TSTP Solution File: LCL806-1 by Otter---3.3
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Otter---3.3
% Problem : LCL806-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : otter-tptp-script %s
% Computer : n018.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 13:05:28 EDT 2022
% Result : Unknown 37.28s 37.36s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL806-1 : TPTP v8.1.0. Released v4.1.0.
% 0.03/0.12 % Command : otter-tptp-script %s
% 0.12/0.33 % Computer : n018.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 09:31:16 EDT 2022
% 0.12/0.33 % CPUTime :
% 37.07/37.19 ----- Otter 3.3f, August 2004 -----
% 37.07/37.19 The process was started by sandbox2 on n018.cluster.edu,
% 37.07/37.19 Wed Jul 27 09:31:16 2022
% 37.07/37.19 The command was "./otter". The process ID is 20382.
% 37.07/37.19
% 37.07/37.19 set(prolog_style_variables).
% 37.07/37.19 set(auto).
% 37.07/37.19 dependent: set(auto1).
% 37.07/37.19 dependent: set(process_input).
% 37.07/37.19 dependent: clear(print_kept).
% 37.07/37.19 dependent: clear(print_new_demod).
% 37.07/37.19 dependent: clear(print_back_demod).
% 37.07/37.19 dependent: clear(print_back_sub).
% 37.07/37.19 dependent: set(control_memory).
% 37.07/37.19 dependent: assign(max_mem, 12000).
% 37.07/37.19 dependent: assign(pick_given_ratio, 4).
% 37.07/37.19 dependent: assign(stats_level, 1).
% 37.07/37.19 dependent: assign(max_seconds, 10800).
% 37.07/37.19 clear(print_given).
% 37.07/37.19
% 37.07/37.19 list(usable).
% 37.07/37.19 0 [] A=A.
% 37.07/37.19 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).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat),tc_nat).
% 37.07/37.19 0 [] hBOOL(hAPP(V_P,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(V_a,V_b,tc_nat)| -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(V_a,V_b,tc_nat))).
% 37.07/37.19 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a).
% 37.07/37.19 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat))=V_m|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_HOL_Oord__class_Oless(V_x,V_y,T_a)| -c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a).
% 37.07/37.19 0 [] -class_OrderedGroup_Opordered__ab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|c_HOL_Oord__class_Oless(V_x_H,V_y_H,T_a)| -c_HOL_Oord__class_Oless(V_x,V_y,T_a).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),V_j,tc_nat)| -c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat).
% 37.07/37.19 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,c_HOL_Ozero__class_Ozero(tc_nat),V_i,T_a)=V_i.
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(V_n,V_m,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n.
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_j,V_n,tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat).
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(c_Suc(V_m),c_Suc(V_n),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m.
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 37.07/37.19 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 37.07/37.19 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a.
% 37.07/37.19 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 37.07/37.19 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_l,V_n,tc_nat),c_HOL_Ominus__class_Ominus(V_l,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_l,tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(c_Suc(V_n),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=V_n.
% 37.07/37.19 0 [] -class_OrderedGroup_Ogroup__add(T_a)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)),V_b)=V_a.
% 37.07/37.19 0 [] -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_x),V_b,tc_nat)))|hBOOL(hAPP(V_P,V_x)).
% 37.07/37.19 0 [] -hBOOL(hAPP(V_P,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_b),V_d),V_b,tc_nat)))|hBOOL(hAPP(V_P,V_d)).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat).
% 37.07/37.19 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,c_Suc(V_n),V_i,T_a)=c_Nat_Osemiring__1__class_Oof__nat__aux(V_inc,V_n,hAPP(V_inc,V_i),T_a).
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(V_n,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat)=c_HOL_Ominus__class_Ominus(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat).
% 37.07/37.19 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_xa,V_y,T_a)!=c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)|V_xa=V_y.
% 37.07/37.19 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_x,T_a)!=c_HOL_Ominus__class_Ominus(V_x_H,V_y_H,T_a)|V_x_H=V_y_H.
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Ominus__class_Ominus(V_x,V_y,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=V_y.
% 37.07/37.19 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 37.07/37.19 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=V_b.
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_j,tc_nat),V_k,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_i,V_k,tc_nat),V_j,tc_nat).
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat),c_Suc(V_k),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat).
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(V_m,c_Suc(V_n),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat),V_n,tc_nat).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_n,tc_nat)=V_m.
% 37.07/37.19 0 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m),V_n,tc_nat)=V_m.
% 37.07/37.19 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),V_b),V_b,T_a)=V_a.
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_n,c_Suc(V_i),tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 37.07/37.19 0 [] c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))=V_n| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(T_a),V_e),V_i),V_T),V_j)=hAPP(V_e,c_HOL_Ominus__class_Ominus(V_j,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 37.07/37.19 0 [] c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=V_n| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 37.07/37.19 0 [] V_n=c_Suc(c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(V_m,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),V_n))|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(V_type1)),c_Type_Otype_Otype__size(V_type2))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 37.07/37.19 0 [] c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,V_type1),V_type2),tc_Type_Otype)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(V_type1,tc_Type_Otype)),c_Nat_Osize__class_Osize(V_type2,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_j)),V_u),V_i)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_j,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_i)),V_s),V_k)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 37.07/37.19 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))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)).
% 37.07/37.19 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))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)).
% 37.07/37.19 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(V_i),V_s,V_k)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(V_i,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(V_k,V_i,tc_nat).
