TSTP Solution File: SWV621-1 by SPASS---3.9
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%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV621-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n021.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 : Wed Jul 20 21:44:36 EDT 2022
% Result : Unsatisfiable 215.38s 215.57s
% Output : Refutation 215.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 94
% Syntax : Number of clauses : 174 ( 90 unt; 2 nHn; 174 RR)
% Number of literals : 284 ( 0 equ; 116 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 46 ( 45 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 8 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(31,axiom,
equal(c_HOL_Otimes__class_Otimes(u,v,tc_nat),c_HOL_Otimes__class_Otimes(v,u,tc_nat)),
file('SWV621-1.p',unknown),
[] ).
cnf(32,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Otimes__class_Otimes(v,w,u),c_HOL_Otimes__class_Otimes(w,v,u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(34,axiom,
( ~ class_Power_Opower(u)
| equal(c_HOL_Otimes__class_Otimes(v,hAPP(c_Power_Opower__class_Opower(v,u),w),u),hAPP(c_Power_Opower__class_Opower(v,u),c_Suc(w))) ),
file('SWV621-1.p',unknown),
[] ).
cnf(35,axiom,
( ~ class_OrderedGroup_Omonoid__mult(u)
| equal(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(v,u),w),v,u),hAPP(c_Power_Opower__class_Opower(v,u),c_Suc(w))) ),
file('SWV621-1.p',unknown),
[] ).
cnf(49,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| c_Ring__and__Field_Odvd__class_Odvd(v,c_HOL_Otimes__class_Otimes(w,v,u),u) ),
file('SWV621-1.p',unknown),
[] ).
cnf(60,axiom,
( ~ class_Orderings_Obot(u)
| hBOOL(hAPP(c_lessequals(c_Orderings_Obot__class_Obot(u),u),v)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(66,axiom,
( ~ equal(c_HOL_Otimes__class_Otimes(u,v,tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))
| equal(v,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
file('SWV621-1.p',unknown),
[] ).
cnf(177,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(u),v,u)
| equal(v,c_HOL_Ozero__class_Ozero(u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(179,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(u)
| equal(c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(220,axiom,
( ~ class_Ring__and__Field_Oring(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Ouminus__class_Ouminus(w,u),u),c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v,w,u),u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(243,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| ~ c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(v,w,u),x,u)
| c_Ring__and__Field_Odvd__class_Odvd(w,x,u) ),
file('SWV621-1.p',unknown),
[] ).
cnf(250,axiom,
~ equal(c_Suc(u),u),
file('SWV621-1.p',unknown),
[] ).
cnf(373,axiom,
( ~ class_OrderedGroup_Omonoid__mult(u)
| equal(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(u),v,u),v) ),
file('SWV621-1.p',unknown),
[] ).
cnf(374,axiom,
( ~ class_OrderedGroup_Ocomm__monoid__mult(u)
| equal(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(u),v,u),v) ),
file('SWV621-1.p',unknown),
[] ).
cnf(376,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Oone__class_Oone(u),u),v) ),
file('SWV621-1.p',unknown),
[] ).
cnf(390,axiom,
( ~ class_Int_Onumber__ring(u)
| equal(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(u),u),v,u),c_HOL_Ouminus__class_Ouminus(v,u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(415,axiom,
( ~ class_Ring__and__Field_Oring(u)
| equal(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u),u),c_HOL_Otimes__class_Otimes(v,w,u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(430,axiom,
( ~ class_Ring__and__Field_Ocomm__ring__1(u)
| ~ c_Ring__and__Field_Odvd__class_Odvd(v,c_HOL_Ouminus__class_Ouminus(w,u),u)
| c_Ring__and__Field_Odvd__class_Odvd(v,w,u) ),
file('SWV621-1.p',unknown),
[] ).
cnf(493,axiom,
( ~ hBOOL(hAPP(c_lessequals(u,tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)))
| equal(u,c_HOL_Ozero__class_Ozero(tc_nat)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(509,axiom,
( ~ class_OrderedGroup_Omonoid__mult(u)
| equal(hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(v,u),w),u),x),hAPP(c_Power_Opower__class_Opower(v,u),c_HOL_Otimes__class_Otimes(w,x,tc_nat))) ),
file('SWV621-1.p',unknown),
[] ).
