TSTP Solution File: SWW194+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWW194+1 : TPTP v8.1.0. Released v5.2.0.
% 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 : Thu Jul 21 01:28:04 EDT 2022
% Result : Theorem 1.36s 1.57s
% Output : Refutation 1.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 75
% Syntax : Number of clauses : 83 ( 79 unt; 0 nHn; 83 RR)
% Number of literals : 90 ( 0 equ; 11 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 70 ( 69 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-2 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(95,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(96,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(97,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(98,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(99,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(100,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(101,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(102,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(103,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(104,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(105,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(106,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(107,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(108,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(109,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(110,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(111,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(112,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(113,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(114,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(115,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(116,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(117,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(118,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(119,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(120,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(121,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(122,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(123,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(124,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(125,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(126,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(127,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(128,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(129,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(130,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(131,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(132,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(133,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(134,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(135,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(136,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(137,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(138,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(139,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(140,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(141,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(142,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(143,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(144,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(145,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(146,axiom,
class_Rings_Osemiring__1(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(147,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(148,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(149,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(150,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(151,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(152,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(153,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(154,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(155,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(156,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(157,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(158,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(159,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(160,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(161,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('SWW194+1.p',unknown),
[] ).
cnf(261,axiom,
equal(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
file('SWW194+1.p',unknown),
[] ).
cnf(279,axiom,
equal(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)),
file('SWW194+1.p',unknown),
[] ).
cnf(403,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(u)
| c_Orderings_Oord__class_Oless__eq(u,c_Groups_Ozero__class_Ozero(u),c_Groups_Oabs__class_Oabs(u,v)) ),
file('SWW194+1.p',unknown),
[] ).
cnf(405,axiom,
equal(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Nat_OSuc(c_Nat_OSuc(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
file('SWW194+1.p',unknown),
[] ).
cnf(648,axiom,
equal(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),u),v),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v),u)),
file('SWW194+1.p',unknown),
[] ).
cnf(822,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('SWW194+1.p',unknown),
[] ).
cnf(1464,axiom,
( ~ class_Rings_Olinordered__semidom(u)
| ~ c_Orderings_Oord__class_Oless__eq(u,v,w)
| ~ c_Orderings_Oord__class_Oless__eq(u,c_Groups_Ozero__class_Ozero(u),v)
| c_Orderings_Oord__class_Oless__eq(u,hAPP(hAPP(c_Power_Opower__class_Opower(u),v),x),hAPP(hAPP(c_Power_Opower__class_Opower(u),w),x)) ),
file('SWW194+1.p',unknown),
[] ).
cnf(1577,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),v_x____))),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
file('SWW194+1.p',unknown),
[] ).
cnf(1691,plain,
equal(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(rew,[status(thm),theory(equality)],[261,405]),
[iquote('0:Rew:261.0,405.0')] ).
cnf(1751,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(rew,[status(thm),theory(equality)],[279,822,648]),
[iquote('0:Rew:279.0,822.0,648.0,822.0')] ).
cnf(1881,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(hAPP(c_Power_Opower__class_Opower(tc_RealDef_Oreal),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_Nat_OSuc(c_Groups_Oone__class_Oone(tc_Nat_Onat)))),
inference(rew,[status(thm),theory(equality)],[279,1577,648,1691]),
[iquote('0:Rew:279.0,1577.0,648.0,1577.0,1691.0,1577.0')] ).
cnf(1932,plain,
( ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(res,[status(thm),theory(equality)],[1464,1881]),
[iquote('0:Res:1464.3,1881.0')] ).
cnf(1938,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_x____),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),
inference(mrr,[status(thm)],[1932,123,1751]),
[iquote('0:MRR:1932.0,1932.2,123.0,1751.0')] ).
cnf(4351,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)) ),
inference(spr,[status(thm),theory(equality)],[279,403]),
[iquote('0:SpR:279.0,403.1')] ).
cnf(4364,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)),
inference(ssi,[status(thm)],[4351,135,129,118,100,155,144,117,101,98,161,158,151,137,126,124,121,111,110,104,103,147,146,145,138,132,131,116,112,105,153,139,130,128,125,115,159,149,120,119,96,148,95,154,142,107,97,109,157,156,136,140,108,143,141,122,150,102,113,106,134,123,127,114,160,152,133,99]),
[iquote('0:SSi:4351.0,135.0,129.0,118.0,100.0,155.0,144.0,117.0,101.0,98.0,161.0,158.0,151.0,137.0,126.0,124.0,121.0,111.0,110.0,104.0,103.0,147.0,146.0,145.0,138.0,132.0,131.0,116.0,112.0,105.0,153.0,139.0,130.0,128.0,125.0,115.0,159.0,149.0,120.0,119.0,96.0,148.0,95.0,154.0,142.0,107.0,97.0,109.0,157.0,156.0,136.0,140.0,108.0,143.0,141.0,122.0,150.0,102.0,113.0,106.0,134.0,123.0,127.0,114.0,160.0,152.0,133.0,99.0')] ).
cnf(4365,plain,
$false,
inference(unc,[status(thm)],[4364,1938]),
[iquote('0:UnC:4364.0,1938.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW194+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.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 : 600
% 0.13/0.34 % DateTime : Sat Jun 4 07:33:25 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.36/1.57
% 1.36/1.57 SPASS V 3.9
% 1.36/1.57 SPASS beiseite: Proof found.