% 37.07/37.19 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)=c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(T_a,T_a,T_a),c_HOL_Oplus__class_Oplus(T_a)),c_HOL_Oone__class_Oone(T_a)),V_n,c_HOL_Ozero__class_Ozero(T_a),T_a).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_List_Ofoldl(c_Lambda_OdB_OApp,V_t,V_ts,tc_Lambda_OdB,tc_Lambda_OdB)),V_T)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)).
% 37.07/37.19 0 [] c_Nat_Ocompow(c_Suc(V_n),V_f,T_a,T_a)=c_Fun_Ocomp(V_f,c_Nat_Ocompow(V_n,V_f,T_a,T_a),T_a,T_a,T_a).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.19 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 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).
% 37.07/37.19 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Oone__class_Oone(T_a)!=c_HOL_Ozero__class_Ozero(T_a).
% 37.07/37.19 0 [] V_m=V_n|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat).
% 37.07/37.19 0 [] V_m=V_n| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 37.07/37.19 0 [] V_n=V_m| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_n,V_m,tc_nat).
% 37.07/37.19 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.19 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OVar(V_i),V_k)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_n))|c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 37.07/37.19 0 [] c_Lambda_Oliftn(V_n,c_Lambda_OdB_OAbs(V_s),V_k)=c_Lambda_OdB_OAbs(c_Lambda_Oliftn(V_n,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 37.07/37.19 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).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_l),tc_nat)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 37.07/37.19 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_Suc(V_i),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_j,V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 37.07/37.19 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).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_a,hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),V_a),c_HOL_Oone__class_Oone(T_a)),T_a).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),V_t,V_k)=V_t.
% 37.07/37.19 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_i,tc_nat).
% 37.07/37.19 0 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_i),V_i,tc_nat).
% 37.07/37.19 0 [] c_Suc(V_n)!=V_n.
% 37.07/37.19 0 [] V_n!=c_Suc(V_n).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_k),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_k),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(V_s)),V_k)=c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,V_s),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(hAPP(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)).
% 37.07/37.19 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)).
% 37.07/37.19 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).
% 37.07/37.19 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),V_j)| -c_HOL_Oord__class_Oless(V_j,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_s),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),hAPP(hAPP(c_Lambda_Olift,V_s),V_i)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)))| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(V_i)),V_k)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),c_HOL_Oone__class_Oone(tc_nat)))|c_HOL_Oord__class_Oless(V_i,V_k,tc_nat).
% 37.07/37.19 0 [] V_T=hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t)),c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_Lambda_OdB_OAbs(V_t)),V_T)).
% 37.07/37.19 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)| -hBOOL(hAPP(hAPP(hAPP(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)| -hBOOL(hAPP(hAPP(hAPP(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)).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a).
% 37.07/37.19 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).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oone__class_Oone(T_a),T_a).
% 37.07/37.19 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).
% 37.07/37.19 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),tc_nat).
% 37.07/37.19 0 [] V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 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).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] v_n____=v_i____.
% 37.07/37.19 0 [] c_HOL_Oone__class_Oone(tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.19 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).
% 37.07/37.19 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H.
% 37.07/37.19 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y.
% 37.07/37.19 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).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] c_Lambda_Oliftn(c_Suc(V_n),V_t,V_k)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(V_n,V_t,V_k)),V_k).
% 37.07/37.19 0 [] V_x!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_a)|V_a=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=V_m|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 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).
% 37.07/37.19 0 [] -class_Nat_Osemiring__char__0(T_a)|c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)!=c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a)|V_m=V_n.
% 37.07/37.19 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)).
% 37.07/37.19 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).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_l)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_m).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 0 [] c_Lambda_Osubstn(c_Lambda_OdB_OAbs(V_t),V_s,V_k)=c_Lambda_OdB_OAbs(c_Lambda_Osubstn(V_t,V_s,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_j),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),V_m),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_j),V_k,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_z,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_x,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_x)),tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_i)),tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_i),V_m)),tc_nat).
% 37.07/37.19 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m).
% 37.07/37.19 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n)=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n))=c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_x),V_x)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(V_r,T_a),V_a),V_a)).
% 37.07/37.19 0 [] c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n),V_f,T_a,T_a)=c_Fun_Ocomp(c_Nat_Ocompow(V_m,V_f,T_a,T_a),c_Nat_Ocompow(V_n,V_f,T_a,T_a),T_a,T_a,T_a).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.19 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),V_n).
% 37.07/37.19 0 [] c_Suc(V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),c_HOL_Oone__class_Oone(tc_nat)).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 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).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),V_z))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_y),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)),V_k)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 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.
% 37.07/37.19 0 [] hAPP(c_COMBK(V_P,T_a,T_b),V_Q)=V_P.
% 37.07/37.19 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 37.07/37.19 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),T_a)=c_HOL_Oone__class_Oone(T_a).
% 37.07/37.19 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)|c_HOL_Ozero__class_Ozero(T_a)!=c_HOL_Oone__class_Oone(T_a).
% 37.07/37.19 0 [] hAPP(V_f,hAPP(c_Nat_Ocompow(V_n,V_f,T_a,T_a),V_x))=hAPP(c_Nat_Ocompow(V_n,V_f,T_a,T_a),hAPP(V_f,V_x)).
% 37.07/37.19 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.19 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Nat_Osemiring__1__class_Oof__nat(c_Suc(V_m),T_a)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_Oof__nat(V_m,T_a)).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(V_m)),V_n)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_Suc(V_n)).
% 37.07/37.19 0 [] v_T____=hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),V_n,tc_nat)|c_Suc(V_m)=V_n| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_y)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),V_z)|V_y=V_z.
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_k)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_n),V_k)|V_m=V_n.
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_m)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),V_n)|V_m=V_n.
