TSTP Solution File: LCL789-1 by Otter---3.3
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- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL789-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Jul 27 13:05:25 EDT 2022
% Result : Unsatisfiable 16.30s 16.40s
% Output : Refutation 16.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of clauses : 8 ( 8 unt; 0 nHn; 6 RR)
% Number of literals : 8 ( 4 equ; 2 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-5 aty)
% Number of variables : 12 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(214,axiom,
~ c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))),
file('LCL789-1.p',unknown),
[] ).
cnf(335,axiom,
c_Type_Otyping(v_e____,v_u____,v_T____),
file('LCL789-1.p',unknown),
[] ).
cnf(336,axiom,
c_List_Ofoldr(A,c_List_Olist_OCons(B,C,D),E,D,F) = hAPP(hAPP(A,B),c_List_Ofoldr(A,C,E,D,F)),
file('LCL789-1.p',unknown),
[] ).
cnf(338,plain,
hAPP(hAPP(A,B),c_List_Ofoldr(A,C,D,E,F)) = c_List_Ofoldr(A,c_List_Olist_OCons(B,C,E),D,E,F),
inference(flip,[status(thm),theory(equality)],[inference(copy,[status(thm)],[336])]),
[iquote('copy,336,flip.1')] ).
cnf(348,axiom,
v_T____ = hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)),
file('LCL789-1.p',unknown),
[] ).
cnf(350,plain,
c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype) = v_T____,
inference(flip,[status(thm),theory(equality)],[inference(demod,[status(thm),theory(equality)],[inference(copy,[status(thm)],[348]),338])]),
[iquote('copy,348,demod,338,flip.1')] ).
cnf(390,plain,
~ c_Type_Otyping(v_e____,v_u____,v_T____),
inference(demod,[status(thm),theory(equality)],[inference(back_demod,[status(thm)],[214]),338,350]),
[iquote('back_demod,214,demod,338,350')] ).
cnf(391,plain,
$false,
inference(binary,[status(thm)],[390,335]),
[iquote('binary,390.1,335.1')] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL789-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.13 % Command : otter-tptp-script %s
% 0.13/0.34 % Computer : n019.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Wed Jul 27 09:32:07 EDT 2022
% 0.19/0.34 % CPUTime :
% 16.30/16.38 ----- Otter 3.3f, August 2004 -----
% 16.30/16.38 The process was started by sandbox2 on n019.cluster.edu,
% 16.30/16.38 Wed Jul 27 09:32:07 2022
% 16.30/16.38 The command was "./otter". The process ID is 14490.
% 16.30/16.38
% 16.30/16.38 set(prolog_style_variables).
% 16.30/16.38 set(auto).
% 16.30/16.38 dependent: set(auto1).
% 16.30/16.38 dependent: set(process_input).
% 16.30/16.38 dependent: clear(print_kept).
% 16.30/16.38 dependent: clear(print_new_demod).
% 16.30/16.38 dependent: clear(print_back_demod).
% 16.30/16.38 dependent: clear(print_back_sub).
% 16.30/16.38 dependent: set(control_memory).
% 16.30/16.38 dependent: assign(max_mem, 12000).
% 16.30/16.38 dependent: assign(pick_given_ratio, 4).
% 16.30/16.38 dependent: assign(stats_level, 1).
% 16.30/16.38 dependent: assign(max_seconds, 10800).
% 16.30/16.38 clear(print_given).
% 16.30/16.38
% 16.30/16.38 list(usable).
% 16.30/16.38 0 [] A=A.
% 16.30/16.38 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 16.30/16.38 0 [] -class_Int_Oring__char__0(T_a)| -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(V_x,T_a)!=c_Int_Onumber__class_Onumber__of(V_y,T_a)|V_x=V_y.
% 16.30/16.38 0 [] c_Type_Otyping(V_e,V_t,c_Type_Osko__Type__Xtypes__snocE__1__2(V_Ts,V_e,V_t,V_ts))| -c_Type_Otypings(V_e,c_List_Oappend(V_ts,c_List_Olist_OCons(V_t,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),V_Ts).
% 16.30/16.38 0 [] c_List_Orev(c_List_Oappend(V_xs,V_ys,T_a),T_a)=c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Orev(V_xs,T_a),T_a).
% 16.30/16.38 0 [] c_List_Orev(c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)|V_ts=c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__e_q__foldl__conv__1__1(V_r,V_s,V_t,V_ts),c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)|V_ts=c_List_Olist_ONil(tc_Lambda_OdB).
% 16.30/16.38 0 [] c_List_Oreplicate(V_m,V_x,T_a)!=c_List_Oreplicate(V_n,V_y,T_a)|V_x=V_y|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 16.30/16.38 0 [] c_List_Orev(V_xs,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_y,T_a).
% 16.30/16.38 0 [] c_List_Olast(c_List_Oreplicate(V_n,V_x,T_a),T_a)=V_x|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 16.30/16.38 0 [] V_x=V_y|hBOOL(hAPP(hAPP(V_r,V_y),V_x))| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_x))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(V_r,T_a,T_a),T_a),V_x),V_y)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(V_r,V_b),V_a))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a),V_b))| -hBOOL(hAPP(hAPP(V_r,V_b),V_a)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(V_r,V_a2),V_a1))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_a1),V_a2)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(V_r,T_a,T_b),V_b),V_a))| -hBOOL(hAPP(hAPP(V_r,V_a),V_b)).
% 16.30/16.38 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_n,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_n,T_a)),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_b,V_n,T_a)).
% 16.30/16.38 0 [] -c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)|c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,V_x,T_a),c_List_Oappend(V_xs,V_x,T_a),T_a).
% 16.30/16.38 0 [] c_ListOrder_Ostep1(V_r,c_List_Oappend(V_x,V_vs,T_a),c_List_Oappend(V_x,V_us,T_a),T_a)| -c_ListOrder_Ostep1(V_r,V_vs,V_us,T_a).
% 16.30/16.38 0 [] c_List_Orotate1(c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] V_x=V_y|V_xs=V_ys| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 16.30/16.38 0 [] -hBOOL(hAPP(hAPP(V_r,V_y),V_xa))|c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_x,T_a),c_List_Olist_OCons(V_xa,V_x,T_a),T_a).
% 16.30/16.38 0 [] c_List_Oreplicate(V_m,V_x,T_a)!=c_List_Oreplicate(V_n,V_y,T_a)|V_m=V_n.
% 16.30/16.38 0 [] c_Type_Otyping(v_ea______,v_ua______,v_T____).
% 16.30/16.38 0 [] c_Wellfounded_Oaccp(V_r,V_b,T_a)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a))| -c_Wellfounded_Oaccp(V_r,V_a,T_a).
% 16.30/16.38 0 [] c_Wellfounded_Oaccp(V_r,V_b,T_a)| -c_Wellfounded_Oaccp(V_r,V_a,T_a)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_a)).
% 16.30/16.38 0 [] c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_t,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 16.30/16.38 0 [] hBOOL(hAPP(c_InductTermi_OIT,V_r))| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_r,tc_Lambda_OdB).
% 16.30/16.38 0 [] c_List_Otake(V_n,c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Orotate1(V_xs,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] V_xs=c_List_Orev(c_List_Orev(V_xs,T_a),T_a).
% 16.30/16.38 0 [] c_List_Orev(c_List_Orev(V_ys,T_a),T_a)=V_ys.
% 16.30/16.38 0 [] c_List_Orev(c_List_Orev(V_xs,T_a),T_a)=V_xs.
% 16.30/16.38 0 [] c_List_Orev(c_List_Oreplicate(V_n,V_x,T_a),T_a)=c_List_Oreplicate(V_n,V_x,T_a).
% 16.30/16.38 0 [] -c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a).
% 16.30/16.38 0 [] -c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a).
% 16.30/16.38 0 [] V_r!=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s),V_xa,tc_Lambda_OdB,tc_Lambda_OdB)|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_Oappend(V_xa,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 16.30/16.38 0 [] c_Predicate_Oconversep(c_fe_qual(T_a),T_a,T_a)=c_fe_qual(T_a).
% 16.30/16.38 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 16.30/16.38 0 [] c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)|V_xs=V_ys| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 16.30/16.38 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_x),c_List_Olistsum(V_xs,T_a)).
% 16.30/16.38 0 [] c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Oreplicate(V_k,V_x,T_a),T_a)=c_List_Oappend(c_List_Oreplicate(V_k,V_x,T_a),c_List_Oreplicate(V_n,V_x,T_a),T_a).
% 16.30/16.38 0 [] c_List_Orev(V_xs,T_a)!=c_List_Orev(V_ys,T_a)|V_xs=V_ys.
% 16.30/16.38 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_List_Olistsum(c_List_Orev(V_xs,T_a),T_a)=c_List_Olistsum(V_xs,T_a).
% 16.30/16.38 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_n,T_a)),V_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,V_n,T_a)).
% 16.30/16.38 0 [] c_List_Olist_ONil(T_a)!=c_List_Orev(V_xs,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_Predicate_Oconversep(c_Predicate_Oconversep(V_r,T_a,T_b),T_b,T_a)=V_r.
% 16.30/16.38 0 [] c_Power_Opower_Opower(V_one,V_times,V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=V_one.
% 16.30/16.38 0 [] c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)|hBOOL(hAPP(hAPP(V_r,V_y),V_x))| -c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_y,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 16.30/16.38 0 [] c_ListOrder_Ostep1(V_r,c_List_Olist_OCons(V_x,V_ys,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)| -c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a).
% 16.30/16.38 0 [] c_List_Obutlast(c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u)=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_ts,c_List_Olist_OCons(V_u,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 16.30/16.38 0 [] c_List_Olist_ONil(T_a)=c_List_Orev(c_List_Olist_ONil(T_a),T_a).
% 16.30/16.38 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(c_List_Oappend(V_xs,V_ys,T_a),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_List_Olistsum(V_xs,T_a)),c_List_Olistsum(V_ys,T_a)).
% 16.30/16.38 0 [] c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)=c_List_Olist_ONil(tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_x,tc_Lambda_OdB,tc_Lambda_OdB)),V_s)=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_List_Oappend(V_x,c_List_Olist_OCons(V_s,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 16.30/16.38 0 [] c_Wellfounded_Oaccp(V_r,V_y,T_a)| -hBOOL(hAPP(hAPP(V_r,V_y),V_a))| -c_Wellfounded_Oaccp(V_r,V_a,T_a).
% 16.30/16.38 0 [] c_Wellfounded_Oaccp(V_r,V_a,T_a)| -hBOOL(hAPP(hAPP(V_r,V_a),V_b))| -c_Wellfounded_Oaccp(V_r,V_b,T_a).
% 16.30/16.38 0 [] c_Int_Onumber__class_Onumber__of(V_v,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_List_Otake(c_Int_Onumber__class_Onumber__of(V_v,tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Oappend(c_List_Obutlast(V_xs,T_a),c_List_Olist_OCons(c_List_Olast(V_xs,T_a),c_List_Olist_ONil(T_a),T_a),T_a)=V_xs|V_xs=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(c_List_Olist_ONil(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 16.30/16.38 0 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a)=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Otake(V_n,V_xs,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 16.30/16.38 0 [] c_List_Olist_ONil(T_a)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),V_x,T_a).
% 16.30/16.38 0 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),V_xs,T_a)=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Oreplicate(V_n,V_x,T_a)!=c_List_Olist_ONil(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 16.30/16.38 0 [] c_List_Olist_ONil(T_a)!=c_List_Oreplicate(V_n,V_x,T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)=c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a).
% 16.30/16.38 0 [] c_List_Olast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olast(V_xs,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Orev(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)!=c_List_Orev(V_xs,T_a)|V_xs=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 16.30/16.38 0 [] c_List_Orev(V_xs,T_a)!=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a)|V_xs=c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a).
% 16.30/16.38 0 [] c_List_Obutlast(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Olast(c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)=V_x.