cnf(511,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(u)
| ~ class_Ring__and__Field_Odivision__ring(u)
| equal(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(v,u),u),w),c_HOL_Oinverse__class_Oinverse(hAPP(c_Power_Opower__class_Opower(v,u),w),u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(514,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(v,u),w),u),x),hAPP(c_Power_Opower__class_Opower(v,u),c_HOL_Otimes__class_Otimes(w,x,tc_nat))) ),
file('SWV621-1.p',unknown),
[] ).
cnf(516,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(v,u),w,u),c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(v,w,u),u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(518,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(v,w,u),u),c_HOL_Oinverse__class_Odivide(w,v,u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(633,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Otimes__class_Otimes(hAPP(c_Power_Opower__class_Opower(v,u),w),v,u),hAPP(c_Power_Opower__class_Opower(v,u),c_Suc(w))) ),
file('SWV621-1.p',unknown),
[] ).
cnf(634,axiom,
( ~ class_Ring__and__Field_Oring(u)
| equal(c_HOL_Otimes__class_Otimes(c_HOL_Ouminus__class_Ouminus(v,u),w,u),c_HOL_Otimes__class_Otimes(v,c_HOL_Ouminus__class_Ouminus(w,u),u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(640,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Oinverse__class_Oinverse(w,u),u),c_HOL_Oinverse__class_Odivide(v,w,u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(722,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(u),v,u),c_HOL_Oinverse__class_Oinverse(v,u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(726,axiom,
equal(c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),u,tc_nat),c_SetInterval_Oord__class_OlessThan(u,tc_nat)),
file('SWV621-1.p',unknown),
[] ).
cnf(728,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),v_k)),
file('SWV621-1.p',unknown),
[] ).
cnf(729,axiom,
hBOOL(hAPP(c_HOL_Oord__class_Oless(v_k,tc_nat),v_n)),
file('SWV621-1.p',unknown),
[] ).
cnf(748,axiom,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(u,tc_nat),v))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),u))
| equal(c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v),tc_Complex_Ocomplex),u),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v,tc_nat),tc_nat,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(753,axiom,
( ~ class_OrderedGroup_Omonoid__mult(u)
| equal(hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(u),u),v),c_HOL_Oone__class_Oone(u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(756,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(v,c_HOL_Oone__class_Oone(u),u),v) ),
file('SWV621-1.p',unknown),
[] ).
cnf(760,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(hAPP(c_Power_Opower__class_Opower(v,u),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(764,axiom,
( ~ class_Ring__and__Field_Odivision__by__zero(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(hAPP(c_Power_Opower__class_Opower(v,u),w),hAPP(c_Power_Opower__class_Opower(x,u),w),u),hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(v,x,u),u),w)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(765,axiom,
equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),u),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
file('SWV621-1.p',unknown),
[] ).
cnf(769,axiom,
( ~ class_OrderedGroup_Oab__group__add(u)
| equal(c_HOL_Ominus__class_Ominus(v,v,u),c_HOL_Ozero__class_Ozero(u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(788,axiom,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(v,u),w),c_HOL_Oone__class_Oone(u),u),c_HOL_Ominus__class_Ominus(v,c_HOL_Oone__class_Oone(u),u),u),c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(v,u),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),w,tc_nat),tc_nat,u))
| equal(v,c_HOL_Oone__class_Oone(u)) ),
file('SWV621-1.p',unknown),
[] ).
cnf(795,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(796,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(797,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(798,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(799,axiom,
class_Ring__and__Field_Oordered__semiring(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(800,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(801,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(802,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(803,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(804,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(805,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(806,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(807,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(808,axiom,
class_Ring__and__Field_Omult__mono1(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(809,axiom,
class_Ring__and__Field_Omult__zero(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(810,axiom,
class_Ring__and__Field_Omult__mono(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(811,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(812,axiom,
class_Ring__and__Field_Odvd(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(813,axiom,
class_Orderings_Opreorder(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(814,axiom,
class_Orderings_Olinorder(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(815,axiom,
class_Orderings_Oorder(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(816,axiom,
class_Orderings_Obot(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(817,axiom,
class_Power_Opower(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(818,axiom,
class_Int_Onumber(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(819,axiom,
class_HOL_Oord(tc_nat),
file('SWV621-1.p',unknown),
[] ).
