TSTP Solution File: SWV629-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : SWV629-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %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 : 300s
% DateTime : Wed Jul 27 13:21:18 EDT 2022
% Result : Unsatisfiable 34.39s 34.50s
% Output : Refutation 34.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 1
% Number of leaves : 4
% Syntax : Number of clauses : 5 ( 4 unt; 0 nHn; 3 RR)
% Number of literals : 6 ( 3 equ; 2 neg)
% Maximal clause size : 2 ( 1 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 3 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(206,axiom,
( ~ class_Ring__and__Field_Ocomm__semiring__1(A)
| c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A) = B ),
file('SWV629-1.p',unknown),
[] ).
cnf(229,axiom,
c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat)) != c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('SWV629-1.p',unknown),
[] ).
cnf(336,axiom,
c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),A,tc_Complex_Ocomplex) = c_HOL_Oone__class_Oone(tc_Complex_Ocomplex),
file('SWV629-1.p',unknown),
[] ).
cnf(363,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex),
file('SWV629-1.p',unknown),
[] ).
cnf(386,plain,
$false,
inference(unit_del,[status(thm)],[inference(para_into,[status(thm),theory(equality)],[336,206]),229,363]),
[iquote('para_into,336.1.1,206.2.1,unit_del,229,363')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SWV629-1 : TPTP v8.1.0. Released v4.1.0.
% 0.13/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n029.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 : 300
% 0.13/0.34 % DateTime : Wed Jul 27 06:21:44 EDT 2022
% 0.13/0.34 % CPUTime :
% 34.15/34.31 ----- Otter 3.3f, August 2004 -----
% 34.15/34.31 The process was started by sandbox on n029.cluster.edu,
% 34.15/34.31 Wed Jul 27 06:21:44 2022
% 34.15/34.31 The command was "./otter". The process ID is 13816.
% 34.15/34.31
% 34.15/34.31 set(prolog_style_variables).
% 34.15/34.31 set(auto).
% 34.15/34.31 dependent: set(auto1).
% 34.15/34.31 dependent: set(process_input).
% 34.15/34.31 dependent: clear(print_kept).
% 34.15/34.31 dependent: clear(print_new_demod).
% 34.15/34.31 dependent: clear(print_back_demod).
% 34.15/34.31 dependent: clear(print_back_sub).
% 34.15/34.31 dependent: set(control_memory).
% 34.15/34.31 dependent: assign(max_mem, 12000).
% 34.15/34.31 dependent: assign(pick_given_ratio, 4).
% 34.15/34.31 dependent: assign(stats_level, 1).
% 34.15/34.31 dependent: assign(max_seconds, 10800).
% 34.15/34.31 clear(print_given).
% 34.15/34.31
% 34.15/34.31 list(usable).
% 34.15/34.31 0 [] A=A.
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_x,c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat),tc_nat)=V_x.
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a)=c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a).
% 34.15/34.31 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat)|V_a=V_b.
% 34.15/34.31 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_a,tc_nat)|V_a=V_b| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,tc_nat).
% 34.15/34.31 0 [] V_x=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat).
% 34.15/34.31 0 [] V_m=V_n| -c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat).
% 34.15/34.31 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)|V_x=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] V_x=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] V_x=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_x,c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat),tc_nat)=V_x.
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_a,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_b,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_x,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_x,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_y,V_z,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_y,V_z,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),c_HOL_Oinverse__class_Odivide(V_z,V_w,T_a),T_a)=c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_y,V_w,T_a),T_a).
% 34.15/34.31 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_x,V_y,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),c_Divides_Odiv__class_Odiv(V_w,V_z,T_a),T_a)=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_x,V_w,T_a),c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_w,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a).
% 34.15/34.31 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_n,V_r,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_m,V_r,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_r,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),V_e,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_e,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_e,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_b,c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_a,c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat),V_k,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_n,V_k,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_n,c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_m,c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_x,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_y,c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_y,V_z,tc_nat),V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat),V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat).
% 34.15/34.31 0 [] -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),V_x,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_a,tc_nat).
% 34.15/34.31 0 [] -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),V_x,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_b,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_b,tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(c_HOL_Ozero__class_Ozero(tc_nat),V_x,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.31 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 34.15/34.31 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)=c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)=c_HOL_Oinverse__class_Odivide(V_b,V_a,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Oone__class_Oone(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)=V_b.
% 34.15/34.31 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)=V_x.
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__ring(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)!=c_HOL_Oinverse__class_Oinverse(V_b,T_a)|V_a=V_b.
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)!=c_HOL_Oinverse__class_Oinverse(V_b,T_a)|V_a=V_b|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__ring(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a).
% 34.15/34.31 0 [] -class_OrderedGroup_Ocomm__monoid__mult(T_a)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__ring(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)=c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)!=c_HOL_Oone__class_Oone(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 34.15/34.31 0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a)=c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a).
% 34.15/34.31 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat)=c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a)=c_HOL_Oone__class_Oone(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_a,T_a)=c_HOL_Oone__class_Oone(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)=c_HOL_Oone__class_Oone(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)=c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)=c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(V_a,T_a),T_a)=c_HOL_Osgn__class_Osgn(V_a,T_a).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_x,c_GCD_Ogcd__class_Ogcd(V_y,V_z,tc_nat),tc_nat),c_GCD_Ogcd__class_Ogcd(c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat),c_GCD_Ogcd__class_Olcm(V_x,V_z,tc_nat),tc_nat),tc_nat).
% 34.15/34.31 0 [] c_HOL_Otimes__class_Otimes(V_k,c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),tc_nat)=c_GCD_Ogcd__class_Ogcd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oabs__class_Oabs(V_k,T_a)=c_HOL_Otimes__class_Otimes(V_k,c_HOL_Osgn__class_Osgn(V_k,T_a),T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),c_Divides_Odiv__class_Odiv(V_c,V_a,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)=c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_a,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_b,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_b,tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_a,T_a),c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(V_b,T_a),c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)=V_a|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] c_Fact_Ofact__class_Ofact(V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.31 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a)=V_a.
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|V_a=c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),V_c,T_a)=V_a|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a)=V_a|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a)=V_a|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)!=c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)|V_m=V_n.
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Oabs__class_Oabs(V_x,T_a),T_a)=V_x.
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|V_x=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_b,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_a,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|V_d=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_d,V_b,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_d,V_a,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat)=V_x| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat)!=V_y|c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat)!=V_m|c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat)=V_m| -c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat)!=V_n|c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat)=V_n| -c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_y,V_x,tc_nat)=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat)=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat),V_z,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat),V_z,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_b,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_a,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_b,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),V_x,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_a,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(V_a,V_b,tc_nat),V_x,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_k,c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_k,c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_k,V_n,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_k,V_n,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oinverse__class_Oinverse(V_x,T_a)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_x,T_a).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),V_a,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),V_b,tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Odvd(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_b,c_HOL_Otimes__class_Otimes(V_b,V_k,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)=c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(T_a),V_a,T_a),V_n,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Odivision__ring(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)=V_a.
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_x,V_p,T_a),V_q,T_a)=c_Power_Opower__class_Opower(V_x,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_nat),T_a).
% 34.15/34.31 0 [] c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)=c_HOL_Otimes__class_Otimes(V_y,V_x,T_a).
% 34.15/34.31 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)=c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)=c_HOL_Otimes__class_Otimes(V_b,V_a,T_a).
% 34.15/34.31 0 [] -class_OrderedGroup_Opordered__ab__group__add__abs(T_a)|c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a)|c_HOL_Oinverse__class_Odivide(V_x,V_x,T_a)=c_HOL_Oone__class_Oone(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a)=c_HOL_Oone__class_Oone(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Odivide(V_a,V_a,T_a)=c_HOL_Oone__class_Oone(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat),c_GCD_Ogcd__class_Ogcd(V_x,V_z,tc_nat),tc_nat),c_GCD_Ogcd__class_Ogcd(V_x,c_GCD_Ogcd__class_Olcm(V_y,V_z,tc_nat),tc_nat),tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_x,V_x,tc_nat)=V_x.
