TSTP Solution File: SWW180+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWW180+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Thu Jul 21 01:28:03 EDT 2022
% Result : Theorem 4.35s 4.55s
% Output : Refutation 4.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 73
% Syntax : Number of clauses : 84 ( 74 unt; 0 nHn; 84 RR)
% Number of literals : 97 ( 0 equ; 18 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 70 ( 69 usr; 1 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 10 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(2,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(108,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(109,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(110,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(111,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(112,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(113,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(114,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(115,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(116,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(117,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(118,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(119,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(120,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(121,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(122,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(123,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(124,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(125,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(126,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(127,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(128,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(129,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(130,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(131,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(132,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(133,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(134,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(135,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(136,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(137,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(138,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(139,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(140,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(141,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(142,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(143,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(144,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(145,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(146,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(147,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(148,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(149,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(150,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(151,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(152,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(153,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(154,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(155,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(156,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(157,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(158,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(159,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(160,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(161,axiom,
class_Groups_Ouminus(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(162,axiom,
class_Groups_Osgn__if(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(163,axiom,
class_Groups_Oabs__if(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(164,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(165,axiom,
class_Groups_Ominus(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(166,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(167,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(168,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(169,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(170,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(171,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(172,axiom,
class_Rings_Odvd(tc_RealDef_Oreal),
file('SWW180+1.p',unknown),
[] ).
cnf(324,axiom,
equal(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)),
file('SWW180+1.p',unknown),
[] ).
cnf(383,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(u)
| c_Orderings_Oord__class_Oless__eq(u,v,c_Groups_Oabs__class_Oabs(u,v)) ),
file('SWW180+1.p',unknown),
[] ).
cnf(390,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,u,v)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v) ),
file('SWW180+1.p',unknown),
[] ).
cnf(492,axiom,
( ~ class_Rings_Olinordered__semidom(u)
| c_Orderings_Oord__class_Oless(u,v,c_Groups_Oplus__class_Oplus(u,v,c_Groups_Oone__class_Oone(u))) ),
file('SWW180+1.p',unknown),
[] ).
cnf(553,axiom,
( ~ class_Rings_Ocomm__semiring__1(u)
| equal(c_Groups_Oplus__class_Oplus(u,v,w),c_Groups_Oplus__class_Oplus(u,w,v)) ),
file('SWW180+1.p',unknown),
[] ).
cnf(1344,axiom,
( ~ class_Groups_Oordered__ab__semigroup__add(u)
| ~ c_Orderings_Oord__class_Oless__eq(u,v,w)
| ~ c_Orderings_Oord__class_Oless__eq(u,x,y)
| c_Orderings_Oord__class_Oless__eq(u,c_Groups_Oplus__class_Oplus(u,x,v),c_Groups_Oplus__class_Oplus(u,y,w)) ),
file('SWW180+1.p',unknown),
[] ).
cnf(1583,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
file('SWW180+1.p',unknown),
[] ).
cnf(1772,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____)))),
inference(rew,[status(thm),theory(equality)],[324,1583]),
[iquote('0:Rew:324.0,1583.0')] ).
cnf(1812,plain,
( ~ class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ),
inference(res,[status(thm),theory(equality)],[1344,1772]),
[iquote('0:Res:1344.3,1772.0')] ).
cnf(1815,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____)))
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal),v_r),v_m____))) ),
inference(mrr,[status(thm)],[1812,116]),
[iquote('0:MRR:1812.0,116.0')] ).
cnf(2207,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)) ),
inference(spr,[status(thm),theory(equality)],[324,383]),
[iquote('0:SpR:324.0,383.1')] ).
cnf(2208,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)),
inference(ssi,[status(thm)],[2207,137,128,112,163,127,115,113,111,171,164,159,158,144,135,133,131,121,162,152,140,126,123,116,161,136,134,122,2,166,165,146,138,130,109,169,155,172,153,108,149,110,156,150,139,167,160,151,147,119,168,148,145,114,157,120,118,129,154,124,117,170,132,143,125,142,141]),
[iquote('0:SSi:2207.0,137.0,128.0,112.0,163.0,127.0,115.0,113.0,111.0,171.0,164.0,159.0,158.0,144.0,135.0,133.0,131.0,121.0,162.0,152.0,140.0,126.0,123.0,116.0,161.0,136.0,134.0,122.0,2.0,166.0,165.0,146.0,138.0,130.0,109.0,169.0,155.0,172.0,153.0,108.0,149.0,110.0,156.0,150.0,139.0,167.0,160.0,151.0,147.0,119.0,168.0,148.0,145.0,114.0,157.0,120.0,118.0,129.0,154.0,124.0,117.0,170.0,132.0,143.0,125.0,142.0,141.0')] ).
