TSTP Solution File: SWV627-1 by SPASS---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV627-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n008.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 : Wed Jul 20 21:44:37 EDT 2022
% Result : Unsatisfiable 81.11s 81.34s
% Output : Refutation 81.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 47
% Syntax : Number of clauses : 100 ( 42 unt; 9 nHn; 100 RR)
% Number of literals : 192 ( 0 equ; 89 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 30 ( 29 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(12,axiom,
( ~ class_Ring__and__Field_Odvd(u)
| c_Ring__and__Field_Odvd__class_Odvd(v,c_HOL_Otimes__class_Otimes(v,w,u),u) ),
file('SWV627-1.p',unknown),
[] ).
cnf(24,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Otimes__class_Otimes(v,w,u),c_HOL_Otimes__class_Otimes(w,v,u)) ),
file('SWV627-1.p',unknown),
[] ).
cnf(108,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u))
| equal(v,w) ),
file('SWV627-1.p',unknown),
[] ).
cnf(152,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v,w,u)
| c_Ring__and__Field_Odvd__class_Odvd(v,c_HOL_Otimes__class_Otimes(w,x,u),u) ),
file('SWV627-1.p',unknown),
[] ).
cnf(153,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(v,w,u),x,u)
| c_Ring__and__Field_Odvd__class_Odvd(v,x,u) ),
file('SWV627-1.p',unknown),
[] ).
cnf(186,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v) ),
file('SWV627-1.p',unknown),
[] ).
cnf(214,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(u),v,u)
| equal(v,c_HOL_Ozero__class_Ozero(u)) ),
file('SWV627-1.p',unknown),
[] ).
cnf(229,axiom,
( ~ class_Ring__and__Field_Odivision__ring(u)
| equal(v,c_HOL_Ozero__class_Ozero(u))
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Oinverse__class_Oinverse(v,u),u),c_HOL_Oone__class_Oone(u)) ),
file('SWV627-1.p',unknown),
[] ).
cnf(309,axiom,
( ~ class_Ring__and__Field_Oidom(u)
| equal(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(v,u),u),c_HOL_Otimes__class_Otimes(v,v,u)) ),
file('SWV627-1.p',unknown),
[] ).
cnf(321,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(u)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(v,u),w,u)
| c_Ring__and__Field_Odvd__class_Odvd(v,w,u) ),
file('SWV627-1.p',unknown),
[] ).
cnf(401,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(u)
| equal(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(u),v,u),v) ),
file('SWV627-1.p',unknown),
[] ).
cnf(404,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(u),v,u),v) ),
file('SWV627-1.p',unknown),
[] ).
cnf(429,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(u)
| equal(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(v,w,u),c_Power_Opower__class_Opower(x,w,u),u),c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(v,x,u),w,u)) ),
file('SWV627-1.p',unknown),
[] ).
cnf(529,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Oinverse__class_Oinverse(w,u),u),c_HOL_Oinverse__class_Odivide(v,w,u)) ),
file('SWV627-1.p',unknown),
[] ).
cnf(625,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(u),v,u),c_HOL_Oinverse__class_Oinverse(v,u)) ),
file('SWV627-1.p',unknown),
[] ).
cnf(647,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(v,c_HOL_Oone__class_Oone(u),u),v) ),
file('SWV627-1.p',unknown),
[] ).
cnf(651,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(v,w,u),c_Power_Opower__class_Opower(x,w,u),u),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v,x,u),w,u)) ),
file('SWV627-1.p',unknown),
[] ).
cnf(652,axiom,
equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),u,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
file('SWV627-1.p',unknown),
[] ).
cnf(660,axiom,
( ~ class_Int_Onumber__ring(u)
| ~ class_Ring__and__Field_Oidom(u)
| equal(c_HOL_Ominus__class_Ominus(v,v,u),c_HOL_Ozero__class_Ozero(u)) ),
file('SWV627-1.p',unknown),
[] ).
cnf(739,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(740,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(741,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(742,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(743,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(744,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(745,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(746,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(747,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(748,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(749,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(750,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(751,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(752,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(753,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(754,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(755,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(756,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(757,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(758,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(759,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(760,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(761,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(762,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(763,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(764,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(765,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('SWV627-1.p',unknown),
[] ).
cnf(766,axiom,
~ equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('SWV627-1.p',unknown),
[] ).
cnf(1133,plain,
( ~ class_Ring__and__Field_Ofield(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(u),u),c_HOL_Oone__class_Oone(u)) ),
inference(spr,[status(thm),theory(equality)],[625,647]),
[iquote('0:SpR:625.1,647.1')] ).
