TSTP Solution File: ALG362-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG362-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n025.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 : Thu Jul 14 18:03:29 EDT 2022
% Result : Unsatisfiable 274.93s 275.20s
% Output : Refutation 280.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 70
% Syntax : Number of clauses : 82 ( 72 unt; 1 nHn; 82 RR)
% Number of literals : 102 ( 0 equ; 27 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 65 ( 64 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(217,axiom,
( ~ class_Orderings_Opreorder(u)
| ~ c_lessequals(v,w,u)
| ~ c_HOL_Oord__class_Oless(w,x,u)
| c_HOL_Oord__class_Oless(v,x,u) ),
file('ALG362-1.p',unknown),
[] ).
cnf(239,axiom,
( ~ class_Orderings_Olinorder(u)
| c_lessequals(v,w,u)
| c_HOL_Oord__class_Oless(w,v,u) ),
file('ALG362-1.p',unknown),
[] ).
cnf(240,axiom,
( ~ class_Orderings_Olinorder(u)
| ~ c_HOL_Oord__class_Oless(v,w,u)
| ~ c_lessequals(w,v,u) ),
file('ALG362-1.p',unknown),
[] ).
cnf(310,axiom,
equal(c_Transcendental_Osin(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal)),
file('ALG362-1.p',unknown),
[] ).
cnf(467,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__add(u)
| ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(u)
| ~ c_lessequals(v,w,u)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(u),x,u)
| c_lessequals(v,c_HOL_Oplus__class_Oplus(w,x,u),u) ),
file('ALG362-1.p',unknown),
[] ).
cnf(605,axiom,
c_lessequals(c_Transcendental_Osin(u),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(624,axiom,
c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(u),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(625,axiom,
c_lessequals(c_RealVector_Onorm__class_Onorm(hAPP(v_s,u),tc_Complex_Ocomplex),v_r,tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(705,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(706,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(707,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(708,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(709,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(710,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(711,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(712,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(713,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(714,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(715,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(716,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(717,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(718,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(719,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(720,axiom,
class_OrderedGroup_Oordered__ab__group__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(721,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(722,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(723,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(724,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(725,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(726,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(727,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(728,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(729,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(730,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(731,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(732,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(733,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(734,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(735,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(736,axiom,
class_Ring__and__Field_Oordered__field(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(737,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(738,axiom,
class_Ring__and__Field_Odivision__ring(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(739,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(740,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(741,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(742,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(743,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(744,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(745,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(746,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(747,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(748,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(749,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(750,axiom,
class_RealVector_Oreal__algebra(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(751,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(752,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(753,axiom,
class_RealVector_Oreal__vector(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(754,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(755,axiom,
class_Ring__and__Field_Oring__1(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(756,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(757,axiom,
class_Ring__and__Field_Ofield(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(758,axiom,
class_RealVector_Odist__norm(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(759,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(760,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(761,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(762,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(763,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(764,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(765,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(800,axiom,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),c_HOL_Oplus__class_Oplus(v_r,c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),tc_RealDef_Oreal),
file('ALG362-1.p',unknown),
[] ).
cnf(871,plain,
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal)
| ~ class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[467,800]),
[iquote('0:Res:467.4,800.0')] ).
cnf(877,plain,
( ~ c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal)
| ~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal) ),
inference(mrr,[status(thm)],[871,706,740]),
[iquote('0:MRR:871.0,871.1,706.0,740.0')] ).
cnf(885,plain,
c_lessequals(c_HOL_Ozero__class_Ozero(tc_RealDef_Oreal),c_HOL_Oone__class_Oone(tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(spr,[status(thm),theory(equality)],[310,605]),
[iquote('0:SpR:310.0,605.0')] ).
cnf(886,plain,
~ c_lessequals(c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),v_r,tc_RealDef_Oreal),
inference(mrr,[status(thm)],[877,885]),
[iquote('0:MRR:877.0,885.0')] ).
cnf(1673,plain,
( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(v_r,c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[239,886]),
[iquote('0:Res:239.1,886.0')] ).
cnf(1678,plain,
c_HOL_Oord__class_Oless(v_r,c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,v_n____)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(ssi,[status(thm)],[1673,737,758,756,755,743,709,707,765,750,749,747,739,734,731,725,724,722,716,713,752,741,733,726,723,721,715,711,708,746,759,757,748,720,705,762,744,764,763,761,760,751,740,745,735,730,714,706,753,719,710,738,728,754,729,718,742,732,712,727,736,717]),
[iquote('0:SSi:1673.0,737.0,758.0,756.0,755.0,743.0,709.0,707.0,765.0,750.0,749.0,747.0,739.0,734.0,731.0,725.0,724.0,722.0,716.0,713.0,752.0,741.0,733.0,726.0,723.0,721.0,715.0,711.0,708.0,746.0,759.0,757.0,748.0,720.0,705.0,762.0,744.0,764.0,763.0,761.0,760.0,751.0,740.0,745.0,735.0,730.0,714.0,706.0,753.0,719.0,710.0,738.0,728.0,754.0,729.0,718.0,742.0,732.0,712.0,727.0,736.0,717.0')] ).
cnf(11203,plain,
( ~ class_Orderings_Olinorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_Complex_ORe(u),tc_RealDef_Oreal),tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[624,240]),
[iquote('0:Res:624.0,240.2')] ).