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_RealVector_Oreal__normed__field(T_a)|c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] V_b!=c_HOL_Otimes__class_Otimes(V_b_H,c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),tc_nat)|V_a!=c_HOL_Otimes__class_Otimes(V_a_H,c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),tc_nat)|c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_GCD_Ogcd__class_Ogcd(V_a_H,V_b_H,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_c,T_a)=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),V_a,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 34.15/34.31 0 [] c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_x,T_a),V_n,T_a)=c_Power_Opower__class_Opower(V_x,V_n,T_a)| -c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)=c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(V_a,T_a),V_n,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)=c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__field(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)=c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Osgn__class_Osgn(V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_HOL_Osgn__class_Osgn(V_x,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)=c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)=c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a),V_z,T_a)=c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),V_y,T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),T_a)=V_b| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_b,V_a,T_a),V_a,T_a)=V_b| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 34.15/34.31 0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(V_n,tc_nat),T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_Complex_Ocnj(c_Power_Opower__class_Opower(V_x,V_n,tc_Complex_Ocomplex))=c_Power_Opower__class_Opower(c_Complex_Ocnj(V_x),V_n,tc_Complex_Ocomplex).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_y,V_z,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_x,V_b,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_x,tc_nat).
% 34.15/34.31 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_x,V_a,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_x,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_y,V_z,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_b,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_a,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat),V_y,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat),V_x,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),V_m,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),V_n,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_a,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_b,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_e,c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_e,V_b,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_e,V_a,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_k,c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_k,c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,tc_nat).
% 34.15/34.31 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(V_a,T_a),T_a)=c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oordered__field(T_a)|c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),T_a)=c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_b,T_a),T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)=c_HOL_Otimes__class_Otimes(c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(c_HOL_Ozero__class_Ozero(tc_nat),V_x,tc_nat)=V_x.
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_x.
% 34.15/34.31 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(V_a,V_a,T_a)=c_HOL_Oone__class_Oone(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_x,V_x,tc_nat)=V_x.
% 34.15/34.31 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Oidom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 34.15/34.31 0 [] -class_OrderedGroup_Opordered__ab__group__add__abs(T_a)|c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)=c_HOL_Oabs__class_Oabs(V_a,T_a).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_d,c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_GCD_Ogcd__class_Ogcd(V_d,V_b,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Ogcd(V_d,c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_GCD_Ogcd__class_Ogcd(V_d,V_a,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.31 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat).
% 34.15/34.31 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat).
% 34.15/34.31 0 [] c_Complex_Ocnj(c_Complex_Ocnj(V_z))=V_z.
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat)=c_GCD_Ogcd__class_Olcm(V_n,V_m,tc_nat).
% 34.15/34.31 0 [] c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat)=c_GCD_Ogcd__class_Olcm(V_y,V_x,tc_nat).
% 34.15/34.31 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a)=c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a).
% 34.15/34.31 0 [] c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)!=c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 34.15/34.31 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 34.15/34.31 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)|V_m=V_n|V_k=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.31 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Ozero__class_Ozero(T_a)=c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a).
% 34.15/34.31 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 34.15/34.31 0 [] -class_Divides_Osemiring__div(T_a)|c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(V_x,V_y,T_a),V_n,T_a)=c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_y,V_n,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,T_a).
% 34.15/34.31 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a)=c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(V_a,T_a),c_HOL_Oabs__class_Oabs(V_a,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_a,V_a,T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)=c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(V_a,T_a),V_n,T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_x,c_GCD_Ogcd__class_Ogcd(V_y,V_z,tc_nat),tc_nat)=c_GCD_Ogcd__class_Ogcd(V_y,c_GCD_Ogcd__class_Ogcd(V_x,V_z,tc_nat),tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(c_GCD_Ogcd__class_Ogcd(V_k,V_m,tc_nat),V_n,tc_nat)=c_GCD_Ogcd__class_Ogcd(V_k,c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat),tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat),V_z,tc_nat)=c_GCD_Ogcd__class_Ogcd(V_x,c_GCD_Ogcd__class_Ogcd(V_y,V_z,tc_nat),tc_nat).
% 34.15/34.32 0 [] V_m!=c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|V_b=c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(V_b,V_c,T_a),V_c,T_a)=V_b|V_c=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.32 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.32 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Omult__zero(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Omult__zero(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|V_z=c_HOL_Ozero__class_Ozero(T_a)| -c_Int_Oiszero(V_z,T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(V_m,T_a),V_k,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oabs__class_Oabs(V_k,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_m,V_k,T_a).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(V_x,c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat),tc_nat)=c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_k,V_n,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_GCD_Ogcd__class_Ogcd(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),V_n,tc_nat)=c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat).
% 34.15/34.32 0 [] -class_RealVector_Oreal__normed__vector(T_a)|c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Osgn__if(T_a)|c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(V_x,c_GCD_Ogcd__class_Olcm(V_y,V_z,tc_nat),tc_nat)=c_GCD_Ogcd__class_Olcm(V_y,c_GCD_Ogcd__class_Olcm(V_x,V_z,tc_nat),tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(c_GCD_Ogcd__class_Olcm(V_n,V_m,tc_nat),V_p,tc_nat)=c_GCD_Ogcd__class_Olcm(V_n,c_GCD_Ogcd__class_Olcm(V_m,V_p,tc_nat),tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(c_GCD_Ogcd__class_Olcm(V_x,V_y,tc_nat),V_z,tc_nat)=c_GCD_Ogcd__class_Olcm(V_x,c_GCD_Ogcd__class_Olcm(V_y,V_z,tc_nat),tc_nat).
% 34.15/34.32 0 [] -class_Ring__and__Field_Odivision__ring(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oinverse__class_Oinverse(V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] c_Complex_Ocnj(V_z)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)|V_z=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 34.15/34.32 0 [] c_Complex_Ocnj(V_x)!=c_Complex_Ocnj(V_y)|V_x=V_y.
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a)=c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oinverse__class_Oinverse(V_b,T_a),T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a)=c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oinverse__class_Oinverse(V_y,T_a),T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Int_Oiszero(c_HOL_Ozero__class_Ozero(T_a),T_a).
% 34.15/34.32 0 [] c_Complex_Oii!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)|c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(V_a,V_b,T_a),V_n,T_a)=c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_c,V_d,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_d,V_b,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_GCD_Ogcd__class_Ogcd(V_d,V_a,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_GCD_Ogcd__class_Ogcd(V_d,c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat)=V_y| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat)=V_x| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat)!=V_x|c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.32 0 [] -class_OrderedGroup_Opordered__ab__group__add__abs(T_a)|c_HOL_Oabs__class_Oabs(V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat)=c_GCD_Ogcd__class_Ogcd(V_n,V_m,tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat)=c_GCD_Ogcd__class_Ogcd(V_y,V_x,tc_nat).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Ozero__class_Ozero(T_a)=c_HOL_Oinverse__class_Odivide(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_x,c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat),tc_nat)=c_GCD_Ogcd__class_Ogcd(V_x,V_y,tc_nat).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a)!=c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a)|V_z=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_z,T_a)=c_HOL_Otimes__class_Otimes(V_w,V_y,T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_z,T_a)!=c_HOL_Otimes__class_Otimes(V_w,V_y,T_a)|V_z=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a)|c_HOL_Oinverse__class_Odivide(V_x,V_y,T_a)=c_HOL_Oinverse__class_Odivide(V_w,V_z,T_a).
% 34.15/34.32 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a)=c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a).
% 34.15/34.32 0 [] -class_RealVector_Oreal__normed__div__algebra(T_a)|c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_x,T_a),c_HOL_Osgn__class_Osgn(V_y,T_a),T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(V_a,T_a),c_HOL_Osgn__class_Osgn(V_b,T_a),T_a).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_A,V_B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_A=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_A,V_B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_B=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.15/34.32 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_x,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_x,V_a,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_x,tc_nat).
% 34.15/34.32 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(V_a,V_b,tc_nat),V_x,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_x,V_b,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_b,V_x,tc_nat).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a),V_c,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oabs__class_Oabs(V_l,T_a)!=c_HOL_Oabs__class_Oabs(V_k,T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_l,V_k,T_a).
% 34.15/34.32 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_y,V_x,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.32 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_z,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_y,V_z,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_x,V_y,tc_nat).
% 34.15/34.32 0 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)|V_m=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)|V_n=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_FFT__Mirabelle_Oroot(V_n)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 34.15/34.32 0 [] -class_Ring__and__Field_Osemiring__1(T_a)| -c_Int_Oiszero(c_HOL_Oone__class_Oone(T_a),T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Odivision__ring(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a)=c_HOL_Oone__class_Oone(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(T_a),T_a)=c_HOL_Oone__class_Oone(T_a).
% 34.15/34.32 0 [] c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Oone__class_Oone(tc_nat),T_a)=V_a.
% 34.15/34.32 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_HOL_Oone__class_Oone(tc_nat),T_a)=V_x.
% 34.15/34.32 0 [] c_Complex_Oii!=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(V_x,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=V_x.
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(c_HOL_Oone__class_Oone(tc_nat),V_x,tc_nat)=V_x.
