TSTP Solution File: SET988+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SET988+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.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 : Tue Apr 30 15:14:12 EDT 2024
% Result : Theorem 0.15s 0.39s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 21
% Syntax : Number of formulae : 86 ( 17 unt; 0 def)
% Number of atoms : 254 ( 57 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 271 ( 103 ~; 88 |; 55 &)
% ( 9 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 168 ( 129 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f247,plain,
$false,
inference(avatar_sat_refutation,[],[f144,f180,f220,f225,f226,f227,f228,f246]) ).
fof(f246,plain,
spl18_2,
inference(avatar_contradiction_clause,[],[f245]) ).
fof(f245,plain,
( $false
| spl18_2 ),
inference(subsumption_resolution,[],[f244,f143]) ).
fof(f143,plain,
( ~ function(sK0)
| spl18_2 ),
inference(avatar_component_clause,[],[f141]) ).
fof(f141,plain,
( spl18_2
<=> function(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
fof(f244,plain,
( function(sK0)
| spl18_2 ),
inference(trivial_inequality_removal,[],[f243]) ).
fof(f243,plain,
( sK5(sK0) != sK5(sK0)
| function(sK0)
| spl18_2 ),
inference(superposition,[],[f107,f240]) ).
fof(f240,plain,
( sK5(sK0) = sK6(sK0)
| spl18_2 ),
inference(subsumption_resolution,[],[f238,f143]) ).
fof(f238,plain,
( sK5(sK0) = sK6(sK0)
| function(sK0)
| spl18_2 ),
inference(resolution,[],[f211,f106]) ).
fof(f106,plain,
! [X0] :
( in(ordered_pair(sK4(X0),sK6(X0)),X0)
| function(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ( function(X0)
| ( sK5(X0) != sK6(X0)
& in(ordered_pair(sK4(X0),sK6(X0)),X0)
& in(ordered_pair(sK4(X0),sK5(X0)),X0) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ function(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6])],[f65,f66]) ).
fof(f66,plain,
! [X0] :
( ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> ( sK5(X0) != sK6(X0)
& in(ordered_pair(sK4(X0),sK6(X0)),X0)
& in(ordered_pair(sK4(X0),sK5(X0)),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0] :
( ( function(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X4,X5,X6] :
( X5 = X6
| ~ in(ordered_pair(X4,X6),X0)
| ~ in(ordered_pair(X4,X5),X0) )
| ~ function(X0) ) ),
inference(rectify,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ( function(X0)
| ? [X1,X2,X3] :
( X2 != X3
& in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) ) )
& ( ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
| ~ function(X0) ) ),
inference(nnf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) ) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( function(X0)
<=> ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
fof(f211,plain,
( ! [X0] :
( ~ in(ordered_pair(sK4(sK0),X0),sK0)
| sK5(sK0) = X0 )
| spl18_2 ),
inference(subsumption_resolution,[],[f207,f143]) ).
fof(f207,plain,
! [X0] :
( sK5(sK0) = X0
| ~ in(ordered_pair(sK4(sK0),X0),sK0)
| function(sK0) ),
inference(resolution,[],[f90,f105]) ).
fof(f105,plain,
! [X0] :
( in(ordered_pair(sK4(X0),sK5(X0)),X0)
| function(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f90,plain,
! [X2,X3,X1] :
( ~ in(ordered_pair(X1,X3),sK0)
| X2 = X3
| ~ in(ordered_pair(X1,X2),sK0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
( ( ~ function(sK0)
| ~ relation(sK0) )
& ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),sK0)
| ~ in(ordered_pair(X1,X2),sK0) )
& ! [X4] :
( ordered_pair(sK1(X4),sK2(X4)) = X4
| ~ in(X4,sK0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f41,f60,f59]) ).
fof(f59,plain,
( ? [X0] :
( ( ~ function(X0)
| ~ relation(X0) )
& ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) )
=> ( ( ~ function(sK0)
| ~ relation(sK0) )
& ! [X3,X2,X1] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),sK0)
| ~ in(ordered_pair(X1,X2),sK0) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,sK0) ) ) ),
introduced(choice_axiom,[]) ).
