TSTP Solution File: MGT026+1 by SnakeForV-SAT---1.0
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- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n027.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 Aug 31 17:51:26 EDT 2022
% Result : Theorem 0.20s 0.58s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 28
% Syntax : Number of formulae : 146 ( 13 unt; 0 def)
% Number of atoms : 518 ( 26 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 660 ( 288 ~; 280 |; 52 &)
% ( 18 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 25 ( 23 usr; 17 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 179 ( 175 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f330,plain,
$false,
inference(avatar_sat_refutation,[],[f77,f100,f110,f130,f245,f246,f248,f250,f252,f254,f260,f264,f274,f276,f283,f288,f293,f329]) ).
fof(f329,plain,
( spl3_20
| ~ spl3_19
| ~ spl3_22
| ~ spl3_7
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f328,f148,f107,f235,f216,f220]) ).
fof(f220,plain,
( spl3_20
<=> ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sK0)
| ~ environment(X0)
| ~ in_environment(X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_20])]) ).
fof(f216,plain,
( spl3_19
<=> in_environment(sK1,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_19])]) ).
fof(f235,plain,
( spl3_22
<=> greater(sK0,sF2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_22])]) ).
fof(f107,plain,
( spl3_7
<=> greater(cardinality_at_time(first_movers,sK0),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_7])]) ).
fof(f148,plain,
( spl3_12
<=> ! [X0] :
( ~ greater(X0,sF2)
| ~ in_environment(sK1,X0)
| greater(cardinality_at_time(efficient_producers,X0),zero) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_12])]) ).
fof(f328,plain,
( ! [X0] :
( ~ greater(sK0,sF2)
| ~ in_environment(sK1,sK0)
| subpopulations(first_movers,efficient_producers,X0,sK0)
| ~ in_environment(X0,sK0)
| ~ environment(X0) )
| ~ spl3_7
| ~ spl3_12 ),
inference(resolution,[],[f316,f109]) ).
fof(f109,plain,
( greater(cardinality_at_time(first_movers,sK0),zero)
| ~ spl3_7 ),
inference(avatar_component_clause,[],[f107]) ).
fof(f316,plain,
( ! [X0,X1] :
( ~ greater(cardinality_at_time(first_movers,X0),zero)
| subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X1)
| ~ greater(X0,sF2)
| ~ in_environment(X1,X0)
| ~ in_environment(sK1,X0) )
| ~ spl3_12 ),
inference(resolution,[],[f149,f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X1,X0] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X1,X0] :
( subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,plain,
! [X1,X0] :
( ( greater(cardinality_at_time(efficient_producers,X1),zero)
& in_environment(X0,X1)
& greater(cardinality_at_time(first_movers,X1),zero)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(rectify,[],[f3]) ).
fof(f3,axiom,
! [X0,X3] :
( ( greater(cardinality_at_time(efficient_producers,X3),zero)
& greater(cardinality_at_time(first_movers,X3),zero)
& environment(X0)
& in_environment(X0,X3) )
=> subpopulations(first_movers,efficient_producers,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f149,plain,
( ! [X0] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(X0,sF2)
| ~ in_environment(sK1,X0) )
| ~ spl3_12 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f293,plain,
( spl3_4
| spl3_12
| ~ spl3_1 ),
inference(avatar_split_clause,[],[f209,f68,f148,f87]) ).
fof(f87,plain,
( spl3_4
<=> appear(efficient_producers,sK1) = sF2 ),
introduced(avatar_definition,[new_symbols(naming,[spl3_4])]) ).
fof(f68,plain,
( spl3_1
<=> environment(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_1])]) ).
fof(f209,plain,
! [X0] :
( ~ environment(sK1)
| greater(cardinality_at_time(efficient_producers,X0),zero)
| appear(efficient_producers,sK1) = sF2
| ~ greater(X0,sF2)
| ~ in_environment(sK1,X0) ),
inference(superposition,[],[f182,f63]) ).
