TSTP Solution File: SEU140+2 by Princess---230619
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%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : SEU140+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n020.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 : Thu Aug 31 17:42:43 EDT 2023
% Result : Theorem 9.33s 2.11s
% Output : Proof 12.66s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU140+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Aug 23 23:43:00 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.21/0.55 ________ _____
% 0.21/0.55 ___ __ \_________(_)________________________________
% 0.21/0.55 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.21/0.55 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.21/0.55 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.21/0.55
% 0.21/0.55 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.21/0.55 (2023-06-19)
% 0.21/0.55
% 0.21/0.55 (c) Philipp Rümmer, 2009-2023
% 0.21/0.55 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.21/0.55 Amanda Stjerna.
% 0.21/0.55 Free software under BSD-3-Clause.
% 0.21/0.55
% 0.21/0.55 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.21/0.55
% 0.21/0.55 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.21/0.56 Running up to 7 provers in parallel.
% 0.21/0.58 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.21/0.58 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.21/0.58 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.21/0.58 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.21/0.58 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.21/0.58 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.21/0.58 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 2.70/1.11 Prover 1: Preprocessing ...
% 2.70/1.11 Prover 4: Preprocessing ...
% 3.26/1.15 Prover 3: Preprocessing ...
% 3.26/1.15 Prover 6: Preprocessing ...
% 3.26/1.15 Prover 5: Preprocessing ...
% 3.26/1.15 Prover 2: Preprocessing ...
% 3.26/1.15 Prover 0: Preprocessing ...
% 6.97/1.66 Prover 1: Warning: ignoring some quantifiers
% 6.97/1.69 Prover 5: Proving ...
% 6.97/1.71 Prover 1: Constructing countermodel ...
% 7.74/1.79 Prover 3: Warning: ignoring some quantifiers
% 7.74/1.81 Prover 2: Proving ...
% 7.74/1.81 Prover 6: Proving ...
% 7.74/1.81 Prover 3: Constructing countermodel ...
% 7.74/1.81 Prover 4: Warning: ignoring some quantifiers
% 8.30/1.88 Prover 4: Constructing countermodel ...
% 8.59/1.92 Prover 0: Proving ...
% 9.33/2.11 Prover 3: proved (1532ms)
% 9.33/2.11
% 9.33/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.33/2.11
% 9.33/2.11 Prover 0: stopped
% 9.33/2.11 Prover 6: stopped
% 9.33/2.12 Prover 2: stopped
% 9.33/2.12 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 9.33/2.12 Prover 5: stopped
% 9.33/2.12 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 9.33/2.12 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 9.33/2.12 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 9.33/2.12 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 10.64/2.21 Prover 7: Preprocessing ...
% 10.64/2.22 Prover 8: Preprocessing ...
% 10.64/2.23 Prover 10: Preprocessing ...
% 11.15/2.25 Prover 11: Preprocessing ...
% 11.33/2.27 Prover 13: Preprocessing ...
% 11.33/2.29 Prover 1: Found proof (size 22)
% 11.33/2.29 Prover 1: proved (1713ms)
% 11.33/2.29 Prover 4: stopped
% 11.33/2.32 Prover 13: stopped
% 11.75/2.34 Prover 11: stopped
% 11.75/2.34 Prover 7: Warning: ignoring some quantifiers
% 11.98/2.35 Prover 10: Warning: ignoring some quantifiers
% 11.98/2.37 Prover 7: Constructing countermodel ...
% 11.98/2.37 Prover 10: Constructing countermodel ...
% 11.98/2.38 Prover 7: stopped
% 11.98/2.39 Prover 10: stopped
% 11.98/2.39 Prover 8: Warning: ignoring some quantifiers
% 11.98/2.41 Prover 8: Constructing countermodel ...
