TSTP Solution File: COM144+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COM144+1 : TPTP v8.1.0. Released v6.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 Sep 6 18:06:15 EDT 2022
% Result : Theorem 2.85s 3.03s
% Output : Proof 2.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : COM144+1 : TPTP v8.1.0. Released v6.4.0.
% 0.09/0.10 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.09/0.30 % Computer : n016.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue Aug 30 15:34:16 EDT 2022
% 0.09/0.30 % CPUTime :
% 0.09/0.31 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.09/0.31 Usage: tptp [options] [-file:]file
% 0.09/0.31 -h, -? prints this message.
% 0.09/0.31 -smt2 print SMT-LIB2 benchmark.
% 0.09/0.31 -m, -model generate model.
% 0.09/0.31 -p, -proof generate proof.
% 0.09/0.31 -c, -core generate unsat core of named formulas.
% 0.09/0.31 -st, -statistics display statistics.
% 0.09/0.31 -t:timeout set timeout (in second).
% 0.09/0.31 -smt2status display status in smt2 format instead of SZS.
% 0.09/0.31 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.09/0.31 -<param>:<value> configuration parameter and value.
% 0.09/0.31 -o:<output-file> file to place output in.
% 2.85/3.03 % SZS status Theorem
% 2.85/3.03 % SZS output start Proof
% 2.85/3.03 tff(vsomeExp_type, type, (
% 2.85/3.03 vsomeExp: $i > $i)).
% 2.85/3.03 tff(tptp_fun_Veout_75_type, type, (
% 2.85/3.03 tptp_fun_Veout_75: $i)).
% 2.85/3.03 tff(vnoExp_type, type, (
% 2.85/3.03 vnoExp: $i)).
% 2.85/3.03 tff(vreduce_type, type, (
% 2.85/3.03 vreduce: $i > $i)).
% 2.85/3.03 tff(vabs_type, type, (
% 2.85/3.03 vabs: ( $i * $i * $i ) > $i)).
% 2.85/3.03 tff(ve1_type, type, (
% 2.85/3.03 ve1: $i)).
% 2.85/3.03 tff(tptp_fun_VS_77_type, type, (
% 2.85/3.03 tptp_fun_VS_77: $i)).
% 2.85/3.03 tff(tptp_fun_Vx_78_type, type, (
% 2.85/3.03 tptp_fun_Vx_78: $i)).
% 2.85/3.03 tff(vtcheck_type, type, (
% 2.85/3.03 vtcheck: ( $i * $i * $i ) > $o)).
% 2.85/3.03 tff(tptp_fun_VT_74_type, type, (
% 2.85/3.03 tptp_fun_VT_74: $i)).
% 2.85/3.03 tff(tptp_fun_VC_76_type, type, (
% 2.85/3.03 tptp_fun_VC_76: $i)).
% 2.85/3.03 tff(1,plain,
% 2.85/3.03 ((~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT)))),
% 2.85/3.03 inference(rewrite,[status(thm)],[])).
% 2.85/3.03 tff(2,plain,
% 2.85/3.03 ((~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : (((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT)) => vtcheck(VC, Veout, VT))) <=> (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT)))),
% 2.85/3.03 inference(rewrite,[status(thm)],[])).
% 2.85/3.03 tff(3,axiom,(~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : (((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT)) => vtcheck(VC, Veout, VT))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',''T-Preservation-T-abs'')).
% 2.85/3.03 tff(4,plain,
% 2.85/3.03 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[3, 2])).
% 2.85/3.03 tff(5,plain,
% 2.85/3.03 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[4, 1])).
% 2.85/3.03 tff(6,plain,
% 2.85/3.03 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[5, 1])).
% 2.85/3.03 tff(7,plain,
% 2.85/3.03 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[6, 1])).
% 2.85/3.03 tff(8,plain,
% 2.85/3.03 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[7, 1])).
% 2.85/3.03 tff(9,plain,
% 2.85/3.03 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[8, 1])).
% 2.85/3.03 tff(10,plain,
% 2.85/3.03 (~![Vx: $i, VS: $i, VC: $i, Veout: $i, VT: $i] : ((~((vreduce(vabs(Vx, VS, ve1)) = vsomeExp(Veout)) & vtcheck(VC, vabs(Vx, VS, ve1), VT))) | vtcheck(VC, Veout, VT))),
% 2.85/3.03 inference(modus_ponens,[status(thm)],[9, 1])).
