TSTP Solution File: ALG370-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : ALG370-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n032.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 18:03:30 EDT 2022
% Result : Unsatisfiable 5.69s 5.88s
% Output : Refutation 5.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 100
% Syntax : Number of clauses : 119 ( 107 unt; 0 nHn; 119 RR)
% Number of literals : 134 ( 0 equ; 19 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 62 ( 61 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 12 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(26,axiom,
( ~ class_Orderings_Oorder(u)
| ~ c_HOL_Oord__class_Oless(v,w,u)
| ~ c_lessequals(x,v,u)
| c_HOL_Oord__class_Oless(x,w,u) ),
file('ALG370-1.p',unknown),
[] ).
cnf(195,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(v,w,u),w,u),v) ),
file('ALG370-1.p',unknown),
[] ).
cnf(200,axiom,
( ~ class_OrderedGroup_Ogroup__add(u)
| equal(c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(v,w,u),w,u),v) ),
file('ALG370-1.p',unknown),
[] ).
cnf(267,axiom,
( ~ class_RealVector_Ometric__space(u)
| equal(c_RealVector_Odist__class_Odist(v,w,u),c_RealVector_Odist__class_Odist(w,v,u)) ),
file('ALG370-1.p',unknown),
[] ).
cnf(364,axiom,
equal(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(u,v,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Odist__class_Odist(u,v,tc_Complex_Ocomplex)),
file('ALG370-1.p',unknown),
[] ).
cnf(386,axiom,
( ~ class_RealVector_Oreal__normed__div__algebra(u)
| equal(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(v,u),c_RealVector_Onorm__class_Onorm(w,u),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(v,w,u),u)) ),
file('ALG370-1.p',unknown),
[] ).
cnf(422,axiom,
c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(423,axiom,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(426,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(427,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(428,axiom,
class_OrderedGroup_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(429,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(481,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(482,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(483,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(484,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(485,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(486,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(487,axiom,
class_OrderedGroup_Opordered__ab__group__add__abs(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(488,axiom,
class_OrderedGroup_Olordered__ab__group__add__abs(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(489,axiom,
class_OrderedGroup_Opordered__comm__monoid__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(490,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(491,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(492,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(493,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(494,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(495,axiom,
class_OrderedGroup_Olordered__ab__group__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(496,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(497,axiom,
class_Ring__and__Field_Opordered__semiring(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(498,axiom,
class_Ring__and__Field_Opordered__ring__abs(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(499,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(500,axiom,
class_Ring__and__Field_Oordered__semiring(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(501,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(502,axiom,
class_Ring__and__Field_Oordered__semidom(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(503,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(504,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(505,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(506,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(507,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(508,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(509,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(510,axiom,
class_Ring__and__Field_Opordered__ring(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(511,axiom,
class_Ring__and__Field_Olordered__ring(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(512,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(513,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(514,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(515,axiom,
class_Ring__and__Field_Oordered__idom(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(516,axiom,
class_Ring__and__Field_Omult__mono1(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(517,axiom,
class_RealVector_Oreal__algebra__1(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(518,axiom,
class_OrderedGroup_Oab__group__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(519,axiom,
class_Ring__and__Field_Omult__zero(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(520,axiom,
class_Ring__and__Field_Omult__mono(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(521,axiom,
class_Ring__and__Field_Ocomm__ring(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(522,axiom,
class_OrderedGroup_Omonoid__mult(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(523,axiom,
class_Ring__and__Field_Osemiring(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(524,axiom,
class_RealVector_Ometric__space(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(525,axiom,
class_OrderedGroup_Omonoid__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(526,axiom,
class_OrderedGroup_Ogroup__add(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(527,axiom,
class_Ring__and__Field_Oabs__if(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(528,axiom,
class_RealVector_Odist__norm(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(529,axiom,
class_Ring__and__Field_Oring(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(530,axiom,
class_Ring__and__Field_Oidom(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(531,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(532,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(533,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(534,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(535,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(536,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(537,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(538,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(539,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(540,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(541,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(542,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(543,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(544,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(545,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(546,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(547,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(548,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(549,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(550,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(551,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(552,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(553,axiom,
class_RealVector_Oreal__algebra__1(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(554,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(555,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(556,axiom,
class_Ring__and__Field_Ocomm__ring(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(557,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(558,axiom,
class_Ring__and__Field_Osemiring(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(559,axiom,
class_RealVector_Ometric__space(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(560,axiom,
class_OrderedGroup_Omonoid__add(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(561,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(562,axiom,
class_RealVector_Odist__norm(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(563,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(564,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(565,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(566,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(567,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('ALG370-1.p',unknown),
[] ).
cnf(614,axiom,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
file('ALG370-1.p',unknown),
[] ).
cnf(632,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_w____,v_z,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[364,614]),
[iquote('0:Rew:364.0,614.0')] ).
cnf(635,plain,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_w____,v_z,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[364,423]),
[iquote('0:Rew:364.0,423.0')] ).
cnf(1090,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| equal(c_RealVector_Odist__class_Odist(c_HOL_Oplus__class_Oplus(u,v,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[200,364]),
[iquote('0:SpR:200.1,364.0')] ).
