TSTP Solution File: SET669+3 by Vampire---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n005.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 : Sun May 5 09:07:55 EDT 2024
% Result : Theorem 0.87s 0.86s
% Output : Refutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 20
% Syntax : Number of formulae : 116 ( 24 unt; 0 def)
% Number of atoms : 355 ( 22 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 413 ( 174 ~; 170 |; 18 &)
% ( 17 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 186 ( 180 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1133,plain,
$false,
inference(avatar_sat_refutation,[],[f165,f369,f433,f733,f1132]) ).
fof(f1132,plain,
spl20_12,
inference(avatar_contradiction_clause,[],[f1131]) ).
fof(f1131,plain,
( $false
| spl20_12 ),
inference(subsumption_resolution,[],[f1130,f432]) ).
fof(f432,plain,
( ~ subset(range_of(sK2),sK1)
| spl20_12 ),
inference(avatar_component_clause,[],[f430]) ).
fof(f430,plain,
( spl20_12
<=> subset(range_of(sK2),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_12])]) ).
fof(f1130,plain,
subset(range_of(sK2),sK1),
inference(duplicate_literal_removal,[],[f1127]) ).
fof(f1127,plain,
( subset(range_of(sK2),sK1)
| subset(range_of(sK2),sK1) ),
inference(resolution,[],[f1109,f185]) ).
fof(f185,plain,
! [X0,X1] :
( member(sK9(X0,X1),X0)
| subset(X0,X1) ),
inference(subsumption_resolution,[],[f184,f95]) ).
fof(f95,plain,
! [X0] : ilf_type(X0,set_type),
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] : ilf_type(X0,set_type),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',p32) ).
fof(f184,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| member(sK9(X0,X1),X0)
| subset(X0,X1) ),
inference(subsumption_resolution,[],[f110,f95]) ).
fof(f110,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| member(sK9(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ( subset(X0,X1)
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( subset(X0,X1)
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',p7) ).
fof(f1109,plain,
! [X0] :
( ~ member(sK9(X0,sK1),range_of(sK2))
| subset(X0,sK1) ),
inference(resolution,[],[f974,f187]) ).
fof(f187,plain,
! [X0,X1] :
( ~ member(sK9(X0,X1),X1)
| subset(X0,X1) ),
inference(subsumption_resolution,[],[f186,f95]) ).
fof(f186,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ member(sK9(X0,X1),X1)
| subset(X0,X1) ),
inference(subsumption_resolution,[],[f111,f95]) ).
fof(f111,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ member(sK9(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f974,plain,
! [X0] :
( member(X0,sK1)
| ~ member(X0,range_of(sK2)) ),
inference(resolution,[],[f523,f167]) ).
fof(f167,plain,
ilf_type(sK2,relation_type(sK0,sK1)),
inference(backward_demodulation,[],[f149,f148]) ).
fof(f148,plain,
relation_type(sK0,sK1) = sF17,
introduced(function_definition,[new_symbols(definition,[sF17])]) ).
fof(f149,plain,
ilf_type(sK2,sF17),
inference(definition_folding,[],[f78,f148]) ).
fof(f78,plain,
ilf_type(sK2,relation_type(sK0,sK1)),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ~ subset(X1,domain(X0,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ( range(X0,X1,X2) != X1
| ~ subset(X1,domain(X0,X1,X2)) )
& subset(identity_relation_of(X1),X2)
& ilf_type(X2,relation_type(X0,X1)) )
& ilf_type(X1,set_type) )
& ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,negated_conjecture,
~ ! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( range(X0,X1,X2) = X1
& subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
inference(negated_conjecture,[],[f33]) ).
fof(f33,conjecture,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ( subset(identity_relation_of(X1),X2)
=> ( range(X0,X1,X2) = X1
& subset(X1,domain(X0,X1,X2)) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',prove_relset_1_32) ).
fof(f523,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,relation_type(X3,X1))
| ~ member(X0,range_of(X2))
| member(X0,X1) ),
inference(resolution,[],[f440,f297]) ).
