TSTP Solution File: LCL782-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL782-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n008.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 13:05:24 EDT 2022
% Result : Unknown 28.80s 28.96s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL782-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n008.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jul 27 09:32:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 28.43/28.64 ----- Otter 3.3f, August 2004 -----
% 28.43/28.64 The process was started by sandbox on n008.cluster.edu,
% 28.43/28.64 Wed Jul 27 09:32:38 2022
% 28.43/28.64 The command was "./otter". The process ID is 19651.
% 28.43/28.64
% 28.43/28.64 set(prolog_style_variables).
% 28.43/28.64 set(auto).
% 28.43/28.64 dependent: set(auto1).
% 28.43/28.64 dependent: set(process_input).
% 28.43/28.64 dependent: clear(print_kept).
% 28.43/28.64 dependent: clear(print_new_demod).
% 28.43/28.64 dependent: clear(print_back_demod).
% 28.43/28.64 dependent: clear(print_back_sub).
% 28.43/28.64 dependent: set(control_memory).
% 28.43/28.64 dependent: assign(max_mem, 12000).
% 28.43/28.64 dependent: assign(pick_given_ratio, 4).
% 28.43/28.64 dependent: assign(stats_level, 1).
% 28.43/28.64 dependent: assign(max_seconds, 10800).
% 28.43/28.64 clear(print_given).
% 28.43/28.64
% 28.43/28.64 list(usable).
% 28.43/28.64 0 [] A=A.
% 28.43/28.64 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).
% 28.43/28.64 0 [] hBOOL(hAPP(V_P,V_t))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB))).
% 28.43/28.64 0 [] -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__4(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(V_P,V_t)).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 28.43/28.64 0 [] V_ys=c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a).
% 28.43/28.64 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),V_ys,T_a)=V_ys.
% 28.43/28.64 0 [] V_xs=c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a).
% 28.43/28.64 0 [] V_x=c_List_Oappend(c_List_Olist_ONil(T_a),V_x,T_a).
% 28.43/28.64 0 [] c_List_Oappend(V_xs,c_List_Olist_ONil(T_a),T_a)=V_xs.
% 28.43/28.64 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.43/28.64 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)).
% 28.43/28.64 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)).
% 28.43/28.64 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)).
% 28.43/28.64 0 [] c_Type_Otyping(v_ea______,v_ua______,v_T____).
% 28.43/28.64 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Oappend(V_xs,V_zs,T_a)|V_ys=V_zs.
% 28.43/28.64 0 [] c_List_Oappend(V_ys,V_xs,T_a)!=c_List_Oappend(V_zs,V_xs,T_a)|V_ys=V_zs.
% 28.43/28.64 0 [] c_List_Olistsp(V_A,c_List_Olist_ONil(T_a),T_a).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a)=hAPP(V_f3,V_dB).
% 28.43/28.64 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 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)).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 0 [] c_Lambda_Osubstn(V_t,V_s,V_n)=hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),c_Lambda_Oliftn(V_n,V_s,c_HOL_Ozero__class_Ozero(tc_nat))),V_n).
% 28.43/28.64 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).
% 28.43/28.64 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)).
% 28.43/28.64 0 [] -class_Orderings_Opreorder(T_a)|c_HOL_Oord__class_Oless(V_x,V_z,T_a)| -c_HOL_Oord__class_Oless(V_y,V_z,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 28.43/28.64 0 [] -class_Orderings_Oorder(T_a)|c_HOL_Oord__class_Oless(V_z,V_x,T_a)| -c_HOL_Oord__class_Oless(V_z,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 28.43/28.64 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).
% 28.43/28.64 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)).
% 28.43/28.64 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)).
% 28.43/28.64 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)).
% 28.43/28.64 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)).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 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)).
% 28.43/28.64 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)).
% 28.43/28.64 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 28.43/28.64 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 28.43/28.64 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.
% 28.43/28.64 0 [] hAPP(c_COMBC(V_P,V_Q,T_b,T_c,T_a),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 28.43/28.64 0 [] c_List_Ofoldr(V_f,c_List_Olist_ONil(T_b),V_a,T_b,T_a)=V_a.
% 28.43/28.64 0 [] c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a)=c_List_Olist_ONil(T_a).
% 28.43/28.64 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).
% 28.43/28.64 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.43/28.64 0 [] c_Type_Otypings(V_e,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_T,tc_Type_Otype),V_ts,V_Ts)| -c_Type_Otyping(V_e,V_u,V_T).
% 28.43/28.64 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 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)).
% 28.43/28.64 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)).
% 28.43/28.64 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)).
% 28.43/28.64 0 [] c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xa,T_b),T_b,T_a)=c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xa,T_b,T_a),T_a).
% 28.43/28.64 0 [] c_List_Olist_OCons(hAPP(V_f,V_xa),c_List_Omap(V_f,V_xb,T_b,T_a),T_a)=c_List_Omap(V_f,c_List_Olist_OCons(V_xa,V_xb,T_b),T_b,T_a).
% 28.43/28.64 0 [] c_List_Omap(V_f,c_List_Olist_OCons(V_x,V_xs,T_b),T_b,T_a)=c_List_Olist_OCons(hAPP(V_f,V_x),c_List_Omap(V_f,V_xs,T_b,T_a),T_a).
% 28.43/28.64 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.43/28.64 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.
% 28.43/28.64 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.
% 28.43/28.64 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.
% 28.43/28.64 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.
% 28.43/28.64 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).
% 28.43/28.64 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).
% 28.43/28.64 0 [] c_List_Olist_OCons(V_x,V_xa,T_a)!=c_List_Olist_ONil(T_a).
% 28.43/28.64 0 [] c_List_Olist_OCons(V_a_H,V_list_H,T_a)!=c_List_Olist_ONil(T_a).
% 28.43/28.64 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).
% 28.43/28.64 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)).
% 28.43/28.64 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)).
% 28.43/28.64 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 28.43/28.64 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)).
% 28.43/28.64 0 [] c_Type_Otypings(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(V_e,V_ts,V_Ts).
% 28.43/28.64 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k)=c_Lambda_OdB_OVar(V_i)| -c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 28.43/28.64 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 28.43/28.64 0 [] c_List_Olist_OCons(V_x,V_t,T_a)!=V_t.
% 28.43/28.64 0 [] V_xs!=c_List_Olist_OCons(V_x,V_xs,T_a).
% 28.43/28.64 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.52/28.64 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_x),V_s,V_x)=c_Lambda_Oliftn(V_x,V_s,c_HOL_Ozero__class_Ozero(tc_nat)).
% 28.52/28.64 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).
% 28.52/28.64 0 [] -c_Type_Otyping(V_e_H,V_u,V_U)| -c_Type_Otyping(c_Type_Oshift(V_e_H,V_i,V_U,tc_Type_Otype),V_t,V_T)|c_Type_Otyping(V_e_H,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),V_T).
% 28.52/28.64 0 [] c_List_Olist_ONil(T_a)=c_List_Omap(V_f,c_List_Olist_ONil(T_b),T_b,T_a).
% 28.52/28.64 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).
% 28.52/28.64 0 [] c_List_Olist_ONil(T_a)=c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a).
% 28.52/28.64 0 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a)=c_Transitive__Closure_Ortranclp(V_r,T_a).
% 28.52/28.64 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.
% 28.52/28.64 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.
% 28.52/28.64 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)).
% 28.52/28.64 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.
% 28.52/28.64 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.
% 28.52/28.64 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.
% 28.52/28.64 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.
% 28.52/28.64 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.
% 28.52/28.64 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)).
% 28.52/28.64 0 [] hAPP(hAPP(V_plus,V_a),V_zero)=V_a| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 28.52/28.64 0 [] hAPP(hAPP(V_plus,V_zero),V_a)=V_a| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 28.52/28.64 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a).
% 28.52/28.64 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 28.52/28.64 0 [] c_List_Olist_ONil(T_a)!=c_List_Omap(V_f,V_xs,T_b,T_a)|V_xs=c_List_Olist_ONil(T_b).
% 28.52/28.64 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i)),hAPP(hAPP(hAPP(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)).
% 28.52/28.64 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_r),V_i)),hAPP(hAPP(hAPP(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)).
% 28.52/28.64 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).
% 28.52/28.64 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).
% 28.52/28.64 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)).
% 28.52/28.64 0 [] -c_ListOrder_Ostep1(V_r,c_List_Olist_ONil(T_a),V_xs,T_a).
% 28.52/28.64 0 [] -c_ListOrder_Ostep1(V_r,V_xs,c_List_Olist_ONil(T_a),T_a).
% 28.52/28.64 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 28.52/28.64 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 28.52/28.64 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 28.52/28.64 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 28.52/28.64 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).
% 28.52/28.64 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).
% 28.52/28.64 0 [] hAPP(c_Type_Oshift(V_e,V_x,V_T,T_a),V_x)=V_T.
