TSTP Solution File: GRP523-1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRP523-1 : TPTP v8.1.0. Released v2.6.0.
% 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 : n011.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 16:22:46 EDT 2022
% Result : Unsatisfiable 2.42s 0.71s
% Output : Refutation 2.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 33 unt; 0 def)
% Number of atoms : 33 ( 32 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 7 ( 7 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 65 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f891,plain,
$false,
inference(trivial_inequality_removal,[],[f890]) ).
fof(f890,plain,
divide(a3,inverse(divide(b3,inverse(c3)))) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(forward_demodulation,[],[f880,f671]) ).
fof(f671,plain,
! [X28,X27] : divide(inverse(X28),X27) = inverse(divide(X28,inverse(X27))),
inference(superposition,[],[f285,f410]) ).
fof(f410,plain,
! [X12,X13] : divide(X12,inverse(X13)) = divide(X13,inverse(X12)),
inference(superposition,[],[f107,f358]) ).
fof(f358,plain,
! [X4,X5] : inverse(X5) = divide(X4,divide(X5,inverse(X4))),
inference(superposition,[],[f210,f36]) ).
fof(f36,plain,
! [X8,X7] : inverse(divide(X7,divide(X8,inverse(X7)))) = X8,
inference(forward_demodulation,[],[f31,f10]) ).
fof(f10,plain,
! [X0,X1] : inverse(X1) = divide(inverse(divide(X0,X0)),X1),
inference(superposition,[],[f3,f3]) ).
fof(f3,axiom,
! [X0,X1] : inverse(X0) = divide(divide(X1,X1),X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f31,plain,
! [X8,X6,X7] : inverse(divide(X7,divide(X8,divide(inverse(divide(X6,X6)),X7)))) = X8,
inference(superposition,[],[f1,f10]) ).
fof(f1,axiom,
! [X2,X0,X1] : divide(X0,divide(X1,divide(X2,divide(X0,X1)))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f210,plain,
! [X1] : inverse(inverse(X1)) = X1,
inference(forward_demodulation,[],[f183,f3]) ).
fof(f183,plain,
! [X0,X1] : divide(divide(X0,X0),inverse(X1)) = X1,
inference(superposition,[],[f107,f3]) ).
fof(f107,plain,
! [X18,X20] : divide(X18,divide(X18,X20)) = X20,
inference(forward_demodulation,[],[f94,f86]) ).
fof(f86,plain,
! [X26,X24,X25] : divide(X24,X25) = divide(X24,divide(X25,divide(X26,X26))),
inference(superposition,[],[f1,f64]) ).
fof(f64,plain,
! [X3,X4] : divide(X4,X4) = divide(X3,X3),
inference(backward_demodulation,[],[f24,f54]) ).
fof(f54,plain,
! [X0,X1] : divide(X1,inverse(divide(X0,X1))) = X0,
inference(superposition,[],[f23,f3]) ).
fof(f23,plain,
! [X2,X0,X1] : divide(X1,divide(divide(X2,divide(X0,X1)),X2)) = X0,
inference(superposition,[],[f1,f1]) ).
fof(f24,plain,
! [X3,X4,X5] : divide(X3,X3) = divide(X4,divide(X5,inverse(divide(X4,X5)))),
inference(superposition,[],[f1,f3]) ).
fof(f94,plain,
! [X18,X19,X20] : divide(X18,divide(X18,divide(X20,divide(X19,X19)))) = X20,
inference(superposition,[],[f1,f64]) ).
fof(f285,plain,
! [X4,X5] : inverse(divide(X5,X4)) = divide(X4,X5),
inference(superposition,[],[f107,f54]) ).
fof(f880,plain,
divide(a3,inverse(divide(b3,inverse(c3)))) != divide(a3,divide(inverse(b3),c3)),
inference(backward_demodulation,[],[f9,f879]) ).
fof(f879,plain,
! [X6,X7,X5] : divide(X5,divide(X6,X7)) = divide(divide(X5,X6),inverse(X7)),
inference(forward_demodulation,[],[f878,f107]) ).
fof(f878,plain,
! [X8,X6,X7,X5] : divide(divide(X5,X6),inverse(divide(X8,divide(X8,X7)))) = divide(X5,divide(X6,X7)),
inference(forward_demodulation,[],[f826,f285]) ).
fof(f826,plain,
! [X8,X6,X7,X5] : divide(X5,divide(X6,X7)) = divide(divide(X5,X6),divide(divide(X8,X7),X8)),
inference(superposition,[],[f1,f120]) ).
fof(f120,plain,
! [X6,X7,X4,X5] : divide(divide(X5,divide(X6,X4)),divide(divide(X5,X6),divide(X7,X4))) = X7,
inference(superposition,[],[f22,f23]) ).
fof(f22,plain,
! [X10,X11,X9,X12] : divide(X9,divide(divide(X10,divide(X11,divide(X9,X10))),divide(X12,X11))) = X12,
inference(superposition,[],[f1,f1]) ).