fof(f297,plain,
! [X2,X0,X1] :
( ilf_type(range_of(X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(backward_subsumption_demodulation,[],[f255,f296]) ).
fof(f296,plain,
! [X2,X0,X1] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f295,f95]) ).
fof(f295,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(subsumption_resolution,[],[f114,f95]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| range(X0,X1,X2) = range_of(X2) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( range(X0,X1,X2) = range_of(X2)
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> range(X0,X1,X2) = range_of(X2) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',p30) ).
fof(f255,plain,
! [X2,X0,X1] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) ),
inference(subsumption_resolution,[],[f254,f95]) ).
fof(f254,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(subsumption_resolution,[],[f96,f95]) ).
fof(f96,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,relation_type(X0,X1))
| ilf_type(range(X0,X1,X2),subset_type(X1)) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ilf_type(range(X0,X1,X2),subset_type(X1))
| ~ ilf_type(X2,relation_type(X0,X1)) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,relation_type(X0,X1))
=> ilf_type(range(X0,X1,X2),subset_type(X1)) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',p31) ).
fof(f440,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,subset_type(X2))
| member(X0,X2)
| ~ member(X0,X1) ),
inference(resolution,[],[f322,f208]) ).
fof(f208,plain,
! [X0,X1] :
( ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f207,f95]) ).
fof(f207,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(subsumption_resolution,[],[f125,f95]) ).
fof(f125,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ilf_type(X1,member_type(power_set(X0)))
| ~ ilf_type(X1,subset_type(X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( ilf_type(X1,subset_type(X0))
<=> ilf_type(X1,member_type(power_set(X0))) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',p16) ).
fof(f322,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,member_type(power_set(X1)))
| ~ member(X0,X2)
| member(X0,X1) ),
inference(subsumption_resolution,[],[f320,f169]) ).
fof(f169,plain,
! [X0] : ~ empty(power_set(X0)),
inference(subsumption_resolution,[],[f134,f95]) ).
fof(f134,plain,
! [X0] :
( ~ ilf_type(X0,set_type)
| ~ empty(power_set(X0)) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0] :
( ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ( ilf_type(power_set(X0),set_type)
& ~ empty(power_set(X0)) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',p21) ).
fof(f320,plain,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,X2)
| empty(power_set(X1))
| ~ ilf_type(X2,member_type(power_set(X1))) ),
inference(resolution,[],[f305,f213]) ).
fof(f213,plain,
! [X0,X1] :
( member(X0,X1)
| empty(X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(subsumption_resolution,[],[f212,f95]) ).
fof(f212,plain,
! [X0,X1] :
( empty(X1)
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(subsumption_resolution,[],[f133,f95]) ).
fof(f133,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| empty(X1)
| ~ ilf_type(X1,set_type)
| member(X0,X1)
| ~ ilf_type(X0,member_type(X1)) ),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f71]) ).
fof(f71,plain,
! [X0] :
( ! [X1] :
( ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) )
| ~ ilf_type(X1,set_type)
| empty(X1) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ( ilf_type(X1,set_type)
& ~ empty(X1) )
=> ( ilf_type(X0,member_type(X1))
<=> member(X0,X1) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',p22) ).
fof(f305,plain,
! [X2,X0,X1] :
( ~ member(X0,power_set(X1))
| member(X2,X1)
| ~ member(X2,X0) ),
inference(subsumption_resolution,[],[f304,f95]) ).
fof(f304,plain,
! [X2,X0,X1] :
( ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1)
| ~ member(X0,power_set(X1)) ),
inference(subsumption_resolution,[],[f303,f95]) ).
fof(f303,plain,
! [X2,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1)
| ~ member(X0,power_set(X1)) ),
inference(subsumption_resolution,[],[f137,f95]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ member(X2,X0)
| member(X2,X1)
| ~ member(X0,power_set(X1)) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f75]) ).
fof(f75,plain,
! [X0] :
( ! [X1] :
( ( member(X0,power_set(X1))
<=> ! [X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ ilf_type(X2,set_type) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( member(X0,power_set(X1))
<=> ! [X2] :
( ilf_type(X2,set_type)
=> ( member(X2,X0)
=> member(X2,X1) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',p20) ).