% 11.98/2.42 Prover 8: stopped
% 11.98/2.42
% 11.98/2.42 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 11.98/2.42
% 11.98/2.42 % SZS output start Proof for theBenchmark
% 11.98/2.43 Assumptions after simplification:
% 11.98/2.43 ---------------------------------
% 11.98/2.43
% 11.98/2.43 (d3_tarski)
% 12.42/2.45 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (subset(v0, v1) = v2)
% 12.42/2.45 | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : ? [v4: int] : ( ~ (v4 = 0) & in(v3,
% 12.42/2.45 v1) = v4 & in(v3, v0) = 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~
% 12.42/2.45 (subset(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0)
% 12.42/2.45 = 0) | ~ $i(v2) | in(v2, v1) = 0))
% 12.42/2.45
% 12.42/2.45 (symmetry_r1_xboole_0)
% 12.42/2.45 ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~ $i(v0)
% 12.42/2.45 | disjoint(v1, v0) = 0)
% 12.42/2.45
% 12.42/2.45 (t3_xboole_0)
% 12.42/2.46 ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0, v1) =
% 12.42/2.46 v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (in(v3, v1) = 0 & in(v3, v0) =
% 12.42/2.46 0 & $i(v3))) & ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~
% 12.42/2.46 $i(v1) | ~ $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | ?
% 12.42/2.46 [v3: int] : ( ~ (v3 = 0) & in(v2, v1) = v3)))
% 12.42/2.46
% 12.42/2.46 (t63_xboole_1)
% 12.42/2.46 ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: int] : ( ~ (v3 = 0) &
% 12.42/2.46 disjoint(v1, v2) = 0 & disjoint(v0, v2) = v3 & subset(v0, v1) = 0 & $i(v2) &
% 12.42/2.46 $i(v1) & $i(v0))
% 12.42/2.46
% 12.42/2.46 (function-axioms)
% 12.42/2.46 ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : !
% 12.42/2.46 [v3: $i] : (v1 = v0 | ~ (disjoint(v3, v2) = v1) | ~ (disjoint(v3, v2) = v0))
% 12.42/2.46 & ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.42/2.46 (set_difference(v3, v2) = v1) | ~ (set_difference(v3, v2) = v0)) & ! [v0:
% 12.42/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.42/2.46 : (v1 = v0 | ~ (subset(v3, v2) = v1) | ~ (subset(v3, v2) = v0)) & ! [v0:
% 12.42/2.46 $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.42/2.46 (set_intersection2(v3, v2) = v1) | ~ (set_intersection2(v3, v2) = v0)) & !
% 12.42/2.46 [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 12.42/2.46 (set_union2(v3, v2) = v1) | ~ (set_union2(v3, v2) = v0)) & ! [v0:
% 12.42/2.46 MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : ! [v3: $i]
% 12.42/2.46 : (v1 = v0 | ~ (proper_subset(v3, v2) = v1) | ~ (proper_subset(v3, v2) =
% 12.42/2.46 v0)) & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2:
% 12.42/2.46 $i] : ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 12.42/2.46 & ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] : (v1
% 12.42/2.46 = v0 | ~ (empty(v2) = v1) | ~ (empty(v2) = v0))
% 12.42/2.46
% 12.42/2.46 Further assumptions not needed in the proof:
% 12.42/2.46 --------------------------------------------
% 12.42/2.46 antisymmetry_r2_hidden, antisymmetry_r2_xboole_0, commutativity_k2_xboole_0,
% 12.42/2.46 commutativity_k3_xboole_0, d10_xboole_0, d1_xboole_0, d2_xboole_0, d3_xboole_0,
% 12.42/2.46 d4_xboole_0, d7_xboole_0, d8_xboole_0, dt_k1_xboole_0, dt_k2_xboole_0,
% 12.42/2.46 dt_k3_xboole_0, dt_k4_xboole_0, fc1_xboole_0, fc2_xboole_0, fc3_xboole_0,
% 12.42/2.46 idempotence_k2_xboole_0, idempotence_k3_xboole_0, irreflexivity_r2_xboole_0,
