TSTP Solution File: LCL760-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL760-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n005.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 13:05:19 EDT 2022
% Result : Unsatisfiable 219.68s 219.74s
% Output : Refutation 219.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 3 RR)
% Number of literals : 8 ( 3 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 21 ( 21 usr; 10 con; 0-5 aty)
% Number of variables : 9 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(459,axiom,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('LCL760-1.p',unknown),
[] ).
cnf(540,axiom,
c_Suc(A) = hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),
file('LCL760-1.p',unknown),
[] ).
cnf(680,axiom,
c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)) = hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)),
file('LCL760-1.p',unknown),
[] ).
cnf(682,plain,
hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)) = c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[680])]),
[iquote('copy,680,flip.1')] ).
cnf(698,axiom,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(A))),c_Suc(B))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(A)),B)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(A),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),B,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
file('LCL760-1.p',unknown),
[] ).
cnf(699,plain,
hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(A)),B),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(A),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),B,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[698]),540,540,682]),
[iquote('copy,698,demod,540,540,682')] ).
cnf(740,plain,
~ hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ia),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),v_ja),c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[459]),540,540,682]),
[iquote('back_demod,459,demod,540,540,682')] ).
cnf(741,plain,
$false,
inference(binary,[status(thm)],[740,699]),
[iquote('binary,740.1,699.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL760-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n005.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 09:13:50 EDT 2022
% 0.13/0.34 % CPUTime :
% 219.60/219.69 ----- Otter 3.3f, August 2004 -----
% 219.60/219.69 The process was started by sandbox on n005.cluster.edu,
% 219.60/219.69 Wed Jul 27 09:13:50 2022
% 219.60/219.69 The command was "./otter". The process ID is 28231.
% 219.60/219.69
% 219.60/219.69 set(prolog_style_variables).
% 219.60/219.69 set(auto).
% 219.60/219.69 dependent: set(auto1).
% 219.60/219.69 dependent: set(process_input).
% 219.60/219.69 dependent: clear(print_kept).
% 219.60/219.69 dependent: clear(print_new_demod).
% 219.60/219.69 dependent: clear(print_back_demod).
% 219.60/219.69 dependent: clear(print_back_sub).
% 219.60/219.69 dependent: set(control_memory).
% 219.60/219.69 dependent: assign(max_mem, 12000).
% 219.60/219.69 dependent: assign(pick_given_ratio, 4).
% 219.60/219.69 dependent: assign(stats_level, 1).
% 219.60/219.69 dependent: assign(max_seconds, 10800).
% 219.60/219.69 clear(print_given).
% 219.60/219.69
% 219.60/219.69 list(usable).
% 219.60/219.69 0 [] A=A.
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat).
% 219.60/219.69 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_b,T_a).
% 219.60/219.69 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).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat).
% 219.60/219.69 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 219.60/219.69 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)))| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.60/219.69 0 [] -class_Ring__and__Field_Osemiring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_e,T_a)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,V_e,T_a)),V_c))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_e,T_a)),V_c).
% 219.60/219.69 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat)),V_k))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_u,tc_nat)),V_k).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 219.60/219.69 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)|V_m=V_n.
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),V_b),V_c,T_a).
% 219.60/219.69 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).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 219.60/219.69 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).
% 219.60/219.69 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))|c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 219.60/219.69 0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_u)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)=V_u.
% 219.60/219.69 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_d)).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_b).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),V_d).
% 219.60/219.69 0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 219.60/219.69 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)).
% 219.60/219.69 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c)).
% 219.60/219.69 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)).
% 219.60/219.69 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)).
% 219.60/219.69 0 [] -class_OrderedGroup_Oab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)),V_z).
% 219.60/219.69 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 219.60/219.69 0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a).
% 219.60/219.69 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).
% 219.60/219.69 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)=c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat).
% 219.60/219.69 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).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a)=c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_Suc(V_n),T_a)=c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a).
% 219.60/219.69 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)=c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a).
% 219.60/219.69 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a).
% 219.60/219.69 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).
% 219.60/219.69 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_m,tc_nat).
% 219.60/219.69 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_m,tc_nat),V_m,tc_nat).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a)).
% 219.60/219.69 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat)).
% 219.60/219.69 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat)).
% 219.60/219.69 0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a)=hAPP(V_f3,V_dB).
% 219.60/219.69 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)).
% 219.60/219.69 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(V_m,V_n,tc_nat),T_a)=c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),V_n,T_a).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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.
% 219.60/219.69 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.
% 219.60/219.69 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.
% 219.60/219.69 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.
% 219.60/219.69 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.
% 219.60/219.69 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat)=V_n.
% 219.60/219.69 0 [] c_HOL_Otimes__class_Otimes(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=V_n.
% 219.60/219.69 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.
% 219.60/219.69 0 [] c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a).
% 219.60/219.69 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_n,tc_nat)=V_m| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 219.60/219.69 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_n,tc_nat)=V_m| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_z,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(V_x,V_z,T_a)),c_Divides_Odiv__class_Odiv(V_y,V_z,T_a))| -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_y,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_z,V_x,T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_m)),tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_i)),tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x)),tc_nat).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_N,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_n,V_N,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_z,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,T_a),T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_m,T_a).
% 219.60/219.69 0 [] c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),V_k,tc_nat)=c_HOL_Oone__class_Oone(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_k,tc_nat).
% 219.60/219.69 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).
% 219.60/219.69 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k)=c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a).
% 219.60/219.69 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a).
% 219.60/219.69 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m).
% 219.60/219.69 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_l)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_x).
% 219.60/219.69 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).
% 219.60/219.69 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.
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.69 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)|V_y=V_z.
% 219.60/219.69 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)|V_m=V_n.
% 219.60/219.69 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)|V_m=V_n.
% 219.60/219.69 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_z)|V_y=V_z.
% 219.60/219.69 0 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 219.60/219.69 0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)|V_b=V_c.
% 219.60/219.69 0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a)|V_b=V_c.
% 219.60/219.69 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k)=c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 219.60/219.69 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).
% 219.60/219.69 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_v),V_i)),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_v),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)),V_v),V_j)| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 0 [] c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_d))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d)).
% 219.60/219.69 0 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(V_dB),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB,tc_Lambda_OdB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),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).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 219.60/219.69 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,V_r),V_i),hAPP(hAPP(c_Lambda_Olift,V_s),V_i))| -c_Lambda_Obeta(V_r,V_s).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Oone__class_Oone(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 219.60/219.69 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),V_j)| -c_HOL_Oord__class_Oless(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.60/219.69 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),c_Suc(V_k))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_i)| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.60/219.69 0 [] c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 219.60/219.69 0 [] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(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_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(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_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(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_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(T_a)|c_HOL_Oord__class_Oless(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_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 219.60/219.69 0 [] c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_a),V_b),V_c,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat))),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat)),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat)),V_c,tc_nat)).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_i,V_m,tc_nat),c_Power_Opower__class_Opower(V_i,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_i,tc_nat).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 0 [] c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.69 0 [] -c_Type_Otyping(V_e_H,V_u,V_U)| -c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)|c_Type_Otyping(V_e_H,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),V_T).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a).
% 219.60/219.69 0 [] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m),V_n,tc_nat)=c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a)),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_m,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_m,T_a).
% 219.60/219.69 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|c_HOL_Oord__class_Oless(V_m,c_HOL_Otimes__class_Otimes(V_n,c_Suc(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)),tc_nat),tc_nat).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a),V_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)),c_HOL_Oone__class_Oone(T_a))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)),c_HOL_Oone__class_Oone(T_a))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)),T_a).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat).
% 219.60/219.69 0 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(V_s),c_Lambda_OdB_OAbs(V_t))| -c_Lambda_Obeta(V_s,V_t).
% 219.60/219.69 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_m,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_n,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_m,T_a).
% 219.60/219.69 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.
% 219.60/219.69 0 [] -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat)),V_j),V_k,tc_nat)))|hBOOL(hAPP(V_P,V_j)).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 219.60/219.69 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 219.60/219.69 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a).
% 219.60/219.69 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 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).
% 219.60/219.69 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.69 0 [] c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a).
% 219.60/219.69 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).
% 219.60/219.69 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a)=c_Power_Opower__class_Opower(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_p),V_q),T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)),V_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.69 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a)),V_b,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),c_Divides_Odiv__class_Odiv(V_a,V_b,T_a))|V_b=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_m),V_m)=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),V_m,T_a).
% 219.60/219.70 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.
% 219.60/219.70 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.
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)|c_Divides_Odiv__class_Omod(V_a,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a_H),V_b_H),V_c,T_a).
% 219.60/219.70 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.70 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_x,tc_nat).
% 219.60/219.70 0 [] c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)).
% 219.60/219.70 0 [] c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)).
% 219.60/219.70 0 [] -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat)),V_j),V_k,tc_nat)))|hBOOL(hAPP(V_P,V_i)).
% 219.60/219.70 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).
% 219.60/219.70 0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 219.60/219.70 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.70 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a)),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.70 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).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Omod(c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)),V_m)),V_n,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_w,V_y,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_w,V_z,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a))|V_y=V_z|V_w=V_x.
% 219.60/219.70 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_d,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a))|V_c=V_d|V_a=V_b.
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,V_c,tc_nat)),c_HOL_Otimes__class_Otimes(V_b,V_d,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,V_d,tc_nat)),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat))|V_c=V_d|V_a=V_b.
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_w,V_y,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_w,V_z,tc_nat)),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat))|V_y=V_z|V_w=V_x.
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)|c_Divides_Odiv__class_Omod(V_a,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_m,T_a)),V_m)=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),V_m,T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_m),c_HOL_Otimes__class_Otimes(V_a,V_m,T_a))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),V_m,T_a).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,c_HOL_Oone__class_Oone(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat).
% 219.60/219.70 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(V_k,V_n,tc_nat).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)=V_m| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.70 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 219.60/219.70 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 219.60/219.70 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 219.60/219.70 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 219.60/219.70 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 219.60/219.70 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 219.60/219.70 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n.
% 219.60/219.70 0 [] hBOOL(hAPP(hAPP(V_P,V_n),V_m))|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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.
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)|V_x=V_y.
% 219.60/219.70 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 219.60/219.70 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 219.60/219.70 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 219.60/219.70 0 [] -c_Ring__and__Field_Odvd__class_Odvd(V_n,V_m,tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 219.60/219.70 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l),tc_nat)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_a,V_a,T_a).
% 219.60/219.70 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_x,V_x,tc_nat).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),V_c,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat)).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat).
% 219.60/219.70 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)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 219.60/219.70 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,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)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 219.60/219.70 0 [] c_Ring__and__Field_Odvd__class_Odvd(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,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).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),V_n,tc_nat).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Otimes__class_Otimes(V_n,V_xa,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),c_HOL_Otimes__class_Otimes(V_n,V_xb,tc_nat))|c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat)=c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_a)|V_a=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),c_HOL_Ozero__class_Ozero(T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_x)=V_x.
% 219.60/219.70 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 219.60/219.70 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Ozero__class_Ozero(T_a)).
% 219.60/219.70 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 219.60/219.70 0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 219.60/219.70 0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Ozero__class_Ozero(T_a))=V_a.