% 28.52/28.64 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 28.52/28.64 0 [] v_T____!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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)).
% 28.52/28.64 0 [] v_T____!=hAPP(hAPP(c_Type_Otype_OFun,V_T1),V_T2)|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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)).
% 28.52/28.64 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 28.52/28.64 0 [] c_List_Olist_ONil(T_a)!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 28.52/28.64 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 28.52/28.64 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_a).
% 28.52/28.64 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=c_List_Olist_ONil(T_a)|V_ys=c_List_Olist_ONil(T_a).
% 28.52/28.64 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.52/28.64 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 28.52/28.64 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 28.52/28.64 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 28.52/28.64 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 28.52/28.64 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 28.52/28.64 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_s)),V_t)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),c_HOL_Ozero__class_Ozero(tc_nat)))).
% 28.52/28.64 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,V_r),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),V_r),V_s)).
% 28.52/28.64 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 28.52/28.64 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).
% 28.52/28.64 0 [] hAPP(hAPP(V_plus,hAPP(hAPP(V_plus,V_a),V_b)),V_c)=hAPP(hAPP(V_plus,V_a),hAPP(hAPP(V_plus,V_b),V_c))| -c_OrderedGroup_Osemigroup__add(V_plus,T_a).
% 28.52/28.64 0 [] c_List_Omap(V_f,c_List_Oappend(V_xs,V_ys,T_b),T_b,T_a)=c_List_Oappend(c_List_Omap(V_f,V_xs,T_b,T_a),c_List_Omap(V_f,V_ys,T_b,T_a),T_a).
% 28.52/28.64 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.52/28.64 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 28.52/28.64 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 28.52/28.64 0 [] c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)|V_m=V_n.
% 28.52/28.64 0 [] hBOOL(hAPP(hAPP(V_P,V_n),V_m))|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat)|V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 28.52/28.64 0 [] c_HOL_Oord__class_Oless(V_y,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)|V_x=V_y.
% 28.52/28.64 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|V_x=V_y.
% 28.52/28.64 0 [] -class_Orderings_Olinorder(T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 28.52/28.64 0 [] -class_Orderings_Olinorder(T_a)|V_x=V_y|c_HOL_Oord__class_Oless(V_x,V_y,T_a)|c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 28.52/28.64 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_d),T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 28.52/28.64 0 [] c_List_Olist_ONil(T_a)!=c_List_Olist_OCons(V_a_H,V_list_H,T_a).
% 28.52/28.64 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)).
% 28.52/28.65 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).
% 28.52/28.65 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.52/28.65 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).
% 28.52/28.65 0 [] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_i)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_t),V_i),c_List_Omap(c_COMBC(c_Lambda_Olift,V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 28.52/28.65 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 28.52/28.65 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).
% 28.52/28.65 0 [] c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),T_a)=hAPP(hAPP(V_f3,V_dB),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB,T_a)).
% 28.52/28.65 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 28.52/28.65 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 28.52/28.65 0 [] -class_OrderedGroup_Osemigroup__add(T_a)|c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(T_a),T_a).
% 28.52/28.65 0 [] hAPP(c_Type_Oshift(V_e,V_i,V_T,T_a),V_j)=hAPP(V_e,V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 28.52/28.65 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).
% 28.52/28.65 0 [] c_Lambda_Osubstn(V_t,V_s,c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),c_HOL_Ozero__class_Ozero(tc_nat)).
% 28.52/28.65 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_b,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),T_a)| -c_HOL_Oord__class_Oless(V_b,V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a).
% 28.52/28.65 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)).
% 28.52/28.65 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_dB),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f3,V_dB))).
% 28.52/28.65 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OAbs(V_xa),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f3,V_xa))).
% 28.52/28.65 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_xs|V_ys=c_List_Olist_ONil(T_a).
% 28.52/28.65 0 [] V_xs!=c_List_Oappend(V_xs,V_ys,T_a)|V_ys=c_List_Olist_ONil(T_a).
% 28.52/28.65 0 [] c_List_Oappend(V_xs,V_ys,T_a)!=V_ys|V_xs=c_List_Olist_ONil(T_a).
% 28.52/28.65 0 [] V_ys!=c_List_Oappend(V_xs,V_ys,T_a)|V_xs=c_List_Olist_ONil(T_a).
% 28.52/28.65 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.
% 28.52/28.65 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.
% 28.52/28.65 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).
% 28.52/28.65 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 28.52/28.65 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 28.52/28.65 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_c),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_b),V_c),T_a).
% 28.52/28.65 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 28.52/28.65 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 28.52/28.65 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_c),V_b),T_a).
% 28.52/28.65 0 [] V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(V_a))),v_sko__InductTermi__XIT__Xcases__5(V_a)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.52/28.65 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.
% 28.52/28.65 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.
% 28.52/28.65 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).
% 28.52/28.65 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).
% 28.52/28.65 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).
% 28.52/28.65 0 [] c_List_Omap(V_f,V_xs,T_b,T_a)!=c_List_Olist_ONil(T_a)|V_xs=c_List_Olist_ONil(T_b).
% 28.52/28.65 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.
% 28.52/28.65 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.
% 28.52/28.65 0 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 28.52/28.65 0 [] c_List_Oappend(c_List_Olist_ONil(T_a),c_List_Olist_ONil(T_a),T_a)=c_List_Olist_ONil(T_a).
% 28.52/28.65 0 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB).
% 28.52/28.65 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).
% 28.52/28.65 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).
% 28.52/28.65 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).
% 28.52/28.65 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).
% 28.52/28.65 0 [] c_Type_Otyping(c_Type_Oshift(V_e,V_i,V_U,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,V_t),V_i),V_T)| -c_Type_Otyping(V_e,V_t,V_T).
% 28.52/28.65 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a).
% 28.52/28.65 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)).
% 28.52/28.65 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)).
% 28.52/28.65 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a).
% 28.52/28.65 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_y,V_x,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 28.52/28.65 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 28.52/28.65 0 [] hBOOL(hAPP(V_P,c_ListApplication_Osko__ListApplication__Xlem__1__3(V_P)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(V_P)),c_ListApplication_Osko__ListApplication__Xlem__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(V_P,V_t)).
% 28.52/28.65 0 [] c_List_Ofoldl(V_plus,hAPP(hAPP(V_plus,V_x),V_y),V_zs,T_a,T_a)=hAPP(hAPP(V_plus,V_x),c_List_Ofoldl(V_plus,V_y,V_zs,T_a,T_a))| -c_OrderedGroup_Osemigroup__add(V_plus,T_a).
% 28.52/28.65 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).
% 28.52/28.65 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_s),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_k)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_s),V_k)).
% 28.52/28.65 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 28.52/28.65 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 28.52/28.65 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).
% 28.52/28.65 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 28.52/28.65 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_xd),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_xd))).
% 28.52/28.65 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),t_a)))|hBOOL(hAPP(V_P,hAPP(V_f1,V_nat))).
% 28.52/28.65 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 28.52/28.65 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.
% 28.52/28.65 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.
% 28.52/28.65 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k)=V_u.
% 28.52/28.65 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_xb),V_xc),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_xb),V_xc))).
% 28.52/28.65 0 [] -hBOOL(hAPP(V_P,c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),t_a)))|hBOOL(hAPP(V_P,hAPP(hAPP(V_f2,V_dB1),V_dB2))).
% 28.52/28.65 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),c_Lambda_OdB_OVar(V_i)),V_j)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 28.52/28.65 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i)=c_Lambda_OdB_OVar(V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 28.52/28.65 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)).
% 28.52/28.65 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.
% 28.52/28.65 0 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)).
% 28.52/28.65 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).
% 28.52/28.65 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.
% 28.52/28.65 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.
% 28.52/28.65 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).
% 28.52/28.65 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.
% 28.52/28.65 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.
% 28.52/28.65 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).
% 28.52/28.65 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).
% 28.52/28.65 0 [] hBOOL(hAPP(V_P,V_t))|hBOOL(hAPP(V_P,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(V_P)))| -hBOOL(hAPP(V_P,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(V_P)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(V_P),tc_Lambda_OdB,tc_Lambda_OdB))).
% 28.52/28.65 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)).
% 28.52/28.65 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.
% 28.52/28.65 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).
% 28.52/28.65 0 [] c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a)=hAPP(V_f1,V_nat).
% 28.52/28.65 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 28.52/28.65 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).
% 28.52/28.65 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 28.52/28.65 0 [] c_List_Ofoldl(V_f,V_a,c_List_Olist_ONil(T_b),T_a,T_b)=V_a.
% 28.52/28.65 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(V_r)),V_s),V_ss,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(c_InductTermi_OIT,V_s))| -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_s),c_HOL_Ozero__class_Ozero(tc_nat)),V_ss,tc_Lambda_OdB,tc_Lambda_OdB))).
