TSTP Solution File: ALG432-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG432-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n020.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 18:03:39 EDT 2022
% Result : Unsatisfiable 186.67s 186.85s
% Output : Refutation 195.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 73
% Syntax : Number of clauses : 144 ( 58 unt; 12 nHn; 144 RR)
% Number of literals : 273 ( 0 equ; 121 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 49 ( 48 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 7 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(65,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(w,x,u) ),
file('ALG432-1.p',unknown),
[] ).
cnf(66,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('ALG432-1.p',unknown),
[] ).
cnf(71,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Oplus__class_Oplus(v,c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v,u),w,u),u),w) ),
file('ALG432-1.p',unknown),
[] ).
cnf(83,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(u),v,u) ),
file('ALG432-1.p',unknown),
[] ).
cnf(92,axiom,
( ~ class_RealVector_Oreal__normed__vector(u)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Osgn__class_Osgn(v,u),u),c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(v,u),u)) ),
file('ALG432-1.p',unknown),
[] ).
cnf(108,axiom,
( ~ class_Orderings_Olinorder(u)
| equal(v,w)
| c_HOL_Oord__class_Oless(v,w,u)
| c_HOL_Oord__class_Oless(w,v,u) ),
file('ALG432-1.p',unknown),
[] ).
cnf(201,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Oplus__class_Oplus(v,c_HOL_Ouminus__class_Ouminus(w,u),u),c_HOL_Ominus__class_Ominus(v,w,u)) ),
file('ALG432-1.p',unknown),
[] ).
cnf(205,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(u)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v,c_HOL_Ouminus__class_Ouminus(w,u),u)
| c_Ring__and__Field_Odvd__class_Odvd(v,w,u) ),
file('ALG432-1.p',unknown),
[] ).
cnf(292,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v,w,u),w,u),v) ),
file('ALG432-1.p',unknown),
[] ).
cnf(323,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(v,c_HOL_Ozero__class_Ozero(u))
| equal(c_HOL_Oinverse__class_Odivide(v,v,u),c_HOL_Oone__class_Oone(u)) ),
file('ALG432-1.p',unknown),
[] ).
cnf(375,axiom,
equal(c_Complex_Ocnj(c_Complex_Ocnj(u)),u),
file('ALG432-1.p',unknown),
[] ).
cnf(427,axiom,
equal(c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
file('ALG432-1.p',unknown),
[] ).
cnf(435,axiom,
( ~ class_Orderings_Olinorder(u)
| ~ c_HOL_Oord__class_Oless(v,v,u) ),
file('ALG432-1.p',unknown),
[] ).
cnf(442,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v,u),v,u),c_HOL_Ozero__class_Ozero(u)) ),
file('ALG432-1.p',unknown),
[] ).
cnf(474,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_Polynomial_Opoly(w,x,u),u),c_Polynomial_Opoly(c_Polynomial_Osmult(v,w,u),x,u)) ),
file('ALG432-1.p',unknown),
[] ).
cnf(547,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Oplus__class_Oplus(v,w,u),u),w) ),
file('ALG432-1.p',unknown),
[] ).
cnf(563,axiom,
( ~ equal(c_Complex_Ocnj(u),c_Complex_Ocnj(v))
| equal(u,v) ),
file('ALG432-1.p',unknown),
[] ).
cnf(570,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('ALG432-1.p',unknown),
[] ).
cnf(640,axiom,
( ~ class_RealVector_Oreal__normed__vector(u)
| equal(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u)) ),
file('ALG432-1.p',unknown),
[] ).
cnf(653,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| c_Ring__and__Field_Odvd__class_Odvd(v,c_HOL_Ozero__class_Ozero(u),u) ),
file('ALG432-1.p',unknown),
[] ).
cnf(658,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('ALG432-1.p',unknown),
[] ).
cnf(678,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Ominus__class_Ominus(v,v,u),c_HOL_Ozero__class_Ozero(u)) ),
file('ALG432-1.p',unknown),
[] ).