cnf(11340,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex),c_HOL_Oabs__class_Oabs(c_Complex_ORe(u),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(ssi,[status(thm)],[11203,737,758,756,755,743,709,707,765,750,749,747,739,734,731,725,724,722,716,713,752,741,733,726,723,721,715,711,708,746,759,757,748,720,705,762,744,764,763,761,760,751,740,745,735,730,714,706,753,719,710,738,728,754,729,718,742,732,712,727,736,717]),
[iquote('0:SSi:11203.0,737.0,758.0,756.0,755.0,743.0,709.0,707.0,765.0,750.0,749.0,747.0,739.0,734.0,731.0,725.0,724.0,722.0,716.0,713.0,752.0,741.0,733.0,726.0,723.0,721.0,715.0,711.0,708.0,746.0,759.0,757.0,748.0,720.0,705.0,762.0,744.0,764.0,763.0,761.0,760.0,751.0,740.0,745.0,735.0,730.0,714.0,706.0,753.0,719.0,710.0,738.0,728.0,754.0,729.0,718.0,742.0,732.0,712.0,727.0,736.0,717.0')] ).
cnf(37154,plain,
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_HOL_Oord__class_Oless(v_r,u,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v),tc_Complex_Ocomplex),u,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[625,217]),
[iquote('0:Res:625.0,217.1')] ).
cnf(37280,plain,
( ~ c_HOL_Oord__class_Oless(v_r,u,tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(hAPP(v_s,v),tc_Complex_Ocomplex),u,tc_RealDef_Oreal) ),
inference(ssi,[status(thm)],[37154,737,758,756,755,743,709,707,765,750,749,747,739,734,731,725,724,722,716,713,752,741,733,726,723,721,715,711,708,746,759,757,748,720,705,762,744,764,763,761,760,751,740,745,735,730,714,706,753,719,710,738,728,754,729,718,742,732,712,727,736,717]),
[iquote('0:SSi:37154.0,737.0,758.0,756.0,755.0,743.0,709.0,707.0,765.0,750.0,749.0,747.0,739.0,734.0,731.0,725.0,724.0,722.0,716.0,713.0,752.0,741.0,733.0,726.0,723.0,721.0,715.0,711.0,708.0,746.0,759.0,757.0,748.0,720.0,705.0,762.0,744.0,764.0,763.0,761.0,760.0,751.0,740.0,745.0,735.0,730.0,714.0,706.0,753.0,719.0,710.0,738.0,728.0,754.0,729.0,718.0,742.0,732.0,712.0,727.0,736.0,717.0')] ).
cnf(148345,plain,
~ c_HOL_Oord__class_Oless(v_r,c_HOL_Oabs__class_Oabs(c_Complex_ORe(hAPP(v_s,u)),tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(res,[status(thm),theory(equality)],[37280,11340]),
[iquote('0:Res:37280.1,11340.0')] ).
cnf(148382,plain,
$false,
inference(unc,[status(thm)],[148345,1678]),
[iquote('0:UnC:148345.0,1678.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : ALG362-1 : TPTP v8.1.0. Released v4.1.0.
% 0.06/0.12 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Wed Jun 8 23:05:35 EDT 2022
% 0.12/0.33 % CPUTime :
% 274.93/275.20
% 274.93/275.20 SPASS V 3.9
% 274.93/275.20 SPASS beiseite: Proof found.
% 274.93/275.20 % SZS status Theorem
% 274.93/275.20 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 274.93/275.20 SPASS derived 111066 clauses, backtracked 542 clauses, performed 3 splits and kept 36477 clauses.
% 274.93/275.20 SPASS allocated 201534 KBytes.
% 274.93/275.20 SPASS spent 0:4:34.57 on the problem.
% 274.93/275.20 0:00:00.06 for the input.
% 274.93/275.20 0:00:00.00 for the FLOTTER CNF translation.
% 274.93/275.20 0:00:02.05 for inferences.
% 274.93/275.20 0:0:12.91 for the backtracking.
% 274.93/275.20 0:4:16.20 for the reduction.
% 274.93/275.20
% 274.93/275.20
% 274.93/275.20 Here is a proof with depth 2, length 82 :
% 274.93/275.20 % SZS output start Refutation
% See solution above
% 280.75/281.02 Formulae used in the proof : cls_order__le__less__trans_0 cls_linorder__not__le_0 cls_linorder__not__le_1 cls_sin__zero_0 cls_add__increasing2_0 cls_sin__le__one_0 cls_abs__Re__le__cmod_0 cls_r_0 clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1 clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1 clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1 clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult clsarity_RealDef__Oreal__Ring__and__Field_Osemiring clsarity_RealDef__Oreal__RealVector_Oreal__algebra clsarity_RealDef__Oreal__RealVector_Ometric__space clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add clsarity_RealDef__Oreal__RealVector_Oreal__vector clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add clsarity_RealDef__Oreal__Ring__and__Field_Oring__1 clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if clsarity_RealDef__Oreal__Ring__and__Field_Ofield clsarity_RealDef__Oreal__RealVector_Odist__norm clsarity_RealDef__Oreal__Ring__and__Field_Oring clsarity_RealDef__Oreal__Ring__and__Field_Oidom clsarity_RealDef__Oreal__Orderings_Opreorder clsarity_RealDef__Oreal__Orderings_Olinorder clsarity_RealDef__Oreal__Orderings_Oorder clsarity_RealDef__Oreal__Int_Onumber__ring clsarity_RealDef__Oreal__Power_Opower cls_conjecture_0
% 280.75/281.02
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