% 28.52/28.65 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(V_a)),v_sko__InductTermi__XIT__Xcases__5(V_a)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(V_a),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.52/28.65 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 28.52/28.65 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))).
% 28.52/28.65 0 [] hAPP(V_e,V_i)=V_T| -c_Type_Otyping(V_e,c_Lambda_OdB_OVar(V_i),V_T).
% 28.52/28.65 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)).
% 28.52/28.65 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|V_a=c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(V_a))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.52/28.65 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,V_s),V_k)),hAPP(hAPP(c_Lambda_Olift,V_t),V_k)).
% 28.52/28.65 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_u),V_i)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,V_u,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),V_i,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 28.52/28.65 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______).
% 28.52/28.65 0 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_r),V_t),V_i)),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_s),V_t),V_i)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_r),V_s)).
% 28.52/28.65 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k)=c_Lambda_OdB_OVar(V_i)|V_i=V_k|c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 28.52/28.65 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).
% 28.52/28.65 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 28.52/28.65 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____).
% 28.52/28.65 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)).
% 28.52/28.65 0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a)=hAPP(hAPP(V_f2,V_dB1),V_dB2).
% 28.52/28.65 0 [] hAPP(hAPP(V_plus,V_x),c_List_Ofoldl(V_plus,V_zero,V_zs,T_a,T_a))=c_List_Ofoldl(V_plus,V_x,V_zs,T_a,T_a)| -c_OrderedGroup_Omonoid__add(V_zero,V_plus,T_a).
% 28.52/28.65 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(V_a)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(V_a)))|V_a=c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(V_a)),v_sko__InductTermi__XIT__Xcases__1(V_a),tc_Lambda_OdB,tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,V_a)).
% 28.52/28.65 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).
% 28.52/28.65 0 [] c_Lambda_OdB_OdB__case(V_f1,V_f2,V_f3,c_Lambda_OdB_OVar(V_nat),T_a)=hAPP(V_f1,V_nat).
% 28.52/28.65 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_x)),V_s),V_x)=V_s.
% 28.52/28.65 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).
% 28.52/28.65 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).
% 28.52/28.65 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).
% 28.52/28.65 0 [] c_Type_Otyping(V_env,c_Lambda_OdB_OVar(V_x),hAPP(V_env,V_x)).
% 28.52/28.65 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.
% 28.52/28.65 0 [] c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2),T_a)=hAPP(hAPP(hAPP(hAPP(V_f2,V_dB1),V_dB2),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB1,T_a)),c_Lambda_OdB_OdB__rec(V_f1,V_f2,V_f3,V_dB2,T_a)).
% 28.52/28.65 0 [] V_t=c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(V_t),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(V_t),tc_Lambda_OdB,tc_Lambda_OdB).
% 28.52/28.65 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).
% 28.52/28.65 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.
% 28.52/28.65 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).
% 28.52/28.65 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 28.52/28.65 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)).
% 28.52/28.65 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)).
% 28.52/28.65 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 28.52/28.65 0 [] c_Lambda_Oliftn(V_n,hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t),V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(V_n,V_s,V_k)),c_Lambda_Oliftn(V_n,V_t,V_k)).
% 28.52/28.65 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k)=V_t.
% 28.52/28.65 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).
% 28.52/28.65 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).
% 28.52/28.65 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)).
% 28.52/28.65 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)).
% 28.52/28.65 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).
% 28.52/28.65 0 [] c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u),V_s,V_k)=hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(V_t,V_s,V_k)),c_Lambda_Osubstn(V_u,V_s,V_k)).
% 28.52/28.65 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).
% 28.52/28.65 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 28.52/28.65 0 [] -hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))).
% 28.52/28.65 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 28.52/28.65 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 28.52/28.65 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 28.52/28.65 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 28.52/28.65 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 28.52/28.65 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 28.52/28.65 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 28.52/28.65 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 28.52/28.65 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 28.52/28.65 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 28.52/28.65 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 28.52/28.65 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 28.52/28.65 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 28.52/28.65 0 [] class_Orderings_Opreorder(tc_nat).
% 28.52/28.65 0 [] class_Orderings_Olinorder(tc_nat).
% 28.52/28.65 0 [] class_Orderings_Oorder(tc_nat).
% 28.52/28.65 0 [] class_Orderings_Opreorder(tc_bool).
% 28.52/28.65 0 [] class_Orderings_Oorder(tc_bool).
% 28.52/28.65 0 [] c_fe_qual(V_x,V_x,T_a).
% 28.52/28.65 0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 28.52/28.65 end_of_list.
% 28.52/28.65
% 28.52/28.65 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 28.52/28.65
% 28.52/28.65 This ia a non-Horn set with equality. The strategy will be
% 28.52/28.65 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 28.52/28.65 deletion, with positive clauses in sos and nonpositive
% 28.52/28.65 clauses in usable.
% 28.52/28.65
% 28.52/28.65 dependent: set(knuth_bendix).
% 28.52/28.65 dependent: set(anl_eq).
% 28.52/28.65 dependent: set(para_from).
% 28.52/28.65 dependent: set(para_into).
% 28.52/28.65 dependent: clear(para_from_right).
% 28.52/28.65 dependent: clear(para_into_right).
% 28.52/28.65 dependent: set(para_from_vars).
% 28.52/28.65 dependent: set(eq_units_both_ways).
% 28.52/28.65 dependent: set(dynamic_demod_all).
% 28.52/28.65 dependent: set(dynamic_demod).
% 28.52/28.65 dependent: set(order_eq).
% 28.52/28.65 dependent: set(back_demod).
% 28.52/28.65 dependent: set(lrpo).
% 28.52/28.65 dependent: set(hyper_res).
% 28.52/28.65 dependent: set(unit_deletion).
% 28.52/28.65 dependent: set(factor).
% 28.52/28.65
% 28.52/28.65 ------------> process usable:
% 28.52/28.65 ** KEPT (pick-wt=16): 2 [copy,1,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).
% 28.52/28.65 ** KEPT (pick-wt=28): 3 [] hBOOL(hAPP(A,B))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(A)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__4(A),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(A)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB))).
% 28.52/28.65 ** KEPT (pick-wt=28): 4 [] -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(c_ListApplication_Osko__ListApplication__Xlem__1__3(A)),c_ListApplication_Osko__ListApplication__Xlem__1__4(A),tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(A)),c_ListApplication_Osko__ListApplication__Xlem__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(A,B)).
% 28.52/28.65 ** KEPT (pick-wt=22): 5 [] 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).
% 28.52/28.65 ** KEPT (pick-wt=22): 6 [] 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).
% 28.52/28.65 ** KEPT (pick-wt=17): 7 [] 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).
% 28.52/28.65 ** KEPT (pick-wt=17): 8 [] 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).
% 28.52/28.65 ** KEPT (pick-wt=28): 9 [] 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).
% 28.52/28.65 ** KEPT (pick-wt=15): 10 [] -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).
% 28.52/28.65 ** KEPT (pick-wt=15): 11 [] -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).
% 28.52/28.65 Following clause subsumed by 10 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).
% 28.52/28.65 ** KEPT (pick-wt=26): 12 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),D),C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,B),D)).
% 28.52/28.65 ** KEPT (pick-wt=19): 14 [copy,13,flip.2] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.65 ** KEPT (pick-wt=24): 15 [] 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)).
% 28.52/28.65 ** KEPT (pick-wt=12): 16 [] c_List_Oappend(A,B,C)!=c_List_Oappend(A,D,C)|B=D.
% 28.52/28.65 ** KEPT (pick-wt=12): 17 [] c_List_Oappend(A,B,C)!=c_List_Oappend(D,B,C)|A=D.
% 28.52/28.65 ** KEPT (pick-wt=17): 18 [] -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).
% 28.52/28.65 ** KEPT (pick-wt=17): 19 [] A=B|C=D| -c_ListOrder_Ostep1(E,c_List_Olist_OCons(B,D,F),c_List_Olist_OCons(A,C,F),F).
% 28.52/28.65 ** KEPT (pick-wt=33): 20 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(A)),v_sko__InductTermi__XIT__Xcases__5(A)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.65 ** KEPT (pick-wt=11): 21 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(D,B,C),C).
% 28.52/28.65 ** KEPT (pick-wt=11): 22 [] c_List_Olistsp(A,B,C)| -c_List_Olistsp(A,c_List_Oappend(B,D,C),C).
% 28.52/28.65 ** KEPT (pick-wt=18): 23 [] 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)).
% 28.52/28.65 ** KEPT (pick-wt=16): 24 [] c_ListOrder_Ostep1(A,c_List_Oappend(B,C,D),c_List_Oappend(B,E,D),D)| -c_ListOrder_Ostep1(A,C,E,D).