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(V_A,V_B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|V_B=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(V_A,V_B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|V_A=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|V_m=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Olcm(V_m,V_n,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|V_n=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(T_a),V_n,T_a)=c_HOL_Oone__class_Oone(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Ozero__class_Ozero(T_a)!=c_HOL_Oone__class_Oone(T_a).
% 34.15/34.32 0 [] c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)|c_HOL_Oinverse__class_Odivide(V_a,c_HOL_Oone__class_Oone(T_a),T_a)=V_a.
% 34.15/34.32 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(T_a),T_a)=c_HOL_Oone__class_Oone(T_a).
% 34.15/34.32 0 [] -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_x,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(c_HOL_Oone__class_Oone(tc_nat),V_x,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_GCD_Ogcd__class_Ogcd(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] V_m=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 34.15/34.32 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),V_x,tc_nat).
% 34.15/34.32 0 [] c_Fact_Ofact__class_Ofact(c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(V_n),V_n,tc_Complex_Ocomplex)=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.15/34.32 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Oone__class_Oone(T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 34.15/34.32 0 [] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 34.15/34.32 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a)=V_a.
% 34.15/34.32 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a)=V_a.
% 34.15/34.32 0 [] -class_OrderedGroup_Ocomm__monoid__mult(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a)=V_a.
% 34.15/34.32 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_x,T_a)=V_x.
% 34.15/34.32 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat)=V_n.
% 34.15/34.32 0 [] c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=V_n.
% 34.15/34.32 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oone__class_Oone(T_a),T_a)=V_a.
% 34.15/34.32 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(T_a),V_a,T_a)=V_a.
% 34.15/34.32 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|V_m=c_HOL_Oone__class_Oone(tc_nat).
% 34.15/34.32 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|V_n=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.32 0 [] -class_RealVector_Oreal__normed__algebra__1(T_a)|c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(T_a),T_a)=c_HOL_Oone__class_Oone(T_a).
% 34.24/34.32 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 34.24/34.32 0 [] -class_Ring__and__Field_Ofield(T_a)| -class_Ring__and__Field_Odivision__by__zero(T_a)|c_HOL_Oinverse__class_Oinverse(V_x,T_a)!=c_HOL_Oone__class_Oone(T_a)|V_x=c_HOL_Oone__class_Oone(T_a).
% 34.24/34.32 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.32 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(V_a,c_HOL_Oone__class_Oone(T_a),T_a)=V_a.
% 34.24/34.32 0 [] c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat))!=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 34.24/34.32 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 34.24/34.32 0 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 34.24/34.32 0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 34.24/34.32 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 34.24/34.32 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 34.24/34.32 0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 34.24/34.32 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 34.24/34.32 0 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 34.24/34.32 0 [] class_Divides_Osemiring__div(tc_nat).
% 34.24/34.32 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 34.24/34.32 0 [] class_Ring__and__Field_Odvd(tc_nat).
% 34.24/34.32 0 [] class_Power_Opower(tc_nat).
% 34.24/34.32 0 [] class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Ofield(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Oidom(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Nat_Osemiring__char__0(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Ring__and__Field_Odvd(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Int_Onumber__ring(tc_Complex_Ocomplex).
% 34.24/34.32 0 [] class_Power_Opower(tc_Complex_Ocomplex).
% 34.24/34.32 end_of_list.
% 34.24/34.32
% 34.24/34.32 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 34.24/34.32
% 34.24/34.32 This ia a non-Horn set with equality. The strategy will be
% 34.24/34.32 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 34.24/34.32 deletion, with positive clauses in sos and nonpositive
% 34.24/34.32 clauses in usable.
% 34.24/34.32
% 34.24/34.32 dependent: set(knuth_bendix).
% 34.24/34.32 dependent: set(anl_eq).
% 34.24/34.32 dependent: set(para_from).
% 34.24/34.32 dependent: set(para_into).
% 34.24/34.32 dependent: clear(para_from_right).
% 34.24/34.32 dependent: clear(para_into_right).
% 34.24/34.32 dependent: set(para_from_vars).
% 34.24/34.32 dependent: set(eq_units_both_ways).
% 34.24/34.32 dependent: set(dynamic_demod_all).
% 34.24/34.32 dependent: set(dynamic_demod).
% 34.24/34.32 dependent: set(order_eq).
% 34.24/34.32 dependent: set(back_demod).
% 34.24/34.32 dependent: set(lrpo).
% 34.24/34.32 dependent: set(hyper_res).
% 34.24/34.32 dependent: set(unit_deletion).
% 34.24/34.32 dependent: set(factor).
% 34.24/34.32
% 34.24/34.32 ------------> process usable:
% 34.24/34.32 ** KEPT (pick-wt=22): 1 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),D,A)=c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A).
% 34.24/34.32 ** KEPT (pick-wt=11): 2 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)|B=A.
% 34.24/34.32 Following clause subsumed by 2 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|B=A| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 34.24/34.32 Following clause subsumed by 2 during input processing: 0 [] A=B| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 34.24/34.32 Following clause subsumed by 2 during input processing: 0 [] A=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 Following clause subsumed by 2 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|B=A| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 34.24/34.32 Following clause subsumed by 2 during input processing: 0 [] A=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 Following clause subsumed by 2 during input processing: 0 [] A=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=11): 3 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(C,B,tc_nat),tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=11): 4 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat).
% 34.24/34.32 Following clause subsumed by 4 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat).
% 34.24/34.32 Following clause subsumed by 3 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(C,B,tc_nat),tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=11): 5 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=11): 6 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 34.24/34.32 Following clause subsumed by 4 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat).
% 34.24/34.32 Following clause subsumed by 3 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(C,B,tc_nat),tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=12): 7 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 Following clause subsumed by 7 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=6): 8 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,B,A).
% 34.24/34.32 ** KEPT (pick-wt=14): 9 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(D,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 34.24/34.32 ** KEPT (pick-wt=14): 10 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A).
% 34.24/34.32 ** KEPT (pick-wt=14): 11 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(C,c_HOL_Ozero__class_Ozero(A),A),A).
% 34.24/34.32 ** KEPT (pick-wt=17): 12 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oabs__class_Oabs(c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A).
% 34.24/34.32 ** KEPT (pick-wt=25): 13 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),c_HOL_Oinverse__class_Odivide(D,E,A),A)=c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A).
% 34.24/34.32 ** KEPT (pick-wt=14): 14 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(B,C,A).
% 34.24/34.32 ** KEPT (pick-wt=19): 15 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=13): 16 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(A)|c_Power_Opower__class_Opower(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=31): 17 [] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,E,A),A)=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(E,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 34.24/34.32 ** KEPT (pick-wt=10): 18 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 34.24/34.32 ** KEPT (pick-wt=10): 19 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 34.24/34.32 ** KEPT (pick-wt=20): 20 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=16): 21 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=17): 22 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=22): 23 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=15): 24 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(A,B,tc_nat),C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 Following clause subsumed by 24 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(A,B,tc_nat),C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 Following clause subsumed by 24 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(A,B,tc_nat),C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 Following clause subsumed by 24 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(A,B,tc_nat),C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 Following clause subsumed by 24 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(A,B,tc_nat),C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=15): 25 [] -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(A,B,tc_nat),C,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=15): 26 [] -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(A,B,tc_nat),C,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=13): 27 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 34.24/34.32 ** KEPT (pick-wt=13): 28 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 34.24/34.32 ** KEPT (pick-wt=13): 29 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 34.24/34.32 ** KEPT (pick-wt=13): 30 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(D,B,A),C,A).
% 34.24/34.32 ** KEPT (pick-wt=15): 31 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Odivide(B,C,A),A)=c_HOL_Oinverse__class_Odivide(C,B,A).
% 34.24/34.32 ** KEPT (pick-wt=14): 32 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Oone__class_Oone(A)|c_HOL_Oinverse__class_Oinverse(B,A)=C.
% 34.24/34.32 ** KEPT (pick-wt=8): 33 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,B,A)=B.
% 34.24/34.32 ** KEPT (pick-wt=14): 34 [] -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(B,A)!=c_HOL_Oinverse__class_Oinverse(C,A)|B=C.
% 34.24/34.32 ** KEPT (pick-wt=20): 35 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Oinverse__class_Oinverse(B,A)!=c_HOL_Oinverse__class_Oinverse(C,A)|B=C|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=11): 36 [] -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=9): 37 [] -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=20): 38 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A).
% 34.24/34.32 ** KEPT (pick-wt=20): 39 [] -class_OrderedGroup_Ocomm__monoid__mult(A)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A).