cnf(688,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| ~ equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))
| equal(v,w) ),
file('ALG432-1.p',unknown),
[] ).
cnf(696,axiom,
( ~ class_RealVector_Oreal__normed__vector(u)
| ~ equal(c_HOL_Osgn__class_Osgn(v,u),c_HOL_Ozero__class_Ozero(u))
| equal(v,c_HOL_Ozero__class_Ozero(u)) ),
file('ALG432-1.p',unknown),
[] ).
cnf(715,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__0(u)
| equal(c_HOL_Oplus__class_Oplus(v,c_HOL_Otimes__class_Otimes(w,c_Polynomial_Opoly(x,w,u),u),u),c_Polynomial_Opoly(c_Polynomial_OpCons(v,x,u),w,u)) ),
file('ALG432-1.p',unknown),
[] ).
cnf(721,axiom,
equal(c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('ALG432-1.p',unknown),
[] ).
cnf(737,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(769,axiom,
class_Orderings_Olinorder(tc_nat),
file('ALG432-1.p',unknown),
[] ).
cnf(844,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(845,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(846,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(847,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(848,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(849,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(850,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(851,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(852,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(853,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(854,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(855,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(856,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(857,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(858,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(859,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(860,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(861,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(862,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(863,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(864,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(865,axiom,
class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(866,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(867,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(868,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(869,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(870,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(871,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(872,axiom,
class_RealVector_Oreal__algebra(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(873,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(874,axiom,
class_RealVector_Oreal__vector(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(875,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(876,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(877,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(878,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(879,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(880,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(881,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(882,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(883,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(884,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(885,axiom,
class_HOL_Ozero(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(886,axiom,
class_HOL_Oeq(tc_Complex_Ocomplex),
file('ALG432-1.p',unknown),
[] ).
cnf(937,axiom,
equal(c_Polynomial_Opoly(v,v_x,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('ALG432-1.p',unknown),
[] ).
cnf(938,axiom,
~ equal(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
file('ALG432-1.p',unknown),
[] ).
cnf(973,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(u)
| equal(c_HOL_Oplus__class_Oplus(v,c_Polynomial_Opoly(c_Polynomial_Osmult(w,x,u),w,u),u),c_Polynomial_Opoly(c_Polynomial_OpCons(v,x,u),w,u)) ),
inference(rew,[status(thm),theory(equality)],[474,715]),
[iquote('0:Rew:474.1,715.1')] ).
cnf(1036,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(res,[status(thm),theory(equality)],[658,938]),
[iquote('0:Res:658.2,938.0')] ).
cnf(1107,plain,
( ~ class_Orderings_Olinorder(u)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),u)
| c_HOL_Oord__class_Oless(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u) ),
inference(res,[status(thm),theory(equality)],[108,938]),
[iquote('0:Res:108.3,938.0')] ).
cnf(1135,plain,
~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(mrr,[status(thm)],[1036,852]),
[iquote('0:MRR:1036.0,852.0')] ).
cnf(1147,plain,
( ~ equal(u,c_Complex_Ocnj(v))
| equal(c_Complex_Ocnj(u),v) ),
inference(spl,[status(thm),theory(equality)],[375,563]),
[iquote('0:SpL:375.0,563.0')] ).
cnf(1156,plain,
( ~ equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_Complex_Ocnj(u),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(spl,[status(thm),theory(equality)],[721,1147]),
[iquote('0:SpL:721.0,1147.0')] ).
cnf(1157,plain,
( ~ equal(u,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| equal(c_Complex_Ocnj(u),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(spl,[status(thm),theory(equality)],[427,1147]),
[iquote('0:SpL:427.0,1147.0')] ).
cnf(1199,plain,
( ~ equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_Complex_Ocnj(c_Complex_Ocnj(u)),c_Complex_Ocnj(u)) ),
inference(spr,[status(thm),theory(equality)],[1156,721]),
[iquote('0:SpR:1156.1,721.0')] ).