% 28.52/28.65 ** KEPT (pick-wt=16): 25 [] -c_ListOrder_Ostep1(A,B,C,D)|c_ListOrder_Ostep1(A,c_List_Oappend(B,E,D),c_List_Oappend(C,E,D),D).
% 28.52/28.65 ** KEPT (pick-wt=13): 26 [] -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).
% 28.52/28.65 ** KEPT (pick-wt=22): 27 [] 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)).
% 28.52/28.65 ** KEPT (pick-wt=14): 28 [] -class_Orderings_Opreorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 28.52/28.65 ** KEPT (pick-wt=14): 29 [] -class_Orderings_Oorder(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(D,C,A).
% 28.52/28.65 ** KEPT (pick-wt=25): 31 [copy,30,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)).
% 28.52/28.65 ** KEPT (pick-wt=25): 32 [] -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)).
% 28.52/28.65 ** KEPT (pick-wt=25): 33 [] -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)).
% 28.52/28.65 ** KEPT (pick-wt=25): 34 [] -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)).
% 28.52/28.65 ** KEPT (pick-wt=25): 35 [] -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)).
% 28.52/28.65 Following clause subsumed by 31 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C)),D)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D)).
% 28.52/28.65 ** KEPT (pick-wt=25): 36 [] -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).
% 28.52/28.65 ** KEPT (pick-wt=25): 37 [] -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)).
% 28.52/28.65 Following clause subsumed by 31 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)).
% 28.52/28.65 ** KEPT (pick-wt=5): 38 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 28.52/28.65 Following clause subsumed by 38 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 28.52/28.65 ** KEPT (pick-wt=28): 39 [] -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.
% 28.52/28.65 ** KEPT (pick-wt=30): 40 [] 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).
% 28.52/28.65 ** KEPT (pick-wt=39): 42 [copy,41,flip.2,flip.3] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(A)),v_sko__InductTermi__XIT__Xcases__5(A)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.65 ** KEPT (pick-wt=32): 43 [] c_Type_Otypings(A,c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,B,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(c_Type_Oshift(A,C,F,tc_Type_Otype),D,E)| -c_Type_Otyping(A,B,F).
% 28.52/28.65 ** KEPT (pick-wt=22): 44 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 28.52/28.65 ** KEPT (pick-wt=24): 45 [] 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)).
% 28.52/28.65 ** KEPT (pick-wt=24): 46 [] 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)).
% 28.52/28.65 ** KEPT (pick-wt=23): 48 [copy,47,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).
% 28.52/28.65 ** KEPT (pick-wt=30): 50 [copy,49,flip.1,flip.2] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.65 ** KEPT (pick-wt=20): 51 [] -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.
% 28.52/28.65 ** KEPT (pick-wt=18): 52 [] -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.
% 28.52/28.65 ** KEPT (pick-wt=18): 53 [] -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.
% 28.52/28.65 ** KEPT (pick-wt=18): 54 [] -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.
% 28.52/28.65 ** KEPT (pick-wt=7): 55 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 28.52/28.65 Following clause subsumed by 55 during input processing: 0 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 28.52/28.65 ** KEPT (pick-wt=20): 56 [] 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).
% 28.52/28.65 ** KEPT (pick-wt=35): 57 [] -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)).
% 28.52/28.65 ** KEPT (pick-wt=32): 58 [] 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)).
% 28.52/28.65 ** KEPT (pick-wt=12): 59 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 28.52/28.65 ** KEPT (pick-wt=16): 60 [] 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)).
% 28.52/28.65 ** KEPT (pick-wt=21): 61 [] c_Type_Otypings(c_Type_Oshift(A,B,C,tc_Type_Otype),c_List_Omap(c_COMBC(c_Lambda_Olift,B,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(A,D,E).
% 28.52/28.65 ** KEPT (pick-wt=13): 62 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(A)),B)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 28.52/28.65 ** KEPT (pick-wt=20): 63 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_Olift,A),B)),hAPP(hAPP(c_Lambda_Olift,C),B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),C)).
% 28.52/28.65 ** KEPT (pick-wt=6): 64 [] c_List_Olist_OCons(A,B,C)!=B.
% 28.52/28.65 Following clause subsumed by 64 during input processing: 0 [flip.1] c_List_Olist_OCons(B,A,C)!=A.
% 28.52/28.65 ** KEPT (pick-wt=36): 66 [copy,65,flip.1,flip.3] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.65 ** KEPT (pick-wt=22): 67 [] -c_Type_Otyping(A,B,C)| -c_Type_Otyping(c_Type_Oshift(A,D,C,tc_Type_Otype),E,F)|c_Type_Otyping(A,hAPP(hAPP(hAPP(c_Lambda_Osubst,E),B),D),F).
% 28.52/28.65 ** KEPT (pick-wt=27): 68 [] 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).
% 28.52/28.65 ** KEPT (pick-wt=11): 69 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 28.52/28.65 ** KEPT (pick-wt=11): 70 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 28.52/28.65 ** KEPT (pick-wt=13): 72 [copy,71,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.
% 28.52/28.65 ** KEPT (pick-wt=11): 73 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 28.52/28.65 ** KEPT (pick-wt=11): 74 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 28.52/28.65 ** KEPT (pick-wt=11): 75 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 28.52/28.65 ** KEPT (pick-wt=11): 76 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 28.52/28.65 Following clause subsumed by 69 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.
% 28.52/28.65 ** KEPT (pick-wt=14): 77 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),B)).
% 28.52/28.65 ** KEPT (pick-wt=11): 78 [] hAPP(hAPP(A,B),C)=B| -c_OrderedGroup_Omonoid__add(C,A,D).
% 28.52/28.65 ** KEPT (pick-wt=11): 79 [] hAPP(hAPP(A,B),C)=C| -c_OrderedGroup_Omonoid__add(B,A,D).
% 28.52/28.65 ** KEPT (pick-wt=17): 80 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A).
% 28.52/28.65 ** KEPT (pick-wt=17): 81 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 28.52/28.65 ** KEPT (pick-wt=12): 82 [] c_List_Olist_ONil(A)!=c_List_Omap(B,C,D,A)|C=c_List_Olist_ONil(D).
% 28.52/28.65 ** KEPT (pick-wt=28): 83 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),D)).
% 28.52/28.65 ** KEPT (pick-wt=28): 84 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),D),C)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),B),D)).
% 28.52/28.65 ** KEPT (pick-wt=15): 85 [] -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).
% 28.52/28.65 ** KEPT (pick-wt=17): 86 [] -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).
% 28.52/28.65 ** KEPT (pick-wt=14): 87 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,C),D)).
% 28.52/28.65 ** KEPT (pick-wt=6): 88 [] -c_ListOrder_Ostep1(A,c_List_Olist_ONil(B),C,B).
% 28.52/28.65 ** KEPT (pick-wt=6): 89 [] -c_ListOrder_Ostep1(A,B,c_List_Olist_ONil(C),C).
% 28.52/28.65 ** KEPT (pick-wt=17): 90 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 28.52/28.65 ** KEPT (pick-wt=17): 91 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 28.52/28.65 ** KEPT (pick-wt=17): 92 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A).
% 28.52/28.65 ** KEPT (pick-wt=17): 93 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),B),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A).
% 28.52/28.65 ** KEPT (pick-wt=23): 94 [] -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).
% 28.52/28.65 ** KEPT (pick-wt=18): 95 [] 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).
% 28.52/28.65 ** KEPT (pick-wt=37): 97 [copy,96,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=v_T____|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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)).
% 28.52/28.65 ** KEPT (pick-wt=37): 99 [copy,98,flip.1] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=v_T____|hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(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)).
% 28.52/28.65 ** KEPT (pick-wt=11): 100 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|B=c_List_Olist_ONil(A).
% 28.52/28.65 ** KEPT (pick-wt=11): 101 [] c_List_Olist_ONil(A)!=c_List_Oappend(B,C,A)|C=c_List_Olist_ONil(A).
% 28.52/28.65 ** KEPT (pick-wt=8): 102 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 28.52/28.65 ** KEPT (pick-wt=11): 103 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|A=c_List_Olist_ONil(C).
% 28.52/28.65 ** KEPT (pick-wt=11): 104 [] c_List_Oappend(A,B,C)!=c_List_Olist_ONil(C)|B=c_List_Olist_ONil(C).
% 28.52/28.65 ** KEPT (pick-wt=19): 105 [] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.65 ** KEPT (pick-wt=4): 106 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 28.52/28.65 Following clause subsumed by 106 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 28.52/28.65 ** KEPT (pick-wt=6): 107 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 28.52/28.65 ** KEPT (pick-wt=6): 108 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 28.52/28.65 ** KEPT (pick-wt=6): 109 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 28.52/28.65 ** KEPT (pick-wt=24): 110 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),hAPP(hAPP(c_Lambda_Olift,A),B)),hAPP(hAPP(c_Lambda_Olift,C),B)))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),A),C)).