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a)),V_a)=V_a.
% 219.60/219.70 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).
% 219.60/219.70 0 [] -hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 219.60/219.70 0 [] -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Omod(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(V_P,V_n)).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__List__Xlexn__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(V_P)))| -hBOOL(hAPP(V_P,V_k)).
% 219.60/219.70 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))|hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 219.60/219.70 0 [] -hBOOL(hAPP(V_P,c_Divides_Odiv__class_Odiv(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_n))|hBOOL(hAPP(V_P,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 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).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 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.
% 219.60/219.70 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.
% 219.60/219.70 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).
% 219.60/219.70 0 [] V_x!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a)|V_a=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=V_m|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__List__Xreplicate__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinducts__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__Nat__Xnat__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 219.60/219.70 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_nat))|hBOOL(hAPP(V_P,v_sko__List__Xupt__Xinduct__1(V_P)))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat).
% 219.60/219.70 0 [] c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat)|V_m=V_n.
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat).
% 219.60/219.70 0 [] V_n=V_m| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 219.60/219.70 0 [] V_m=V_n| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 219.60/219.70 0 [] V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n)=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n))=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))|c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))=V_n.
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)|c_Suc(V_m)=V_n| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 219.60/219.70 0 [] -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_n,tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 219.60/219.70 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 219.60/219.70 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_xb),V_xc),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xb),V_xc))).
% 219.60/219.70 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_dB1),V_dB2))).
% 219.60/219.70 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)).
% 219.60/219.70 0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a)=hAPP(hAPP(V_f2,V_dB1),V_dB2).
% 219.60/219.70 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t))| -c_Lambda_Obeta(V_s,V_t).
% 219.60/219.70 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u))| -c_Lambda_Obeta(V_s,V_t).
% 219.60/219.70 0 [] c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)).
% 219.60/219.70 0 [] c_List_Omap(V_f,V_xs,T_b,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_b).
% 219.60/219.70 0 [] c_List_Olist_ONil(T_a)!=c_List_Omap(V_f,V_xs,T_b,T_a)|V_xs=c_List_Olist_ONil(T_b).
% 219.60/219.70 0 [] c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a)=c_List_Olist_ONil(T_a).
% 219.60/219.70 0 [] c_List_Olist_ONil(T_a)=c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a).
% 219.60/219.70 0 [] c_Lambda_OdB_OAbs(V_r)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 219.60/219.70 0 [] c_Lambda_OdB_OAbs(V_r)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.70 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(V_r)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 219.60/219.70 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(V_r).
% 219.60/219.70 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 219.60/219.70 0 [] -class_OrderedGroup_Osemigroup__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),V_y),V_zs,T_a,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_y,V_zs,T_a,T_a)).
% 219.60/219.70 0 [] c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i))| -c_Lambda_Obeta(V_r,V_s).
% 219.60/219.70 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k)=V_t.
% 219.60/219.70 0 [] c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(V_e,V_ts,V_Ts).
% 219.60/219.70 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 219.60/219.70 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_xd),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_xd))).
% 219.60/219.70 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))).
% 219.60/219.70 0 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(V_i),V_t).
% 219.60/219.70 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 219.60/219.70 0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_Power_Opower__class_Opower(V_a,V_m,T_a)!=c_Power_Opower__class_Opower(V_a,V_n,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)|V_m=V_n.
% 219.60/219.70 0 [] c_Power_Opower__class_Opower(V_p,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Odiv(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_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat).
% 219.60/219.70 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).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Odiv(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)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a)=c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),V_x,T_a)=c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a).
% 219.60/219.70 0 [] hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j)=hAPP(V_e,V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,c_Suc(V_n),tc_nat),tc_nat,T_a)=c_HOL_Ozero__class_Ozero(T_a)| -c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)| -c_HOL_Oord__class_Oless(V_b,V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Omod(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(V_a,V_b,tc_nat)).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(V_a,V_c,T_a)| -c_Ring__and__Field_Odvd__class_Odvd(V_c,V_b,T_a).
% 219.60/219.70 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f3,V_dB))).
% 219.60/219.70 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_xa),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f3,V_xa))).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_b,V_x,T_a),c_Power_Opower__class_Opower(V_b,V_y,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_b,T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_a,V_N,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(V_n,V_N,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 219.60/219.70 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat).
% 219.60/219.70 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),V_a,T_a).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Odiv(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat).
% 219.60/219.70 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).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(V_q,V_c,tc_nat),tc_nat)),V_r),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_r,V_b,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_c,tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Otimes__class_Otimes(V_r,V_c,T_a))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_HOL_Otimes__class_Otimes(V_r,V_d,T_a))|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat))|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a))!=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a))!=c_HOL_Ozero__class_Ozero(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Ring__and__Field_Odvd__class_Odvd(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 219.60/219.70 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 219.60/219.70 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 219.60/219.70 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a).
% 219.60/219.70 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 219.60/219.70 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 219.60/219.70 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.70 0 [] c_Type_Otyping(V_e,V_t_H,V_T)| -c_Lambda_Obeta(V_t,V_t_H)| -c_Type_Otyping(V_e,V_t,V_T).
% 219.60/219.70 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,c_Suc(V_n),tc_nat),tc_nat,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a)),hAPP(V_f,V_n))|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 219.60/219.70 0 [] V_n=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 219.60/219.70 0 [] V_n=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 219.60/219.70 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)=V_x.
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a))=V_a.
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a))=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 219.60/219.70 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a).
% 219.60/219.70 0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_x,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(V_x,V_n,tc_nat),tc_nat).
% 219.60/219.70 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Divides_Odiv__class_Omod(V_a,V_c,T_a)),V_b),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a)),V_c,T_a)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a).
% 219.60/219.70 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(V_m,V_n,tc_nat),tc_nat,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),hAPP(V_f,V_m)),c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(V_m),V_n,tc_nat),tc_nat,T_a))| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))=V_a.
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a))=V_a.
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|V_a=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a)),c_Divides_Odiv__class_Omod(V_a,V_b,T_a)).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(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_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a).
% 219.60/219.70 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(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_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a).
% 219.60/219.70 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k)=c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 219.60/219.70 0 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(V_dB))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring(T_a)|c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_c,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_a,V_c,T_a)),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a)).
% 219.60/219.70 0 [] c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_k,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)).
% 219.60/219.70 0 [] c_HOL_Otimes__class_Otimes(V_k,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)).
% 219.60/219.70 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_y),V_z),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a)).
% 219.60/219.70 0 [] c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,V_t),V_i),V_T)| -c_Type_Otyping(V_e,V_t,V_T).
% 219.60/219.70 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 219.60/219.70 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 219.60/219.70 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 219.60/219.70 0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a)=hAPP(V_f1,V_nat).
% 219.60/219.70 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 219.60/219.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 219.60/219.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 219.60/219.70 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(V_f,c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Ozero__class_Ozero(T_a)|c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat),tc_nat,T_a)=c_Finite__Set_Osetsum(V_f,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat),tc_nat,T_a).
% 219.60/219.70 0 [] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(V_dB1)),c_Lambda_OdB_OdB__size(V_dB2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_dB1,tc_Lambda_OdB)),c_Nat_Osize__class_Osize(V_dB2,tc_Lambda_OdB))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] V_v=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB,tc_Lambda_OdB)| -c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB),V_v).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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).
% 219.60/219.70 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_Suc(V_n),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 219.60/219.70 0 [] V_y=c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(V_y))|V_y=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))|hBOOL(hAPP(V_P,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(V_P))))| -hBOOL(hAPP(V_P,V_k)).
% 219.60/219.70 0 [] c_Power_Opower__class_Opower(V_x,V_m,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_x=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xlexn__Xinduct__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 219.60/219.70 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 219.60/219.70 0 [] c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] c_Type_Oshift(c_Type_Oshift(V_e,V_i,V_U,T_a),c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a)=c_Type_Oshift(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),V_T,T_a),c_Suc(V_i),V_U,T_a).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_n))| -hBOOL(hAPP(V_P,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xreplicate__Xinduct__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__List__Xupt__Xinduct__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] V_v=c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(V_v))|V_v=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__Nat__Xnat__Xinduct__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 219.60/219.70 0 [] hBOOL(hAPP(V_P,V_nat))| -hBOOL(hAPP(V_P,c_Suc(v_sko__Nat__Xnat__Xinducts__1(V_P))))| -hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] V_n=c_Suc(c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(V_n))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] c_Ring__and__Field_Odvd__class_Odvd(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_k,tc_nat).
% 219.60/219.70 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.70 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat).
% 219.60/219.70 0 [] c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))!=V_n|c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] c_Power_Opower__class_Opower(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))| -c_Ring__and__Field_Odvd__class_Odvd(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 219.60/219.70 0 [] c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=V_m.
% 219.60/219.70 0 [] -class_OrderedGroup_Omonoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_zs,T_a,T_a))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_x,V_zs,T_a,T_a).
% 219.60/219.70 0 [] c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.70 0 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(V_nat),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(V_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.70 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)=V_t.
% 219.60/219.70 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(V_r)|V_s=c_Lambda_OdB_OAbs(V_r).
% 219.60/219.70 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_r=V_s.
% 219.60/219.70 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_rs=V_ss.
% 219.60/219.70 0 [] c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB))| -c_Lambda_Obeta(V_r,V_s).
% 219.60/219.70 0 [] c_Lambda_OdB_OAbs(V_r)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OAbs(V_r)=V_s.
% 219.60/219.70 0 [] c_Type_Otypings(V_e,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_T,tc_Type_Otype),V_ts,V_Ts)| -c_Type_Otyping(V_e,V_u,V_T).
% 219.60/219.70 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i)=c_Lambda_OdB_OVar(V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 219.60/219.70 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_x)),V_s),V_x)=V_s.
% 219.60/219.70 0 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB).
% 219.60/219.70 0 [] V_T=V_U| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_U)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 219.60/219.70 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ts,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r),V_ss,tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.70 0 [] c_Lambda_OdB_OVar(V_m)=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.70 0 [] c_Lambda_OdB_OVar(V_m)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_ss=c_List_Olist_ONil(tc_Lambda_OdB).
% 219.60/219.70 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_List_Olistsp(c_InductTermi_OIT,V_rs,tc_Lambda_OdB).
% 219.60/219.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(c_InductTermi_OIT,V_s))| -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))).
% 219.60/219.70 0 [] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.70 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)).
% 219.60/219.70 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 219.60/219.70 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_m=V_n.
% 219.60/219.70 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_m),V_rs,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_n),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|V_rs=V_ss.
% 219.60/219.70 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k)=V_u.
% 219.60/219.70 0 [] V_n!=c_Suc(V_n).
% 219.60/219.70 0 [] c_Suc(V_n)!=V_n.
% 219.60/219.70 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.70 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)|V_dB1=V_dB1_H.
% 219.60/219.70 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)|V_dB2=V_dB2_H.
% 219.60/219.70 0 [] c_Lambda_OdB_OVar(V_m)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OVar(V_m)=V_s.
