%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM924^1 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:19:01 AM UTC 2026
% Result : Theorem 0.21s 0.36s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 46 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 40 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 502 ( 8 ~; 0 |; 0 &; 494 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 27 usr; 11 con; 0-2 aty)
% Number of variables : 18 ( 0 ^; 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
int: $tType ).
thf(type_def_6,type,
nat: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
one_one_int: int ).
thf(func_def_1,type,
one_one_nat: nat ).
thf(func_def_2,type,
plus_plus_int: int > int > int ).
thf(func_def_3,type,
plus_plus_nat: nat > nat > nat ).
thf(func_def_4,type,
times_times_int: int > int > int ).
thf(func_def_5,type,
times_times_nat: nat > nat > nat ).
thf(func_def_6,type,
zero_zero_int: int ).
thf(func_def_7,type,
zero_zero_nat: nat ).
thf(func_def_8,type,
zprime: int > $o ).
thf(func_def_9,type,
bit0: int > int ).
thf(func_def_10,type,
bit1: int > int ).
thf(func_def_11,type,
pls: int ).
thf(func_def_12,type,
number_number_of_int: int > int ).
thf(func_def_13,type,
number_number_of_nat: int > nat ).
thf(func_def_14,type,
ord_less_int: int > int > $o ).
thf(func_def_15,type,
ord_less_nat: nat > nat > $o ).
thf(func_def_16,type,
ord_less_eq_int: int > int > $o ).
thf(func_def_17,type,
ord_less_eq_nat: nat > nat > $o ).
thf(func_def_18,type,
power_power_int: int > nat > int ).
thf(func_def_19,type,
power_power_nat: nat > nat > nat ).
thf(func_def_20,type,
twoSqu1013291560sum2sq: int > $o ).
thf(func_def_21,type,
m: int ).
thf(func_def_22,type,
s: int ).
thf(func_def_23,type,
t: int ).
thf(func_def_27,type,
sK0: int ).
thf(func_def_28,type,
vNOT: $o > $o ).
thf(f3,axiom,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096) ).
thf(f4,axiom,
( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
= ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_t) ).
thf(f25,axiom,
! [X0: int] :
( ( number_number_of_int @ X0 )
= X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_number__of__is__id) ).
thf(f26,axiom,
! [X1: int,X0: int] :
( ( times_times_int @ X0 @ X1 )
= ( times_times_int @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_zmult__commute) ).
thf(f66,axiom,
( ( plus_plus_nat @ one_one_nat @ one_one_nat )
= ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_nat__1__add__1) ).
thf(f67,axiom,
! [X0: int] :
( ( times_times_int @ pls @ X0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_mult__Pls) ).
thf(f105,axiom,
! [X1: int,X0: int] :
( ( plus_plus_int @ X0 @ X1 )
= ( plus_plus_int @ X1 @ X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_104_zadd__commute) ).
thf(f106,axiom,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_105_zero__is__num__zero) ).
thf(f107,conjecture,
ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(f108,negated_conjecture,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(negated_conjecture,[status(cth)],[f107]) ).
thf(f195,plain,
ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ),
inference(rectify,[],[f3]) ).
thf(f196,plain,
( ( ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) )
= $true ),
inference(fool_elimination,[],[f195]) ).
thf(f209,plain,
~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int ),
inference(rectify,[],[f108]) ).
thf(f210,plain,
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int )
!= $true ),
inference(fool_elimination,[],[f209]) ).
thf(f243,plain,
! [X1: int,X0: int] :
( ( plus_plus_int @ X0 @ X1 )
= ( plus_plus_int @ X1 @ X0 ) ),
inference(rectify,[],[f105]) ).
thf(f248,plain,
! [X0: int,X1: int] :
( ( times_times_int @ X0 @ X1 )
= ( times_times_int @ X1 @ X0 ) ),
inference(rectify,[],[f26]) ).
thf(f255,plain,
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int )
!= $true ),
inference(flattening,[],[f210]) ).
thf(f298,plain,
! [X0: int,X1: int] :
( ( plus_plus_int @ X0 @ X1 )
= ( plus_plus_int @ X1 @ X0 ) ),
inference(rectify,[],[f243]) ).
thf(f374,plain,
( zero_zero_int
= ( number_number_of_int @ pls ) ),
inference(cnf_transformation,[],[f106]) ).
thf(f382,plain,
( ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) )
= ( plus_plus_nat @ one_one_nat @ one_one_nat ) ),
inference(cnf_transformation,[],[f66]) ).
thf(f385,plain,
( ( ord_less_int @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) )
= $true ),
inference(cnf_transformation,[],[f196]) ).
thf(f387,plain,
! [X0: int,X1: int] :
( ( plus_plus_int @ X0 @ X1 )
= ( plus_plus_int @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f298]) ).
thf(f394,plain,
! [X0: int] :
( pls
= ( times_times_int @ pls @ X0 ) ),
inference(cnf_transformation,[],[f67]) ).
thf(f398,plain,
! [X0: int] :
( ( number_number_of_int @ X0 )
= X0 ),
inference(cnf_transformation,[],[f25]) ).