cnf(866,axiom,
class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(867,axiom,
class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(868,axiom,
class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(869,axiom,
class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(870,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(871,axiom,
class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(872,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(873,axiom,
class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(874,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(875,axiom,
class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(876,axiom,
class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(877,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(878,axiom,
class_Ring__and__Field_Ozero__neq__one(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(879,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(880,axiom,
class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(881,axiom,
class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(882,axiom,
class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(883,axiom,
class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(884,axiom,
class_OrderedGroup_Ogroup__add(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(885,axiom,
class_Ring__and__Field_Oring__1(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(886,axiom,
class_Ring__and__Field_Ofield(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(887,axiom,
class_Ring__and__Field_Oring(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(888,axiom,
class_Ring__and__Field_Oidom(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(889,axiom,
class_Ring__and__Field_Odvd(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(890,axiom,
class_Int_Oring__char__0(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(891,axiom,
class_Int_Onumber__ring(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(892,axiom,
class_Power_Opower(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(893,axiom,
class_SEQ_Obanach(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(894,axiom,
class_Int_Onumber(tc_Complex_Ocomplex),
file('SWV621-1.p',unknown),
[] ).
cnf(897,axiom,
~ equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),v_n),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),v_n,tc_nat),tc_nat,tc_Complex_Ocomplex)),
file('SWV621-1.p',unknown),
[] ).
cnf(903,plain,
( ~ class_Ring__and__Field_Oring(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,u),u),u),c_HOL_Otimes__class_Otimes(v,w,u)) ),
inference(rew,[status(thm),theory(equality)],[634,415]),
[iquote('0:Rew:634.1,415.1')] ).
cnf(904,plain,
( ~ class_Ring__and__Field_Oring(u)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v,c_HOL_Ouminus__class_Ouminus(w,u),u),u),c_HOL_Otimes__class_Otimes(v,w,u)) ),
inference(rew,[status(thm),theory(equality)],[220,903]),
[iquote('0:Rew:220.1,903.1')] ).
cnf(907,plain,
( ~ class_Ring__and__Field_Oring(u)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v,w,u),u),u),c_HOL_Otimes__class_Otimes(v,w,u)) ),
inference(rew,[status(thm),theory(equality)],[220,904]),
[iquote('0:Rew:220.1,904.1')] ).
cnf(908,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Otimes__class_Otimes(v,hAPP(c_Power_Opower__class_Opower(v,u),w),u),hAPP(c_Power_Opower__class_Opower(v,u),c_Suc(w))) ),
inference(rew,[status(thm),theory(equality)],[32,633]),
[iquote('0:Rew:32.1,633.1')] ).
cnf(931,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(u,tc_nat),v))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),u))
| equal(c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v),tc_Complex_Ocomplex),u),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(v,tc_nat),tc_nat,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[726,748]),
[iquote('0:Rew:726.0,748.2')] ).
cnf(932,plain,
( ~ class_Ring__and__Field_Ofield(u)
| equal(v,c_HOL_Oone__class_Oone(u))
| equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(v,u),w),c_HOL_Oone__class_Oone(u),u),c_HOL_Ominus__class_Ominus(v,c_HOL_Oone__class_Oone(u),u),u),c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(v,u),c_SetInterval_Oord__class_OlessThan(w,tc_nat),tc_nat,u)) ),
inference(rew,[status(thm),theory(equality)],[726,788]),
[iquote('0:Rew:726.0,788.1')] ).
cnf(933,plain,
~ equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),v_n),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(v_n,tc_nat),tc_nat,tc_Complex_Ocomplex)),
inference(rew,[status(thm),theory(equality)],[726,897]),
[iquote('0:Rew:726.0,897.0')] ).
cnf(944,plain,
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(res,[status(thm),theory(equality)],[932,933]),
[iquote('0:Res:932.1,933.0')] ).
cnf(995,plain,
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[722,944]),
[iquote('0:Rew:722.1,944.1')] ).
cnf(996,plain,
equal(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(mrr,[status(thm)],[995,886]),
[iquote('0:MRR:995.0,886.0')] ).
cnf(1041,plain,
( ~ class_OrderedGroup_Ocomm__monoid__mult(tc_nat)
| equal(c_HOL_Otimes__class_Otimes(u,c_HOL_Oone__class_Oone(tc_nat),tc_nat),u) ),
inference(spr,[status(thm),theory(equality)],[374,31]),
[iquote('0:SpR:374.1,31.0')] ).