fof(f63,plain,
sF2 = critical_point(sK1),
introduced(function_definition,[]) ).
fof(f182,plain,
! [X0,X1] :
( ~ greater(X1,critical_point(X0))
| greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| critical_point(X0) = appear(efficient_producers,X0)
| ~ in_environment(X0,X1) ),
inference(duplicate_literal_removal,[],[f180]) ).
fof(f180,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ greater(X1,critical_point(X0))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| critical_point(X0) = appear(efficient_producers,X0) ),
inference(resolution,[],[f179,f57]) ).
fof(f57,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X1] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ environment(X0)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
! [X0,X1] :
( ( environment(X0)
& greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,X1) )
=> greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X0,X3] :
( ( environment(X0)
& greater_or_equal(X3,appear(efficient_producers,X0))
& in_environment(X0,X3) )
=> greater(cardinality_at_time(efficient_producers,X3),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6) ).
fof(f179,plain,
! [X6,X5] :
( greater_or_equal(X6,appear(efficient_producers,X5))
| appear(efficient_producers,X5) = critical_point(X5)
| ~ greater(X6,critical_point(X5))
| ~ environment(X5) ),
inference(resolution,[],[f118,f45]) ).
fof(f45,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| greater_or_equal(X1,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f15,plain,
! [X1,X0] :
( greater_or_equal(X1,X0)
<=> ( X0 = X1
| greater(X1,X0) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X5,X4] :
( greater_or_equal(X4,X5)
<=> ( greater(X4,X5)
| X4 = X5 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f118,plain,
! [X0,X1] :
( greater(X1,appear(efficient_producers,X0))
| critical_point(X0) = appear(efficient_producers,X0)
| ~ greater(X1,critical_point(X0))
| ~ environment(X0) ),
inference(resolution,[],[f79,f56]) ).
fof(f56,plain,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ greater(X0,X1)
| greater(X0,X2) ),
inference(cnf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ greater(X0,X1)
| ~ greater(X1,X2)
| greater(X0,X2) ),
inference(flattening,[],[f31]) ).
fof(f31,plain,
! [X2,X0,X1] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ( greater(X1,X2)
& greater(X0,X1) )
=> greater(X0,X2) ),
inference(rectify,[],[f7]) ).
fof(f7,axiom,
! [X4,X5,X6] :
( ( greater(X5,X6)
& greater(X4,X5) )
=> greater(X4,X6) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f79,plain,
! [X1] :
( greater(critical_point(X1),appear(efficient_producers,X1))
| critical_point(X1) = appear(efficient_producers,X1)
| ~ environment(X1) ),
inference(resolution,[],[f44,f52]) ).
fof(f52,plain,
! [X0] :
( greater_or_equal(critical_point(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0] :
( ~ environment(X0)
| greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( environment(X0)
=> greater_or_equal(critical_point(X0),appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_after_EP) ).
fof(f44,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,X0)
| X0 = X1
| greater(X1,X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f288,plain,
( ~ spl3_1
| ~ spl3_20
| ~ spl3_27 ),
inference(avatar_split_clause,[],[f287,f281,f220,f68]) ).
fof(f281,plain,
( spl3_27
<=> ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_27])]) ).
fof(f287,plain,
( ~ environment(sK1)
| ~ spl3_20
| ~ spl3_27 ),
inference(resolution,[],[f286,f49]) ).
fof(f49,plain,
in_environment(sK1,sK0),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
? [X1,X0] :
( environment(X0)
& in_environment(X0,X1)
& ~ selection_favors(efficient_producers,first_movers,X1)
& greater(X1,critical_point(X0)) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
? [X0,X1] :
( ~ selection_favors(efficient_producers,first_movers,X1)
& greater(X1,critical_point(X0))
& in_environment(X0,X1)
& environment(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,plain,
~ ! [X0,X1] :
( ( greater(X1,critical_point(X0))
& in_environment(X0,X1)
& environment(X0) )
=> selection_favors(efficient_producers,first_movers,X1) ),
inference(rectify,[],[f12]) ).