% 28.52/28.65 ** KEPT (pick-wt=22): 111 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A).
% 28.52/28.65 ** KEPT (pick-wt=19): 112 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=22): 113 [] hAPP(hAPP(A,hAPP(hAPP(A,B),C)),D)=hAPP(hAPP(A,B),hAPP(hAPP(A,C),D))| -c_OrderedGroup_Osemigroup__add(A,E).
% 28.52/28.66 ** KEPT (pick-wt=33): 115 [copy,114,flip.2] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(A)),v_sko__InductTermi__XIT__Xcases__5(A)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.66 ** KEPT (pick-wt=13): 116 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 28.52/28.66 ** KEPT (pick-wt=13): 117 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 28.52/28.66 Following clause subsumed by 117 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 28.52/28.66 Following clause subsumed by 117 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B|c_HOL_Oord__class_Oless(C,B,A).
% 28.52/28.66 Following clause subsumed by 117 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 28.52/28.66 ** KEPT (pick-wt=24): 118 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),E),A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A).
% 28.52/28.66 ** KEPT (pick-wt=7): 119 [] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 28.52/28.66 ** KEPT (pick-wt=20): 120 [] 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)).
% 28.52/28.66 ** KEPT (pick-wt=19): 122 [copy,121,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).
% 28.52/28.66 ** KEPT (pick-wt=36): 124 [copy,123,flip.1,flip.2,flip.3] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.66 ** KEPT (pick-wt=25): 125 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=15): 126 [] c_List_Olistsp(A,c_List_Oappend(B,C,D),D)| -c_List_Olistsp(A,C,D)| -c_List_Olistsp(A,B,D).
% 28.52/28.66 Following clause subsumed by 106 during input processing: 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 28.52/28.66 ** KEPT (pick-wt=6): 127 [] -class_OrderedGroup_Osemigroup__add(A)|c_OrderedGroup_Osemigroup__add(c_HOL_Oplus__class_Oplus(A),A).
% 28.52/28.66 ** KEPT (pick-wt=15): 128 [] hAPP(c_Type_Oshift(A,B,C,D),E)=hAPP(A,E)| -c_HOL_Oord__class_Oless(E,B,tc_nat).
% 28.52/28.66 ** KEPT (pick-wt=41): 130 [copy,129,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).
% 28.52/28.66 ** KEPT (pick-wt=20): 131 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A).
% 28.52/28.66 ** KEPT (pick-wt=16): 132 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 28.52/28.66 Following clause subsumed by 132 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OAbs(E),t_a)))|hBOOL(hAPP(A,hAPP(D,E))).
% 28.52/28.66 ** KEPT (pick-wt=10): 133 [] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 28.52/28.66 Following clause subsumed by 133 during input processing: 0 [flip.1] c_List_Oappend(A,B,C)!=A|B=c_List_Olist_ONil(C).
% 28.52/28.66 ** KEPT (pick-wt=10): 134 [] c_List_Oappend(A,B,C)!=B|A=c_List_Olist_ONil(C).
% 28.52/28.66 Following clause subsumed by 134 during input processing: 0 [flip.1] c_List_Oappend(B,A,C)!=A|B=c_List_Olist_ONil(C).
% 28.52/28.66 ** KEPT (pick-wt=14): 135 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|B=D.
% 28.52/28.66 ** KEPT (pick-wt=14): 136 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|A=C.
% 28.52/28.66 ** KEPT (pick-wt=20): 137 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 28.52/28.66 ** KEPT (pick-wt=20): 138 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A)| -c_HOL_Oord__class_Oless(B,D,A).
% 28.52/28.66 ** KEPT (pick-wt=20): 139 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),C),D),A).
% 28.52/28.66 ** KEPT (pick-wt=20): 140 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 28.52/28.66 ** KEPT (pick-wt=20): 141 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),D),A)| -c_HOL_Oord__class_Oless(C,D,A).
% 28.52/28.66 ** KEPT (pick-wt=20): 142 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),D),C),A).
% 28.52/28.66 ** KEPT (pick-wt=30): 144 [copy,143,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__4(A))),v_sko__InductTermi__XIT__Xcases__5(A)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)=A|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Olistsp(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB)| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.66 ** KEPT (pick-wt=12): 145 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|A=D.
% 28.52/28.66 ** KEPT (pick-wt=12): 146 [] c_List_Olist_OCons(A,B,C)!=c_List_Olist_OCons(D,E,C)|B=E.
% 28.52/28.66 ** KEPT (pick-wt=14): 147 [] c_Type_Otyping(A,B,C)| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,D),B))| -c_Type_Otyping(A,D,C).
% 28.52/28.66 ** KEPT (pick-wt=22): 148 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=16): 149 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=12): 150 [] c_List_Omap(A,B,C,D)!=c_List_Olist_ONil(D)|B=c_List_Olist_ONil(C).
% 28.52/28.66 ** KEPT (pick-wt=20): 151 [] 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.
% 28.52/28.66 ** KEPT (pick-wt=20): 152 [] 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.
% 28.52/28.66 ** KEPT (pick-wt=18): 153 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(c_COMBC(c_Lambda_Olift,c_HOL_Ozero__class_Ozero(tc_nat),tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),A,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_List_Olistsp(c_InductTermi_OIT,A,tc_Lambda_OdB).
% 28.52/28.66 ** KEPT (pick-wt=16): 154 [] c_Type_Otyping(c_Type_Oshift(A,B,C,tc_Type_Otype),hAPP(hAPP(c_Lambda_Olift,D),B),E)| -c_Type_Otyping(A,D,E).
% 28.52/28.66 ** KEPT (pick-wt=10): 155 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 28.52/28.66 ** KEPT (pick-wt=22): 156 [] 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)).
% 28.52/28.66 ** KEPT (pick-wt=22): 157 [] 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)).
% 28.52/28.66 ** KEPT (pick-wt=10): 158 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 28.52/28.66 ** KEPT (pick-wt=10): 159 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 28.52/28.66 Following clause subsumed by 159 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 28.52/28.66 ** KEPT (pick-wt=17): 161 [copy,160,factor_simp] hBOOL(hAPP(A,c_ListApplication_Osko__ListApplication__Xlem__1__3(A)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__Xlem__1__1(A)),c_ListApplication_Osko__ListApplication__Xlem__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB))).
% 28.52/28.66 ** KEPT (pick-wt=24): 163 [copy,162,flip.1] hAPP(hAPP(A,B),c_List_Ofoldl(A,C,D,E,E))=c_List_Ofoldl(A,hAPP(hAPP(A,B),C),D,E,E)| -c_OrderedGroup_Osemigroup__add(A,E).
% 28.52/28.66 ** KEPT (pick-wt=5): 164 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 28.52/28.66 ** KEPT (pick-wt=8): 165 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 28.52/28.66 ** KEPT (pick-wt=18): 166 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=8): 167 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 28.52/28.66 ** KEPT (pick-wt=16): 168 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 28.52/28.66 Following clause subsumed by 168 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,c_Lambda_OdB_OVar(E),t_a)))|hBOOL(hAPP(A,hAPP(B,E))).
% 28.52/28.66 ** KEPT (pick-wt=8): 169 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 28.52/28.66 ** KEPT (pick-wt=18): 170 [] 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.
% 28.52/28.66 ** KEPT (pick-wt=18): 171 [] 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.
% 28.52/28.66 ** KEPT (pick-wt=21): 172 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,hAPP(hAPP(c_Lambda_OdB_OApp,E),F),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,E),F))).
% 28.52/28.66 Following clause subsumed by 172 during input processing: 0 [] -hBOOL(hAPP(A,c_Lambda_OdB_OdB__case(B,C,D,hAPP(hAPP(c_Lambda_OdB_OApp,E),F),t_a)))|hBOOL(hAPP(A,hAPP(hAPP(C,E),F))).
% 28.52/28.66 ** KEPT (pick-wt=15): 173 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_OdB_OVar(B)),C)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.66 ** KEPT (pick-wt=15): 174 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(A)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 28.52/28.66 ** KEPT (pick-wt=26): 175 [] 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)).
% 28.52/28.66 ** KEPT (pick-wt=20): 176 [] 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.
% 28.52/28.66 ** KEPT (pick-wt=7): 177 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(A)),B)).
% 28.52/28.66 ** KEPT (pick-wt=13): 178 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=18): 179 [] 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.
% 28.52/28.66 ** KEPT (pick-wt=18): 180 [] 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.
% 28.52/28.66 ** KEPT (pick-wt=14): 181 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=14): 182 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 28.52/28.66 ** KEPT (pick-wt=14): 183 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 28.52/28.66 ** KEPT (pick-wt=23): 184 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=21): 185 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=17): 187 [copy,186,factor_simp] hBOOL(hAPP(A,c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__3(A)))| -hBOOL(hAPP(A,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__1(A)),c_ListApplication_Osko__ListApplication__XApps__dB__induct__1__2(A),tc_Lambda_OdB,tc_Lambda_OdB))).