cnf(1047,plain,
equal(c_HOL_Otimes__class_Otimes(u,c_HOL_Oone__class_Oone(tc_nat),tc_nat),u),
inference(ssi,[status(thm)],[1041,808,795,812,810,803,799,798,816,804,796,807,806,800,819,818,809,811,814,817,805,813,797,815,801,802]),
[iquote('0:SSi:1041.0,808.0,795.0,812.0,810.0,803.0,799.0,798.0,816.0,804.0,796.0,807.0,806.0,800.0,819.0,818.0,809.0,811.0,814.0,817.0,805.0,813.0,797.0,815.0,801.0,802.0')] ).
cnf(1377,plain,
( ~ class_Orderings_Obot(tc_nat)
| equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)) ),
inference(res,[status(thm),theory(equality)],[60,493]),
[iquote('0:Res:60.1,493.0')] ).
cnf(1378,plain,
equal(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_nat)),
inference(ssi,[status(thm)],[1377,808,795,812,810,803,799,798,816,804,796,807,806,800,819,818,809,811,814,817,805,813,797,815,801,802]),
[iquote('0:SSi:1377.0,808.0,795.0,812.0,810.0,803.0,799.0,798.0,816.0,804.0,796.0,807.0,806.0,800.0,819.0,818.0,809.0,811.0,814.0,817.0,805.0,813.0,797.0,815.0,801.0,802.0')] ).
cnf(1380,plain,
hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),v_k)),
inference(rew,[status(thm),theory(equality)],[1378,728]),
[iquote('0:Rew:1378.0,728.0')] ).
cnf(1396,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(u,tc_nat),v))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),u))
| equal(c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v),tc_Complex_Ocomplex),u),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(v,tc_nat),tc_nat,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[1378,931]),
[iquote('0:Rew:1378.0,931.1')] ).
cnf(1419,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(hAPP(c_Power_Opower__class_Opower(v,u),c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(u)) ),
inference(rew,[status(thm),theory(equality)],[1378,760]),
[iquote('0:Rew:1378.0,760.1')] ).
cnf(1423,plain,
( ~ equal(c_HOL_Otimes__class_Otimes(u,v,tc_nat),c_Suc(c_Orderings_Obot__class_Obot(tc_nat)))
| equal(v,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) ),
inference(rew,[status(thm),theory(equality)],[1378,66]),
[iquote('0:Rew:1378.0,66.0')] ).
cnf(1444,plain,
( ~ equal(c_HOL_Otimes__class_Otimes(u,v,tc_nat),c_Suc(c_Orderings_Obot__class_Obot(tc_nat)))
| equal(v,c_Suc(c_Orderings_Obot__class_Obot(tc_nat))) ),
inference(rew,[status(thm),theory(equality)],[1378,1423]),
[iquote('0:Rew:1378.0,1423.1')] ).
cnf(1605,plain,
( ~ class_Ring__and__Field_Ofield(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(u),u),c_HOL_Oone__class_Oone(u)) ),
inference(spr,[status(thm),theory(equality)],[722,756]),
[iquote('0:SpR:722.1,756.1')] ).
cnf(1607,plain,
( ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(u),u),c_HOL_Oone__class_Oone(u)) ),
inference(obv,[status(thm),theory(equality)],[1605]),
[iquote('0:Obv:1605.0')] ).
cnf(1795,plain,
( ~ equal(u,c_Suc(c_Orderings_Obot__class_Obot(tc_nat)))
| equal(c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)) ),
inference(spl,[status(thm),theory(equality)],[1047,1444]),
[iquote('0:SpL:1047.0,1444.0')] ).
cnf(1815,plain,
equal(c_Suc(c_Orderings_Obot__class_Obot(tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),
inference(aed,[status(thm),theory(equality)],[250,1795]),
[iquote('0:AED:250.0,1795.0')] ).
cnf(2366,plain,
( ~ class_Int_Onumber__ring(u)
| ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| c_Ring__and__Field_Odvd__class_Odvd(v,c_HOL_Ouminus__class_Ouminus(v,u),u) ),
inference(spr,[status(thm),theory(equality)],[390,49]),
[iquote('0:SpR:390.1,49.1')] ).
