TSTP Solution File: SEU674^2 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SEU674^2 : TPTP v8.2.0. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:50:33 EDT 2024
% Result : Theorem 0.21s 0.39s
% Output : Refutation 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SEU674^2 : TPTP v8.2.0. Released v3.7.0.
% 0.14/0.15 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule file --schedule_file /export/starexec/sandbox/solver/bin/quickGreedyProduceRating_steal_pow3.txt --cores 8 -m 12000 -t %d %s
% 0.14/0.36 % Computer : n025.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 16:16:08 EDT 2024
% 0.21/0.36 % CPUTime :
% 0.21/0.36 This is a TH0_THM_EQU_NAR problem
% 0.21/0.36 Running vampire_ho --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_hol --cores 8 -m 12000 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.38 % (21216)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (21213)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on theBenchmark for (2999ds/183Mi)
% 0.21/0.38 % (21215)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on theBenchmark for (2999ds/27Mi)
% 0.21/0.38 % (21214)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on theBenchmark for (2999ds/4Mi)
% 0.21/0.38 % (21217)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.21/0.38 % (21218)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on theBenchmark for (2999ds/275Mi)
% 0.21/0.38 % (21219)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on theBenchmark for (2999ds/18Mi)
% 0.21/0.38 % (21220)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.21/0.38 % (21216)Instruction limit reached!
% 0.21/0.38 % (21216)------------------------------
% 0.21/0.38 % (21216)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (21216)Termination reason: Unknown
% 0.21/0.38 % (21216)Termination phase: shuffling
% 0.21/0.38
% 0.21/0.38 % (21216)Memory used [KB]: 895
% 0.21/0.38 % (21216)Time elapsed: 0.003 s
% 0.21/0.38 % (21216)Instructions burned: 2 (million)
% 0.21/0.38 % (21216)------------------------------
% 0.21/0.38 % (21216)------------------------------
% 0.21/0.38 % (21217)Instruction limit reached!
% 0.21/0.38 % (21217)------------------------------
% 0.21/0.38 % (21217)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (21217)Termination reason: Unknown
% 0.21/0.38 % (21217)Termination phase: Function definition elimination
% 0.21/0.38
% 0.21/0.38 % (21217)Memory used [KB]: 1023
% 0.21/0.38 % (21217)Time elapsed: 0.004 s
% 0.21/0.38 % (21217)Instructions burned: 3 (million)
% 0.21/0.38 % (21217)------------------------------
% 0.21/0.38 % (21217)------------------------------
% 0.21/0.38 % (21220)Instruction limit reached!
% 0.21/0.38 % (21220)------------------------------
% 0.21/0.38 % (21220)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (21220)Termination reason: Unknown
% 0.21/0.38 % (21220)Termination phase: Function definition elimination
% 0.21/0.38
% 0.21/0.38 % (21220)Memory used [KB]: 1023
% 0.21/0.38 % (21220)Time elapsed: 0.004 s
% 0.21/0.38 % (21220)Instructions burned: 3 (million)
% 0.21/0.38 % (21220)------------------------------
% 0.21/0.38 % (21220)------------------------------
% 0.21/0.38 % (21214)Instruction limit reached!
% 0.21/0.38 % (21214)------------------------------
% 0.21/0.38 % (21214)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.38 % (21214)Termination reason: Unknown
% 0.21/0.38 % (21214)Termination phase: Saturation
% 0.21/0.38
% 0.21/0.38 % (21214)Memory used [KB]: 5500
% 0.21/0.38 % (21214)Time elapsed: 0.004 s
% 0.21/0.38 % (21214)Instructions burned: 4 (million)
% 0.21/0.38 % (21214)------------------------------
% 0.21/0.38 % (21214)------------------------------
% 0.21/0.38 % (21218)First to succeed.
% 0.21/0.39 % (21218)Refutation found. Thanks to Tanya!
% 0.21/0.39 % SZS status Theorem for theBenchmark
% 0.21/0.39 % SZS output start Proof for theBenchmark
% 0.21/0.39 thf(func_def_0, type, in: $i > $i > $o).
% 0.21/0.39 thf(func_def_2, type, setadjoin: $i > $i > $i).
% 0.21/0.39 thf(func_def_3, type, setunion: $i > $i).
% 0.21/0.39 thf(func_def_4, type, dsetconstr: $i > ($i > $o) > $i).
% 0.21/0.39 thf(func_def_5, type, subset: $i > $i > $o).
% 0.21/0.39 thf(func_def_6, type, kpair: $i > $i > $i).
% 0.21/0.39 thf(func_def_7, type, cartprod: $i > $i > $i).