cnf(1202,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v,c_Complex_Ocnj(u),tc_Complex_Ocomplex) ),
inference(spr,[status(thm),theory(equality)],[1156,653]),
[iquote('0:SpR:1156.1,653.1')] ).
cnf(1213,plain,
( ~ equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_Complex_Ocnj(u),u) ),
inference(rew,[status(thm),theory(equality)],[375,1199]),
[iquote('0:Rew:375.0,1199.1')] ).
cnf(1218,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v,u,tc_Complex_Ocomplex) ),
inference(rew,[status(thm),theory(equality)],[1213,1202]),
[iquote('0:Rew:1213.1,1202.2')] ).
cnf(1219,plain,
( ~ equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v,u,tc_Complex_Ocomplex) ),
inference(ssi,[status(thm)],[1218,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:1218.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(1237,plain,
( ~ equal(u,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| equal(c_Complex_Ocnj(c_Complex_Ocnj(u)),c_Complex_Ocnj(u)) ),
inference(spr,[status(thm),theory(equality)],[1157,427]),
[iquote('0:SpR:1157.1,427.0')] ).
cnf(1239,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ equal(u,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(c_Complex_Ocnj(u),v,tc_Complex_Ocomplex) ),
inference(spr,[status(thm),theory(equality)],[1157,83]),
[iquote('0:SpR:1157.1,83.1')] ).
cnf(1251,plain,
( ~ equal(u,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| equal(c_Complex_Ocnj(u),u) ),
inference(rew,[status(thm),theory(equality)],[375,1237]),
[iquote('0:Rew:375.0,1237.1')] ).
cnf(1254,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ equal(u,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(u,v,tc_Complex_Ocomplex) ),
inference(rew,[status(thm),theory(equality)],[1251,1239]),
[iquote('0:Rew:1251.1,1239.2')] ).
cnf(1255,plain,
( ~ equal(u,c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(u,v,tc_Complex_Ocomplex) ),
inference(ssi,[status(thm)],[1254,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:1254.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(1672,plain,
( ~ class_OrderedGroup_Ogroup__add(u)
| ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(u),v,u),v) ),
inference(spr,[status(thm),theory(equality)],[678,292]),
[iquote('0:SpR:678.1,292.1')] ).
cnf(1678,plain,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(u),v,u),v) ),
inference(obv,[status(thm),theory(equality)],[1672]),
[iquote('0:Obv:1672.0')] ).
cnf(2894,plain,
( ~ class_RealVector_Oreal__normed__vector(u)
| ~ class_RealVector_Oreal__normed__vector(u)
| equal(c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u)) ),
inference(spr,[status(thm),theory(equality)],[640,92]),
[iquote('0:SpR:640.1,92.1')] ).
cnf(2902,plain,
( ~ class_RealVector_Oreal__normed__vector(u)
| equal(c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u)) ),
inference(obv,[status(thm),theory(equality)],[2894]),
[iquote('0:Obv:2894.0')] ).
cnf(4463,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v,u),c_HOL_Ozero__class_Ozero(u)) ),
inference(spr,[status(thm),theory(equality)],[201,442]),
[iquote('0:SpR:201.1,442.1')] ).
cnf(4495,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v,u),c_HOL_Ozero__class_Ozero(u)) ),
inference(obv,[status(thm),theory(equality)],[4463]),
[iquote('0:Obv:4463.0')] ).
cnf(4655,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| ~ class_OrderedGroup_Oab__group__add(u)
| ~ equal(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u))
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v) ),
inference(spl,[status(thm),theory(equality)],[4495,688]),
[iquote('0:SpL:4495.1,688.1')] ).
cnf(4666,plain,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v) ),
inference(obv,[status(thm),theory(equality)],[4655]),
[iquote('0:Obv:4655.2')] ).
