk0_1),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f62,plain,
m1_group_2(sk0_1,sk0_0),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f63,plain,
k1_funct_1(k1_latsubgr(sk0_0),sk0_1) = k1_xboole_0,
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f84,plain,
! [A] :
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ v4_group_1(A)
| ~ l1_group_1(A)
| ! [B] :
( ~ v1_funct_1(B)
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ( B = k1_latsubgr(A)
<=> ! [C] :
( ~ v1_group_1(C)
| ~ m1_group_2(C,A)
| k1_funct_1(B,C) = u1_struct_0(C) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f85,plain,
! [A] :
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ v4_group_1(A)
| ~ l1_group_1(A)
| ! [B] :
( ~ v1_funct_1(B)
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ( ( B != k1_latsubgr(A)
| ! [C] :
( ~ v1_group_1(C)
| ~ m1_group_2(C,A)
| k1_funct_1(B,C) = u1_struct_0(C) ) )
& ( B = k1_latsubgr(A)
| ? [C] :
( v1_group_1(C)
& m1_group_2(C,A)
& k1_funct_1(B,C) != u1_struct_0(C) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f84]) ).
fof(f86,plain,
! [A] :
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ v4_group_1(A)
| ~ l1_group_1(A)
| ! [B] :
( ~ v1_funct_1(B)
| ~ v1_funct_2(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ~ m2_relset_1(B,k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
| ( ( B != k1_latsubgr(A)
| ! [C] :
( ~ v1_group_1(C)
| ~ m1_group_2(C,A)
| k1_funct_1(B,C) = u1_struct_0(C) ) )
& ( B = k1_latsubgr(A)
| ( v1_group_1(sk0_2(B,A))
& m1_group_2(sk0_2(B,A),A)
& k1_funct_1(B,sk0_2(B,A)) != u1_struct_0(sk0_2(B,A)) ) ) ) ) ),
inference(skolemization,[status(esa)],[f85]) ).
fof(f87,plain,
! [X0,X1,X2] :
( v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_funct_1(X1)
| ~ v1_funct_2(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(X1,k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| X1 != k1_latsubgr(X0)
| ~ v1_group_1(X2)
| ~ m1_group_2(X2,X0)
| k1_funct_1(X1,X2) = u1_struct_0(X2) ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f94,plain,
! [A] :
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ v4_group_1(A)
| ~ l1_group_1(A)
| ( v1_funct_1(k1_latsubgr(A))
& v1_funct_2(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A)))
& m2_relset_1(k1_latsubgr(A),k1_group_3(A),k1_zfmisc_1(u1_struct_0(A))) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f95,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| v1_funct_1(k1_latsubgr(X0)) ),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f96,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f97,plain,
! [X0] :
( v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0))) ),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f98,plain,
! [A] :
( ~ l1_group_1(A)
| l1_struct_0(A) ),
inference(pre_NNF_transformation,[status(esa)],[f17]) ).
fof(f99,plain,
! [X0] :
( ~ l1_group_1(X0)
| l1_struct_0(X0) ),
inference(cnf_transformation,[status(esa)],[f98]) ).
fof(f100,plain,
! [A] :
( v3_struct_0(A)
| ~ v3_group_1(A)
| ~ l1_group_1(A)
| ! [B] :
( ~ m1_group_2(B,A)
| ( ~ v3_struct_0(B)
& v3_group_1(B)
& l1_group_1(B) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f101,plain,
! [X0,X1] :
( v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| ~ v3_struct_0(X1) ),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f103,plain,
! [X0,X1] :
( v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ l1_group_1(X0)
| ~ m1_group_2(X1,X0)
| l1_group_1(X1) ),
inference(cnf_transformation,[status(esa)],[f100]) ).
fof(f125,plain,
! [A] :
( v3_struct_0(A)
| ~ l1_struct_0(A)
| ~ v1_xboole_0(u1_struct_0(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f32]) ).
fof(f126,plain,
! [X0] :
( v3_struct_0(X0)
| ~ l1_struct_0(X0)
| ~ v1_xboole_0(u1_struct_0(X0)) ),
inference(cnf_transformation,[status(esa)],[f125]) ).
fof(f128,plain,
v1_xboole_0(k1_xboole_0),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f189,plain,
! [X0,X1] :
( v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_funct_1(k1_latsubgr(X0))
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1) ),
inference(destructive_equality_resolution,[status(esa)],[f87]) ).
fof(f190,plain,
( spl0_0
<=> v3_struct_0(sk0_0) ),
introduced(split_symbol_definition) ).
fof(f191,plain,
( v3_struct_0(sk0_0)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f190]) ).
fof(f193,plain,
( spl0_1
<=> v3_group_1(sk0_0) ),
introduced(split_symbol_definition) ).
fof(f195,plain,
( ~ v3_group_1(sk0_0)
| spl0_1 ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,plain,
( spl0_2
<=> l1_group_1(sk0_0) ),
introduced(split_symbol_definition) ).
fof(f198,plain,
( ~ l1_group_1(sk0_0)
| spl0_2 ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,plain,
( spl0_3
<=> v3_struct_0(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f202,plain,
( v3_struct_0(sk0_0)
| ~ v3_group_1(sk0_0)
| ~ l1_group_1(sk0_0)
| ~ v3_struct_0(sk0_1) ),
inference(resolution,[status(thm)],[f101,f62]) ).
fof(f203,plain,
( spl0_0
| ~ spl0_1
| ~ spl0_2
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f202,f190,f193,f196,f199]) ).
fof(f209,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f198,f60]) ).
fof(f210,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f209]) ).
fof(f211,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f195,f58]) ).
fof(f212,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f211]) ).