fof(f733,plain,
( ~ spl20_1
| ~ spl20_11 ),
inference(avatar_contradiction_clause,[],[f732]) ).
fof(f732,plain,
( $false
| ~ spl20_1
| ~ spl20_11 ),
inference(subsumption_resolution,[],[f729,f160]) ).
fof(f160,plain,
( sP15(sK1)
| ~ spl20_1 ),
inference(avatar_component_clause,[],[f158]) ).
fof(f158,plain,
( spl20_1
<=> sP15(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_1])]) ).
fof(f729,plain,
( ~ sP15(sK1)
| ~ spl20_11 ),
inference(backward_demodulation,[],[f299,f428]) ).
fof(f428,plain,
( sK1 = range_of(sK2)
| ~ spl20_11 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f426,plain,
( spl20_11
<=> sK1 = range_of(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_11])]) ).
fof(f299,plain,
~ sP15(range_of(sK2)),
inference(subsumption_resolution,[],[f298,f167]) ).
fof(f298,plain,
( ~ sP15(range_of(sK2))
| ~ ilf_type(sK2,relation_type(sK0,sK1)) ),
inference(superposition,[],[f171,f296]) ).
fof(f171,plain,
~ sP15(range(sK0,sK1,sK2)),
inference(backward_demodulation,[],[f153,f152]) ).
fof(f152,plain,
range(sK0,sK1,sK2) = sF19,
introduced(function_definition,[new_symbols(definition,[sF19])]) ).
fof(f153,plain,
~ sP15(sF19),
inference(definition_folding,[],[f141,f152]) ).
fof(f141,plain,
~ sP15(range(sK0,sK1,sK2)),
introduced(inequality_splitting_name_introduction,[new_symbols(naming,[sP15])]) ).
fof(f433,plain,
( spl20_11
| ~ spl20_12 ),
inference(avatar_split_clause,[],[f407,f430,f426]) ).
fof(f407,plain,
( ~ subset(range_of(sK2),sK1)
| sK1 = range_of(sK2) ),
inference(resolution,[],[f396,f193]) ).
fof(f193,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(subsumption_resolution,[],[f192,f95]) ).
fof(f192,plain,
! [X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(subsumption_resolution,[],[f90,f95]) ).
fof(f90,plain,
! [X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ subset(X0,X1)
| ~ subset(X1,X0)
| X0 = X1 ),
inference(cnf_transformation,[],[f40]) ).
fof(f40,plain,
! [X0] :
( ! [X1] :
( ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ( X0 = X1
<=> ( subset(X1,X0)
& subset(X0,X1) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',p9) ).
fof(f396,plain,
subset(sK1,range_of(sK2)),
inference(subsumption_resolution,[],[f395,f167]) ).
fof(f395,plain,
( subset(sK1,range_of(sK2))
| ~ ilf_type(sK2,relation_type(sK0,sK1)) ),
inference(superposition,[],[f391,f296]) ).
fof(f391,plain,
subset(sK1,range(sK0,sK1,sK2)),
inference(resolution,[],[f351,f166]) ).
fof(f166,plain,
subset(identity_relation_of(sK1),sK2),
inference(backward_demodulation,[],[f147,f146]) ).
fof(f146,plain,
identity_relation_of(sK1) = sF16,
introduced(function_definition,[new_symbols(definition,[sF16])]) ).
fof(f147,plain,
subset(sF16,sK2),
inference(definition_folding,[],[f79,f146]) ).
fof(f79,plain,
subset(identity_relation_of(sK1),sK2),
inference(cnf_transformation,[],[f37]) ).
fof(f351,plain,
! [X0] :
( ~ subset(identity_relation_of(X0),sK2)
| subset(X0,range(sK0,sK1,sK2)) ),
inference(resolution,[],[f349,f167]) ).
fof(f349,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3)) ),
inference(subsumption_resolution,[],[f348,f95]) ).
fof(f348,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3)) ),
inference(subsumption_resolution,[],[f347,f95]) ).