% 34.24/34.32 ** KEPT (pick-wt=17): 40 [] -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(B,C,A),A)=c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),C,A).
% 34.24/34.32 ** KEPT (pick-wt=16): 41 [] -class_Ring__and__Field_Ofield(A)|c_HOL_Oinverse__class_Odivide(B,C,A)!=c_HOL_Oone__class_Oone(A)|C=c_HOL_Ozero__class_Ozero(A)|B=C.
% 34.24/34.32 ** KEPT (pick-wt=17): 42 [] -class_OrderedGroup_Oab__semigroup__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 34.24/34.32 ** KEPT (pick-wt=17): 43 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 34.24/34.32 ** KEPT (pick-wt=17): 44 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 34.24/34.32 Following clause subsumed by 44 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 34.24/34.32 ** KEPT (pick-wt=17): 45 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A)=c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(B,D,A),A).
% 34.24/34.32 Following clause subsumed by 44 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A).
% 34.24/34.32 ** KEPT (pick-wt=15): 46 [] -class_Ring__and__Field_Ofield(A)|c_HOL_Oinverse__class_Oinverse(B,A)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=15): 47 [] -class_Ring__and__Field_Ofield(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),B,A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=15): 48 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),B,A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=15): 49 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(B,A),A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=21): 50 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_Divides_Odiv__class_Odiv(C,D,A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=21): 51 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)=c_Divides_Odiv__class_Odiv(B,D,A)|C=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=11): 52 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Osgn__class_Osgn(c_HOL_Osgn__class_Osgn(B,A),A)=c_HOL_Osgn__class_Osgn(B,A).
% 34.24/34.32 ** KEPT (pick-wt=12): 54 [copy,53,flip.2] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Osgn__class_Osgn(B,A),A)=c_HOL_Oabs__class_Oabs(B,A).
% 34.24/34.32 ** KEPT (pick-wt=24): 55 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,D,A),c_Divides_Odiv__class_Odiv(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(D,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(D,B,A).
% 34.24/34.32 ** KEPT (pick-wt=24): 56 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(c_Divides_Odiv__class_Odiv(B,C,A),c_Divides_Odiv__class_Odiv(D,C,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 34.24/34.32 ** KEPT (pick-wt=11): 57 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oabs__class_Oabs(c_Nat_Osemiring__1__class_Oof__nat(B,A),A)=c_Nat_Osemiring__1__class_Oof__nat(B,A).
% 34.24/34.32 ** KEPT (pick-wt=13): 58 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=15): 59 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=15): 60 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=19): 61 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(B,A),c_HOL_Oinverse__class_Oinverse(C,A),A).
% 34.24/34.32 ** KEPT (pick-wt=25): 62 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Oinverse(C,A),c_HOL_Oinverse__class_Oinverse(B,A),A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=11): 63 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Ozero__class_Ozero(A),B,A).
% 34.24/34.32 ** KEPT (pick-wt=13): 64 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A)=B|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=9): 65 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=6): 66 [] c_Fact_Ofact__class_Ofact(A,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.32 Following clause subsumed by 7 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=15): 68 [copy,67,flip.3] -class_Ring__and__Field_Ofield(A)|B=c_HOL_Ozero__class_Ozero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(C,B,A),B,A)=C.
% 34.24/34.32 Following clause subsumed by 68 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)|B=c_HOL_Ozero__class_Ozero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(C,B,A),B,A)=C.
% 34.24/34.32 Following clause subsumed by 68 during input processing: 0 [flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 Following clause subsumed by 68 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 Following clause subsumed by 45 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(D,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),E,A),A).
% 34.24/34.32 Following clause subsumed by 44 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(D,E,A),A),A).
% 34.24/34.32 ** KEPT (pick-wt=23): 69 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A).
% 34.24/34.32 ** KEPT (pick-wt=15): 70 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=15): 71 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),B,A)=C|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=17): 72 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=17): 73 [] -class_Ring__and__Field_Ono__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 Following clause subsumed by 73 during input processing: 0 [] -class_Ring__and__Field_Ono__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=15): 74 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=10): 75 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=10): 76 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=12): 77 [] -class_Nat_Osemiring__char__0(A)|c_Nat_Osemiring__1__class_Oof__nat(B,A)!=c_Nat_Osemiring__1__class_Oof__nat(C,A)|B=C.
% 34.24/34.32 ** KEPT (pick-wt=11): 78 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A),A).
% 34.24/34.32 ** KEPT (pick-wt=12): 79 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Oabs__class_Oabs(B,A),A)=B.
% 34.24/34.32 ** KEPT (pick-wt=19): 80 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|C=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat).
% 34.24/34.32 Following clause subsumed by 80 during input processing: 0 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|C=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=10): 81 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)=A| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=10): 82 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)!=B|c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=10): 83 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)!=A|c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 34.24/34.32 Following clause subsumed by 81 during input processing: 0 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)=A| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 34.24/34.32 Following clause subsumed by 82 during input processing: 0 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)!=B|c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=10): 84 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)=B| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 Following clause subsumed by 81 during input processing: 0 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)=A| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 34.24/34.32 Following clause subsumed by 84 during input processing: 0 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)=B| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=11): 85 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(C,A,tc_nat),B,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=11): 86 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(A,C,tc_nat),B,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=11): 87 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=11): 88 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 Following clause subsumed by 85 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(C,A,tc_nat),B,tc_nat).
% 34.24/34.32 Following clause subsumed by 86 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(A,C,tc_nat),B,tc_nat).
% 34.24/34.32 Following clause subsumed by 88 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 Following clause subsumed by 87 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=18): 89 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=18): 90 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=15): 91 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=11): 92 [] -class_Ring__and__Field_Ofield(A)|c_HOL_Oinverse__class_Oinverse(B,A)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A).
% 34.24/34.32 Following clause subsumed by 92 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber__ring(A)|c_HOL_Oinverse__class_Oinverse(B,A)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A).
% 34.24/34.32 ** KEPT (pick-wt=12): 93 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=12): 94 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=9): 95 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(C,B,A),A).
% 34.24/34.32 ** KEPT (pick-wt=9): 96 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A).
% 34.24/34.32 ** KEPT (pick-wt=9): 97 [] -class_Ring__and__Field_Odvd(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A).
% 34.24/34.32 ** KEPT (pick-wt=21): 99 [copy,98,flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),B,A),C,A)=c_HOL_Oinverse__class_Odivide(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A).
% 34.24/34.32 ** KEPT (pick-wt=11): 100 [] -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oinverse__class_Oinverse(B,A),A)=B.
% 34.24/34.32 ** KEPT (pick-wt=17): 101 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A)=c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),A).
% 34.24/34.32 ** KEPT (pick-wt=11): 102 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 34.24/34.32 Following clause subsumed by 102 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 34.24/34.32 ** KEPT (pick-wt=9): 103 [] -class_OrderedGroup_Opordered__ab__group__add__abs(A)|c_HOL_Oabs__class_Oabs(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=16): 104 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)!=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=13): 105 [] -class_Ring__and__Field_Ofield(A)|B=c_HOL_Ozero__class_Ozero(A)|c_HOL_Oinverse__class_Odivide(B,B,A)=c_HOL_Oone__class_Oone(A).
% 34.24/34.32 Following clause subsumed by 105 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)|c_HOL_Oinverse__class_Odivide(B,B,A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 Following clause subsumed by 105 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(B,B,A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=10): 106 [] -class_Ring__and__Field_Ofield(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=12): 107 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 Following clause subsumed by 107 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=10): 108 [] -class_RealVector_Oreal__normed__field(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=32): 110 [copy,109,flip.1,flip.2] c_HOL_Otimes__class_Otimes(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)!=C|c_HOL_Otimes__class_Otimes(D,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)!=B|c_GCD_Ogcd__class_Ogcd(B,C,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)|c_GCD_Ogcd__class_Ogcd(D,A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=21): 111 [] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),D,A)=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,D,A),C,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 34.24/34.32 ** KEPT (pick-wt=16): 112 [] -class_Ring__and__Field_Oordered__idom(A)|c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),C,A)=c_Power_Opower__class_Opower(B,C,A)| -c_Parity_Oeven__odd__class_Oeven(C,tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=15): 113 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oabs__class_Oabs(c_Power_Opower__class_Opower(B,C,A),A)=c_Power_Opower__class_Opower(c_HOL_Oabs__class_Oabs(B,A),C,A).
% 34.24/34.32 ** KEPT (pick-wt=16): 114 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 34.24/34.32 ** KEPT (pick-wt=15): 116 [copy,115,flip.3] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(B,A),A)=c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(B,A),A).