cnf(12394,plain,
( ~ class_Ring__and__Field_Ofield(u)
| ~ class_Ring__and__Field_Odivision__by__zero(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(v,c_HOL_Oone__class_Oone(u),u),c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(v,u),u)) ),
inference(spr,[status(thm),theory(equality)],[722,518]),
[iquote('0:SpR:722.1,518.2')] ).
cnf(12408,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Odivide(v,c_HOL_Oone__class_Oone(u),u),c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(v,u),u)) ),
inference(obv,[status(thm),theory(equality)],[12394]),
[iquote('0:Obv:12394.0')] ).
cnf(12409,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(u)
| ~ class_Ring__and__Field_Ofield(u)
| equal(c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(v,u),u),v) ),
inference(rew,[status(thm),theory(equality)],[756,12408]),
[iquote('0:Rew:756.1,12408.2')] ).
cnf(15991,plain,
( ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),c_Suc(u)),c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[765,35]),
[iquote('0:SpR:765.0,35.1')] ).
cnf(16029,plain,
( ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),c_Suc(u)),c_FFT__Mirabelle_Oroot(u)) ),
inference(rew,[status(thm),theory(equality)],[373,15991]),
[iquote('0:Rew:373.1,15991.1')] ).
cnf(16030,plain,
equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),c_Suc(u)),c_FFT__Mirabelle_Oroot(u)),
inference(ssi,[status(thm)],[16029,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:16029.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(16652,plain,
( ~ class_Power_Opower(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),c_Suc(u)),c_HOL_Otimes__class_Otimes(c_FFT__Mirabelle_Oroot(u),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[765,34]),
[iquote('0:SpR:765.0,34.1')] ).
cnf(16686,plain,
( ~ class_Power_Opower(tc_Complex_Ocomplex)
| equal(c_HOL_Otimes__class_Otimes(c_FFT__Mirabelle_Oroot(u),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(u)) ),
inference(rew,[status(thm),theory(equality)],[16030,16652]),
[iquote('0:Rew:16030.0,16652.1')] ).
cnf(16687,plain,
equal(c_HOL_Otimes__class_Otimes(c_FFT__Mirabelle_Oroot(u),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(u)),
inference(ssi,[status(thm)],[16686,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:16686.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(16725,plain,
( ~ class_Ring__and__Field_Oring(tc_Complex_Ocomplex)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(u)) ),
inference(spr,[status(thm),theory(equality)],[16687,907]),
[iquote('0:SpR:16687.0,907.1')] ).
cnf(16735,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_FFT__Mirabelle_Oroot(u)),
inference(ssi,[status(thm)],[16725,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:16725.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(16897,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Oone__class_Oone(u),u),hAPP(c_Power_Opower__class_Opower(v,u),c_Suc(c_Orderings_Obot__class_Obot(tc_nat)))) ),
inference(spr,[status(thm),theory(equality)],[1419,908]),
[iquote('0:SpR:1419.1,908.1')] ).
cnf(16934,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(c_HOL_Otimes__class_Otimes(v,c_HOL_Oone__class_Oone(u),u),hAPP(c_Power_Opower__class_Opower(v,u),c_Suc(c_Orderings_Obot__class_Obot(tc_nat)))) ),
inference(obv,[status(thm),theory(equality)],[16897]),
[iquote('0:Obv:16897.0')] ).
cnf(16935,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(u)
| equal(hAPP(c_Power_Opower__class_Opower(v,u),c_HOL_Oone__class_Oone(tc_nat)),v) ),
inference(rew,[status(thm),theory(equality)],[376,16934,1815]),
[iquote('0:Rew:376.1,16934.1,1815.0,16934.1')] ).
cnf(16962,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| equal(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[16935,765]),
[iquote('0:SpR:16935.1,765.0')] ).
cnf(16977,plain,
equal(c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[16962,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:16962.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(16983,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(spr,[status(thm),theory(equality)],[16977,16735]),
[iquote('0:SpR:16977.0,16735.0')] ).
cnf(17165,plain,
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Odivide(c_HOL_Ouminus__class_Ouminus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),u,tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[16983,516]),
[iquote('0:SpR:16983.0,516.1')] ).