% 16.30/16.38 0 [] c_List_Obutlast(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Obutlast(V_xs,T_a),T_a)|V_xs=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Oappend(V_ys,V_zs,T_a)!=c_List_Olist_OCons(V_x,V_xs,T_a)|c_List_Oappend(c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)=V_xs|V_zs=c_List_Olist_OCons(V_x,V_xs,T_a).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,V_xs,T_a)!=c_List_Oappend(V_ys,V_zs,T_a)|c_List_Olist_OCons(V_x,c_List_Osko__List__XCons__e_q__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)=V_ys|c_List_Olist_OCons(V_x,V_xs,T_a)=V_zs.
% 16.30/16.38 0 [] c_List_Oappend(V_ys,V_zs,T_a)!=c_List_Olist_OCons(V_x,V_xs,T_a)|V_ys=c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)|V_zs=c_List_Olist_OCons(V_x,V_xs,T_a).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,V_xs,T_a)!=c_List_Oappend(V_ys,V_zs,T_a)|V_xs=c_List_Oappend(c_List_Osko__List__XCons__e_q__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)|c_List_Olist_OCons(V_x,V_xs,T_a)=V_zs.
% 16.30/16.38 0 [] c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Oappend(c_List_Oreplicate(V_n,V_x,T_a),V_xs,T_a),T_a).
% 16.30/16.38 0 [] c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Obutlast(V_xs,T_a).
% 16.30/16.38 0 [] c_List_Olast(c_List_Oappend(V_xs,V_ys,T_a),T_a)=c_List_Olast(V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Olast(c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Olast(V_xs,T_a).
% 16.30/16.38 0 [] c_List_Obutlast(c_List_Oappend(V_xs,V_ys,T_a),T_a)=c_List_Oappend(V_xs,c_List_Obutlast(V_ys,T_a),T_a)|V_ys=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_rs,tc_Lambda_OdB,tc_Lambda_OdB)),c_List_Ofoldl(c_Lambda_OdB_OApp,V_r,V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,V_ss,tc_Lambda_OdB).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,V_xs,T_a)!=c_List_Oappend(V_ys,V_zs,T_a)|V_xs=c_List_Oappend(c_List_Osko__List__XCons__e_q__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Oappend(V_ys,V_zs,T_a)!=c_List_Olist_OCons(V_x,V_xs,T_a)|V_ys=c_List_Olist_OCons(V_x,c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)|V_ys=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Olast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a)=V_x.
% 16.30/16.38 0 [] c_List_Obutlast(c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a)=V_xs.
% 16.30/16.38 0 [] V_ys=V_xs|V_y=V_x| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(V_r,V_y),V_x))|V_y=V_x| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 16.30/16.38 0 [] c_List_Oappend(V_ys,V_zs,T_a)!=c_List_Olist_OCons(V_x,V_xs,T_a)|c_List_Oappend(c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),V_zs,T_a)=V_xs|V_ys=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,V_xs,T_a)!=c_List_Oappend(V_ys,V_zs,T_a)|c_List_Olist_OCons(V_x,c_List_Osko__List__XCons__e_q__append__conv__1__1(V_x,V_xs,V_ys,V_zs,T_a),T_a)=V_ys|V_ys=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Orev(c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Oappend(c_List_Orev(V_xs,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(V_r,V_y),V_x))|c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 16.30/16.38 0 [] c_List_Orev(V_xs,T_a)!=c_List_Olist_OCons(V_y,V_ys,T_a)|V_xs=c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a).
% 16.30/16.38 0 [] c_List_Orev(c_List_Oappend(c_List_Orev(V_ys,T_a),c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),T_a)=c_List_Olist_OCons(V_y,V_ys,T_a).
% 16.30/16.38 0 [] c_List_Orotate1(c_List_Olist_OCons(V_x,V_xs,T_b),T_b)=c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_b),T_b),T_b).
% 16.30/16.38 0 [] V_ys=V_xs|c_ListOrder_Ostep1(V_r,V_ys,V_xs,T_a)| -c_ListOrder_Ostep1(V_r,c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a),c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a),T_a).
% 16.30/16.38 0 [] c_List_Oappend(c_List_Oreplicate(V_i,V_x,T_a),c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)=c_List_Olist_OCons(V_x,c_List_Oreplicate(V_i,V_x,T_a),T_a).
% 16.30/16.38 0 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_ONil(T_a).
% 16.30/16.38 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,c_Lambda_Osubst(V_t,V_u,V_i),V_T).
% 16.30/16.38 0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,V_a,T_a,T_a)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a).
% 16.30/16.38 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_r,c_Lambda_OdB_OVar(V_i),V_j)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 16.30/16.38 0 [] c_Type_Otyping(V_e,V_t_H,V_T)| -c_Type_Otyping(V_e,V_t,V_T)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)).
% 16.30/16.38 0 [] c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______).
% 16.30/16.38 0 [] c_ListOrder_Ostep1(c_Lambda_Obeta,V_rs,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(V_n,V_rs,V_v),tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(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)).
% 16.30/16.38 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).
% 16.30/16.38 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.
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_s_H)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t_H)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),hAPP(hAPP(c_Lambda_OdB_OApp,V_s_H),V_t_H)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_t),V_t_H))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_s),V_s_H)).
% 16.30/16.38 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).
% 16.30/16.38 0 [] -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),V_s,tc_Lambda_OdB)|c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),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),tc_Lambda_OdB).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c))| -hBOOL(hAPP(hAPP(V_r,V_b),V_c))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_b)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_c))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_b),V_c))| -hBOOL(hAPP(hAPP(V_r,V_a),V_b)).
% 16.30/16.38 0 [] c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(V_t,V_s,V_k)),c_Lambda_Osubst(V_u,V_s,V_k)).
% 16.30/16.38 0 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(V_k),V_u,V_k)=V_u.
% 16.30/16.38 0 [] c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a)| -c_List_Olistsp(V_A,V_ys,T_a)| -c_List_Olistsp(V_A,V_xs,T_a).
% 16.30/16.38 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(V_xs,T_a)=c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a).
% 16.30/16.38 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(T_a),V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y))| -hBOOL(hAPP(hAPP(V_r,V_x),V_y)).
% 16.30/16.38 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).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_t,V_r,V_i)),c_Lambda_Osubst(V_t,V_s,V_i)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_r,V_t,V_i)),c_Lambda_Osubst(V_s,V_t,V_i)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 16.30/16.38 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).
% 16.30/16.38 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)).
% 16.30/16.38 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).
% 16.30/16.38 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).
% 16.30/16.38 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).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(V_t,V_r,V_i)),c_Lambda_Osubst(V_t,V_s,V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_z))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_y),V_z))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_y)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)).
% 16.30/16.38 0 [] c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(V_r,V_t,V_i)),c_Lambda_Osubst(V_s,V_t,V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 16.30/16.38 0 [] c_List_Olistsp(V_A,V_ys,T_a)| -c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a).
% 16.30/16.38 0 [] c_List_Olistsp(V_A,V_xs,T_a)| -c_List_Olistsp(V_A,c_List_Oappend(V_xs,V_ys,T_a),T_a).
% 16.30/16.38 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Olistsum(V_xs,T_a)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a).
% 16.30/16.38 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).
% 16.30/16.38 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).
% 16.30/16.38 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)).
% 16.30/16.38 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)).
% 16.30/16.38 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)).
% 16.30/16.38 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)).
% 16.30/16.38 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).
% 16.30/16.38 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).
% 16.30/16.38 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)).
% 16.30/16.38 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)).
% 16.30/16.38 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.
% 16.30/16.38 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_r),V_s)!=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)|V_r=c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,c_ListApplication_Osko__ListApplication__XApp__e_q__foldl__conv__1__1(V_r,V_s,V_t,V_ts),tc_Lambda_OdB,tc_Lambda_OdB)|V_ts=c_List_Olist_ONil(tc_Lambda_OdB).
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 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)).
% 16.30/16.38 0 [] v_rs____=c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB).
% 16.30/16.38 0 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a)=c_Transitive__Closure_Ortranclp(V_r,T_a).
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 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)).
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),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)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 16.30/16.38 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).
% 16.30/16.38 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).
% 16.30/16.38 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).
% 16.30/16.38 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).
% 16.30/16.38 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).
% 16.30/16.38 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).
% 16.30/16.38 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),V_a,V_xs,T_a,T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a)).
% 16.30/16.38 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_List_Ofoldl(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ozero__class_Ozero(T_a),V_xs,T_a,T_a)=c_List_Ofoldr(c_HOL_Oplus__class_Oplus(T_a),V_xs,c_HOL_Ozero__class_Ozero(T_a),T_a,T_a).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),c_Lambda_Osubst(V_s,V_t,c_HOL_Ozero__class_Ozero(tc_nat)))).
% 16.30/16.38 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)| -hBOOL(hAPP(hAPP(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)).
% 16.30/16.38 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).
% 16.30/16.38 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,c_Lambda_Osubst(V_r,V_s,c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))).
% 16.30/16.38 0 [] c_Type_Otypings(V_e,V_us,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us))| -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_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 16.30/16.38 0 [] v_T____!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_t,V_u,V_i)))| -c_Type_Otyping(V_e,V_u,V_T1)| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T1,tc_Type_Otype),V_t,V_Ta)| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 16.30/16.38 0 [] v_T____!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(V_t,V_u,V_i)))| -c_Type_Otyping(V_e,V_u,V_T2)| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_T2,tc_Type_Otype),V_t,V_Ta)| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 16.30/16.38 0 [] V_U=c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(V_T,V_U,V_e,V_us),V_T,tc_Type_Otype,tc_Type_Otype)| -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_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_us,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 16.30/16.38 0 [] c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____).
% 16.30/16.38 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____).
% 16.30/16.38 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 16.30/16.38 0 [] c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a)=hAPP(V_f1,V_nat).
% 16.30/16.38 0 [] c_List_Ofoldl(V_f,V_a,c_List_Oappend(V_xs,V_ys,T_b),T_a,T_b)=c_List_Ofoldl(V_f,c_List_Ofoldl(V_f,V_a,V_xs,T_a,T_b),V_ys,T_a,T_b).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(V_s)),c_Lambda_OdB_OAbs(V_t)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)).
% 16.30/16.38 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).
% 16.30/16.38 0 [] c_List_Olist_ONil(T_a)=c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a).
% 16.30/16.38 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),c_Lambda_OdB_OVar(V_i))))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,V_xs,T_a)=c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a).
% 16.30/16.38 0 [] V_xs!=c_List_Olist_OCons(V_x,V_xs,T_a).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,V_t,T_a)!=V_t.
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_u)),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_s)),hAPP(hAPP(c_Lambda_OdB_OApp,V_u),V_t)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_s),V_t)).
% 16.30/16.38 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 16.30/16.38 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.
% 16.30/16.38 0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))).
% 16.30/16.38 0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,c_Type_Otype_OAtom(V_xc),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_xc))).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_a_H,V_list_H,T_a)!=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,V_xa,T_a)!=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,c_List_Oappend(V_xs1,V_zs,T_a),T_a)=c_List_Oappend(c_List_Olist_OCons(V_x,V_xs1,T_a),V_zs,T_a).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a)=c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a).
% 16.30/16.38 0 [] c_List_Oappend(c_List_Olist_OCons(V_x,V_xs,T_a),V_ys,T_a)=c_List_Olist_OCons(V_x,c_List_Oappend(V_xs,V_ys,T_a),T_a).
% 16.30/16.38 0 [] c_List_Oappend(c_List_Olist_OCons(V_x,V_xa,T_a),V_zs,T_a)=c_List_Olist_OCons(V_x,c_List_Oappend(V_xa,V_zs,T_a),T_a).
% 16.30/16.38 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.
% 16.30/16.38 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_OCons(V_x,V_xs,T_b),T_a,T_b)=c_List_Ofoldl(V_f,hAPP(hAPP(V_f,V_a),V_x),V_xs,T_a,T_b).
% 16.30/16.38 0 [] hBOOL(hAPP(V_P,V_T))| -hBOOL(hAPP(V_P,c_Type_Osko__Type__Xtype__induct__1__1(V_P))).
% 16.30/16.38 0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 16.30/16.38 0 [] c_Type_Otyping(V_e,V_u,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u))| -c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T).