fof(f12,negated_conjecture,
~ ! [X0,X3] :
( ( greater(X3,critical_point(X0))
& environment(X0)
& in_environment(X0,X3) )
=> selection_favors(efficient_producers,first_movers,X3) ),
inference(negated_conjecture,[],[f11]) ).
fof(f11,conjecture,
! [X0,X3] :
( ( greater(X3,critical_point(X0))
& environment(X0)
& in_environment(X0,X3) )
=> selection_favors(efficient_producers,first_movers,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l8) ).
fof(f286,plain,
( ! [X0] :
( ~ in_environment(X0,sK0)
| ~ environment(X0) )
| ~ spl3_20
| ~ spl3_27 ),
inference(duplicate_literal_removal,[],[f285]) ).
fof(f285,plain,
( ! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sK0)
| ~ environment(X0) )
| ~ spl3_20
| ~ spl3_27 ),
inference(resolution,[],[f282,f221]) ).
fof(f221,plain,
( ! [X0] :
( subpopulations(first_movers,efficient_producers,X0,sK0)
| ~ environment(X0)
| ~ in_environment(X0,sK0) )
| ~ spl3_20 ),
inference(avatar_component_clause,[],[f220]) ).
fof(f282,plain,
( ! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK0)
| ~ environment(X0) )
| ~ spl3_27 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f283,plain,
( spl3_23
| spl3_27
| ~ spl3_25 ),
inference(avatar_split_clause,[],[f277,f268,f281,f239]) ).
fof(f239,plain,
( spl3_23
<=> selection_favors(efficient_producers,first_movers,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_23])]) ).
fof(f268,plain,
( spl3_25
<=> greater(growth_rate(efficient_producers,sK0),growth_rate(first_movers,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_25])]) ).
fof(f277,plain,
( ! [X0] :
( ~ environment(X0)
| selection_favors(efficient_producers,first_movers,sK0)
| ~ subpopulations(first_movers,efficient_producers,X0,sK0) )
| ~ spl3_25 ),
inference(resolution,[],[f270,f43]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ~ greater(growth_rate(X0,X1),growth_rate(X2,X1))
| ~ subpopulations(X2,X0,X3,X1)
| selection_favors(X0,X2,X1)
| ~ environment(X3) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X2,X0,X1,X3] :
( ~ environment(X3)
| ~ greater(growth_rate(X0,X1),growth_rate(X2,X1))
| ~ subpopulations(X2,X0,X3,X1)
| selection_favors(X0,X2,X1) ),
inference(flattening,[],[f23]) ).
fof(f23,plain,
! [X3,X0,X2,X1] :
( selection_favors(X0,X2,X1)
| ~ subpopulations(X2,X0,X3,X1)
| ~ environment(X3)
| ~ greater(growth_rate(X0,X1),growth_rate(X2,X1)) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,plain,
! [X3,X0,X2,X1] :
( ( subpopulations(X2,X0,X3,X1)
& environment(X3)
& greater(growth_rate(X0,X1),growth_rate(X2,X1)) )
=> selection_favors(X0,X2,X1) ),
inference(rectify,[],[f1]) ).
fof(f1,axiom,
! [X2,X3,X1,X0] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3)
& greater(growth_rate(X2,X3),growth_rate(X1,X3)) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f270,plain,
( greater(growth_rate(efficient_producers,sK0),growth_rate(first_movers,sK0))
| ~ spl3_25 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f276,plain,
( ~ spl3_22
| ~ spl3_1
| ~ spl3_19
| ~ spl3_26 ),
inference(avatar_split_clause,[],[f275,f272,f216,f68,f235]) ).
fof(f272,plain,
( spl3_26
<=> ! [X0] :
( ~ in_environment(X0,sK0)
| ~ environment(X0)
| ~ greater(sK0,critical_point(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_26])]) ).