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_v),V_i)),c_Suc(V_j))),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_u),V_v),V_j)),V_i)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)),V_v),V_j)| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_j),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 37.07/37.19 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.
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),V_n)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_x,V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat).
% 37.07/37.19 0 [] -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_m),tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 37.07/37.19 0 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),c_Suc(V_k))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_i)| -c_HOL_Oord__class_Oless(V_i,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),hAPP(hAPP(c_HOL_Oplus__class_Oplus(T_a),c_HOL_Oone__class_Oone(T_a)),c_HOL_Oone__class_Oone(T_a)),T_a).
% 37.07/37.19 0 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(V_r,T_a),T_a)=c_Transitive__Closure_Ortranclp(V_r,T_a).
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 0 [] V_x=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_x),c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),V_n)=V_n.
% 37.07/37.19 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_m),c_HOL_Ozero__class_Ozero(tc_nat))=V_m.
% 37.07/37.19 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)).
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 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)).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_Suc(V_x),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_n,tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat).
% 37.07/37.19 0 [] c_HOL_Oord__class_Oless(c_Suc(V_m),c_Suc(V_n),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 0 [] hAPP(c_Fun_Ocomp(c_COMBK(V_c,T_b,T_c),V_f,T_c,T_b,t_a),v_x)=V_c.
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_u),c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_T)).
% 37.07/37.19 0 [] c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),V_f,T_a,T_a)=c_Fun_Oid(T_a).
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(V_t)),V_s),V_k)=c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),hAPP(hAPP(c_Lambda_Olift,V_s),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),V_k),c_HOL_Oone__class_Oone(tc_nat)))).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t_H),V_T))| -hBOOL(hAPP(hAPP(hAPP(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)).
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(c_Type_Oshift(T_a),hAPP(hAPP(hAPP(c_Type_Oshift(T_a),V_e),V_i),V_U)),c_HOL_Ozero__class_Ozero(tc_nat)),V_T)=hAPP(hAPP(hAPP(c_Type_Oshift(T_a),hAPP(hAPP(hAPP(c_Type_Oshift(T_a),V_e),c_HOL_Ozero__class_Ozero(tc_nat)),V_T)),c_Suc(V_i)),V_U).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(V_T,V_e,V_t))),V_t),c_Type_Osko__Type__Xtyping__elims__3__2(V_T,V_e,V_t)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_Lambda_OdB_OAbs(V_t)),V_T)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(V_e,V_t))),V_t),c_Type_Osko__Type__Xabs__typeE__1__2(V_e,V_t)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_Lambda_OdB_OAbs(V_t)),V_T)).
% 37.07/37.19 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))| -hBOOL(hAPP(hAPP(hAPP(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)| -hBOOL(hAPP(hAPP(hAPP(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)).
% 37.07/37.19 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))| -hBOOL(hAPP(hAPP(hAPP(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)).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(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)| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),c_List_Ofoldr(c_Type_Otype_OFun,V_Ts,V_T,tc_Type_Otype,tc_Type_Otype))).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_Lambda_OdB_OVar(v_n____)),hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype)))).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 0 [] c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____).
% 37.07/37.19 0 [] V_T=V_U| -hBOOL(hAPP(hAPP(hAPP(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))| -hBOOL(hAPP(hAPP(hAPP(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)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(V_T,V_e,V_t,V_u)),V_T)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),hAPP(hAPP(c_Lambda_OdB_OApp,V_t),V_u)),V_T)).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat).
% 37.07/37.19 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Nat_Osemiring__1__class_Oof__nat(V_n,T_a),T_a).
% 37.07/37.19 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(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 37.07/37.19 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))).
% 37.07/37.19 0 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB).
% 37.07/37.19 0 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_List_Olistsp(c_InductTermi_OIT,V_ts,tc_Lambda_OdB).
% 37.07/37.19 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(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),V_u)),V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 37.07/37.19 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H)!=c_Lambda_OdB_OVar(V_nat).
% 37.07/37.19 0 [] hAPP(c_Fun_Oid(T_a),V_x)=V_x.
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 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).
% 37.07/37.19 0 [] c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),V_i),V_U),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(V_e,V_ts,V_Ts).
% 37.07/37.19 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)).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a)!=c_Fun_Ocomp(c_Fun_Oid(T_b),V_c,T_b,T_b,T_a)|hAPP(V_a,hAPP(V_b,V_v))=hAPP(V_c,V_v).
% 37.07/37.19 0 [] c_List_Omap(V_f,c_List_Omap(V_g,V_xs,T_c,T_b),T_b,T_a)=c_List_Omap(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_xs,T_c,T_a).
% 37.07/37.19 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.
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(c_COMBC(T_b,T_c,T_a),V_P),V_Q),V_R)=hAPP(hAPP(V_P,V_R),V_Q).
% 37.07/37.19 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 37.07/37.19 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 0 [] c_Fun_Ocomp(c_Fun_Oid(T_b),V_g,T_b,T_b,T_a)=V_g.
% 37.07/37.19 0 [] c_Fun_Ocomp(V_f,c_Fun_Oid(T_a),T_a,T_b,T_a)=V_f.
% 37.07/37.19 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).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x)=hAPP(V_f,hAPP(V_g,V_x)).
% 37.07/37.19 0 [] hAPP(V_a,hAPP(V_b,V_v))=hAPP(c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a),V_v).
% 37.07/37.19 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OAbs(V_dB_H).
% 37.07/37.19 0 [] c_Lambda_OdB_OAbs(V_dB)!=c_Lambda_OdB_OAbs(V_dB_H)|V_dB=V_dB_H.
