%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : LAT237-1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n026.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 : Fri Sep 25 01:58:25 PM UTC 2026
% Result : Unsatisfiable 22.48s 5.26s
% Output : CNFRefutation 22.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of formulae : 98 ( 93 unt; 3 def)
% Number of atoms : 191 ( 104 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 13 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 107 !; 0 ?; 85 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0,X1] : meet(X0,join(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
fof(f4,axiom,
! [X0,X1] : join(X0,meet(X0,X1)) = X0,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption2) ).
fof(f5,axiom,
! [X0,X1] : meet(X0,X1) = meet(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
fof(f6,axiom,
! [X0,X1] : join(X0,X1) = join(X1,X0),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
fof(f7,axiom,
! [X2,X0,X1] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
fof(f8,axiom,
! [X2,X0,X1] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
fof(f9,axiom,
! [X0] : join(X0,complement(X0)) = one,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_join) ).
fof(f10,axiom,
! [X0] : meet(X0,complement(X0)) = zero,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',complement_meet) ).
fof(f11,axiom,
! [X0,X1] :
( complement(X0) = X1
| join(X0,X1) != one
| meet(X0,X1) != zero ),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-4.ax',meet_join_complement) ).
fof(f12,axiom,
! [X2,X3,X0,X1] : meet(X0,join(X1,meet(X2,join(X0,X3)))) = meet(X0,join(X1,meet(X2,join(X3,meet(X2,join(X0,X1)))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equation_H40) ).
fof(f13,axiom,
meet(b,a) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity_hypothesis) ).
fof(f14,plain,
a = meet(b,a),
inference(reorient_equations,[],[f13]) ).
fof(f15,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_distributivity) ).
fof(f16,plain,
complement(a) != join(complement(b),complement(a)),
inference(reorient_equations,[],[f15]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] : meet(X0,join(X0,X1)) = X0,
inference(cnf_transformation,[],[f3]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : join(X0,meet(X0,X1)) = X0,
inference(cnf_transformation,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : meet(X0,X1) = meet(X1,X0),
inference(cnf_transformation,[],[f5]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : join(X0,X1) = join(X1,X0),
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] : meet(meet(X0,X1),X2) = meet(X0,meet(X1,X2)),
inference(cnf_transformation,[],[f7]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] : join(join(X0,X1),X2) = join(X0,join(X1,X2)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i] : join(X0,complement(X0)) = one,
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,plain,
! [X0: $i] : meet(X0,complement(X0)) = zero,
inference(cnf_transformation,[],[f10]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( ( complement(X0) = X1 )
| ( meet(X0,X1) != zero )
| ( join(X0,X1) != one ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : meet(X0,join(X1,meet(X2,join(X3,meet(X2,join(X0,X1)))))) = meet(X0,join(X1,meet(X2,join(X0,X3)))),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,plain,
meet(b,a) = a,
inference(cnf_transformation,[],[f14]) ).
tcf(c_76,negated_conjecture,
join(complement(b),complement(a)) != complement(a),
inference(cnf_transformation,[],[f16]) ).
tcf(c_89,plain,
meet(a,b) = a,
inference(theory_normalisation,[status(thm)],[c_75,c_69,c_67,c_70,c_68]) ).
tcf(c_90,negated_conjecture,
join(complement(a),complement(b)) != complement(a),
inference(theory_normalisation,[status(thm)],[c_76,c_69,c_67,c_70,c_68]) ).
tcf(c_131,definition,
iPr_def_10 = complement(a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_132,definition,
iPr_def_11 = complement(b),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_133,definition,
iPr_def_12 = join(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_134,negated_conjecture,
iPr_def_12 != iPr_def_10,
inference(demodulation,[status(thm)],[c_90,c_132,c_131,c_133]) ).
tcf(c_204,plain,
! [X0: $i,X1: $i,X2: $i] : join(X0,join(X1,X2)) = join(X1,join(X0,X2)),
inference(superposition,[status(thm)],[c_70,c_68]) ).
tcf(c_211,plain,
join(a,iPr_def_10) = one,
inference(superposition,[status(thm)],[c_131,c_71]) ).
tcf(c_212,plain,
join(iPr_def_10,a) = one,
inference(theory_normalisation,[status(thm)],[c_211,c_70,c_68,c_69,c_67]) ).
tcf(c_221,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_11)) = join(X0,iPr_def_12),
inference(superposition,[status(thm)],[c_133,c_204]) ).
tcf(c_232,plain,
meet(a,iPr_def_10) = zero,
inference(superposition,[status(thm)],[c_131,c_72]) ).
tcf(c_233,plain,
meet(iPr_def_10,a) = zero,
inference(theory_normalisation,[status(thm)],[c_232,c_70,c_68,c_69,c_67]) ).