fof(f347,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3)) ),
inference(subsumption_resolution,[],[f100,f95]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,range(X0,X1,X3)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) )
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(flattening,[],[f47]) ).
fof(f47,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) )
| ~ subset(identity_relation_of(X2),X3)
| ~ ilf_type(X3,relation_type(X0,X1)) )
| ~ ilf_type(X2,set_type) )
| ~ ilf_type(X1,set_type) )
| ~ ilf_type(X0,set_type) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( ilf_type(X0,set_type)
=> ! [X1] :
( ilf_type(X1,set_type)
=> ! [X2] :
( ilf_type(X2,set_type)
=> ! [X3] :
( ilf_type(X3,relation_type(X0,X1))
=> ( subset(identity_relation_of(X2),X3)
=> ( subset(X2,range(X0,X1,X3))
& subset(X2,domain(X0,X1,X3)) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163',p2) ).
fof(f369,plain,
spl20_2,
inference(avatar_contradiction_clause,[],[f368]) ).
fof(f368,plain,
( $false
| spl20_2 ),
inference(subsumption_resolution,[],[f366,f170]) ).
fof(f170,plain,
( ~ subset(sK1,domain(sK0,sK1,sK2))
| spl20_2 ),
inference(backward_demodulation,[],[f164,f150]) ).
fof(f150,plain,
domain(sK0,sK1,sK2) = sF18,
introduced(function_definition,[new_symbols(definition,[sF18])]) ).
fof(f164,plain,
( ~ subset(sK1,sF18)
| spl20_2 ),
inference(avatar_component_clause,[],[f162]) ).
fof(f162,plain,
( spl20_2
<=> subset(sK1,sF18) ),
introduced(avatar_definition,[new_symbols(naming,[spl20_2])]) ).
fof(f366,plain,
subset(sK1,domain(sK0,sK1,sK2)),
inference(resolution,[],[f343,f166]) ).
fof(f343,plain,
! [X0] :
( ~ subset(identity_relation_of(X0),sK2)
| subset(X0,domain(sK0,sK1,sK2)) ),
inference(resolution,[],[f341,f167]) ).
fof(f341,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(subsumption_resolution,[],[f340,f95]) ).
fof(f340,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(subsumption_resolution,[],[f339,f95]) ).
fof(f339,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(subsumption_resolution,[],[f99,f95]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( ~ ilf_type(X0,set_type)
| ~ ilf_type(X1,set_type)
| ~ ilf_type(X2,set_type)
| ~ ilf_type(X3,relation_type(X0,X1))
| ~ subset(identity_relation_of(X2),X3)
| subset(X2,domain(X0,X1,X3)) ),
inference(cnf_transformation,[],[f48]) ).
fof(f165,plain,
( spl20_1
| ~ spl20_2 ),
inference(avatar_split_clause,[],[f151,f162,f158]) ).
fof(f151,plain,
( ~ subset(sK1,sF18)
| sP15(sK1) ),
inference(definition_folding,[],[f142,f150]) ).
fof(f142,plain,
( ~ subset(sK1,domain(sK0,sK1,sK2))
| sP15(sK1) ),
inference(inequality_splitting,[],[f77,f141]) ).
fof(f77,plain,
( ~ subset(sK1,domain(sK0,sK1,sK2))
| sK1 != range(sK0,sK1,sK2) ),
inference(cnf_transformation,[],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : SET669+3 : TPTP v8.1.2. Released v2.2.0.