fof(f213,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f191,f57]) ).
fof(f214,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f213]) ).
fof(f215,plain,
( spl0_5
<=> l1_group_1(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f216,plain,
( l1_group_1(sk0_1)
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f215]) ).
fof(f218,plain,
( v3_struct_0(sk0_0)
| ~ v3_group_1(sk0_0)
| ~ l1_group_1(sk0_0)
| l1_group_1(sk0_1) ),
inference(resolution,[status(thm)],[f103,f62]) ).
fof(f219,plain,
( spl0_0
| ~ spl0_1
| ~ spl0_2
| spl0_5 ),
inference(split_clause,[status(thm)],[f218,f190,f193,f196,f215]) ).
fof(f220,plain,
! [X0,X1] :
( v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ m2_relset_1(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f189,f95]) ).
fof(f227,plain,
( l1_struct_0(sk0_1)
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f216,f99]) ).
fof(f228,plain,
! [X0,X1] :
( v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_funct_2(k1_latsubgr(X0),k1_group_3(X0),k1_zfmisc_1(u1_struct_0(X0)))
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f220,f97]) ).
fof(f229,plain,
! [X0,X1] :
( v3_struct_0(X0)
| ~ v3_group_1(X0)
| ~ v4_group_1(X0)
| ~ l1_group_1(X0)
| ~ v1_group_1(X1)
| ~ m1_group_2(X1,X0)
| k1_funct_1(k1_latsubgr(X0),X1) = u1_struct_0(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f228,f96]) ).
fof(f232,plain,
( spl0_6
<=> v4_group_1(sk0_0) ),
introduced(split_symbol_definition) ).
fof(f234,plain,
( ~ v4_group_1(sk0_0)
| spl0_6 ),
inference(component_clause,[status(thm)],[f232]) ).
fof(f235,plain,
( spl0_7
<=> v1_group_1(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f237,plain,
( ~ v1_group_1(sk0_1)
| spl0_7 ),
inference(component_clause,[status(thm)],[f235]) ).
fof(f238,plain,
( spl0_8
<=> m1_group_2(sk0_1,sk0_0) ),
introduced(split_symbol_definition) ).
fof(f240,plain,
( ~ m1_group_2(sk0_1,sk0_0)
| spl0_8 ),
inference(component_clause,[status(thm)],[f238]) ).
fof(f241,plain,
( spl0_9
<=> k1_xboole_0 = u1_struct_0(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f242,plain,
( k1_xboole_0 = u1_struct_0(sk0_1)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f241]) ).
fof(f244,plain,
( v3_struct_0(sk0_0)
| ~ v3_group_1(sk0_0)
| ~ v4_group_1(sk0_0)
| ~ l1_group_1(sk0_0)
| ~ v1_group_1(sk0_1)
| ~ m1_group_2(sk0_1,sk0_0)
| k1_xboole_0 = u1_struct_0(sk0_1) ),
inference(paramodulation,[status(thm)],[f63,f229]) ).
fof(f245,plain,
( spl0_0
| ~ spl0_1
| ~ spl0_6
| ~ spl0_2
| ~ spl0_7
| ~ spl0_8
| spl0_9 ),
inference(split_clause,[status(thm)],[f244,f190,f193,f232,f196,f235,f238,f241]) ).
fof(f246,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f240,f62]) ).
fof(f247,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f248,plain,
( $false
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f237,f61]) ).
fof(f249,plain,
spl0_7,
inference(contradiction_clause,[status(thm)],[f248]) ).
fof(f250,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f59]) ).
fof(f251,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f250]) ).
fof(f336,plain,
( spl0_20
<=> l1_struct_0(sk0_1) ),
introduced(split_symbol_definition) ).
fof(f338,plain,
( ~ l1_struct_0(sk0_1)
| spl0_20 ),
inference(component_clause,[status(thm)],[f336]) ).
fof(f339,plain,
( spl0_21
<=> v1_xboole_0(k1_xboole_0) ),
introduced(split_symbol_definition) ).
fof(f341,plain,
( ~ v1_xboole_0(k1_xboole_0)
| spl0_21 ),
inference(component_clause,[status(thm)],[f339]) ).
fof(f342,plain,
( v3_struct_0(sk0_1)
| ~ l1_struct_0(sk0_1)
| ~ v1_xboole_0(k1_xboole_0)
| ~ spl0_9 ),
inference(paramodulation,[status(thm)],[f242,f126]) ).
fof(f343,plain,
( spl0_3
| ~ spl0_20
| ~ spl0_21
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f342,f199,f336,f339,f241]) ).
fof(f344,plain,
( $false
| ~ spl0_5
| spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f338,f227]) ).
fof(f345,plain,
( ~ spl0_5
| spl0_20 ),
inference(contradiction_clause,[status(thm)],[f344]) ).
fof(f346,plain,
( $false
| spl0_21 ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f128]) ).
fof(f347,plain,
spl0_21,
inference(contradiction_clause,[status(thm)],[f346]) ).
fof(f348,plain,
$false,
inference(sat_refutation,[status(thm)],[f203,f210,f212,f214,f219,f245,f247,f249,f251,f343,f345,f347]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.10 % Problem : GRP642+1 : TPTP v8.1.2. Released v3.4.0.
% 0.02/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n031.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 11:52:37 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.15/0.31 % Drodi V3.5.1
% 0.15/0.32 % Refutation found
% 0.15/0.32 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.57 % Elapsed time: 0.037933 seconds
% 0.16/0.57 % CPU time: 0.018382 seconds
% 0.16/0.57 % Memory used: 3.921 MB
%------------------------------------------------------------------------------