% 219.60/219.70 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 219.60/219.70 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 219.60/219.70 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 219.60/219.70 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.70 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 219.60/219.70 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 219.60/219.70 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 219.60/219.70 0 [] c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_s,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)|V_r=V_s.
% 219.60/219.70 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 219.60/219.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),v_s),c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))).
% 219.60/219.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(V_i))),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_j,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))).
% 219.60/219.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_s)).
% 219.60/219.70 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(V_i)),V_j))).
% 219.60/219.70 0 [] -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))).
% 219.60/219.70 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 219.60/219.70 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 219.60/219.70 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Osemiring(tc_nat).
% 219.60/219.70 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 219.60/219.70 0 [] class_Divides_Osemiring__div(tc_nat).
% 219.60/219.70 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 219.60/219.70 0 [] class_Ring__and__Field_Odvd(tc_nat).
% 219.60/219.70 0 [] class_Orderings_Opreorder(tc_nat).
% 219.60/219.70 0 [] class_Orderings_Olinorder(tc_nat).
% 219.60/219.70 0 [] class_Orderings_Oorder(tc_nat).
% 219.60/219.70 0 [] class_Power_Opower(tc_nat).
% 219.60/219.70 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 219.60/219.70 0 [] c_COMBB(V_P,V_Q,V_R,T_b,T_a,T_c)=hAPP(V_P,hAPP(V_Q,V_R)).
% 219.60/219.70 0 [] c_fe_qual(V_x,V_x,T_a).
% 219.60/219.70 0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 219.60/219.70 end_of_list.
% 219.60/219.70
% 219.60/219.70 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 219.60/219.70
% 219.60/219.70 This ia a non-Horn set with equality. The strategy will be
% 219.60/219.70 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 219.60/219.70 deletion, with positive clauses in sos and nonpositive
% 219.60/219.70 clauses in usable.
% 219.60/219.70
% 219.60/219.70 dependent: set(knuth_bendix).
% 219.60/219.70 dependent: set(anl_eq).
% 219.60/219.70 dependent: set(para_from).
% 219.60/219.70 dependent: set(para_into).
% 219.60/219.70 dependent: clear(para_from_right).
% 219.60/219.70 dependent: clear(para_into_right).
% 219.60/219.70 dependent: set(para_from_vars).
% 219.60/219.70 dependent: set(eq_units_both_ways).
% 219.60/219.70 dependent: set(dynamic_demod_all).
% 219.60/219.70 dependent: set(dynamic_demod).
% 219.60/219.70 dependent: set(order_eq).
% 219.60/219.70 dependent: set(back_demod).
% 219.60/219.70 dependent: set(lrpo).
% 219.60/219.70 dependent: set(hyper_res).
% 219.60/219.70 dependent: set(unit_deletion).
% 219.60/219.70 dependent: set(factor).
% 219.60/219.70
% 219.60/219.70 ------------> process usable:
% 219.60/219.70 ** KEPT (pick-wt=13): 1 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=13): 2 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=22): 3 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.70 ** KEPT (pick-wt=13): 4 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)=c_HOL_Ozero__class_Ozero(A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 219.60/219.70 ** KEPT (pick-wt=13): 5 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 219.60/219.70 ** KEPT (pick-wt=21): 6 [] -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).
% 219.60/219.70 ** KEPT (pick-wt=10): 7 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.70 ** KEPT (pick-wt=16): 8 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(A),C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=16): 9 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(C),A,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(C),B,tc_nat),tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=43): 10 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),D)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),D)),hAPP(hAPP(c_Lambda_Olift,B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)))| -c_HOL_Oord__class_Oless(D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=34): 12 [copy,11,flip.2] -class_Ring__and__Field_Osemiring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A)),E)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,D,A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(C,D,A)),E)).
% 219.60/219.70 ** KEPT (pick-wt=20): 13 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 219.60/219.70 ** KEPT (pick-wt=16): 14 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)).
% 219.60/219.70 ** KEPT (pick-wt=15): 15 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=15): 16 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_nat),c_HOL_Otimes__class_Otimes(C,A,tc_nat),tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=17): 17 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|B=C.
% 219.60/219.70 ** KEPT (pick-wt=9): 18 [] -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).
% 219.60/219.70 ** KEPT (pick-wt=11): 19 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=11): 20 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Oone__class_Oone(tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=24): 22 [copy,21,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A).
% 219.60/219.70 ** KEPT (pick-wt=24): 24 [copy,23,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 219.60/219.70 ** KEPT (pick-wt=20): 25 [] -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).
% 219.60/219.70 ** KEPT (pick-wt=12): 26 [] c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=10): 27 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(A),B,A)=c_HOL_Oone__class_Oone(A).
% 219.60/219.70 ** KEPT (pick-wt=28): 28 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)=E.
% 219.60/219.70 ** KEPT (pick-wt=22): 29 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A).
% 219.60/219.70 ** KEPT (pick-wt=20): 30 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=25): 31 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 219.60/219.70 ** KEPT (pick-wt=25): 32 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 219.60/219.70 ** KEPT (pick-wt=25): 33 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),C).
% 219.60/219.70 Following clause subsumed by 31 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 219.60/219.70 ** KEPT (pick-wt=25): 34 [] -class_OrderedGroup_Oab__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 219.60/219.70 ** KEPT (pick-wt=25): 35 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 219.60/219.70 ** KEPT (pick-wt=25): 36 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 219.60/219.70 ** KEPT (pick-wt=25): 37 [] -class_OrderedGroup_Oab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)).
% 219.60/219.70 Following clause subsumed by 31 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 219.60/219.70 ** KEPT (pick-wt=14): 38 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(D,C,A).
% 219.60/219.70 ** KEPT (pick-wt=14): 39 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 219.60/219.70 ** KEPT (pick-wt=21): 40 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(C),A),c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 219.60/219.70 ** KEPT (pick-wt=27): 42 [copy,41,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),c_Divides_Odiv__class_Omod(D,C,A)),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 219.60/219.70 ** KEPT (pick-wt=11): 43 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A).
% 219.60/219.70 Following clause subsumed by 43 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).
% 219.60/219.70 ** KEPT (pick-wt=15): 44 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 219.60/219.70 Following clause subsumed by 44 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 219.60/219.70 ** KEPT (pick-wt=15): 45 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 219.60/219.70 ** KEPT (pick-wt=15): 46 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A).
% 219.60/219.70 ** KEPT (pick-wt=17): 47 [] -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).
% 219.60/219.70 ** KEPT (pick-wt=13): 48 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),A,tc_nat).
% 219.60/219.70 ** KEPT (pick-wt=13): 49 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat),A,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=29): 50 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(B,D,A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,D,A)),c_HOL_Otimes__class_Otimes(B,C,A)).
% 219.60/219.71 Following clause subsumed by 50 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(B,D,A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,D,A)),c_HOL_Otimes__class_Otimes(B,C,A)).
% 219.60/219.71 ** KEPT (pick-wt=14): 51 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A)=c_Divides_Odiv__class_Omod(B,C,A).
% 219.60/219.71 ** KEPT (pick-wt=15): 52 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_Power_Opower__class_Opower(B,C,tc_nat),A)=c_Power_Opower__class_Opower(c_Nat_Osemiring__1__class_Oof__nat(B,A),C,A).
% 219.60/219.71 ** KEPT (pick-wt=13): 53 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=9): 54 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=9): 55 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=9): 56 [] -class_Ring__and__Field_Odvd(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Otimes__class_Otimes(B,C,A),A).
% 219.60/219.71 ** KEPT (pick-wt=9): 57 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 219.60/219.71 ** KEPT (pick-wt=9): 58 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A)=B.
% 219.60/219.71 ** KEPT (pick-wt=9): 59 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oone__class_Oone(A),A)=B.
% 219.60/219.71 ** KEPT (pick-wt=9): 60 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 219.60/219.71 ** KEPT (pick-wt=9): 61 [] -class_OrderedGroup_Ocomm__monoid__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(A),B,A)=B.
% 219.60/219.71 Following clause subsumed by 57 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.
% 219.60/219.71 ** KEPT (pick-wt=14): 62 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat)=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=14): 63 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat)=B| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=16): 64 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=16): 65 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=14): 66 [] 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).
% 219.60/219.71 ** KEPT (pick-wt=20): 67 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 219.60/219.71 ** KEPT (pick-wt=32): 69 [copy,68,flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_Divides_Odiv__class_Odiv(D,C,A))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(C,B,A).
% 219.60/219.71 ** KEPT (pick-wt=29): 70 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A)),c_Divides_Odiv__class_Omod(C,B,A))),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D).
% 219.60/219.71 ** KEPT (pick-wt=29): 71 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A)),c_Divides_Odiv__class_Omod(B,C,A))),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D).
% 219.60/219.71 ** KEPT (pick-wt=26): 72 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(D,C,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=13): 73 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=13): 74 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=13): 75 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 219.60/219.71 Following clause subsumed by 73 during input processing: 0 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.71 Following clause subsumed by 74 during input processing: 0 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=17): 76 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A).
% 219.60/219.71 ** KEPT (pick-wt=17): 77 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 219.60/219.71 Following clause subsumed by 76 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,C,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A).
% 219.60/219.71 Following clause subsumed by 77 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_Divides_Odiv__class_Omod(C,D,A),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 219.60/219.71 ** KEPT (pick-wt=16): 78 [] c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Otimes__class_Otimes(A,B,tc_nat)),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=15): 79 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 219.60/219.71 ** KEPT (pick-wt=15): 80 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 219.60/219.71 ** KEPT (pick-wt=21): 81 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)| -c_HOL_Oord__class_Oless(C,B,tc_nat)|c_HOL_Oord__class_Oless(A,D,tc_nat).
% 219.60/219.71 Following clause subsumed by 79 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B).
% 219.60/219.71 ** KEPT (pick-wt=11): 82 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=12): 83 [] -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.
% 219.60/219.71 ** KEPT (pick-wt=12): 84 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,A),C,A)=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=16): 85 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 219.60/219.71 ** KEPT (pick-wt=16): 86 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 219.60/219.71 Following clause subsumed by 85 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 219.60/219.71 ** KEPT (pick-wt=20): 87 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 219.60/219.71 ** KEPT (pick-wt=18): 88 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 219.60/219.71 ** KEPT (pick-wt=18): 89 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)|C=D.
% 219.60/219.71 ** KEPT (pick-wt=18): 90 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C)|B=D.
% 219.60/219.71 ** KEPT (pick-wt=16): 91 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=48): 92 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),C)),c_Suc(D))),hAPP(hAPP(hAPP(c_Lambda_Osubst,E),B),D)),C)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),E),C)),B),D)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.60/219.71 Following clause subsumed by 67 during input processing: 0 [flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A).
% 219.60/219.71 ** KEPT (pick-wt=20): 94 [copy,93,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A).
% 219.60/219.71 ** KEPT (pick-wt=24): 95 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=24): 96 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=11): 97 [] c_Divides_Odiv__class_Odiv(A,B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=22): 98 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,B,A)),c_HOL_Otimes__class_Otimes(C,C,A)),A)|B=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=22): 99 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,B,A)),c_HOL_Otimes__class_Otimes(C,C,A)),A)|C=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=35): 100 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),E)).