cnf(2209,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_c____))),
inference(mrr,[status(thm)],[1815,2208]),
[iquote('0:MRR:1815.1,2208.0')] ).
cnf(8213,plain,
( ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))) ),
inference(res,[status(thm),theory(equality)],[492,390]),
[iquote('0:Res:492.1,390.0')] ).
cnf(8224,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,c_Groups_Oone__class_Oone(tc_RealDef_Oreal))),
inference(ssi,[status(thm)],[8213,137,128,112,163,127,115,113,111,171,164,159,158,144,135,133,131,121,162,152,140,126,123,116,161,136,134,122,2,166,165,146,138,130,109,169,155,172,153,108,149,110,156,150,139,167,160,151,147,119,168,148,145,114,157,120,118,129,154,124,117,170,132,143,125,142,141]),
[iquote('0:SSi:8213.0,137.0,128.0,112.0,163.0,127.0,115.0,113.0,111.0,171.0,164.0,159.0,158.0,144.0,135.0,133.0,131.0,121.0,162.0,152.0,140.0,126.0,123.0,116.0,161.0,136.0,134.0,122.0,2.0,166.0,165.0,146.0,138.0,130.0,109.0,169.0,155.0,172.0,153.0,108.0,149.0,110.0,156.0,150.0,139.0,167.0,160.0,151.0,147.0,119.0,168.0,148.0,145.0,114.0,157.0,120.0,118.0,129.0,154.0,124.0,117.0,170.0,132.0,143.0,125.0,142.0,141.0')] ).
cnf(17446,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),u)) ),
inference(spr,[status(thm),theory(equality)],[553,8224]),
[iquote('0:SpR:553.1,8224.0')] ).
cnf(17675,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),u)),
inference(ssi,[status(thm)],[17446,137,128,112,163,127,115,113,111,171,164,159,158,144,135,133,131,121,162,152,140,126,123,116,161,136,134,122,2,166,165,146,138,130,109,169,155,172,153,108,149,110,156,150,139,167,160,151,147,119,168,148,145,114,157,120,118,129,154,124,117,170,132,143,125,142,141]),
[iquote('0:SSi:17446.0,137.0,128.0,112.0,163.0,127.0,115.0,113.0,111.0,171.0,164.0,159.0,158.0,144.0,135.0,133.0,131.0,121.0,162.0,152.0,140.0,126.0,123.0,116.0,161.0,136.0,134.0,122.0,2.0,166.0,165.0,146.0,138.0,130.0,109.0,169.0,155.0,172.0,153.0,108.0,149.0,110.0,156.0,150.0,139.0,167.0,160.0,151.0,147.0,119.0,168.0,148.0,145.0,114.0,157.0,120.0,118.0,129.0,154.0,124.0,117.0,170.0,132.0,143.0,125.0,142.0,141.0')] ).
cnf(17676,plain,
$false,
inference(unc,[status(thm)],[17675,2209]),
[iquote('0:UnC:17675.0,2209.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW180+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 5 14:41:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 4.35/4.55
% 4.35/4.55 SPASS V 3.9
% 4.35/4.55 SPASS beiseite: Proof found.
% 4.35/4.55 % SZS status Theorem
% 4.35/4.55 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.35/4.55 SPASS derived 13564 clauses, backtracked 0 clauses, performed 0 splits and kept 3973 clauses.
% 4.35/4.55 SPASS allocated 108471 KBytes.
% 4.35/4.55 SPASS spent 0:00:04.19 on the problem.
% 4.35/4.55 0:00:00.05 for the input.
% 4.35/4.55 0:00:00.34 for the FLOTTER CNF translation.
% 4.35/4.55 0:00:00.15 for inferences.
% 4.35/4.55 0:00:00.00 for the backtracking.
% 4.35/4.55 0:00:03.43 for the reduction.
