TSTP Solution File: KLE118+1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : KLE118+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 : 600s
% DateTime : Sun Jul 17 02:28:36 EDT 2022
% Result : Theorem 79.37s 79.61s
% Output : Refutation 81.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 22
% Syntax : Number of clauses : 94 ( 89 unt; 0 nHn; 94 RR)
% Number of literals : 99 ( 0 equ; 11 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(addition(skc3,skc4),skc4),
file('KLE118+1.p',unknown),
[] ).
cnf(2,axiom,
equal(addition(u,zero),u),
file('KLE118+1.p',unknown),
[] ).
cnf(3,axiom,
equal(addition(u,u),u),
file('KLE118+1.p',unknown),
[] ).
cnf(4,axiom,
equal(multiplication(u,one),u),
file('KLE118+1.p',unknown),
[] ).
cnf(5,axiom,
equal(multiplication(one,u),u),
file('KLE118+1.p',unknown),
[] ).
cnf(7,axiom,
equal(multiplication(zero,u),zero),
file('KLE118+1.p',unknown),
[] ).
cnf(8,axiom,
equal(multiplication(antidomain(u),u),zero),
file('KLE118+1.p',unknown),
[] ).
cnf(9,axiom,
equal(domain__dfg(u),antidomain(antidomain(u))),
file('KLE118+1.p',unknown),
[] ).
cnf(12,axiom,
equal(c(u),antidomain(domain__dfg(u))),
file('KLE118+1.p',unknown),
[] ).
cnf(13,axiom,
equal(addition(u,v),addition(v,u)),
file('KLE118+1.p',unknown),
[] ).
cnf(14,axiom,
equal(addition(antidomain(antidomain(u)),antidomain(u)),one),
file('KLE118+1.p',unknown),
[] ).
cnf(16,axiom,
( ~ leq(u,v)
| equal(addition(u,v),v) ),
file('KLE118+1.p',unknown),
[] ).
cnf(17,axiom,
( ~ equal(addition(u,v),v)
| leq(u,v) ),
file('KLE118+1.p',unknown),
[] ).
cnf(18,axiom,
equal(multiplication(domain__dfg(u),antidomain(v)),domain_difference(u,v)),
file('KLE118+1.p',unknown),
[] ).
cnf(19,axiom,
equal(domain__dfg(multiplication(u,domain__dfg(v))),forward_diamond(u,v)),
file('KLE118+1.p',unknown),
[] ).
cnf(21,axiom,
equal(c(forward_diamond(u,c(v))),forward_box(u,v)),
file('KLE118+1.p',unknown),
[] ).
cnf(23,axiom,
equal(addition(addition(u,v),w),addition(u,addition(v,w))),
file('KLE118+1.p',unknown),
[] ).
cnf(24,axiom,
equal(multiplication(multiplication(u,v),w),multiplication(u,multiplication(v,w))),
file('KLE118+1.p',unknown),
[] ).
cnf(25,axiom,
equal(multiplication(u,addition(v,w)),addition(multiplication(u,v),multiplication(u,w))),
file('KLE118+1.p',unknown),
[] ).
cnf(26,axiom,
equal(multiplication(addition(u,v),w),addition(multiplication(u,w),multiplication(v,w))),
file('KLE118+1.p',unknown),
[] ).
cnf(27,axiom,
~ equal(addition(forward_box(skc3,domain__dfg(skc5)),forward_box(skc4,domain__dfg(skc5))),forward_box(skc3,domain__dfg(skc5))),
file('KLE118+1.p',unknown),
[] ).
cnf(28,axiom,
equal(addition(antidomain(multiplication(u,v)),antidomain(multiplication(u,antidomain(antidomain(v))))),antidomain(multiplication(u,antidomain(antidomain(v))))),
file('KLE118+1.p',unknown),
[] ).
cnf(30,plain,
equal(c(u),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[9,12]),
[iquote('0:Rew:9.0,12.0')] ).
cnf(32,plain,
equal(addition(antidomain(u),antidomain(antidomain(u))),one),
inference(rew,[status(thm),theory(equality)],[13,14]),
[iquote('0:Rew:13.0,14.0')] ).
cnf(34,plain,
equal(antidomain(antidomain(antidomain(forward_diamond(u,antidomain(antidomain(antidomain(v))))))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[30,21]),
[iquote('0:Rew:30.0,21.0,30.0,21.0')] ).