fof(f60,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK1(X4),sK2(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f41,plain,
? [X0] :
( ( ~ function(X0)
| ~ relation(X0) )
& ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
? [X0] :
( ( ~ function(X0)
| ~ relation(X0) )
& ! [X1,X2,X3] :
( X2 = X3
| ~ in(ordered_pair(X1,X3),X0)
| ~ in(ordered_pair(X1,X2),X0) )
& ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
~ ! [X0] :
( ( ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 )
& ! [X4] :
~ ( ! [X5,X6] : ordered_pair(X5,X6) != X4
& in(X4,X0) ) )
=> ( function(X0)
& relation(X0) ) ),
inference(rectify,[],[f32]) ).
fof(f32,negated_conjecture,
~ ! [X0] :
( ( ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 )
& ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
=> ( function(X0)
& relation(X0) ) ),
inference(negated_conjecture,[],[f31]) ).
fof(f31,conjecture,
! [X0] :
( ( ! [X1,X2,X3] :
( ( in(ordered_pair(X1,X3),X0)
& in(ordered_pair(X1,X2),X0) )
=> X2 = X3 )
& ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
=> ( function(X0)
& relation(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
fof(f107,plain,
! [X0] :
( sK5(X0) != sK6(X0)
| function(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f228,plain,
~ spl18_4,
inference(avatar_contradiction_clause,[],[f221]) ).
fof(f221,plain,
( $false
| ~ spl18_4 ),
inference(resolution,[],[f219,f92]) ).
fof(f92,plain,
empty(empty_set),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
empty(empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f219,plain,
( ! [X0] : ~ empty(X0)
| ~ spl18_4 ),
inference(avatar_component_clause,[],[f218]) ).
fof(f218,plain,
( spl18_4
<=> ! [X0] : ~ empty(X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
fof(f227,plain,
~ spl18_4,
inference(avatar_contradiction_clause,[],[f222]) ).
fof(f222,plain,
( $false
| ~ spl18_4 ),
inference(resolution,[],[f219,f113]) ).
fof(f113,plain,
! [X0] : empty(sK11(X0)),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f21,f75]) ).
fof(f75,plain,
! [X0] :
( ? [X1] :
( empty(X1)
& element(X1,powerset(X0)) )
=> ( empty(sK11(X0))
& element(sK11(X0),powerset(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
! [X0] :
? [X1] :
( empty(X1)
& element(X1,powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc2_subset_1) ).
fof(f226,plain,
~ spl18_4,
inference(avatar_contradiction_clause,[],[f223]) ).
fof(f223,plain,
( $false
| ~ spl18_4 ),
inference(resolution,[],[f219,f128]) ).
fof(f128,plain,
empty(sK13),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
empty(sK13),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13])],[f26,f79]) ).
fof(f79,plain,
( ? [X0] : empty(X0)
=> empty(sK13) ),
introduced(choice_axiom,[]) ).
fof(f26,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f225,plain,
~ spl18_4,
inference(avatar_contradiction_clause,[],[f224]) ).
fof(f224,plain,
( $false
| ~ spl18_4 ),
inference(resolution,[],[f219,f134]) ).
fof(f134,plain,
empty(sK17),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( relation(sK17)
& empty(sK17) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK17])],[f22,f87]) ).
fof(f87,plain,
( ? [X0] :
( relation(X0)
& empty(X0) )
=> ( relation(sK17)
& empty(sK17) ) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] :
( relation(X0)
& empty(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rc1_relat_1) ).
fof(f220,plain,
( spl18_3
| spl18_4 ),
inference(avatar_split_clause,[],[f203,f218,f215]) ).
fof(f215,plain,
( spl18_3
<=> ! [X1] : ~ in(X1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
fof(f203,plain,
! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,empty_set) ),
inference(resolution,[],[f126,f155]) ).
fof(f155,plain,
! [X0] : element(empty_set,powerset(X0)),
inference(forward_demodulation,[],[f112,f148]) ).
fof(f148,plain,
! [X0] : empty_set = sK11(X0),
inference(resolution,[],[f103,f113]) ).
fof(f103,plain,
! [X0] :
( ~ empty(X0)
| empty_set = X0 ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_boole) ).
fof(f112,plain,
! [X0] : element(sK11(X0),powerset(X0)),
inference(cnf_transformation,[],[f76]) ).
fof(f126,plain,
! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t5_subset) ).
