TSTP Solution File: SWW230+1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWW230+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n019.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 118.12s 118.31s
% Output : Refutation 119.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 75
% Syntax : Number of clauses : 98 ( 89 unt; 2 nHn; 98 RR)
% Number of literals : 107 ( 0 equ; 13 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 65 ( 64 usr; 1 prp; 0-3 aty)
% Number of functors : 27 ( 27 usr; 12 con; 0-3 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(80,axiom,
class_Groups_Oordered__cancel__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(81,axiom,
class_Groups_Oordered__ab__semigroup__add__imp__le(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(82,axiom,
class_Rings_Olinordered__comm__semiring__strict(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(83,axiom,
class_Fields_Olinordered__field__inverse__zero(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(84,axiom,
class_Rings_Olinordered__semiring__1__strict(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(85,axiom,
class_RealVector_Oreal__normed__div__algebra(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(86,axiom,
class_Rings_Olinordered__semiring__strict(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(87,axiom,
class_Rings_Odivision__ring__inverse__zero(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(88,axiom,
class_RealVector_Oreal__normed__algebra__1(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(89,axiom,
class_Groups_Oordered__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(90,axiom,
class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(91,axiom,
class_RealVector_Oreal__normed__algebra(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(92,axiom,
class_Groups_Oordered__comm__monoid__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(93,axiom,
class_Groups_Olinordered__ab__group__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(94,axiom,
class_Groups_Ocancel__ab__semigroup__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(95,axiom,
class_Rings_Oring__1__no__zero__divisors(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(96,axiom,
class_Rings_Oordered__cancel__semiring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(97,axiom,
class_RealVector_Oreal__normed__vector(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(98,axiom,
class_Rings_Olinordered__ring__strict(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(99,axiom,
class_RealVector_Oreal__normed__field(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(100,axiom,
class_Rings_Oring__no__zero__divisors(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(101,axiom,
class_Rings_Oordered__comm__semiring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(102,axiom,
class_Rings_Olinordered__semiring__1(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(103,axiom,
class_Groups_Oordered__ab__group__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(104,axiom,
class_Groups_Ocancel__semigroup__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(105,axiom,
class_Rings_Olinordered__semiring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(106,axiom,
class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(107,axiom,
class_Rings_Olinordered__semidom(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(108,axiom,
class_Groups_Oab__semigroup__mult(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(109,axiom,
class_Groups_Ocomm__monoid__mult(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(110,axiom,
class_Groups_Oab__semigroup__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(111,axiom,
class_Fields_Olinordered__field(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(112,axiom,
class_Rings_Oordered__semiring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(113,axiom,
class_Rings_Oordered__ring__abs(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(114,axiom,
class_Rings_Ono__zero__divisors(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(115,axiom,
class_Groups_Ocomm__monoid__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(116,axiom,
class_Rings_Olinordered__ring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(117,axiom,
class_Rings_Olinordered__idom(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(118,axiom,
class_Rings_Ocomm__semiring__1(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(119,axiom,
class_RealVector_Oreal__field(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(120,axiom,
class_Rings_Odivision__ring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(121,axiom,
class_Rings_Ocomm__semiring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(122,axiom,
class_Groups_Oab__group__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(123,axiom,
class_Rings_Ozero__neq__one(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(124,axiom,
class_Rings_Oordered__ring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(125,axiom,
class_Orderings_Olinorder(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(126,axiom,
class_Groups_Omonoid__mult(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(127,axiom,
class_Groups_Omonoid__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(128,axiom,
class_Groups_Ogroup__add(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(129,axiom,
class_Rings_Omult__zero(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(130,axiom,
class_Int_Oring__char__0(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(131,axiom,
class_Int_Onumber__ring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(132,axiom,
class_Rings_Osemiring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(133,axiom,
class_Groups_Oabs__if(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(134,axiom,
class_Rings_Oring__1(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(135,axiom,
class_Fields_Ofield(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(136,axiom,
class_Groups_Ozero(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(137,axiom,
class_Rings_Oring(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(138,axiom,
class_Rings_Oidom(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(139,axiom,
class_Int_Onumber(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(140,axiom,
class_Groups_Oone(tc_RealDef_Oreal),
file('SWW230+1.p',unknown),
[] ).
cnf(271,axiom,
equal(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)),
file('SWW230+1.p',unknown),
[] ).