% 28.52/28.66 ** KEPT (pick-wt=22): 188 [] 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)).
% 28.52/28.66 ** KEPT (pick-wt=13): 189 [] 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.
% 28.52/28.66 ** KEPT (pick-wt=13): 190 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=8): 191 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 28.52/28.66 ** KEPT (pick-wt=15): 192 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=12): 193 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,A),B)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.66 ** KEPT (pick-wt=34): 194 [] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B),C,tc_Lambda_OdB,tc_Lambda_OdB)))| -hBOOL(hAPP(c_InductTermi_OIT,B))| -hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)),C,tc_Lambda_OdB,tc_Lambda_OdB))).
% 28.52/28.66 ** KEPT (pick-wt=39): 196 [copy,195,flip.3] hBOOL(hAPP(c_InductTermi_OIT,c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_sko__InductTermi__XIT__Xcases__4(A)),v_sko__InductTermi__XIT__Xcases__5(A)),c_HOL_Ozero__class_Ozero(tc_nat)),v_sko__InductTermi__XIT__Xcases__6(A),tc_Lambda_OdB,tc_Lambda_OdB)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.66 ** KEPT (pick-wt=5): 197 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 28.52/28.66 ** KEPT (pick-wt=10): 198 [] hAPP(A,B)=C| -c_Type_Otyping(A,c_Lambda_OdB_OVar(B),C).
% 28.52/28.66 ** KEPT (pick-wt=27): 200 [copy,199,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).
% 28.52/28.66 ** KEPT (pick-wt=25): 202 [copy,201,flip.2,flip.3] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|c_Lambda_OdB_OAbs(v_sko__InductTermi__XIT__Xcases__3(A))=A|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.66 ** KEPT (pick-wt=24): 203 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),D)).
% 28.52/28.66 ** KEPT (pick-wt=24): 204 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=24): 206 [copy,205,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)).
% 28.52/28.66 ** KEPT (pick-wt=21): 207 [] hAPP(hAPP(A,B),c_List_Ofoldl(A,C,D,E,E))=c_List_Ofoldl(A,B,D,E,E)| -c_OrderedGroup_Omonoid__add(C,A,E).
% 28.52/28.66 ** KEPT (pick-wt=25): 209 [copy,208,flip.3] hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__5(A)))|hBOOL(hAPP(c_InductTermi_OIT,v_sko__InductTermi__XIT__Xcases__3(A)))|c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_sko__InductTermi__XIT__Xcases__2(A)),v_sko__InductTermi__XIT__Xcases__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.66 ** KEPT (pick-wt=28): 211 [copy,210,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).
% 28.52/28.66 ** KEPT (pick-wt=13): 212 [] 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.
% 28.52/28.66 ** KEPT (pick-wt=13): 213 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=16): 214 [] 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.
% 28.52/28.66 ** KEPT (pick-wt=37): 215 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=9): 216 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.66 ** KEPT (pick-wt=20): 217 [] 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)).
% 28.52/28.66 ** KEPT (pick-wt=20): 218 [] 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)).
% 28.52/28.66 ** KEPT (pick-wt=13): 219 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=13): 220 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B))))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 28.52/28.66 ** KEPT (pick-wt=20): 221 [] 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)).
% 28.52/28.66 ** KEPT (pick-wt=14): 222 [] 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).
% 28.52/28.66 ** KEPT (pick-wt=8): 223 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 28.52/28.66 ** KEPT (pick-wt=16): 224 [] -hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_u____),v_i____))).
% 28.52/28.66 ** KEPT (pick-wt=6): 225 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 28.52/28.66 ** KEPT (pick-wt=6): 226 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 28.52/28.66 ** KEPT (pick-wt=7): 227 [] A=B| -c_fe_qual(A,B,C).
% 28.52/28.66 Following clause subsumed by 119 during input processing: 0 [copy,55,flip.1] c_List_Olist_ONil(A)!=c_List_Olist_OCons(B,C,A).
% 28.52/28.66 Following clause subsumed by 55 during input processing: 0 [copy,119,flip.1] c_List_Olist_OCons(A,B,C)!=c_List_Olist_ONil(C).
% 28.52/28.66 Following clause subsumed by 197 during input processing: 0 [copy,164,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 28.52/28.66 Following clause subsumed by 169 during input processing: 0 [copy,165,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 28.52/28.66 Following clause subsumed by 165 during input processing: 0 [copy,169,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 28.52/28.66 Following clause subsumed by 223 during input processing: 0 [copy,191,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 28.52/28.66 ** KEPT (pick-wt=15): 241 [copy,192,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).
% 28.52/28.66 Following clause subsumed by 164 during input processing: 0 [copy,197,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 28.52/28.66 ** KEPT (pick-wt=14): 242 [copy,222,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).
% 28.52/28.66 Following clause subsumed by 191 during input processing: 0 [copy,223,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 28.52/28.66 Following clause subsumed by 192 during input processing: 0 [copy,241,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).
% 28.52/28.66 Following clause subsumed by 222 during input processing: 0 [copy,242,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).
% 28.52/28.66
% 28.52/28.66 ------------> process sos:
% 28.52/28.66 ** KEPT (pick-wt=3): 243 [] A=A.
% 28.52/28.66 ** KEPT (pick-wt=21): 244 [] 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).
% 28.52/28.66 ---> New Demodulator: 245 [new_demod,244] 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).
% 28.52/28.66 ** KEPT (pick-wt=7): 247 [copy,246,flip.1] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 28.52/28.66 ---> New Demodulator: 248 [new_demod,247] c_List_Oappend(c_List_Olist_ONil(A),B,A)=B.
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,248] B=B.
% 28.52/28.66 ** KEPT (pick-wt=7): 250 [copy,249,flip.1] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 28.52/28.66 ---> New Demodulator: 251 [new_demod,250] c_List_Oappend(A,c_List_Olist_ONil(B),B)=A.
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,248] A=A.
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,251] A=A.
% 28.52/28.66 ** KEPT (pick-wt=8): 252 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 28.52/28.66 Following clause subsumed by 252 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 28.52/28.66 ** KEPT (pick-wt=4): 253 [] c_Type_Otyping(v_ea______,v_ua______,v_T____).
% 28.52/28.66 ** KEPT (pick-wt=5): 254 [] c_List_Olistsp(A,c_List_Olist_ONil(B),B).
% 28.52/28.66 ** KEPT (pick-wt=11): 255 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 28.52/28.66 ** KEPT (pick-wt=16): 257 [copy,256,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_Oliftn(B,C,c_HOL_Ozero__class_Ozero(tc_nat))),B)=c_Lambda_Osubstn(A,C,B).
% 28.52/28.66 ---> New Demodulator: 258 [new_demod,257] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_Oliftn(B,C,c_HOL_Ozero__class_Ozero(tc_nat))),B)=c_Lambda_Osubstn(A,C,B).
% 28.52/28.66 ** KEPT (pick-wt=14): 259 [] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 28.52/28.66 ** KEPT (pick-wt=9): 260 [] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 28.52/28.66 ---> New Demodulator: 261 [new_demod,260] c_List_Ofoldr(A,c_List_Olist_ONil(B),C,B,D)=C.
% 28.52/28.66 ** KEPT (pick-wt=9): 262 [] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 28.52/28.66 ** KEPT (pick-wt=15): 264 [copy,263,flip.1] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 28.52/28.66 ---> New Demodulator: 265 [new_demod,264] c_List_Olist_OCons(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,265] c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C)=c_List_Oappend(c_List_Olist_OCons(A,B,C),D,C).
% 28.52/28.66 ** KEPT (pick-wt=19): 267 [copy,266,flip.1] c_List_Olist_OCons(hAPP(A,B),c_List_Omap(A,C,D,E),E)=c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E).
% 28.52/28.66 ---> New Demodulator: 268 [new_demod,267] c_List_Olist_OCons(hAPP(A,B),c_List_Omap(A,C,D,E),E)=c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,268] c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E)=c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,268] c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E)=c_List_Omap(A,c_List_Olist_OCons(B,C,D),D,E).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,265] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,265] c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D)=c_List_Oappend(c_List_Olist_OCons(A,B,D),C,D).
% 28.52/28.66 ** KEPT (pick-wt=11): 270 [copy,269,unit_del,106] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 28.52/28.66 ---> New Demodulator: 271 [new_demod,270] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,248] c_List_Olist_OCons(A,B,C)=c_List_Olist_OCons(A,B,C).
% 28.52/28.66 ** KEPT (pick-wt=9): 272 [] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,251] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 28.52/28.66 ** KEPT (pick-wt=9): 273 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 28.52/28.66 ---> New Demodulator: 274 [new_demod,273] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 28.52/28.66 ** KEPT (pick-wt=9): 275 [] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 28.52/28.66 ---> New Demodulator: 276 [new_demod,275] hAPP(c_Type_Oshift(A,B,C,D),B)=C.
