TSTP Solution File: RNG028-2 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : RNG028-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 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 : Mon Jul 18 20:41:15 EDT 2022
% Result : Unsatisfiable 19.74s 20.01s
% Output : Refutation 20.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of clauses : 75 ( 75 unt; 0 nHn; 75 RR)
% Number of literals : 75 ( 0 equ; 7 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
equal(add(multiply(multiply(u,v),w),additive_inverse(multiply(u,multiply(v,w)))),associator(u,v,w)),
file('RNG028-2.p',unknown),
[] ).
cnf(3,axiom,
equal(additive_inverse(associator(u,v,w)),associator(v,u,w)),
file('RNG028-2.p',unknown),
[] ).
cnf(4,axiom,
equal(additive_inverse(associator(u,v,w)),associator(w,v,u)),
file('RNG028-2.p',unknown),
[] ).
cnf(5,axiom,
~ equal(multiply(multiply(cx,multiply(cy,cx)),cz),multiply(cx,multiply(cy,multiply(cx,cz)))),
file('RNG028-2.p',unknown),
[] ).
cnf(6,axiom,
equal(add(additive_identity,u),u),
file('RNG028-2.p',unknown),
[] ).
cnf(9,axiom,
equal(add(additive_inverse(u),u),additive_identity),
file('RNG028-2.p',unknown),
[] ).
cnf(10,axiom,
equal(additive_inverse(add(u,v)),add(additive_inverse(u),additive_inverse(v))),
file('RNG028-2.p',unknown),
[] ).
cnf(11,axiom,
equal(additive_inverse(additive_inverse(u)),u),
file('RNG028-2.p',unknown),
[] ).
cnf(12,axiom,
equal(multiply(u,add(v,w)),add(multiply(u,v),multiply(u,w))),
file('RNG028-2.p',unknown),
[] ).
cnf(14,axiom,
equal(multiply(multiply(u,v),v),multiply(u,multiply(v,v))),
file('RNG028-2.p',unknown),
[] ).
cnf(15,axiom,
equal(multiply(multiply(u,u),v),multiply(u,multiply(u,v))),
file('RNG028-2.p',unknown),
[] ).
cnf(16,axiom,
equal(additive_inverse(multiply(u,v)),multiply(additive_inverse(u),v)),
file('RNG028-2.p',unknown),
[] ).
cnf(17,axiom,
equal(additive_inverse(multiply(u,v)),multiply(u,additive_inverse(v))),
file('RNG028-2.p',unknown),
[] ).
cnf(19,axiom,
equal(add(u,v),add(v,u)),
file('RNG028-2.p',unknown),
[] ).
cnf(20,axiom,
equal(add(add(u,v),w),add(u,add(v,w))),
file('RNG028-2.p',unknown),
[] ).
cnf(23,plain,
equal(add(u,additive_inverse(u)),additive_identity),
inference(rew,[status(thm),theory(equality)],[19,9]),
[iquote('0:Rew:19.0,9.0')] ).
cnf(24,plain,
equal(multiply(u,additive_inverse(v)),multiply(additive_inverse(u),v)),
inference(rew,[status(thm),theory(equality)],[17,16]),
[iquote('0:Rew:17.0,16.0')] ).
cnf(25,plain,
equal(associator(u,v,w),associator(v,w,u)),
inference(rew,[status(thm),theory(equality)],[4,3]),
[iquote('0:Rew:4.0,3.0')] ).
cnf(26,plain,
equal(add(multiply(multiply(u,v),w),multiply(u,multiply(v,additive_inverse(w)))),associator(u,v,w)),
inference(rew,[status(thm),theory(equality)],[17,1]),
[iquote('0:Rew:17.0,1.0,17.0,1.0')] ).
cnf(61,plain,
equal(multiply(additive_inverse(u),additive_inverse(v)),multiply(u,v)),
inference(spr,[status(thm),theory(equality)],[11,24]),
[iquote('0:SpR:11.0,24.0')] ).