% 16.30/16.38 0 [] c_Type_Otyping(c_Type_Oshift(V_e,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t),tc_Type_Otype),V_t,c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t))| -c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T).
% 16.30/16.38 0 [] c_List_Oappend(V_ys,V_xs,T_a)!=c_List_Oappend(V_zs,V_xs,T_a)|V_ys=V_zs.
% 16.30/16.38 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Oappend(V_xs,V_zs,T_a)|V_ys=V_zs.
% 16.30/16.38 0 [] c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a)=V_xs.
% 16.30/16.38 0 [] V_x=c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a).
% 16.30/16.38 0 [] V_xs=c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a).
% 16.30/16.38 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a)=V_ys.
% 16.30/16.38 0 [] V_ys=c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a).
% 16.30/16.38 0 [] c_Type_Otype_OAtom(V_nat)!=c_Type_Otype_OAtom(V_nat_H)|V_nat=V_nat_H.
% 16.30/16.38 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))).
% 16.30/16.38 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 16.30/16.38 0 [] v_n____=v_i____.
% 16.30/16.38 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 16.30/16.38 0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 16.30/16.38 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).
% 16.30/16.38 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 16.30/16.38 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_ys=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 16.30/16.38 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.
% 16.30/16.38 0 [] c_Type_Otype_Otype__rec(V_f1,V_f2,c_Type_Otype_OAtom(V_nat),T_a)=hAPP(V_f1,V_nat).
% 16.30/16.38 0 [] hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 16.30/16.38 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).
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 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).
% 16.30/16.38 0 [] c_List_Olist_ONil(T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a).
% 16.30/16.38 0 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)).
% 16.30/16.38 0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 16.30/16.38 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_xs|V_ys=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] V_xs!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_ys|V_xs=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] V_ys!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_OCons(V_x,V_xs,T_a),T_a)=c_List_Olist_OCons(V_x,V_xs,T_a).
% 16.30/16.38 0 [] c_List_Olist_OCons(V_a,V_list,T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a)|V_a=V_a_H.
% 16.30/16.38 0 [] c_List_Olist_OCons(V_a,V_list,T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a)|V_list=V_list_H.
% 16.30/16.38 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.
% 16.30/16.38 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.
% 16.30/16.38 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 16.30/16.38 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 16.30/16.38 0 [] c_Type_Otypings(V_e,V_ts,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts))| -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).
% 16.30/16.38 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 16.30/16.38 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 16.30/16.38 0 [] c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)!=c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)|V_xs=V_ys.
% 16.30/16.38 0 [] c_List_Oappend(V_xs,c_List_Olist_OCons(V_x,c_List_Olist_ONil(T_a),T_a),T_a)!=c_List_Oappend(V_ys,c_List_Olist_OCons(V_y,c_List_Olist_ONil(T_a),T_a),T_a)|V_x=V_y.
% 16.30/16.38 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 16.30/16.38 0 [] c_List_Oappend(c_List_Oappend(V_xs,V_ys,T_a),V_zs,T_a)=c_List_Oappend(V_xs,c_List_Oappend(V_ys,V_zs,T_a),T_a).
% 16.30/16.38 0 [] c_List_Oappend(V_xs,c_List_Oappend(V_xs1,V_us,T_a),T_a)=c_List_Oappend(c_List_Oappend(V_xs,V_xs1,T_a),V_us,T_a).
% 16.30/16.38 0 [] c_List_Oappend(c_List_Oappend(V_zs,V_x,T_a),V_ys,T_a)=c_List_Oappend(V_zs,c_List_Oappend(V_x,V_ys,T_a),T_a).
% 16.30/16.38 0 [] c_List_Oappend(V_xs,c_List_Oappend(V_x,V_ts,T_a),T_a)=c_List_Oappend(c_List_Oappend(V_xs,V_x,T_a),V_ts,T_a).
% 16.30/16.38 0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)!=c_Type_Otype_OAtom(V_nat).
% 16.30/16.38 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 16.30/16.38 0 [] V_T=hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t)),c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t))| -c_Type_Otyping(V_e,c_Lambda_OdB_OAbs(V_t),V_T).
% 16.30/16.38 0 [] c_Type_Otyping(V_e,V_t_H,V_T)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))| -c_Type_Otyping(V_e,V_t,V_T).
% 16.30/16.38 0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)|V_type1=V_type1_H.
% 16.30/16.38 0 [] hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H)|V_type2=V_type2_H.
% 16.30/16.38 0 [] c_List_Ofoldr(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),V_a,T_b,T_a)=hAPP(hAPP(V_f,V_x),c_List_Ofoldr(V_f,V_xs,V_a,T_b,T_a)).
% 16.30/16.38 0 [] c_Type_Osko__Type__Xtype__induct__1__1(V_P)!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|hBOOL(hAPP(V_P,V_T))|hBOOL(hAPP(V_P,V_T2)).
% 16.30/16.38 0 [] c_Type_Osko__Type__Xtype__induct__1__1(V_P)!=hAPP(hAPP(c_Type_Otype_OFun,V_T1a),V_x)|hBOOL(hAPP(V_P,V_T))|hBOOL(hAPP(V_P,V_T1a)).
% 16.30/16.38 0 [] c_Type_Otyping(V_env,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_U)| -c_Type_Otyping(V_env,V_t,V_T)| -c_Type_Otyping(V_env,V_s,hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U)).
% 16.30/16.38 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____).
% 16.30/16.38 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OAbs(V_t),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))| -c_Type_Otyping(c_Type_Oshift(V_env,c_HOL_Ozero__class_Ozero(tc_nat),V_T,tc_Type_Otype),V_t,V_U).
% 16.30/16.38 0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 16.30/16.38 0 [] c_List_Ofoldr(V_f,c_List_Oappend(V_xs,V_ys,T_b),V_a,T_b,T_a)=c_List_Ofoldr(V_f,V_xs,c_List_Ofoldr(V_f,V_ys,V_a,T_b,T_a),T_b,T_a).
% 16.30/16.38 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_n____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))).
% 16.30/16.38 0 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 16.30/16.38 0 [] c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 16.30/16.38 0 [] c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(V_T,V_e,V_i,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -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).
% 16.30/16.38 0 [] c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T)| -c_Type_Otypings(V_e,V_ts,V_Ts)| -c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype)).
% 16.30/16.38 0 [] c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a)=V_a.
% 16.30/16.38 0 [] v_T____=hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 16.30/16.38 0 [] c_Type_Otype_Otype__rec(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a)=hAPP(hAPP(hAPP(hAPP(V_f2,V_type1),V_type2),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type1,T_a)),c_Type_Otype_Otype__rec(V_f1,V_f2,V_type2,T_a)).
% 16.30/16.38 0 [] c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),T_a)=hAPP(hAPP(V_f2,V_type1),V_type2).
% 16.30/16.38 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 16.30/16.38 0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_xa),V_xb),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xa),V_xb))).
% 16.30/16.38 0 [] -hBOOL(hAPP(V_P,c_Type_Otype_Otype__case(V_f1,V_f2,hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_type1),V_type2))).
% 16.30/16.38 0 [] c_Type_Otype_OAtom(V_nat)!=hAPP(hAPP(c_Type_Otype_OFun,V_type1_H),V_type2_H).
% 16.30/16.38 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 16.30/16.38 0 [] c_Type_Otyping(V_e,V_t,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(V_T,V_e,V_t,V_ts),V_T,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(V_e,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_T).
% 16.30/16.38 0 [] c_Type_Otyping(V_e,V_t,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)),V_T))| -c_Type_Otyping(V_e,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_T).
% 16.30/16.39 0 [] v_T____=hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 16.30/16.39 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 16.30/16.39 0 [] -c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))).
% 16.30/16.39 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 16.30/16.39 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 16.30/16.39 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 16.30/16.39 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 16.30/16.39 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 16.30/16.39 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 16.30/16.39 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 16.30/16.39 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 16.30/16.39 0 [] class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint).
% 16.30/16.39 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint).
% 16.30/16.39 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint).
% 16.30/16.39 0 [] class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint).
% 16.30/16.39 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint).
% 16.30/16.39 0 [] class_OrderedGroup_Osemigroup__add(tc_Int_Oint).
% 16.30/16.39 0 [] class_OrderedGroup_Oab__group__add(tc_Int_Oint).
% 16.30/16.39 0 [] class_OrderedGroup_Omonoid__add(tc_Int_Oint).
% 16.30/16.39 0 [] class_Ring__and__Field_Oidom(tc_Int_Oint).
% 16.30/16.39 0 [] class_Int_Oring__char__0(tc_Int_Oint).
% 16.30/16.39 0 [] class_Int_Onumber__ring(tc_Int_Oint).
% 16.30/16.39 0 [] hBOOL(hAPP(hAPP(c_fe_qual(T_a),V_x),V_x)).
% 16.30/16.39 0 [] V_X=V_Y| -hBOOL(hAPP(hAPP(c_fe_qual(T_a),V_X),V_Y)).
% 16.30/16.39 end_of_list.
% 16.30/16.39
% 16.30/16.39 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 16.30/16.39
% 16.30/16.39 This ia a non-Horn set with equality. The strategy will be
% 16.30/16.39 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 16.30/16.39 deletion, with positive clauses in sos and nonpositive
% 16.30/16.39 clauses in usable.
% 16.30/16.39
% 16.30/16.39 dependent: set(knuth_bendix).
% 16.30/16.39 dependent: set(anl_eq).
% 16.30/16.39 dependent: set(para_from).
% 16.30/16.39 dependent: set(para_into).
% 16.30/16.39 dependent: clear(para_from_right).
% 16.30/16.39 dependent: clear(para_into_right).
% 16.30/16.39 dependent: set(para_from_vars).
% 16.30/16.39 dependent: set(eq_units_both_ways).
% 16.30/16.39 dependent: set(dynamic_demod_all).
% 16.30/16.39 dependent: set(dynamic_demod).
% 16.30/16.39 dependent: set(order_eq).
% 16.30/16.39 dependent: set(back_demod).
% 16.30/16.39 dependent: set(lrpo).
% 16.30/16.39 dependent: set(hyper_res).
% 16.30/16.39 dependent: set(unit_deletion).
% 16.30/16.39 dependent: set(factor).
% 16.30/16.39
% 16.30/16.39 ------------> process usable:
% 16.30/16.39 ** KEPT (pick-wt=14): 1 [] -class_Int_Oring__char__0(A)| -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_Int_Onumber__class_Onumber__of(C,A)|B=C.
% 16.30/16.39 ** KEPT (pick-wt=19): 2 [] c_Type_Otyping(A,B,c_Type_Osko__Type__Xtypes__snocE__1__2(C,A,B,D))| -c_Type_Otypings(A,c_List_Oappend(D,c_List_Olist_OCons(B,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),C).
% 16.30/16.39 ** KEPT (pick-wt=30): 4 [copy,3,flip.2] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,C,D,tc_Lambda_OdB,tc_Lambda_OdB)|c_List_Oappend(c_ListApplication_Osko__ListApplication__XApp__e_q__foldl__conv__1__1(A,B,C,D),c_List_Olist_OCons(B,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)=D|D=c_List_Olist_ONil(tc_Lambda_OdB).
% 16.30/16.39 ** KEPT (pick-wt=16): 5 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|B=E|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 16.30/16.39 ** KEPT (pick-wt=10): 6 [] c_List_Orev(A,B)!=c_List_Olist_ONil(B)|A=c_List_Olist_ONil(B).
% 16.30/16.39 ** KEPT (pick-wt=20): 7 [] A=B|hBOOL(hAPP(hAPP(C,B),A))| -c_ListOrder_Ostep1(C,c_List_Olist_OCons(B,D,E),c_List_Olist_OCons(A,F,E),E).
% 16.30/16.39 ** KEPT (pick-wt=19): 8 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(A,B,B),B),C),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),D),C)).
% 16.30/16.39 ** KEPT (pick-wt=19): 9 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Predicate_Oconversep(A,B,B),B),D),C)).
% 16.30/16.39 ** KEPT (pick-wt=15): 10 [] hBOOL(hAPP(hAPP(A,B),C))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,D,E),C),B)).