fof(f9,plain,
divide(divide(a3,inverse(b3)),inverse(c3)) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(forward_demodulation,[],[f8,f5]) ).
fof(f5,plain,
! [X0,X1] : multiply(X0,X1) = divide(X0,inverse(X1)),
inference(forward_demodulation,[],[f2,f3]) ).
fof(f2,axiom,
! [X2,X0,X1] : multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f8,plain,
divide(a3,inverse(divide(b3,inverse(c3)))) != divide(multiply(a3,b3),inverse(c3)),
inference(forward_demodulation,[],[f7,f5]) ).
fof(f7,plain,
multiply(multiply(a3,b3),c3) != divide(a3,inverse(divide(b3,inverse(c3)))),
inference(forward_demodulation,[],[f6,f5]) ).
fof(f6,plain,
multiply(multiply(a3,b3),c3) != divide(a3,inverse(multiply(b3,c3))),
inference(forward_demodulation,[],[f4,f5]) ).
fof(f4,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GRP523-1 : TPTP v8.1.0. Released v2.6.0.
% 0.14/0.14 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 29 22:28:25 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.20/0.54 % (12328)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 0.20/0.55 TRYING [1]
% 0.20/0.55 TRYING [2]
% 0.20/0.55 TRYING [3]
% 0.20/0.55 TRYING [4]
% 0.20/0.55 % (12344)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 (3000ds/498Mi)
% 0.20/0.56 % (12323)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 0.20/0.57 % (12335)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/99Mi)
% 0.20/0.57 % (12336)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 (3000ds/68Mi)
% 0.20/0.58 % (12345)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 (3000ds/467Mi)
% 0.20/0.58 % (12331)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 (3000ds/51Mi)
% 0.20/0.58 % (12337)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 (3000ds/75Mi)
% 0.20/0.58 TRYING [5]
% 0.20/0.58 % (12339)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/59Mi)
% 0.20/0.58 TRYING [1]
% 0.20/0.59 TRYING [2]
% 1.65/0.59 % (12322)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 (3000ds/191324Mi)
% 1.65/0.59 TRYING [3]
% 1.65/0.59 TRYING [1]
% 1.65/0.59 TRYING [2]
% 1.65/0.59 % (12333)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 1.65/0.59 % (12327)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 (3000ds/48Mi)
% 1.65/0.59 TRYING [3]
% 1.65/0.59 % (12334)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/101Mi)
% 1.65/0.59 % (12329)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/7Mi)
% 1.65/0.60 TRYING [4]
% 1.65/0.61 % (12332)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/50Mi)
% 1.65/0.61 % (12328)Instruction limit reached!
% 1.65/0.61 % (12328)------------------------------
% 1.65/0.61 % (12328)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.97/0.61 % (12346)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/482Mi)
% 1.97/0.61 % (12325)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 1.97/0.61 % (12328)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.97/0.61 % (12328)Termination reason: Unknown
% 1.97/0.61 % (12328)Termination phase: Finite model building constraint generation
% 1.97/0.61
% 1.97/0.61 % (12328)Memory used [KB]: 7036
% 1.97/0.61 % (12328)Time elapsed: 0.188 s
% 1.97/0.61 % (12328)Instructions burned: 52 (million)
% 1.97/0.61 % (12328)------------------------------
% 1.97/0.61 % (12328)------------------------------
% 1.97/0.61 % (12326)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/51Mi)
% 1.97/0.62 TRYING [4]
% 1.97/0.62 % (12338)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 (3000ds/99Mi)
% 1.97/0.62 % (12324)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 (3000ds/37Mi)
% 1.97/0.63 % (12351)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/355Mi)
% 1.97/0.63 % (12350)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/439Mi)
% 1.97/0.63 % (12330)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/2Mi)
% 1.97/0.63 % (12347)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/500Mi)
% 1.97/0.63 % (12349)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 (3000ds/177Mi)
% 1.97/0.63 % (12330)Instruction limit reached!
% 1.97/0.63 % (12330)------------------------------
% 1.97/0.63 % (12330)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.97/0.63 % (12330)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.97/0.63 % (12330)Termination reason: Unknown
% 1.97/0.63 % (12330)Termination phase: Saturation
% 1.97/0.63
% 1.97/0.63 % (12330)Memory used [KB]: 5373
% 1.97/0.63 % (12330)Time elapsed: 0.209 s
% 1.97/0.63 % (12330)Instructions burned: 2 (million)
% 1.97/0.63 % (12330)------------------------------
% 1.97/0.63 % (12330)------------------------------
% 1.97/0.63 % (12329)Instruction limit reached!
