TSTP Solution File: SWW233+1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWW233+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n029.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 01:28:09 EDT 2022
% Result : Theorem 171.29s 171.48s
% Output : Refutation 173.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 114
% Syntax : Number of clauses : 142 ( 117 unt; 3 nHn; 142 RR)
% Number of literals : 178 ( 0 equ; 42 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 67 ( 66 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(1,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(2,axiom,
class_Groups_Ocancel__comm__monoid__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(102,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(103,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(104,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(105,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(106,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(107,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(108,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(109,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(110,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(111,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(112,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(113,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(114,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(115,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(116,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(117,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(118,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(119,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(120,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(121,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(122,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(123,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(124,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(125,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(126,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(127,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(128,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(129,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(130,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(131,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(132,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(133,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(134,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(135,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(136,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(137,axiom,
class_Rings_Ocomm__semiring__0(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(138,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(139,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(140,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(141,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(142,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(143,axiom,
class_Orderings_Opreorder(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(144,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(145,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(146,axiom,
class_Rings_Ocomm__ring__1(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(147,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(148,axiom,
class_Rings_Osemiring__0(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(149,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(150,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(151,axiom,
class_Rings_Ocomm__ring(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(152,axiom,
class_Orderings_Oorder(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(153,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(154,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(155,axiom,
class_Orderings_Oord(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(156,axiom,
class_Groups_Osgn__if(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(157,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(158,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(159,axiom,
class_Power_Opower(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(160,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(161,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(162,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(163,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('SWW233+1.p',unknown),
[] ).
cnf(164,axiom,
class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(165,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(166,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(167,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(168,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(169,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(170,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(171,axiom,
class_Rings_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(172,axiom,
class_Groups_Ocancel__semigroup__add(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(173,axiom,
class_Groups_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(174,axiom,
class_Groups_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(175,axiom,
class_Groups_Oab__semigroup__add(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(176,axiom,
class_Rings_Ono__zero__divisors(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(177,axiom,
class_Groups_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(178,axiom,
class_Rings_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(179,axiom,
class_Rings_Ocomm__semiring__0(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(180,axiom,
class_RealVector_Oreal__field(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(181,axiom,
class_Rings_Ocomm__semiring(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(182,axiom,
class_Groups_Oab__group__add(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(183,axiom,
class_Rings_Ozero__neq__one(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(184,axiom,
class_Groups_Omonoid__mult(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(185,axiom,
class_Rings_Ocomm__ring__1(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(186,axiom,
class_Groups_Omonoid__add(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(187,axiom,
class_Rings_Osemiring__0(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(188,axiom,
class_Groups_Ogroup__add(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(189,axiom,
class_Rings_Omult__zero(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(190,axiom,
class_Rings_Ocomm__ring(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(191,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(192,axiom,
class_Rings_Osemiring(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(193,axiom,
class_Rings_Oring__1(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(194,axiom,
class_Fields_Ofield(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(195,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(196,axiom,
class_Groups_Ozero(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(197,axiom,
class_Rings_Oring(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(198,axiom,
class_Rings_Oidom(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(199,axiom,
class_Groups_Oone(tc_Complex_Ocomplex),
file('SWW233+1.p',unknown),
[] ).
cnf(307,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('SWW233+1.p',unknown),
[] ).
cnf(349,axiom,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v,u) ),
file('SWW233+1.p',unknown),
[] ).
cnf(395,axiom,
( ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,u,v)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v) ),
file('SWW233+1.p',unknown),
[] ).
cnf(396,axiom,
( ~ equal(u,v)
| ~ c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,u,v) ),
file('SWW233+1.p',unknown),
[] ).
cnf(490,axiom,
c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u))),
file('SWW233+1.p',unknown),
[] ).
cnf(497,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('SWW233+1.p',unknown),
[] ).
cnf(551,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
file('SWW233+1.p',unknown),
[] ).
cnf(578,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('SWW233+1.p',unknown),
[] ).
cnf(635,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v,u)
| equal(v,u) ),
file('SWW233+1.p',unknown),
[] ).