% 1.36/1.57 % SZS status Theorem
% 1.36/1.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.36/1.57 SPASS derived 2200 clauses, backtracked 0 clauses, performed 0 splits and kept 2062 clauses.
% 1.36/1.57 SPASS allocated 104211 KBytes.
% 1.36/1.57 SPASS spent 0:00:01.22 on the problem.
% 1.36/1.57 0:00:00.06 for the input.
% 1.36/1.57 0:00:00.31 for the FLOTTER CNF translation.
% 1.36/1.57 0:00:00.03 for inferences.
% 1.36/1.57 0:00:00.00 for the backtracking.
% 1.36/1.57 0:00:00.67 for the reduction.
% 1.36/1.57
% 1.36/1.57
% 1.36/1.57 Here is a proof with depth 1, length 83 :
% 1.36/1.57 % SZS output start Refutation
% See solution above
% 1.36/1.60 Formulae used in the proof : arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict arity_RealDef__Oreal__Fields_Olinordered__field__inverse__zero arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra arity_RealDef__Oreal__Rings_Olinordered__semiring__strict arity_RealDef__Oreal__Rings_Odivision__ring__inverse__zero arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs arity_RealDef__Oreal__RealVector_Oreal__normed__algebra arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add arity_RealDef__Oreal__Groups_Olinordered__ab__group__add arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors arity_RealDef__Oreal__Rings_Oordered__cancel__semiring arity_RealDef__Oreal__RealVector_Oreal__normed__vector arity_RealDef__Oreal__Rings_Olinordered__ring__strict arity_RealDef__Oreal__RealVector_Oreal__normed__field arity_RealDef__Oreal__Rings_Oring__no__zero__divisors arity_RealDef__Oreal__Rings_Oordered__comm__semiring arity_RealDef__Oreal__Rings_Olinordered__semiring__1 arity_RealDef__Oreal__Groups_Oordered__ab__group__add arity_RealDef__Oreal__Groups_Ocancel__semigroup__add arity_RealDef__Oreal__Rings_Olinordered__semiring arity_RealDef__Oreal__Fields_Ofield__inverse__zero arity_RealDef__Oreal__Rings_Olinordered__semidom arity_RealDef__Oreal__Groups_Oab__semigroup__mult arity_RealDef__Oreal__Groups_Ocomm__monoid__mult arity_RealDef__Oreal__Groups_Oab__semigroup__add arity_RealDef__Oreal__Fields_Olinordered__field arity_RealDef__Oreal__Rings_Oordered__semiring arity_RealDef__Oreal__Rings_Oordered__ring__abs arity_RealDef__Oreal__Rings_Ono__zero__divisors arity_RealDef__Oreal__Groups_Ocomm__monoid__add arity_RealDef__Oreal__Rings_Olinordered__ring arity_RealDef__Oreal__Rings_Olinordered__idom arity_RealDef__Oreal__Rings_Ocomm__semiring__1 arity_RealDef__Oreal__RealVector_Oreal__field arity_RealDef__Oreal__Rings_Odivision__ring arity_RealDef__Oreal__Rings_Ocomm__semiring arity_RealDef__Oreal__Groups_Oab__group__add arity_RealDef__Oreal__Rings_Ozero__neq__one arity_RealDef__Oreal__Rings_Oordered__ring arity_RealDef__Oreal__Orderings_Opreorder arity_RealDef__Oreal__Orderings_Olinorder arity_RealDef__Oreal__Groups_Omonoid__mult arity_RealDef__Oreal__Rings_Ocomm__ring__1 arity_RealDef__Oreal__Groups_Omonoid__add arity_RealDef__Oreal__Rings_Osemiring__1 arity_RealDef__Oreal__Rings_Osemiring__0 arity_RealDef__Oreal__Groups_Ogroup__add arity_RealDef__Oreal__Rings_Omult__zero arity_RealDef__Oreal__Orderings_Oorder arity_RealDef__Oreal__Int_Oring__char__0 arity_RealDef__Oreal__Int_Onumber__ring arity_RealDef__Oreal__Rings_Osemiring arity_RealDef__Oreal__Orderings_Oord arity_RealDef__Oreal__Rings_Oring__1 arity_RealDef__Oreal__Fields_Ofield arity_RealDef__Oreal__Power_Opower arity_RealDef__Oreal__Groups_Ozero arity_RealDef__Oreal__Rings_Oring arity_RealDef__Oreal__Int_Onumber arity_RealDef__Oreal__Groups_Oone fact_One__nat__def fact_real__norm__def fact_abs__ge__zero fact_semiring__norm_I115_J fact_real__mult__commute fact__096abs_A_I2_A_K_Ax_J_A_060_061_A1_096 fact_power__mono conj_0
% 1.36/1.60
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