thf(f448,plain,
( ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) @ zero_zero_int )
!= $true ),
inference(cnf_transformation,[],[f255]) ).
thf(f460,plain,
( ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t )
= ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f466,plain,
! [X0: int,X1: int] :
( ( times_times_int @ X0 @ X1 )
= ( times_times_int @ X1 @ X0 ) ),
inference(cnf_transformation,[],[f248]) ).
thf(f571,plain,
zero_zero_int = pls,
inference(forward_demodulation,[],[f374,f398]) ).
thf(f583,plain,
( $true
!= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ),
inference(forward_demodulation,[],[f448,f387]) ).
thf(f598,plain,
( ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t )
= ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ),
inference(forward_demodulation,[],[f460,f387]) ).
thf(f601,plain,
( ( ord_less_int @ ( times_times_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ zero_zero_int ) )
= $true ),
inference(forward_demodulation,[],[f385,f466]) ).
thf(f623,plain,
( $true
!= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) @ zero_zero_int ) ),
inference(forward_demodulation,[],[f583,f382]) ).
thf(f635,plain,
( ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t )
= ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) ),
inference(forward_demodulation,[],[f598,f382]) ).
thf(f638,plain,
( ( ord_less_int @ ( times_times_int @ t @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) ) ) @ ( times_times_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) ) @ zero_zero_int ) )
= $true ),
inference(forward_demodulation,[],[f601,f387]) ).
thf(f648,plain,
( $true
!= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) @ pls ) ),
inference(forward_demodulation,[],[f623,f571]) ).
thf(f656,plain,
( ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) )
= ( times_times_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ),
inference(forward_demodulation,[],[f635,f466]) ).
thf(f657,plain,
( $true
= ( ord_less_int @ ( times_times_int @ t @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) @ ( times_times_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ zero_zero_int ) ) ),
inference(forward_demodulation,[],[f638,f466]) ).
thf(f666,plain,
( ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) )
= ( times_times_int @ t @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) ) ) ),
inference(forward_demodulation,[],[f656,f387]) ).
thf(f667,plain,
( ( ord_less_int @ ( times_times_int @ t @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( times_times_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) )
= $true ),
inference(forward_demodulation,[],[f657,f398]) ).
thf(f679,plain,
( ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) )
= ( times_times_int @ t @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f666,f466]) ).
thf(f680,plain,
( ( ord_less_int @ ( times_times_int @ t @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( times_times_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[],[f667,f466]) ).
thf(f682,plain,
( ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) )
= ( times_times_int @ t @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f679,f398]) ).
thf(f683,plain,
( ( ord_less_int @ ( times_times_int @ t @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( times_times_int @ pls @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) )
= $true ),
inference(forward_demodulation,[],[f680,f571]) ).
thf(f684,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) @ ( times_times_int @ pls @ ( plus_plus_int @ one_one_int @ ( times_times_int @ m @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ),
inference(forward_demodulation,[],[f683,f682]) ).
thf(f685,plain,
( $true
= ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( power_power_int @ s @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ) ) @ pls ) ),
inference(forward_demodulation,[],[f684,f394]) ).
thf(f686,plain,
$false,
inference(forward_subsumption_resolution,[],[f685,f648]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM924^1 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.22 % Computer : n016.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Sep 29 13:10:04 UTC 2026
% 0.09/0.22 % CPUTime :
% 0.09/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.26 Running higher-order theorem proving
% 0.21/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.36 % (312944)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.36 % (312949)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3729640681:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.36 % (312950)lrs+10_16_si=on:nwc=1.5:random_seed=2911262321:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.36 % (312952)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=3271097855:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.21/0.36 % (312950)Instruction limit reached!
% 0.21/0.36 % (312950)------------------------------
% 0.21/0.36 % (312950)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (312950)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (312950)CaDiCaL version: 2.1.3
% 0.21/0.36 % (312950)Termination reason: Instruction limit
% 0.21/0.36 % (312950)Termination phase: Property scanning
% 0.21/0.36 % (312950)Time elapsed: 0.017 s
% 0.21/0.36 % (312950)Peak memory usage: 10 MB
% 0.21/0.36 % (312950)Instructions burned: 20 (million)
% 0.21/0.36 % (312949) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-312944-312949"...
% 0.21/0.36 % (312949)...printing done.
% 0.21/0.36 % (312949)Refutation found. Thanks to Tanya!
% 0.21/0.36 % SZS status Theorem for theBenchmark
% 0.21/0.36 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.36 % (312949)------------------------------
% 0.21/0.36 % (312949)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.36 % (312949)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.36 % (312949)CaDiCaL version: 2.1.3
% 0.21/0.36 % (312949)Termination reason: Refutation
% 0.21/0.36 % (312949)Time elapsed: 0.023 s
% 0.21/0.36 % (312949)Peak memory usage: 12 MB
% 0.21/0.36 % (312949)Instructions burned: 43 (million)
% 0.21/0.36 % (312944)Success in time 0.07 s
% 0.21/0.36 % Vampire exiting
%------------------------------------------------------------------------------