% 219.60/219.71 ** KEPT (pick-wt=9): 101 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=19): 102 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_Ring__and__Field_Odvd__class_Odvd(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(B,C,A).
% 219.60/219.71 ** KEPT (pick-wt=22): 103 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 219.60/219.71 ** KEPT (pick-wt=20): 104 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 219.60/219.71 ** KEPT (pick-wt=22): 105 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 219.60/219.71 ** KEPT (pick-wt=20): 106 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 219.60/219.71 ** KEPT (pick-wt=15): 107 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=15): 108 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=13): 109 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(A)),B)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=14): 110 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_Olift,A),B),hAPP(hAPP(c_Lambda_Olift,C),B))| -c_Lambda_Obeta(A,C).
% 219.60/219.71 ** KEPT (pick-wt=25): 111 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Oone__class_Oone(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 219.60/219.71 ** KEPT (pick-wt=43): 112 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),D)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,B),D)),C)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=30): 113 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,A),B)),c_Suc(C))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,A),C)),B)| -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=19): 114 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=19): 115 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 219.60/219.71 Following clause subsumed by 115 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 219.60/219.71 Following clause subsumed by 114 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=19): 116 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 219.60/219.71 Following clause subsumed by 115 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=21): 117 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=21): 118 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=21): 119 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A).
% 219.60/219.71 ** KEPT (pick-wt=21): 120 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 219.60/219.71 Following clause subsumed by 118 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,C,A).
% 219.60/219.71 ** KEPT (pick-wt=21): 121 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(C,D,A).
% 219.60/219.71 Following clause subsumed by 120 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 219.60/219.71 Following clause subsumed by 118 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=21): 122 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,B,A).
% 219.60/219.71 ** KEPT (pick-wt=21): 123 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 219.60/219.71 ** KEPT (pick-wt=21): 124 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 219.60/219.71 Following clause subsumed by 122 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(D,B,A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=21): 125 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(C,D,A).
% 219.60/219.71 ** KEPT (pick-wt=19): 126 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,A,tc_nat),c_Power_Opower__class_Opower(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=21): 127 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=21): 128 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=22): 129 [] -c_Type_Otyping(A,B,C)| -c_Type_Otyping(c_Type_Oshift(A,D,C,tc_Type_Otype),E,F)|c_Type_Otyping(A,hAPP(hAPP(hAPP(c_Lambda_Osubst,E),B),D),F).
% 219.60/219.71 ** KEPT (pick-wt=14): 130 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A).
% 219.60/219.71 ** KEPT (pick-wt=19): 131 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,D,A)),D,A)=c_Divides_Odiv__class_Omod(B,D,A).
% 219.60/219.71 ** KEPT (pick-wt=19): 132 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,D,A)),C,A)=c_Divides_Odiv__class_Omod(B,C,A).
% 219.60/219.71 ** KEPT (pick-wt=24): 133 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(D,C,A))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 219.60/219.71 ** KEPT (pick-wt=16): 134 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(A,c_Suc(c_Divides_Odiv__class_Odiv(B,A,tc_nat)),tc_nat),tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=18): 135 [] 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).
% 219.60/219.71 ** KEPT (pick-wt=20): 136 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=20): 137 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=26): 139 [copy,138,flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_HOL_Oone__class_Oone(A))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),B),C,A)|C=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=26): 141 [copy,140,flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Odiv(B,C,A)),c_HOL_Oone__class_Oone(A))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A)|C=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=22): 142 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)),A).
% 219.60/219.71 ** KEPT (pick-wt=8): 143 [] c_Lambda_Obeta(c_Lambda_OdB_OAbs(A),c_Lambda_OdB_OAbs(B))| -c_Lambda_Obeta(A,B).
% 219.60/219.71 ** KEPT (pick-wt=20): 144 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 219.60/219.71 ** KEPT (pick-wt=9): 145 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,c_HOL_Oone__class_Oone(A),A)=B.
% 219.60/219.71 ** KEPT (pick-wt=27): 146 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(C,c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(B,D,tc_nat)),A),B,tc_nat)))|hBOOL(hAPP(C,A)).
% 219.60/219.71 Following clause subsumed by 74 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 219.60/219.71 Following clause subsumed by 73 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=17): 147 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A).
% 219.60/219.71 ** KEPT (pick-wt=17): 148 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 219.60/219.71 ** KEPT (pick-wt=16): 149 [] -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).
% 219.60/219.71 Following clause subsumed by 149 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).
% 219.60/219.71 ** KEPT (pick-wt=19): 150 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=13): 151 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=10): 152 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=10): 153 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=10): 154 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=10): 155 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=10): 156 [] -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).
% 219.60/219.71 ** 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).
% 219.60/219.71 Following clause subsumed by 152 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).
% 219.60/219.71 ** KEPT (pick-wt=7): 158 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=7): 160 [copy,159,flip.2] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 219.60/219.71 ** KEPT (pick-wt=17): 161 [] -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).
% 219.60/219.71 Following clause subsumed by 161 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)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=17): 162 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=10): 163 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=10): 164 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=15): 165 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 Following clause subsumed by 97 during input processing: 0 [] c_Divides_Odiv__class_Odiv(A,B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=23): 167 [copy,166,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),c_Divides_Odiv__class_Omod(D,C,A),A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),C,A).
% 219.60/219.71 ** KEPT (pick-wt=17): 168 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=22): 170 [copy,169,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A).
% 219.60/219.71 ** KEPT (pick-wt=28): 171 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,D,A)),C,A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),c_Divides_Odiv__class_Odiv(B,C,A))|C=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=28): 172 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,D,A)),D,A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_Divides_Odiv__class_Odiv(B,D,A))|D=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=20): 173 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B)=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),B,A).
% 219.60/219.71 ** KEPT (pick-wt=9): 174 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 219.60/219.71 ** KEPT (pick-wt=9): 175 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_HOL_Oone__class_Oone(tc_nat),A)=B.
% 219.60/219.71 ** KEPT (pick-wt=39): 176 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_Divides_Odiv__class_Omod(D,C,A)|c_Divides_Odiv__class_Omod(E,C,A)!=c_Divides_Odiv__class_Omod(F,C,A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),E),B),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),F),D),C,A).
% 219.60/219.71 ** KEPT (pick-wt=17): 177 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=17): 178 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=17): 179 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=17): 180 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=20): 181 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A).
% 219.60/219.71 ** KEPT (pick-wt=20): 182 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A).
% 219.60/219.71 ** KEPT (pick-wt=20): 183 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 219.60/219.71 ** KEPT (pick-wt=20): 184 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=18): 185 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=15): 186 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 219.60/219.71 ** KEPT (pick-wt=13): 187 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=27): 188 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)| -hBOOL(hAPP(C,c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(B,D,tc_nat)),A),B,tc_nat)))|hBOOL(hAPP(C,D)).
% 219.60/219.71 ** KEPT (pick-wt=24): 189 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=8): 190 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=8): 191 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 219.60/219.71 ** KEPT (pick-wt=18): 192 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,B,A)),c_HOL_Otimes__class_Otimes(C,C,A)),c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.71 ** KEPT (pick-wt=17): 193 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=35): 194 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(D,E,A))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,E,A)),c_HOL_Otimes__class_Otimes(D,C,A))|C=E|B=D.
% 219.60/219.71 Following clause subsumed by 194 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(D,E,A))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,E,A)),c_HOL_Otimes__class_Otimes(D,C,A))|C=E|B=D.
% 219.60/219.71 ** KEPT (pick-wt=31): 195 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(C,D,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,D,tc_nat)),c_HOL_Otimes__class_Otimes(C,B,tc_nat))|B=D|A=C.
% 219.60/219.71 Following clause subsumed by 195 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(C,D,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,D,tc_nat)),c_HOL_Otimes__class_Otimes(C,B,tc_nat))|B=D|A=C.
% 219.60/219.71 ** KEPT (pick-wt=15): 196 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=15): 197 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=14): 199 [copy,198,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).
% 219.60/219.71 ** KEPT (pick-wt=35): 200 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_Divides_Odiv__class_Omod(D,C,A)|c_Divides_Odiv__class_Omod(E,C,A)!=c_Divides_Odiv__class_Omod(F,C,A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,B,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(F,D,A),C,A).
% 219.60/219.71 ** KEPT (pick-wt=23): 201 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=23): 202 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=23): 203 [] -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).
% 219.60/219.71 ** KEPT (pick-wt=22): 204 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),C)=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),C,A).
% 219.60/219.71 ** KEPT (pick-wt=22): 205 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,B,A))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),c_HOL_Oone__class_Oone(A)),B,A).
% 219.60/219.71 ** KEPT (pick-wt=10): 206 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,c_HOL_Oone__class_Oone(A),A)=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.71 ** KEPT (pick-wt=13): 207 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=13): 208 [] c_Ring__and__Field_Odvd__class_Odvd(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=10): 209 [] c_Divides_Odiv__class_Omod(A,B,tc_nat)=A| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=4): 210 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 219.60/219.71 Following clause subsumed by 210 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 219.60/219.71 ** KEPT (pick-wt=6): 211 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 219.60/219.71 ** KEPT (pick-wt=6): 212 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 219.60/219.71 ** KEPT (pick-wt=6): 213 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 219.60/219.71 ** KEPT (pick-wt=22): 214 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 219.60/219.71 ** KEPT (pick-wt=18): 215 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 219.60/219.71 ** KEPT (pick-wt=13): 216 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 219.60/219.72 ** KEPT (pick-wt=13): 217 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 219.60/219.72 ** KEPT (pick-wt=11): 218 [] A=B| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat).
% 219.60/219.72 Following clause subsumed by 218 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).
% 219.60/219.72 Following clause subsumed by 218 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).
% 219.60/219.72 Following clause subsumed by 218 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).
% 219.60/219.72 Following clause subsumed by 218 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).
% 219.60/219.72 Following clause subsumed by 218 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).
% 219.60/219.72 Following clause subsumed by 218 during input processing: 0 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(B,A,tc_nat)|B=A.
% 219.60/219.72 Following clause subsumed by 217 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 219.60/219.72 Following clause subsumed by 217 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B|c_HOL_Oord__class_Oless(C,B,A).
% 219.60/219.72 Following clause subsumed by 217 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 219.60/219.72 ** KEPT (pick-wt=13): 219 [] -c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=24): 220 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 219.60/219.72 ** KEPT (pick-wt=22): 221 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat)| -c_HOL_Oord__class_Oless(B,D,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=14): 222 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=6): 223 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,B,A).
% 219.60/219.72 ** KEPT (pick-wt=20): 224 [] 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).
% 219.60/219.72 ** KEPT (pick-wt=12): 225 [] 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).
% 219.60/219.72 ** KEPT (pick-wt=16): 226 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_Power_Opower__class_Opower(B,c_Suc(C),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 219.60/219.72 ** KEPT (pick-wt=14): 227 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=14): 228 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A).
% 219.60/219.72 ** KEPT (pick-wt=14): 229 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=14): 230 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=8): 231 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A).