fof(f275,plain,
( ~ in_environment(sK1,sK0)
| ~ environment(sK1)
| ~ greater(sK0,sF2)
| ~ spl3_26 ),
inference(superposition,[],[f273,f63]) ).
fof(f273,plain,
( ! [X0] :
( ~ greater(sK0,critical_point(X0))
| ~ environment(X0)
| ~ in_environment(X0,sK0) )
| ~ spl3_26 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f274,plain,
( spl3_25
| spl3_26
| ~ spl3_20 ),
inference(avatar_split_clause,[],[f266,f220,f272,f268]) ).
fof(f266,plain,
( ! [X0] :
( ~ in_environment(X0,sK0)
| ~ greater(sK0,critical_point(X0))
| ~ environment(X0)
| greater(growth_rate(efficient_producers,sK0),growth_rate(first_movers,sK0)) )
| ~ spl3_20 ),
inference(duplicate_literal_removal,[],[f265]) ).
fof(f265,plain,
( ! [X0] :
( ~ greater(sK0,critical_point(X0))
| ~ environment(X0)
| ~ in_environment(X0,sK0)
| greater(growth_rate(efficient_producers,sK0),growth_rate(first_movers,sK0))
| ~ environment(X0) )
| ~ spl3_20 ),
inference(resolution,[],[f221,f62]) ).
fof(f62,plain,
! [X2,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ greater(X2,critical_point(X1)) ),
inference(equality_resolution,[],[f53]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ~ environment(X1)
| ~ greater(X2,X0)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| critical_point(X1) != X0 ),
inference(cnf_transformation,[],[f30]) ).
fof(f30,plain,
! [X1,X0] :
( critical_point(X1) != X0
| ( ! [X2] :
( ~ subpopulations(first_movers,efficient_producers,X1,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X0) )
& ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) )
| ~ environment(X1) ),
inference(flattening,[],[f29]) ).
fof(f29,plain,
! [X1,X0] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(X2,X0) )
& ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) )
| critical_point(X1) != X0
| ~ environment(X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X1,X0] :
( ( critical_point(X1) = X0
& environment(X1) )
=> ( ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X1,X2)
& greater(X2,X0) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X7,X0] :
( ( critical_point(X0) = X7
& environment(X0) )
=> ( ~ greater(growth_rate(efficient_producers,X7),growth_rate(first_movers,X7))
& ! [X3] :
( ( greater(X3,X7)
& subpopulations(first_movers,efficient_producers,X0,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
fof(f264,plain,
( ~ spl3_21
| spl3_20
| ~ spl3_19
| ~ spl3_7
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f261,f128,f107,f216,f220,f223]) ).
fof(f223,plain,
( spl3_21
<=> greater_or_equal(sK0,sF2) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_21])]) ).
fof(f128,plain,
( spl3_9
<=> ! [X0] :
( ~ greater_or_equal(X0,sF2)
| greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_9])]) ).
fof(f261,plain,
( ! [X0] :
( ~ in_environment(sK1,sK0)
| subpopulations(first_movers,efficient_producers,X0,sK0)
| ~ environment(X0)
| ~ greater_or_equal(sK0,sF2)
| ~ in_environment(X0,sK0) )
| ~ spl3_7
| ~ spl3_9 ),
inference(resolution,[],[f109,f204]) ).
fof(f204,plain,
( ! [X0,X1] :
( ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ in_environment(sK1,X0)
| ~ in_environment(X1,X0)
| ~ environment(X1)
| subpopulations(first_movers,efficient_producers,X1,X0)
| ~ greater_or_equal(X0,sF2) )
| ~ spl3_9 ),
inference(resolution,[],[f129,f51]) ).
fof(f129,plain,
( ! [X0] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sK1,X0)
| ~ greater_or_equal(X0,sF2) )
| ~ spl3_9 ),
inference(avatar_component_clause,[],[f128]) ).