% 34.24/34.32 ** KEPT (pick-wt=19): 117 [] -class_Ring__and__Field_Oordered__field(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A)=c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A).
% 34.24/34.32 ** KEPT (pick-wt=12): 118 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Osgn__class_Osgn(B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=12): 119 [] -class_RealVector_Oreal__normed__vector(A)|c_HOL_Osgn__class_Osgn(B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=23): 120 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)=c_HOL_Oinverse__class_Odivide(B,D,A)|C=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=23): 121 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_HOL_Oinverse__class_Odivide(C,D,A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=19): 122 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),D,A)=c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 34.24/34.32 ** KEPT (pick-wt=15): 123 [] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A)=C| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 34.24/34.32 ** KEPT (pick-wt=15): 124 [] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A)=B| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 34.24/34.32 ** KEPT (pick-wt=10): 125 [] -class_Nat_Osemiring__char__0(A)|c_Nat_Osemiring__1__class_Oof__nat(c_Fact_Ofact__class_Ofact(B,tc_nat),A)!=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.32 ** KEPT (pick-wt=20): 126 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)|D=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 34.24/34.32 ** KEPT (pick-wt=20): 127 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)|D=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A).
% 34.24/34.32 ** KEPT (pick-wt=18): 128 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|C=c_HOL_Ozero__class_Ozero(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat).
% 34.24/34.32 ** KEPT (pick-wt=15): 129 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 Following clause subsumed by 3 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat).
% 34.24/34.32 Following clause subsumed by 4 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 34.24/34.32 Following clause subsumed by 129 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.32 Following clause subsumed by 129 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.33 Following clause subsumed by 129 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.33 Following clause subsumed by 129 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.33 Following clause subsumed by 129 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.33 Following clause subsumed by 7 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 34.24/34.33 Following clause subsumed by 7 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=17): 131 [copy,130,flip.2] -class_Ring__and__Field_Oordered__field(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oabs__class_Oabs(B,A),A)=c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Oinverse(B,A),A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=21): 132 [] -class_Ring__and__Field_Oordered__field(A)|c_HOL_Oabs__class_Oabs(c_HOL_Oinverse__class_Odivide(B,C,A),A)=c_HOL_Oinverse__class_Odivide(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(C,A),A)|C=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 Following clause subsumed by 18 during input processing: 0 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 34.24/34.33 ** KEPT (pick-wt=13): 133 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,B,A)=c_HOL_Oone__class_Oone(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=14): 134 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=16): 135 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(C,D,A).
% 34.24/34.33 ** KEPT (pick-wt=16): 136 [] -class_Ring__and__Field_Oidom(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 34.24/34.33 ** KEPT (pick-wt=11): 137 [] -class_OrderedGroup_Opordered__ab__group__add__abs(A)|c_HOL_Oabs__class_Oabs(c_HOL_Oabs__class_Oabs(B,A),A)=c_HOL_Oabs__class_Oabs(B,A).
% 34.24/34.33 ** KEPT (pick-wt=17): 138 [] c_GCD_Ogcd__class_Ogcd(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_GCD_Ogcd__class_Ogcd(A,C,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=17): 139 [] c_GCD_Ogcd__class_Ogcd(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=9): 140 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=9): 141 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=17): 142 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 34.24/34.33 ** KEPT (pick-wt=16): 143 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(C,B,tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)|A=C.
% 34.24/34.33 ** KEPT (pick-wt=16): 144 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=C.
% 34.24/34.33 Following clause subsumed by 144 during input processing: 0 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)|B=C|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=15): 146 [copy,145,flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=24): 147 [] -class_Divides_Osemiring__div(A)|c_Power_Opower__class_Opower(c_Divides_Odiv__class_Odiv(B,C,A),D,A)=c_Divides_Odiv__class_Odiv(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 34.24/34.33 ** KEPT (pick-wt=17): 148 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Otimes__class_Otimes(B,C,tc_nat),A)=c_HOL_Otimes__class_Otimes(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A).
% 34.24/34.33 ** KEPT (pick-wt=15): 149 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oabs__class_Oabs(B,A),c_HOL_Oabs__class_Oabs(B,A),A)=c_HOL_Otimes__class_Otimes(B,B,A).
% 34.24/34.33 ** KEPT (pick-wt=19): 150 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Oinverse__class_Oinverse(c_Power_Opower__class_Opower(B,C,A),A)=c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Oinverse(B,A),C,A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=14): 152 [copy,151,flip.1] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=A|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=7): 153 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(A),A).
% 34.24/34.33 ** KEPT (pick-wt=17): 155 [copy,154,flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 Following clause subsumed by 155 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oinverse__class_Odivide(B,C,A),C,A)=B|C=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=10): 156 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=10): 157 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=10): 158 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 Following clause subsumed by 158 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=10): 159 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 Following clause subsumed by 159 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 Following clause subsumed by 156 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=10): 160 [] -class_Ring__and__Field_Omult__zero(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=10): 161 [] -class_Ring__and__Field_Omult__zero(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=10): 162 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=10): 163 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=9): 164 [] -class_Ring__and__Field_Osemiring__1(A)|B=c_HOL_Ozero__class_Ozero(A)| -c_Int_Oiszero(B,A).
% 34.24/34.33 ** KEPT (pick-wt=12): 165 [] -class_Ring__and__Field_Oordered__idom(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(B,A),C,A).
% 34.24/34.33 ** KEPT (pick-wt=12): 166 [] -class_Ring__and__Field_Oordered__idom(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oabs__class_Oabs(B,A),C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 34.24/34.33 ** KEPT (pick-wt=12): 167 [] -class_Ring__and__Field_Oordered__idom(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oabs__class_Oabs(C,A),A).
% 34.24/34.33 ** KEPT (pick-wt=12): 168 [] -class_Ring__and__Field_Oordered__idom(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Oabs__class_Oabs(C,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 34.24/34.33 ** KEPT (pick-wt=19): 169 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_GCD_Ogcd__class_Ogcd(c_HOL_Otimes__class_Otimes(A,C,tc_nat),B,tc_nat)=c_GCD_Ogcd__class_Ogcd(C,B,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=9): 170 [] -class_RealVector_Oreal__normed__vector(A)|c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=9): 171 [] -class_Ring__and__Field_Osgn__if(A)|c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=9): 172 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Osgn__class_Osgn(c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=14): 173 [] -class_Ring__and__Field_Odivision__ring(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=12): 174 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Oinverse__class_Oinverse(B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=9): 175 [] c_Complex_Ocnj(A)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)|A=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=8): 176 [] c_Complex_Ocnj(A)!=c_Complex_Ocnj(B)|A=B.
% 34.24/34.33 ** KEPT (pick-wt=13): 178 [copy,177,flip.2] -class_Ring__and__Field_Ofield(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(C,A),A)=c_HOL_Oinverse__class_Odivide(B,C,A).
% 34.24/34.33 Following clause subsumed by 178 during input processing: 0 [flip.3] -class_Ring__and__Field_Ofield(A)| -class_Int_Onumber__ring(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oinverse__class_Oinverse(C,A),A)=c_HOL_Oinverse__class_Odivide(B,C,A).
% 34.24/34.33 ** KEPT (pick-wt=6): 179 [] -class_Ring__and__Field_Osemiring__1(A)|c_Int_Oiszero(c_HOL_Ozero__class_Ozero(A),A).
% 34.24/34.33 ** KEPT (pick-wt=4): 181 [copy,180,flip.1] c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)!=c_Complex_Oii.
% 34.24/34.33 ** KEPT (pick-wt=24): 182 [] -class_Ring__and__Field_Ofield(A)|c_Power_Opower__class_Opower(c_HOL_Oinverse__class_Odivide(B,C,A),D,A)=c_HOL_Oinverse__class_Odivide(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A)|C=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=20): 183 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(C,E,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 34.24/34.33 ** KEPT (pick-wt=24): 184 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_GCD_Ogcd__class_Ogcd(A,C,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|c_GCD_Ogcd__class_Ogcd(A,c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=10): 185 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=10): 186 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)=A| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=10): 187 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=A|c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=12): 188 [] -class_OrderedGroup_Opordered__ab__group__add__abs(A)|c_HOL_Oabs__class_Oabs(B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=12): 189 [] c_Parity_Oeven__odd__class_Oeven(A,tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat).
% 34.24/34.33 Following clause subsumed by 107 during input processing: 0 [flip.3] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=28): 190 [] -class_Ring__and__Field_Ofield(A)|c_HOL_Oinverse__class_Odivide(B,C,A)!=c_HOL_Oinverse__class_Odivide(D,E,A)|E=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|c_HOL_Otimes__class_Otimes(B,E,A)=c_HOL_Otimes__class_Otimes(D,C,A).