% 37.07/37.19 0 [] c_Lambda_OdB_OVar(V_nat)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1_H),V_dB2_H).
% 37.07/37.19 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat).
% 37.07/37.19 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat).
% 37.07/37.19 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 37.07/37.19 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 37.07/37.19 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a).
% 37.07/37.19 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)))).
% 37.07/37.19 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.
% 37.07/37.19 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).
% 37.07/37.19 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.
% 37.07/37.19 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).
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_env),hAPP(hAPP(c_Lambda_OdB_OApp,V_s),V_t)),V_U))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_env),V_t),V_T))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_env),V_s),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U))).
% 37.07/37.19 0 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(V_i)),V_t)).
% 37.07/37.19 0 [] hAPP(c_Fun_Ofcomp(V_f,V_g,T_b,T_c,T_a),V_x)=hAPP(V_g,hAPP(V_f,V_x)).
% 37.07/37.19 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).
% 37.07/37.19 0 [] c_Fun_Ocomp(V_f,c_Fun_Ocomp(V_g,V_h,T_d,T_c,T_a),T_c,T_b,T_a)=c_Fun_Ocomp(c_Fun_Ocomp(V_f,V_g,T_c,T_b,T_d),V_h,T_d,T_b,T_a).
% 37.07/37.19 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 37.07/37.19 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).
% 37.07/37.19 0 [] c_Fun_Ofcomp(V_f,c_Fun_Oid(T_b),T_a,T_b,T_b)=V_f.
% 37.07/37.19 0 [] c_Fun_Ofcomp(c_Fun_Oid(T_a),V_g,T_a,T_a,T_b)=V_g.
% 37.07/37.19 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.
% 37.07/37.19 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.
% 37.07/37.19 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2).
% 37.07/37.19 0 [] c_Lambda_OdB_OVar(V_nat)!=c_Lambda_OdB_OVar(V_nat_H)|V_nat=V_nat_H.
% 37.07/37.19 0 [] hAPP(hAPP(c_Lambda_OdB_OApp,V_dB1),V_dB2)!=c_Lambda_OdB_OAbs(V_dB_H).
% 37.07/37.19 0 [] c_Lambda_OdB_OAbs(V_dB_H)!=c_Lambda_OdB_OVar(V_nat).
% 37.07/37.19 0 [] c_Fun_Ocomp(V_a,V_b,T_c,T_b,T_a)!=c_Fun_Ocomp(V_c,V_d,T_d,T_b,T_a)|hAPP(V_a,hAPP(V_b,V_v))=hAPP(V_c,hAPP(V_d,V_v)).
% 37.07/37.19 0 [] hAPP(V_f,hAPP(V_g,V_x))!=hAPP(V_f_H,hAPP(V_g_H,V_x_H))|hAPP(c_Fun_Ocomp(V_f,V_g,T_b,T_a,T_c),V_x)=hAPP(c_Fun_Ocomp(V_f_H,V_g_H,T_d,T_a,T_e),V_x_H).
% 37.07/37.19 0 [] c_Fun_Ofcomp(c_Fun_Ofcomp(V_f,V_g,T_a,T_d,T_c),V_h,T_a,T_c,T_b)=c_Fun_Ofcomp(V_f,c_Fun_Ofcomp(V_g,V_h,T_d,T_c,T_b),T_a,T_d,T_b).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 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).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),V_i),V_U)),hAPP(hAPP(c_Lambda_Olift,V_t),V_i)),V_T))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),V_T)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)).
% 37.07/37.19 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H)).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t_H),V_T))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,V_t),V_t_H))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_t),V_T)).
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(V_k)),V_u),V_k)=V_u.
% 37.07/37.19 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)).
% 37.07/37.19 0 [] hAPP(c_Fun_Ocomp(V_f,V_g,T_c,T_b,t_a),v_x)=hAPP(V_f,hAPP(V_g,v_x)).
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(T_a),V_e),V_i),V_T),V_j)=hAPP(V_e,V_j)| -c_HOL_Oord__class_Oless(V_j,V_i,tc_nat).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)).
% 37.07/37.19 0 [] hAPP(c_Fun_Oid(t_a),v_x)=v_x.
% 37.07/37.19 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,V_t),V_i)))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 37.07/37.19 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)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_u),V_T2))| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),V_i),V_T2)),V_t),V_Ta))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 37.07/37.19 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)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_u),V_T1))| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),V_i),V_T1)),V_t),V_Ta))| -hBOOL(hAPP(c_InductTermi_OIT,V_t)).
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(T_a),V_e),V_x),V_T),V_x)=V_T.
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_env),c_Lambda_OdB_OAbs(V_t)),hAPP(hAPP(c_Type_Otype_OFun,V_T),V_U)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_env),c_HOL_Ozero__class_Ozero(tc_nat)),V_T)),V_t),V_U)).
% 37.07/37.19 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(V_n))).
% 37.07/37.19 0 [] hAPP(V_e,V_i)=V_T| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),c_Lambda_OdB_OVar(V_i)),V_T)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)).
% 37.07/37.19 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)).
% 37.07/37.19 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))).
% 37.07/37.19 0 [] c_Type_Otypings(V_e,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),V_u)),V_i),V_ts,tc_Lambda_OdB,tc_Lambda_OdB),V_Ts)| -c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e),V_i),V_T),V_ts,V_Ts)| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e),V_u),V_T)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_env),c_Lambda_OdB_OVar(V_x)),hAPP(V_env,V_x))).
% 37.07/37.19 0 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(V_r)))| -hBOOL(hAPP(c_InductTermi_OIT,V_r)).