% 0.03/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.16/0.35 % Computer : n005.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Fri May 3 16:40:08 EDT 2024
% 0.16/0.35 % CPUTime :
% 0.16/0.35 This is a FOF_THM_RFO_SEQ problem
% 0.16/0.36 Running vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox2/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t 300 /export/starexec/sandbox2/tmp/tmp.hamfGMrm97/Vampire---4.8_20163
% 0.60/0.75 % (20409)dis-1011_2:1_sil=2000:lsd=20:nwc=5.0:flr=on:mep=off:st=3.0:i=34:sd=1:ep=RS:ss=axioms_0 on Vampire---4 for (2996ds/34Mi)
% 0.60/0.75 % (20412)ott+1011_1:1_sil=2000:urr=on:i=33:sd=1:kws=inv_frequency:ss=axioms:sup=off_0 on Vampire---4 for (2996ds/33Mi)
% 0.60/0.75 % (20411)lrs+1011_1:1_sil=8000:sp=occurrence:nwc=10.0:i=78:ss=axioms:sgt=8_0 on Vampire---4 for (2996ds/78Mi)
% 0.60/0.75 % (20410)lrs+1011_461:32768_sil=16000:irw=on:sp=frequency:lsd=20:fd=preordered:nwc=10.0:s2agt=32:alpa=false:cond=fast:s2a=on:i=51:s2at=3.0:awrs=decay:awrsf=691:bd=off:nm=20:fsr=off:amm=sco:uhcvi=on:rawr=on_0 on Vampire---4 for (2996ds/51Mi)
% 0.60/0.75 % (20413)lrs+2_1:1_sil=16000:fde=none:sos=all:nwc=5.0:i=34:ep=RS:s2pl=on:lma=on:afp=100000_0 on Vampire---4 for (2996ds/34Mi)
% 0.60/0.75 % (20414)lrs+1002_1:16_to=lpo:sil=32000:sp=unary_frequency:sos=on:i=45:bd=off:ss=axioms_0 on Vampire---4 for (2996ds/45Mi)
% 0.60/0.75 % (20416)lrs-21_1:1_to=lpo:sil=2000:sp=frequency:sos=on:lma=on:i=56:sd=2:ss=axioms:ep=R_0 on Vampire---4 for (2996ds/56Mi)
% 0.60/0.75 % (20415)lrs+21_1:5_sil=2000:sos=on:urr=on:newcnf=on:slsq=on:i=83:slsql=off:bd=off:nm=2:ss=axioms:st=1.5:sp=const_min:gsp=on:rawr=on_0 on Vampire---4 for (2996ds/83Mi)
% 0.60/0.75 % (20414)Refutation not found, incomplete strategy% (20414)------------------------------
% 0.60/0.75 % (20414)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.75 % (20414)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.75
% 0.60/0.75 % (20414)Memory used [KB]: 1085
% 0.60/0.75 % (20414)Time elapsed: 0.008 s
% 0.60/0.75 % (20414)Instructions burned: 5 (million)
% 0.60/0.75 % (20414)------------------------------
% 0.60/0.75 % (20414)------------------------------
% 0.60/0.76 % (20409)Instruction limit reached!
% 0.60/0.76 % (20409)------------------------------
% 0.60/0.76 % (20409)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76 % (20409)Termination reason: Unknown
% 0.60/0.76 % (20409)Termination phase: Saturation
% 0.60/0.76
% 0.60/0.76 % (20409)Memory used [KB]: 1255
% 0.60/0.76 % (20409)Time elapsed: 0.013 s
% 0.60/0.76 % (20409)Instructions burned: 37 (million)
% 0.60/0.76 % (20409)------------------------------
% 0.60/0.76 % (20409)------------------------------
% 0.60/0.76 % (20417)lrs+21_1:16_sil=2000:sp=occurrence:urr=on:flr=on:i=55:sd=1:nm=0:ins=3:ss=included:rawr=on:br=off_0 on Vampire---4 for (2996ds/55Mi)
% 0.60/0.76 % (20412)Instruction limit reached!
% 0.60/0.76 % (20412)------------------------------
% 0.60/0.76 % (20412)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.76 % (20412)Termination reason: Unknown
% 0.60/0.76 % (20412)Termination phase: Saturation
% 0.60/0.76
% 0.60/0.76 % (20412)Memory used [KB]: 1466
% 0.60/0.76 % (20412)Time elapsed: 0.018 s
% 0.60/0.76 % (20412)Instructions burned: 33 (million)
% 0.60/0.76 % (20412)------------------------------
% 0.60/0.76 % (20412)------------------------------
% 0.60/0.77 % (20418)dis+3_25:4_sil=16000:sos=all:erd=off:i=50:s2at=4.0:bd=off:nm=60:sup=off:cond=on:av=off:ins=2:nwc=10.0:etr=on:to=lpo:s2agt=20:fd=off:bsr=unit_only:slsq=on:slsqr=28,19:awrs=converge:awrsf=500:tgt=ground:bs=unit_only_0 on Vampire---4 for (2996ds/50Mi)
% 0.60/0.78 % (20413)Instruction limit reached!