tcf(c_235,plain,
! [X0: $i] : meet(X0,one) = X0,
inference(superposition,[status(thm)],[c_71,c_65]) ).
tcf(c_238,plain,
meet(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_133,c_65]) ).
tcf(c_239,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(X1,join(X0,X2))) = X0,
inference(superposition,[status(thm)],[c_204,c_65]) ).
tcf(c_242,plain,
! [X0: $i] : join(X0,zero) = X0,
inference(superposition,[status(thm)],[c_72,c_66]) ).
tcf(c_251,plain,
! [X0: $i,X1: $i] : join(X0,meet(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_67,c_66]) ).
tcf(c_275,plain,
! [X0: $i] : meet(one,X0) = X0,
inference(superposition,[status(thm)],[c_235,c_67]) ).
tcf(c_288,plain,
! [X0: $i] : join(one,X0) = one,
inference(superposition,[status(thm)],[c_275,c_66]) ).
tcf(c_314,plain,
! [X0: $i,X1: $i] : meet(X0,join(X1,X0)) = X0,
inference(superposition,[status(thm)],[c_68,c_65]) ).
tcf(c_316,plain,
! [X0: $i] : join(zero,X0) = X0,
inference(superposition,[status(thm)],[c_68,c_242]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,meet(join(X0,X1),X2)) = meet(X0,X2),
inference(superposition,[status(thm)],[c_65,c_69]) ).
tcf(c_382,plain,
! [X0: $i] : join(iPr_def_10,join(a,X0)) = join(one,X0),
inference(superposition,[status(thm)],[c_212,c_70]) ).
tcf(c_394,plain,
! [X0: $i] : join(iPr_def_10,join(a,X0)) = one,
inference(light_normalisation,[status(thm)],[c_382,c_288]) ).
tcf(c_538,plain,
! [X0: $i] : meet(zero,X0) = zero,
inference(superposition,[status(thm)],[c_316,c_66]) ).
tcf(c_587,plain,
! [X0: $i] : meet(X0,zero) = zero,
inference(superposition,[status(thm)],[c_538,c_67]) ).
tcf(c_614,plain,
join(b,a) = b,
inference(superposition,[status(thm)],[c_89,c_251]) ).
tcf(c_618,plain,
join(iPr_def_12,iPr_def_10) = iPr_def_12,
inference(superposition,[status(thm)],[c_238,c_251]) ).
tcf(c_628,plain,
join(iPr_def_10,iPr_def_12) = iPr_def_12,
inference(theory_normalisation,[status(thm)],[c_618,c_70,c_68,c_69,c_67]) ).
tcf(c_629,plain,
join(a,b) = b,
inference(theory_normalisation,[status(thm)],[c_614,c_70,c_68,c_69,c_67]) ).
tcf(c_674,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(complement(X0),meet(X1,join(X2,meet(X1,one))))) = meet(X0,join(complement(X0),meet(X1,join(X0,X2)))),
inference(superposition,[status(thm)],[c_71,c_74]) ).
tcf(c_854,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(X1,join(X2,X0))) = X0,
inference(superposition,[status(thm)],[c_70,c_314]) ).
tcf(c_1168,plain,
! [X0: $i] : meet(iPr_def_10,join(X0,iPr_def_12)) = iPr_def_10,
inference(superposition,[status(thm)],[c_221,c_65]) ).
tcf(c_1174,plain,
join(a,iPr_def_12) = one,
inference(superposition,[status(thm)],[c_221,c_394]) ).
tcf(c_1177,plain,
join(iPr_def_12,a) = one,
inference(theory_normalisation,[status(thm)],[c_1174,c_70,c_68,c_69,c_67]) ).
tcf(c_1227,plain,
! [X0: $i] : meet(iPr_def_10,join(iPr_def_12,X0)) = iPr_def_10,
inference(superposition,[status(thm)],[c_68,c_1168]) ).
tcf(c_1266,plain,
! [X0: $i] : join(join(iPr_def_12,X0),iPr_def_10) = join(iPr_def_12,X0),
inference(superposition,[status(thm)],[c_1227,c_251]) ).
tcf(c_1267,plain,
! [X0: $i] : join(iPr_def_10,join(X0,iPr_def_12)) = join(iPr_def_12,X0),
inference(theory_normalisation,[status(thm)],[c_1266,c_70,c_68,c_69,c_67]) ).
tcf(c_1330,plain,
! [X0: $i] : meet(a,join(X0,b)) = a,
inference(superposition,[status(thm)],[c_629,c_239]) ).
tcf(c_1451,plain,
! [X0: $i] : meet(a,join(b,X0)) = a,
inference(superposition,[status(thm)],[c_68,c_1330]) ).