cnf(17208,plain,
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(u,tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[722,17165,516]),
[iquote('0:Rew:722.1,17165.1,516.1,17165.1,722.1,17165.1')] ).
cnf(17209,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Oinverse__class_Oinverse(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Oinverse__class_Oinverse(u,tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[17208,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:17208.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(17382,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),u) ),
inference(spr,[status(thm),theory(equality)],[12409,17209]),
[iquote('0:SpR:12409.2,17209.0')] ).
cnf(17408,plain,
equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),u),
inference(ssi,[status(thm)],[17382,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:17382.1,17382.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(17457,plain,
( ~ class_Int_Onumber__ring(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),u,tc_Complex_Ocomplex) ),
inference(spr,[status(thm),theory(equality)],[17408,2366]),
[iquote('0:SpR:17408.0,2366.2')] ).
cnf(17525,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),u,tc_Complex_Ocomplex),
inference(ssi,[status(thm)],[17457,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:17457.1,17457.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(17570,plain,
c_Ring__and__Field_Odvd__class_Odvd(u,c_HOL_Ouminus__class_Ouminus(u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(spr,[status(thm),theory(equality)],[17408,17525]),
[iquote('0:SpR:17408.0,17525.0')] ).
cnf(17627,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v,u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(res,[status(thm),theory(equality)],[17570,243]),
[iquote('0:Res:17570.0,243.1')] ).
cnf(17633,plain,
c_Ring__and__Field_Odvd__class_Odvd(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Otimes__class_Otimes(v,u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(ssi,[status(thm)],[17627,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:17627.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(19101,plain,
( ~ class_Ring__and__Field_Ocomm__ring__1(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(u,c_HOL_Otimes__class_Otimes(v,u,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(res,[status(thm),theory(equality)],[17633,430]),
[iquote('0:Res:17633.0,430.1')] ).
cnf(19110,plain,
c_Ring__and__Field_Odvd__class_Odvd(u,c_HOL_Otimes__class_Otimes(v,u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(ssi,[status(thm)],[19101,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:19101.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(19155,plain,
( ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oinverse__class_Oinverse(u,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(v,u,tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(spr,[status(thm),theory(equality)],[640,19110]),
[iquote('0:SpR:640.1,19110.0')] ).
cnf(19179,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oinverse__class_Oinverse(u,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(v,u,tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(ssi,[status(thm)],[19155,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:19155.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(20549,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex) ),
inference(spr,[status(thm),theory(equality)],[179,19179]),
[iquote('0:SpR:179.1,19179.0')] ).
cnf(20557,plain,
c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),
inference(ssi,[status(thm)],[20549,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:20549.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(20580,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| equal(c_HOL_Oinverse__class_Odivide(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(res,[status(thm),theory(equality)],[20557,177]),
[iquote('0:Res:20557.0,177.1')] ).
cnf(20584,plain,
equal(c_HOL_Oinverse__class_Odivide(u,c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[20580,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:20580.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(39359,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex)
| equal(c_HOL_Oinverse__class_Oinverse(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[511,996]),
[iquote('0:SpR:511.2,996.0')] ).
cnf(39402,plain,
equal(c_HOL_Oinverse__class_Oinverse(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[39359,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:39359.1,39359.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(39432,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k),c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[39402,12409]),
[iquote('0:SpR:39402.0,12409.2')] ).
cnf(39492,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[1607,39432]),
[iquote('0:Rew:1607.1,39432.2')] ).
cnf(39493,plain,
equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[39492,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:39492.1,39492.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(39899,plain,
( ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(u,v,tc_nat)),hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v)) ),
inference(spr,[status(thm),theory(equality)],[765,509]),
[iquote('0:SpR:765.0,509.1')] ).
cnf(39929,plain,
( ~ class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(u,v,tc_nat)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[753,39899]),
[iquote('0:Rew:753.1,39899.1')] ).
cnf(39930,plain,
equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(u,v,tc_nat)),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[39929,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:39929.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(40115,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(u),tc_Complex_Ocomplex),c_HOL_Otimes__class_Otimes(u,v,tc_nat)),hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v)) ),
inference(spr,[status(thm),theory(equality)],[765,514]),
[iquote('0:SpR:765.0,514.1')] ).
cnf(40148,plain,
( ~ class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),u),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[39930,40115]),
[iquote('0:Rew:39930.0,40115.1')] ).