% 16.30/16.39 ** KEPT (pick-wt=15): 11 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,B,C),D),E))| -hBOOL(hAPP(hAPP(A,E),D)).
% 16.30/16.39 Following clause subsumed by 10 during input processing: 0 [] hBOOL(hAPP(hAPP(A,B),C))| -hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,D,E),C),B)).
% 16.30/16.39 Following clause subsumed by 11 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Predicate_Oconversep(A,B,C),D),E))| -hBOOL(hAPP(hAPP(A,E),D)).
% 16.30/16.39 ** KEPT (pick-wt=36): 13 [copy,12,flip.2] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),B,C,A)),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),D,C,A))=c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),C,A).
% 16.30/16.39 ** KEPT (pick-wt=16): 14 [] -c_ListOrder_Ostep1(A,B,C,D)|c_ListOrder_Ostep1(A,c_List_Oappend(B,E,D),c_List_Oappend(C,E,D),D).
% 16.30/16.39 ** KEPT (pick-wt=16): 15 [] c_ListOrder_Ostep1(A,c_List_Oappend(B,C,D),c_List_Oappend(B,E,D),D)| -c_ListOrder_Ostep1(A,C,E,D).
% 16.30/16.39 ** KEPT (pick-wt=17): 16 [] A=B|C=D| -c_ListOrder_Ostep1(E,c_List_Olist_OCons(B,D,F),c_List_Olist_OCons(A,C,F),F).
% 16.30/16.39 ** KEPT (pick-wt=17): 17 [] -hBOOL(hAPP(hAPP(A,B),C))|c_ListOrder_Ostep1(A,c_List_Olist_OCons(B,D,E),c_List_Olist_OCons(C,D,E),E).
% 16.30/16.39 ** KEPT (pick-wt=12): 18 [] c_List_Oreplicate(A,B,C)!=c_List_Oreplicate(D,E,C)|A=D.
% 16.30/16.39 ** KEPT (pick-wt=16): 19 [] c_Wellfounded_Oaccp(A,B,C)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,C),B),D))| -c_Wellfounded_Oaccp(A,D,C).
% 16.30/16.39 Following clause subsumed by 19 during input processing: 0 [] c_Wellfounded_Oaccp(A,B,C)| -c_Wellfounded_Oaccp(A,D,C)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,C),B),D)).
% 16.30/16.39 ** KEPT (pick-wt=11): 20 [] c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),A,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 16.30/16.39 ** KEPT (pick-wt=11): 21 [] hBOOL(hAPP(c_InductTermi_OIT,A))| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),A,tc_Lambda_OdB).
% 16.30/16.39 ** KEPT (pick-wt=10): 22 [] c_List_Orotate1(A,B)!=c_List_Olist_ONil(B)|A=c_List_Olist_ONil(B).
% 16.30/16.39 ** KEPT (pick-wt=6): 23 [] -c_ListOrder_Ostep1(A,c_List_Olist_ONil(B),C,B).
% 16.30/16.39 ** KEPT (pick-wt=6): 24 [] -c_ListOrder_Ostep1(A,B,c_List_Olist_ONil(C),C).
% 16.30/16.39 ** KEPT (pick-wt=35): 26 [copy,25,flip.1,flip.2] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,A),B),C,tc_Lambda_OdB,tc_Lambda_OdB)!=A|c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,A),B),c_List_Oappend(C,c_List_Olist_OCons(B,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 16.30/16.39 ** KEPT (pick-wt=14): 27 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A).
% 16.30/16.39 ** KEPT (pick-wt=19): 28 [] c_ListOrder_Ostep1(A,B,C,D)|C=B| -c_ListOrder_Ostep1(A,c_List_Olist_OCons(E,B,D),c_List_Olist_OCons(F,C,D),D).
% 16.30/16.39 ** KEPT (pick-wt=17): 30 [copy,29,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Olistsum(C,A))=c_List_Olistsum(c_List_Olist_OCons(B,C,A),A).
% 16.30/16.39 ** KEPT (pick-wt=10): 31 [] c_List_Orev(A,B)!=c_List_Orev(C,B)|A=C.
% 16.30/16.39 ** KEPT (pick-wt=11): 32 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_List_Olistsum(c_List_Orev(B,A),A)=c_List_Olistsum(B,A).
% 16.30/16.39 ** KEPT (pick-wt=29): 33 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),B,C,A)),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),B,C,A)).
% 16.30/16.39 ** KEPT (pick-wt=10): 34 [] c_List_Olist_ONil(A)!=c_List_Orev(B,A)|B=c_List_Olist_ONil(A).
% 16.30/16.39 ** KEPT (pick-wt=22): 35 [] c_ListOrder_Ostep1(A,B,C,D)|hBOOL(hAPP(hAPP(A,E),F))| -c_ListOrder_Ostep1(A,c_List_Olist_OCons(E,B,D),c_List_Olist_OCons(F,C,D),D).
% 16.30/16.39 ** KEPT (pick-wt=16): 36 [] c_ListOrder_Ostep1(A,c_List_Olist_OCons(B,C,D),c_List_Olist_OCons(B,E,D),D)| -c_ListOrder_Ostep1(A,C,E,D).
% 16.30/16.39 ** KEPT (pick-wt=19): 38 [copy,37,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_List_Olistsum(B,A)),c_List_Olistsum(C,A))=c_List_Olistsum(c_List_Oappend(B,C,A),A).
% 16.30/16.39 ** KEPT (pick-wt=14): 39 [] c_Wellfounded_Oaccp(A,B,C)| -hBOOL(hAPP(hAPP(A,B),D))| -c_Wellfounded_Oaccp(A,D,C).
% 16.30/16.39 Following clause subsumed by 39 during input processing: 0 [] c_Wellfounded_Oaccp(A,B,C)| -hBOOL(hAPP(hAPP(A,B),D))| -c_Wellfounded_Oaccp(A,D,C).
% 16.30/16.39 ** KEPT (pick-wt=18): 40 [] c_Int_Onumber__class_Onumber__of(A,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_List_Otake(c_Int_Onumber__class_Onumber__of(A,tc_nat),c_List_Olist_OCons(B,C,D),D)=c_List_Olist_ONil(D).
% 16.30/16.39 ** KEPT (pick-wt=9): 41 [] -class_OrderedGroup_Omonoid__add(A)|c_List_Olistsum(c_List_Olist_ONil(A),A)=c_HOL_Ozero__class_Ozero(A).
% 16.30/16.39 ** KEPT (pick-wt=15): 42 [] c_List_Otake(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 16.30/16.39 ** KEPT (pick-wt=11): 43 [] c_List_Oreplicate(A,B,C)!=c_List_Olist_ONil(C)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 16.30/16.39 ** KEPT (pick-wt=11): 44 [] c_List_Olist_ONil(A)!=c_List_Oreplicate(B,C,A)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 16.30/16.39 ** KEPT (pick-wt=16): 45 [] c_List_Olist_OCons(A,c_List_Olist_ONil(B),B)!=c_List_Orev(C,B)|C=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 16.30/16.39 ** KEPT (pick-wt=16): 46 [] c_List_Orev(A,B)!=c_List_Olist_OCons(C,c_List_Olist_ONil(B),B)|A=c_List_Olist_OCons(C,c_List_Olist_ONil(B),B).
% 16.30/16.39 ** KEPT (pick-wt=26): 47 [] c_List_Oappend(A,B,C)!=c_List_Olist_OCons(D,E,C)|c_List_Oappend(c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(D,E,A,B,C),B,C)=E|B=c_List_Olist_OCons(D,E,C).
% 16.30/16.39 ** KEPT (pick-wt=26): 48 [] c_List_Olist_OCons(A,B,C)!=c_List_Oappend(D,E,C)|c_List_Olist_OCons(A,c_List_Osko__List__XCons__e_q__append__conv__1__1(A,B,D,E,C),C)=D|c_List_Olist_OCons(A,B,C)=E.
% 16.30/16.39 ** KEPT (pick-wt=26): 50 [copy,49,flip.2] c_List_Oappend(A,B,C)!=c_List_Olist_OCons(D,E,C)|c_List_Olist_OCons(D,c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(D,E,A,B,C),C)=A|B=c_List_Olist_OCons(D,E,C).
% 16.30/16.39 ** KEPT (pick-wt=26): 52 [copy,51,flip.2] c_List_Olist_OCons(A,B,C)!=c_List_Oappend(D,E,C)|c_List_Oappend(c_List_Osko__List__XCons__e_q__append__conv__1__1(A,B,D,E,C),E,C)=B|c_List_Olist_OCons(A,B,C)=E.
% 16.30/16.39 ** KEPT (pick-wt=21): 53 [] hBOOL(hAPP(hAPP(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,A,C,tc_Lambda_OdB,tc_Lambda_OdB)))| -c_ListOrder_Ostep1(c_Lambda_Obeta,B,C,tc_Lambda_OdB).
% 16.30/16.39 ** KEPT (pick-wt=24): 55 [copy,54,flip.2] c_List_Olist_OCons(A,B,C)!=c_List_Oappend(D,E,C)|c_List_Oappend(c_List_Osko__List__XCons__e_q__append__conv__1__1(A,B,D,E,C),E,C)=B|D=c_List_Olist_ONil(C).
% 16.30/16.39 ** KEPT (pick-wt=24): 57 [copy,56,flip.2] c_List_Oappend(A,B,C)!=c_List_Olist_OCons(D,E,C)|c_List_Olist_OCons(D,c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(D,E,A,B,C),C)=A|A=c_List_Olist_ONil(C).
% 16.30/16.39 ** KEPT (pick-wt=25): 58 [] A=B|C=D| -c_ListOrder_Ostep1(E,c_List_Oappend(A,c_List_Olist_OCons(C,c_List_Olist_ONil(F),F),F),c_List_Oappend(B,c_List_Olist_OCons(D,c_List_Olist_ONil(F),F),F),F).
% 16.30/16.39 ** KEPT (pick-wt=28): 59 [] hBOOL(hAPP(hAPP(A,B),C))|B=C| -c_ListOrder_Ostep1(A,c_List_Oappend(D,c_List_Olist_OCons(B,c_List_Olist_ONil(E),E),E),c_List_Oappend(F,c_List_Olist_OCons(C,c_List_Olist_ONil(E),E),E),E).
% 16.30/16.39 ** KEPT (pick-wt=24): 60 [] c_List_Oappend(A,B,C)!=c_List_Olist_OCons(D,E,C)|c_List_Oappend(c_List_Osko__List__Xappend__e_q__Cons__conv__1__1(D,E,A,B,C),B,C)=E|A=c_List_Olist_ONil(C).
% 16.30/16.39 ** KEPT (pick-wt=24): 61 [] c_List_Olist_OCons(A,B,C)!=c_List_Oappend(D,E,C)|c_List_Olist_OCons(A,c_List_Osko__List__XCons__e_q__append__conv__1__1(A,B,D,E,C),C)=D|D=c_List_Olist_ONil(C).
% 16.30/16.39 ** KEPT (pick-wt=30): 62 [] hBOOL(hAPP(hAPP(A,B),C))|c_ListOrder_Ostep1(A,D,E,F)| -c_ListOrder_Ostep1(A,c_List_Oappend(D,c_List_Olist_OCons(B,c_List_Olist_ONil(F),F),F),c_List_Oappend(E,c_List_Olist_OCons(C,c_List_Olist_ONil(F),F),F),F).
% 16.30/16.39 ** KEPT (pick-wt=20): 63 [] c_List_Orev(A,B)!=c_List_Olist_OCons(C,D,B)|A=c_List_Oappend(c_List_Orev(D,B),c_List_Olist_OCons(C,c_List_Olist_ONil(B),B),B).
% 16.30/16.39 ** KEPT (pick-wt=27): 64 [] A=B|c_ListOrder_Ostep1(C,A,B,D)| -c_ListOrder_Ostep1(C,c_List_Oappend(A,c_List_Olist_OCons(E,c_List_Olist_ONil(D),D),D),c_List_Oappend(B,c_List_Olist_OCons(F,c_List_Olist_ONil(D),D),D),D).