cnf(1135,plain,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(u),u),c_HOL_Oone__class_Oone(u)) ),
inference(obv,[status(thm),theory(equality)],[1133]),
[iquote('0:Obv:1133.0')] ).
cnf(2154,plain,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ class_OrderedGroup_Ogroup__add(u)
| ~ equal(v,c_HOL_Ouminus__class_Ouminus(w,u))
| equal(c_HOL_Ouminus__class_Ouminus(v,u),w) ),
inference(spl,[status(thm),theory(equality)],[186,108]),
[iquote('0:SpL:186.1,108.1')] ).
cnf(2167,plain,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ equal(v,c_HOL_Ouminus__class_Ouminus(w,u))
| equal(c_HOL_Ouminus__class_Ouminus(v,u),w) ),
inference(obv,[status(thm),theory(equality)],[2154]),
[iquote('0:Obv:2154.0')] ).
cnf(2198,plain,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ class_OrderedGroup_Ogroup__add(u)
| ~ equal(v,w)
| equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u)) ),
inference(spl,[status(thm),theory(equality)],[186,2167]),
[iquote('0:SpL:186.1,2167.1')] ).
cnf(2201,plain,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ equal(v,w)
| equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u)) ),
inference(obv,[status(thm),theory(equality)],[2198]),
[iquote('0:Obv:2198.0')] ).
cnf(2429,plain,
( ~ class_Ring__and__Field_Ofield(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Oone__class_Oone(u),u),c_HOL_Oinverse__class_Odivide(v,c_HOL_Oone__class_Oone(u),u)) ),
inference(spr,[status(thm),theory(equality)],[1135,529]),
[iquote('0:SpR:1135.1,529.1')] ).
cnf(2435,plain,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Oone__class_Oone(u),u),c_HOL_Oinverse__class_Odivide(v,c_HOL_Oone__class_Oone(u),u)) ),
inference(obv,[status(thm),theory(equality)],[2429]),
[iquote('0:Obv:2429.0')] ).
cnf(2436,plain,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Oone__class_Oone(u),u),v) ),
inference(rew,[status(thm),theory(equality)],[647,2435]),
[iquote('0:Rew:647.1,2435.1')] ).
cnf(4743,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v,c_HOL_Oone__class_Oone(u),u)
| c_Ring__and__Field_Odvd__class_Odvd(v,w,u) ),
inference(spr,[status(thm),theory(equality)],[404,152]),
[iquote('0:SpR:404.1,152.2')] ).
cnf(4766,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v,c_HOL_Oone__class_Oone(u),u)
| c_Ring__and__Field_Odvd__class_Odvd(v,w,u) ),
inference(obv,[status(thm),theory(equality)],[4743]),
[iquote('0:Obv:4743.0')] ).
cnf(9086,plain,
( ~ class_Ring__and__Field_Oidom(u)
| ~ class_Ring__and__Field_Odvd(u)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Otimes__class_Otimes(v,v,u),u) ),
inference(spr,[status(thm),theory(equality)],[309,12]),
[iquote('0:SpR:309.1,12.1')] ).
cnf(46690,plain,
( ~ class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex)
| equal(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(u,v,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(u,c_FFT__Mirabelle_Oroot(v),tc_Complex_Ocomplex),v,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[652,429]),
[iquote('0:SpR:652.0,429.1')] ).
cnf(46700,plain,
( ~ class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex)
| equal(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_Power_Opower__class_Opower(u,v,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_FFT__Mirabelle_Oroot(v),u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[652,429]),
[iquote('0:SpR:652.0,429.1')] ).
cnf(46717,plain,
( ~ class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex)
| equal(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_FFT__Mirabelle_Oroot(u),v,tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v,u,tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[401,46700]),
[iquote('0:Rew:401.1,46700.1')] ).
cnf(46718,plain,
equal(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(c_FFT__Mirabelle_Oroot(u),v,tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(v,u,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[46717,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:46717.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(46719,plain,
equal(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(u,v,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(u,c_FFT__Mirabelle_Oroot(v),tc_Complex_Ocomplex),v,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[46690,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:46690.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(46777,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| equal(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(u,c_FFT__Mirabelle_Oroot(v),tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(u,v,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[24,46718]),
[iquote('0:SpR:24.1,46718.0')] ).
cnf(46778,plain,
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),u,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[2436,46718]),
[iquote('0:SpR:2436.1,46718.0')] ).