% 219.60/219.72 ** KEPT (pick-wt=14): 232 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=14): 233 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 219.60/219.72 Following clause subsumed by 66 during input processing: 0 [] 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)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=19): 234 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,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)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 219.60/219.72 Following clause subsumed by 234 during input processing: 0 [] c_Ring__and__Field_Odvd__class_Odvd(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,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).
% 219.60/219.72 ** KEPT (pick-wt=12): 235 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A).
% 219.60/219.72 ** KEPT (pick-wt=17): 236 [] c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Odiv(A,B,tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(tc_nat),B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=14): 237 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=31): 238 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=28): 239 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(B,C,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Otimes__class_Otimes(B,E,tc_nat))|c_Divides_Odiv__class_Omod(A,B,tc_nat)=c_Divides_Odiv__class_Omod(D,B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=14): 240 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=14): 241 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A).
% 219.60/219.72 ** KEPT (pick-wt=7): 242 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(A),B,A).
% 219.60/219.72 ** KEPT (pick-wt=16): 244 [copy,243,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)!=B|C=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.72 ** KEPT (pick-wt=9): 245 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.72 ** KEPT (pick-wt=9): 246 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 219.60/219.72 ** KEPT (pick-wt=10): 247 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.72 ** KEPT (pick-wt=13): 248 [] -class_OrderedGroup_Olordered__ab__group__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),c_HOL_Ozero__class_Ozero(A))=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.72 Following clause subsumed by 160 during input processing: 0 [] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 219.60/219.72 ** KEPT (pick-wt=11): 249 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=11): 250 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 219.60/219.72 ** KEPT (pick-wt=11): 251 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 219.60/219.72 ** KEPT (pick-wt=13): 253 [copy,252,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 219.60/219.72 ** KEPT (pick-wt=11): 254 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 219.60/219.72 ** KEPT (pick-wt=11): 255 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 219.60/219.72 ** KEPT (pick-wt=11): 256 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 219.60/219.72 ** KEPT (pick-wt=11): 257 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 219.60/219.72 Following clause subsumed by 250 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 219.60/219.72 ** KEPT (pick-wt=13): 258 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=12): 259 [] -hBOOL(hAPP(A,B))|hBOOL(hAPP(A,c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 219.60/219.72 ** KEPT (pick-wt=12): 260 [] -hBOOL(hAPP(A,c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(A,B)).
% 219.60/219.72 ** KEPT (pick-wt=10): 262 [copy,261,factor_simp] hBOOL(hAPP(A,v_sko__List__Xlexn__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.72 ** KEPT (pick-wt=10): 264 [copy,263,factor_simp] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -hBOOL(hAPP(A,c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(A))).
% 219.60/219.72 Following clause subsumed by 210 during input processing: 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=13): 265 [] hBOOL(hAPP(A,c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.72 Following clause subsumed by 265 during input processing: 0 [] -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))|hBOOL(hAPP(A,c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat))).
% 219.60/219.72 ** KEPT (pick-wt=13): 266 [] -hBOOL(hAPP(A,c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)))|hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.72 ** KEPT (pick-wt=10): 268 [copy,267,factor_simp] hBOOL(hAPP(A,c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.72 ** KEPT (pick-wt=15): 269 [] 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).
% 219.60/219.72 ** KEPT (pick-wt=13): 270 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=13): 271 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=16): 272 [] 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.
% 219.60/219.72 ** KEPT (pick-wt=16): 273 [] 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.
% 219.60/219.72 Following clause subsumed by 273 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).
% 219.60/219.72 ** KEPT (pick-wt=12): 275 [copy,274,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.72 Following clause subsumed by 275 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=10): 277 [copy,276,factor_simp] hBOOL(hAPP(A,v_sko__List__Xreplicate__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.72 ** KEPT (pick-wt=10): 279 [copy,278,factor_simp] hBOOL(hAPP(A,v_sko__Nat__Xnat__Xinducts__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.72 ** KEPT (pick-wt=10): 281 [copy,280,factor_simp] hBOOL(hAPP(A,v_sko__Nat__Xnat__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.72 ** KEPT (pick-wt=5): 282 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 219.60/219.72 Following clause subsumed by 282 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=10): 284 [copy,283,factor_simp] hBOOL(hAPP(A,v_sko__List__Xupt__Xinduct__1(A)))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.72 ** KEPT (pick-wt=19): 285 [] c_HOL_Oord__class_Oless(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=19): 286 [] c_HOL_Oord__class_Oless(A,c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=21): 287 [] c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=14): 288 [] c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat)!=c_HOL_Otimes__class_Otimes(c_Suc(A),C,tc_nat)|B=C.
% 219.60/219.72 ** KEPT (pick-wt=9): 289 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=9): 290 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=13): 291 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)| -c_HOL_Oord__class_Oless(C,B,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=12): 292 [] A=B| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=12): 293 [] A=B| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 219.60/219.72 Following clause subsumed by 292 during input processing: 0 [] A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=13): 294 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)|c_Suc(A)=B| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=9): 295 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=10): 296 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=10): 297 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat).
% 219.60/219.72 Following clause subsumed by 296 during input processing: 0 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=8): 298 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 219.60/219.72 ** KEPT (pick-wt=8): 299 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 219.60/219.72 ** KEPT (pick-wt=21): 300 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,hAPP(hAPP(c_Lambda_OdB_OApp,E),F),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,E),F))).
% 219.60/219.72 Following clause subsumed by 300 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,hAPP(hAPP(c_Lambda_OdB_OApp,E),F),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,E),F))).
% 219.60/219.72 ** KEPT (pick-wt=14): 301 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),hAPP(hAPP(c_Lambda_OdB_OApp,A),C))| -c_Lambda_Obeta(B,C).
% 219.60/219.72 ** KEPT (pick-wt=14): 302 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),hAPP(hAPP(c_Lambda_OdB_OApp,C),B))| -c_Lambda_Obeta(A,C).
% 219.60/219.72 ** KEPT (pick-wt=12): 303 [] c_List_Omap(A,B,C,D)!=c_List_Olist_ONil(D)|B=c_List_Olist_ONil(C).
% 219.60/219.72 ** KEPT (pick-wt=12): 304 [] c_List_Olist_ONil(A)!=c_List_Omap(B,C,D,A)|C=c_List_Olist_ONil(D).
% 219.60/219.72 ** KEPT (pick-wt=13): 305 [] c_Lambda_OdB_OAbs(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|C=c_List_Olist_ONil(tc_Lambda_OdB).
% 219.60/219.72 ** KEPT (pick-wt=13): 306 [] c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(C)|B=c_List_Olist_ONil(tc_Lambda_OdB).
% 219.60/219.72 ** KEPT (pick-wt=27): 308 [copy,307,flip.2] -class_OrderedGroup_Osemigroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,D,A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A,A).
% 219.60/219.72 ** KEPT (pick-wt=18): 309 [] c_Lambda_Obeta(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C))| -c_Lambda_Obeta(A,D).
% 219.60/219.72 ** KEPT (pick-wt=21): 310 [] c_Type_Otypings(c_Type_Oshift(A,B,C,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,B,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(A,D,E).
% 219.60/219.72 ** KEPT (pick-wt=5): 311 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 219.60/219.72 ** KEPT (pick-wt=16): 312 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 219.60/219.72 Following clause subsumed by 312 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 219.60/219.72 ** KEPT (pick-wt=4): 313 [] -c_Lambda_Obeta(c_Lambda_OdB_OVar(A),B).
% 219.60/219.72 ** KEPT (pick-wt=5): 314 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 219.60/219.72 ** KEPT (pick-wt=10): 315 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 219.60/219.72 ** KEPT (pick-wt=19): 316 [] -class_Ring__and__Field_Oordered__semidom(A)|c_Power_Opower__class_Opower(B,C,A)!=c_Power_Opower__class_Opower(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A)|C=D.
% 219.60/219.72 ** KEPT (pick-wt=10): 317 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 219.60/219.72 ** KEPT (pick-wt=10): 318 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=20): 319 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=17): 320 [] -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).
% 219.60/219.72 Following clause subsumed by 44 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A).
% 219.60/219.72 ** KEPT (pick-wt=15): 322 [copy,321,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A).
% 219.60/219.72 ** KEPT (pick-wt=16): 323 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A)=c_Divides_Odiv__class_Omod(B,C,A).
% 219.60/219.72 ** KEPT (pick-wt=16): 324 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),B,A)=c_Divides_Odiv__class_Omod(C,B,A).
% 219.60/219.72 ** KEPT (pick-wt=15): 325 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,E)| -c_HOL_Oord__class_Oless(E,B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=20): 326 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 219.60/219.72 ** KEPT (pick-wt=20): 327 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 219.60/219.72 Following clause subsumed by 326 during input processing: 0 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 219.60/219.72 ** KEPT (pick-wt=13): 328 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=13): 329 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=13): 330 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=13): 331 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=18): 332 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,c_Suc(D),tc_nat),tc_nat,A)=c_HOL_Ozero__class_Ozero(A)| -c_HOL_Oord__class_Oless(D,C,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=20): 333 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 219.60/219.72 ** KEPT (pick-wt=18): 334 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),D,A)=c_Divides_Odiv__class_Omod(B,D,A)| -c_Ring__and__Field_Odvd__class_Odvd(D,C,A).
% 219.60/219.72 ** KEPT (pick-wt=16): 335 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 219.60/219.72 Following clause subsumed by 335 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 219.60/219.72 ** KEPT (pick-wt=21): 336 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 219.60/219.72 ** KEPT (pick-wt=21): 337 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A).
% 219.60/219.72 Following clause subsumed by 336 during input processing: 0 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A)| -c_HOL_Oord__class_Oless(C,D,tc_nat).
% 219.60/219.72 Following clause subsumed by 337 during input processing: 0 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(D,B,A),c_Power_Opower__class_Opower(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),D,A).
% 219.60/219.72 ** KEPT (pick-wt=9): 338 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=9): 339 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=20): 340 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),B,A).
% 219.60/219.72 ** KEPT (pick-wt=20): 341 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=27): 342 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat)),D),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(D,A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=30): 343 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,D,A))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Otimes__class_Otimes(C,E,A))|D=E|C=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.72 ** KEPT (pick-wt=26): 344 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(B,C,tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(B,D,tc_nat))|C=D|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=21): 345 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,B,A)),c_HOL_Otimes__class_Otimes(C,C,A))!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.72 ** KEPT (pick-wt=21): 346 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,B,A)),c_HOL_Otimes__class_Otimes(C,C,A))!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.72 ** KEPT (pick-wt=14): 347 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Ring__and__Field_Odvd__class_Odvd(B,c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=20): 348 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 219.60/219.72 ** KEPT (pick-wt=20): 349 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 219.60/219.72 ** KEPT (pick-wt=20): 350 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 219.60/219.72 ** KEPT (pick-wt=20): 351 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 219.60/219.72 ** KEPT (pick-wt=20): 352 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 219.60/219.72 ** KEPT (pick-wt=20): 353 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A).
% 219.60/219.72 ** KEPT (pick-wt=18): 354 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=18): 355 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=18): 356 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=11): 357 [] c_Type_Otyping(A,B,C)| -c_Lambda_Obeta(D,B)| -c_Type_Otyping(A,D,C).