% 16.30/16.39 ** KEPT (pick-wt=19): 65 [] -c_Type_Otyping(A,B,C)| -c_Type_Otyping(c_Type_Oshift(A,D,C,tc_Type_Otype),E,F)|c_Type_Otyping(A,c_Lambda_Osubst(E,B,D),F).
% 16.30/16.39 ** KEPT (pick-wt=17): 66 [] -class_OrderedGroup_Oab__semigroup__add(A)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,C,A,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),C,B,A,A).
% 16.30/16.39 ** KEPT (pick-wt=12): 67 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(A,c_Lambda_OdB_OVar(B),C)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 16.30/16.39 ** KEPT (pick-wt=16): 68 [] c_Type_Otyping(A,B,C)| -c_Type_Otyping(A,D,C)| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),D),B)).
% 16.30/16.39 ** KEPT (pick-wt=20): 69 [] c_ListOrder_Ostep1(c_Lambda_Obeta,A,c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1(B,A,C),tc_Lambda_OdB)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(B),A,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 16.30/16.39 ** KEPT (pick-wt=20): 70 [] 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.
% 16.30/16.39 ** KEPT (pick-wt=18): 71 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),B)).
% 16.30/16.39 ** KEPT (pick-wt=24): 72 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,A),C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),C)).
% 16.30/16.39 ** KEPT (pick-wt=24): 73 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,C),B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 16.30/16.39 ** KEPT (pick-wt=32): 74 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,C),D)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 16.30/16.39 ** KEPT (pick-wt=23): 75 [] -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).
% 16.30/16.39 ** KEPT (pick-wt=40): 76 [] -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),B,tc_Lambda_OdB)|c_Wellfounded_Oaccp(c_Predicate_Oconversep(c_Lambda_Obeta,tc_Lambda_OdB,tc_Lambda_OdB),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),tc_Lambda_OdB).
% 16.30/16.39 ** KEPT (pick-wt=22): 77 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,E),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),E)).
% 16.30/16.39 ** KEPT (pick-wt=22): 78 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),E),D))| -hBOOL(hAPP(hAPP(A,C),E)).
% 16.30/16.39 ** KEPT (pick-wt=15): 79 [] c_List_Olistsp(A,c_List_Oappend(B,C,D),D)| -c_List_Olistsp(A,C,D)| -c_List_Olistsp(A,B,D).
% 16.30/16.39 ** KEPT (pick-wt=14): 80 [] -class_OrderedGroup_Omonoid__add(A)|c_List_Olistsum(B,A)=c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A).
% 16.30/16.39 ** KEPT (pick-wt=14): 81 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_Power_Opower_Opower(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Ozero__class_Ozero(A).
% 16.30/16.39 ** KEPT (pick-wt=14): 82 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,C),D)).
% 16.30/16.39 ** KEPT (pick-wt=15): 83 [] -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).
% 16.30/16.39 ** KEPT (pick-wt=22): 84 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(A,D,C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),D)).
% 16.30/16.39 ** KEPT (pick-wt=22): 85 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),D)).
% 16.30/16.39 ** KEPT (pick-wt=16): 87 [copy,86,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).
% 16.30/16.39 ** KEPT (pick-wt=27): 89 [copy,88,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).
% 16.30/16.39 ** KEPT (pick-wt=15): 90 [] -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).
% 16.30/16.39 ** KEPT (pick-wt=15): 91 [] -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).
% 16.30/16.39 Following clause subsumed by 90 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).
% 16.30/16.39 ** KEPT (pick-wt=20): 92 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(A,D,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,B),D)).
% 16.30/16.39 ** KEPT (pick-wt=24): 93 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),E),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),E)).
% 16.30/16.39 ** KEPT (pick-wt=18): 94 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),D)).
% 16.30/16.39 ** KEPT (pick-wt=11): 95 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(D,B,C),C).
% 16.30/16.39 ** KEPT (pick-wt=11): 96 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(B,D,C),C).
% 16.30/16.39 ** KEPT (pick-wt=14): 97 [] -class_OrderedGroup_Omonoid__add(A)|c_List_Olistsum(B,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A).
% 16.30/16.39 ** KEPT (pick-wt=13): 98 [] -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).
% 16.30/16.39 ** KEPT (pick-wt=25): 100 [copy,99,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)).
% 16.30/16.39 ** KEPT (pick-wt=25): 101 [] -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)).
% 16.30/16.39 ** KEPT (pick-wt=25): 102 [] -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)).
% 16.30/16.39 ** KEPT (pick-wt=25): 103 [] -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)).
% 16.30/16.39 ** KEPT (pick-wt=25): 104 [] -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)).
% 16.30/16.39 Following clause subsumed by 100 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)).
% 16.30/16.39 ** KEPT (pick-wt=25): 105 [] -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).
% 16.30/16.39 ** KEPT (pick-wt=25): 106 [] -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)).
% 16.30/16.39 Following clause subsumed by 100 during input processing: 0 [] -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)).
% 16.30/16.39 ** KEPT (pick-wt=28): 107 [] -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.
% 16.30/16.39 ** KEPT (pick-wt=28): 109 [copy,108,flip.2] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_List_Ofoldl(c_Lambda_OdB_OApp,C,D,tc_Lambda_OdB,tc_Lambda_OdB)|c_List_Ofoldl(c_Lambda_OdB_OApp,C,c_ListApplication_Osko__ListApplication__XApp__e_q__foldl__conv__1__1(A,B,C,D),tc_Lambda_OdB,tc_Lambda_OdB)=A|D=c_List_Olist_ONil(tc_Lambda_OdB).
% 16.30/16.39 ** KEPT (pick-wt=20): 110 [] -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.
% 16.30/16.39 ** KEPT (pick-wt=18): 111 [] -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.
% 16.30/16.39 ** KEPT (pick-wt=18): 112 [] -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.
% 16.30/16.39 ** KEPT (pick-wt=18): 113 [] -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.
% 16.30/16.39 ** KEPT (pick-wt=35): 114 [] -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)).
% 16.30/16.39 ** KEPT (pick-wt=11): 115 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 16.30/16.39 ** KEPT (pick-wt=11): 116 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 16.30/16.39 ** KEPT (pick-wt=13): 118 [copy,117,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.
% 16.30/16.39 ** KEPT (pick-wt=11): 119 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 16.30/16.39 ** KEPT (pick-wt=11): 120 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 16.30/16.39 ** KEPT (pick-wt=11): 121 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 16.30/16.39 ** KEPT (pick-wt=11): 122 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 16.30/16.39 Following clause subsumed by 115 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.
% 16.30/16.39 ** KEPT (pick-wt=26): 123 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),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)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 16.30/16.39 ** KEPT (pick-wt=13): 124 [] 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).
% 16.30/16.39 ** KEPT (pick-wt=13): 125 [] 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).
% 16.30/16.39 ** KEPT (pick-wt=13): 126 [] 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).
% 16.30/16.39 ** KEPT (pick-wt=23): 128 [copy,127,flip.2] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),C,c_HOL_Ozero__class_Ozero(A),A,A))=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),B,C,A,A).
% 16.30/16.39 ** KEPT (pick-wt=19): 130 [copy,129,flip.2] -class_OrderedGroup_Omonoid__add(A)|c_List_Ofoldr(c_HOL_Oplus__class_Oplus(A),B,c_HOL_Ozero__class_Ozero(A),A,A)=c_List_Ofoldl(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A),B,A,A).
% 16.30/16.39 ** KEPT (pick-wt=24): 132 [copy,131,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| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 16.30/16.39 ** KEPT (pick-wt=14): 133 [] 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).
% 16.30/16.39 ** KEPT (pick-wt=31): 134 [] 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,c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB))).
% 16.30/16.39 ** KEPT (pick-wt=37): 135 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__types__1__1(C,D,A,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),D)| -c_Type_Otypings(A,F,G)| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 16.30/16.39 ** KEPT (pick-wt=34): 137 [copy,136,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=v_T____|hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(C,D,E)))| -c_Type_Otyping(F,D,A)| -hBOOL(hAPP(c_InductTermi_OIT,D))| -c_Type_Otyping(c_Type_Oshift(F,E,A,tc_Type_Otype),C,G)| -hBOOL(hAPP(c_InductTermi_OIT,C)).
% 16.30/16.39 ** KEPT (pick-wt=34): 139 [copy,138,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=v_T____|hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_Osubst(C,D,E)))| -c_Type_Otyping(F,D,B)| -hBOOL(hAPP(c_InductTermi_OIT,D))| -c_Type_Otyping(c_Type_Oshift(F,E,B,tc_Type_Otype),C,G)| -hBOOL(hAPP(c_InductTermi_OIT,C)).
% 16.30/16.39 ** KEPT (pick-wt=41): 141 [copy,140,flip.1] c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__types__1__1(A,B,C,D),A,tc_Type_Otype,tc_Type_Otype)=B| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),B)| -c_Type_Otypings(C,F,G)| -c_Type_Otyping(C,c_List_Ofoldl(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(E),F,tc_Lambda_OdB,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),A).
% 16.30/16.39 ** KEPT (pick-wt=8): 142 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 16.30/16.39 ** KEPT (pick-wt=14): 143 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),B)).
% 16.30/16.39 ** KEPT (pick-wt=14): 144 [] 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).
% 16.30/16.39 ** KEPT (pick-wt=13): 145 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B))))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 16.30/16.39 ** KEPT (pick-wt=6): 147 [copy,146,flip.1] c_List_Olist_OCons(A,B,C)!=B.
% 16.30/16.39 Following clause subsumed by 147 during input processing: 0 [] c_List_Olist_OCons(A,B,C)!=B.
% 16.30/16.39 ** KEPT (pick-wt=20): 148 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,C),B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)).
% 16.30/16.39 ** KEPT (pick-wt=20): 149 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),hAPP(hAPP(c_Lambda_OdB_OApp,A),C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,B),C)).
% 16.30/16.39 ** KEPT (pick-wt=9): 150 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 16.30/16.39 ** KEPT (pick-wt=16): 151 [] 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.
% 16.30/16.39 ** KEPT (pick-wt=15): 152 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,c_Type_Otype_OAtom(D),t_a)))|hBOOL(hAPP(A,hAPP(B,D))).
% 16.30/16.39 Following clause subsumed by 152 during input processing: 0 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,c_Type_Otype_OAtom(D),t_a)))|hBOOL(hAPP(A,hAPP(B,D))).
% 16.30/16.39 ** KEPT (pick-wt=7): 153 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 16.30/16.39 Following clause subsumed by 153 during input processing: 0 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 16.30/16.39 ** KEPT (pick-wt=13): 154 [] 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.
% 16.30/16.39 ** KEPT (pick-wt=9): 155 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_Type_Osko__Type__Xtype__induct__1__1(A))).
% 16.30/16.39 ** KEPT (pick-wt=17): 156 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xlist__app__typeE__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,D,B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 16.30/16.39 ** KEPT (pick-wt=16): 157 [] c_Type_Otyping(A,B,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,D,B))| -c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,D),B),C).
% 16.30/16.39 ** KEPT (pick-wt=20): 158 [] c_Type_Otyping(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),c_Type_Osko__Type__Xtyping__elims__3__1(B,A,C),tc_Type_Otype),C,c_Type_Osko__Type__Xtyping__elims__3__2(B,A,C))| -c_Type_Otyping(A,c_Lambda_OdB_OAbs(C),B).
% 16.30/16.39 ** KEPT (pick-wt=12): 159 [] c_List_Oappend(A,B,C)!=c_List_Oappend(D,B,C)|A=D.
% 16.30/16.39 ** KEPT (pick-wt=12): 160 [] c_List_Oappend(A,B,C)!=c_List_Oappend(A,D,C)|B=D.
% 16.30/16.39 ** KEPT (pick-wt=8): 161 [] c_Type_Otype_OAtom(A)!=c_Type_Otype_OAtom(B)|A=B.
% 16.30/16.39 ** KEPT (pick-wt=5): 162 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 16.30/16.39 ** KEPT (pick-wt=15): 163 [] 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).