cnf(6131,plain,
( ~ class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v,u,tc_Complex_Ocomplex) ),
inference(res,[status(thm),theory(equality)],[1219,205]),
[iquote('0:Res:1219.1,205.1')] ).
cnf(6135,plain,
( ~ equal(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| c_Ring__and__Field_Odvd__class_Odvd(v,u,tc_Complex_Ocomplex) ),
inference(ssi,[status(thm)],[6131,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:6131.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(6137,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(res,[status(thm),theory(equality)],[6135,658]),
[iquote('0:Res:6135.1,658.1')] ).
cnf(6142,plain,
( ~ equal(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(ssi,[status(thm)],[6137,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:6137.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(6163,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Osgn__class_Osgn(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(spl,[status(thm),theory(equality)],[92,6142]),
[iquote('0:SpL:92.1,6142.0')] ).
cnf(6169,plain,
( ~ equal(c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Osgn__class_Osgn(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(ssi,[status(thm)],[6163,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:6163.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(7508,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Osgn__class_Osgn(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(spl,[status(thm),theory(equality)],[4666,6169]),
[iquote('0:SpL:4666.1,6169.0')] ).
cnf(7521,plain,
( ~ equal(c_HOL_Osgn__class_Osgn(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(ssi,[status(thm)],[7508,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:7508.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(7535,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[7521,2902]),
[iquote('0:SpR:7521.1,2902.1')] ).
cnf(7564,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Osgn__class_Osgn(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| ~ equal(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(spl,[status(thm),theory(equality)],[7521,696]),
[iquote('0:SpL:7521.1,696.1')] ).
cnf(7566,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[640,7535]),
[iquote('0:Rew:640.1,7535.1')] ).
cnf(7567,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(obv,[status(thm),theory(equality)],[7566]),
[iquote('0:Obv:7566.1')] ).
cnf(7568,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[7567,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:7567.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(7574,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Osgn__class_Osgn(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(obv,[status(thm),theory(equality)],[7564]),
[iquote('0:Obv:7564.2')] ).
cnf(7575,plain,
( ~ equal(c_HOL_Osgn__class_Osgn(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(ssi,[status(thm)],[7574,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:7574.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(7923,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Osgn__class_Osgn(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Oplus__class_Oplus(u,c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),tc_Complex_Ocomplex),v) ),
inference(spr,[status(thm),theory(equality)],[7575,71]),
[iquote('0:SpR:7575.1,71.1')] ).
cnf(8022,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Osgn__class_Osgn(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Oplus__class_Oplus(u,v,tc_Complex_Ocomplex),v) ),
inference(rew,[status(thm),theory(equality)],[1678,7923]),
[iquote('0:Rew:1678.1,7923.2')] ).
cnf(8023,plain,
( ~ equal(c_HOL_Osgn__class_Osgn(u,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Oplus__class_Oplus(u,v,tc_Complex_Ocomplex),v) ),
inference(ssi,[status(thm)],[8022,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:8022.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(8332,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Oplus__class_Oplus(u,v,tc_Complex_Ocomplex),v) ),
inference(spr,[status(thm),theory(equality)],[8023,547]),
[iquote('0:SpR:8023.1,547.1')] ).
cnf(8345,plain,
( ~ equal(c_HOL_Osgn__class_Osgn(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Oplus__class_Oplus(u,v,tc_Complex_Ocomplex),v) ),
inference(ssi,[status(thm)],[8332,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:8332.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(10108,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),u) ),
inference(spl,[status(thm),theory(equality)],[2902,8345]),
[iquote('0:SpL:2902.1,8345.0')] ).
cnf(10114,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),u) ),
inference(rew,[status(thm),theory(equality)],[7568,10108]),
[iquote('0:Rew:7568.0,10108.1')] ).
cnf(10115,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),u) ),
inference(obv,[status(thm),theory(equality)],[10114]),
[iquote('0:Obv:10114.1')] ).