% 219.60/219.72 ** KEPT (pick-wt=31): 358 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,c_Suc(D),tc_nat),tc_nat,A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A)),hAPP(B,D))|c_HOL_Oord__class_Oless(D,C,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=16): 359 [] A=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(B,A,tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=16): 360 [] A=c_HOL_Oone__class_Oone(tc_nat)| -c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=8): 361 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,B,A)=B.
% 219.60/219.72 ** KEPT (pick-wt=12): 362 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),C,A)=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.72 ** KEPT (pick-wt=12): 363 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.72 ** KEPT (pick-wt=9): 364 [] 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).
% 219.60/219.72 ** KEPT (pick-wt=19): 365 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A))=B.
% 219.60/219.72 ** KEPT (pick-wt=21): 366 [] -class_Ring__and__Field_Oordered__ring__strict(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A))=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.72 ** KEPT (pick-wt=21): 367 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 219.60/219.72 ** KEPT (pick-wt=21): 368 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 219.60/219.72 ** KEPT (pick-wt=21): 369 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 219.60/219.72 ** KEPT (pick-wt=21): 370 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A).
% 219.60/219.72 ** KEPT (pick-wt=17): 371 [] A=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(B,A,tc_nat),tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=21): 372 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)).
% 219.60/219.72 ** KEPT (pick-wt=20): 373 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=20): 374 [] -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).
% 219.60/219.72 Following clause subsumed by 24 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Divides_Odiv__class_Omod(B,C,A)),D),C,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 219.60/219.72 Following clause subsumed by 22 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Divides_Odiv__class_Omod(C,D,A)),D,A)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A).
% 219.60/219.72 ** KEPT (pick-wt=31): 376 [copy,375,flip.2] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(B,C)),c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(C),D,tc_nat),tc_nat,A))=c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(C,D,tc_nat),tc_nat,A)| -c_HOL_Oord__class_Oless(C,D,tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=17): 378 [copy,377,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).
% 219.60/219.72 ** KEPT (pick-wt=19): 379 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A)),c_Divides_Odiv__class_Omod(C,B,A))=C.
% 219.60/219.72 ** KEPT (pick-wt=19): 380 [] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A)),c_Divides_Odiv__class_Omod(B,C,A))=B.
% 219.60/219.72 Following clause subsumed by 380 during input processing: 0 [flip.2] -class_Divides_Osemiring__div(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A)),c_Divides_Odiv__class_Omod(B,C,A))=B.
% 219.60/219.72 ** KEPT (pick-wt=20): 382 [copy,381,flip.2] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A).
% 219.60/219.72 ** KEPT (pick-wt=20): 384 [copy,383,flip.2] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,A),A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A).
% 219.60/219.72 ** KEPT (pick-wt=11): 385 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(A,B,tc_nat)|A=c_HOL_Oone__class_Oone(tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=11): 386 [] c_HOL_Oone__class_Oone(tc_nat)!=c_HOL_Otimes__class_Otimes(A,B,tc_nat)|B=c_HOL_Oone__class_Oone(tc_nat).
% 219.60/219.72 ** KEPT (pick-wt=17): 387 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=17): 388 [] -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).
% 219.60/219.72 ** KEPT (pick-wt=17): 389 [] -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).
% 219.60/219.72 Following clause subsumed by 389 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).
% 219.60/219.72 ** KEPT (pick-wt=17): 390 [] -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).
% 219.60/219.72 Following clause subsumed by 389 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).
% 219.60/219.72 Following clause subsumed by 133 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,D,A)),c_HOL_Otimes__class_Otimes(C,D,A))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),D,A).
% 219.60/219.72 ** KEPT (pick-wt=24): 392 [copy,391,flip.2] -class_Ring__and__Field_Ocomm__semiring(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(D,C,A))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 219.60/219.73 ** KEPT (pick-wt=24): 394 [copy,393,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Otimes__class_Otimes(B,C,A)),c_HOL_Otimes__class_Otimes(B,D,A))=c_HOL_Otimes__class_Otimes(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 219.60/219.73 ** KEPT (pick-wt=16): 395 [] c_Type_Otyping(c_Type_Oshift(A,B,C,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,D),B),E)| -c_Type_Otyping(A,D,E).
% 219.60/219.73 ** KEPT (pick-wt=10): 396 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 219.60/219.73 ** KEPT (pick-wt=10): 397 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 219.60/219.73 Following clause subsumed by 225 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).
% 219.60/219.73 Following clause subsumed by 225 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).
% 219.60/219.73 ** KEPT (pick-wt=10): 398 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 219.60/219.73 Following clause subsumed by 398 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 219.60/219.73 ** KEPT (pick-wt=12): 399 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,A),B)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 219.60/219.73 ** KEPT (pick-wt=9): 400 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 219.60/219.73 ** KEPT (pick-wt=29): 401 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(B,c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Ozero__class_Ozero(A)|c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_nat),tc_nat,A)=c_Finite__Set_Osetsum(B,c_SetInterval_Oord__class_OatLeastLessThan(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat),tc_nat,A).
% 219.60/219.73 ** KEPT (pick-wt=21): 403 [copy,402,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(A,B,C),tc_Lambda_OdB,tc_Lambda_OdB)=C| -c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 219.60/219.73 ** KEPT (pick-wt=20): 404 [] -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).
% 219.60/219.73 ** KEPT (pick-wt=16): 405 [] -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).
% 219.60/219.73 ** KEPT (pick-wt=16): 406 [] -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).
% 219.60/219.73 ** KEPT (pick-wt=9): 407 [] -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).
% 219.60/219.73 ** KEPT (pick-wt=13): 408 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A)=c_HOL_Ozero__class_Ozero(A).
% 219.60/219.73 ** KEPT (pick-wt=18): 409 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.73 ** KEPT (pick-wt=20): 410 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.73 ** KEPT (pick-wt=15): 411 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))|hBOOL(hAPP(A,c_Suc(c_ATP__Linkup_Osko__Nat__Xzero__induct__1__1(A))))| -hBOOL(hAPP(A,B)).
% 219.60/219.73 ** KEPT (pick-wt=17): 412 [] c_Power_Opower__class_Opower(A,B,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.73 ** KEPT (pick-wt=15): 413 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__List__Xlexn__Xinduct__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.73 ** KEPT (pick-wt=18): 414 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.73 ** KEPT (pick-wt=20): 415 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.73 ** KEPT (pick-wt=15): 416 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(c_ATP__Linkup_Osko__Nat__Xnat__induct__1__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.73 ** KEPT (pick-wt=13): 417 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.73 ** KEPT (pick-wt=13): 418 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.73 ** KEPT (pick-wt=15): 419 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__List__Xreplicate__Xinduct__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.73 ** KEPT (pick-wt=15): 420 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__List__Xupt__Xinduct__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.73 ** KEPT (pick-wt=15): 421 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__Nat__Xnat__Xinduct__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.73 ** KEPT (pick-wt=10): 422 [] A=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 219.60/219.73 ** KEPT (pick-wt=15): 423 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Suc(v_sko__Nat__Xnat__Xinducts__1(A))))| -hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.60/219.73 ** KEPT (pick-wt=19): 424 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.73 ** KEPT (pick-wt=19): 425 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.73 ** KEPT (pick-wt=15): 426 [] c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat))!=B|c_Divides_Odiv__class_Omod(c_Suc(A),B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.73 ** KEPT (pick-wt=19): 427 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.73 ** KEPT (pick-wt=19): 428 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.60/219.73 ** KEPT (pick-wt=11): 429 [] A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))| -c_Ring__and__Field_Odvd__class_Odvd(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 219.60/219.73 ** KEPT (pick-wt=23): 430 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),C,A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A).
% 219.60/219.73 ** KEPT (pick-wt=20): 431 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=C.
% 219.60/219.73 ** KEPT (pick-wt=13): 432 [] c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_Lambda_OdB_OAbs(C)|A=c_Lambda_OdB_OAbs(C).
% 219.60/219.73 ** KEPT (pick-wt=18): 433 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|A=C.
% 219.60/219.74 ** KEPT (pick-wt=18): 434 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|B=D.
% 219.60/219.74 ** KEPT (pick-wt=16): 435 [] c_Lambda_Obeta(c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB))| -c_Lambda_Obeta(A,C).
% 219.60/219.74 ** KEPT (pick-wt=13): 436 [] c_Lambda_OdB_OAbs(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OAbs(A)=B.
% 219.60/219.74 ** KEPT (pick-wt=32): 437 [] c_Type_Otypings(A,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,B,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(c_Type_Oshift(A,C,F,tc_Type_Otype),D,E)| -c_Type_Otyping(A,B,F).
% 219.60/219.74 ** KEPT (pick-wt=15): 438 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 219.60/219.74 ** KEPT (pick-wt=18): 439 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),A,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_List_Olistsp(c_InductTermi_OIT,A,tc_Lambda_OdB).
% 219.60/219.74 ** KEPT (pick-wt=23): 440 [] A=B| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),E,tc_Lambda_OdB,tc_Lambda_OdB),B)| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),E,tc_Lambda_OdB,tc_Lambda_OdB),A).
% 219.60/219.74 ** KEPT (pick-wt=15): 441 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.74 ** KEPT (pick-wt=13): 442 [] c_Lambda_OdB_OVar(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|C=c_List_Olist_ONil(tc_Lambda_OdB).
% 219.60/219.74 ** KEPT (pick-wt=14): 443 [] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.74 ** KEPT (pick-wt=14): 444 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_List_Olistsp(c_InductTermi_OIT,B,tc_Lambda_OdB).
% 219.60/219.74 ** KEPT (pick-wt=34): 445 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),C,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(c_InductTermi_OIT,B))| -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB))).
% 219.60/219.74 ** KEPT (pick-wt=8): 446 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 219.60/219.74 ** KEPT (pick-wt=18): 447 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|A=C.
% 219.60/219.74 ** KEPT (pick-wt=18): 448 [] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB)|B=D.
% 219.60/219.74 ** KEPT (pick-wt=4): 450 [copy,449,flip.1] c_Suc(A)!=A.
% 219.60/219.74 Following clause subsumed by 450 during input processing: 0 [] c_Suc(A)!=A.
% 219.60/219.74 ** KEPT (pick-wt=5): 451 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.74 Following clause subsumed by 451 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.74 ** KEPT (pick-wt=14): 452 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 219.60/219.74 ** KEPT (pick-wt=14): 453 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 219.60/219.74 ** KEPT (pick-wt=13): 454 [] c_Lambda_OdB_OVar(A)!=c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB)|c_Lambda_OdB_OVar(A)=B.
% 219.60/219.74 ** KEPT (pick-wt=8): 455 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 219.60/219.74 ** KEPT (pick-wt=8): 456 [] c_Suc(A)!=c_Suc(B)|A=B.
% 219.60/219.74 Following clause subsumed by 456 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 219.60/219.74 Following clause subsumed by 451 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.74 Following clause subsumed by 451 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.60/219.74 ** KEPT (pick-wt=16): 457 [] c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,C,B,tc_Lambda_OdB,tc_Lambda_OdB)|A=C.