% 12.42/2.46 l32_xboole_1, rc1_xboole_0, rc2_xboole_0, reflexivity_r1_tarski, t12_xboole_1,
% 12.42/2.46 t17_xboole_1, t19_xboole_1, t1_boole, t1_xboole_1, t26_xboole_1, t28_xboole_1,
% 12.42/2.46 t2_boole, t2_tarski, t2_xboole_1, t33_xboole_1, t36_xboole_1, t37_xboole_1,
% 12.42/2.46 t39_xboole_1, t3_boole, t3_xboole_1, t40_xboole_1, t45_xboole_1, t48_xboole_1,
% 12.42/2.46 t4_boole, t4_xboole_0, t60_xboole_1, t6_boole, t7_boole, t7_xboole_1, t8_boole,
% 12.42/2.46 t8_xboole_1
% 12.42/2.46
% 12.42/2.46 Those formulas are unsatisfiable:
% 12.42/2.46 ---------------------------------
% 12.42/2.46
% 12.42/2.46 Begin of proof
% 12.42/2.47 |
% 12.42/2.47 | ALPHA: (d3_tarski) implies:
% 12.42/2.47 | (1) ! [v0: $i] : ! [v1: $i] : ( ~ (subset(v0, v1) = 0) | ~ $i(v1) | ~
% 12.42/2.47 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | in(v2, v1)
% 12.42/2.47 | = 0))
% 12.42/2.47 |
% 12.42/2.47 | ALPHA: (t3_xboole_0) implies:
% 12.42/2.47 | (2) ! [v0: $i] : ! [v1: $i] : ( ~ (disjoint(v0, v1) = 0) | ~ $i(v1) | ~
% 12.42/2.47 | $i(v0) | ! [v2: $i] : ( ~ (in(v2, v0) = 0) | ~ $i(v2) | ? [v3:
% 12.42/2.47 | int] : ( ~ (v3 = 0) & in(v2, v1) = v3)))
% 12.42/2.47 | (3) ! [v0: $i] : ! [v1: $i] : ! [v2: int] : (v2 = 0 | ~ (disjoint(v0,
% 12.42/2.47 | v1) = v2) | ~ $i(v1) | ~ $i(v0) | ? [v3: $i] : (in(v3, v1) = 0
% 12.42/2.47 | & in(v3, v0) = 0 & $i(v3)))
% 12.42/2.47 |
% 12.42/2.47 | ALPHA: (function-axioms) implies:
% 12.42/2.47 | (4) ! [v0: MultipleValueBool] : ! [v1: MultipleValueBool] : ! [v2: $i] :
% 12.42/2.47 | ! [v3: $i] : (v1 = v0 | ~ (in(v3, v2) = v1) | ~ (in(v3, v2) = v0))
% 12.42/2.47 |
% 12.42/2.47 | DELTA: instantiating (t63_xboole_1) with fresh symbols all_60_0, all_60_1,
% 12.42/2.47 | all_60_2, all_60_3 gives:
% 12.66/2.47 | (5) ~ (all_60_0 = 0) & disjoint(all_60_2, all_60_1) = 0 &
% 12.66/2.47 | disjoint(all_60_3, all_60_1) = all_60_0 & subset(all_60_3, all_60_2) =
% 12.66/2.47 | 0 & $i(all_60_1) & $i(all_60_2) & $i(all_60_3)
% 12.66/2.47 |
% 12.66/2.47 | ALPHA: (5) implies:
% 12.66/2.47 | (6) ~ (all_60_0 = 0)
% 12.66/2.47 | (7) $i(all_60_3)
% 12.66/2.47 | (8) $i(all_60_2)
% 12.66/2.47 | (9) $i(all_60_1)
% 12.66/2.47 | (10) subset(all_60_3, all_60_2) = 0
% 12.66/2.48 | (11) disjoint(all_60_3, all_60_1) = all_60_0
% 12.66/2.48 | (12) disjoint(all_60_2, all_60_1) = 0
% 12.66/2.48 |
% 12.66/2.48 | GROUND_INST: instantiating (1) with all_60_3, all_60_2, simplifying with (7),
% 12.66/2.48 | (8), (10) gives:
% 12.66/2.48 | (13) ! [v0: $i] : ( ~ (in(v0, all_60_3) = 0) | ~ $i(v0) | in(v0,
% 12.66/2.48 | all_60_2) = 0)
% 12.66/2.48 |
% 12.66/2.48 | GROUND_INST: instantiating (3) with all_60_3, all_60_1, all_60_0, simplifying
% 12.66/2.48 | with (7), (9), (11) gives:
% 12.66/2.48 | (14) all_60_0 = 0 | ? [v0: $i] : (in(v0, all_60_1) = 0 & in(v0, all_60_3)
% 12.66/2.48 | = 0 & $i(v0))
% 12.66/2.48 |
% 12.66/2.48 | GROUND_INST: instantiating (symmetry_r1_xboole_0) with all_60_2, all_60_1,
% 12.66/2.48 | simplifying with (8), (9), (12) gives:
% 12.66/2.48 | (15) disjoint(all_60_1, all_60_2) = 0
% 12.66/2.48 |
% 12.66/2.48 | BETA: splitting (14) gives:
% 12.66/2.48 |
% 12.66/2.48 | Case 1:
% 12.66/2.48 | |
% 12.66/2.48 | | (16) all_60_0 = 0
% 12.66/2.48 | |
% 12.66/2.48 | | REDUCE: (6), (16) imply:
% 12.66/2.48 | | (17) $false
% 12.66/2.48 | |
% 12.66/2.48 | | CLOSE: (17) is inconsistent.