fof(f260,plain,
( ~ spl3_1
| ~ spl3_24 ),
inference(avatar_split_clause,[],[f259,f243,f68]) ).
fof(f243,plain,
( spl3_24
<=> ! [X1] :
( ~ subpopulation(efficient_producers,X1,sK0)
| ~ environment(X1)
| ~ subpopulation(first_movers,X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_24])]) ).
fof(f259,plain,
( ~ environment(sK1)
| ~ spl3_24 ),
inference(resolution,[],[f258,f49]) ).
fof(f258,plain,
( ! [X0] :
( ~ in_environment(X0,sK0)
| ~ environment(X0) )
| ~ spl3_24 ),
inference(duplicate_literal_removal,[],[f257]) ).
fof(f257,plain,
( ! [X0] :
( ~ in_environment(X0,sK0)
| ~ environment(X0)
| ~ in_environment(X0,sK0)
| ~ environment(X0) )
| ~ spl3_24 ),
inference(resolution,[],[f256,f58]) ).
fof(f58,plain,
! [X0,X1] :
( subpopulation(first_movers,X0,X1)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) )
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f27]) ).
fof(f27,plain,
! [X1,X0] :
( ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,plain,
! [X1,X0] :
( ( environment(X0)
& in_environment(X0,X1) )
=> ( subpopulation(efficient_producers,X0,X1)
& subpopulation(first_movers,X0,X1) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X0,X3] :
( ( in_environment(X0,X3)
& environment(X0) )
=> ( subpopulation(first_movers,X0,X3)
& subpopulation(efficient_producers,X0,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_subpopulations) ).
fof(f256,plain,
( ! [X0] :
( ~ subpopulation(first_movers,X0,sK0)
| ~ in_environment(X0,sK0)
| ~ environment(X0) )
| ~ spl3_24 ),
inference(duplicate_literal_removal,[],[f255]) ).
fof(f255,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulation(first_movers,X0,sK0)
| ~ in_environment(X0,sK0)
| ~ environment(X0) )
| ~ spl3_24 ),
inference(resolution,[],[f244,f59]) ).
fof(f59,plain,
! [X0,X1] :
( subpopulation(efficient_producers,X0,X1)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f244,plain,
( ! [X1] :
( ~ subpopulation(efficient_producers,X1,sK0)
| ~ environment(X1)
| ~ subpopulation(first_movers,X1,sK0) )
| ~ spl3_24 ),
inference(avatar_component_clause,[],[f243]) ).
fof(f254,plain,
~ spl3_23,
inference(avatar_contradiction_clause,[],[f253]) ).
fof(f253,plain,
( $false
| ~ spl3_23 ),
inference(resolution,[],[f241,f48]) ).
fof(f48,plain,
~ selection_favors(efficient_producers,first_movers,sK0),
inference(cnf_transformation,[],[f41]) ).
fof(f241,plain,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ spl3_23 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f252,plain,
spl3_22,
inference(avatar_contradiction_clause,[],[f251]) ).
fof(f251,plain,
( $false
| spl3_22 ),
inference(resolution,[],[f237,f64]) ).
fof(f64,plain,
greater(sK0,sF2),
inference(definition_folding,[],[f47,f63]) ).
fof(f47,plain,
greater(sK0,critical_point(sK1)),
inference(cnf_transformation,[],[f41]) ).
fof(f237,plain,
( ~ greater(sK0,sF2)
| spl3_22 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f250,plain,
spl3_21,
inference(avatar_contradiction_clause,[],[f249]) ).
fof(f249,plain,
( $false
| spl3_21 ),
inference(resolution,[],[f225,f65]) ).
fof(f65,plain,
greater_or_equal(sK0,sF2),
inference(resolution,[],[f45,f64]) ).
fof(f225,plain,
( ~ greater_or_equal(sK0,sF2)
| spl3_21 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f248,plain,
spl3_19,
inference(avatar_contradiction_clause,[],[f247]) ).