cnf(37,plain,
equal(forward_diamond(u,v),antidomain(antidomain(multiplication(u,antidomain(antidomain(v)))))),
inference(rew,[status(thm),theory(equality)],[9,19]),
[iquote('0:Rew:9.0,19.0,9.0,19.0')] ).
cnf(38,plain,
equal(antidomain(antidomain(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v))))))))))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[37,34]),
[iquote('0:Rew:37.0,34.0')] ).
cnf(39,plain,
equal(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,v)),
inference(rew,[status(thm),theory(equality)],[9,18]),
[iquote('0:Rew:9.0,18.0')] ).
cnf(40,plain,
~ equal(addition(forward_box(skc3,antidomain(antidomain(skc5))),forward_box(skc4,antidomain(antidomain(skc5)))),forward_box(skc3,antidomain(antidomain(skc5)))),
inference(rew,[status(thm),theory(equality)],[9,27]),
[iquote('0:Rew:9.0,27.0')] ).
cnf(56,plain,
equal(antidomain(one),zero),
inference(spr,[status(thm),theory(equality)],[8,4]),
[iquote('0:SpR:8.0,4.0')] ).
cnf(67,plain,
equal(addition(zero,u),u),
inference(spr,[status(thm),theory(equality)],[13,2]),
[iquote('0:SpR:13.0,2.0')] ).
cnf(90,plain,
equal(addition(zero,antidomain(zero)),one),
inference(spr,[status(thm),theory(equality)],[56,32]),
[iquote('0:SpR:56.0,32.0')] ).
cnf(92,plain,
equal(antidomain(zero),one),
inference(rew,[status(thm),theory(equality)],[67,90]),
[iquote('0:Rew:67.0,90.0')] ).
cnf(101,plain,
( ~ leq(u,v)
| equal(addition(v,u),v) ),
inference(spr,[status(thm),theory(equality)],[16,13]),
[iquote('0:SpR:16.1,13.0')] ).
cnf(181,plain,
equal(multiplication(antidomain(u),multiplication(u,v)),multiplication(zero,v)),
inference(spr,[status(thm),theory(equality)],[8,24]),
[iquote('0:SpR:8.0,24.0')] ).
cnf(191,plain,
equal(multiplication(antidomain(u),multiplication(u,v)),zero),
inference(rew,[status(thm),theory(equality)],[7,181]),
[iquote('0:Rew:7.0,181.0')] ).
cnf(251,plain,
equal(addition(u,addition(u,v)),addition(u,v)),
inference(spr,[status(thm),theory(equality)],[3,23]),
[iquote('0:SpR:3.0,23.0')] ).
cnf(304,plain,
equal(addition(multiplication(skc3,u),multiplication(skc4,u)),multiplication(skc4,u)),
inference(spr,[status(thm),theory(equality)],[1,26]),
[iquote('0:SpR:1.0,26.0')] ).
cnf(314,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),multiplication(one,v)),
inference(spr,[status(thm),theory(equality)],[32,26]),
[iquote('0:SpR:32.0,26.0')] ).
cnf(324,plain,
equal(addition(multiplication(antidomain(u),v),multiplication(antidomain(antidomain(u)),v)),v),
inference(rew,[status(thm),theory(equality)],[5,314]),
[iquote('0:Rew:5.0,314.0')] ).
cnf(366,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),multiplication(antidomain(addition(u,v)),v)),zero),
inference(spr,[status(thm),theory(equality)],[25,8]),
[iquote('0:SpR:25.0,8.0')] ).
cnf(383,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),multiplication(u,one)),
inference(spr,[status(thm),theory(equality)],[32,25]),
[iquote('0:SpR:32.0,25.0')] ).
cnf(394,plain,
equal(addition(multiplication(u,antidomain(v)),multiplication(u,antidomain(antidomain(v)))),u),
inference(rew,[status(thm),theory(equality)],[4,383]),
[iquote('0:Rew:4.0,383.0')] ).