cnf(71,plain,
equal(add(multiply(u,v),multiply(u,additive_inverse(v))),additive_identity),
inference(spr,[status(thm),theory(equality)],[17,23]),
[iquote('0:SpR:17.0,23.0')] ).
cnf(73,plain,
equal(multiply(u,multiply(v,additive_inverse(w))),multiply(additive_inverse(u),multiply(v,w))),
inference(spr,[status(thm),theory(equality)],[17,24]),
[iquote('0:SpR:17.0,24.0')] ).
cnf(132,plain,
equal(add(multiply(u,multiply(v,w)),multiply(u,multiply(v,additive_inverse(w)))),additive_identity),
inference(spr,[status(thm),theory(equality)],[17,71]),
[iquote('0:SpR:17.0,71.0')] ).
cnf(135,plain,
equal(add(multiply(u,v),multiply(additive_inverse(u),v)),additive_identity),
inference(spr,[status(thm),theory(equality)],[24,71]),
[iquote('0:SpR:24.0,71.0')] ).
cnf(650,plain,
equal(add(add(u,v),w),add(v,add(u,w))),
inference(spr,[status(thm),theory(equality)],[19,20]),
[iquote('0:SpR:19.0,20.0')] ).
cnf(651,plain,
equal(add(u,add(additive_inverse(u),v)),add(additive_identity,v)),
inference(spr,[status(thm),theory(equality)],[23,20]),
[iquote('0:SpR:23.0,20.0')] ).
cnf(657,plain,
equal(add(multiply(u,v),add(multiply(additive_inverse(u),v),w)),add(additive_identity,w)),
inference(spr,[status(thm),theory(equality)],[135,20]),
[iquote('0:SpR:135.0,20.0')] ).
cnf(667,plain,
equal(add(u,add(additive_inverse(u),v)),v),
inference(rew,[status(thm),theory(equality)],[6,651]),
[iquote('0:Rew:6.0,651.0')] ).
cnf(684,plain,
equal(add(u,add(v,w)),add(v,add(u,w))),
inference(rew,[status(thm),theory(equality)],[20,650]),
[iquote('0:Rew:20.0,650.0')] ).
cnf(708,plain,
equal(add(multiply(u,v),add(multiply(additive_inverse(u),v),w)),w),
inference(rew,[status(thm),theory(equality)],[6,657]),
[iquote('0:Rew:6.0,657.0')] ).
cnf(773,plain,
equal(add(associator(u,v,w),add(associator(w,v,u),x)),x),
inference(spr,[status(thm),theory(equality)],[4,667]),
[iquote('0:SpR:4.0,667.0')] ).
cnf(1330,plain,
equal(add(additive_inverse(multiply(multiply(u,v),w)),additive_inverse(multiply(u,multiply(v,additive_inverse(w))))),additive_inverse(associator(u,v,w))),
inference(spr,[status(thm),theory(equality)],[26,10]),
[iquote('0:SpR:26.0,10.0')] ).
cnf(1335,plain,
equal(add(multiply(u,multiply(multiply(v,w),x)),multiply(u,multiply(v,multiply(w,additive_inverse(x))))),multiply(u,associator(v,w,x))),
inference(spr,[status(thm),theory(equality)],[26,12]),
[iquote('0:SpR:26.0,12.0')] ).
cnf(1339,plain,
equal(add(multiply(multiply(u,v),additive_inverse(w)),multiply(u,multiply(v,w))),associator(u,v,additive_inverse(w))),
inference(spr,[status(thm),theory(equality)],[11,26]),
[iquote('0:SpR:11.0,26.0')] ).
cnf(1347,plain,
equal(add(multiply(multiply(u,v),w),multiply(u,multiply(additive_inverse(v),w))),associator(u,v,w)),
inference(spr,[status(thm),theory(equality)],[24,26]),
[iquote('0:SpR:24.0,26.0')] ).