cnf(40149,plain,
equal(hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),u),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[40148,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:40148.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(73568,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(c_HOL_Oinverse__class_Odivide(hAPP(c_Power_Opower__class_Opower(u,tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(u,c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k)) ),
inference(spr,[status(thm),theory(equality)],[39493,764]),
[iquote('0:SpR:39493.0,764.2')] ).
cnf(73644,plain,
( ~ class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex)
| ~ class_Ring__and__Field_Ofield(tc_Complex_Ocomplex)
| equal(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(u,c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),hAPP(c_Power_Opower__class_Opower(u,tc_Complex_Ocomplex),v_k)) ),
inference(rew,[status(thm),theory(equality)],[756,73568]),
[iquote('0:Rew:756.1,73568.2')] ).
cnf(73645,plain,
equal(hAPP(c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(u,c_FFT__Mirabelle_Oroot(v_n),tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),hAPP(c_Power_Opower__class_Opower(u,tc_Complex_Ocomplex),v_k)),
inference(ssi,[status(thm)],[73644,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:73644.1,73644.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(73646,plain,
~ equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),v_n),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(hAPP(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),v_k),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(v_n,tc_nat),tc_nat,tc_Complex_Ocomplex)),
inference(rew,[status(thm),theory(equality)],[73645,933]),
[iquote('0:Rew:73645.0,933.0')] ).
cnf(73772,plain,
~ equal(c_HOL_Oinverse__class_Odivide(c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_HOL_Ominus__class_Ominus(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(v_n,tc_nat),tc_nat,tc_Complex_Ocomplex)),
inference(rew,[status(thm),theory(equality)],[40149,73646]),
[iquote('0:Rew:40149.0,73646.0,40149.0,73646.0')] ).
cnf(73964,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ equal(c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(v_n,tc_nat),tc_nat,tc_Complex_Ocomplex),c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex),tc_Complex_Ocomplex)) ),
inference(spl,[status(thm),theory(equality)],[769,73772]),
[iquote('0:SpL:769.1,73772.0')] ).
cnf(73971,plain,
( ~ class_OrderedGroup_Oab__group__add(tc_Complex_Ocomplex)
| ~ equal(c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(v_n,tc_nat),tc_nat,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(rew,[status(thm),theory(equality)],[20584,73964]),
[iquote('0:Rew:20584.0,73964.1')] ).
cnf(73972,plain,
~ equal(c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(v_n,tc_nat),tc_nat,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)),
inference(ssi,[status(thm)],[73971,890,885,873,866,889,872,893,874,867,891,880,887,881,879,878,871,868,894,882,883,876,884,892,888,877,875,870,886,869]),
[iquote('0:SSi:73971.0,890.0,885.0,873.0,866.0,889.0,872.0,893.0,874.0,867.0,891.0,880.0,887.0,881.0,879.0,878.0,871.0,868.0,894.0,882.0,883.0,876.0,884.0,892.0,888.0,877.0,875.0,870.0,886.0,869.0')] ).
cnf(155578,plain,
( ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(v_k,tc_nat),v_n))
| ~ hBOOL(hAPP(c_HOL_Oord__class_Oless(c_Orderings_Obot__class_Obot(tc_nat),tc_nat),v_k))
| equal(c_Finite__Set_Osetsum(c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),tc_Complex_Ocomplex),c_SetInterval_Oord__class_OlessThan(v_n,tc_nat),tc_nat,tc_Complex_Ocomplex),c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)) ),
inference(spr,[status(thm),theory(equality)],[39493,1396]),
[iquote('0:SpR:39493.0,1396.2')] ).
cnf(155593,plain,
$false,
inference(mrr,[status(thm)],[155578,729,1380,73972]),
[iquote('0:MRR:155578.0,155578.1,155578.2,729.0,1380.0,73972.0')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWV621-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : run_spass %d %s
% 0.12/0.34 % Computer : n021.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Tue Jun 14 20:06:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 215.38/215.57
% 215.38/215.57 SPASS V 3.9
% 215.38/215.57 SPASS beiseite: Proof found.
% 215.38/215.57 % SZS status Theorem
% 215.38/215.57 Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p
% 215.38/215.57 SPASS derived 110478 clauses, backtracked 1495 clauses, performed 1 splits and kept 26894 clauses.