% 37.07/37.19 0 [] hAPP(c_Fun_Ofcomp(V_f,V_g,t_a,T_c,T_b),v_x)=hAPP(V_g,hAPP(V_f,v_x)).
% 37.07/37.19 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 37.07/37.19 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,V_t),V_k)),V_s),V_k)=V_t.
% 37.07/37.19 0 [] -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e_H),V_u),V_U))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_e_H),V_i),V_U)),V_t),V_T))|hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_e_H),hAPP(hAPP(hAPP(c_Lambda_Osubst,V_t),V_u),V_i)),V_T)).
% 37.07/37.19 0 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB).
% 37.07/37.19 0 [] c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))).
% 37.07/37.19 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),V_u),V_ia)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,V_ea),V_u),v_T____))| -hBOOL(hAPP(c_InductTermi_OIT,V_u))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),V_ea),V_ia),v_T____)),v_b____),V_T_H)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)).
% 37.07/37.19 0 [] hBOOL(hAPP(c_InductTermi_OIT,v_xb)).
% 37.07/37.19 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)).
% 37.07/37.19 0 [] -hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))).
% 37.07/37.19 0 [] class_Orderings_Opreorder(tc_fun(T_2,T_1))| -class_Orderings_Opreorder(T_1).
% 37.07/37.19 0 [] class_Orderings_Oorder(tc_fun(T_2,T_1))| -class_Orderings_Oorder(T_1).
% 37.07/37.19 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 37.07/37.19 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 37.07/37.19 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 37.07/37.19 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 37.07/37.19 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 37.07/37.19 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 37.07/37.19 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 37.07/37.19 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 37.07/37.19 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 37.07/37.19 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 37.07/37.19 0 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 37.07/37.19 0 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 37.07/37.19 0 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 37.07/37.19 0 [] class_Nat_Osemiring__char__0(tc_nat).
% 37.07/37.19 0 [] class_Orderings_Opreorder(tc_nat).
% 37.07/37.19 0 [] class_Orderings_Olinorder(tc_nat).
% 37.07/37.19 0 [] class_Orderings_Oorder(tc_nat).
% 37.07/37.19 0 [] class_Orderings_Opreorder(tc_bool).
% 37.07/37.19 0 [] class_Orderings_Oorder(tc_bool).
% 37.07/37.19 0 [] c_fe_qual(V_x,V_x,T_a).
% 37.07/37.19 0 [] V_X=V_Y| -c_fe_qual(V_X,V_Y,T_a).
% 37.07/37.19 end_of_list.
% 37.07/37.19
% 37.07/37.19 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6.
% 37.07/37.19
% 37.07/37.19 This ia a non-Horn set with equality. The strategy will be
% 37.07/37.19 Knuth-Bendix, ordered hyper_res, factoring, and unit
% 37.07/37.19 deletion, with positive clauses in sos and nonpositive
% 37.07/37.19 clauses in usable.
% 37.07/37.19
% 37.07/37.19 dependent: set(knuth_bendix).
% 37.07/37.19 dependent: set(anl_eq).
% 37.07/37.19 dependent: set(para_from).
% 37.07/37.19 dependent: set(para_into).
% 37.07/37.19 dependent: clear(para_from_right).
% 37.07/37.19 dependent: clear(para_into_right).
% 37.07/37.19 dependent: set(para_from_vars).
% 37.07/37.19 dependent: set(eq_units_both_ways).
% 37.07/37.19 dependent: set(dynamic_demod_all).
% 37.07/37.19 dependent: set(dynamic_demod).
% 37.07/37.19 dependent: set(order_eq).
% 37.07/37.19 dependent: set(back_demod).
% 37.07/37.19 dependent: set(lrpo).
% 37.07/37.19 dependent: set(hyper_res).
% 37.07/37.19 dependent: set(unit_deletion).
% 37.07/37.19 dependent: set(factor).
% 37.07/37.19
% 37.07/37.19 ------------> process usable:
% 37.07/37.19 ** KEPT (pick-wt=21): 1 [] 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).
% 37.07/37.19 ** KEPT (pick-wt=17): 2 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 37.07/37.19 ** KEPT (pick-wt=12): 3 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,A,tc_nat).
% 37.07/37.19 ** KEPT (pick-wt=12): 4 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ominus__class_Ominus(B,A,tc_nat),tc_nat).
% 37.07/37.19 ** KEPT (pick-wt=16): 5 [] hBOOL(hAPP(A,c_HOL_Ozero__class_Ozero(tc_nat)))| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat))).
% 37.07/37.19 ** KEPT (pick-wt=14): 6 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,C,A).
% 37.07/37.19 ** KEPT (pick-wt=14): 7 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ozero__class_Ozero(A),A).
% 37.07/37.19 ** KEPT (pick-wt=19): 8 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(D,E,A).
% 37.07/37.19 ** KEPT (pick-wt=19): 9 [] -class_OrderedGroup_Opordered__ab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,E,A)|c_HOL_Oord__class_Oless(D,E,A)| -c_HOL_Oord__class_Oless(B,C,A).
% 37.07/37.19 ** KEPT (pick-wt=16): 10 [] c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 37.07/37.19 ** KEPT (pick-wt=16): 11 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,tc_nat)| -c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat).
% 37.07/37.19 ** KEPT (pick-wt=10): 12 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat__aux(B,c_HOL_Ozero__class_Ozero(tc_nat),C,A)=C.
% 37.07/37.19 ** KEPT (pick-wt=17): 13 [] c_HOL_Ominus__class_Ominus(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Ominus__class_Ominus(B,A,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=A.