% 0.21/0.39 thf(func_def_8, type, singleton: $i > $o).
% 0.21/0.39 thf(func_def_10, type, ex1: $i > ($i > $o) > $o).
% 0.21/0.39 thf(func_def_11, type, breln: $i > $i > $i > $o).
% 0.21/0.39 thf(func_def_12, type, func: $i > $i > $i > $o).
% 0.21/0.39 thf(func_def_14, type, ap: $i > $i > $i > $i > $i).
% 0.21/0.39 thf(func_def_36, type, ph9: !>[X0: $tType]:(X0)).
% 0.21/0.39 thf(f54,plain,(
% 0.21/0.39 $false),
% 0.21/0.39 inference(subsumption_resolution,[],[f53,f35])).
% 0.21/0.39 thf(f35,plain,(
% 0.21/0.39 ((in @ sK3 @ sK1) = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f28])).
% 0.21/0.39 thf(f28,plain,(
% 0.21/0.39 (($true = (func @ sK1 @ sK0 @ sK2)) & (((in @ (ap @ sK1 @ sK0 @ sK2 @ sK3) @ sK0) != $true) & ((in @ sK3 @ sK1) = $true))) & (apProp = $true)),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f27,f26])).
% 0.21/0.39 thf(f26,plain,(
% 0.21/0.39 ? [X0,X1,X2] : (((func @ X1 @ X0 @ X2) = $true) & ? [X3] : (((in @ (ap @ X1 @ X0 @ X2 @ X3) @ X0) != $true) & ((in @ X3 @ X1) = $true))) => (($true = (func @ sK1 @ sK0 @ sK2)) & ? [X3] : (((in @ (ap @ sK1 @ sK0 @ sK2 @ X3) @ sK0) != $true) & ((in @ X3 @ sK1) = $true)))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f27,plain,(
% 0.21/0.39 ? [X3] : (((in @ (ap @ sK1 @ sK0 @ sK2 @ X3) @ sK0) != $true) & ((in @ X3 @ sK1) = $true)) => (((in @ (ap @ sK1 @ sK0 @ sK2 @ sK3) @ sK0) != $true) & ((in @ sK3 @ sK1) = $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f25,plain,(
% 0.21/0.39 ? [X0,X1,X2] : (((func @ X1 @ X0 @ X2) = $true) & ? [X3] : (((in @ (ap @ X1 @ X0 @ X2 @ X3) @ X0) != $true) & ((in @ X3 @ X1) = $true))) & (apProp = $true)),
% 0.21/0.39 inference(ennf_transformation,[],[f23])).
% 0.21/0.39 thf(f23,plain,(
% 0.21/0.39 ~((apProp = $true) => ! [X0,X1,X2] : (((func @ X1 @ X0 @ X2) = $true) => ! [X3] : (((in @ X3 @ X1) = $true) => ((in @ (ap @ X1 @ X0 @ X2 @ X3) @ X0) = $true))))),
% 0.21/0.39 inference(fool_elimination,[],[f22])).
% 0.21/0.39 thf(f22,plain,(
% 0.21/0.39 ~(apProp => ! [X0,X1,X2] : ((func @ X1 @ X0 @ X2) => ! [X3] : ((in @ X3 @ X1) => (in @ (ap @ X1 @ X0 @ X2 @ X3) @ X0))))),
% 0.21/0.39 inference(rectify,[],[f8])).
% 0.21/0.39 thf(f8,negated_conjecture,(
% 0.21/0.39 ~(apProp => ! [X3,X0,X7] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => (in @ (ap @ X0 @ X3 @ X7 @ X1) @ X3))))),
% 0.21/0.39 inference(negated_conjecture,[],[f7])).
% 0.21/0.39 thf(f7,conjecture,(
% 0.21/0.39 apProp => ! [X3,X0,X7] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => (in @ (ap @ X0 @ X3 @ X7 @ X1) @ X3)))),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',app)).
% 0.21/0.39 thf(f53,plain,(
% 0.21/0.39 ((in @ sK3 @ sK1) != $true)),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f52])).
% 0.21/0.39 thf(f52,plain,(
% 0.21/0.39 ((in @ sK3 @ sK1) != $true) | ($true != $true)),
% 0.21/0.39 inference(superposition,[],[f51,f37])).
% 0.21/0.39 thf(f37,plain,(
% 0.21/0.39 ($true = (func @ sK1 @ sK0 @ sK2))),
% 0.21/0.39 inference(cnf_transformation,[],[f28])).
% 0.21/0.39 thf(f51,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (((func @ X0 @ sK0 @ sK2) != $true) | ($true != (in @ sK3 @ X0))) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f50])).