% 2.85/3.03 tff(11,plain,(
% 2.85/3.03 ~((~((vreduce(vabs(Vx!78, VS!77, ve1)) = vsomeExp(Veout!75)) & vtcheck(VC!76, vabs(Vx!78, VS!77, ve1), VT!74))) | vtcheck(VC!76, Veout!75, VT!74))),
% 2.85/3.03 inference(skolemize,[status(sab)],[10])).
% 2.85/3.03 tff(12,plain,
% 2.85/3.03 ((vreduce(vabs(Vx!78, VS!77, ve1)) = vsomeExp(Veout!75)) & vtcheck(VC!76, vabs(Vx!78, VS!77, ve1), VT!74)),
% 2.85/3.03 inference(or_elim,[status(thm)],[11])).
% 2.85/3.03 tff(13,plain,
% 2.85/3.03 (vreduce(vabs(Vx!78, VS!77, ve1)) = vsomeExp(Veout!75)),
% 2.85/3.03 inference(and_elim,[status(thm)],[12])).
% 2.85/3.03 tff(14,plain,
% 2.85/3.03 (vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1))),
% 2.85/3.03 inference(symmetry,[status(thm)],[13])).
% 2.85/3.03 tff(15,plain,
% 2.85/3.03 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve)))) <=> ![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(16,plain,
% 2.85/3.04 (^[Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : trans(monotonicity(rewrite(((RESULT = vreduce(VExp0)) => (RESULT = vnoExp)) <=> ((~(RESULT = vreduce(VExp0))) | (RESULT = vnoExp))), (((VExp0 = vabs(Vx, VS, Ve)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp))) <=> ((VExp0 = vabs(Vx, VS, Ve)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vnoExp))))), rewrite(((VExp0 = vabs(Vx, VS, Ve)) => ((~(RESULT = vreduce(VExp0))) | (RESULT = vnoExp))) <=> ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))), (((VExp0 = vabs(Vx, VS, Ve)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp))) <=> ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))))),
% 2.85/3.04 inference(bind,[status(th)],[])).
% 2.85/3.04 tff(17,plain,
% 2.85/3.04 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((VExp0 = vabs(Vx, VS, Ve)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp))) <=> ![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 2.85/3.04 inference(quant_intro,[status(thm)],[16])).
% 2.85/3.04 tff(18,axiom,(![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((VExp0 = vabs(Vx, VS, Ve)) => ((RESULT = vreduce(VExp0)) => (RESULT = vnoExp)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax','reduce1')).
% 2.85/3.04 tff(19,plain,
% 2.85/3.04 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[18, 17])).
% 2.85/3.04 tff(20,plain,
% 2.85/3.04 (![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[19, 15])).
% 2.85/3.04 tff(21,plain,(
% 2.85/3.04 ![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))),
% 2.85/3.04 inference(skolemize,[status(sab)],[20])).
% 2.85/3.04 tff(22,plain,
% 2.85/3.04 (((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))) | ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))))) <=> ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))) | (vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(23,plain,
% 2.85/3.04 (((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))) | $false) <=> ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(24,plain,
% 2.85/3.04 ((~$true) <=> $false),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(25,plain,
% 2.85/3.04 ((vabs(Vx!78, VS!77, ve1) = vabs(Vx!78, VS!77, ve1)) <=> $true),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(26,plain,
% 2.85/3.04 ((~(vabs(Vx!78, VS!77, ve1) = vabs(Vx!78, VS!77, ve1))) <=> (~$true)),
% 2.85/3.04 inference(monotonicity,[status(thm)],[25])).
% 2.85/3.04 tff(27,plain,
% 2.85/3.04 ((~(vabs(Vx!78, VS!77, ve1) = vabs(Vx!78, VS!77, ve1))) <=> $false),
% 2.85/3.04 inference(transitivity,[status(thm)],[26, 24])).
% 2.85/3.04 tff(28,plain,
% 2.85/3.04 (((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))) | (~(vabs(Vx!78, VS!77, ve1) = vabs(Vx!78, VS!77, ve1)))) <=> ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))) | $false)),
% 2.85/3.04 inference(monotonicity,[status(thm)],[27])).