cnf(572,plain,
( ~ leq(forward_box(skc4,antidomain(antidomain(skc5))),forward_box(skc3,antidomain(antidomain(skc5))))
| ~ equal(forward_box(skc3,antidomain(antidomain(skc5))),forward_box(skc3,antidomain(antidomain(skc5)))) ),
inference(spl,[status(thm),theory(equality)],[101,40]),
[iquote('0:SpL:101.1,40.0')] ).
cnf(573,plain,
~ leq(forward_box(skc4,antidomain(antidomain(skc5))),forward_box(skc3,antidomain(antidomain(skc5)))),
inference(obv,[status(thm),theory(equality)],[572]),
[iquote('0:Obv:572.1')] ).
cnf(745,plain,
equal(addition(antidomain(u),one),one),
inference(spr,[status(thm),theory(equality)],[32,251]),
[iquote('0:SpR:32.0,251.0')] ).
cnf(747,plain,
( ~ equal(addition(u,v),addition(u,v))
| leq(u,addition(u,v)) ),
inference(spl,[status(thm),theory(equality)],[251,17]),
[iquote('0:SpL:251.0,17.0')] ).
cnf(757,plain,
equal(addition(one,antidomain(u)),one),
inference(rew,[status(thm),theory(equality)],[13,745]),
[iquote('0:Rew:13.0,745.0')] ).
cnf(760,plain,
leq(u,addition(u,v)),
inference(obv,[status(thm),theory(equality)],[747]),
[iquote('0:Obv:747.0')] ).
cnf(786,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),
inference(spr,[status(thm),theory(equality)],[8,28]),
[iquote('0:SpR:8.0,28.0')] ).
cnf(794,plain,
equal(addition(antidomain(zero),antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v)))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v)))))),
inference(spr,[status(thm),theory(equality)],[191,28]),
[iquote('0:SpR:191.0,28.0')] ).
cnf(809,plain,
equal(addition(one,antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(u))))),
inference(rew,[status(thm),theory(equality)],[92,786]),
[iquote('0:Rew:92.0,786.0')] ).
cnf(810,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(u)))),one),
inference(rew,[status(thm),theory(equality)],[757,809]),
[iquote('0:Rew:757.0,809.0')] ).
cnf(813,plain,
equal(addition(one,antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v)))))),antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v)))))),
inference(rew,[status(thm),theory(equality)],[92,794]),
[iquote('0:Rew:92.0,794.0')] ).
cnf(814,plain,
equal(antidomain(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v))))),one),
inference(rew,[status(thm),theory(equality)],[757,813]),
[iquote('0:Rew:757.0,813.0')] ).
cnf(833,plain,
leq(u,addition(v,u)),
inference(spr,[status(thm),theory(equality)],[13,760]),
[iquote('0:SpR:13.0,760.0')] ).
cnf(924,plain,
equal(addition(multiplication(one,u),multiplication(antidomain(v),u)),multiplication(one,u)),
inference(spr,[status(thm),theory(equality)],[757,26]),
[iquote('0:SpR:757.0,26.0')] ).
cnf(939,plain,
equal(addition(u,multiplication(antidomain(v),u)),u),
inference(rew,[status(thm),theory(equality)],[5,924]),
[iquote('0:Rew:5.0,924.0')] ).
cnf(1056,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(u)))),zero),
inference(spr,[status(thm),theory(equality)],[810,8]),
[iquote('0:SpR:810.0,8.0')] ).
cnf(1087,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(u))),zero),
inference(rew,[status(thm),theory(equality)],[5,1056]),
[iquote('0:Rew:5.0,1056.0')] ).
cnf(2132,plain,
leq(multiplication(antidomain(u),v),v),
inference(spr,[status(thm),theory(equality)],[939,833]),
[iquote('0:SpR:939.0,833.0')] ).
cnf(2187,plain,
leq(domain_difference(u,v),antidomain(v)),
inference(spr,[status(thm),theory(equality)],[39,2132]),
[iquote('0:SpR:39.0,2132.0')] ).
cnf(4091,plain,
equal(addition(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[1087,324]),
[iquote('0:SpR:1087.0,324.0')] ).
cnf(4134,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(antidomain(antidomain(u)))),
inference(rew,[status(thm),theory(equality)],[67,4091,13]),
[iquote('0:Rew:67.0,4091.0,13.0,4091.0')] ).