% 0.60/0.78 % (20413)------------------------------
% 0.60/0.78 % (20413)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.78 % (20413)Termination reason: Unknown
% 0.60/0.78 % (20413)Termination phase: Saturation
% 0.60/0.78
% 0.60/0.78 % (20413)Memory used [KB]: 1285
% 0.60/0.78 % (20413)Time elapsed: 0.033 s
% 0.60/0.78 % (20413)Instructions burned: 35 (million)
% 0.60/0.78 % (20413)------------------------------
% 0.60/0.78 % (20413)------------------------------
% 0.60/0.78 % (20419)lrs+1010_1:2_sil=4000:tgt=ground:nwc=10.0:st=2.0:i=208:sd=1:bd=off:ss=axioms_0 on Vampire---4 for (2995ds/208Mi)
% 0.60/0.78 % (20417)Instruction limit reached!
% 0.60/0.78 % (20417)------------------------------
% 0.60/0.78 % (20417)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.78 % (20417)Termination reason: Unknown
% 0.60/0.78 % (20417)Termination phase: Saturation
% 0.60/0.78
% 0.60/0.78 % (20417)Memory used [KB]: 1640
% 0.60/0.78 % (20417)Time elapsed: 0.021 s
% 0.60/0.78 % (20417)Instructions burned: 56 (million)
% 0.60/0.78 % (20417)------------------------------
% 0.60/0.78 % (20417)------------------------------
% 0.60/0.78 % (20421)lrs-1010_1:1_to=lpo:sil=2000:sp=reverse_arity:sos=on:urr=ec_only:i=518:sd=2:bd=off:ss=axioms:sgt=16_0 on Vampire---4 for (2995ds/518Mi)
% 0.60/0.78 % (20420)lrs-1011_1:1_sil=4000:plsq=on:plsqr=32,1:sp=frequency:plsql=on:nwc=10.0:i=52:aac=none:afr=on:ss=axioms:er=filter:sgt=16:rawr=on:etr=on:lma=on_0 on Vampire---4 for (2995ds/52Mi)
% 0.60/0.79 % (20421)Refutation not found, incomplete strategy% (20421)------------------------------
% 0.60/0.79 % (20421)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79 % (20421)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.79
% 0.60/0.79 % (20421)Memory used [KB]: 1146
% 0.60/0.79 % (20421)Time elapsed: 0.006 s
% 0.60/0.79 % (20421)Instructions burned: 7 (million)
% 0.60/0.79 % (20421)------------------------------
% 0.60/0.79 % (20421)------------------------------
% 0.60/0.79 % (20416)Instruction limit reached!