% 37.07/37.19 ** KEPT (pick-wt=11): 14 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 37.07/37.19 ** KEPT (pick-wt=11): 15 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 37.07/37.19 ** KEPT (pick-wt=9): 16 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 37.07/37.19 ** KEPT (pick-wt=9): 17 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A)=B.
% 37.07/37.19 Following clause subsumed by 16 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 37.07/37.19 ** KEPT (pick-wt=9): 18 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A).
% 37.07/37.19 ** KEPT (pick-wt=18): 19 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_HOL_Ominus__class_Ominus(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(C,A,tc_nat)| -c_HOL_Oord__class_Oless(C,B,tc_nat).
% 37.07/37.19 ** KEPT (pick-wt=13): 20 [] -class_OrderedGroup_Ogroup__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ominus__class_Ominus(B,C,A)),C)=B.
% 37.07/37.19 ** KEPT (pick-wt=16): 21 [] -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),B,tc_nat)))|hBOOL(hAPP(A,C)).
% 37.07/37.19 Following clause subsumed by 21 during input processing: 0 [] -hBOOL(hAPP(A,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),B,tc_nat)))|hBOOL(hAPP(A,C)).
% 37.07/37.20 ** KEPT (pick-wt=16): 22 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat__aux(B,c_Suc(C),D,A)=c_Nat_Osemiring__1__class_Oof__nat__aux(B,C,hAPP(B,D),A).
% 37.07/37.20 ** KEPT (pick-wt=14): 23 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,D,A)|B=C.
% 37.07/37.20 ** KEPT (pick-wt=14): 24 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)!=c_HOL_Ominus__class_Ominus(C,D,A)|C=D.
% 37.07/37.20 ** KEPT (pick-wt=14): 25 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 37.07/37.20 ** KEPT (pick-wt=12): 26 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 37.07/37.20 ** KEPT (pick-wt=12): 27 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C.
% 37.07/37.20 ** KEPT (pick-wt=20): 28 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=13): 29 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),C),C,A)=B.
% 37.07/37.20 ** KEPT (pick-wt=13): 30 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,c_Suc(B),tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=14): 31 [] c_Suc(c_HOL_Ominus__class_Ominus(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=22): 32 [] hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(A),B),C),D),E)=hAPP(B,c_HOL_Ominus__class_Ominus(E,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(C,E,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=13): 33 [] c_Suc(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 37.07/37.20 Following clause subsumed by 33 during input processing: 0 [flip.1] c_Suc(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=24): 35 [copy,34,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)).
% 37.07/37.20 ** KEPT (pick-wt=19): 36 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(C,A,tc_nat).
% 37.07/37.20 Following clause subsumed by 36 during input processing: 0 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),C)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(C,A,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=21): 37 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xlist__app__typeE__1__1(C,A,D,B))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_List_Ofoldl(c_Lambda_OdB_OApp,D,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 37.07/37.20 ** KEPT (pick-wt=21): 38 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xlist__app__typeD__1__1(C,A,D,B))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_List_Ofoldl(c_Lambda_OdB_OApp,D,B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 37.07/37.20 ** KEPT (pick-wt=16): 39 [] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,C)=c_Lambda_OdB_OVar(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat))| -c_HOL_Oord__class_Oless(C,A,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=21): 40 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(B,A)=c_Nat_Osemiring__1__class_Oof__nat__aux(hAPP(hAPP(c_COMBC(A,A,A),c_HOL_Oplus__class_Oplus(A)),c_HOL_Oone__class_Oone(A)),B,c_HOL_Ozero__class_Ozero(A),A).
% 37.07/37.20 ** KEPT (pick-wt=30): 41 [] hBOOL(hAPP(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 37.07/37.20 ** KEPT (pick-wt=30): 42 [] hBOOL(hAPP(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_List_Ofoldl(c_Lambda_OdB_OApp,B,D,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 37.07/37.20 ** KEPT (pick-wt=14): 43 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,C),D)).
% 37.07/37.20 ** KEPT (pick-wt=20): 44 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.20 ** KEPT (pick-wt=18): 45 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=23): 46 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=7): 48 [copy,47,flip.2] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 37.07/37.20 ** KEPT (pick-wt=12): 49 [] A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=12): 50 [] A=B| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 37.07/37.20 Following clause subsumed by 49 during input processing: 0 [] A=B| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=24): 51 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=22): 52 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D),tc_nat)| -c_HOL_Oord__class_Oless(B,D,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=5): 53 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 Following clause subsumed by 53 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=13): 54 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)| -c_HOL_Oord__class_Oless(C,B,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=19): 56 [copy,55,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).
% 37.07/37.20 ** KEPT (pick-wt=12): 57 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Oone__class_Oone(A)),A).
% 37.07/37.20 ** KEPT (pick-wt=26): 58 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=9): 59 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=9): 60 [] -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=4): 61 [] c_Suc(A)!=A.
% 37.07/37.20 Following clause subsumed by 61 during input processing: 0 [flip.1] c_Suc(A)!=A.
% 37.07/37.20 ** KEPT (pick-wt=20): 62 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=20): 63 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=20): 64 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=20): 65 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=20): 66 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=20): 67 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=18): 68 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=18): 69 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=18): 70 [] c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=9): 71 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=9): 72 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=21): 73 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_Nat_Osemiring__1__class_Oof__nat(B,A)),c_Nat_Osemiring__1__class_Oof__nat(C,A)).
% 37.07/37.20 ** KEPT (pick-wt=20): 74 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.20 ** KEPT (pick-wt=18): 75 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=22): 76 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=22): 77 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),D))| -hBOOL(hAPP(hAPP(A,E),D))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),E)).