cnf(364,axiom,
( c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,u,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal))
| equal(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u),u) ),
file('SWW230+1.p',unknown),
[] ).
cnf(469,axiom,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u),v)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v) ),
file('SWW230+1.p',unknown),
[] ).
cnf(471,axiom,
equal(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v)),c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,u,v)),
file('SWW230+1.p',unknown),
[] ).
cnf(473,axiom,
equal(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,v)),
file('SWW230+1.p',unknown),
[] ).
cnf(523,axiom,
( ~ class_Groups_Oordered__ab__group__add__abs(u)
| ~ c_Orderings_Oord__class_Oless(u,c_Groups_Oabs__class_Oabs(u,v),c_Groups_Ozero__class_Ozero(u)) ),
file('SWW230+1.p',unknown),
[] ).
cnf(730,axiom,
( ~ class_Fields_Ofield__inverse__zero(u)
| equal(c_Rings_Oinverse__class_Oinverse(u,c_Rings_Oinverse__class_Odivide(u,v,w)),c_Rings_Oinverse__class_Odivide(u,w,v)) ),
file('SWW230+1.p',unknown),
[] ).
cnf(779,axiom,
equal(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,v),w),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v,w))),
file('SWW230+1.p',unknown),
[] ).
cnf(829,axiom,
equal(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,v),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,u)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v,u)),
file('SWW230+1.p',unknown),
[] ).
cnf(963,axiom,
equal(c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v))),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,v,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,u)))),
file('SWW230+1.p',unknown),
[] ).
cnf(1019,axiom,
equal(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,v),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,w,v)),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,w),v)),
file('SWW230+1.p',unknown),
[] ).
cnf(1190,axiom,
equal(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),u),
file('SWW230+1.p',unknown),
[] ).
cnf(1691,axiom,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____))))),
file('SWW230+1.p',unknown),
[] ).
cnf(1695,axiom,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____)),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))),c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____))))),
file('SWW230+1.p',unknown),
[] ).
cnf(1723,plain,
( equal(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u),u)
| c_Orderings_Oord__class_Oless(tc_RealDef_Oreal,u,c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal)) ),
inference(rew,[status(thm),theory(equality)],[271,364]),
[iquote('0:Rew:271.0,364.1')] ).
cnf(1733,plain,
( ~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u),v)
| c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,u,v) ),
inference(rew,[status(thm),theory(equality)],[271,469]),
[iquote('0:Rew:271.0,469.0')] ).
cnf(1824,plain,
equal(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,u,v)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,v,u))),
inference(rew,[status(thm),theory(equality)],[271,963,471]),
[iquote('0:Rew:271.0,963.0,471.0,963.0,271.0,963.0,471.0,963.0')] ).
cnf(1919,plain,
c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____))))),
inference(rew,[status(thm),theory(equality)],[1824,1691,271]),
[iquote('0:Rew:1824.0,1691.0,271.0,1691.0,1824.0,1691.0,271.0,1691.0')] ).
cnf(1923,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____))))),
inference(rew,[status(thm),theory(equality)],[1824,1695,271]),
[iquote('0:Rew:1824.0,1695.0,271.0,1695.0,1824.0,1695.0,271.0,1695.0')] ).
cnf(1932,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____)))),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____))))),
inference(res,[status(thm),theory(equality)],[1733,1923]),
[iquote('0:Res:1733.1,1923.0')] ).
cnf(11008,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| equal(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u)),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,u)) ),
inference(res,[status(thm),theory(equality)],[1723,523]),
[iquote('0:Res:1723.1,523.1')] ).
cnf(11017,plain,
( ~ class_Groups_Oordered__ab__group__add__abs(tc_RealDef_Oreal)
| equal(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)) ),
inference(rew,[status(thm),theory(equality)],[271,11008]),
[iquote('0:Rew:271.0,11008.1')] ).