% 34.24/34.33 ** KEPT (pick-wt=28): 191 [] -class_Ring__and__Field_Ofield(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Otimes__class_Otimes(D,E,A)|C=c_HOL_Ozero__class_Ozero(A)|E=c_HOL_Ozero__class_Ozero(A)|c_HOL_Oinverse__class_Odivide(B,E,A)=c_HOL_Oinverse__class_Odivide(D,C,A).
% 34.24/34.33 ** KEPT (pick-wt=17): 193 [copy,192,flip.2] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A)=c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),A).
% 34.24/34.33 ** KEPT (pick-wt=17): 194 [] -class_RealVector_Oreal__normed__div__algebra(A)|c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Osgn__class_Osgn(C,A),A).
% 34.24/34.33 ** KEPT (pick-wt=17): 195 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Osgn__class_Osgn(c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Osgn__class_Osgn(B,A),c_HOL_Osgn__class_Osgn(C,A),A).
% 34.24/34.33 ** KEPT (pick-wt=11): 196 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=11): 197 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 Following clause subsumed by 197 during input processing: 0 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 Following clause subsumed by 196 during input processing: 0 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 Following clause subsumed by 5 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),C,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.33 Following clause subsumed by 6 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),C,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat).
% 34.24/34.33 Following clause subsumed by 146 during input processing: 0 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Odivide(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 34.24/34.33 ** KEPT (pick-wt=13): 198 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oabs__class_Oabs(B,A)!=c_HOL_Oabs__class_Oabs(C,A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 34.24/34.33 Following clause subsumed by 7 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(C,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.33 Following clause subsumed by 7 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(B,C,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,C,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=11): 199 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(A,B,tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=11): 200 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(A,B,tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=5): 201 [] c_FFT__Mirabelle_Oroot(A)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=6): 202 [] -class_Ring__and__Field_Osemiring__1(A)| -c_Int_Oiszero(c_HOL_Oone__class_Oone(A),A).
% 34.24/34.33 ** KEPT (pick-wt=9): 203 [] -class_Ring__and__Field_Odivision__ring(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A)=c_HOL_Oone__class_Oone(A).
% 34.24/34.33 ** KEPT (pick-wt=11): 204 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(c_HOL_Oone__class_Oone(A),A)=c_HOL_Oone__class_Oone(A).
% 34.24/34.33 ** KEPT (pick-wt=9): 205 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 34.24/34.33 ** KEPT (pick-wt=9): 206 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 34.24/34.33 ** KEPT (pick-wt=4): 208 [copy,207,flip.1] c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)!=c_Complex_Oii.
% 34.24/34.33 ** KEPT (pick-wt=11): 209 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=11): 210 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 Following clause subsumed by 210 during input processing: 0 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 Following clause subsumed by 209 during input processing: 0 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=10): 211 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A)=c_HOL_Oone__class_Oone(A).
% 34.24/34.33 ** KEPT (pick-wt=9): 212 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 34.24/34.33 ** KEPT (pick-wt=7): 213 [] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 34.24/34.33 ** KEPT (pick-wt=9): 214 [] -class_Ring__and__Field_Ofield(A)|c_HOL_Oinverse__class_Odivide(B,c_HOL_Oone__class_Oone(A),A)=B.
% 34.24/34.33 ** KEPT (pick-wt=9): 215 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oabs__class_Oabs(c_HOL_Oone__class_Oone(A),A)=c_HOL_Oone__class_Oone(A).
% 34.24/34.33 ** KEPT (pick-wt=4): 216 [] -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=9): 217 [] A=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=7): 218 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),B,A).
% 34.24/34.33 Following clause subsumed by 213 during input processing: 0 [flip.2] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 34.24/34.33 ** KEPT (pick-wt=9): 219 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A)=B.
% 34.24/34.33 ** KEPT (pick-wt=9): 220 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 34.24/34.33 ** KEPT (pick-wt=9): 221 [] -class_OrderedGroup_Ocomm__monoid__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 34.24/34.33 ** KEPT (pick-wt=9): 222 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 34.24/34.33 ** KEPT (pick-wt=9): 223 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A)=B.
% 34.24/34.33 Following clause subsumed by 222 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 34.24/34.33 ** KEPT (pick-wt=11): 224 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=11): 225 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=9): 226 [] -class_RealVector_Oreal__normed__algebra__1(A)|c_HOL_Osgn__class_Osgn(c_HOL_Oone__class_Oone(A),A)=c_HOL_Oone__class_Oone(A).
% 34.24/34.33 ** KEPT (pick-wt=14): 227 [] -class_Ring__and__Field_Ofield(A)| -class_Ring__and__Field_Odivision__by__zero(A)|c_HOL_Oinverse__class_Oinverse(B,A)!=c_HOL_Oone__class_Oone(A)|B=c_HOL_Oone__class_Oone(A).
% 34.24/34.33 ** KEPT (pick-wt=9): 228 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A)=B.
% 34.24/34.33 ** KEPT (pick-wt=6): 229 [] c_FFT__Mirabelle_Oroot(c_HOL_Oone__class_Oone(tc_nat))!=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.24/34.33 37 back subsumes 36.
% 34.24/34.33 ** KEPT (pick-wt=6): 243 [copy,66,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Fact_Ofact__class_Ofact(A,tc_nat).
% 34.24/34.33 85 back subsumes 26.
% 34.24/34.33 86 back subsumes 25.
% 34.24/34.33 87 back subsumes 60.
% 34.24/34.33 88 back subsumes 59.
% 34.24/34.33 92 back subsumes 46.
% 34.24/34.33 106 back subsumes 58.
% 34.24/34.33 174 back subsumes 173.
% 34.24/34.33 ** KEPT (pick-wt=5): 258 [copy,201,flip.1] c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex)!=c_FFT__Mirabelle_Oroot(A).
% 34.24/34.33 218 back subsumes 78.
% 34.24/34.33 Following clause subsumed by 66 during input processing: 0 [copy,243,flip.1] c_Fact_Ofact__class_Ofact(A,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 Following clause subsumed by 201 during input processing: 0 [copy,258,flip.1] c_FFT__Mirabelle_Oroot(A)!=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 34.24/34.33
% 34.24/34.33 ------------> process sos:
% 34.24/34.33 ** KEPT (pick-wt=3): 259 [] A=A.
% 34.24/34.33 ** KEPT (pick-wt=9): 260 [] c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),tc_nat)=A.
% 34.24/34.33 ---> New Demodulator: 261 [new_demod,260] c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),tc_nat)=A.
% 34.24/34.33 ** KEPT (pick-wt=9): 262 [] c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Olcm(A,B,tc_nat),tc_nat)=A.
% 34.24/34.33 ---> New Demodulator: 263 [new_demod,262] c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Olcm(A,B,tc_nat),tc_nat)=A.
% 34.24/34.33 ** KEPT (pick-wt=4): 264 [] c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=12): 265 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=7): 266 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(B,A,tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=7): 267 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(A,B,tc_nat),tc_nat).
% 34.24/34.33 Following clause subsumed by 266 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(B,A,tc_nat),tc_nat).
% 34.24/34.33 Following clause subsumed by 267 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(A,B,tc_nat),tc_nat).
% 34.24/34.33 Following clause subsumed by 267 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(A,B,tc_nat),tc_nat).
% 34.24/34.33 Following clause subsumed by 266 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_GCD_Ogcd__class_Olcm(B,A,tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=8): 268 [] c_GCD_Ogcd__class_Olcm(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ---> New Demodulator: 269 [new_demod,268] c_GCD_Ogcd__class_Olcm(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=8): 270 [] c_GCD_Ogcd__class_Olcm(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ---> New Demodulator: 271 [new_demod,270] c_GCD_Ogcd__class_Olcm(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [demod,269] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [demod,271] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=11): 272 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=11): 273 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=15): 274 [] c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat)=c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 34.24/34.33 ---> New Demodulator: 275 [new_demod,274] c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat)=c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=19): 276 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat),c_GCD_Ogcd__class_Ogcd(c_GCD_Ogcd__class_Olcm(A,B,tc_nat),c_GCD_Ogcd__class_Olcm(A,C,tc_nat),tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=18): 277 [] c_HOL_Otimes__class_Otimes(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)=c_GCD_Ogcd__class_Ogcd(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 34.24/34.33 ---> New Demodulator: 278 [new_demod,277] c_HOL_Otimes__class_Otimes(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)=c_GCD_Ogcd__class_Ogcd(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=6): 279 [] c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 34.24/34.33 ---> New Demodulator: 280 [new_demod,279] c_Complex_Ocnj(c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex))=c_HOL_Ozero__class_Ozero(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=9): 281 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=19): 282 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Olcm(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),c_GCD_Ogcd__class_Ogcd(A,C,tc_nat),tc_nat),c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=6): 283 [] c_GCD_Ogcd__class_Olcm(A,A,tc_nat)=A.