% 37.07/37.20 ** KEPT (pick-wt=32): 78 [] hBOOL(hAPP(hAPP(hAPP(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)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(B),D,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 37.07/37.20 ** KEPT (pick-wt=14): 79 [] 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).
% 37.07/37.20 ** KEPT (pick-wt=43): 80 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),D)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)))),hAPP(hAPP(c_Lambda_Olift,B),D)),C)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=43): 81 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C)),D)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),D)),hAPP(hAPP(c_Lambda_Olift,B),D)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)))| -c_HOL_Oord__class_Oless(D,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=22): 83 [copy,82,flip.1] hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__3__1(A,B,C)),c_Type_Osko__Type__Xtyping__elims__3__2(A,B,C))=A| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,B),c_Lambda_OdB_OAbs(C)),A)).
% 37.07/37.20 ** KEPT (pick-wt=49): 85 [copy,84,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| -hBOOL(hAPP(hAPP(hAPP(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)| -hBOOL(hAPP(hAPP(hAPP(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)).
% 37.07/37.20 ** KEPT (pick-wt=17): 86 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=17): 87 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=9): 88 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_HOL_Ozero__class_Ozero(A),A).
% 37.07/37.20 ** KEPT (pick-wt=22): 89 [] -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).
% 37.07/37.20 ** 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).
% 37.07/37.20 ** 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).
% 37.07/37.20 ** 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).
% 37.07/37.20 ** 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).
% 37.07/37.20 ** KEPT (pick-wt=8): 94 [] -class_Ring__and__Field_Oordered__semidom(A)| -c_HOL_Oord__class_Oless(c_HOL_Oone__class_Oone(A),c_HOL_Ozero__class_Ozero(A),A).
% 37.07/37.20 ** KEPT (pick-wt=22): 95 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=8): 96 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oone__class_Oone(A),A).
% 37.07/37.20 ** KEPT (pick-wt=20): 97 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=9): 98 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Ozero__class_Ozero(tc_nat),A)=c_HOL_Ozero__class_Ozero(A).
% 37.07/37.20 ** KEPT (pick-wt=14): 99 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=14): 100 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_Nat_Osemiring__1__class_Oof__nat(B,A),c_Nat_Osemiring__1__class_Oof__nat(C,A),A).
% 37.07/37.20 ** KEPT (pick-wt=15): 101 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=15): 102 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=20): 103 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A),tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=10): 104 [] A=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=32): 105 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=24): 106 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=24): 107 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=22): 108 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=13): 109 [] 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.
% 37.07/37.20 ** KEPT (pick-wt=18): 110 [] 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.
% 37.07/37.20 ** KEPT (pick-wt=18): 111 [] 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.
% 37.07/37.20 ** KEPT (pick-wt=13): 112 [] 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).
% 37.07/37.20 ** KEPT (pick-wt=18): 113 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=17): 114 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=8): 115 [] c_Suc(A)!=c_Suc(B)|A=B.
% 37.07/37.20 Following clause subsumed by 115 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B.
% 37.07/37.20 ** KEPT (pick-wt=15): 116 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=13): 117 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=13): 118 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=12): 120 [copy,119,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 Following clause subsumed by 120 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=16): 122 [copy,121,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).
% 37.07/37.20 ** KEPT (pick-wt=12): 123 [] -class_Nat_Osemiring__char__0(A)|c_Nat_Osemiring__1__class_Oof__nat(B,A)!=c_Nat_Osemiring__1__class_Oof__nat(C,A)|B=C.
% 37.07/37.20 ** KEPT (pick-wt=27): 125 [copy,124,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).
% 37.07/37.20 ** KEPT (pick-wt=15): 126 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=21): 127 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),D)| -c_HOL_Oord__class_Oless(C,B,tc_nat)|c_HOL_Oord__class_Oless(A,D,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=15): 128 [] -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).
% 37.07/37.20 Following clause subsumed by 126 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).
% 37.07/37.20 ** KEPT (pick-wt=13): 129 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=13): 130 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=13): 131 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),B,tc_nat).
% 37.07/37.20 Following clause subsumed by 129 during input processing: 0 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat).
% 37.07/37.20 Following clause subsumed by 130 during input processing: 0 [] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 37.07/37.20 Following clause subsumed by 53 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 Following clause subsumed by 53 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=24): 132 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=13): 133 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=25): 135 [copy,134,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)).
% 37.07/37.20 ** KEPT (pick-wt=25): 136 [] -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)).
% 37.07/37.20 ** KEPT (pick-wt=25): 137 [] -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)).
% 37.07/37.20 ** KEPT (pick-wt=25): 138 [] -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)).
% 37.07/37.20 ** KEPT (pick-wt=25): 139 [] -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)).
% 37.07/37.20 Following clause subsumed by 135 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)).
% 37.07/37.20 ** KEPT (pick-wt=25): 140 [] -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).
% 37.07/37.20 ** KEPT (pick-wt=25): 141 [] -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)).
% 37.07/37.20 Following clause subsumed by 135 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)).
% 37.07/37.20 ** KEPT (pick-wt=28): 142 [] -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.
% 37.07/37.20 ** KEPT (pick-wt=9): 143 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_HOL_Oone__class_Oone(tc_nat),A)=c_HOL_Oone__class_Oone(A).
% 37.07/37.20 Following clause subsumed by 48 during input processing: 0 [] -class_Ring__and__Field_Ozero__ne_q__one(A)|c_HOL_Ozero__class_Ozero(A)!=c_HOL_Oone__class_Oone(A).