% 28.52/28.66 ** KEPT (pick-wt=15): 277 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(A)|A=C|c_HOL_Oord__class_Oless(C,A,tc_nat).
% 28.52/28.66 ** KEPT (pick-wt=18): 278 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)),hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat)))).
% 28.52/28.66 ** KEPT (pick-wt=21): 280 [copy,279,flip.1] c_List_Oappend(c_List_Omap(A,B,C,D),c_List_Omap(A,E,C,D),D)=c_List_Omap(A,c_List_Oappend(B,E,C),C,D).
% 28.52/28.66 ---> New Demodulator: 281 [new_demod,280] c_List_Oappend(c_List_Omap(A,B,C,D),c_List_Omap(A,E,C,D),D)=c_List_Omap(A,c_List_Oappend(B,E,C),C,D).
% 28.52/28.66 ** KEPT (pick-wt=11): 282 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 28.52/28.66 Following clause subsumed by 282 during input processing: 0 [] hBOOL(hAPP(hAPP(A,B),C))|c_HOL_Oord__class_Oless(B,C,tc_nat)|C=B|c_HOL_Oord__class_Oless(C,B,tc_nat).
% 28.52/28.66 Following clause subsumed by 282 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 28.52/28.66 ** KEPT (pick-wt=30): 283 [] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C),c_List_Omap(c_COMBC(c_Lambda_Olift,C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 28.52/28.66 ---> New Demodulator: 284 [new_demod,283] hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C),c_List_Omap(c_COMBC(c_Lambda_Olift,C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 28.52/28.66 ** KEPT (pick-wt=9): 285 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 28.52/28.66 ** KEPT (pick-wt=18): 286 [] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(hAPP(C,D),c_Lambda_OdB_OdB__rec(A,B,C,D,E)).
% 28.52/28.66 ** KEPT (pick-wt=7): 287 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 28.52/28.66 ---> New Demodulator: 288 [new_demod,287] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 28.52/28.66 ** KEPT (pick-wt=14): 290 [copy,289,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 28.52/28.66 ---> New Demodulator: 291 [new_demod,290] hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),c_HOL_Ozero__class_Ozero(tc_nat))=c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 28.52/28.66 ** KEPT (pick-wt=20): 293 [copy,292,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).
% 28.52/28.66 ---> New Demodulator: 294 [new_demod,293] 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).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,248] c_List_Olist_OCons(B,C,A)=c_List_Olist_OCons(B,C,A).
% 28.52/28.66 ** KEPT (pick-wt=4): 295 [] c_Type_Otyping(v_e____,v_u____,v_T____).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,251] c_List_Olist_ONil(A)=c_List_Olist_ONil(A).
% 28.52/28.66 ** KEPT (pick-wt=15): 296 [] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 28.52/28.66 ---> New Demodulator: 297 [new_demod,296] c_List_Oappend(c_List_Oappend(A,B,C),D,C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,297] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,297] c_List_Oappend(A,c_List_Oappend(B,D,C),C)=c_List_Oappend(A,c_List_Oappend(B,D,C),C).
% 28.52/28.66 Following clause subsumed by 243 during input processing: 0 [demod,297] c_List_Oappend(A,c_List_Oappend(B,C,D),D)=c_List_Oappend(A,c_List_Oappend(B,C,D),D).
% 28.52/28.66 ** KEPT (pick-wt=17): 299 [copy,298,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).
% 28.52/28.66 ---> New Demodulator: 300 [new_demod,299] 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).
% 28.52/28.66 ** KEPT (pick-wt=29): 301 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C),D)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D)),hAPP(hAPP(hAPP(c_Lambda_Osubst,B),C),D)).
% 28.52/28.66 ** KEPT (pick-wt=10): 302 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 28.52/28.66 ---> New Demodulator: 303 [new_demod,302] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 28.52/28.66 ** KEPT (pick-wt=11): 304 [] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 28.52/28.66 ** KEPT (pick-wt=9): 305 [] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 28.52/28.66 ---> New Demodulator: 306 [new_demod,305] c_List_Ofoldl(A,B,c_List_Olist_ONil(C),D,C)=B.
% 28.52/28.66 ** KEPT (pick-wt=5): 307 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))).
% 28.52/28.66 ** KEPT (pick-wt=23): 308 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C)),hAPP(hAPP(c_Lambda_Olift,B),C)).
% 28.52/28.66 ** KEPT (pick-wt=41): 309 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C),D)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,C,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),D,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 28.52/28.67 ** KEPT (pick-wt=14): 310 [] 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______).
% 28.52/28.67 ** KEPT (pick-wt=18): 311 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(A)|A=C|c_HOL_Oord__class_Oless(C,A,tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=4): 312 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 28.52/28.67 ** KEPT (pick-wt=14): 313 [] 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____).
% 28.52/28.67 ** KEPT (pick-wt=16): 314 [] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 28.52/28.67 Following clause subsumed by 243 during input processing: 0 [demod,306] c_Lambda_OdB_OVar(A)=c_Lambda_OdB_OVar(A).
% 28.52/28.67 ** KEPT (pick-wt=11): 315 [] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 28.52/28.67 Following clause subsumed by 243 during input processing: 0 [demod,303,unit_del,106] B=B.
% 28.52/28.67 ** KEPT (pick-wt=20): 316 [] 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).
% 28.52/28.67 Following clause subsumed by 243 during input processing: 0 [demod,306] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 28.52/28.67 ** KEPT (pick-wt=7): 317 [] c_Type_Otyping(A,c_Lambda_OdB_OVar(B),hAPP(A,B)).
% 28.52/28.67 ** KEPT (pick-wt=30): 319 [copy,318,flip.1] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Lambda_OdB_OdB__rec(D,A,E,B,F)),c_Lambda_OdB_OdB__rec(D,A,E,C,F))=c_Lambda_OdB_OdB__rec(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 28.52/28.67 ---> New Demodulator: 320 [new_demod,319] hAPP(hAPP(hAPP(hAPP(A,B),C),c_Lambda_OdB_OdB__rec(D,A,E,B,F)),c_Lambda_OdB_OdB__rec(D,A,E,C,F))=c_Lambda_OdB_OdB__rec(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 28.52/28.67 ** KEPT (pick-wt=10): 322 [copy,321,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(A),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A.
% 28.52/28.67 ---> New Demodulator: 323 [new_demod,322] c_List_Ofoldl(c_Lambda_OdB_OApp,c_ListApplication_Osko__ListApplication__Xex__head__tail__1__2(A),c_ListApplication_Osko__ListApplication__Xex__head__tail__1__1(A),tc_Lambda_OdB,tc_Lambda_OdB)=A.
% 28.52/28.67 ** KEPT (pick-wt=4): 324 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 28.52/28.67 ** KEPT (pick-wt=20): 326 [copy,325,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(A,B,C)),c_Lambda_Oliftn(A,D,C))=c_Lambda_Oliftn(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C).
% 28.52/28.67 ---> New Demodulator: 327 [new_demod,326] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Oliftn(A,B,C)),c_Lambda_Oliftn(A,D,C))=c_Lambda_Oliftn(A,hAPP(hAPP(c_Lambda_OdB_OApp,B),D),C).
% 28.52/28.67 ** KEPT (pick-wt=13): 328 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 28.52/28.67 ---> New Demodulator: 329 [new_demod,328] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 28.52/28.67 Following clause subsumed by 243 during input processing: 0 [demod,306] c_Lambda_OdB_OAbs(A)=c_Lambda_OdB_OAbs(A).
% 28.52/28.67 ** KEPT (pick-wt=20): 331 [copy,330,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(A,B,C)),c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 28.52/28.67 ---> New Demodulator: 332 [new_demod,331] hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_Osubstn(A,B,C)),c_Lambda_Osubstn(D,B,C))=c_Lambda_Osubstn(hAPP(hAPP(c_Lambda_OdB_OApp,A),D),B,C).
% 28.52/28.67 ** KEPT (pick-wt=21): 333 [] 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).
% 28.52/28.67 ** KEPT (pick-wt=2): 334 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 335 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 336 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 337 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 338 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 339 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 340 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 341 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 342 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 343 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 344 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 345 [] class_Orderings_Opreorder(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 346 [] class_Orderings_Olinorder(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 347 [] class_Orderings_Oorder(tc_nat).
% 28.52/28.67 ** KEPT (pick-wt=2): 348 [] class_Orderings_Opreorder(tc_bool).
% 28.52/28.67 ** KEPT (pick-wt=2): 349 [] class_Orderings_Oorder(tc_bool).
% 28.52/28.67 ** KEPT (pick-wt=4): 350 [] c_fe_qual(A,A,B).