cnf(1358,plain,
equal(add(multiply(multiply(additive_inverse(u),v),w),multiply(u,additive_inverse(multiply(v,additive_inverse(w))))),associator(additive_inverse(u),v,w)),
inference(spr,[status(thm),theory(equality)],[24,26]),
[iquote('0:SpR:24.0,26.0')] ).
cnf(1371,plain,
equal(add(multiply(multiply(u,multiply(u,v)),w),multiply(multiply(u,u),multiply(v,additive_inverse(w)))),associator(multiply(u,u),v,w)),
inference(spr,[status(thm),theory(equality)],[15,26]),
[iquote('0:SpR:15.0,26.0')] ).
cnf(1372,plain,
equal(add(multiply(multiply(u,multiply(v,v)),w),multiply(multiply(u,v),multiply(v,additive_inverse(w)))),associator(multiply(u,v),v,w)),
inference(spr,[status(thm),theory(equality)],[14,26]),
[iquote('0:SpR:14.0,26.0')] ).
cnf(1380,plain,
equal(add(multiply(u,multiply(u,v)),multiply(u,multiply(u,additive_inverse(v)))),associator(u,u,v)),
inference(spr,[status(thm),theory(equality)],[15,26]),
[iquote('0:SpR:15.0,26.0')] ).
cnf(1398,plain,
equal(associator(u,u,v),additive_identity),
inference(rew,[status(thm),theory(equality)],[132,1380]),
[iquote('0:Rew:132.0,1380.0')] ).
cnf(1400,plain,
equal(add(multiply(u,multiply(v,w)),multiply(multiply(u,v),additive_inverse(w))),associator(u,v,additive_inverse(w))),
inference(rew,[status(thm),theory(equality)],[19,1339]),
[iquote('0:Rew:19.0,1339.0')] ).
cnf(1416,plain,
equal(add(multiply(u,multiply(v,w)),multiply(multiply(additive_inverse(u),v),w)),associator(additive_inverse(u),v,w)),
inference(rew,[status(thm),theory(equality)],[19,1358,11,17]),
[iquote('0:Rew:19.0,1358.0,11.0,1358.0,17.0,1358.0')] ).
cnf(1422,plain,
equal(add(multiply(u,multiply(v,w)),multiply(multiply(u,v),additive_inverse(w))),associator(w,v,u)),
inference(rew,[status(thm),theory(equality)],[19,1330,17,11,4]),
[iquote('0:Rew:19.0,1330.0,17.0,1330.0,11.0,1330.0,17.0,1330.0,17.0,1330.0,4.0,1330.0')] ).
cnf(1423,plain,
equal(associator(u,v,additive_inverse(w)),associator(w,v,u)),
inference(rew,[status(thm),theory(equality)],[1400,1422]),
[iquote('0:Rew:1400.0,1422.0')] ).
cnf(1425,plain,
equal(add(multiply(multiply(u,multiply(v,v)),w),multiply(multiply(u,v),multiply(v,additive_inverse(w)))),associator(v,w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[25,1372]),
[iquote('0:Rew:25.0,1372.0')] ).
cnf(1426,plain,
equal(add(multiply(multiply(u,multiply(u,v)),w),multiply(u,multiply(u,multiply(v,additive_inverse(w))))),associator(multiply(u,u),v,w)),
inference(rew,[status(thm),theory(equality)],[15,1371]),
[iquote('0:Rew:15.0,1371.0')] ).
cnf(1667,plain,
equal(associator(additive_inverse(u),v,w),associator(u,w,v)),
inference(spr,[status(thm),theory(equality)],[1423,25]),
[iquote('0:SpR:1423.0,25.0')] ).
cnf(1679,plain,
equal(associator(u,v,w),associator(u,w,additive_inverse(v))),
inference(spr,[status(thm),theory(equality)],[1423,25]),
[iquote('0:SpR:1423.0,25.0')] ).