% 215.38/215.57 SPASS allocated 184999 KBytes.
% 215.38/215.57 SPASS spent 0:3:35.01 on the problem.
% 215.38/215.57 0:00:00.07 for the input.
% 215.38/215.57 0:00:00.00 for the FLOTTER CNF translation.
% 215.38/215.57 0:00:01.52 for inferences.
% 215.38/215.57 0:00:00.57 for the backtracking.
% 215.38/215.57 0:3:31.84 for the reduction.
% 215.38/215.57
% 215.38/215.57
% 215.38/215.57 Here is a proof with depth 12, length 174 :
% 215.38/215.57 % SZS output start Refutation
% See solution above
% 215.38/215.57 Formulae used in the proof : cls_nat__mult__commute_0 cls_class__semiring_Omul__c_0 cls_power__Suc_0 cls_power__Suc2_0 cls_dvd__triv__right_0 cls_bot__least_0 cls_mult__eq__1__iff_1 cls_dvd__0__left_0 cls_inverse__zero_0 cls_minus__mult__right_0 cls_dvd__mult__right_0 cls_n__not__Suc__n_0 cls_mult__1__left_0 cls_mult__1_0 cls_class__semiring_Osemiring__rules_I12_J_0 cls_class__ring_Oneg__mul_0 cls_minus__mult__minus_0 cls_dvd__minus__iff_0 cls_le__0__eq_0 cls_power__mult_0 cls_power__inverse_0 cls_class__semiring_Opwr__pwr_0 cls_minus__divide__left_0 cls_inverse__divide_0 cls_class__semiring_Osemiring__rules_I28_J_0 cls_minus__mult__commute_0 cls_divide__inverse_0 cls_inverse__eq__divide_0 cls_atLeast0LessThan_0 cls_k_I1_J_0 cls_k_I2_J_0 cls_root__summation_0 cls_power__one_0 cls_divide__1_0 cls_class__semiring_Opwr__0_0 cls_power__divide_0 cls_root__unity_0 cls_eq__iff__diff__eq__0_0 cls_geometric__sum_0 clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict clsarity_nat__Ring__and__Field_Opordered__cancel__semiring clsarity_nat__Ring__and__Field_Oordered__semiring__strict clsarity_nat__Ring__and__Field_Opordered__semiring clsarity_nat__Ring__and__Field_Oordered__semiring clsarity_nat__Ring__and__Field_Ono__zero__divisors clsarity_nat__Ring__and__Field_Oordered__semidom clsarity_nat__Ring__and__Field_Ocomm__semiring__1 clsarity_nat__OrderedGroup_Oab__semigroup__mult clsarity_nat__OrderedGroup_Ocomm__monoid__mult clsarity_nat__OrderedGroup_Ocomm__monoid__add clsarity_nat__Ring__and__Field_Ozero__neq__one clsarity_nat__Ring__and__Field_Osemiring__0 clsarity_nat__Ring__and__Field_Omult__mono1 clsarity_nat__Ring__and__Field_Omult__zero clsarity_nat__Ring__and__Field_Omult__mono clsarity_nat__OrderedGroup_Omonoid__mult clsarity_nat__Ring__and__Field_Odvd clsarity_nat__Orderings_Opreorder clsarity_nat__Orderings_Olinorder clsarity_nat__Orderings_Oorder clsarity_nat__Orderings_Obot clsarity_nat__Power_Opower clsarity_nat__Int_Onumber clsarity_nat__HOL_Oord clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1 clsarity_Complex__Ocomplex__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__Ring__and__Field_Odivision__ring clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1 clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0 clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1 clsarity_Complex__Ocomplex__Ring__and__Field_Ofield clsarity_Complex__Ocomplex__Ring__and__Field_Oring clsarity_Complex__Ocomplex__Ring__and__Field_Oidom clsarity_Complex__Ocomplex__Ring__and__Field_Odvd clsarity_Complex__Ocomplex__Int_Oring__char__0 clsarity_Complex__Ocomplex__Int_Onumber__ring clsarity_Complex__Ocomplex__Power_Opower clsarity_Complex__Ocomplex__SEQ_Obanach clsarity_Complex__Ocomplex__Int_Onumber cls_conjecture_0
% 225.27/225.48
%------------------------------------------------------------------------------