cnf(10116,plain,
equal(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),u),
inference(ssi,[status(thm)],[10115,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:10115.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(11366,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)],[1255,66]),
[iquote('0:Res:1255.1,66.1')] ).
cnf(11373,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)],[11366,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:11366.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(11416,plain,
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| ~ equal(c_HOL_Oinverse__class_Odivide(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(spl,[status(thm),theory(equality)],[570,11373]),
[iquote('0:SpL:570.1,11373.0')] ).
cnf(11430,plain,
( ~ equal(c_HOL_Oinverse__class_Odivide(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)],[11416,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:11416.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(11475,plain,
( ~ class_Ring__and__Field_Ofield(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)],[323,11430]),
[iquote('0:SpL:323.2,11430.0')] ).
cnf(11476,plain,
( ~ class_Ring__and__Field_Ofield(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)],[11475]),
[iquote('0:Obv:11475.1')] ).
cnf(11477,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)],[11476,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:11476.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(11584,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(v,w,tc_Complex_Ocomplex) ),
inference(res,[status(thm),theory(equality)],[11477,65]),
[iquote('0:Res:11477.1,65.1')] ).
cnf(11600,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(v,w,tc_Complex_Ocomplex) ),
inference(ssi,[status(thm)],[11584,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:11584.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(11726,plain,
equal(c_HOL_Otimes__class_Otimes(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(res,[status(thm),theory(equality)],[11600,1135]),
[iquote('0:Res:11600.1,1135.0')] ).
cnf(60384,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| equal(c_Polynomial_Opoly(c_Polynomial_Osmult(u,v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[937,474]),
[iquote('0:SpR:937.0,474.1')] ).
cnf(60420,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| equal(c_Polynomial_Opoly(c_Polynomial_Osmult(u,v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[11726,60384]),
[iquote('0:Rew:11726.0,60384.1')] ).
cnf(60421,plain,
equal(c_Polynomial_Opoly(c_Polynomial_Osmult(u,v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[60420,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:60420.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(136002,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex)
| equal(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_Osmult(v,u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[973,10116]),
[iquote('0:SpR:973.1,10116.0')] ).
cnf(136090,plain,
equal(c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_Osmult(v,u,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[136002,877,849,847,876,872,844,871,860,858,855,846,873,866,857,848,845,884,881,869,865,863,850,737,879,874,868,870,883,856,864,882,861,854,862,867,859,875,886,885,880,853,878,852,851]),
[iquote('0:SSi:136002.0,877.0,849.0,847.0,876.0,872.0,844.0,871.0,860.0,858.0,855.0,846.0,873.0,866.0,857.0,848.0,845.0,884.0,881.0,869.0,865.0,863.0,850.0,737.0,879.0,874.0,868.0,870.0,883.0,856.0,864.0,882.0,861.0,854.0,862.0,867.0,859.0,875.0,886.0,885.0,880.0,853.0,878.0,852.0,851.0')] ).
cnf(136097,plain,
( ~ class_Orderings_Olinorder(u)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),u)
| c_HOL_Oord__class_Oless(c_Polynomial_Opoly(c_Polynomial_Osmult(v_x,v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u) ),
inference(rew,[status(thm),theory(equality)],[136090,1107]),
[iquote('0:Rew:136090.0,1107.2')] ).
cnf(136272,plain,
( ~ class_Orderings_Olinorder(u)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_OpCons(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),u)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u) ),
inference(rew,[status(thm),theory(equality)],[60421,136097]),
[iquote('0:Rew:60421.0,136097.2')] ).
cnf(136273,plain,
( ~ class_Orderings_Olinorder(u)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_Polynomial_Opoly(c_Polynomial_Osmult(v_x,v,tc_Complex_Ocomplex),v_x,tc_Complex_Ocomplex),u)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u) ),
inference(rew,[status(thm),theory(equality)],[136090,136272]),
[iquote('0:Rew:136090.0,136272.1')] ).