% 34.24/34.33 ---> New Demodulator: 284 [new_demod,283] c_GCD_Ogcd__class_Olcm(A,A,tc_nat)=A.
% 34.24/34.33 ** KEPT (pick-wt=7): 285 [] c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ---> New Demodulator: 286 [new_demod,285] c_Fact_Ofact__class_Ofact(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=11): 287 [] c_Complex_Ocnj(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex))=c_Power_Opower__class_Opower(c_Complex_Ocnj(A),B,tc_Complex_Ocomplex).
% 34.24/34.33 ---> New Demodulator: 288 [new_demod,287] c_Complex_Ocnj(c_Power_Opower__class_Opower(A,B,tc_Complex_Ocomplex))=c_Power_Opower__class_Opower(c_Complex_Ocnj(A),B,tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=7): 289 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),B,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=7): 290 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),A,tc_nat).
% 34.24/34.33 Following clause subsumed by 290 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),A,tc_nat).
% 34.24/34.33 Following clause subsumed by 289 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),B,tc_nat).
% 34.24/34.33 Following clause subsumed by 290 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),A,tc_nat).
% 34.24/34.33 Following clause subsumed by 289 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),B,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=15): 292 [copy,291,flip.1] c_HOL_Otimes__class_Otimes(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),c_GCD_Ogcd__class_Olcm(A,B,tc_nat),tc_nat)=c_HOL_Otimes__class_Otimes(A,B,tc_nat).
% 34.24/34.33 ---> New Demodulator: 293 [new_demod,292] c_HOL_Otimes__class_Otimes(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),c_GCD_Ogcd__class_Olcm(A,B,tc_nat),tc_nat)=c_HOL_Otimes__class_Otimes(A,B,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=7): 294 [] c_GCD_Ogcd__class_Ogcd(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 34.24/34.33 ---> New Demodulator: 295 [new_demod,294] c_GCD_Ogcd__class_Ogcd(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A.
% 34.24/34.33 ** KEPT (pick-wt=7): 296 [] c_GCD_Ogcd__class_Ogcd(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 34.24/34.33 ---> New Demodulator: 297 [new_demod,296] c_GCD_Ogcd__class_Ogcd(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 34.24/34.33 ** KEPT (pick-wt=10): 298 [] c_Ring__and__Field_Odvd__class_Odvd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=6): 299 [] c_GCD_Ogcd__class_Ogcd(A,A,tc_nat)=A.
% 34.24/34.33 ---> New Demodulator: 300 [new_demod,299] c_GCD_Ogcd__class_Ogcd(A,A,tc_nat)=A.
% 34.24/34.33 ** KEPT (pick-wt=5): 301 [] c_Complex_Ocnj(c_Complex_Ocnj(A))=A.
% 34.24/34.33 ---> New Demodulator: 302 [new_demod,301] c_Complex_Ocnj(c_Complex_Ocnj(A))=A.
% 34.24/34.33 ** KEPT (pick-wt=9): 303 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)=c_GCD_Ogcd__class_Olcm(B,A,tc_nat).
% 34.24/34.33 Following clause subsumed by 303 during input processing: 0 [] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)=c_GCD_Ogcd__class_Olcm(B,A,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=4): 304 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=15): 305 [] c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)=c_GCD_Ogcd__class_Ogcd(B,c_GCD_Ogcd__class_Ogcd(A,C,tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=15): 306 [] c_GCD_Ogcd__class_Ogcd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),C,tc_nat)=c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat).
% 34.24/34.33 ---> New Demodulator: 307 [new_demod,306] c_GCD_Ogcd__class_Ogcd(c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),C,tc_nat)=c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat).
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [demod,307] c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)=c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=5): 308 [] c_Ring__and__Field_Odvd__class_Odvd(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=8): 309 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ---> New Demodulator: 310 [new_demod,309] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=8): 311 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ---> New Demodulator: 312 [new_demod,311] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=12): 313 [] c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Olcm(A,B,tc_nat),tc_nat)=c_GCD_Ogcd__class_Olcm(A,B,tc_nat).
% 34.24/34.33 ---> New Demodulator: 314 [new_demod,313] c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Olcm(A,B,tc_nat),tc_nat)=c_GCD_Ogcd__class_Olcm(A,B,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=15): 315 [] c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat)=c_GCD_Ogcd__class_Olcm(B,c_GCD_Ogcd__class_Olcm(A,C,tc_nat),tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=15): 316 [] c_GCD_Ogcd__class_Olcm(c_GCD_Ogcd__class_Olcm(A,B,tc_nat),C,tc_nat)=c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat).
% 34.24/34.33 ---> New Demodulator: 317 [new_demod,316] c_GCD_Ogcd__class_Olcm(c_GCD_Ogcd__class_Olcm(A,B,tc_nat),C,tc_nat)=c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat).
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [demod,317] c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat)=c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat).
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [demod,300] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=9): 318 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)=c_GCD_Ogcd__class_Ogcd(B,A,tc_nat).
% 34.24/34.33 Following clause subsumed by 318 during input processing: 0 [] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)=c_GCD_Ogcd__class_Ogcd(B,A,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=12): 319 [] c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),tc_nat)=c_GCD_Ogcd__class_Ogcd(A,B,tc_nat).
% 34.24/34.33 ---> New Demodulator: 320 [new_demod,319] c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Ogcd(A,B,tc_nat),tc_nat)=c_GCD_Ogcd__class_Ogcd(A,B,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=6): 321 [] c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.24/34.33 ---> New Demodulator: 322 [new_demod,321] c_Complex_Ocnj(c_HOL_Oone__class_Oone(tc_Complex_Ocomplex))=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [demod,284] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=7): 323 [] c_GCD_Ogcd__class_Olcm(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 34.24/34.33 ---> New Demodulator: 324 [new_demod,323] c_GCD_Ogcd__class_Olcm(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 34.24/34.33 ** KEPT (pick-wt=7): 325 [] c_GCD_Ogcd__class_Olcm(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=A.
% 34.24/34.33 ---> New Demodulator: 326 [new_demod,325] c_GCD_Ogcd__class_Olcm(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=A.
% 34.24/34.33 ** KEPT (pick-wt=6): 327 [] c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.24/34.33 ---> New Demodulator: 328 [new_demod,327] c_FFT__Mirabelle_Oroot(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=8): 329 [] c_GCD_Ogcd__class_Ogcd(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ---> New Demodulator: 330 [new_demod,329] c_GCD_Ogcd__class_Ogcd(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=8): 331 [] c_GCD_Ogcd__class_Ogcd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ---> New Demodulator: 332 [new_demod,331] c_GCD_Ogcd__class_Ogcd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [demod,330] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=5): 333 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=7): 334 [] c_Fact_Ofact__class_Ofact(c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ---> New Demodulator: 335 [new_demod,334] c_Fact_Ofact__class_Ofact(c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=8): 336 [] c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),A,tc_Complex_Ocomplex)=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=9): 338 [copy,337,flip.1] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ---> New Demodulator: 339 [new_demod,338] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=7): 340 [] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=A.
% 34.24/34.33 ---> New Demodulator: 341 [new_demod,340] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=A.
% 34.24/34.33 ** KEPT (pick-wt=7): 342 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 34.24/34.33 ---> New Demodulator: 343 [new_demod,342] c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 34.24/34.33 Following clause subsumed by 264 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [demod,343] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 344 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 345 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 346 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 347 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 348 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 349 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 350 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 351 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 352 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 353 [] class_Divides_Osemiring__div(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 354 [] class_Nat_Osemiring__char__0(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 355 [] class_Ring__and__Field_Odvd(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 356 [] class_Power_Opower(tc_nat).