% 0.21/0.39 thf(f50,plain,(
% 0.21/0.39 ( ! [X0 : $i] : (($true != $true) | ((func @ X0 @ sK0 @ sK2) != $true) | ($true != (in @ sK3 @ X0))) )),
% 0.21/0.39 inference(superposition,[],[f49,f48])).
% 0.21/0.39 thf(f48,plain,(
% 0.21/0.39 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ (setunion @ (dsetconstr @ X5 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ X6)))) @ X5) = $true) | ((in @ X7 @ X4) != $true) | ($true != (func @ X4 @ X5 @ X6))) )),
% 0.21/0.39 inference(trivial_inequality_removal,[],[f47])).
% 0.21/0.39 thf(f47,plain,(
% 0.21/0.39 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (((in @ (setunion @ (dsetconstr @ X5 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ X6)))) @ X5) = $true) | ($true != (func @ X4 @ X5 @ X6)) | ((in @ X7 @ X4) != $true) | ($true != $true)) )),
% 0.21/0.39 inference(definition_unfolding,[],[f39,f34])).
% 0.21/0.39 thf(f34,plain,(
% 0.21/0.39 (apProp = $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f28])).
% 0.21/0.39 thf(f39,plain,(
% 0.21/0.39 ( ! [X6 : $i,X7 : $i,X4 : $i,X5 : $i] : (($true != (func @ X4 @ X5 @ X6)) | ((in @ X7 @ X4) != $true) | ((in @ (setunion @ (dsetconstr @ X5 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ X6)))) @ X5) = $true) | (apProp != $true)) )),
% 0.21/0.39 inference(cnf_transformation,[],[f33])).
% 0.21/0.39 thf(f33,plain,(
% 0.21/0.39 ((apProp = $true) | (((func @ sK4 @ sK5 @ sK6) = $true) & (($true = (in @ sK7 @ sK4)) & ((in @ (setunion @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK6)))) @ sK5) != $true)))) & (! [X4,X5,X6] : (($true != (func @ X4 @ X5 @ X6)) | ! [X7] : (((in @ X7 @ X4) != $true) | ((in @ (setunion @ (dsetconstr @ X5 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ X6)))) @ X5) = $true))) | (apProp != $true))),
% 0.21/0.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7])],[f30,f32,f31])).
% 0.21/0.39 thf(f31,plain,(
% 0.21/0.39 ? [X0,X1,X2] : (((func @ X0 @ X1 @ X2) = $true) & ? [X3] : (((in @ X3 @ X0) = $true) & ($true != (in @ (setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X2)))) @ X1)))) => (((func @ sK4 @ sK5 @ sK6) = $true) & ? [X3] : (((in @ X3 @ sK4) = $true) & ($true != (in @ (setunion @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ sK6)))) @ sK5))))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f32,plain,(
% 0.21/0.39 ? [X3] : (((in @ X3 @ sK4) = $true) & ($true != (in @ (setunion @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ sK6)))) @ sK5))) => (($true = (in @ sK7 @ sK4)) & ((in @ (setunion @ (dsetconstr @ sK5 @ (^[Y0 : $i]: (in @ (kpair @ sK7 @ Y0) @ sK6)))) @ sK5) != $true))),
% 0.21/0.39 introduced(choice_axiom,[])).
% 0.21/0.39 thf(f30,plain,(
% 0.21/0.39 ((apProp = $true) | ? [X0,X1,X2] : (((func @ X0 @ X1 @ X2) = $true) & ? [X3] : (((in @ X3 @ X0) = $true) & ($true != (in @ (setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X2)))) @ X1))))) & (! [X4,X5,X6] : (($true != (func @ X4 @ X5 @ X6)) | ! [X7] : (((in @ X7 @ X4) != $true) | ((in @ (setunion @ (dsetconstr @ X5 @ (^[Y0 : $i]: (in @ (kpair @ X7 @ Y0) @ X6)))) @ X5) = $true))) | (apProp != $true))),
% 0.21/0.39 inference(rectify,[],[f29])).
% 0.21/0.39 thf(f29,plain,(
% 0.21/0.39 ((apProp = $true) | ? [X0,X1,X2] : (((func @ X0 @ X1 @ X2) = $true) & ? [X3] : (((in @ X3 @ X0) = $true) & ($true != (in @ (setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X2)))) @ X1))))) & (! [X0,X1,X2] : (((func @ X0 @ X1 @ X2) != $true) | ! [X3] : (((in @ X3 @ X0) != $true) | ($true = (in @ (setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X2)))) @ X1)))) | (apProp != $true))),
% 0.21/0.39 inference(nnf_transformation,[],[f24])).