% 1.97/0.63 % (12329)------------------------------
% 1.97/0.63 % (12329)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.97/0.63 % (12329)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.97/0.63 % (12329)Termination reason: Unknown
% 1.97/0.63 % (12329)Termination phase: Saturation
% 1.97/0.63
% 1.97/0.63 % (12329)Memory used [KB]: 5500
% 1.97/0.63 % (12329)Time elapsed: 0.134 s
% 1.97/0.63 % (12329)Instructions burned: 7 (million)
% 1.97/0.63 % (12329)------------------------------
% 1.97/0.63 % (12329)------------------------------
% 1.97/0.63 TRYING [5]
% 1.97/0.63 % (12341)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 (3000ds/100Mi)
% 1.97/0.63 % (12343)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/138Mi)
% 1.97/0.64 % (12342)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 (3000ds/176Mi)
% 1.97/0.65 % (12323)Instruction limit reached!
% 1.97/0.65 % (12323)------------------------------
% 1.97/0.65 % (12323)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.97/0.66 % (12323)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.97/0.66 % (12323)Termination reason: Unknown
% 1.97/0.66 % (12323)Termination phase: Saturation
% 1.97/0.66
% 1.97/0.66 % (12323)Memory used [KB]: 6012
% 1.97/0.66 % (12323)Time elapsed: 0.219 s
% 1.97/0.66 % (12323)Instructions burned: 50 (million)
% 1.97/0.66 % (12323)------------------------------
% 1.97/0.66 % (12323)------------------------------
% 1.97/0.66 % (12348)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 (3000ds/68Mi)
% 2.42/0.66 % (12340)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (3000ds/100Mi)
% 2.42/0.66 TRYING [5]
% 2.42/0.67 % (12339)Instruction limit reached!
% 2.42/0.67 % (12339)------------------------------
% 2.42/0.67 % (12339)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.42/0.67 % (12339)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.42/0.67 % (12339)Termination reason: Unknown
% 2.42/0.67 % (12339)Termination phase: Finite model building SAT solving
% 2.42/0.67
% 2.42/0.67 % (12339)Memory used [KB]: 7547
% 2.42/0.67 % (12339)Time elapsed: 0.234 s
% 2.42/0.67 % (12339)Instructions burned: 60 (million)
% 2.42/0.67 % (12339)------------------------------
% 2.42/0.67 % (12339)------------------------------
% 2.42/0.67 % (12331)Instruction limit reached!
% 2.42/0.67 % (12331)------------------------------
% 2.42/0.67 % (12331)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.42/0.67 % (12331)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.42/0.67 % (12331)Termination reason: Unknown
% 2.42/0.67 % (12331)Termination phase: Saturation
% 2.42/0.67
% 2.42/0.67 % (12331)Memory used [KB]: 1663
% 2.42/0.67 % (12331)Time elapsed: 0.240 s
% 2.42/0.67 % (12331)Instructions burned: 52 (million)
% 2.42/0.67 % (12331)------------------------------
% 2.42/0.67 % (12331)------------------------------
% 2.42/0.68 % (12336)Instruction limit reached!
% 2.42/0.68 % (12336)------------------------------
% 2.42/0.68 % (12336)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.42/0.68 % (12336)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.42/0.68 % (12336)Termination reason: Unknown
% 2.42/0.68 % (12336)Termination phase: Saturation
% 2.42/0.68
% 2.42/0.68 % (12336)Memory used [KB]: 6908
% 2.42/0.68 % (12336)Time elapsed: 0.063 s
% 2.42/0.68 % (12336)Instructions burned: 69 (million)
% 2.42/0.68 % (12336)------------------------------
% 2.42/0.68 % (12336)------------------------------
% 2.42/0.70 % (12324)Instruction limit reached!
% 2.42/0.70 % (12324)------------------------------
% 2.42/0.70 % (12324)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.42/0.70 % (12324)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.42/0.70 % (12324)Termination reason: Unknown
% 2.42/0.70 % (12324)Termination phase: Saturation
% 2.42/0.70
% 2.42/0.70 % (12324)Memory used [KB]: 1535
% 2.42/0.70 % (12324)Time elapsed: 0.280 s
% 2.42/0.70 % (12324)Instructions burned: 39 (million)
% 2.42/0.70 % (12324)------------------------------
% 2.42/0.70 % (12324)------------------------------
% 2.42/0.70 % (12345)First to succeed.
% 2.42/0.71 % (12345)Refutation found. Thanks to Tanya!
% 2.42/0.71 % SZS status Unsatisfiable for theBenchmark
% 2.42/0.71 % SZS output start Proof for theBenchmark
% See solution above
% 2.42/0.71 % (12345)------------------------------
% 2.42/0.71 % (12345)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.42/0.71 % (12345)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.42/0.71 % (12345)Termination reason: Refutation
% 2.42/0.71
% 2.42/0.71 % (12345)Memory used [KB]: 6140
% 2.42/0.71 % (12345)Time elapsed: 0.215 s
% 2.42/0.71 % (12345)Instructions burned: 48 (million)
% 2.42/0.71 % (12345)------------------------------
% 2.42/0.71 % (12345)------------------------------
% 2.42/0.71 % (12321)Success in time 0.345 s
%------------------------------------------------------------------------------