fof(f247,plain,
( $false
| spl3_19 ),
inference(resolution,[],[f218,f49]) ).
fof(f218,plain,
( ~ in_environment(sK1,sK0)
| spl3_19 ),
inference(avatar_component_clause,[],[f216]) ).
fof(f246,plain,
( spl3_23
| spl3_24
| ~ spl3_19
| ~ spl3_21
| ~ spl3_6
| ~ spl3_9 ),
inference(avatar_split_clause,[],[f230,f128,f103,f223,f216,f243,f239]) ).
fof(f103,plain,
( spl3_6
<=> zero = cardinality_at_time(first_movers,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_6])]) ).
fof(f230,plain,
( ! [X0] :
( ~ greater_or_equal(sK0,sF2)
| ~ in_environment(sK1,sK0)
| ~ subpopulation(first_movers,X0,sK0)
| ~ environment(X0)
| ~ subpopulation(efficient_producers,X0,sK0)
| selection_favors(efficient_producers,first_movers,sK0) )
| ~ spl3_6
| ~ spl3_9 ),
inference(resolution,[],[f229,f129]) ).
fof(f229,plain,
( ! [X0,X1] :
( ~ greater(cardinality_at_time(X1,sK0),zero)
| ~ subpopulation(X1,X0,sK0)
| ~ environment(X0)
| ~ subpopulation(first_movers,X0,sK0)
| selection_favors(X1,first_movers,sK0) )
| ~ spl3_6 ),
inference(trivial_inequality_removal,[],[f228]) ).
fof(f228,plain,
( ! [X0,X1] :
( zero != zero
| ~ subpopulation(first_movers,X0,sK0)
| selection_favors(X1,first_movers,sK0)
| ~ environment(X0)
| ~ greater(cardinality_at_time(X1,sK0),zero)
| ~ subpopulation(X1,X0,sK0) )
| ~ spl3_6 ),
inference(superposition,[],[f42,f105]) ).
fof(f105,plain,
( zero = cardinality_at_time(first_movers,sK0)
| ~ spl3_6 ),
inference(avatar_component_clause,[],[f103]) ).
fof(f42,plain,
! [X2,X3,X0,X1] :
( zero != cardinality_at_time(X3,X2)
| ~ subpopulation(X3,X0,X2)
| ~ environment(X0)
| ~ greater(cardinality_at_time(X1,X2),zero)
| ~ subpopulation(X1,X0,X2)
| selection_favors(X1,X3,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f26,plain,
! [X1,X2,X0,X3] :
( ~ greater(cardinality_at_time(X1,X2),zero)
| ~ environment(X0)
| zero != cardinality_at_time(X3,X2)
| ~ subpopulation(X3,X0,X2)
| selection_favors(X1,X3,X2)
| ~ subpopulation(X1,X0,X2) ),
inference(flattening,[],[f25]) ).
fof(f25,plain,
! [X3,X0,X1,X2] :
( selection_favors(X1,X3,X2)
| ~ greater(cardinality_at_time(X1,X2),zero)
| zero != cardinality_at_time(X3,X2)
| ~ subpopulation(X1,X0,X2)
| ~ environment(X0)
| ~ subpopulation(X3,X0,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,plain,
! [X3,X0,X1,X2] :
( ( greater(cardinality_at_time(X1,X2),zero)
& zero = cardinality_at_time(X3,X2)
& subpopulation(X1,X0,X2)
& environment(X0)
& subpopulation(X3,X0,X2) )
=> selection_favors(X1,X3,X2) ),
inference(rectify,[],[f2]) ).
fof(f2,axiom,
! [X0,X1,X3,X2] :
( ( greater(cardinality_at_time(X1,X3),zero)
& subpopulation(X2,X0,X3)
& subpopulation(X1,X0,X3)
& zero = cardinality_at_time(X2,X3)
& environment(X0) )
=> selection_favors(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp2_favour_members) ).