% 4.35/4.55
% 4.35/4.55
% 4.35/4.55 Here is a proof with depth 2, length 84 :
% 4.35/4.55 % SZS output start Refutation
% See solution above
% 4.42/4.62 Formulae used in the proof : arity_RealDef__Oreal__Groups_Ocancel__comm__monoid__add arity_RealDef__Oreal__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct arity_RealDef__Oreal__Groups_Oordered__cancel__ab__semigroup__add arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add__imp__le arity_RealDef__Oreal__Rings_Olinordered__comm__semiring__strict arity_RealDef__Oreal__Rings_Olinordered__semiring__1__strict arity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra arity_RealDef__Oreal__Rings_Olinordered__semiring__strict arity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1 arity_RealDef__Oreal__Groups_Oordered__ab__semigroup__add arity_RealDef__Oreal__Groups_Oordered__ab__group__add__abs arity_RealDef__Oreal__RealVector_Oreal__normed__algebra arity_RealDef__Oreal__Groups_Oordered__comm__monoid__add arity_RealDef__Oreal__Groups_Olinordered__ab__group__add arity_RealDef__Oreal__Groups_Ocancel__ab__semigroup__add arity_RealDef__Oreal__Rings_Oring__1__no__zero__divisors arity_RealDef__Oreal__Rings_Oordered__cancel__semiring arity_RealDef__Oreal__RealVector_Oreal__normed__vector arity_RealDef__Oreal__Rings_Olinordered__ring__strict arity_RealDef__Oreal__Rings_Oring__no__zero__divisors arity_RealDef__Oreal__Rings_Oordered__comm__semiring arity_RealDef__Oreal__Rings_Olinordered__semiring__1 arity_RealDef__Oreal__Groups_Oordered__ab__group__add arity_RealDef__Oreal__Groups_Ocancel__semigroup__add arity_RealDef__Oreal__Rings_Olinordered__semiring arity_RealDef__Oreal__Rings_Olinordered__semidom arity_RealDef__Oreal__Groups_Oab__semigroup__mult arity_RealDef__Oreal__Groups_Ocomm__monoid__mult arity_RealDef__Oreal__Groups_Oab__semigroup__add arity_RealDef__Oreal__Rings_Oordered__semiring arity_RealDef__Oreal__Rings_Oordered__ring__abs arity_RealDef__Oreal__Rings_Ono__zero__divisors arity_RealDef__Oreal__Groups_Ocomm__monoid__add arity_RealDef__Oreal__Rings_Olinordered__ring arity_RealDef__Oreal__Rings_Olinordered__idom arity_RealDef__Oreal__Rings_Ocomm__semiring__1 arity_RealDef__Oreal__Rings_Ocomm__semiring__0 arity_RealDef__Oreal__Rings_Ocomm__semiring arity_RealDef__Oreal__Groups_Oab__group__add arity_RealDef__Oreal__Rings_Ozero__neq__one arity_RealDef__Oreal__Rings_Oordered__ring arity_RealDef__Oreal__Orderings_Opreorder arity_RealDef__Oreal__Orderings_Olinorder arity_RealDef__Oreal__Groups_Omonoid__mult arity_RealDef__Oreal__Rings_Ocomm__ring__1 arity_RealDef__Oreal__Groups_Omonoid__add arity_RealDef__Oreal__Rings_Osemiring__0 arity_RealDef__Oreal__Groups_Ogroup__add arity_RealDef__Oreal__Rings_Omult__zero arity_RealDef__Oreal__Rings_Ocomm__ring arity_RealDef__Oreal__Orderings_Oorder arity_RealDef__Oreal__Int_Oring__char__0 arity_RealDef__Oreal__Rings_Osemiring arity_RealDef__Oreal__Orderings_Oord arity_RealDef__Oreal__Groups_Ouminus arity_RealDef__Oreal__Groups_Osgn__if arity_RealDef__Oreal__Groups_Oabs__if arity_RealDef__Oreal__Rings_Oring__1 arity_RealDef__Oreal__Groups_Ominus arity_RealDef__Oreal__Fields_Ofield arity_RealDef__Oreal__Power_Opower arity_RealDef__Oreal__Groups_Ozero arity_RealDef__Oreal__Rings_Oring arity_RealDef__Oreal__Rings_Oidom arity_RealDef__Oreal__Groups_Oone arity_RealDef__Oreal__Rings_Odvd fact_real__norm__def fact_abs__ge__self fact_less__eq__real__def fact_less__add__one fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J fact_add__mono conj_0
% 4.42/4.62
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