cnf(1706,plain,
equal(add(multiply(u,multiply(v,w)),multiply(multiply(additive_inverse(u),v),w)),associator(u,w,v)),
inference(rew,[status(thm),theory(equality)],[1667,1416]),
[iquote('0:Rew:1667.0,1416.0')] ).
cnf(13581,plain,
equal(add(multiply(multiply(u,v),multiply(w,additive_inverse(x))),multiply(u,multiply(additive_inverse(additive_inverse(v)),multiply(w,x)))),associator(u,v,multiply(w,additive_inverse(x)))),
inference(spr,[status(thm),theory(equality)],[73,1347]),
[iquote('0:SpR:73.0,1347.0')] ).
cnf(13798,plain,
equal(add(multiply(u,multiply(v,multiply(w,x))),multiply(multiply(u,v),multiply(w,additive_inverse(x)))),associator(u,v,multiply(w,additive_inverse(x)))),
inference(rew,[status(thm),theory(equality)],[19,13581,11]),
[iquote('0:Rew:19.0,13581.0,11.0,13581.0')] ).
cnf(14588,plain,
equal(multiply(multiply(additive_inverse(additive_inverse(u)),v),w),add(multiply(u,multiply(v,w)),associator(additive_inverse(u),w,v))),
inference(spr,[status(thm),theory(equality)],[1706,708]),
[iquote('0:SpR:1706.0,708.0')] ).
cnf(14726,plain,
equal(multiply(multiply(u,v),w),add(associator(u,v,w),multiply(u,multiply(v,w)))),
inference(rew,[status(thm),theory(equality)],[11,14588,19,1667]),
[iquote('0:Rew:11.0,14588.0,19.0,14588.0,1667.0,14588.0')] ).
cnf(14732,plain,
~ equal(add(associator(cx,multiply(cy,cx),cz),multiply(cx,multiply(multiply(cy,cx),cz))),multiply(cx,multiply(cy,multiply(cx,cz)))),
inference(rew,[status(thm),theory(equality)],[14726,5]),
[iquote('0:Rew:14726.0,5.0')] ).
cnf(14950,plain,
equal(add(multiply(u,add(associator(v,w,x),multiply(v,multiply(w,x)))),multiply(u,multiply(v,multiply(w,additive_inverse(x))))),multiply(u,associator(v,w,x))),
inference(rew,[status(thm),theory(equality)],[14726,1335]),
[iquote('0:Rew:14726.0,1335.0')] ).
cnf(14990,plain,
equal(add(multiply(u,multiply(v,multiply(w,x))),add(associator(u,v,multiply(w,additive_inverse(x))),multiply(u,multiply(v,multiply(w,additive_inverse(x)))))),associator(u,v,multiply(w,additive_inverse(x)))),
inference(rew,[status(thm),theory(equality)],[14726,13798]),
[iquote('0:Rew:14726.0,13798.0')] ).
cnf(14995,plain,
equal(add(multiply(multiply(u,multiply(v,v)),w),add(associator(u,v,multiply(v,additive_inverse(w))),multiply(u,multiply(v,multiply(v,additive_inverse(w)))))),associator(v,w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[14726,1425]),
[iquote('0:Rew:14726.0,1425.0')] ).
cnf(15003,plain,
equal(add(add(associator(u,multiply(u,v),w),multiply(u,multiply(multiply(u,v),w))),multiply(u,multiply(u,multiply(v,additive_inverse(w))))),associator(multiply(u,u),v,w)),
inference(rew,[status(thm),theory(equality)],[14726,1426]),
[iquote('0:Rew:14726.0,1426.0')] ).
cnf(15358,plain,
~ equal(add(associator(cx,multiply(cy,cx),cz),multiply(cx,add(associator(cy,cx,cz),multiply(cy,multiply(cx,cz))))),multiply(cx,multiply(cy,multiply(cx,cz)))),
inference(rew,[status(thm),theory(equality)],[14726,14732]),
[iquote('0:Rew:14726.0,14732.0')] ).