cnf(713,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v,w)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,w) ),
file('SWW233+1.p',unknown),
[] ).
cnf(714,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(u)
| ~ c_Orderings_Oord__class_Oless__eq(u,c_Groups_Ozero__class_Ozero(u),v)
| equal(c_Groups_Oabs__class_Oabs(u,v),v) ),
file('SWW233+1.p',unknown),
[] ).
cnf(716,axiom,
( ~ class_RealVector_Oreal__normed__vector(u)
| ~ equal(v,c_Groups_Ozero__class_Ozero(u))
| equal(c_RealVector_Onorm__class_Onorm(u,v),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
file('SWW233+1.p',unknown),
[] ).
cnf(785,axiom,
( ~ class_RealVector_Oreal__normed__vector(u)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(u,v),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| equal(v,c_Groups_Ozero__class_Ozero(u)) ),
file('SWW233+1.p',unknown),
[] ).
cnf(915,axiom,
( ~ class_Orderings_Opreorder(u)
| ~ c_Orderings_Oord__class_Oless__eq(u,v,w)
| ~ c_Orderings_Oord__class_Oless__eq(u,x,v)
| c_Orderings_Oord__class_Oless__eq(u,x,w) ),
file('SWW233+1.p',unknown),
[] ).
cnf(1815,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),v_r____),
inference(res,[status(thm),theory(equality)],[349,307]),
[iquote('0:Res:349.1,307.0')] ).
cnf(4195,plain,
~ equal(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(res,[status(thm),theory(equality)],[490,396]),
[iquote('0:Res:490.0,396.1')] ).
cnf(4196,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u))),
inference(res,[status(thm),theory(equality)],[490,395]),
[iquote('0:Res:490.0,395.0')] ).
cnf(7391,plain,
( ~ class_Rings_Olinordered__semidom(tc_RealDef_Oreal)
| ~ equal(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),u) ),
inference(res,[status(thm),theory(equality)],[497,396]),
[iquote('0:Res:497.1,396.1')] ).
cnf(7392,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)],[497,395]),
[iquote('0:Res:497.1,395.0')] ).
cnf(7405,plain,
~ equal(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),u),
inference(ssi,[status(thm)],[7391,138,156,131,122,106,157,121,116,109,107,105,163,158,154,153,139,129,127,125,115,161,151,148,147,146,134,120,117,110,141,132,130,128,2,150,124,123,103,149,140,102,144,104,145,133,114,162,159,155,142,113,143,112,160,108,137,152,111,126,118,136,119,135]),
[iquote('0:SSi:7391.0,138.0,156.0,131.0,122.0,106.0,157.0,121.0,116.0,109.0,107.0,105.0,163.0,158.0,154.0,153.0,139.0,129.0,127.0,125.0,115.0,161.0,151.0,148.0,147.0,146.0,134.0,120.0,117.0,110.0,141.0,132.0,130.0,128.0,2.0,150.0,124.0,123.0,103.0,149.0,140.0,102.0,144.0,104.0,145.0,133.0,114.0,162.0,159.0,155.0,142.0,113.0,143.0,112.0,160.0,108.0,137.0,152.0,111.0,126.0,118.0,136.0,119.0,135.0')] ).
cnf(7406,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)],[7392,138,156,131,122,106,157,121,116,109,107,105,163,158,154,153,139,129,127,125,115,161,151,148,147,146,134,120,117,110,141,132,130,128,2,150,124,123,103,149,140,102,144,104,145,133,114,162,159,155,142,113,143,112,160,108,137,152,111,126,118,136,119,135]),
[iquote('0:SSi:7392.0,138.0,156.0,131.0,122.0,106.0,157.0,121.0,116.0,109.0,107.0,105.0,163.0,158.0,154.0,153.0,139.0,129.0,127.0,125.0,115.0,161.0,151.0,148.0,147.0,146.0,134.0,120.0,117.0,110.0,141.0,132.0,130.0,128.0,2.0,150.0,124.0,123.0,103.0,149.0,140.0,102.0,144.0,104.0,145.0,133.0,114.0,162.0,159.0,155.0,142.0,113.0,143.0,112.0,160.0,108.0,137.0,152.0,111.0,126.0,118.0,136.0,119.0,135.0')] ).