cnf(1101,plain,
equal(c_RealVector_Odist__class_Odist(c_HOL_Oplus__class_Oplus(u,v,tc_Complex_Ocomplex),v,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(u,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[1090,562,541,539,565,552,550,549,548,546,542,538,560,557,555,540,558,553,537,427,426,567,563,561,559,556,547,554,545,566,544,564,551,543]),
[iquote('0:SSi:1090.0,562.0,541.0,539.0,565.0,552.0,550.0,549.0,548.0,546.0,542.0,538.0,560.0,557.0,555.0,540.0,558.0,553.0,537.0,427.0,426.0,567.0,563.0,561.0,559.0,556.0,547.0,554.0,545.0,566.0,544.0,564.0,551.0,543.0')] ).
cnf(1201,plain,
( ~ class_RealVector_Ometric__space(tc_Complex_Ocomplex)
| equal(c_RealVector_Odist__class_Odist(u,c_HOL_Oplus__class_Oplus(v,u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(v,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[267,1101]),
[iquote('0:SpR:267.1,1101.0')] ).
cnf(1226,plain,
equal(c_RealVector_Odist__class_Odist(u,c_HOL_Oplus__class_Oplus(v,u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(v,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[1201,562,541,539,565,552,550,549,548,546,542,538,560,557,555,540,558,553,537,427,426,567,563,561,559,556,547,554,545,566,544,564,551,543]),
[iquote('0:SSi:1201.0,562.0,541.0,539.0,565.0,552.0,550.0,549.0,548.0,546.0,542.0,538.0,560.0,557.0,555.0,540.0,558.0,553.0,537.0,427.0,426.0,567.0,563.0,561.0,559.0,556.0,547.0,554.0,545.0,566.0,544.0,564.0,551.0,543.0')] ).
cnf(1297,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| equal(c_RealVector_Onorm__class_Onorm(c_HOL_Ominus__class_Ominus(u,v,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_RealVector_Odist__class_Odist(v,u,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[195,1226]),
[iquote('0:SpR:195.1,1226.0')] ).
cnf(1306,plain,
( ~ class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex)
| equal(c_RealVector_Odist__class_Odist(u,v,tc_Complex_Ocomplex),c_RealVector_Odist__class_Odist(v,u,tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[364,1297]),
[iquote('0:Rew:364.0,1297.1')] ).
cnf(1307,plain,
equal(c_RealVector_Odist__class_Odist(u,v,tc_Complex_Ocomplex),c_RealVector_Odist__class_Odist(v,u,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[1306,562,541,539,565,552,550,549,548,546,542,538,560,557,555,540,558,553,537,427,426,567,563,561,559,556,547,554,545,566,544,564,551,543]),
[iquote('0:SSi:1306.0,562.0,541.0,539.0,565.0,552.0,550.0,549.0,548.0,546.0,542.0,538.0,560.0,557.0,555.0,540.0,558.0,553.0,537.0,427.0,426.0,567.0,563.0,561.0,559.0,556.0,547.0,554.0,545.0,566.0,544.0,564.0,551.0,543.0')] ).
cnf(1316,plain,
~ c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_z,v_w____,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),v_e,tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[1307,632]),
[iquote('0:Rew:1307.0,632.0')] ).
cnf(1317,plain,
c_lessequals(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(v_z,v_w____,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_RealDef_Oreal),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[1307,635]),
[iquote('0:Rew:1307.0,635.0')] ).
cnf(9679,plain,
( ~ class_Orderings_Oorder(tc_RealDef_Oreal)
| ~ c_lessequals(u,c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(u,v_e,tc_RealDef_Oreal) ),
inference(res,[status(thm),theory(equality)],[422,26]),
[iquote('0:Res:422.0,26.1')] ).
cnf(9703,plain,
( ~ c_lessequals(u,c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal)
| c_HOL_Oord__class_Oless(u,v_e,tc_RealDef_Oreal) ),
inference(ssi,[status(thm)],[9679,528,511,499,493,527,516,488,483,534,520,514,512,509,508,506,501,500,497,491,525,522,519,496,486,484,523,517,498,490,429,428,536,529,481,526,524,521,507,494,532,518,505,502,495,533,531,535,504,489,530,510,482,513,485,487,503,515,492]),
[iquote('0:SSi:9679.0,528.0,511.0,499.0,493.0,527.0,516.0,488.0,483.0,534.0,520.0,514.0,512.0,509.0,508.0,506.0,501.0,500.0,497.0,491.0,525.0,522.0,519.0,496.0,486.0,484.0,523.0,517.0,498.0,490.0,429.0,428.0,536.0,529.0,481.0,526.0,524.0,521.0,507.0,494.0,532.0,518.0,505.0,502.0,495.0,533.0,531.0,535.0,504.0,489.0,530.0,510.0,482.0,513.0,485.0,487.0,503.0,515.0,492.0')] ).
cnf(11303,plain,
( ~ class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex)
| equal(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(u,v,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(w,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(u,v,tc_Complex_Ocomplex),w,tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[364,386]),
[iquote('0:SpR:364.0,386.1')] ).