tcf(c_1682,plain,
! [X0: $i] : join(join(b,X0),a) = join(b,X0),
inference(superposition,[status(thm)],[c_1451,c_251]) ).
tcf(c_1683,plain,
! [X0: $i] : join(a,join(X0,b)) = join(b,X0),
inference(theory_normalisation,[status(thm)],[c_1682,c_70,c_68,c_69,c_67]) ).
tcf(c_3183,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : meet(X0,join(X1,join(X2,join(X3,X0)))) = X0,
inference(superposition,[status(thm)],[c_70,c_854]) ).
tcf(c_6746,plain,
! [X0: $i,X1: $i] : meet(X0,complement(join(X0,X1))) = meet(X0,zero),
inference(superposition,[status(thm)],[c_72,c_325]) ).
tcf(c_6884,plain,
! [X0: $i,X1: $i] : meet(X0,complement(join(X0,X1))) = zero,
inference(light_normalisation,[status(thm)],[c_6746,c_587]) ).
tcf(c_6926,plain,
! [X0: $i,X1: $i,X2: $i] : meet(join(X0,X1),complement(join(X0,join(X1,X2)))) = zero,
inference(superposition,[status(thm)],[c_70,c_6884]) ).
tcf(c_64120,plain,
! [X0: $i,X1: $i,X2: $i] : meet(X0,join(complement(X0),meet(X1,join(X0,X2)))) = meet(X0,join(complement(X0),X1)),
inference(demodulation,[status(thm)],[c_674,c_235,c_314]) ).
tcf(c_78098,plain,
! [X0: $i] : meet(join(iPr_def_10,X0),complement(join(iPr_def_12,X0))) = zero,
inference(superposition,[status(thm)],[c_1267,c_6926]) ).
tcf(c_78101,plain,
! [X0: $i] : meet(join(a,X0),complement(join(b,X0))) = zero,
inference(superposition,[status(thm)],[c_1683,c_6926]) ).
tcf(c_80605,plain,
! [X0: $i] : meet(join(iPr_def_10,meet(iPr_def_12,X0)),complement(iPr_def_12)) = zero,
inference(superposition,[status(thm)],[c_66,c_78098]) ).
tcf(c_80798,plain,
! [X0: $i] : meet(complement(iPr_def_12),join(iPr_def_10,meet(iPr_def_12,X0))) = zero,
inference(theory_normalisation,[status(thm)],[c_80605,c_70,c_68,c_69,c_67]) ).
tcf(c_81598,plain,
! [X0: $i] : meet(join(a,meet(b,X0)),complement(b)) = zero,
inference(superposition,[status(thm)],[c_66,c_78101]) ).
tcf(c_81748,plain,
! [X0: $i] : meet(complement(b),join(a,meet(b,X0))) = zero,
inference(theory_normalisation,[status(thm)],[c_81598,c_70,c_68,c_69,c_67]) ).
tcf(c_81749,plain,
! [X0: $i] : meet(iPr_def_11,join(a,meet(b,X0))) = zero,
inference(light_normalisation,[status(thm)],[c_81748,c_132]) ).
tcf(c_82586,plain,
meet(a,join(complement(a),zero)) = meet(a,join(complement(a),iPr_def_11)),
inference(superposition,[status(thm)],[c_81749,c_64120]) ).
tcf(c_82624,plain,
meet(a,join(zero,complement(a))) = meet(a,join(iPr_def_11,complement(a))),
inference(theory_normalisation,[status(thm)],[c_82586,c_70,c_68,c_69,c_67]) ).
tcf(c_82625,plain,
meet(a,join(zero,iPr_def_10)) = meet(a,join(iPr_def_11,iPr_def_10)),
inference(light_normalisation,[status(thm)],[c_82624,c_131]) ).
tcf(c_82626,plain,
meet(a,join(iPr_def_10,zero)) = meet(a,join(iPr_def_10,iPr_def_11)),
inference(theory_normalisation,[status(thm)],[c_82625,c_70,c_68,c_69,c_67]) ).
tcf(c_82627,plain,
meet(a,join(iPr_def_10,zero)) = meet(a,iPr_def_12),
inference(light_normalisation,[status(thm)],[c_82626,c_133]) ).
tcf(c_82628,plain,
meet(a,join(iPr_def_10,zero)) = meet(iPr_def_12,a),
inference(theory_normalisation,[status(thm)],[c_82627,c_70,c_68,c_69,c_67]) ).
tcf(c_84152,plain,
meet(iPr_def_12,a) = zero,
inference(demodulation,[status(thm)],[c_82628,c_67,c_233,c_242]) ).