cnf(23126,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| equal(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(res,[status(thm),theory(equality)],[4196,635]),
[iquote('0:Res:4196.0,635.0')] ).
cnf(23143,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),u)
| equal(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),u) ),
inference(res,[status(thm),theory(equality)],[7406,635]),
[iquote('0:Res:7406.0,635.0')] ).
cnf(23203,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),u),
inference(mrr,[status(thm)],[23143,7405]),
[iquote('0:MRR:23143.1,7405.0')] ).
cnf(23219,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(mrr,[status(thm)],[23126,4195]),
[iquote('0:MRR:23126.1,4195.0')] ).
cnf(29220,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ equal(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_z____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(spr,[status(thm),theory(equality)],[716,551]),
[iquote('0:SpR:716.2,551.0')] ).
cnf(29252,plain,
( ~ equal(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_z____)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____)),c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(ssi,[status(thm)],[29220,180,193,169,166,165,199,194,192,191,181,175,173,168,197,190,187,186,185,171,183,176,174,1,189,172,188,182,164,184,177,198,195,167,196,179,170,178]),
[iquote('0:SSi:29220.0,180.0,193.0,169.0,166.0,165.0,199.0,194.0,192.0,191.0,181.0,175.0,173.0,168.0,197.0,190.0,187.0,186.0,185.0,171.0,183.0,176.0,174.0,1.0,189.0,172.0,188.0,182.0,164.0,184.0,177.0,198.0,195.0,167.0,196.0,179.0,170.0,178.0')] ).
cnf(29253,plain,
~ equal(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_z____),
inference(mrr,[status(thm)],[29252,23219]),
[iquote('0:MRR:29252.1,23219.0')] ).
cnf(32848,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,u)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____),u) ),
inference(res,[status(thm),theory(equality)],[1815,713]),
[iquote('0:Res:1815.0,713.0')] ).
cnf(33248,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| equal(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u),u) ),
inference(res,[status(thm),theory(equality)],[349,714]),
[iquote('0:Res:349.0,714.1')] ).
cnf(33419,plain,
( c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| equal(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u),u) ),
inference(ssi,[status(thm)],[33248,138,156,131,122,106,157,121,116,109,107,105,163,158,154,153,139,129,127,125,115,161,151,148,147,146,134,120,117,110,141,132,130,128,2,150,124,123,103,149,140,102,144,104,145,133,114,162,159,155,142,113,143,112,160,108,137,152,111,126,118,136,119,135]),
[iquote('0:SSi:33248.0,138.0,156.0,131.0,122.0,106.0,157.0,121.0,116.0,109.0,107.0,105.0,163.0,158.0,154.0,153.0,139.0,129.0,127.0,125.0,115.0,161.0,151.0,148.0,147.0,146.0,134.0,120.0,117.0,110.0,141.0,132.0,130.0,128.0,2.0,150.0,124.0,123.0,103.0,149.0,140.0,102.0,144.0,104.0,145.0,133.0,114.0,162.0,159.0,155.0,142.0,113.0,143.0,112.0,160.0,108.0,137.0,152.0,111.0,126.0,118.0,136.0,119.0,135.0')] ).
cnf(60415,plain,
( ~ class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| equal(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_z____) ),
inference(res,[status(thm),theory(equality)],[32848,785]),
[iquote('0:Res:32848.1,785.1')] ).