% 28.52/28.67 Following clause subsumed by 243 during input processing: 0 [copy,243,flip.1] A=A.
% 28.52/28.67 243 back subsumes 240.
% 28.52/28.67 243 back subsumes 235.
% 28.52/28.67 243 back subsumes 234.
% 28.52/28.67 >>>> Starting back demodulation with 245.
% 28.52/28.67 >>>> Starting back demodulation with 248.
% 28.52/28.67 >>>> Starting back demodulation with 251.
% 28.52/28.67 ** KEPT (pick-wt=11): 351 [copy,255,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(C,D,A,c_Lambda_OdB_OAbs(B),E).
% 28.52/28.67 >>>> Starting back demodulation with 258.
% 28.52/28.67 ** KEPT (pick-wt=14): 352 [copy,259,flip.1] hAPP(hAPP(A,B),C)=hAPP(c_COMBC(A,C,D,E,F),B).
% 28.52/28.67 >>>> Starting back demodulation with 261.
% 28.52/28.67 Following clause subsumed by 272 during input processing: 0 [copy,262,flip.1] c_List_Olist_ONil(A)=c_List_Omap(B,c_List_Olist_ONil(C),C,A).
% 28.52/28.67 >>>> Starting back demodulation with 265.
% 28.52/28.67 >>>> Starting back demodulation with 268.
% 28.52/28.67 >>>> Starting back demodulation with 271.
% 28.52/28.67 Following clause subsumed by 262 during input processing: 0 [copy,272,flip.1] c_List_Omap(A,c_List_Olist_ONil(B),B,C)=c_List_Olist_ONil(C).
% 28.52/28.67 >>>> Starting back demodulation with 274.
% 28.52/28.67 >>>> Starting back demodulation with 276.
% 28.52/28.67 >>>> Starting back demodulation with 281.
% 28.52/28.67 >>>> Starting back demodulation with 284.
% 28.52/28.67 ** KEPT (pick-wt=18): 353 [copy,286,flip.1] hAPP(hAPP(A,B),c_Lambda_OdB_OdB__rec(C,D,A,B,E))=c_Lambda_OdB_OdB__rec(C,D,A,c_Lambda_OdB_OAbs(B),E).
% 28.52/28.67 >>>> Starting back demodulation with 288.
% 28.52/28.67 >>>> Starting back demodulation with 291.
% 28.52/28.67 >> back demodulating 278 with 291.
% 28.52/28.67 >> back demodulating 196 with 291.
% 28.52/28.67 >> back demodulating 194 with 291.
% 28.52/28.67 >> back demodulating 115 with 291.
% 28.52/28.67 >> back demodulating 42 with 291.
% 28.52/28.67 >> back demodulating 20 with 291.
% 28.52/28.67 >>>> Starting back demodulation with 294.
% 28.52/28.67 >> back demodulating 48 with 294.
% 28.52/28.67 >>>> Starting back demodulation with 297.
% 28.52/28.67 >>>> Starting back demodulation with 300.
% 28.52/28.67 ** KEPT (pick-wt=29): 361 [copy,301,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),hAPP(hAPP(hAPP(c_Lambda_Osubst,D),B),C))=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,A),D)),B),C).
% 28.52/28.67 >>>> Starting back demodulation with 303.
% 28.52/28.67 ** KEPT (pick-wt=11): 362 [copy,304,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__rec(A,C,D,c_Lambda_OdB_OVar(B),E).
% 28.52/28.67 >>>> Starting back demodulation with 306.
% 28.52/28.67 >> back demodulating 299 with 306.
% 28.52/28.67 >> back demodulating 176 with 306.
% 28.52/28.67 ** KEPT (pick-wt=23): 363 [copy,308,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),B)),hAPP(hAPP(c_Lambda_Olift,C),B))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,A),C)),B).
% 28.52/28.67 ** KEPT (pick-wt=41): 364 [copy,309,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,B,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),C,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),D,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,A,D,tc_Lambda_OdB,tc_Lambda_OdB)),B),C).
% 28.52/28.67 ** KEPT (pick-wt=16): 365 [copy,314,flip.1] hAPP(hAPP(A,B),C)=c_Lambda_OdB_OdB__case(D,A,E,hAPP(hAPP(c_Lambda_OdB_OApp,B),C),F).
% 28.52/28.67 ** KEPT (pick-wt=11): 366 [copy,315,flip.1] hAPP(A,B)=c_Lambda_OdB_OdB__case(A,C,D,c_Lambda_OdB_OVar(B),E).
% 28.52/28.67 ** KEPT (pick-wt=20): 367 [copy,316,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).
% 28.52/28.67 >>>> Starting back demodulation with 320.
% 28.52/28.67 >>>> Starting back demodulation with 323.
% 28.52/28.67 >>>> Starting back demodulation with 327.
% 28.52/28.67 >>>> Starting back demodulation with 329.
% 28.52/28.67 >>>> Starting back demodulation with 332.
% 28.80/28.96 ** KEPT (pick-wt=21): 368 [copy,333,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).
% 28.80/28.96 Following clause subsumed by 255 during input processing: 0 [copy,351,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(C,D).
% 28.80/28.96 Following clause subsumed by 259 during input processing: 0 [copy,352,flip.1] hAPP(c_COMBC(A,B,C,D,E),F)=hAPP(hAPP(A,F),B).
% 28.80/28.96 Following clause subsumed by 286 during input processing: 0 [copy,353,flip.1] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OAbs(D),E)=hAPP(hAPP(C,D),c_Lambda_OdB_OdB__rec(A,B,C,D,E)).
% 28.80/28.96 Following clause subsumed by 301 during input processing: 0 [copy,361,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C),D)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D)),hAPP(hAPP(hAPP(c_Lambda_Osubst,B),C),D)).
% 28.80/28.96 Following clause subsumed by 304 during input processing: 0 [copy,362,flip.1] c_Lambda_OdB_OdB__rec(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 28.80/28.96 Following clause subsumed by 308 during input processing: 0 [copy,363,flip.1] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_OdB_OApp,A),B)),C)=hAPP(hAPP(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),C)),hAPP(hAPP(c_Lambda_Olift,B),C)).
% 28.80/28.96 Following clause subsumed by 309 during input processing: 0 [copy,364,flip.1] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_List_Ofoldl(c_Lambda_OdB_OApp,A,B,tc_Lambda_OdB,tc_Lambda_OdB)),C),D)=c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),C),D),c_List_Omap(c_COMBC(c_COMBC(c_Lambda_Osubst,C,tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),D,tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 28.80/28.96 Following clause subsumed by 314 during input processing: 0 [copy,365,flip.1] c_Lambda_OdB_OdB__case(A,B,C,hAPP(hAPP(c_Lambda_OdB_OApp,D),E),F)=hAPP(hAPP(B,D),E).
% 28.80/28.96 Following clause subsumed by 315 during input processing: 0 [copy,366,flip.1] c_Lambda_OdB_OdB__case(A,B,C,c_Lambda_OdB_OVar(D),E)=hAPP(A,D).
% 28.80/28.96 Following clause subsumed by 316 during input processing: 0 [copy,367,flip.1] 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).
% 28.80/28.96 Following clause subsumed by 333 during input processing: 0 [copy,368,flip.1] 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).
% 28.80/28.96
% 28.80/28.96 ======= end of input processing =======
% 28.80/28.96
% 28.80/28.96 =========== start of search ===========
% 28.80/28.96
% 28.80/28.96
% 28.80/28.96 Resetting weight limit to 2.
% 28.80/28.96
% 28.80/28.96
% 28.80/28.96 Resetting weight limit to 2.
% 28.80/28.96
% 28.80/28.96 sos_size=85
% 28.80/28.96
% 28.80/28.96 Search stopped because sos empty.
% 28.80/28.96
% 28.80/28.96
% 28.80/28.96 Search stopped because sos empty.
% 28.80/28.96
% 28.80/28.96 ============ end of search ============
% 28.80/28.96
% 28.80/28.96 -------------- statistics -------------
% 28.80/28.96 clauses given 86
% 28.80/28.96 clauses generated 31330
% 28.80/28.96 clauses kept 306
% 28.80/28.96 clauses forward subsumed 69
% 28.80/28.96 clauses back subsumed 3
% 28.80/28.96 Kbytes malloced 7812
% 28.80/28.96
% 28.80/28.96 ----------- times (seconds) -----------
% 28.80/28.96 user CPU time 0.33 (0 hr, 0 min, 0 sec)
% 28.80/28.96 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 28.80/28.96 wall-clock time 29 (0 hr, 0 min, 29 sec)
% 28.80/28.96
% 28.80/28.96 Process 19651 finished Wed Jul 27 09:33:07 2022
% 28.80/28.96 Otter interrupted
% 28.80/28.96 PROOF NOT FOUND
%------------------------------------------------------------------------------