fof(f245,plain,
( ~ spl3_22
| spl3_23
| ~ spl3_19
| spl3_24
| ~ spl3_6
| ~ spl3_12 ),
inference(avatar_split_clause,[],[f231,f148,f103,f243,f216,f239,f235]) ).
fof(f231,plain,
( ! [X1] :
( ~ subpopulation(efficient_producers,X1,sK0)
| ~ subpopulation(first_movers,X1,sK0)
| ~ in_environment(sK1,sK0)
| ~ environment(X1)
| selection_favors(efficient_producers,first_movers,sK0)
| ~ greater(sK0,sF2) )
| ~ spl3_6
| ~ spl3_12 ),
inference(resolution,[],[f229,f149]) ).
fof(f130,plain,
( ~ spl3_1
| spl3_9
| ~ spl3_4 ),
inference(avatar_split_clause,[],[f125,f87,f128,f68]) ).
fof(f125,plain,
( ! [X0] :
( ~ greater_or_equal(X0,sF2)
| ~ environment(sK1)
| ~ in_environment(sK1,X0)
| greater(cardinality_at_time(efficient_producers,X0),zero) )
| ~ spl3_4 ),
inference(superposition,[],[f57,f89]) ).
fof(f89,plain,
( appear(efficient_producers,sK1) = sF2
| ~ spl3_4 ),
inference(avatar_component_clause,[],[f87]) ).
fof(f110,plain,
( spl3_6
| spl3_7
| ~ spl3_5 ),
inference(avatar_split_clause,[],[f101,f97,f107,f103]) ).
fof(f97,plain,
( spl3_5
<=> greater_or_equal(cardinality_at_time(first_movers,sK0),zero) ),
introduced(avatar_definition,[new_symbols(naming,[spl3_5])]) ).
fof(f101,plain,
( greater(cardinality_at_time(first_movers,sK0),zero)
| zero = cardinality_at_time(first_movers,sK0)
| ~ spl3_5 ),
inference(resolution,[],[f99,f44]) ).
fof(f99,plain,
( greater_or_equal(cardinality_at_time(first_movers,sK0),zero)
| ~ spl3_5 ),
inference(avatar_component_clause,[],[f97]) ).
fof(f100,plain,
( ~ spl3_1
| spl3_5 ),
inference(avatar_split_clause,[],[f95,f97,f68]) ).
fof(f95,plain,
( greater_or_equal(cardinality_at_time(first_movers,sK0),zero)
| ~ environment(sK1) ),
inference(resolution,[],[f55,f49]) ).
fof(f55,plain,
! [X0,X1] :
( ~ in_environment(X1,X0)
| ~ environment(X1)
| greater_or_equal(cardinality_at_time(first_movers,X0),zero) ),
inference(cnf_transformation,[],[f34]) ).
fof(f34,plain,
! [X1,X0] :
( ~ in_environment(X1,X0)
| greater_or_equal(cardinality_at_time(first_movers,X0),zero)
| ~ environment(X1) ),
inference(flattening,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( greater_or_equal(cardinality_at_time(first_movers,X0),zero)
| ~ environment(X1)
| ~ in_environment(X1,X0) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,plain,
! [X0,X1] :
( ( environment(X1)
& in_environment(X1,X0) )
=> greater_or_equal(cardinality_at_time(first_movers,X0),zero) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X3,X0] :
( ( in_environment(X0,X3)
& environment(X0) )
=> greater_or_equal(cardinality_at_time(first_movers,X3),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_exist) ).
fof(f77,plain,
spl3_1,
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f76,plain,
( $false
| spl3_1 ),
inference(resolution,[],[f70,f50]) ).
fof(f50,plain,
environment(sK1),
inference(cnf_transformation,[],[f41]) ).
fof(f70,plain,
( ~ environment(sK1)
| spl3_1 ),
inference(avatar_component_clause,[],[f68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : MGT026+1 : TPTP v8.1.0. Released v2.0.0.