cnf(60417,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| equal(c_Groups_Ozero__class_Ozero(tc_Complex_Ocomplex),v_z____) ),
inference(ssi,[status(thm)],[60415,180,193,169,166,165,199,194,192,191,181,175,173,168,197,190,187,186,185,171,183,176,174,1,189,172,188,182,164,184,177,198,195,167,196,179,170,178]),
[iquote('0:SSi:60415.0,180.0,193.0,169.0,166.0,165.0,199.0,194.0,192.0,191.0,181.0,175.0,173.0,168.0,197.0,190.0,187.0,186.0,185.0,171.0,183.0,176.0,174.0,1.0,189.0,172.0,188.0,182.0,164.0,184.0,177.0,198.0,195.0,167.0,196.0,179.0,170.0,178.0')] ).
cnf(60418,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,v_r____,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)),
inference(mrr,[status(thm)],[60417,29253]),
[iquote('0:MRR:60417.1,29253.0')] ).
cnf(60515,plain,
equal(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,v_r____),v_r____),
inference(res,[status(thm),theory(equality)],[33419,60418]),
[iquote('0:Res:33419.0,60418.0')] ).
cnf(60523,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oone__class_Oone(tc_RealDef_Oreal),v_r____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(rew,[status(thm),theory(equality)],[60515,551]),
[iquote('0:Rew:60515.0,551.0')] ).
cnf(60576,plain,
( ~ class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_r____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)) ),
inference(spr,[status(thm),theory(equality)],[578,60523]),
[iquote('0:SpR:578.1,60523.0')] ).
cnf(60580,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_r____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____)),
inference(ssi,[status(thm)],[60576,138,156,131,122,106,157,121,116,109,107,105,163,158,154,153,139,129,127,125,115,161,151,148,147,146,134,120,117,110,141,132,130,128,2,150,124,123,103,149,140,102,144,104,145,133,114,162,159,155,142,113,143,112,160,108,137,152,111,126,118,136,119,135]),
[iquote('0:SSi:60576.0,138.0,156.0,131.0,122.0,106.0,157.0,121.0,116.0,109.0,107.0,105.0,163.0,158.0,154.0,153.0,139.0,129.0,127.0,125.0,115.0,161.0,151.0,148.0,147.0,146.0,134.0,120.0,117.0,110.0,141.0,132.0,130.0,128.0,2.0,150.0,124.0,123.0,103.0,149.0,140.0,102.0,144.0,104.0,145.0,133.0,114.0,162.0,159.0,155.0,142.0,113.0,143.0,112.0,160.0,108.0,137.0,152.0,111.0,126.0,118.0,136.0,119.0,135.0')] ).
cnf(78849,plain,
( ~ class_Orderings_Opreorder(tc_RealDef_Oreal)
| ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v_r____) ),
inference(res,[status(thm),theory(equality)],[1815,915]),
[iquote('0:Res:1815.0,915.1')] ).
cnf(79194,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,v_z____))
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v_r____) ),
inference(ssi,[status(thm)],[78849,138,156,131,122,106,157,121,116,109,107,105,163,158,154,153,139,129,127,125,115,161,151,148,147,146,134,120,117,110,141,132,130,128,2,150,124,123,103,149,140,102,144,104,145,133,114,162,159,155,142,113,143,112,160,108,137,152,111,126,118,136,119,135]),
[iquote('0:SSi:78849.0,138.0,156.0,131.0,122.0,106.0,157.0,121.0,116.0,109.0,107.0,105.0,163.0,158.0,154.0,153.0,139.0,129.0,127.0,125.0,115.0,161.0,151.0,148.0,147.0,146.0,134.0,120.0,117.0,110.0,141.0,132.0,130.0,128.0,2.0,150.0,124.0,123.0,103.0,149.0,140.0,102.0,144.0,104.0,145.0,133.0,114.0,162.0,159.0,155.0,142.0,113.0,143.0,112.0,160.0,108.0,137.0,152.0,111.0,126.0,118.0,136.0,119.0,135.0')] ).
cnf(134851,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v_r____,c_Groups_Oone__class_Oone(tc_RealDef_Oreal)),v_r____),
inference(res,[status(thm),theory(equality)],[60580,79194]),
[iquote('0:Res:60580.0,79194.0')] ).
cnf(134888,plain,
$false,
inference(mrr,[status(thm)],[134851,23203]),
[iquote('0:MRR:134851.0,23203.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW233+1 : TPTP v8.1.0. Released v5.2.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.33 % Computer : n029.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jun 5 17:28:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 171.29/171.48
% 171.29/171.48 SPASS V 3.9
% 171.29/171.48 SPASS beiseite: Proof found.
