TSTP Solution File: CSR048+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CSR048+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n005.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 20 14:27:34 EDT 2022
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 30
% Syntax : Number of formulae : 61 ( 11 unt; 8 typ; 0 def)
% Number of atoms : 236 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 317 ( 153 ~; 117 |; 16 &)
% ( 24 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 19 ( 19 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 3 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 70 ( 50 !; 12 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
tff(borderson_type,type,
borderson: ( $i * $i ) > $o ).
tff(c_georegion_l4_x45_y10_type,type,
c_georegion_l4_x45_y10: $i ).
tff(c_georegion_l4_x45_y9_type,type,
c_georegion_l4_x45_y9: $i ).
tff(mtvisible_type,type,
mtvisible: $i > $o ).
tff(c_tptpgeo_spindlecollectormt_type,type,
c_tptpgeo_spindlecollectormt: $i ).
tff(c_tptpgeo_member1_mt_type,type,
c_tptpgeo_member1_mt: $i ).
tff(c_universalvocabularymt_type,type,
c_universalvocabularymt: $i ).
tff(genlmt_type,type,
genlmt: ( $i * $i ) > $o ).
tff(1,plain,
^ [ARG2: $i] :
refl(
( ~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) )
<=> ~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [ARG2: $i] :
~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) )
<=> ! [ARG2: $i] :
~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ~ ? [ARG2: $i] :
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) )
<=> ~ ? [ARG2: $i] :
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,plain,
( ~ ? [ARG2: $i] :
( mtvisible(c_tptpgeo_spindlecollectormt)
=> borderson(c_georegion_l4_x45_y9,ARG2) )
<=> ~ ? [ARG2: $i] :
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ) ),
inference(rewrite,[status(thm)],]) ).
tff(5,axiom,
~ ? [ARG2: $i] :
( mtvisible(c_tptpgeo_spindlecollectormt)
=> borderson(c_georegion_l4_x45_y9,ARG2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',query48) ).
tff(6,plain,
~ ? [ARG2: $i] :
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ),
inference(modus_ponens,[status(thm)],[5,4]) ).
tff(7,plain,
~ ? [ARG2: $i] :
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ),
inference(modus_ponens,[status(thm)],[6,3]) ).
tff(8,plain,
~ ? [ARG2: $i] :
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ),
inference(modus_ponens,[status(thm)],[7,3]) ).
tff(9,plain,
~ ? [ARG2: $i] :
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ),
inference(modus_ponens,[status(thm)],[8,3]) ).
tff(10,plain,
~ ? [ARG2: $i] :
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ),
inference(modus_ponens,[status(thm)],[9,3]) ).
tff(11,plain,
~ ? [ARG2: $i] :
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ),
inference(modus_ponens,[status(thm)],[10,3]) ).
tff(12,plain,
~ ? [ARG2: $i] :
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ),
inference(modus_ponens,[status(thm)],[11,3]) ).
tff(13,plain,
^ [ARG2: $i] :
refl(
$oeq(
~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ),
~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ))),
inference(bind,[status(th)],]) ).
tff(14,plain,
! [ARG2: $i] :
~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ),
inference(nnf-neg,[status(sab)],[12,13]) ).
tff(15,plain,
! [ARG2: $i] :
~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) ),
inference(modus_ponens,[status(thm)],[14,2]) ).
tff(16,plain,
( ~ ! [ARG2: $i] :
~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) )
| ~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,c_universalvocabularymt) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(17,plain,
~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,c_universalvocabularymt) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,c_universalvocabularymt)
| mtvisible(c_tptpgeo_spindlecollectormt) ),
inference(tautology,[status(thm)],]) ).
tff(19,plain,
mtvisible(c_tptpgeo_spindlecollectormt),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
^ [SPECMT: $i,GENLMT: $i] :
refl(
( ( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
<=> ( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
<=> ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
^ [SPECMT: $i,GENLMT: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
<=> ~ ( ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) ) )),
( ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
<=> ~ ~ ( ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) ) )),
rewrite(
( ~ ~ ( ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) )
<=> ( ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) ) )),
( ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
<=> ( ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) ) )),
( ( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) )
<=> ( mtvisible(GENLMT)
| ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) ) )),
rewrite(
( ( mtvisible(GENLMT)
| ~ mtvisible(SPECMT)
| ~ genlmt(SPECMT,GENLMT) )
<=> ( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ) )),
( ( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) )
<=> ( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) )
<=> ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) )
<=> ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
^ [SPECMT: $i,GENLMT: $i] :
rewrite(
( ( ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
=> mtvisible(GENLMT) )
<=> ( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [SPECMT: $i,GENLMT: $i] :
( ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
=> mtvisible(GENLMT) )
<=> ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,axiom,
! [SPECMT: $i,GENLMT: $i] :
( ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) )
=> mtvisible(GENLMT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',just31) ).
tff(28,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ ( mtvisible(SPECMT)
& genlmt(SPECMT,GENLMT) ) ),
inference(skolemize,[status(sab)],[29]) ).
tff(31,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ),
inference(modus_ponens,[status(thm)],[30,23]) ).
tff(32,plain,
! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) ),
inference(modus_ponens,[status(thm)],[31,21]) ).
tff(33,plain,
( genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt)
<=> genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt) ),
inference(rewrite,[status(thm)],]) ).
tff(34,axiom,
genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',just1) ).
tff(35,plain,
genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( mtvisible(c_tptpgeo_member1_mt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt) )
<=> ( mtvisible(c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member1_mt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
( ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member1_mt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt) )
<=> ( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member1_mt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,plain,
( ~ ! [SPECMT: $i,GENLMT: $i] :
( mtvisible(GENLMT)
| ~ genlmt(SPECMT,GENLMT)
| ~ mtvisible(SPECMT) )
| mtvisible(c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt)
| ~ genlmt(c_tptpgeo_spindlecollectormt,c_tptpgeo_member1_mt) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
( mtvisible(c_tptpgeo_member1_mt)
| ~ mtvisible(c_tptpgeo_spindlecollectormt) ),
inference(unit_resolution,[status(thm)],[41,35,32]) ).
tff(43,plain,
mtvisible(c_tptpgeo_member1_mt),
inference(unit_resolution,[status(thm)],[42,19]) ).
tff(44,plain,
( ( ~ mtvisible(c_tptpgeo_member1_mt)
| borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10) )
<=> ( ~ mtvisible(c_tptpgeo_member1_mt)
| borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( mtvisible(c_tptpgeo_member1_mt)
=> borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10) )
<=> ( ~ mtvisible(c_tptpgeo_member1_mt)
| borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,axiom,
( mtvisible(c_tptpgeo_member1_mt)
=> borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',just2) ).
tff(47,plain,
( ~ mtvisible(c_tptpgeo_member1_mt)
| borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( ~ mtvisible(c_tptpgeo_member1_mt)
| borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10) ),
inference(modus_ponens,[status(thm)],[47,44]) ).
tff(49,plain,
borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10),
inference(unit_resolution,[status(thm)],[48,43]) ).
tff(50,plain,
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10)
| ~ borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10) ),
inference(tautology,[status(thm)],]) ).
tff(51,plain,
( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( ~ ! [ARG2: $i] :
~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,ARG2) )
| ~ ( ~ mtvisible(c_tptpgeo_spindlecollectormt)
| borderson(c_georegion_l4_x45_y9,c_georegion_l4_x45_y10) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
$false,
inference(unit_resolution,[status(thm)],[52,15,51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : CSR048+1 : TPTP v8.1.0. Released v3.4.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n005.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 : Tue Aug 30 18:32:18 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------