% 2.85/3.04 tff(29,plain,
% 2.85/3.04 (((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))) | (~(vabs(Vx!78, VS!77, ve1) = vabs(Vx!78, VS!77, ve1)))) <=> ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))))),
% 2.85/3.04 inference(transitivity,[status(thm)],[28, 23])).
% 2.85/3.04 tff(30,plain,
% 2.85/3.04 (((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))) | ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))) | (~(vabs(Vx!78, VS!77, ve1) = vabs(Vx!78, VS!77, ve1))))) <=> ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))) | ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1))))))),
% 2.85/3.04 inference(monotonicity,[status(thm)],[29])).
% 2.85/3.04 tff(31,plain,
% 2.85/3.04 (((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))) | ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))) | (~(vabs(Vx!78, VS!77, ve1) = vabs(Vx!78, VS!77, ve1))))) <=> ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))) | (vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))))),
% 2.85/3.04 inference(transitivity,[status(thm)],[30, 22])).
% 2.85/3.04 tff(32,plain,
% 2.85/3.04 ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))) | ((vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1)))) | (~(vabs(Vx!78, VS!77, ve1) = vabs(Vx!78, VS!77, ve1))))),
% 2.85/3.04 inference(quant_inst,[status(thm)],[])).
% 2.85/3.04 tff(33,plain,
% 2.85/3.04 ((~![Vx: $i, VS: $i, Ve: $i, VExp0: $i, RESULT: $i] : ((RESULT = vnoExp) | (~(RESULT = vreduce(VExp0))) | (~(VExp0 = vabs(Vx, VS, Ve))))) | (vsomeExp(Veout!75) = vnoExp) | (~(vsomeExp(Veout!75) = vreduce(vabs(Vx!78, VS!77, ve1))))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[32, 31])).
% 2.85/3.04 tff(34,plain,
% 2.85/3.04 (vsomeExp(Veout!75) = vnoExp),
% 2.85/3.04 inference(unit_resolution,[status(thm)],[33, 21, 14])).
% 2.85/3.04 tff(35,plain,
% 2.85/3.04 (vnoExp = vsomeExp(Veout!75)),
% 2.85/3.04 inference(symmetry,[status(thm)],[34])).
% 2.85/3.04 tff(36,plain,
% 2.85/3.04 (^[VExp0: $i] : refl((~(vnoExp = vsomeExp(VExp0))) <=> (~(vnoExp = vsomeExp(VExp0))))),
% 2.85/3.04 inference(bind,[status(th)],[])).
% 2.85/3.04 tff(37,plain,
% 2.85/3.04 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0))) <=> ![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 2.85/3.04 inference(quant_intro,[status(thm)],[36])).
% 2.85/3.04 tff(38,plain,
% 2.85/3.04 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0))) <=> ![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 2.85/3.04 inference(rewrite,[status(thm)],[])).
% 2.85/3.04 tff(39,axiom,(![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))), file('/export/starexec/sandbox/benchmark/Axioms/COM001+0.ax',''DIFF-noExp-someExp'')).
% 2.85/3.04 tff(40,plain,
% 2.85/3.04 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[39, 38])).
% 2.85/3.04 tff(41,plain,(
% 2.85/3.04 ![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 2.85/3.04 inference(skolemize,[status(sab)],[40])).
% 2.85/3.04 tff(42,plain,
% 2.85/3.04 (![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))),
% 2.85/3.04 inference(modus_ponens,[status(thm)],[41, 37])).
% 2.85/3.04 tff(43,plain,
% 2.85/3.04 ((~![VExp0: $i] : (~(vnoExp = vsomeExp(VExp0)))) | (~(vnoExp = vsomeExp(Veout!75)))),
% 2.85/3.05 inference(quant_inst,[status(thm)],[])).
% 2.85/3.05 tff(44,plain,
% 2.85/3.05 (~(vnoExp = vsomeExp(Veout!75))),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[43, 42])).
% 2.85/3.05 tff(45,plain,
% 2.85/3.05 ($false),
% 2.85/3.05 inference(unit_resolution,[status(thm)],[44, 35])).
% 2.85/3.05 % SZS output end Proof
%------------------------------------------------------------------------------