% 0.60/0.79 % (20416)------------------------------
% 0.60/0.79 % (20416)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.79 % (20416)Termination reason: Unknown
% 0.60/0.79 % (20416)Termination phase: Saturation
% 0.60/0.79
% 0.60/0.79 % (20416)Memory used [KB]: 1296
% 0.60/0.79 % (20416)Time elapsed: 0.044 s
% 0.60/0.79 % (20416)Instructions burned: 56 (million)
% 0.60/0.79 % (20416)------------------------------
% 0.60/0.79 % (20416)------------------------------
% 0.60/0.79 % (20422)lrs+1011_87677:1048576_sil=8000:sos=on:spb=non_intro:nwc=10.0:kmz=on:i=42:ep=RS:nm=0:ins=1:uhcvi=on:rawr=on:fde=unused:afp=2000:afq=1.444:plsq=on:nicw=on_0 on Vampire---4 for (2995ds/42Mi)
% 0.60/0.80 % (20422)Refutation not found, incomplete strategy% (20422)------------------------------
% 0.60/0.80 % (20422)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.80 % (20422)Termination reason: Refutation not found, incomplete strategy
% 0.60/0.80
% 0.60/0.80 % (20422)Memory used [KB]: 1116
% 0.60/0.80 % (20422)Time elapsed: 0.005 s
% 0.60/0.80 % (20422)Instructions burned: 6 (million)
% 0.60/0.80 % (20422)------------------------------
% 0.60/0.80 % (20422)------------------------------
% 0.60/0.80 % (20423)dis+1011_1258907:1048576_bsr=unit_only:to=lpo:drc=off:sil=2000:tgt=full:fde=none:sp=frequency:spb=goal:rnwc=on:nwc=6.70083:sac=on:newcnf=on:st=2:i=243:bs=unit_only:sd=3:afp=300:awrs=decay:awrsf=218:nm=16:ins=3:afq=3.76821:afr=on:ss=axioms:sgt=5:rawr=on:add=off:bsd=on_0 on Vampire---4 for (2995ds/243Mi)
% 0.60/0.80 % (20424)lrs+1011_2:9_sil=2000:lsd=10:newcnf=on:i=117:sd=2:awrs=decay:ss=included:amm=off:ep=R_0 on Vampire---4 for (2995ds/117Mi)
% 0.60/0.80 % (20410)Instruction limit reached!
% 0.60/0.80 % (20410)------------------------------
% 0.60/0.80 % (20410)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.80 % (20410)Termination reason: Unknown
% 0.60/0.80 % (20410)Termination phase: Saturation
% 0.60/0.80
% 0.60/0.80 % (20410)Memory used [KB]: 1711
% 0.60/0.80 % (20410)Time elapsed: 0.056 s
% 0.60/0.80 % (20410)Instructions burned: 51 (million)
% 0.60/0.80 % (20410)------------------------------
% 0.60/0.80 % (20410)------------------------------
% 0.60/0.81 % (20425)dis+1011_11:1_sil=2000:avsq=on:i=143:avsqr=1,16:ep=RS:rawr=on:aac=none:lsd=100:mep=off:fde=none:newcnf=on:bsr=unit_only_0 on Vampire---4 for (2995ds/143Mi)
% 0.60/0.81 % (20418)Instruction limit reached!
% 0.60/0.81 % (20418)------------------------------
% 0.60/0.81 % (20418)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.60/0.81 % (20418)Termination reason: Unknown
% 0.60/0.81 % (20418)Termination phase: Saturation
% 0.60/0.81
% 0.60/0.81 % (20418)Memory used [KB]: 1554
% 0.60/0.81 % (20418)Time elapsed: 0.049 s
% 0.60/0.81 % (20418)Instructions burned: 50 (million)
% 0.60/0.81 % (20418)------------------------------
% 0.60/0.81 % (20418)------------------------------
% 0.87/0.82 % (20426)lrs+1011_1:2_to=lpo:sil=8000:plsqc=1:plsq=on:plsqr=326,59:sp=weighted_frequency:plsql=on:nwc=10.0:newcnf=on:i=93:awrs=converge:awrsf=200:bd=off:ins=1:rawr=on:alpa=false:avsq=on:avsqr=1,16_0 on Vampire---4 for (2995ds/93Mi)
% 0.87/0.83 % (20411)Instruction limit reached!
% 0.87/0.83 % (20411)------------------------------
% 0.87/0.83 % (20411)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.87/0.83 % (20411)Termination reason: Unknown
% 0.87/0.83 % (20411)Termination phase: Saturation
% 0.87/0.83
% 0.87/0.83 % (20411)Memory used [KB]: 1809
% 0.87/0.83 % (20411)Time elapsed: 0.083 s
% 0.87/0.83 % (20411)Instructions burned: 78 (million)
% 0.87/0.83 % (20411)------------------------------
% 0.87/0.83 % (20411)------------------------------
% 0.87/0.83 % (20415)Instruction limit reached!