% 34.24/34.33 ** KEPT (pick-wt=2): 357 [] class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 358 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 359 [] class_RealVector_Oreal__normed__div__algebra(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 360 [] class_RealVector_Oreal__normed__algebra__1(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 361 [] class_Ring__and__Field_Ono__zero__divisors(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 362 [] class_Ring__and__Field_Odivision__by__zero(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 363 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 364 [] class_RealVector_Oreal__normed__algebra(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 365 [] class_OrderedGroup_Oab__semigroup__mult(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 366 [] class_RealVector_Oreal__normed__vector(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 367 [] class_OrderedGroup_Ocomm__monoid__mult(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 368 [] class_Ring__and__Field_Odivision__ring(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 369 [] class_RealVector_Oreal__normed__field(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 370 [] class_Ring__and__Field_Ozero__ne_q__one(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 371 [] class_Ring__and__Field_Osemiring__1(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 372 [] class_Ring__and__Field_Osemiring__0(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 373 [] class_Ring__and__Field_Omult__zero(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 374 [] class_OrderedGroup_Omonoid__mult(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 375 [] class_Ring__and__Field_Ofield(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 376 [] class_Ring__and__Field_Oidom(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 377 [] class_Nat_Osemiring__char__0(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 378 [] class_Ring__and__Field_Odvd(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 379 [] class_Int_Onumber__ring(tc_Complex_Ocomplex).
% 34.24/34.33 ** KEPT (pick-wt=2): 380 [] class_Power_Opower(tc_Complex_Ocomplex).
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [copy,259,flip.1] A=A.
% 34.24/34.33 259 back subsumes 237.
% 34.24/34.33 259 back subsumes 236.
% 34.24/34.33 259 back subsumes 235.
% 34.24/34.33 259 back subsumes 234.
% 34.24/34.33 259 back subsumes 230.
% 34.24/34.33 >>>> Starting back demodulation with 261.
% 34.24/34.33 >>>> Starting back demodulation with 263.
% 34.24/34.33 >>>> Starting back demodulation with 269.
% 34.24/34.33 >>>> Starting back demodulation with 271.
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [copy,272,flip.1,demod,310,310] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 Following clause subsumed by 259 during input processing: 0 [copy,273,flip.1,demod,312,312] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 34.24/34.33 >>>> Starting back demodulation with 275.
% 34.24/34.33 >>>> Starting back demodulation with 278.
% 34.24/34.33 >> back demodulating 249 with 278.
% 34.24/34.33 >> back demodulating 110 with 278.
% 34.24/34.33 >>>> Starting back demodulation with 280.
% 34.24/34.33 Following clause subsumed by 281 during input processing: 0 [copy,281,flip.1] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 34.24/34.33 >>>> Starting back demodulation with 284.
% 34.24/34.33 >> back demodulating 248 with 284.
% 34.24/34.33 >> back demodulating 233 with 284.
% 34.24/34.33 >>>> Starting back demodulation with 286.
% 34.24/34.33 >>>> Starting back demodulation with 288.
% 34.24/34.33 >>>> Starting back demodulation with 293.
% 34.24/34.33 >>>> Starting back demodulation with 295.
% 34.24/34.33 >>>> Starting back demodulation with 297.
% 34.39/34.50 >>>> Starting back demodulation with 300.
% 34.39/34.50 >> back demodulating 250 with 300.
% 34.39/34.50 >> back demodulating 247 with 300.
% 34.39/34.50 >> back demodulating 232 with 300.
% 34.39/34.50 >>>> Starting back demodulation with 302.
% 34.39/34.50 Following clause subsumed by 303 during input processing: 0 [copy,303,flip.1] c_GCD_Ogcd__class_Olcm(A,B,tc_nat)=c_GCD_Ogcd__class_Olcm(B,A,tc_nat).
% 34.39/34.50 Following clause subsumed by 305 during input processing: 0 [copy,305,flip.1] c_GCD_Ogcd__class_Ogcd(A,c_GCD_Ogcd__class_Ogcd(B,C,tc_nat),tc_nat)=c_GCD_Ogcd__class_Ogcd(B,c_GCD_Ogcd__class_Ogcd(A,C,tc_nat),tc_nat).
% 34.39/34.50 >>>> Starting back demodulation with 307.
% 34.39/34.50 >>>> Starting back demodulation with 310.
% 34.39/34.50 >> back demodulating 272 with 310.
% 34.39/34.50 >> back demodulating 252 with 310.
% 34.39/34.50 >>>> Starting back demodulation with 312.
% 34.39/34.50 >> back demodulating 273 with 312.
% 34.39/34.50 >> back demodulating 265 with 312.
% 34.39/34.50 >> back demodulating 251 with 312.
% 34.39/34.50 >>>> Starting back demodulation with 314.
% 34.39/34.50 Following clause subsumed by 315 during input processing: 0 [copy,315,flip.1] c_GCD_Ogcd__class_Olcm(A,c_GCD_Ogcd__class_Olcm(B,C,tc_nat),tc_nat)=c_GCD_Ogcd__class_Olcm(B,c_GCD_Ogcd__class_Olcm(A,C,tc_nat),tc_nat).
% 34.39/34.50 >>>> Starting back demodulation with 317.
% 34.39/34.50 Following clause subsumed by 318 during input processing: 0 [copy,318,flip.1] c_GCD_Ogcd__class_Ogcd(A,B,tc_nat)=c_GCD_Ogcd__class_Ogcd(B,A,tc_nat).
% 34.39/34.50 >>>> Starting back demodulation with 320.
% 34.39/34.50 >>>> Starting back demodulation with 322.
% 34.39/34.50 >>>> Starting back demodulation with 324.
% 34.39/34.50 >>>> Starting back demodulation with 326.
% 34.39/34.50 >>>> Starting back demodulation with 328.
% 34.39/34.50 >>>> Starting back demodulation with 330.
% 34.39/34.50 >>>> Starting back demodulation with 332.
% 34.39/34.50 333 back subsumes 94.
% 34.39/34.50 333 back subsumes 93.
% 34.39/34.50 >>>> Starting back demodulation with 335.
% 34.39/34.50 ** KEPT (pick-wt=8): 385 [copy,336,flip.1] c_HOL_Oone__class_Oone(tc_Complex_Ocomplex)=c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),A,tc_Complex_Ocomplex).
% 34.39/34.50 >>>> Starting back demodulation with 339.
% 34.39/34.50 >>>> Starting back demodulation with 341.
% 34.39/34.50 >> back demodulating 338 with 341.
% 34.39/34.50 >>>> Starting back demodulation with 343.
% 34.39/34.50 Following clause subsumed by 336 during input processing: 0 [copy,385,flip.1] c_Power_Opower__class_Opower(c_FFT__Mirabelle_Oroot(A),A,tc_Complex_Ocomplex)=c_HOL_Oone__class_Oone(tc_Complex_Ocomplex).
% 34.39/34.50
% 34.39/34.50 ======= end of input processing =======
% 34.39/34.50
% 34.39/34.50 =========== start of search ===========
% 34.39/34.50
% 34.39/34.50
% 34.39/34.50 Resetting weight limit to 2.
% 34.39/34.50
% 34.39/34.50
% 34.39/34.50 Resetting weight limit to 2.
% 34.39/34.50
% 34.39/34.50 sos_size=89
% 34.39/34.50
% 34.39/34.50 -------- PROOF --------
% 34.39/34.50
% 34.39/34.50 -----> EMPTY CLAUSE at 0.20 sec ----> 386 [para_into,336.1.1,206.2.1,unit_del,229,363] $F.
% 34.39/34.50
% 34.39/34.50 Length of proof is 0. Level of proof is 0.
% 34.39/34.50
% 34.39/34.50 ---------------- PROOF ----------------
% 34.39/34.50 % SZS status Unsatisfiable
% 34.39/34.50 % SZS output start Refutation
% See solution above
% 34.39/34.50 ------------ end of proof -------------
% 34.39/34.50
% 34.39/34.50
% 34.39/34.50 Search stopped by max_proofs option.
% 34.39/34.50
% 34.39/34.50
% 34.39/34.50 Search stopped by max_proofs option.
% 34.39/34.50
% 34.39/34.50 ============ end of search ============
% 34.39/34.50
% 34.39/34.50 -------------- statistics -------------
% 34.39/34.50 clauses given 77
% 34.39/34.50 clauses generated 17836
% 34.39/34.50 clauses kept 339
% 34.39/34.50 clauses forward subsumed 107
% 34.39/34.50 clauses back subsumed 16
% 34.39/34.50 Kbytes malloced 4882
% 34.39/34.50
% 34.39/34.50 ----------- times (seconds) -----------
% 34.39/34.50 user CPU time 0.20 (0 hr, 0 min, 0 sec)
% 34.39/34.50 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 34.39/34.50 wall-clock time 34 (0 hr, 0 min, 34 sec)
% 34.39/34.50
% 34.39/34.50 That finishes the proof of the theorem.
% 34.39/34.50
% 34.39/34.50 Process 13816 finished Wed Jul 27 06:22:18 2022
% 34.39/34.50 Otter interrupted
% 34.39/34.50 PROOF FOUND
%------------------------------------------------------------------------------