% 16.30/16.39 ** KEPT (pick-wt=11): 164 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|B=c_List_Olist_ONil(A).
% 16.30/16.39 ** KEPT (pick-wt=11): 165 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|C=c_List_Olist_ONil(A).
% 16.30/16.39 ** KEPT (pick-wt=8): 166 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 16.30/16.39 ** KEPT (pick-wt=11): 167 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|A=c_List_Olist_ONil(C).
% 16.30/16.39 ** KEPT (pick-wt=11): 168 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C).
% 16.30/16.39 ** KEPT (pick-wt=8): 169 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 16.30/16.39 ** KEPT (pick-wt=13): 170 [] 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.
% 16.30/16.39 ** KEPT (pick-wt=22): 171 [] hBOOL(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)).
% 16.30/16.39 ** KEPT (pick-wt=23): 172 [] 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).
% 16.30/16.39 ** KEPT (pick-wt=14): 173 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 16.30/16.39 ** KEPT (pick-wt=14): 174 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 16.30/16.39 ** KEPT (pick-wt=18): 175 [] 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.
% 16.30/16.39 ** KEPT (pick-wt=18): 176 [] 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.
% 16.30/16.40 ** KEPT (pick-wt=13): 177 [] 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).
% 16.30/16.40 ** KEPT (pick-wt=7): 178 [] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 16.30/16.40 ** KEPT (pick-wt=7): 179 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(A)),B)).
% 16.30/16.40 ** KEPT (pick-wt=17): 180 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xlist__app__typeD__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,D,B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 16.30/16.40 ** KEPT (pick-wt=10): 181 [] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 16.30/16.40 Following clause subsumed by 181 during input processing: 0 [flip.1] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 16.30/16.40 ** KEPT (pick-wt=10): 182 [] c_List_Oappend(A,B,C)!=B|A=c_List_Olist_ONil(C).
% 16.30/16.40 Following clause subsumed by 182 during input processing: 0 [flip.1] c_List_Oappend(B,A,C)!=A|B=c_List_Olist_ONil(C).
% 16.30/16.40 ** KEPT (pick-wt=12): 183 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|A=D.
% 16.30/16.40 ** KEPT (pick-wt=12): 184 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|B=E.
% 16.30/16.40 ** KEPT (pick-wt=18): 185 [] 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.
% 16.30/16.40 ** KEPT (pick-wt=18): 186 [] 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.
% 16.30/16.40 ** KEPT (pick-wt=8): 187 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 16.30/16.40 ** KEPT (pick-wt=8): 188 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 16.30/16.40 ** KEPT (pick-wt=18): 189 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__typesE__1__1(C,A,D,B))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),B,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 16.30/16.40 ** KEPT (pick-wt=8): 190 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 16.30/16.40 ** KEPT (pick-wt=5): 191 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 16.30/16.40 ** KEPT (pick-wt=20): 192 [] c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)!=c_List_Oappend(D,c_List_Olist_OCons(E,c_List_Olist_ONil(C),C),C)|A=D.
% 16.30/16.40 ** KEPT (pick-wt=20): 193 [] c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)!=c_List_Oappend(D,c_List_Olist_OCons(E,c_List_Olist_ONil(C),C),C)|B=E.
% 16.30/16.40 ** KEPT (pick-wt=8): 194 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=c_Type_Otype_OAtom(C).
% 16.30/16.40 ** KEPT (pick-wt=18): 196 [copy,195,flip.1] hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(A,B,C)),c_Type_Osko__Type__Xtyping__elims__3__2(A,B,C))=A| -c_Type_Otyping(B,c_Lambda_OdB_OAbs(C),A).
% 16.30/16.40 ** KEPT (pick-wt=14): 197 [] c_Type_Otyping(A,B,C)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,D),B))| -c_Type_Otyping(A,D,C).
% 16.30/16.40 ** KEPT (pick-wt=14): 198 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|A=C.
% 16.30/16.40 ** KEPT (pick-wt=14): 199 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|B=D.
% 16.30/16.40 ** KEPT (pick-wt=12): 201 [copy,200,factor_simp] c_Type_Osko__Type__Xtype__induct__1__1(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C)|hBOOL(hAPP(A,C)).
% 16.30/16.40 ** KEPT (pick-wt=12): 203 [copy,202,factor_simp] c_Type_Osko__Type__Xtype__induct__1__1(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C)|hBOOL(hAPP(A,B)).
% 16.30/16.40 ** KEPT (pick-wt=20): 204 [] c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),D)| -c_Type_Otyping(A,C,E)| -c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,E),D)).
% 16.30/16.40 ** KEPT (pick-wt=18): 205 [] c_Type_Otyping(A,c_Lambda_OdB_OAbs(B),hAPP(hAPP(c_Type_Otype_OFun,C),D))| -c_Type_Otyping(c_Type_Oshift(A,c_HOL_Ozero__class_Ozero(tc_nat),C,tc_Type_Otype),B,D).
% 16.30/16.40 ** KEPT (pick-wt=10): 206 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 16.30/16.40 ** KEPT (pick-wt=22): 207 [] c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeE__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 16.30/16.40 ** KEPT (pick-wt=24): 208 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xvar__app__typesE__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(B),D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 16.30/16.40 ** KEPT (pick-wt=22): 209 [] c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,C,tc_Lambda_OdB,tc_Lambda_OdB),D)| -c_Type_Otypings(A,C,E)| -c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,E,D,tc_Type_Otype,tc_Type_Otype)).
% 16.30/16.40 ** KEPT (pick-wt=20): 210 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,hAPP(hAPP(c_Type_Otype_OFun,D),E),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,D),E))).
% 16.30/16.40 Following clause subsumed by 210 during input processing: 0 [] -hBOOL(hAPP(A,c_Type_Otype_Otype__case(B,C,hAPP(hAPP(c_Type_Otype_OFun,D),E),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,D),E))).
% 16.30/16.40 ** KEPT (pick-wt=8): 211 [] c_Type_Otype_OAtom(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C).
% 16.30/16.40 ** KEPT (pick-wt=22): 212 [] c_Type_Otyping(A,B,c_List_Ofoldr(c_Type_Otype_OFun,c_Type_Osko__Type__Xlist__app__typeD__1__1(C,A,B,D),C,tc_Type_Otype,tc_Type_Otype))| -c_Type_Otyping(A,c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB),C).
% 16.30/16.40 ** KEPT (pick-wt=20): 213 [] c_Type_Otyping(A,B,hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,B,D)),C))| -c_Type_Otyping(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C).
% 16.30/16.40 ** KEPT (pick-wt=13): 214 [] -c_Type_Otyping(v_e____,v_u____,hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))).
% 16.30/16.40 ** KEPT (pick-wt=10): 215 [] A=B| -hBOOL(hAPP(hAPP(c_fe_qual(C),A),B)).
% 16.30/16.40 91 back subsumes 33.
% 16.30/16.40 Following clause subsumed by 169 during input processing: 0 [copy,142,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 16.30/16.40 ** KEPT (pick-wt=14): 223 [copy,144,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).
% 16.30/16.40 Following clause subsumed by 178 during input processing: 0 [copy,153,flip.1] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 16.30/16.40 Following clause subsumed by 191 during input processing: 0 [copy,162,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 16.30/16.40 ** KEPT (pick-wt=15): 224 [copy,163,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).
% 16.30/16.40 Following clause subsumed by 142 during input processing: 0 [copy,169,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 16.30/16.40 Following clause subsumed by 153 during input processing: 0 [copy,178,flip.1] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 16.30/16.40 Following clause subsumed by 190 during input processing: 0 [copy,187,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 16.30/16.40 Following clause subsumed by 187 during input processing: 0 [copy,190,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 16.30/16.40 Following clause subsumed by 162 during input processing: 0 [copy,191,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 16.30/16.40 Following clause subsumed by 211 during input processing: 0 [copy,194,flip.1] c_Type_Otype_OAtom(A)!=hAPP(hAPP(c_Type_Otype_OFun,B),C).
% 16.30/16.40 Following clause subsumed by 194 during input processing: 0 [copy,211,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=c_Type_Otype_OAtom(C).
% 16.30/16.40 Following clause subsumed by 144 during input processing: 0 [copy,223,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).
% 16.30/16.40 Following clause subsumed by 163 during input processing: 0 [copy,224,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).
% 16.30/16.40
% 16.30/16.40 ------------> process sos:
% 16.30/16.40 ** KEPT (pick-wt=3): 226 [] A=A.
% 16.30/16.40 ** KEPT (pick-wt=4): 227 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 16.30/16.40 ** KEPT (pick-wt=15): 228 [] c_List_Orev(c_List_Oappend(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Orev(A,C),C).
% 16.30/16.40 ---> New Demodulator: 229 [new_demod,228] c_List_Orev(c_List_Oappend(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Orev(A,C),C).
% 16.30/16.40 ** KEPT (pick-wt=7): 230 [] c_List_Orev(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 16.30/16.40 ---> New Demodulator: 231 [new_demod,230] c_List_Orev(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 16.30/16.40 ** KEPT (pick-wt=11): 232 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),C,B).
% 16.30/16.40 ** KEPT (pick-wt=12): 233 [] c_List_Olast(c_List_Oreplicate(A,B,C),C)=B|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 16.30/16.40 ** KEPT (pick-wt=7): 234 [] c_List_Orotate1(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 16.30/16.40 ---> New Demodulator: 235 [new_demod,234] c_List_Orotate1(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 16.30/16.40 ** KEPT (pick-wt=4): 236 [] c_Type_Otyping(v_ea______,v_ua______,v_T____).
% 16.30/16.40 ** KEPT (pick-wt=8): 237 [] c_List_Otake(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 16.30/16.40 ---> New Demodulator: 238 [new_demod,237] c_List_Otake(A,c_List_Olist_ONil(B),B)=c_List_Olist_ONil(B).
% 16.30/16.40 ** KEPT (pick-wt=7): 240 [copy,239,flip.1] c_List_Orev(c_List_Orev(A,B),B)=A.
% 16.30/16.40 ---> New Demodulator: 241 [new_demod,240] c_List_Orev(c_List_Orev(A,B),B)=A.
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,241] A=A.
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,241] A=A.
% 16.30/16.40 ** KEPT (pick-wt=11): 242 [] c_List_Orev(c_List_Oreplicate(A,B,C),C)=c_List_Oreplicate(A,B,C).
% 16.30/16.40 ---> New Demodulator: 243 [new_demod,242] c_List_Orev(c_List_Oreplicate(A,B,C),C)=c_List_Oreplicate(A,B,C).
% 16.30/16.40 ** KEPT (pick-wt=8): 244 [] c_Predicate_Oconversep(c_fe_qual(A),A,A)=c_fe_qual(A).
% 16.30/16.40 ---> New Demodulator: 245 [new_demod,244] c_Predicate_Oconversep(c_fe_qual(A),A,A)=c_fe_qual(A).
% 16.30/16.40 ** KEPT (pick-wt=21): 246 [] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Oreplicate(D,B,C),C)=c_List_Oappend(c_List_Oreplicate(D,B,C),c_List_Oreplicate(A,B,C),C).
% 16.30/16.40 ** KEPT (pick-wt=9): 247 [] c_Predicate_Oconversep(c_Predicate_Oconversep(A,B,C),C,B)=A.
% 16.30/16.40 ---> New Demodulator: 248 [new_demod,247] c_Predicate_Oconversep(c_Predicate_Oconversep(A,B,C),C,B)=A.
% 16.30/16.40 ** KEPT (pick-wt=9): 249 [] c_Power_Opower_Opower(A,B,C,c_HOL_Ozero__class_Ozero(tc_nat),D)=A.
% 16.30/16.40 ---> New Demodulator: 250 [new_demod,249] c_Power_Opower_Opower(A,B,C,c_HOL_Ozero__class_Ozero(tc_nat),D)=A.