% 171.29/171.48 % SZS status Theorem
% 171.29/171.48 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 171.29/171.48 SPASS derived 107862 clauses, backtracked 0 clauses, performed 4 splits and kept 27745 clauses.
% 171.29/171.48 SPASS allocated 184806 KBytes.
% 171.29/171.48 SPASS spent 0:2:50.94 on the problem.
% 171.29/171.48 0:00:00.06 for the input.
% 171.29/171.48 0:00:00.63 for the FLOTTER CNF translation.
% 171.29/171.48 0:00:01.85 for inferences.
% 171.29/171.48 0:00:09.58 for the backtracking.
% 171.29/171.48 0:2:37.08 for the reduction.
% 171.29/171.48
% 171.29/171.48
% 171.29/171.48 Here is a proof with depth 4, length 142 :
% 171.29/171.48 % SZS output start Refutation
% See solution above
% 173.54/173.79 Formulae used in the proof : arity_Complex__Ocomplex__Groups_Ocancel__comm__monoid__add 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__RealVector_Oreal__field 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_Osgn__if arity_RealDef__Oreal__Rings_Oring__1 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_Complex__Ocomplex__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct arity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1 arity_Complex__Ocomplex__RealVector_Oreal__normed__algebra arity_Complex__Ocomplex__Groups_Ocancel__ab__semigroup__add arity_Complex__Ocomplex__Rings_Oring__1__no__zero__divisors arity_Complex__Ocomplex__RealVector_Oreal__normed__vector arity_Complex__Ocomplex__Rings_Oring__no__zero__divisors arity_Complex__Ocomplex__Groups_Ocancel__semigroup__add arity_Complex__Ocomplex__Groups_Oab__semigroup__mult arity_Complex__Ocomplex__Groups_Ocomm__monoid__mult arity_Complex__Ocomplex__Groups_Oab__semigroup__add arity_Complex__Ocomplex__Rings_Ono__zero__divisors arity_Complex__Ocomplex__Groups_Ocomm__monoid__add arity_Complex__Ocomplex__Rings_Ocomm__semiring__1 arity_Complex__Ocomplex__Rings_Ocomm__semiring__0 arity_Complex__Ocomplex__RealVector_Oreal__field arity_Complex__Ocomplex__Rings_Ocomm__semiring arity_Complex__Ocomplex__Groups_Oab__group__add arity_Complex__Ocomplex__Rings_Ozero__neq__one arity_Complex__Ocomplex__Groups_Omonoid__mult arity_Complex__Ocomplex__Rings_Ocomm__ring__1 arity_Complex__Ocomplex__Groups_Omonoid__add arity_Complex__Ocomplex__Rings_Osemiring__0 arity_Complex__Ocomplex__Groups_Ogroup__add arity_Complex__Ocomplex__Rings_Omult__zero arity_Complex__Ocomplex__Rings_Ocomm__ring arity_Complex__Ocomplex__Int_Oring__char__0 arity_Complex__Ocomplex__Rings_Osemiring arity_Complex__Ocomplex__Rings_Oring__1 arity_Complex__Ocomplex__Fields_Ofield arity_Complex__Ocomplex__Power_Opower arity_Complex__Ocomplex__Groups_Ozero arity_Complex__Ocomplex__Rings_Oring arity_Complex__Ocomplex__Rings_Oidom arity_Complex__Ocomplex__Groups_Oone conj_0 fact_real__le__linear fact_real__less__def fact_abs__add__one__gt__zero fact_less__add__one fact_h fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J fact_real__le__antisym fact_real__le__trans fact_abs__of__nonneg fact_norm__eq__zero fact_norm__le__zero__iff fact_order__trans
% 173.54/173.79
%------------------------------------------------------------------------------