cnf(136274,plain,
( ~ class_Orderings_Olinorder(u)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u) ),
inference(rew,[status(thm),theory(equality)],[60421,136273]),
[iquote('0:Rew:60421.0,136273.1')] ).
cnf(136275,plain,
( ~ class_Orderings_Olinorder(u)
| c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),u) ),
inference(obv,[status(thm),theory(equality)],[136274]),
[iquote('0:Obv:136274.1')] ).
cnf(136276,plain,
~ class_Orderings_Olinorder(u),
inference(mrr,[status(thm)],[136275,435]),
[iquote('0:MRR:136275.1,435.1')] ).
cnf(136277,plain,
$false,
inference(unc,[status(thm)],[136276,769]),
[iquote('0:UnC:136276.0,769.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09 % Problem : ALG432-1 : TPTP v8.1.0. Released v4.1.0.
% 0.02/0.09 % Command : run_spass %d %s
% 0.09/0.29 % Computer : n020.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 8 02:40:06 EDT 2022
% 0.09/0.29 % CPUTime :
% 186.67/186.85
% 186.67/186.85 SPASS V 3.9
% 186.67/186.85 SPASS beiseite: Proof found.
% 186.67/186.85 % SZS status Theorem
% 186.67/186.85 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 186.67/186.85 SPASS derived 94958 clauses, backtracked 1 clauses, performed 1 splits and kept 22012 clauses.
% 186.67/186.85 SPASS allocated 182669 KBytes.
% 186.67/186.85 SPASS spent 0:03:06.31 on the problem.
% 186.67/186.85 0:00:00.06 for the input.
% 186.67/186.85 0:00:00.00 for the FLOTTER CNF translation.
% 186.67/186.85 0:00:01.49 for inferences.
% 186.67/186.85 0:00:01.41 for the backtracking.
% 186.67/186.85 0:03:02.33 for the reduction.
% 186.67/186.85
% 186.67/186.85
% 186.67/186.85 Here is a proof with depth 12, length 144 :
% 186.67/186.85 % SZS output start Refutation
% See solution above
% 195.95/196.12 Formulae used in the proof : cls_dvd__mult__right_0 cls_dvd__mult__left_0 cls_add__minus__cancel_0 cls_one__dvd_0 cls_sgn__minus_0 cls_linorder__neqE_0 cls_ab__diff__minus_0 cls_dvd__minus__iff_0 cls_diff__add__cancel_0 cls_divide__self_0 cls_complex__cnj__cnj_0 cls_complex__cnj__one_0 cls_linorder__neq__iff_1 cls_ab__left__minus_0 cls_poly__smult_0 cls_minus__add__cancel_0 cls_complex__cnj__cancel__iff_0 cls_divide__inverse_0 cls_sgn__zero_0 cls_dvd__0__right_0 cls_dvd__0__left_0 cls_diff__self_0 cls_eq__iff__diff__eq__0_1 cls_sgn__zero__iff_0 cls_poly__pCons_0 cls_cnj_Ozero_0 clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add clsarity_nat__Orderings_Olinorder clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1 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__Ring__and__Field_Ocomm__semiring__0 clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add 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__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__Ring__and__Field_Ocomm__ring clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring clsarity_Complex__Ocomplex__RealVector_Oreal__algebra clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add clsarity_Complex__Ocomplex__RealVector_Oreal__vector clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1 clsarity_Complex__Ocomplex__RealVector_Oreal__field 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_Onumber__ring clsarity_Complex__Ocomplex__Power_Opower clsarity_Complex__Ocomplex__SEQ_Obanach clsarity_Complex__Ocomplex__HOL_Ozero clsarity_Complex__Ocomplex__HOL_Oeq cls_conjecture_0 cls_conjecture_1
% 195.95/196.12
%------------------------------------------------------------------------------