% 0.87/0.83 % (20415)------------------------------
% 0.87/0.83 % (20415)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.87/0.83 % (20415)Termination reason: Unknown
% 0.87/0.83 % (20415)Termination phase: Saturation
% 0.87/0.83
% 0.87/0.83 % (20415)Memory used [KB]: 1897
% 0.87/0.83 % (20415)Time elapsed: 0.084 s
% 0.87/0.83 % (20415)Instructions burned: 83 (million)
% 0.87/0.83 % (20415)------------------------------
% 0.87/0.83 % (20415)------------------------------
% 0.87/0.83 % (20427)lrs+1666_1:1_sil=4000:sp=occurrence:sos=on:urr=on:newcnf=on:i=62:amm=off:ep=R:erd=off:nm=0:plsq=on:plsqr=14,1_0 on Vampire---4 for (2995ds/62Mi)
% 0.87/0.84 % (20420)Instruction limit reached!
% 0.87/0.84 % (20420)------------------------------
% 0.87/0.84 % (20420)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.87/0.84 % (20420)Termination reason: Unknown
% 0.87/0.84 % (20420)Termination phase: Saturation
% 0.87/0.84
% 0.87/0.84 % (20420)Memory used [KB]: 1481
% 0.87/0.84 % (20420)Time elapsed: 0.054 s
% 0.87/0.84 % (20420)Instructions burned: 53 (million)
% 0.87/0.84 % (20420)------------------------------
% 0.87/0.84 % (20420)------------------------------
% 0.87/0.84 % (20428)lrs+21_2461:262144_anc=none:drc=off:sil=2000:sp=occurrence:nwc=6.0:updr=off:st=3.0:i=32:sd=2:afp=4000:erml=3:nm=14:afq=2.0:uhcvi=on:ss=included:er=filter:abs=on:nicw=on:ile=on:sims=off:s2a=on:s2agt=50:s2at=-1.0:plsq=on:plsql=on:plsqc=2:plsqr=1,32:newcnf=on:bd=off:to=lpo_0 on Vampire---4 for (2995ds/32Mi)
% 0.87/0.84 % (20429)dis+1011_1:1_sil=16000:nwc=7.0:s2agt=64:s2a=on:i=1919:ss=axioms:sgt=8:lsd=50:sd=7_0 on Vampire---4 for (2995ds/1919Mi)
% 0.87/0.85 % (20428)Instruction limit reached!
% 0.87/0.85 % (20428)------------------------------
% 0.87/0.85 % (20428)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.87/0.85 % (20428)Termination reason: Unknown
% 0.87/0.85 % (20428)Termination phase: Saturation
% 0.87/0.85
% 0.87/0.85 % (20428)Memory used [KB]: 1288
% 0.87/0.85 % (20428)Time elapsed: 0.021 s
% 0.87/0.85 % (20428)Instructions burned: 32 (million)
% 0.87/0.85 % (20428)------------------------------
% 0.87/0.85 % (20428)------------------------------
% 0.87/0.86 % (20423)First to succeed.
% 0.87/0.86 % (20430)ott-32_5:1_sil=4000:sp=occurrence:urr=full:rp=on:nwc=5.0:newcnf=on:st=5.0:s2pl=on:i=55:sd=2:ins=2:ss=included:rawr=on:anc=none:sos=on:s2agt=8:spb=intro:ep=RS:avsq=on:avsqr=27,155:lma=on_0 on Vampire---4 for (2995ds/55Mi)
% 0.87/0.86 % (20423)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-20317"
% 0.87/0.86 % (20423)Refutation found. Thanks to Tanya!
% 0.87/0.86 % SZS status Theorem for Vampire---4
% 0.87/0.86 % SZS output start Proof for Vampire---4
% See solution above
% 0.87/0.86 % (20423)------------------------------
% 0.87/0.86 % (20423)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.87/0.86 % (20423)Termination reason: Refutation
% 0.87/0.86
% 0.87/0.86 % (20423)Memory used [KB]: 1491
% 0.87/0.86 % (20423)Time elapsed: 0.066 s
% 0.87/0.86 % (20423)Instructions burned: 75 (million)
% 0.87/0.86 % (20317)Success in time 0.491 s
% 0.87/0.86 % Vampire---4.8 exiting
%------------------------------------------------------------------------------