% 16.30/16.40 ** KEPT (pick-wt=7): 251 [] c_List_Obutlast(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 16.30/16.40 ---> New Demodulator: 252 [new_demod,251] c_List_Obutlast(c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 16.30/16.40 ** KEPT (pick-wt=24): 253 [] hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_List_Oappend(B,c_List_Olist_OCons(C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,231] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 16.30/16.40 Following clause subsumed by 253 during input processing: 0 [] c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB)=c_List_Olist_ONil(tc_Lambda_OdB)|hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,C,A,tc_Lambda_OdB,tc_Lambda_OdB)),B)=c_List_Ofoldl(c_Lambda_OdB_OApp,C,c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 16.30/16.40 ** KEPT (pick-wt=18): 254 [] c_List_Oappend(c_List_Obutlast(A,B),c_List_Olist_OCons(c_List_Olast(A,B),c_List_Olist_ONil(B),B),B)=A|A=c_List_Olist_ONil(B).
% 16.30/16.40 ** KEPT (pick-wt=8): 255 [] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 16.30/16.40 ** KEPT (pick-wt=8): 256 [] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 16.30/16.40 ** KEPT (pick-wt=8): 257 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 16.30/16.40 ** KEPT (pick-wt=13): 259 [copy,258,flip.1] c_List_Orev(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 16.30/16.40 ---> New Demodulator: 260 [new_demod,259] c_List_Orev(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 16.30/16.40 ** KEPT (pick-wt=14): 261 [] c_List_Olast(c_List_Olist_OCons(A,B,C),C)=c_List_Olast(B,C)|B=c_List_Olist_ONil(C).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,260] c_List_Olist_OCons(A,c_List_Olist_ONil(B),B)=c_List_Olist_OCons(A,c_List_Olist_ONil(B),B).
% 16.30/16.40 ** KEPT (pick-wt=10): 262 [] c_List_Obutlast(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=c_List_Olist_ONil(B).
% 16.30/16.40 ---> New Demodulator: 263 [new_demod,262] c_List_Obutlast(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=c_List_Olist_ONil(B).
% 16.30/16.40 ** KEPT (pick-wt=9): 264 [] c_List_Olast(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=A.
% 16.30/16.40 ---> New Demodulator: 265 [new_demod,264] c_List_Olast(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),B)=A.
% 16.30/16.40 ** KEPT (pick-wt=17): 266 [] c_List_Obutlast(c_List_Olist_OCons(A,B,C),C)=c_List_Olist_OCons(A,c_List_Obutlast(B,C),C)|B=c_List_Olist_ONil(C).
% 16.30/16.40 ** KEPT (pick-wt=21): 268 [copy,267,flip.1] c_List_Olist_OCons(A,c_List_Oappend(c_List_Oreplicate(B,A,C),D,C),C)=c_List_Oappend(c_List_Oreplicate(B,A,C),c_List_Olist_OCons(A,D,C),C).
% 16.30/16.40 ---> New Demodulator: 269 [new_demod,268] c_List_Olist_OCons(A,c_List_Oappend(c_List_Oreplicate(B,A,C),D,C),C)=c_List_Oappend(c_List_Oreplicate(B,A,C),c_List_Olist_OCons(A,D,C),C).
% 16.30/16.40 ** KEPT (pick-wt=11): 270 [] c_List_Obutlast(c_List_Oappend(A,c_List_Olist_ONil(B),B),B)=c_List_Obutlast(A,B).
% 16.30/16.40 ---> New Demodulator: 271 [new_demod,270] c_List_Obutlast(c_List_Oappend(A,c_List_Olist_ONil(B),B),B)=c_List_Obutlast(A,B).
% 16.30/16.40 ** KEPT (pick-wt=14): 272 [] c_List_Olast(c_List_Oappend(A,B,C),C)=c_List_Olast(B,C)|B=c_List_Olist_ONil(C).
% 16.30/16.40 ** KEPT (pick-wt=11): 273 [] c_List_Olast(c_List_Oappend(A,c_List_Olist_ONil(B),B),B)=c_List_Olast(A,B).
% 16.30/16.40 ---> New Demodulator: 274 [new_demod,273] c_List_Olast(c_List_Oappend(A,c_List_Olist_ONil(B),B),B)=c_List_Olast(A,B).
% 16.30/16.40 ** KEPT (pick-wt=17): 275 [] c_List_Obutlast(c_List_Oappend(A,B,C),C)=c_List_Oappend(A,c_List_Obutlast(B,C),C)|B=c_List_Olist_ONil(C).
% 16.30/16.40 ** KEPT (pick-wt=12): 276 [] c_List_Olast(c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C),C)=B.
% 16.30/16.40 ---> New Demodulator: 277 [new_demod,276] c_List_Olast(c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C),C)=B.
% 16.30/16.40 ** KEPT (pick-wt=12): 278 [] c_List_Obutlast(c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C),C)=A.
% 16.30/16.40 ---> New Demodulator: 279 [new_demod,278] c_List_Obutlast(c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C),C)=A.
% 16.30/16.40 ** KEPT (pick-wt=17): 280 [] c_List_Orev(c_List_Olist_OCons(A,B,C),C)=c_List_Oappend(c_List_Orev(B,C),c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 16.30/16.40 ** KEPT (pick-wt=13): 282 [copy,281,demod,229,260,241] c_List_Oappend(c_List_Olist_OCons(A,c_List_Olist_ONil(B),B),C,B)=c_List_Olist_OCons(A,C,B).
% 16.30/16.40 ** KEPT (pick-wt=15): 283 [] c_List_Orotate1(c_List_Olist_OCons(A,B,C),C)=c_List_Oappend(B,c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 16.30/16.40 ** KEPT (pick-wt=19): 284 [] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)=c_List_Olist_OCons(B,c_List_Oreplicate(A,B,C),C).
% 16.30/16.40 Following clause subsumed by 257 during input processing: 0 [] c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),c_List_Olist_OCons(A,B,C),C)=c_List_Olist_ONil(C).
% 16.30/16.40 ** KEPT (pick-wt=14): 285 [] c_Type_Otyping(c_Type_Oshift(v_ea______,v_ia______,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_Ha______).
% 16.30/16.40 ** KEPT (pick-wt=17): 287 [copy,286,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,A),B),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 16.30/16.40 ---> New Demodulator: 288 [new_demod,287] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,A),B),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(c_Lambda_OdB_OApp,A),B).
% 16.30/16.40 ** KEPT (pick-wt=20): 290 [copy,289,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 16.30/16.40 ---> New Demodulator: 291 [new_demod,290] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubst(A,B,C)),c_Lambda_Osubst(D,B,C))=c_Lambda_Osubst(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 16.30/16.40 ** KEPT (pick-wt=7): 292 [] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 16.30/16.40 ---> New Demodulator: 293 [new_demod,292] c_Lambda_Osubst(c_Lambda_OdB_OVar(A),B,A)=B.
% 16.30/16.40 ** KEPT (pick-wt=8): 294 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 16.30/16.40 Following clause subsumed by 294 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 16.30/16.40 ** KEPT (pick-wt=5): 295 [] c_List_Olistsp(A,c_List_Olist_ONil(B),B).
% 16.30/16.40 ** KEPT (pick-wt=6): 297 [copy,296,flip.1] c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB)=v_rs____.
% 16.30/16.40 ---> New Demodulator: 298 [new_demod,297] c_List_Olist_OCons(v_a____,v_as____,tc_Lambda_OdB)=v_rs____.
% 16.30/16.40 ** KEPT (pick-wt=9): 299 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 16.30/16.40 ---> New Demodulator: 300 [new_demod,299] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 16.30/16.40 ** KEPT (pick-wt=11): 301 [] 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).
% 16.30/16.40 ---> New Demodulator: 302 [new_demod,301] 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).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,302] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 16.30/16.40 ** KEPT (pick-wt=11): 304 [copy,303,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OVar(A).
% 16.30/16.40 ---> New Demodulator: 305 [new_demod,304] c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(A),c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=c_Lambda_OdB_OVar(A).
% 16.30/16.40 ** KEPT (pick-wt=15): 306 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)),c_Lambda_Osubst(A,B,c_HOL_Ozero__class_Ozero(tc_nat)))).
% 16.30/16.40 ** KEPT (pick-wt=8): 307 [] c_Type_Otypings(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_as____,v_Ts____).
% 16.30/16.40 ** KEPT (pick-wt=14): 308 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB),v_T_H____).
% 16.30/16.40 ** KEPT (pick-wt=10): 309 [] c_Type_Otype_Otype__case(A,B,c_Type_Otype_OAtom(C),D)=hAPP(A,C).
% 16.30/16.40 ** KEPT (pick-wt=21): 310 [] c_List_Ofoldl(A,B,c_List_Oappend(C,D,E),F,E)=c_List_Ofoldl(A,c_List_Ofoldl(A,B,C,F,E),D,F,E).
% 16.30/16.40 ** KEPT (pick-wt=9): 312 [copy,311,flip.1] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 16.30/16.40 ---> New Demodulator: 313 [new_demod,312] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_ONil(A),A)=c_List_Olist_ONil(A).
% 16.30/16.40 ** KEPT (pick-wt=13): 315 [copy,314,flip.1] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_OCons(B,C,A),A)=c_List_Olist_OCons(B,C,A).
% 16.30/16.40 ---> New Demodulator: 316 [new_demod,315] c_List_Oappend(c_List_Olist_ONil(A),c_List_Olist_OCons(B,C,A),A)=c_List_Olist_OCons(B,C,A).
% 16.30/16.40 ** KEPT (pick-wt=15): 317 [] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 16.30/16.40 ---> New Demodulator: 318 [new_demod,317] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,318] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,318] c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C)=c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,318] c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C)=c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C).
% 16.30/16.40 ** KEPT (pick-wt=20): 319 [] c_List_Ofoldl(A,B,c_List_Olist_OCons(C,D,E),F,E)=c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,F,E).
% 16.30/16.40 ** KEPT (pick-wt=7): 320 [] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 16.30/16.40 ---> New Demodulator: 321 [new_demod,320] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 16.30/16.40 ** KEPT (pick-wt=7): 323 [copy,322,flip.1] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 16.30/16.40 ---> New Demodulator: 324 [new_demod,323] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,321] A=A.
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,324] B=B.
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,324] A=A.
% 16.30/16.40 ** KEPT (pick-wt=5): 325 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))).
% 16.30/16.40 ** KEPT (pick-wt=3): 326 [] v_n____=v_i____.
% 16.30/16.40 ---> New Demodulator: 327 [new_demod,326] v_n____=v_i____.
% 16.30/16.40 ** KEPT (pick-wt=9): 328 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 16.30/16.40 ---> New Demodulator: 329 [new_demod,328] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 16.30/16.40 ** KEPT (pick-wt=9): 330 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 16.30/16.40 ---> New Demodulator: 331 [new_demod,330] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 16.30/16.40 ** KEPT (pick-wt=10): 332 [] c_Type_Otype_Otype__rec(A,B,c_Type_Otype_OAtom(C),D)=hAPP(A,C).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,324] c_List_Olist_OCons(B,C,A)=c_List_Olist_OCons(B,C,A).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,321] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 16.30/16.40 ** KEPT (pick-wt=15): 333 [] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 16.30/16.40 ---> New Demodulator: 334 [new_demod,333] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,334] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,334] c_List_Oappend(A,c_List_Oappend(B,D,C),C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,334] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 16.30/16.40 ** KEPT (pick-wt=4): 335 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 16.30/16.40 ** KEPT (pick-wt=20): 337 [copy,336,flip.1] hAPP(hAPP(A,B),c_List_Ofoldr(A,C,D,E,F))=c_List_Ofoldr(A,c_List_Olist_OCons(B,C,E),D,E,F).
% 16.30/16.40 ---> New Demodulator: 338 [new_demod,337] hAPP(hAPP(A,B),c_List_Ofoldr(A,C,D,E,F))=c_List_Ofoldr(A,c_List_Olist_OCons(B,C,E),D,E,F).
% 16.30/16.40 ** KEPT (pick-wt=8): 339 [] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),v_a____,v_T_H_H____).
% 16.30/16.40 ** KEPT (pick-wt=21): 340 [] c_List_Ofoldr(A,c_List_Oappend(B,C,D),E,D,F)=c_List_Ofoldr(A,B,c_List_Ofoldr(A,C,E,D,F),D,F).