% 0.21/0.39 thf(f24,plain,(
% 0.21/0.39 (apProp = $true) <=> ! [X0,X1,X2] : (((func @ X0 @ X1 @ X2) != $true) | ! [X3] : (((in @ X3 @ X0) != $true) | ($true = (in @ (setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X2)))) @ X1))))),
% 0.21/0.39 inference(ennf_transformation,[],[f15])).
% 0.21/0.39 thf(f15,plain,(
% 0.21/0.39 ! [X0,X1,X2] : (((func @ X0 @ X1 @ X2) = $true) => ! [X3] : (((in @ X3 @ X0) = $true) => ($true = (in @ (setunion @ (dsetconstr @ X1 @ (^[Y0 : $i]: (in @ (kpair @ X3 @ Y0) @ X2)))) @ X1)))) <=> (apProp = $true)),
% 0.21/0.39 inference(fool_elimination,[],[f14])).
% 0.21/0.39 thf(f14,plain,(
% 0.21/0.39 (! [X0,X1,X2] : ((func @ X0 @ X1 @ X2) => ! [X3] : ((in @ X3 @ X0) => (in @ (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2)))) @ X1))) = apProp)),
% 0.21/0.39 inference(rectify,[],[f5])).
% 0.21/0.39 thf(f5,axiom,(
% 0.21/0.39 (! [X0,X3,X7] : ((func @ X0 @ X3 @ X7) => ! [X1] : ((in @ X1 @ X0) => (in @ (setunion @ (dsetconstr @ X3 @ (^[X6 : $i] : (in @ (kpair @ X1 @ X6) @ X7)))) @ X3))) = apProp)),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp)).
% 0.21/0.39 thf(f49,plain,(
% 0.21/0.39 ($true != (in @ (setunion @ (dsetconstr @ sK0 @ (^[Y0 : $i]: (in @ (kpair @ sK3 @ Y0) @ sK2)))) @ sK0))),
% 0.21/0.39 inference(beta_eta_normalization,[],[f43])).
% 0.21/0.39 thf(f43,plain,(
% 0.21/0.39 ((in @ ((^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))) @ sK1 @ sK0 @ sK2 @ sK3) @ sK0) != $true)),
% 0.21/0.39 inference(definition_unfolding,[],[f36,f38])).
% 0.21/0.39 thf(f38,plain,(
% 0.21/0.39 (ap = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))),
% 0.21/0.39 inference(cnf_transformation,[],[f17])).
% 0.21/0.39 thf(f17,plain,(
% 0.21/0.39 (ap = (^[Y0 : $i]: ((^[Y1 : $i]: ((^[Y2 : $i]: ((^[Y3 : $i]: (setunion @ (dsetconstr @ Y1 @ (^[Y4 : $i]: (in @ (kpair @ Y3 @ Y4) @ Y2))))))))))))),
% 0.21/0.39 inference(fool_elimination,[],[f16])).
% 0.21/0.39 thf(f16,plain,(
% 0.21/0.39 ((^[X0 : $i, X1 : $i, X2 : $i, X3 : $i] : (setunion @ (dsetconstr @ X1 @ (^[X4 : $i] : (in @ (kpair @ X3 @ X4) @ X2))))) = ap)),
% 0.21/0.39 inference(rectify,[],[f6])).
% 0.21/0.39 thf(f6,axiom,(
% 0.21/0.39 ((^[X0 : $i, X3 : $i, X7 : $i, X1 : $i] : (setunion @ (dsetconstr @ X3 @ (^[X6 : $i] : (in @ (kpair @ X1 @ X6) @ X7))))) = ap)),
% 0.21/0.39 file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap)).
% 0.21/0.39 thf(f36,plain,(
% 0.21/0.39 ((in @ (ap @ sK1 @ sK0 @ sK2 @ sK3) @ sK0) != $true)),
% 0.21/0.39 inference(cnf_transformation,[],[f28])).
% 0.21/0.39 % SZS output end Proof for theBenchmark
% 0.21/0.39 % (21218)------------------------------
% 0.21/0.39 % (21218)Version: Vampire 4.8 HO - Sledgehammer schedules (2023-10-19)
% 0.21/0.39 % (21218)Termination reason: Refutation
% 0.21/0.39
% 0.21/0.39 % (21218)Memory used [KB]: 5500
% 0.21/0.39 % (21218)Time elapsed: 0.008 s
% 0.21/0.39 % (21218)Instructions burned: 5 (million)
% 0.21/0.39 % (21218)------------------------------
% 0.21/0.39 % (21218)------------------------------
% 0.21/0.39 % (21212)Success in time 0.009 s
% 0.21/0.39 % Vampire---4.8 exiting
%------------------------------------------------------------------------------