tcf(c_84164,plain,
( ( complement(iPr_def_12) = a )
| ( join(iPr_def_12,a) != one ) ),
inference(superposition,[status(thm)],[c_84152,c_73]) ).
tcf(c_84240,plain,
complement(iPr_def_12) = a,
inference(ground_joinability,[status(thm)],[c_84164,c_1177]) ).
tcf(c_84245,plain,
! [X0: $i] : meet(a,join(iPr_def_10,meet(iPr_def_12,X0))) = zero,
inference(demodulation,[status(thm)],[c_80798,c_84240]) ).
tcf(c_86104,plain,
! [X0: $i] :
( ( join(iPr_def_10,meet(iPr_def_12,X0)) = complement(a) )
| ( join(a,join(iPr_def_10,meet(iPr_def_12,X0))) != one ) ),
inference(superposition,[status(thm)],[c_84245,c_73]) ).
tcf(c_86187,plain,
! [X0: $i] :
( ( join(iPr_def_10,meet(iPr_def_12,X0)) = complement(a) )
| ( join(iPr_def_10,join(a,meet(iPr_def_12,X0))) != one ) ),
inference(theory_normalisation,[status(thm)],[c_86104,c_70,c_68,c_69,c_67]) ).
tcf(c_86188,plain,
! [X0: $i] : join(iPr_def_10,meet(iPr_def_12,X0)) = complement(a),
inference(ground_joinability,[status(thm)],[c_86187,c_394]) ).
tcf(c_86189,plain,
! [X0: $i] : join(iPr_def_10,meet(iPr_def_12,X0)) = iPr_def_10,
inference(light_normalisation,[status(thm)],[c_86188,c_131]) ).
tcf(c_86244,plain,
join(iPr_def_10,iPr_def_12) = iPr_def_10,
inference(superposition,[status(thm)],[c_3183,c_86189]) ).
tcf(c_86376,plain,
iPr_def_10 = iPr_def_12,
inference(demodulation,[status(thm)],[c_628,c_86244]) ).
tcf(c_86520,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_134,c_86376]) ).
tcf(c_86521,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_86520]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LAT237-1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 20:41:54 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.12/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.39 Running first-order theorem proving
% 0.12/0.39 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.40
% 0.12/0.40 % Detected problem language: tptp
% 0.12/0.42 % Proving...
% 22.48/5.26 % SZS status Started for theBenchmark.p
% 22.48/5.26 % SZS status Unsatisfiable for theBenchmark.p
% 22.48/5.26
% 22.48/5.26 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 22.48/5.26
% 22.48/5.26 % ------ iProver source info
% 22.48/5.26
% 22.48/5.26 % git: date: 2026-07-19 20:42:38 +0200
% 22.48/5.26 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 22.48/5.26 % git: non_committed_changes: false
% 22.48/5.26
% 22.48/5.26 % ------ Parsing...% successful
% 22.48/5.26
% 22.48/5.26
% 22.48/5.26 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 22.48/5.26
% 22.48/5.26 % ------ Preprocessing... sup_sim: 0 sf_s rm: 0 0s sf_e pe_s pe_e %
% 22.48/5.26
% 22.48/5.26 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 22.48/5.26
% 22.48/5.26 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 22.48/5.26 % ------ Proving...
% 22.48/5.26 % ------ Problem Properties
% 22.48/5.26
% 22.48/5.26 %
% 22.48/5.26 % clauses 17
% 22.48/5.26 % conjectures 1
% 22.48/5.26 % EPR 1
% 22.48/5.26 % Horn 17
% 22.48/5.26 % unary 16
% 22.48/5.26 % binary 0
% 22.48/5.26 % lits 19
% 22.48/5.26 % lits eq 19
% 22.48/5.26 % fd_pure 0
% 22.48/5.26 % fd_pseudo 0
% 22.48/5.26 % fd_cond 0
% 22.48/5.26 % fd_pseudo_cond 1
% 22.48/5.26 % AC symbols 2
% 22.48/5.26
% 22.48/5.26 % ------ Schedule dynamic 5 is on
% 22.48/5.26
% 22.48/5.26 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 22.48/5.26
% 22.48/5.26
% 22.48/5.26 % ------
% 22.48/5.26 % Current options:
% 22.48/5.26 % ------
% 22.48/5.26
% 22.48/5.26
% 22.48/5.26 %
% 22.48/5.26
% 22.48/5.26 % ------ Proving...
% 22.48/5.26 %
% 22.48/5.26
% 22.48/5.26 % SZS status Unsatisfiable for theBenchmark.p
% 22.48/5.26
% 22.48/5.26 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 22.48/5.26
% 22.48/5.26
%------------------------------------------------------------------------------