cnf(46805,plain,
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[652,46778]),
[iquote('0:Rew:652.0,46778.1')] ).
cnf(46806,plain,
equal(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[46805,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:46805.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(46809,plain,
equal(c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(u,c_FFT__Mirabelle_Oroot(v),tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(u,v,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[46777,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:46777.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(46810,plain,
equal(c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(u,v,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(u,v,tc_Complex_Ocomplex)),
inference(rew,[status(thm),theory(equality)],[46809,46719]),
[iquote('0:Rew:46809.0,46719.0')] ).
cnf(46930,plain,
equal(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(spr,[status(thm),theory(equality)],[652,46810]),
[iquote('0:SpR:652.0,46810.0')] ).
cnf(47135,plain,
( ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odvd(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(spr,[status(thm),theory(equality)],[46930,9086]),
[iquote('0:SpR:46930.0,9086.2')] ).
cnf(47206,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(ssi,[status(thm)],[47135,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:47135.1,47135.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(47240,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),u,tc_Complex_Ocomplex) ),
inference(res,[status(thm),theory(equality)],[47206,4766]),
[iquote('0:Res:47206.0,4766.1')] ).
cnf(47242,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),
inference(ssi,[status(thm)],[47240,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:47240.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(47250,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),u)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex) ),
inference(spr,[status(thm),theory(equality)],[2201,47242]),
[iquote('0:SpR:2201.2,47242.0')] ).
cnf(47271,plain,
( ~ equal(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),u)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex) ),
inference(ssi,[status(thm)],[47250,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:47250.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(48450,plain,
( ~ class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),u)
| c_Ring__and__Field_Odvd__class_Odvd(u,v,tc_Complex_Ocomplex) ),
inference(res,[status(thm),theory(equality)],[47271,321]),
[iquote('0:Res:47271.1,321.1')] ).
cnf(48451,plain,
( ~ equal(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),u)
| c_Ring__and__Field_Odvd__class_Odvd(u,v,tc_Complex_Ocomplex) ),
inference(ssi,[status(thm)],[48450,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:48450.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(48468,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Otimes__class_Otimes(u,v,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(u,w,tc_Complex_Ocomplex) ),
inference(res,[status(thm),theory(equality)],[48451,153]),
[iquote('0:Res:48451.1,153.1')] ).
cnf(48473,plain,
( ~ equal(c_HOL_Otimes__class_Otimes(u,v,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(u,w,tc_Complex_Ocomplex) ),
inference(ssi,[status(thm)],[48468,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:48468.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(48672,plain,
( ~ class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(u,v,tc_Complex_Ocomplex) ),
inference(spl,[status(thm),theory(equality)],[229,48473]),
[iquote('0:SpL:229.2,48473.0')] ).
cnf(48698,plain,
( ~ class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(u,v,tc_Complex_Ocomplex) ),
inference(obv,[status(thm),theory(equality)],[48672]),
[iquote('0:Obv:48672.1')] ).
cnf(48699,plain,
( equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(u,v,tc_Complex_Ocomplex) ),
inference(ssi,[status(thm)],[48698,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:48698.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(48735,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| equal(c_HOL_Otimes__class_Otimes(u,v,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(u,w,tc_Complex_Ocomplex) ),
inference(res,[status(thm),theory(equality)],[48699,153]),
[iquote('0:Res:48699.1,153.1')] ).
cnf(48744,plain,
( equal(c_HOL_Otimes__class_Otimes(u,v,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(u,w,tc_Complex_Ocomplex) ),
inference(ssi,[status(thm)],[48735,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:48735.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(49702,plain,
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(u,v,tc_Complex_Ocomplex)
| equal(c_HOL_Oinverse__class_Odivide(u,w,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[48744,529]),
[iquote('0:SpR:48744.0,529.1')] ).
cnf(49786,plain,
( c_Ring__and__Field_Odvd__class_Odvd(u,v,tc_Complex_Ocomplex)
| equal(c_HOL_Oinverse__class_Odivide(u,w,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(ssi,[status(thm)],[49702,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:49702.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(50318,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(v,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(res,[status(thm),theory(equality)],[49786,214]),
[iquote('0:Res:49786.0,214.1')] ).
cnf(50331,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(con,[status(thm)],[50318]),
[iquote('0:Con:50318.2')] ).
cnf(77666,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(u,v,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(u,c_FFT__Mirabelle_Oroot(v),tc_Complex_Ocomplex),v,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[652,651]),
[iquote('0:SpR:652.0,651.2')] ).