cnf(11018,plain,
equal(c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)),c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,u)),
inference(ssi,[status(thm)],[11017,119,113,102,84,134,133,101,88,82,140,136,130,125,123,121,114,110,108,105,94,138,129,127,126,116,115,109,100,96,95,89,85,132,112,104,80,99,122,137,107,81,118,91,87,124,92,135,86,93,106,103,97,128,120,90,117,98,139,111,131,83]),
[iquote('0:SSi:11017.0,119.0,113.0,102.0,84.0,134.0,133.0,101.0,88.0,82.0,140.0,136.0,130.0,125.0,123.0,121.0,114.0,110.0,108.0,105.0,94.0,138.0,129.0,127.0,126.0,116.0,115.0,109.0,100.0,96.0,95.0,89.0,85.0,132.0,112.0,104.0,80.0,99.0,122.0,137.0,107.0,81.0,118.0,91.0,87.0,124.0,92.0,135.0,86.0,93.0,106.0,103.0,97.0,128.0,120.0,90.0,117.0,98.0,139.0,111.0,131.0,83.0')] ).
cnf(37726,plain,
( ~ class_Fields_Ofield__inverse__zero(tc_RealDef_Oreal)
| equal(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v,w)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,w,v))) ),
inference(spr,[status(thm),theory(equality)],[730,473]),
[iquote('0:SpR:730.1,473.0')] ).
cnf(37771,plain,
equal(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v,w)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,w,v))),
inference(ssi,[status(thm)],[37726,119,113,102,84,134,133,101,88,82,140,136,130,125,123,121,114,110,108,105,94,138,129,127,126,116,115,109,100,96,95,89,85,132,112,104,80,99,122,137,107,81,118,91,87,124,92,135,86,93,106,103,97,128,120,90,117,98,139,111,131,83]),
[iquote('0:SSi:37726.0,119.0,113.0,102.0,84.0,134.0,133.0,101.0,88.0,82.0,140.0,136.0,130.0,125.0,123.0,121.0,114.0,110.0,108.0,105.0,94.0,138.0,129.0,127.0,126.0,116.0,115.0,109.0,100.0,96.0,95.0,89.0,85.0,132.0,112.0,104.0,80.0,99.0,122.0,137.0,107.0,81.0,118.0,91.0,87.0,124.0,92.0,135.0,86.0,93.0,106.0,103.0,97.0,128.0,120.0,90.0,117.0,98.0,139.0,111.0,131.0,83.0')] ).
cnf(41832,plain,
equal(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,v,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,w))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,v),w)),
inference(spr,[status(thm),theory(equality)],[779,473]),
[iquote('0:SpR:779.0,473.0')] ).
cnf(41898,plain,
equal(c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v,w)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,v),w)),
inference(rew,[status(thm),theory(equality)],[473,41832]),
[iquote('0:Rew:473.0,41832.0')] ).
cnf(41899,plain,
equal(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,v),w),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,w,v))),
inference(rew,[status(thm),theory(equality)],[37771,41898]),
[iquote('0:Rew:37771.0,41898.0')] ).
cnf(41900,plain,
equal(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,u,u),v)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v,u)),
inference(rew,[status(thm),theory(equality)],[41899,829]),
[iquote('0:Rew:41899.0,829.0')] ).
cnf(41904,plain,
equal(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v,u))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,v,u)),
inference(rew,[status(thm),theory(equality)],[41899,41900]),
[iquote('0:Rew:41899.0,41900.0')] ).
cnf(94058,plain,
equal(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,v),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,w,c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v))),c_Groups_Otimes__class_Otimes(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,w),c_Rings_Oinverse__class_Oinverse(tc_RealDef_Oreal,v))),
inference(spr,[status(thm),theory(equality)],[473,1019]),
[iquote('0:SpR:473.0,1019.0')] ).
cnf(94152,plain,
equal(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,u,v),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,w,v)),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,w),v)),
inference(rew,[status(thm),theory(equality)],[473,94058]),
[iquote('0:Rew:473.0,94058.0,473.0,94058.0')] ).
cnf(94153,plain,
equal(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,u,u),c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),u),
inference(rew,[status(thm),theory(equality)],[94152,1190]),
[iquote('0:Rew:94152.0,1190.0')] ).
cnf(94360,plain,
equal(c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),c_Rings_Oinverse__class_Odivide(tc_RealDef_Oreal,c_Int_Onumber__class_Onumber__of(tc_RealDef_Oreal,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),u)),u),
inference(spr,[status(thm),theory(equality)],[94153,41904]),
[iquote('0:SpR:94153.0,41904.0')] ).
cnf(95874,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____))))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____))))),
inference(rew,[status(thm),theory(equality)],[94360,1932,37771]),
[iquote('0:Rew:94360.0,1932.0,37771.0,1932.0')] ).