fof(f180,plain,
spl18_1,
inference(avatar_contradiction_clause,[],[f179]) ).
fof(f179,plain,
( $false
| spl18_1 ),
inference(subsumption_resolution,[],[f178,f139]) ).
fof(f139,plain,
( ~ relation(sK0)
| spl18_1 ),
inference(avatar_component_clause,[],[f137]) ).
fof(f137,plain,
( spl18_1
<=> relation(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
fof(f178,plain,
( relation(sK0)
| spl18_1 ),
inference(equality_resolution,[],[f171]) ).
fof(f171,plain,
( ! [X0] :
( sK7(X0) != sK7(sK0)
| relation(X0) )
| spl18_1 ),
inference(superposition,[],[f110,f169]) ).
fof(f169,plain,
( sK7(sK0) = ordered_pair(sK1(sK7(sK0)),sK2(sK7(sK0)))
| spl18_1 ),
inference(subsumption_resolution,[],[f168,f139]) ).
fof(f168,plain,
( sK7(sK0) = ordered_pair(sK1(sK7(sK0)),sK2(sK7(sK0)))
| relation(sK0) ),
inference(resolution,[],[f89,f109]) ).
fof(f109,plain,
! [X0] :
( in(sK7(X0),X0)
| relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ( relation(X0)
| ( ! [X2,X3] : ordered_pair(X2,X3) != sK7(X0)
& in(sK7(X0),X0) ) )
& ( ! [X4] :
( ordered_pair(sK8(X4),sK9(X4)) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9])],[f69,f71,f70]) ).
fof(f70,plain,
! [X0] :
( ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) )
=> ( ! [X3,X2] : ordered_pair(X2,X3) != sK7(X0)
& in(sK7(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
=> ordered_pair(sK8(X4),sK9(X4)) = X4 ),
introduced(choice_axiom,[]) ).
fof(f69,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X4] :
( ? [X5,X6] : ordered_pair(X5,X6) = X4
| ~ in(X4,X0) )
| ~ relation(X0) ) ),
inference(rectify,[],[f68]) ).
fof(f68,plain,
! [X0] :
( ( relation(X0)
| ? [X1] :
( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) )
& ( ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) )
| ~ relation(X0) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( relation(X0)
<=> ! [X1] :
( ? [X2,X3] : ordered_pair(X2,X3) = X1
| ~ in(X1,X0) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( relation(X0)
<=> ! [X1] :
~ ( ! [X2,X3] : ordered_pair(X2,X3) != X1
& in(X1,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(f89,plain,
! [X4] :
( ~ in(X4,sK0)
| ordered_pair(sK1(X4),sK2(X4)) = X4 ),
inference(cnf_transformation,[],[f61]) ).
fof(f110,plain,
! [X2,X3,X0] :
( ordered_pair(X2,X3) != sK7(X0)
| relation(X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f144,plain,
( ~ spl18_1
| ~ spl18_2 ),
inference(avatar_split_clause,[],[f91,f141,f137]) ).
fof(f91,plain,
( ~ function(sK0)
| ~ relation(sK0) ),
inference(cnf_transformation,[],[f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET988+1 : TPTP v8.1.2. Released v3.2.0.
% 0.14/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n007.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 01:16:18 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (28452)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (28459)WARNING: value z3 for option sas not known
% 0.15/0.38 % (28457)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (28458)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (28460)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (28459)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (28461)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (28463)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 % (28462)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.38 TRYING [2]
% 0.15/0.39 TRYING [3]
% 0.15/0.39 TRYING [1]
% 0.15/0.39 % (28459)First to succeed.
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (28459)Refutation found. Thanks to Tanya!
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.39 % (28459)------------------------------
% 0.15/0.39 % (28459)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.15/0.39 % (28459)Termination reason: Refutation
% 0.15/0.39
% 0.15/0.39 % (28459)Memory used [KB]: 884
% 0.15/0.39 % (28459)Time elapsed: 0.010 s
% 0.15/0.39 % (28459)Instructions burned: 11 (million)
% 0.15/0.39 % (28459)------------------------------
% 0.15/0.39 % (28459)------------------------------
% 0.15/0.39 % (28452)Success in time 0.026 s
%------------------------------------------------------------------------------