cnf(77705,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(u,c_FFT__Mirabelle_Oroot(v),tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(u,v,tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[647,77666]),
[iquote('0:Rew:647.1,77666.2')] ).
cnf(77706,plain,
equal(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(u,c_FFT__Mirabelle_Oroot(v),tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),c_Power_Opower__class_Opower(u,v,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[77705,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:77705.1,77705.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(77714,plain,
~ equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),v_n,tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(rew,[status(thm),theory(equality)],[77706,766]),
[iquote('0:Rew:77706.0,766.0')] ).
cnf(77767,plain,
~ equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(rew,[status(thm),theory(equality)],[46806,77714]),
[iquote('0:Rew:46806.0,77714.0,46806.0,77714.0')] ).
cnf(103764,plain,
( ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k,tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(spl,[status(thm),theory(equality)],[660,77767]),
[iquote('0:SpL:660.2,77767.0')] ).
cnf(103804,plain,
equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[50331,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:50331.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
cnf(103967,plain,
( ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[103804,103764]),
[iquote('0:Rew:103804.0,103764.2')] ).
cnf(103968,plain,
( ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Oidom(tc_Complex_Ocomplex) ),
inference(obv,[status(thm),theory(equality)],[103967]),
[iquote('0:Obv:103967.2')] ).
cnf(103969,plain,
$false,
inference(ssi,[status(thm)],[103968,761,756,739,760,751,745,764,746,740,752,749,741,763,758,754,753,750,744,765,762,748,755,759,747,743,757,742]),
[iquote('0:SSi:103968.1,103968.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0,761.0,756.0,739.0,760.0,751.0,745.0,764.0,746.0,740.0,752.0,749.0,741.0,763.0,758.0,754.0,753.0,750.0,744.0,765.0,762.0,748.0,755.0,759.0,747.0,743.0,757.0,742.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SWV627-1 : TPTP v8.1.0. Released v4.1.0.
% 0.04/0.09 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n008.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 600
% 0.09/0.29 % DateTime : Wed Jun 15 15:17:22 EDT 2022
% 0.09/0.29 % CPUTime :
% 81.11/81.34
% 81.11/81.34 SPASS V 3.9
% 81.11/81.34 SPASS beiseite: Proof found.
% 81.11/81.34 % SZS status Theorem
% 81.11/81.34 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 81.11/81.34 SPASS derived 79004 clauses, backtracked 439 clauses, performed 4 splits and kept 18373 clauses.
% 81.11/81.34 SPASS allocated 152283 KBytes.
% 81.11/81.34 SPASS spent 0:1:20.93 on the problem.
% 81.11/81.34 0:00:00.05 for the input.
% 81.11/81.34 0:00:00.00 for the FLOTTER CNF translation.
% 81.11/81.34 0:00:00.91 for inferences.
% 81.11/81.34 0:00:02.72 for the backtracking.
% 81.11/81.34 0:1:16.69 for the reduction.
% 81.11/81.34
% 81.11/81.34
% 81.11/81.34 Here is a proof with depth 11, length 100 :
% 81.11/81.34 % SZS output start Refutation
% See solution above
% 81.11/81.35 Formulae used in the proof : cls_dvdI_0 cls_class__semiring_Osemiring__rules_I7_J_0 cls_neg__equal__iff__equal_0 cls_dvd__mult2_0 cls_dvd__mult__left_0 cls_minus__minus_0 cls_dvd__0__left_0 cls_right__inverse_0 cls_square__eq__iff_1 cls_minus__dvd__iff_0 cls_mult__1_0 cls_class__semiring_Osemiring__rules_I11_J_0 cls_power__mult__distrib_0 cls_divide__inverse_0 cls_inverse__eq__divide_0 cls_divide__1_0 cls_power__divide_0 cls_root__unity_0 cls_class__ringb_Osubr0__iff_1 clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1 clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0 clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1 clsarity_Complex__Ocomplex__Ring__and__Field_Ofield clsarity_Complex__Ocomplex__Ring__and__Field_Oring clsarity_Complex__Ocomplex__Ring__and__Field_Oidom clsarity_Complex__Ocomplex__Ring__and__Field_Odvd clsarity_Complex__Ocomplex__Int_Oring__char__0 clsarity_Complex__Ocomplex__Int_Onumber__ring clsarity_Complex__Ocomplex__Power_Opower clsarity_Complex__Ocomplex__SEQ_Obanach clsarity_Complex__Ocomplex__Int_Onumber cls_conjecture_0
% 89.40/89.57
%------------------------------------------------------------------------------