cnf(15359,plain,
~ equal(add(multiply(cx,associator(cx,cz,cy)),add(associator(cx,multiply(cy,cx),cz),multiply(cx,multiply(cy,multiply(cx,cz))))),multiply(cx,multiply(cy,multiply(cx,cz)))),
inference(rew,[status(thm),theory(equality)],[684,15358,12,25]),
[iquote('0:Rew:684.0,15358.0,12.0,15358.0,25.0,15358.0')] ).
cnf(15606,plain,
equal(add(multiply(u,associator(v,w,x)),add(multiply(u,multiply(v,multiply(w,x))),multiply(u,multiply(v,multiply(w,additive_inverse(x)))))),multiply(u,associator(v,w,x))),
inference(rew,[status(thm),theory(equality)],[20,14950,12]),
[iquote('0:Rew:20.0,14950.0,12.0,14950.0')] ).
cnf(15675,plain,
equal(add(associator(u,multiply(u,v),w),add(multiply(u,multiply(multiply(u,v),w)),multiply(u,multiply(u,multiply(v,additive_inverse(w)))))),associator(multiply(u,u),v,w)),
inference(rew,[status(thm),theory(equality)],[20,15003]),
[iquote('0:Rew:20.0,15003.0')] ).
cnf(15676,plain,
equal(add(associator(u,multiply(u,v),w),add(multiply(u,add(associator(u,v,w),multiply(u,multiply(v,w)))),multiply(u,multiply(u,multiply(v,additive_inverse(w)))))),associator(multiply(u,u),v,w)),
inference(rew,[status(thm),theory(equality)],[14726,15675]),
[iquote('0:Rew:14726.0,15675.0')] ).
cnf(15677,plain,
equal(add(associator(u,multiply(u,v),w),add(multiply(u,associator(u,v,w)),add(multiply(u,multiply(u,multiply(v,w))),multiply(u,multiply(u,multiply(v,additive_inverse(w))))))),associator(multiply(u,u),v,w)),
inference(rew,[status(thm),theory(equality)],[20,15676,12]),
[iquote('0:Rew:20.0,15676.0,12.0,15676.0')] ).
cnf(15678,plain,
equal(add(associator(u,multiply(u,v),w),multiply(u,associator(u,v,w))),associator(multiply(u,u),v,w)),
inference(rew,[status(thm),theory(equality)],[15606,15677]),
[iquote('0:Rew:15606.0,15677.0')] ).
cnf(15766,plain,
equal(add(add(associator(u,multiply(v,v),w),multiply(u,add(associator(v,v,w),multiply(v,multiply(v,w))))),add(associator(u,v,multiply(v,additive_inverse(w))),multiply(u,multiply(v,multiply(v,additive_inverse(w)))))),associator(v,w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[14726,14995]),
[iquote('0:Rew:14726.0,14995.0,14726.0,14995.0')] ).
cnf(15767,plain,
equal(add(associator(u,multiply(v,v),w),add(multiply(u,multiply(v,multiply(v,w))),add(associator(u,v,multiply(v,additive_inverse(w))),multiply(u,multiply(v,multiply(v,additive_inverse(w))))))),associator(v,w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[20,15766,6,1398]),
[iquote('0:Rew:20.0,15766.0,6.0,15766.0,1398.0,15766.0')] ).
cnf(15802,plain,
equal(add(associator(u,multiply(v,v),w),associator(u,v,multiply(v,additive_inverse(w)))),associator(v,w,multiply(u,v))),
inference(rew,[status(thm),theory(equality)],[14990,15767]),
[iquote('0:Rew:14990.0,15767.0')] ).
cnf(19402,plain,
equal(add(associator(u,multiply(u,v),w),add(multiply(u,associator(u,v,w)),x)),add(associator(multiply(u,u),v,w),x)),
inference(spr,[status(thm),theory(equality)],[15678,20]),
[iquote('0:SpR:15678.0,20.0')] ).