% 0.03/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.34 % Computer : n027.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Aug 30 03:29:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.20/0.54 % (13296)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.55 % (13293)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.20/0.55 % (13314)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.55 % (13289)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.55 % (13291)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.55 % (13313)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 0.20/0.55 % (13316)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 0.20/0.55 % (13296)Instruction limit reached!
% 0.20/0.55 % (13296)------------------------------
% 0.20/0.55 % (13296)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.55 % (13296)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.55 % (13296)Termination reason: Unknown
% 0.20/0.55 % (13296)Termination phase: Saturation
% 0.20/0.55
% 0.20/0.55 % (13296)Memory used [KB]: 5373
% 0.20/0.55 % (13296)Time elapsed: 0.005 s
% 0.20/0.55 % (13296)Instructions burned: 3 (million)
% 0.20/0.55 % (13296)------------------------------
% 0.20/0.55 % (13296)------------------------------
% 0.20/0.55 % (13299)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.55 % (13288)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.55 % (13290)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.20/0.55 TRYING [1]
% 0.20/0.55 TRYING [2]
% 0.20/0.55 % (13312)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.20/0.55 % (13310)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.20/0.55 % (13291)First to succeed.
% 0.20/0.55 TRYING [3]
% 0.20/0.55 % (13295)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.20/0.55 % (13301)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.56 % (13297)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.56 % (13302)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.20/0.56 % (13289)Refutation not found, incomplete strategy% (13289)------------------------------
% 0.20/0.56 % (13289)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56 % (13306)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.56 % (13289)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56 % (13289)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.56
% 0.20/0.56 % (13289)Memory used [KB]: 5500
% 0.20/0.56 % (13289)Time elapsed: 0.150 s
% 0.20/0.56 % (13289)Instructions burned: 2 (million)
% 0.20/0.56 % (13289)------------------------------
% 0.20/0.56 % (13289)------------------------------
% 0.20/0.56 % (13295)Instruction limit reached!
% 0.20/0.56 % (13295)------------------------------
% 0.20/0.56 % (13295)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56 % (13295)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56 % (13295)Termination reason: Unknown
% 0.20/0.56 % (13295)Termination phase: Saturation
% 0.20/0.56
% 0.20/0.56 % (13295)Memory used [KB]: 5500
% 0.20/0.56 % (13295)Time elapsed: 0.152 s
% 0.20/0.56 % (13295)Instructions burned: 7 (million)
% 0.20/0.56 % (13295)------------------------------
% 0.20/0.56 % (13295)------------------------------
% 0.20/0.56 % (13307)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 0.20/0.56 % (13308)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 0.20/0.56 % (13304)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.56 % (13311)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 0.20/0.56 % (13315)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 0.20/0.56 % (13294)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.57 % (13303)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 0.20/0.57 % (13305)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.57 % (13292)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.57 TRYING [1]
% 0.20/0.57 % (13298)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.57 TRYING [2]
% 0.20/0.57 TRYING [1]
% 0.20/0.57 TRYING [3]
% 0.20/0.57 TRYING [4]
% 0.20/0.57 TRYING [2]
% 0.20/0.58 % (13291)Refutation found. Thanks to Tanya!
% 0.20/0.58 % SZS status Theorem for theBenchmark
% 0.20/0.58 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.58 % (13291)------------------------------
% 0.20/0.58 % (13291)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.58 % (13291)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.58 % (13291)Termination reason: Refutation
% 0.20/0.58
% 0.20/0.58 % (13291)Memory used [KB]: 5628
% 0.20/0.58 % (13291)Time elapsed: 0.158 s
% 0.20/0.58 % (13291)Instructions burned: 7 (million)
% 0.20/0.58 % (13291)------------------------------
% 0.20/0.58 % (13291)------------------------------
% 0.20/0.58 % (13287)Success in time 0.22 s
%------------------------------------------------------------------------------