cnf(95875,plain,
~ c_Orderings_Oord__class_Oless__eq(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____)))),c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal,c_RealVector_Onorm__class_Onorm(tc_RealDef_Oreal,c_Groups_Ominus__class_Ominus(tc_RealDef_Oreal,c_Groups_Ouminus__class_Ouminus(tc_RealDef_Oreal,v_s____),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____))))))),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Ominus__class_Ominus(tc_Complex_Ocomplex,c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_g____(hAPP(v_f____,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,v_N1____,v_N2____)))),c_Polynomial_Opoly(tc_Complex_Ocomplex,v,v_z____))))),
inference(rew,[status(thm),theory(equality)],[11018,95874]),
[iquote('0:Rew:11018.0,95874.0')] ).
cnf(95876,plain,
$false,
inference(mrr,[status(thm)],[95875,1919]),
[iquote('0:MRR:95875.0,1919.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW230+1 : TPTP v8.1.0. Released v5.2.0.
% 0.04/0.13 % Command : run_spass %d %s
% 0.13/0.34 % Computer : n019.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 : Sat Jun 4 20:26:55 EDT 2022
% 0.13/0.35 % CPUTime :
% 118.12/118.31
% 118.12/118.31 SPASS V 3.9
% 118.12/118.31 SPASS beiseite: Proof found.
% 118.12/118.31 % SZS status Theorem
% 118.12/118.31 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 118.12/118.31 SPASS derived 70608 clauses, backtracked 2525 clauses, performed 2 splits and kept 23106 clauses.
% 118.12/118.31 SPASS allocated 164713 KBytes.
% 118.12/118.31 SPASS spent 0:1:57.83 on the problem.
% 118.12/118.31 0:00:00.06 for the input.
% 118.12/118.31 0:00:00.39 for the FLOTTER CNF translation.
% 118.12/118.31 0:00:01.56 for inferences.
% 118.12/118.31 0:00:02.45 for the backtracking.
% 118.12/118.31 0:1:51.54 for the reduction.
% 118.12/118.31
% 118.12/118.31
% 118.12/118.31 Here is a proof with depth 1, length 98 :
% 118.12/118.31 % SZS output start Refutation
% See solution above
% 119.62/119.89 Formulae used in the proof : 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__Fields_Olinordered__field__inverse__zero 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__Rings_Odivision__ring__inverse__zero 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__RealVector_Oreal__normed__field 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__Fields_Ofield__inverse__zero 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__Fields_Olinordered__field 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__RealVector_Oreal__field arity_RealDef__Oreal__Rings_Odivision__ring 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_Olinorder arity_RealDef__Oreal__Groups_Omonoid__mult arity_RealDef__Oreal__Groups_Omonoid__add arity_RealDef__Oreal__Groups_Ogroup__add arity_RealDef__Oreal__Rings_Omult__zero arity_RealDef__Oreal__Int_Oring__char__0 arity_RealDef__Oreal__Int_Onumber__ring arity_RealDef__Oreal__Rings_Osemiring arity_RealDef__Oreal__Groups_Oabs__if arity_RealDef__Oreal__Rings_Oring__1 arity_RealDef__Oreal__Fields_Ofield arity_RealDef__Oreal__Groups_Ozero arity_RealDef__Oreal__Rings_Oring arity_RealDef__Oreal__Rings_Oidom arity_RealDef__Oreal__Int_Onumber arity_RealDef__Oreal__Groups_Oone fact_real__norm__def fact_real__abs__def fact_abs__le__interval__iff fact_minus__real__def fact_real__divide__def fact_abs__not__less__zero fact_inverse__divide fact_real__mult__assoc fact_real__divide__square__eq fact_abs__minus__add__cancel fact_real__add__mult__distrib fact_real__sum__of__halves fact__096abs_A_Icmod_A_Ipoly_Ap_Az_J_A_N_A_N_As_J_060_061_Aabs_A_Icmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_J_A_N_A_N_As_J_A_L_Acmod_A_Ipoly_Ap_A_Ig_A_If_A_IN1_A_L_AN2_J_J_J_A_N_Apoly_Ap_Az_J_096 conj_0
% 119.62/119.89
%------------------------------------------------------------------------------