cnf(20558,plain,
equal(add(associator(additive_inverse(u),multiply(additive_inverse(v),additive_inverse(v)),w),associator(additive_inverse(u),additive_inverse(v),multiply(additive_inverse(v),additive_inverse(w)))),associator(additive_inverse(v),w,multiply(u,v))),
inference(spr,[status(thm),theory(equality)],[61,15802]),
[iquote('0:SpR:61.0,15802.0')] ).
cnf(20763,plain,
equal(add(associator(u,v,multiply(w,w)),associator(u,w,multiply(w,v))),associator(w,multiply(u,w),v)),
inference(rew,[status(thm),theory(equality)],[1667,20558,61,1679]),
[iquote('0:Rew:1667.0,20558.0,61.0,20558.0,1679.0,20558.0,1667.0,20558.0,61.0,20558.0,1667.0,20558.0')] ).
cnf(20764,plain,
~ equal(add(multiply(cx,associator(cx,cz,cy)),add(add(associator(cy,cz,multiply(cx,cx)),associator(cy,cx,multiply(cx,cz))),multiply(cx,multiply(cy,multiply(cx,cz))))),multiply(cx,multiply(cy,multiply(cx,cz)))),
inference(rew,[status(thm),theory(equality)],[20763,15359]),
[iquote('0:Rew:20763.0,15359.0')] ).
cnf(20854,plain,
~ equal(add(associator(cy,cz,multiply(cx,cx)),add(associator(cx,multiply(cx,cz),cy),add(multiply(cx,associator(cx,cz,cy)),multiply(cx,multiply(cy,multiply(cx,cz)))))),multiply(cx,multiply(cy,multiply(cx,cz)))),
inference(rew,[status(thm),theory(equality)],[684,20764,20,25]),
[iquote('0:Rew:684.0,20764.0,684.0,20764.0,20.0,20764.0,25.0,20764.0')] ).
cnf(20855,plain,
~ equal(multiply(cx,multiply(cy,multiply(cx,cz))),multiply(cx,multiply(cy,multiply(cx,cz)))),
inference(rew,[status(thm),theory(equality)],[773,20854,19402]),
[iquote('0:Rew:773.0,20854.0,19402.0,20854.0')] ).
cnf(20856,plain,
$false,
inference(obv,[status(thm),theory(equality)],[20855]),
[iquote('0:Obv:20855.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : RNG028-2 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.00/0.10 % Command : run_spass %d %s
% 0.10/0.30 % Computer : n019.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Mon May 30 16:23:40 EDT 2022
% 0.10/0.30 % CPUTime :
% 19.74/20.01
% 19.74/20.01 SPASS V 3.9
% 19.74/20.01 SPASS beiseite: Proof found.
% 19.74/20.01 % SZS status Theorem
% 19.74/20.01 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.74/20.01 SPASS derived 12726 clauses, backtracked 0 clauses, performed 0 splits and kept 3545 clauses.
% 19.74/20.01 SPASS allocated 89540 KBytes.
% 19.74/20.01 SPASS spent 0:0:19.67 on the problem.
% 19.74/20.01 0:00:00.03 for the input.
% 19.74/20.01 0:00:00.00 for the FLOTTER CNF translation.
% 19.74/20.01 0:00:00.17 for inferences.
% 19.74/20.01 0:00:00.00 for the backtracking.
% 19.74/20.01 0:0:19.43 for the reduction.
% 19.74/20.01
% 19.74/20.01
% 19.74/20.01 Here is a proof with depth 4, length 75 :
% 19.74/20.01 % SZS output start Refutation
% See solution above
% 20.13/20.36 Formulae used in the proof : associator associator_skew_symmetry1 associator_skew_symmetry2 prove_left_moufang left_additive_identity add_inverse sum_of_inverses additive_inverse_additive_inverse multiply_over_add1 right_alternative left_alternative inverse_product1 inverse_product2 commutativity_for_addition associativity_for_addition
% 20.13/20.36
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