cnf(4502,plain,
equal(addition(multiplication(antidomain(antidomain(u)),antidomain(v)),domain_difference(u,antidomain(v))),antidomain(antidomain(u))),
inference(spr,[status(thm),theory(equality)],[39,394]),
[iquote('0:SpR:39.0,394.0')] ).
cnf(4519,plain,
equal(addition(zero,multiplication(antidomain(u),antidomain(antidomain(antidomain(u))))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[1087,394]),
[iquote('0:SpR:1087.0,394.0')] ).
cnf(4544,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(antidomain(u)))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[67,4519]),
[iquote('0:Rew:67.0,4519.0')] ).
cnf(4545,plain,
equal(antidomain(antidomain(antidomain(u))),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4134,4544]),
[iquote('0:Rew:4134.0,4544.0')] ).
cnf(4546,plain,
equal(antidomain(antidomain(antidomain(multiplication(u,antidomain(antidomain(antidomain(antidomain(antidomain(v))))))))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4545,38]),
[iquote('0:Rew:4545.0,38.0')] ).
cnf(4644,plain,
equal(addition(domain_difference(u,v),domain_difference(u,antidomain(v))),antidomain(antidomain(u))),
inference(rew,[status(thm),theory(equality)],[39,4502]),
[iquote('0:Rew:39.0,4502.0')] ).
cnf(4646,plain,
equal(antidomain(multiplication(u,antidomain(v))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4545,4546]),
[iquote('0:Rew:4545.0,4546.0,4545.0,4546.0,4545.0,4546.0')] ).
cnf(4661,plain,
equal(forward_box(antidomain(u),antidomain(multiplication(u,v))),one),
inference(rew,[status(thm),theory(equality)],[4646,814]),
[iquote('0:Rew:4646.0,814.0')] ).
cnf(4817,plain,
equal(multiplication(forward_box(u,v),multiplication(u,antidomain(v))),zero),
inference(spr,[status(thm),theory(equality)],[4646,8]),
[iquote('0:SpR:4646.0,8.0')] ).
cnf(4980,plain,
equal(multiplication(antidomain(u),antidomain(v)),domain_difference(antidomain(u),v)),
inference(spr,[status(thm),theory(equality)],[4545,39]),
[iquote('0:SpR:4545.0,39.0')] ).
cnf(5001,plain,
equal(antidomain(multiplication(u,antidomain(v))),forward_box(u,antidomain(antidomain(v)))),
inference(spr,[status(thm),theory(equality)],[4545,4646]),
[iquote('0:SpR:4545.0,4646.0')] ).
cnf(5031,plain,
equal(forward_box(u,antidomain(antidomain(v))),forward_box(u,v)),
inference(rew,[status(thm),theory(equality)],[4646,5001]),
[iquote('0:Rew:4646.0,5001.0')] ).
cnf(5035,plain,
~ leq(forward_box(skc4,skc5),forward_box(skc3,antidomain(antidomain(skc5)))),
inference(rew,[status(thm),theory(equality)],[5031,573]),
[iquote('0:Rew:5031.0,573.0')] ).
cnf(5037,plain,
~ leq(forward_box(skc4,skc5),forward_box(skc3,skc5)),
inference(rew,[status(thm),theory(equality)],[5031,5035]),
[iquote('0:Rew:5031.0,5035.0')] ).
cnf(9849,plain,
equal(addition(multiplication(antidomain(addition(u,v)),u),zero),zero),
inference(spr,[status(thm),theory(equality)],[366,251]),
[iquote('0:SpR:366.0,251.0')] ).
cnf(9972,plain,
equal(multiplication(antidomain(addition(u,v)),u),zero),
inference(rew,[status(thm),theory(equality)],[67,9849,13]),
[iquote('0:Rew:67.0,9849.0,13.0,9849.0')] ).
cnf(13594,plain,
equal(addition(zero,multiplication(antidomain(antidomain(addition(u,v))),u)),u),
inference(spr,[status(thm),theory(equality)],[9972,324]),
[iquote('0:SpR:9972.0,324.0')] ).
cnf(13678,plain,
equal(multiplication(antidomain(antidomain(addition(u,v))),u),u),
inference(rew,[status(thm),theory(equality)],[67,13594]),
[iquote('0:Rew:67.0,13594.0')] ).
