TSTP Solution File: SWW215+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWW215+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n023.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 01:28:06 EDT 2022
% Result : Theorem 134.95s 135.13s
% Output : Refutation 139.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 77
% Syntax : Number of clauses : 84 ( 78 unt; 0 nHn; 84 RR)
% Number of literals : 94 ( 0 equ; 15 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 74 ( 73 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(106,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(107,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(108,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(109,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(110,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(111,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(112,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(113,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(114,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(115,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(116,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(117,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(118,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(119,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(120,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(121,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(122,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(123,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(124,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(125,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(126,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(127,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(128,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(129,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(130,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(131,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(132,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(133,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(134,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(135,axiom,
class_Orderings_Odense__linorder(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(136,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(137,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(138,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(139,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(140,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(141,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(142,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(143,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(144,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(145,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(146,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(147,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(148,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(149,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(150,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(151,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(152,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(153,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(154,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(155,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(156,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(157,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(158,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(159,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(160,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(161,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(162,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(163,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(164,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(165,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(166,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(167,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(168,axiom,
class_Groups_Ominus(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(169,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(170,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(171,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(172,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(173,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(174,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(175,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('SWW215+1.p',unknown),
[] ).
cnf(225,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,v_da____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('SWW215+1.p',unknown),
[] ).
cnf(398,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
file('SWW215+1.p',unknown),
[] ).
cnf(400,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,u,v)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v) ),
file('SWW215+1.p',unknown),
[] ).
cnf(469,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
file('SWW215+1.p',unknown),
[] ).
cnf(530,axiom,
( ~ class_Orderings_Opreorder(u)
| ~ c_Orderings_Oord__class_Oless(u,v,w)
| c_Orderings_Oord__class_Oless__eq(u,v,w) ),
file('SWW215+1.p',unknown),
[] ).
cnf(853,axiom,
( ~ class_Orderings_Opreorder(u)
| ~ c_Orderings_Oord__class_Oless(u,v,w)
| ~ c_Orderings_Oord__class_Oless__eq(u,x,v)
| c_Orderings_Oord__class_Oless(u,x,w) ),
file('SWW215+1.p',unknown),
[] ).
cnf(1792,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),
inference(res,[status(thm),theory(equality)],[400,469]),
[iquote('0:Res:400.1,469.0')] ).
cnf(51653,plain,
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v_da____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,u,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(res,[status(thm),theory(equality)],[225,853]),
[iquote('0:Res:225.0,853.1')] ).
cnf(51861,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v_da____)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,u,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)) ),
inference(ssi,[status(thm)],[51653,148,141,129,115,112,111,167,128,122,114,109,174,165,164,150,138,136,135,132,121,172,158,157,144,127,123,116,152,142,140,137,2,168,162,161,159,131,130,126,107,171,160,175,106,170,155,108,156,151,149,120,166,153,133,143,119,154,118,113,124,173,147,117,163,134,139,169,125,145,146,110]),
[iquote('0:SSi:51653.0,148.0,141.0,129.0,115.0,112.0,111.0,167.0,128.0,122.0,114.0,109.0,174.0,165.0,164.0,150.0,138.0,136.0,135.0,132.0,121.0,172.0,158.0,157.0,144.0,127.0,123.0,116.0,152.0,142.0,140.0,137.0,2.0,168.0,162.0,161.0,159.0,131.0,130.0,126.0,107.0,171.0,160.0,175.0,106.0,170.0,155.0,108.0,156.0,151.0,149.0,120.0,166.0,153.0,133.0,143.0,119.0,154.0,118.0,113.0,124.0,173.0,147.0,117.0,163.0,134.0,139.0,169.0,125.0,145.0,146.0,110.0')] ).
cnf(106889,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
inference(res,[status(thm),theory(equality)],[51861,1792]),
[iquote('0:Res:51861.1,1792.0')] ).
cnf(107457,plain,
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____) ),
inference(res,[status(thm),theory(equality)],[530,106889]),
[iquote('0:Res:530.2,106889.0')] ).
cnf(107470,plain,
~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,v_w____,v_z)),v_da____),
inference(ssi,[status(thm)],[107457,148,141,129,115,112,111,167,128,122,114,109,174,165,164,150,138,136,135,132,121,172,158,157,144,127,123,116,152,142,140,137,2,168,162,161,159,131,130,126,107,171,160,175,106,170,155,108,156,151,149,120,166,153,133,143,119,154,118,113,124,173,147,117,163,134,139,169,125,145,146,110]),
[iquote('0:SSi:107457.0,148.0,141.0,129.0,115.0,112.0,111.0,167.0,128.0,122.0,114.0,109.0,174.0,165.0,164.0,150.0,138.0,136.0,135.0,132.0,121.0,172.0,158.0,157.0,144.0,127.0,123.0,116.0,152.0,142.0,140.0,137.0,2.0,168.0,162.0,161.0,159.0,131.0,130.0,126.0,107.0,171.0,160.0,175.0,106.0,170.0,155.0,108.0,156.0,151.0,149.0,120.0,166.0,153.0,133.0,143.0,119.0,154.0,118.0,113.0,124.0,173.0,147.0,117.0,163.0,134.0,139.0,169.0,125.0,145.0,146.0,110.0')] ).
cnf(107471,plain,
$false,
inference(mrr,[status(thm)],[107470,398]),
[iquote('0:MRR:107470.0,398.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW215+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Mon Jun 6 02:35:09 EDT 2022
% 0.12/0.34 % CPUTime :
% 134.95/135.13
% 134.95/135.13 SPASS V 3.9
% 134.95/135.13 SPASS beiseite: Proof found.
% 134.95/135.13 % SZS status Theorem
% 134.95/135.13 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 134.95/135.13 SPASS derived 83908 clauses, backtracked 11 clauses, performed 15 splits and kept 30977 clauses.
% 134.95/135.13 SPASS allocated 185054 KBytes.
% 134.95/135.13 SPASS spent 0:2:14.62 on the problem.
% 134.95/135.13 0:00:00.06 for the input.
% 134.95/135.13 0:00:00.58 for the FLOTTER CNF translation.
% 134.95/135.13 0:00:01.68 for inferences.
% 134.95/135.13 0:00:01.90 for the backtracking.
% 134.95/135.13 0:02:08.52 for the reduction.
% 134.95/135.13
% 134.95/135.13
% 134.95/135.13 Here is a proof with depth 3, length 84 :
% 134.95/135.13 % SZS output start Refutation
% See solution above
% 139.37/139.56 Formulae used in the proof : arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add 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__Orderings_Odense__linorder 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__Rings_Ocomm__semiring__0 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__0 arity_RealDef__Oreal__Groups_Ogroup__add arity_RealDef__Oreal__Rings_Omult__zero arity_RealDef__Oreal__Rings_Ocomm__ring arity_RealDef__Oreal__Orderings_Oorder arity_RealDef__Oreal__Int_Oring__char__0 arity_RealDef__Oreal__Rings_Osemiring arity_RealDef__Oreal__Orderings_Oord arity_RealDef__Oreal__Rings_Oring__1 arity_RealDef__Oreal__Groups_Ominus arity_RealDef__Oreal__Fields_Ofield arity_RealDef__Oreal__Power_Opower arity_RealDef__Oreal__Groups_Ozero arity_RealDef__Oreal__Rings_Oring arity_RealDef__Oreal__Rings_Oidom arity_RealDef__Oreal__Groups_Oone arity_RealDef__Oreal__Rings_Odvd fact_H_I2_J fact_H_I5_J fact_real__less__def conj_0 fact_less__le__not__le fact_order__le__less__trans
% 139.37/139.56
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