cnf(11337,plain,
equal(c_HOL_Otimes__class_Otimes(c_RealVector_Odist__class_Odist(u,v,tc_Complex_Ocomplex),c_RealVector_Onorm__class_Onorm(w,tc_Complex_Ocomplex),tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(u,v,tc_Complex_Ocomplex),w,tc_Complex_Ocomplex),tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[11303,562,541,539,565,552,550,549,548,546,542,538,560,557,555,540,558,553,537,427,426,567,563,561,559,556,547,554,545,566,544,564,551,543]),
[iquote('0:SSi:11303.0,562.0,541.0,539.0,565.0,552.0,550.0,549.0,548.0,546.0,542.0,538.0,560.0,557.0,555.0,540.0,558.0,553.0,537.0,427.0,426.0,567.0,563.0,561.0,559.0,556.0,547.0,554.0,545.0,566.0,544.0,564.0,551.0,543.0')] ).
cnf(11342,plain,
~ c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(v_z,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[11337,1316]),
[iquote('0:Rew:11337.0,1316.0')] ).
cnf(11344,plain,
c_lessequals(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(v_z,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(v_da____,v_m____,tc_RealDef_Oreal),tc_RealDef_Oreal),
inference(rew,[status(thm),theory(equality)],[11337,1317]),
[iquote('0:Rew:11337.0,1317.0')] ).
cnf(23369,plain,
c_HOL_Oord__class_Oless(c_RealVector_Onorm__class_Onorm(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(v_z,v_w____,tc_Complex_Ocomplex),c_Polynomial_Opoly(v_cs____,c_HOL_Ominus__class_Ominus(v_w____,v_z,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_e,tc_RealDef_Oreal),
inference(res,[status(thm),theory(equality)],[11344,9703]),
[iquote('0:Res:11344.0,9703.0')] ).
cnf(23382,plain,
$false,
inference(mrr,[status(thm)],[23369,11342]),
[iquote('0:MRR:23369.0,11342.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : ALG370-1 : TPTP v8.1.0. Released v4.1.0.
% 0.09/0.11 % Command : run_spass %d %s
% 0.09/0.30 % Computer : n032.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 600
% 0.09/0.30 % DateTime : Wed Jun 8 21:49:22 EDT 2022
% 0.09/0.30 % CPUTime :
% 5.69/5.88
% 5.69/5.88 SPASS V 3.9
% 5.69/5.88 SPASS beiseite: Proof found.
% 5.69/5.88 % SZS status Theorem
% 5.69/5.88 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.69/5.88 SPASS derived 18377 clauses, backtracked 9 clauses, performed 1 splits and kept 5363 clauses.
% 5.69/5.88 SPASS allocated 94413 KBytes.
% 5.69/5.88 SPASS spent 0:00:05.54 on the problem.
% 5.69/5.88 0:00:00.04 for the input.
% 5.69/5.88 0:00:00.00 for the FLOTTER CNF translation.
% 5.69/5.88 0:00:00.23 for inferences.
% 5.69/5.88 0:00:00.00 for the backtracking.
% 5.69/5.88 0:00:05.16 for the reduction.
% 5.69/5.88
% 5.69/5.88
% 5.69/5.88 Here is a proof with depth 3, length 119 :
% 5.69/5.88 % SZS output start Refutation
% See solution above
% 5.69/5.88 Formulae used in the proof : cls_xt1_I7_J_0 cls_diff__add__cancel_0 cls_add__diff__cancel_0 cls_dist__commute_0 cls_dist__complex__def_0 cls_norm__mult_0 cls_CHAINED_0 cls_CHAINED_0_01 clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1 clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1 clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1 clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1 clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0 clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1 clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1 clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult clsarity_RealDef__Oreal__Ring__and__Field_Osemiring clsarity_RealDef__Oreal__RealVector_Ometric__space clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if clsarity_RealDef__Oreal__RealVector_Odist__norm clsarity_RealDef__Oreal__Ring__and__Field_Oring clsarity_RealDef__Oreal__Ring__and__Field_Oidom clsarity_RealDef__Oreal__Orderings_Opreorder clsarity_RealDef__Oreal__Orderings_Olinorder clsarity_RealDef__Oreal__Orderings_Oorder clsarity_RealDef__Oreal__Int_Oring__char__0 clsarity_RealDef__Oreal__Int_Onumber__ring clsarity_RealDef__Oreal__Int_Onumber 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_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_Ocomm__semiring clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1 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_Ometric__space clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add clsarity_Complex__Ocomplex__RealVector_Odist__norm clsarity_Complex__Ocomplex__Ring__and__Field_Oring clsarity_Complex__Ocomplex__Ring__and__Field_Oidom clsarity_Complex__Ocomplex__Int_Oring__char__0 clsarity_Complex__Ocomplex__Int_Onumber__ring clsarity_Complex__Ocomplex__Int_Onumber cls_conjecture_0
% 5.89/6.08
%------------------------------------------------------------------------------