% 219.60/219.74 ** KEPT (pick-wt=8): 458 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 219.60/219.74 ** KEPT (pick-wt=49): 459 [] -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(c_Suc(v_ia))),c_Suc(v_ja))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(v_ia)),v_ja)),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(v_ia),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),v_ja,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))).
% 219.60/219.74 ** KEPT (pick-wt=6): 460 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 219.60/219.74 ** KEPT (pick-wt=6): 461 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 219.60/219.74 ** KEPT (pick-wt=7): 462 [] A=B| -c_fe_qual(A,B,C).
% 219.60/219.74 149 back subsumes 25.
% 219.60/219.74 225 back subsumes 224.
% 219.60/219.74 225 back subsumes 149.
% 219.60/219.74 232 back subsumes 116.
% 219.60/219.74 232 back subsumes 9.
% 219.60/219.74 242 back subsumes 82.
% 219.60/219.74 Following clause subsumed by 299 during input processing: 0 [copy,298,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 219.60/219.74 Following clause subsumed by 298 during input processing: 0 [copy,299,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 219.60/219.74 Following clause subsumed by 314 during input processing: 0 [copy,311,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 219.60/219.74 Following clause subsumed by 311 during input processing: 0 [copy,314,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 219.60/219.74 317 back subsumes 258.
% 219.60/219.74 389 back subsumes 202.
% 219.60/219.74 390 back subsumes 203.
% 219.60/219.74 ** KEPT (pick-wt=15): 525 [copy,441,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.74 ** KEPT (pick-wt=14): 526 [copy,443,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C)),D).
% 219.60/219.74 Following clause subsumed by 458 during input processing: 0 [copy,455,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 219.60/219.74 Following clause subsumed by 455 during input processing: 0 [copy,458,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 219.60/219.74 Following clause subsumed by 441 during input processing: 0 [copy,525,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.74 Following clause subsumed by 443 during input processing: 0 [copy,526,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(C),D,tc_Lambda_OdB,tc_Lambda_OdB).
% 219.60/219.74
% 219.60/219.74 ------------> process sos:
% 219.60/219.74 ** KEPT (pick-wt=3): 527 [] A=A.
% 219.60/219.74 ** KEPT (pick-wt=6): 528 [] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 219.60/219.74 ** KEPT (pick-wt=32): 530 [copy,529,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat)),D)).
% 219.60/219.74 ---> New Demodulator: 531 [new_demod,530] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat)),D)).
% 219.60/219.74 ** KEPT (pick-wt=19): 532 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(A)),B)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 219.60/219.74 ** KEPT (pick-wt=23): 533 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 219.60/219.74 ---> New Demodulator: 534 [new_demod,533] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 219.60/219.74 ** KEPT (pick-wt=23): 535 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).
% 219.60/219.74 ** KEPT (pick-wt=9): 536 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 219.60/219.74 ** KEPT (pick-wt=25): 537 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(A,C,tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat)),c_HOL_Otimes__class_Otimes(A,B,tc_nat)).
% 219.60/219.74 Following clause subsumed by 537 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(A,C,tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat)),c_HOL_Otimes__class_Otimes(A,B,tc_nat)).
% 219.60/219.74 ** KEPT (pick-wt=11): 538 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 219.60/219.74 ** KEPT (pick-wt=10): 539 [] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 219.60/219.74 ---> New Demodulator: 540 [new_demod,539] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 219.60/219.74 ** KEPT (pick-wt=15): 542 [copy,541,demod,540] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A).
% 219.60/219.74 ** KEPT (pick-wt=7): 543 [] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=A.
% 219.60/219.74 ---> New Demodulator: 544 [new_demod,543] c_HOL_Otimes__class_Otimes(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=A.
% 219.60/219.74 ** KEPT (pick-wt=7): 545 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 219.60/219.74 ---> New Demodulator: 546 [new_demod,545] c_HOL_Otimes__class_Otimes(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 219.60/219.74 ** KEPT (pick-wt=5): 547 [] c_List_Olistsp(A,c_List_Olist_ONil(B),B).
% 219.60/219.74 ** KEPT (pick-wt=15): 549 [copy,548,demod,540,534] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),tc_nat).
% 219.60/219.74 ** KEPT (pick-wt=15): 551 [copy,550,demod,540,534] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat))),tc_nat).
% 219.60/219.74 Following clause subsumed by 549 during input processing: 0 [demod,540,534] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),tc_nat).
% 219.60/219.74 Following clause subsumed by 527 during input processing: 0 [demod,546] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.60/219.74 ** KEPT (pick-wt=17): 553 [copy,552,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Osubstn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Osubstn(c_Lambda_OdB_OAbs(A),B,C).
% 219.60/219.74 ---> New Demodulator: 554 [new_demod,553] c_Lambda_OdB_OAbs(c_Lambda_Osubstn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Osubstn(c_Lambda_OdB_OAbs(A),B,C).
% 219.60/219.74 ** KEPT (pick-wt=13): 555 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 219.60/219.74 ** KEPT (pick-wt=28): 557 [copy,556,flip.1] c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(A)),B),C).
% 219.60/219.74 ---> New Demodulator: 558 [new_demod,557] c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(A)),B),C).
% 219.68/219.74 ** KEPT (pick-wt=20): 560 [copy,559,demod,540] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))).
% 219.68/219.74 ---> New Demodulator: 561 [new_demod,560] c_Nat_Osize__class_Osize(c_Lambda_OdB_OAbs(A),tc_Lambda_OdB)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,546] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=18): 562 [] c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 219.68/219.74 ---> New Demodulator: 563 [new_demod,562] c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=18): 564 [] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 219.68/219.74 ---> New Demodulator: 565 [new_demod,564] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=41): 567 [copy,566,demod,534,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(C,B,tc_nat)),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_Divides_Odiv__class_Omod(C,B,tc_nat)),B,tc_nat)))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 219.68/219.74 ---> New Demodulator: 568 [new_demod,567] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(A,B,tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Odiv(C,B,tc_nat)),c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_Divides_Odiv__class_Omod(C,B,tc_nat)),B,tc_nat)))=c_Divides_Odiv__class_Odiv(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=19): 569 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(B,C,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=17): 570 [] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),C),B,tc_nat)=c_Divides_Odiv__class_Omod(C,B,tc_nat).
% 219.68/219.74 ---> New Demodulator: 571 [new_demod,570] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),C),B,tc_nat)=c_Divides_Odiv__class_Omod(C,B,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=9): 572 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat),tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=20): 574 [copy,573,demod,540] c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Otimes__class_Otimes(A,B,tc_nat)).
% 219.68/219.74 ** KEPT (pick-wt=20): 576 [copy,575,demod,540] c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Otimes__class_Otimes(A,B,tc_nat)).
% 219.68/219.74 ** KEPT (pick-wt=9): 577 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 219.68/219.74 ---> New Demodulator: 578 [new_demod,577] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 219.68/219.74 ** KEPT (pick-wt=15): 579 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)|A=C|c_HOL_Oord__class_Oless(C,A,tc_nat).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,540,534,571,540] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=11): 580 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 219.68/219.74 Following clause subsumed by 580 during input processing: 0 [] hBOOL(hAPP(hAPP(A,B),C))|c_HOL_Oord__class_Oless(B,C,tc_nat)|C=B|c_HOL_Oord__class_Oless(C,B,tc_nat).
% 219.68/219.74 Following clause subsumed by 580 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 219.68/219.74 ** KEPT (pick-wt=4): 581 [] c_Ring__and__Field_Odvd__class_Odvd(A,A,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=12): 582 [] 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).
% 219.68/219.74 ** KEPT (pick-wt=32): 584 [copy,583,demod,563,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat),C,tc_nat))=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat).
% 219.68/219.74 ---> New Demodulator: 585 [new_demod,584] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat)),c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat),C,tc_nat))=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=11): 586 [] 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).
% 219.68/219.74 ** KEPT (pick-wt=11): 587 [] 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).
% 219.68/219.74 ** KEPT (pick-wt=9): 588 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=8): 589 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ---> New Demodulator: 590 [new_demod,589] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=8): 591 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ---> New Demodulator: 592 [new_demod,591] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=11): 593 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ---> New Demodulator: 594 [new_demod,593] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=9): 596 [copy,595,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 219.68/219.74 ---> New Demodulator: 597 [new_demod,596] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 219.68/219.74 ** KEPT (pick-wt=9): 598 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 219.68/219.74 ---> New Demodulator: 599 [new_demod,598] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,597] A=A.
% 219.68/219.74 ** KEPT (pick-wt=24): 601 [copy,600,demod,540,540,flip.1] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat).
% 219.68/219.74 ---> New Demodulator: 602 [new_demod,601] c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=10): 604 [copy,603,demod,540] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.68/219.74 Following clause subsumed by 604 during input processing: 0 [demod,540] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=25): 606 [copy,605,demod,540,534,540,534] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,540,540,534] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 219.68/219.74 ** KEPT (pick-wt=33): 608 [copy,607,demod,540,540,540,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=c_Divides_Odiv__class_Omod(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),B,tc_nat)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(A,B,tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=B.
% 219.68/219.74 Following clause subsumed by 606 during input processing: 0 [demod,540,534,540] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))).
% 219.68/219.74 Following clause subsumed by 604 during input processing: 0 [demod,540,unit_del,210] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=14): 610 [copy,609,demod,540] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=23): 611 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C)),hAPP(hAPP(c_Lambda_Olift,B),C)).
% 219.68/219.74 ** KEPT (pick-wt=16): 612 [] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 219.68/219.74 ** KEPT (pick-wt=20): 614 [copy,613,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(A,B,C)),c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 219.68/219.74 ---> New Demodulator: 615 [new_demod,614] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(A,B,C)),c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 219.68/219.74 ** KEPT (pick-wt=9): 616 [] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 219.68/219.74 ** KEPT (pick-wt=9): 617 [] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 219.68/219.74 ** KEPT (pick-wt=11): 619 [copy,618,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(A).
% 219.68/219.74 ---> New Demodulator: 620 [new_demod,619] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OAbs(A).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,620] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 219.68/219.74 ** KEPT (pick-wt=9): 621 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 219.68/219.74 ---> New Demodulator: 622 [new_demod,621] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 219.68/219.74 ** KEPT (pick-wt=13): 623 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 219.68/219.74 ---> New Demodulator: 624 [new_demod,623] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 219.68/219.74 ** KEPT (pick-wt=8): 625 [] c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 ---> New Demodulator: 626 [new_demod,625] c_Power_Opower__class_Opower(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=9): 628 [copy,627,demod,592,592] c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ---> New Demodulator: 629 [new_demod,628] c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=29): 631 [copy,630,demod,563,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(B,A,tc_nat))=c_Divides_Odiv__class_Omod(B,c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 219.68/219.74 ---> New Demodulator: 632 [new_demod,631] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)),c_Divides_Odiv__class_Omod(B,A,tc_nat))=c_Divides_Odiv__class_Omod(B,c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=15): 633 [] c_Divides_Odiv__class_Odiv(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=10): 634 [] c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=19): 636 [copy,635,flip.1] c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(A)),B).
% 219.68/219.74 ---> New Demodulator: 637 [new_demod,636] c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(A)),B).