% 12.66/2.48 | |
% 12.66/2.48 | Case 2:
% 12.66/2.48 | |
% 12.66/2.48 | | (18) ? [v0: $i] : (in(v0, all_60_1) = 0 & in(v0, all_60_3) = 0 & $i(v0))
% 12.66/2.48 | |
% 12.66/2.48 | | DELTA: instantiating (18) with fresh symbol all_96_0 gives:
% 12.66/2.48 | | (19) in(all_96_0, all_60_1) = 0 & in(all_96_0, all_60_3) = 0 &
% 12.66/2.48 | | $i(all_96_0)
% 12.66/2.48 | |
% 12.66/2.48 | | ALPHA: (19) implies:
% 12.66/2.48 | | (20) $i(all_96_0)
% 12.66/2.48 | | (21) in(all_96_0, all_60_3) = 0
% 12.66/2.48 | | (22) in(all_96_0, all_60_1) = 0
% 12.66/2.48 | |
% 12.66/2.48 | | GROUND_INST: instantiating (13) with all_96_0, simplifying with (20), (21)
% 12.66/2.48 | | gives:
% 12.66/2.48 | | (23) in(all_96_0, all_60_2) = 0
% 12.66/2.48 | |
% 12.66/2.48 | | GROUND_INST: instantiating (2) with all_60_1, all_60_2, simplifying with
% 12.66/2.48 | | (8), (9), (15) gives:
% 12.66/2.48 | | (24) ! [v0: $i] : ( ~ (in(v0, all_60_1) = 0) | ~ $i(v0) | ? [v1: int]
% 12.66/2.48 | | : ( ~ (v1 = 0) & in(v0, all_60_2) = v1))
% 12.66/2.48 | |
% 12.66/2.48 | | GROUND_INST: instantiating (24) with all_96_0, simplifying with (20), (22)
% 12.66/2.48 | | gives:
% 12.66/2.49 | | (25) ? [v0: int] : ( ~ (v0 = 0) & in(all_96_0, all_60_2) = v0)
% 12.66/2.49 | |
% 12.66/2.49 | | DELTA: instantiating (25) with fresh symbol all_130_0 gives:
% 12.66/2.49 | | (26) ~ (all_130_0 = 0) & in(all_96_0, all_60_2) = all_130_0
% 12.66/2.49 | |
% 12.66/2.49 | | ALPHA: (26) implies:
% 12.66/2.49 | | (27) ~ (all_130_0 = 0)
% 12.66/2.49 | | (28) in(all_96_0, all_60_2) = all_130_0
% 12.66/2.49 | |
% 12.66/2.49 | | GROUND_INST: instantiating (4) with 0, all_130_0, all_60_2, all_96_0,
% 12.66/2.49 | | simplifying with (23), (28) gives:
% 12.66/2.49 | | (29) all_130_0 = 0
% 12.66/2.49 | |
% 12.66/2.49 | | REDUCE: (27), (29) imply:
% 12.66/2.49 | | (30) $false
% 12.66/2.49 | |
% 12.66/2.49 | | CLOSE: (30) is inconsistent.
% 12.66/2.49 | |
% 12.66/2.49 | End of split
% 12.66/2.49 |
% 12.66/2.49 End of proof
% 12.66/2.49 % SZS output end Proof for theBenchmark
% 12.66/2.49
% 12.66/2.49 1933ms
%------------------------------------------------------------------------------