% 16.30/16.40 ---> New Demodulator: 341 [new_demod,340] c_List_Ofoldr(A,c_List_Oappend(B,C,D),E,D,F)=c_List_Ofoldr(A,B,c_List_Ofoldr(A,C,E,D,F),D,F).
% 16.30/16.40 ** KEPT (pick-wt=17): 343 [copy,342,demod,327,338] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),c_Lambda_OdB_OVar(v_i____),c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 16.30/16.40 ** KEPT (pick-wt=18): 345 [copy,344,demod,327] c_Type_Otyping(c_Type_Oshift(v_e____,v_i____,v_T____,tc_Type_Otype),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 16.30/16.40 ** KEPT (pick-wt=9): 346 [] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 16.30/16.40 ---> New Demodulator: 347 [new_demod,346] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 16.30/16.40 ** KEPT (pick-wt=11): 349 [copy,348,demod,338,flip.1] c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)=v_T____.
% 16.30/16.40 ---> New Demodulator: 350 [new_demod,349] c_List_Ofoldr(c_Type_Otype_OFun,c_List_Olist_OCons(v_T_H_H____,v_Ts____,tc_Type_Otype),v_T_H____,tc_Type_Otype,tc_Type_Otype)=v_T____.
% 16.30/16.40 ** KEPT (pick-wt=27): 352 [copy,351,flip.1] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Type_Otype_Otype__rec(D,A,B,E)),c_Type_Otype_Otype__rec(D,A,C,E))=c_Type_Otype_Otype__rec(D,A,hAPP(hAPP(c_Type_Otype_OFun,B),C),E).
% 16.30/16.40 ---> New Demodulator: 353 [new_demod,352] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Type_Otype_Otype__rec(D,A,B,E)),c_Type_Otype_Otype__rec(D,A,C,E))=c_Type_Otype_Otype__rec(D,A,hAPP(hAPP(c_Type_Otype_OFun,B),C),E).
% 16.30/16.40 ** KEPT (pick-wt=15): 354 [] c_Type_Otype_Otype__case(A,B,hAPP(hAPP(c_Type_Otype_OFun,C),D),E)=hAPP(hAPP(B,C),D).
% 16.30/16.40 ** KEPT (pick-wt=7): 355 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 16.30/16.40 ** KEPT (pick-wt=4): 356 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [demod,338,350] v_T____=v_T____.
% 16.30/16.40 Following clause subsumed by 335 during input processing: 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 16.30/16.40 ** KEPT (pick-wt=2): 357 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 16.30/16.40 ** KEPT (pick-wt=2): 358 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 16.30/16.40 ** KEPT (pick-wt=2): 359 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 16.30/16.40 ** KEPT (pick-wt=2): 360 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 16.30/16.40 ** KEPT (pick-wt=2): 361 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 16.30/16.40 ** KEPT (pick-wt=2): 362 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 16.30/16.40 ** KEPT (pick-wt=2): 363 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 16.30/16.40 ** KEPT (pick-wt=2): 364 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 365 [] class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 366 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 367 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 368 [] class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 369 [] class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 370 [] class_OrderedGroup_Osemigroup__add(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 371 [] class_OrderedGroup_Oab__group__add(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 372 [] class_OrderedGroup_Omonoid__add(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 373 [] class_Ring__and__Field_Oidom(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 374 [] class_Int_Oring__char__0(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=2): 375 [] class_Int_Onumber__ring(tc_Int_Oint).
% 16.30/16.40 ** KEPT (pick-wt=7): 376 [] hBOOL(hAPP(hAPP(c_fe_qual(A),B),B)).
% 16.30/16.40 Following clause subsumed by 226 during input processing: 0 [copy,226,flip.1] A=A.
% 16.30/16.40 226 back subsumes 225.
% 16.30/16.40 >>>> Starting back demodulation with 229.
% 16.30/16.40 >>>> Starting back demodulation with 231.
% 16.30/16.40 Following clause subsumed by 232 during input processing: 0 [copy,232,flip.1] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),C,B).
% 16.30/16.40 >>>> Starting back demodulation with 235.
% 16.30/16.40 >>>> Starting back demodulation with 238.
% 16.30/16.40 >>>> Starting back demodulation with 241.
% 16.30/16.40 >>>> Starting back demodulation with 243.
% 16.30/16.40 >>>> Starting back demodulation with 245.
% 16.30/16.40 Following clause subsumed by 246 during input processing: 0 [copy,246,flip.1] c_List_Oappend(c_List_Oreplicate(A,B,C),c_List_Oreplicate(D,B,C),C)=c_List_Oappend(c_List_Oreplicate(D,B,C),c_List_Oreplicate(A,B,C),C).
% 16.30/16.40 >>>> Starting back demodulation with 248.
% 16.30/16.40 >>>> Starting back demodulation with 250.
% 16.30/16.40 >> back demodulating 81 with 250.
% 16.30/16.40 >>>> Starting back demodulation with 252.
% 16.30/16.40 ** KEPT (pick-wt=24): 377 [copy,253,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,A,c_List_Oappend(B,c_List_Olist_OCons(C,c_List_Olist_ONil(tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(c_Lambda_OdB_OApp,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C).
% 16.30/16.40 Following clause subsumed by 256 during input processing: 0 [copy,255,flip.1] c_List_Olist_ONil(A)=c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 16.30/16.40 Following clause subsumed by 255 during input processing: 0 [copy,256,flip.1] c_List_Oreplicate(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=c_List_Olist_ONil(B).
% 16.30/16.40 ** KEPT (pick-wt=8): 378 [copy,257,flip.1] c_List_Olist_ONil(A)=c_List_Otake(c_HOL_Ozero__class_Ozero(tc_nat),B,A).
% 16.30/16.40 >>>> Starting back demodulation with 260.
% 16.30/16.40 >>>> Starting back demodulation with 263.
% 16.30/16.40 >>>> Starting back demodulation with 265.
% 16.30/16.40 >>>> Starting back demodulation with 269.
% 16.30/16.40 >>>> Starting back demodulation with 271.
% 16.30/16.40 >>>> Starting back demodulation with 274.
% 16.30/16.40 >>>> Starting back demodulation with 277.
% 16.30/16.40 >>>> Starting back demodulation with 279.
% 16.30/16.40 ** KEPT (pick-wt=17): 379 [copy,280,flip.1] c_List_Oappend(c_List_Orev(A,B),c_List_Olist_OCons(C,c_List_Olist
% 16.30/16.40 -------- PROOF --------
% 16.30/16.40 _ONil(B),B),B)=c_List_Orev(c_List_Olist_OCons(C,A,B),B).
% 16.30/16.40 ** KEPT (pick-wt=13): 380 [copy,282,flip.1] c_List_Olist_OCons(A,B,C)=c_List_Oappend(c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),B,C).
% 16.30/16.40 ** KEPT (pick-wt=15): 381 [copy,283,flip.1] c_List_Oappend(A,c_List_Olist_OCons(B,c_List_Olist_ONil(C),C),C)=c_List_Orotate1(c_List_Olist_OCons(B,A,C),C).
% 16.30/16.40 ** KEPT (pick-wt=19): 382 [copy,284,flip.1] c_List_Olist_OCons(A,c_List_Oreplicate(B,A,C),C)=c_List_Oappend(c_List_Oreplicate(B,A,C),c_List_Olist_OCons(A,c_List_Olist_ONil(C),C),C).
% 16.30/16.40 >>>> Starting back demodulation with 288.
% 16.30/16.40 >>>> Starting back demodulation with 291.
% 16.30/16.40 >>>> Starting back demodulation with 293.
% 16.30/16.40 >>>> Starting back demodulation with 298.
% 16.30/16.40 >>>> Starting back demodulation with 300.
% 16.30/16.40 >>>> Starting back demodulation with 302.
% 16.30/16.40 >>>> Starting back demodulation with 305.
% 16.30/16.40 ** KEPT (pick-wt=10): 383 [copy,309,flip.1] hAPP(A,B)=c_Type_Otype_Otype__case(A,C,c_Type_Otype_OAtom(B),D).
% 16.30/16.40 ** KEPT (pick-wt=21): 384 [copy,310,flip.1] c_List_Ofoldl(A,c_List_Ofoldl(A,B,C,D,E),F,D,E)=c_List_Ofoldl(A,B,c_List_Oappend(C,F,E),D,E).
% 16.30/16.40 >>>> Starting back demodulation with 313.
% 16.30/16.40 >>>> Starting back demodulation with 316.
% 16.30/16.40 >>>> Starting back demodulation with 318.
% 16.30/16.40 >> back demodulating 268 with 318.
% 16.30/16.40 ** KEPT (pick-wt=20): 386 [copy,319,flip.1] c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,E,F)=c_List_Ofoldl(A,B,c_List_Olist_OCons(C,D,F),E,F).
% 16.30/16.40 >>>> Starting back demodulation with 321.
% 16.30/16.40 >> back demodulating 312 with 321.
% 16.30/16.40 >> back demodulating 273 with 321.
% 16.30/16.40 >> back demodulating 270 with 321.
% 16.30/16.40 >>>> Starting back demodulation with 324.
% 16.30/16.40 >> back demodulating 315 with 324.
% 16.30/16.40 >>>> Starting back demodulation with 327.
% 16.30/16.40 >> back demodulating 308 with 327.
% 16.30/16.40 >> back demodulating 285 with 327.
% 16.30/16.40 >>>> Starting back demodulation with 329.
% 16.30/16.40 >> back demodulating 304 with 329.
% 16.30/16.40 >> back demodulating 301 with 329.
% 16.30/16.40 >> back demodulating 287 with 329.
% 16.30/16.40 >> back demodulating 70 with 329.
% 16.30/16.40 >>>> Starting back demodulation with 331.
% 16.30/16.40 ** KEPT (pick-wt=10): 389 [copy,332,flip.1] hAPP(A,B)=c_Type_Otype_Otype__rec(A,C,c_Type_Otype_OAtom(B),D).
% 16.30/16.40 >>>> Starting back demodulation with 334.
% 16.30/16.40 >>>> Starting back demodulation with 338.
% 16.30/16.40 >> back demodulating 214 with 338.
% 16.30/16.40
% 16.30/16.40 ----> UNIT CONFLICT at 0.04 sec ----> 391 [binary,390.1,335.1] $F.
% 16.30/16.40
% 16.30/16.40 Length of proof is 3. Level of proof is 3.
% 16.30/16.40
% 16.30/16.40 ---------------- PROOF ----------------
% 16.30/16.40 % SZS status Unsatisfiable
% 16.30/16.40 % SZS output start Refutation
% See solution above
% 16.30/16.40 ------------ end of proof -------------
% 16.30/16.40
% 16.30/16.40
% 16.30/16.40 Search stopped by max_proofs option.
% 16.30/16.40
% 16.30/16.40
% 16.30/16.40 Search stopped by max_proofs option.
% 16.30/16.40
% 16.30/16.40 ============ end of search ============
% 16.30/16.40
% 16.30/16.40 -------------- statistics -------------
% 16.30/16.40 clauses given 0
% 16.30/16.40 clauses generated 9
% 16.30/16.40 clauses kept 311
% 16.30/16.40 clauses forward subsumed 60
% 16.30/16.40 clauses back subsumed 2
% 16.30/16.40 Kbytes malloced 6835
% 16.30/16.40
% 16.30/16.40 ----------- times (seconds) -----------
% 16.30/16.40 user CPU time 0.04 (0 hr, 0 min, 0 sec)
% 16.30/16.40 system CPU time 0.00 (0 hr, 0 min, 0 sec)
% 16.30/16.40 wall-clock time 16 (0 hr, 0 min, 16 sec)
% 16.30/16.40
% 16.30/16.40 That finishes the proof of the theorem.
% 16.30/16.40
% 16.30/16.40 Process 14490 finished Wed Jul 27 09:32:23 2022
% 16.30/16.40 Otter interrupted
% 16.30/16.40 PROOF FOUND
%------------------------------------------------------------------------------