cnf(22919,plain,
equal(multiplication(one,multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v))))),zero),
inference(spr,[status(thm),theory(equality)],[4661,4817]),
[iquote('0:SpR:4661.0,4817.0')] ).
cnf(23063,plain,
equal(multiplication(antidomain(u),antidomain(antidomain(multiplication(u,v)))),zero),
inference(rew,[status(thm),theory(equality)],[5,22919]),
[iquote('0:Rew:5.0,22919.0')] ).
cnf(23064,plain,
equal(domain_difference(antidomain(u),antidomain(multiplication(u,v))),zero),
inference(rew,[status(thm),theory(equality)],[4980,23063]),
[iquote('0:Rew:4980.0,23063.0')] ).
cnf(73853,plain,
equal(addition(domain_difference(antidomain(u),multiplication(u,v)),zero),antidomain(antidomain(antidomain(u)))),
inference(spr,[status(thm),theory(equality)],[23064,4644]),
[iquote('0:SpR:23064.0,4644.0')] ).
cnf(73982,plain,
equal(domain_difference(antidomain(u),multiplication(u,v)),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[67,73853,13,4545]),
[iquote('0:Rew:67.0,73853.0,13.0,73853.0,4545.0,73853.0')] ).
cnf(136283,plain,
leq(antidomain(u),antidomain(multiplication(u,v))),
inference(spr,[status(thm),theory(equality)],[73982,2187]),
[iquote('0:SpR:73982.0,2187.0')] ).
cnf(136773,plain,
leq(antidomain(antidomain(antidomain(addition(u,v)))),antidomain(u)),
inference(spr,[status(thm),theory(equality)],[13678,136283]),
[iquote('0:SpR:13678.0,136283.0')] ).
cnf(136954,plain,
leq(antidomain(addition(u,v)),antidomain(u)),
inference(rew,[status(thm),theory(equality)],[4545,136773]),
[iquote('0:Rew:4545.0,136773.0')] ).
cnf(138009,plain,
leq(antidomain(multiplication(skc4,u)),antidomain(multiplication(skc3,u))),
inference(spr,[status(thm),theory(equality)],[304,136954]),
[iquote('0:SpR:304.0,136954.0')] ).
cnf(143853,plain,
leq(antidomain(multiplication(skc4,antidomain(u))),forward_box(skc3,u)),
inference(spr,[status(thm),theory(equality)],[4646,138009]),
[iquote('0:SpR:4646.0,138009.0')] ).
cnf(143912,plain,
leq(forward_box(skc4,u),forward_box(skc3,u)),
inference(rew,[status(thm),theory(equality)],[4646,143853]),
[iquote('0:Rew:4646.0,143853.0')] ).
cnf(143913,plain,
$false,
inference(unc,[status(thm)],[143912,5037]),
[iquote('0:UnC:143912.0,5037.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE118+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : run_spass %d %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 07:57:24 EDT 2022
% 0.13/0.33 % CPUTime :
% 79.37/79.61
% 79.37/79.61 SPASS V 3.9
% 79.37/79.61 SPASS beiseite: Proof found.
% 79.37/79.61 % SZS status Theorem
% 79.37/79.61 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 79.37/79.61 SPASS derived 97423 clauses, backtracked 0 clauses, performed 0 splits and kept 13586 clauses.
% 79.37/79.61 SPASS allocated 197668 KBytes.
% 79.37/79.61 SPASS spent 0:1:19.12 on the problem.
% 79.37/79.61 0:00:00.03 for the input.
% 79.37/79.61 0:00:00.03 for the FLOTTER CNF translation.
% 79.37/79.61 0:00:00.61 for inferences.
% 79.37/79.61 0:00:00.00 for the backtracking.
% 79.37/79.61 0:1:18.19 for the reduction.
% 79.37/79.61
% 79.37/79.61
% 79.37/79.61 Here is a proof with depth 9, length 94 :
% 79.37/79.61 % SZS output start Refutation
% See solution above
% 81.49/81.65 Formulae used in the proof : goals additive_identity additive_idempotence multiplicative_right_identity multiplicative_left_identity left_annihilation domain1 domain4 complement additive_commutativity domain3 order domain_difference forward_diamond forward_box additive_associativity multiplicative_associativity right_distributivity left_distributivity domain2
% 81.49/81.65
%------------------------------------------------------------------------------