% 219.68/219.74 ** KEPT (pick-wt=12): 639 [copy,638,demod,540,599] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_HOL_Oone__class_Oone(tc_nat)).
% 219.68/219.74 ---> New Demodulator: 640 [new_demod,639] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OAbs(A))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),c_HOL_Oone__class_Oone(tc_nat)).
% 219.68/219.74 ** KEPT (pick-wt=15): 641 [] 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).
% 219.68/219.74 ---> New Demodulator: 642 [new_demod,641] 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).
% 219.68/219.74 ** KEPT (pick-wt=22): 644 [copy,643,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(C,B,tc_nat))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 219.68/219.74 ---> New Demodulator: 645 [new_demod,644] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(C,B,tc_nat))=c_HOL_Otimes__class_Otimes(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=22): 647 [copy,646,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(A,C,tc_nat))=c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 219.68/219.74 ---> New Demodulator: 648 [new_demod,647] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat)),c_HOL_Otimes__class_Otimes(A,C,tc_nat))=c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=11): 649 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 219.68/219.74 ** KEPT (pick-wt=7): 650 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 219.68/219.74 ** KEPT (pick-wt=21): 652 [copy,651,demod,540,599,534] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(B)),c_HOL_Oone__class_Oone(tc_nat))).
% 219.68/219.74 ---> New Demodulator: 653 [new_demod,652] c_Lambda_OdB_OdB__size(hAPP(hAPP(c_Lambda_OdB_OApp,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(A)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Lambda_OdB_OdB__size(B)),c_HOL_Oone__class_Oone(tc_nat))).
% 219.68/219.74 ** KEPT (pick-wt=24): 655 [copy,654,demod,540,599,534,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 219.68/219.74 ---> New Demodulator: 656 [new_demod,655] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Lambda_OdB)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(B,tc_Lambda_OdB)),c_HOL_Oone__class_Oone(tc_nat)))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Lambda_OdB_OApp,A),B),tc_Lambda_OdB).
% 219.68/219.74 ** KEPT (pick-wt=15): 657 [] c_Lambda_Obeta(hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat))).
% 219.68/219.74 ** KEPT (pick-wt=14): 659 [copy,658,demod,540,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__Xexhaust__1__1(A)),c_HOL_Oone__class_Oone(tc_nat))=A|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,540,599,599,540,599] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,540,599,540,599,597] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=8): 661 [copy,660,demod,540,599] c_Divides_Odiv__class_Omod(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,540,599,540,599,546,540,599] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 Following clause subsumed by 581 during input processing: 0 [demod,540,599,540,599] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=6): 663 [copy,662,demod,540,599] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oone__class_Oone(tc_nat),tc_nat).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,540,599] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=27): 665 [copy,664,demod,540] c_Type_Oshift(c_Type_Oshift(A,B,C,D),c_HOL_Ozero__class_Ozero(tc_nat),E,D)=c_Type_Oshift(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),E,D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat)),C,D).
% 219.68/219.74 ** KEPT (pick-wt=14): 667 [copy,666,demod,540,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnat__Xnchotomy__1__1(A)),c_HOL_Oone__class_Oone(tc_nat))=A|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,626,540,599] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,540,599,597,540,599] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=14): 669 [copy,668,demod,540,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_ATP__Linkup_Osko__Nat__Xnot0__implies__Suc__1__1(A)),c_HOL_Oone__class_Oone(tc_nat))=A|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=5): 671 [copy,670,demod,540,599] c_Ring__and__Field_Odvd__class_Odvd(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,540,599,540,599,599] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=11): 673 [copy,672,demod,540] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.68/219.74 Following clause subsumed by 673 during input processing: 0 [demod,540] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=8): 675 [copy,674,demod,540,599,540,599] c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 ---> New Demodulator: 676 [new_demod,675] c_Power_Opower__class_Opower(c_HOL_Oone__class_Oone(tc_nat),A,tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,540,599,676,540,599] c_HOL_Oone__class_Oone(tc_nat)=c_HOL_Oone__class_Oone(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=7): 678 [copy,677,demod,540,599] c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 219.68/219.74 ---> New Demodulator: 679 [new_demod,678] c_Divides_Odiv__class_Odiv(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 219.68/219.74 ** KEPT (pick-wt=14): 681 [copy,680,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.68/219.74 ---> New Demodulator: 682 [new_demod,681] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 219.68/219.74 ** KEPT (pick-wt=7): 683 [] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ---> New Demodulator: 684 [new_demod,683] c_Nat_Osize__class_Osize(c_Lambda_OdB_OVar(A),tc_Lambda_OdB)=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=6): 685 [] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 ---> New Demodulator: 686 [new_demod,685] c_Lambda_OdB_OdB__size(c_Lambda_OdB_OVar(A))=c_HOL_Ozero__class_Ozero(tc_nat).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,622] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 219.68/219.74 ** KEPT (pick-wt=18): 687 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(A)|A=C|c_HOL_Oord__class_Oless(C,A,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=10): 689 [copy,688,unit_del,210] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 219.68/219.74 ---> New Demodulator: 690 [new_demod,689] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,622] c_Lambda_OdB_OVar(A)=c_Lambda_OdB_OVar(A).
% 219.68/219.74 ** KEPT (pick-wt=30): 691 [] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C),c_List_Omap(c_COMBC(c_Lambda_Olift,C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 219.68/219.74 ---> New Demodulator: 692 [new_demod,691] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C),c_List_Omap(c_COMBC(c_Lambda_Olift,C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 219.68/219.74 ** KEPT (pick-wt=29): 693 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C),D)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D)),hAPP(hAPP(hAPP(c_Lambda_Osubst,B),C),D)).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [demod,690] B=B.
% 219.68/219.74 ** KEPT (pick-wt=41): 694 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C),D)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,C,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),D,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 219.68/219.74 ** KEPT (pick-wt=14): 695 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 219.68/219.74 ** KEPT (pick-wt=13): 697 [copy,696,demod,682] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(v_ra,v_s,c_HOL_Ozero__class_Ozero(tc_nat)),v_ss,tc_Lambda_OdB,tc_Lambda_OdB))).
% 219.68/219.74 ** KEPT (pick-wt=56): 699 [copy,698,demod,540,540,682] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubstn(hAPP(hAPP(hAPP(c_Lambda_Osubst,v_ra),c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))),hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(A)),B),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,c_Lambda_OdB_OVar(A),tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),B,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),v_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB))).
% 219.68/219.74 ** KEPT (pick-wt=4): 700 [] hBOOL(hAPP(c_InductTermi_OIT,v_s)).
% 219.68/219.74 ** KEPT (pick-wt=11): 701 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_s),c_Lambda_OdB_OVar(A)),B))).
% 219.68/219.74 ** KEPT (pick-wt=2): 702 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 703 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 704 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 705 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 706 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 707 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 708 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 709 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 710 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 711 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 712 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 713 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 714 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 715 [] class_Ring__and__Field_Ocomm__semiring(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 716 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 717 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 718 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 719 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 720 [] class_Ring__and__Field_Osemiring__0(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 721 [] class_Ring__and__Field_Omult__zero(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 722 [] class_OrderedGroup_Omonoid__mult(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 723 [] class_Ring__and__Field_Osemiring(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 724 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 725 [] class_Divides_Osemiring__div(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 726 [] class_Nat_Osemiring__char__0(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 727 [] class_Ring__and__Field_Odvd(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 728 [] class_Orderings_Opreorder(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 729 [] class_Orderings_Olinorder(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 730 [] class_Orderings_Oorder(tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=2): 731 [] class_Power_Opower(tc_nat).
% 219.68/219.74 Following clause subsumed by 695 during input processing: 0 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 219.68/219.74 ** KEPT (pick-wt=13): 732 [] c_COMBB(A,B,C,D,E,F)=hAPP(A,hAPP(B,C)).
% 219.68/219.74 ** KEPT (pick-wt=4): 733 [] c_fe_qual(A,A,B).
% 219.68/219.74 Following clause subsumed by 527 during input processing: 0 [copy,527,flip.1] A=A.
% 219.68/219.74 527 back subsumes 524.
% 219.68/219.74 527 back subsumes 500.
% 219.68/219.74 527 back subsumes 499.
% 219.68/219.74 527 back subsumes 498.
% 219.68/219.74 >>>> Starting back demodulation with 531.
% 219.68/219.74 >>>> Starting back demodulation with 534.
% 219.68/219.74 Following clause subsumed by 535 during input processing: 0 [copy,535,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(
% 219.68/219.74 -------- PROOF --------
% 219.68/219.74 c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).
% 219.68/219.74 Following clause subsumed by 536 during input processing: 0 [copy,536,flip.1] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=19): 734 [copy,537,flip.1,demod,648,648] c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)=c_HOL_Otimes__class_Otimes(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 219.68/219.74 ** KEPT (pick-wt=11): 735 [copy,538,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(C,D,A,c_Lambda_OdB_OAbs(B),E).
% 219.68/219.74 >>>> Starting back demodulation with 540.
% 219.68/219.74 >> back demodulating 523 with 540.
% 219.68/219.74 >> back demodulating 522 with 540.
% 219.68/219.74 >> back demodulating 521 with 540.
% 219.68/219.74 >> back demodulating 520 with 540.
% 219.68/219.74 >> back demodulating 508 with 540.
% 219.68/219.74 >> back demodulating 507 with 540.
% 219.68/219.74 >> back demodulating 459 with 540.
% 219.68/219.74
% 219.68/219.74 ----> UNIT CONFLICT at 0.08 sec ----> 741 [binary,740.1,699.1] $F.
% 219.68/219.74
% 219.68/219.74 Length of proof is 3. Level of proof is 2.
% 219.68/219.74
% 219.68/219.74 ---------------- PROOF ----------------
% 219.68/219.74 % SZS status Unsatisfiable
% 219.68/219.74 % SZS output start Refutation
% See solution above
% 219.68/219.74 ------------ end of proof -------------
% 219.68/219.74
% 219.68/219.74
% 219.68/219.74 Search stopped by max_proofs option.
% 219.68/219.74
% 219.68/219.74
% 219.68/219.74 Search stopped by max_proofs option.
% 219.68/219.74
% 219.68/219.74 ============ end of search ============
% 219.68/219.74
% 219.68/219.74 -------------- statistics -------------
% 219.68/219.74 clauses given 0
% 219.68/219.74 clauses generated 86
% 219.68/219.74 clauses kept 626
% 219.68/219.74 clauses forward subsumed 119
% 219.68/219.74 clauses back subsumed 13
% 219.68/219.74 Kbytes malloced 10742
% 219.68/219.74
% 219.68/219.74 ----------- times (seconds) -----------
% 219.68/219.74 user CPU time 0.08 (0 hr, 0 min, 0 sec)
% 219.68/219.74 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 219.68/219.74 wall-clock time 220 (0 hr, 3 min, 40 sec)
% 219.68/219.74
% 219.68/219.74 That finishes the proof of the theorem.
% 219.68/219.74
% 219.68/219.74 Process 28231 finished Wed Jul 27 09:17:30 2022
% 219.68/219.75 Otter interrupted
% 219.68/219.75 PROOF FOUND
%------------------------------------------------------------------------------