% 37.07/37.20 ** KEPT (pick-wt=19): 144 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=19): 145 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.20 ** KEPT (pick-wt=16): 146 [] -class_Ring__and__Field_Osemiring__1(A)|c_Nat_Osemiring__1__class_Oof__nat(c_Suc(B),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_Nat_Osemiring__1__class_Oof__nat(B,A)).
% 37.07/37.20 ** KEPT (pick-wt=23): 148 [copy,147,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).
% 37.07/37.20 ** KEPT (pick-wt=13): 149 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)|c_Suc(A)=B| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=16): 150 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 37.07/37.20 ** KEPT (pick-wt=16): 151 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B)|A=C.
% 37.07/37.20 Following clause subsumed by 150 during input processing: 0 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)|B=C.
% 37.07/37.20 ** KEPT (pick-wt=20): 152 [] -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.
% 37.07/37.20 ** KEPT (pick-wt=18): 153 [] -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.
% 37.07/37.20 ** KEPT (pick-wt=18): 154 [] -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.
% 37.07/37.20 ** KEPT (pick-wt=18): 155 [] -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.
% 37.07/37.20 ** KEPT (pick-wt=48): 156 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),C)),c_Suc(D))),hAPP(hAPP(hAPP(c_Lambda_Osubst,E),B),D)),C)=hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),E),C)),B),D)| -c_HOL_Oord__class_Oless(C,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),D),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=16): 157 [] 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.
% 37.07/37.20 ** KEPT (pick-wt=19): 158 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=19): 159 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.20 ** KEPT (pick-wt=35): 160 [] -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)).
% 37.07/37.20 ** KEPT (pick-wt=9): 161 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=30): 162 [] hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,A),B)),c_Suc(C))=hAPP(hAPP(c_Lambda_Olift,hAPP(hAPP(c_Lambda_Olift,A),C)),B)| -c_HOL_Oord__class_Oless(B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat)),tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=14): 163 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Oone__class_Oone(A)),c_HOL_Oone__class_Oone(A)),A).
% 37.07/37.20 ** KEPT (pick-wt=11): 164 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 37.07/37.20 ** KEPT (pick-wt=11): 165 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 37.07/37.20 ** KEPT (pick-wt=13): 167 [copy,166,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.
% 37.07/37.20 ** KEPT (pick-wt=11): 168 [] -class_OrderedGroup_Ocomm__monoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 37.07/37.20 ** KEPT (pick-wt=11): 169 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),c_HOL_Ozero__class_Ozero(A)),B)=B.
% 37.07/37.20 ** KEPT (pick-wt=11): 170 [] -class_OrderedGroup_Omonoid__add(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 37.07/37.20 ** KEPT (pick-wt=11): 171 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|hAPP(hAPP(c_HOL_Oplus__class_Oplus(A),B),c_HOL_Ozero__class_Ozero(A))=B.
% 37.07/37.20 Following clause subsumed by 164 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.
% 37.07/37.20 ** KEPT (pick-wt=10): 172 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=10): 173 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat).
% 37.07/37.20 Following clause subsumed by 172 during input processing: 0 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=12): 174 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(B)| -c_HOL_Oord__class_Oless(B,C,tc_nat).
% 37.07/37.20 ** KEPT (pick-wt=26): 175 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=28): 176 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=28): 177 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=13): 178 [] 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.
% 37.07/37.20 ** KEPT (pick-wt=18): 179 [] 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.
% 37.07/37.20 ** KEPT (pick-wt=18): 180 [] 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.
% 37.07/37.20 ** KEPT (pick-wt=24): 181 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),B),c_Type_Osko__Type__Xtyping__elims__2__1(C,A,D,B)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),hAPP(hAPP(c_Lambda_OdB_OApp,D),B)),C)).
% 37.07/37.20 ** KEPT (pick-wt=24): 182 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),B),C))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),D),C))| -hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(c_Lambda_Obeta,tc_Lambda_OdB),D),B)).
% 37.07/37.20 ** KEPT (pick-wt=31): 183 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),A),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xtyping__elims__3__1(B,A,C))),C),c_Type_Osko__Type__Xtyping__elims__3__2(B,A,C)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_Lambda_OdB_OAbs(C)),B)).
% 37.07/37.20 ** KEPT (pick-wt=29): 184 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),A),c_HOL_Ozero__class_Ozero(tc_nat)),c_Type_Osko__Type__Xabs__typeE__1__1(A,B))),B),c_Type_Osko__Type__Xabs__typeE__1__2(A,B)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_Lambda_OdB_OAbs(B)),C)).
% 37.07/37.20 ** KEPT (pick-wt=45): 185 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__types__1__1(C,D,A,B))| -hBOOL(hAPP(hAPP(hAPP(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)| -hBOOL(hAPP(hAPP(hAPP(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)).
% 37.07/37.20 ** KEPT (pick-wt=22): 186 [] c_Type_Otypings(A,B,c_Type_Osko__Type__Xvar__app__typesE__1__1(C,A,D,B))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),B,tc_Lambda_OdB,tc_Lambda_OdB)),C)).
% 37.07/37.20 ** KEPT (pick-wt=24): 187 [] 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)).
% 37.07/37.20 ** KEPT (pick-wt=30): 188 [] hBOOL(hAPP(hAPP(hAPP(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)| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),B),c_List_Ofoldr(c_Type_Otype_OFun,E,D,tc_Type_Otype,tc_Type_Otype))).
% 37.07/37.20 ** KEPT (pick-wt=14): 189 [] 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).
% 37.07/37.20 ** KEPT (pick-wt=15): 190 [] 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).
% 37.07/37.20 ** KEPT (pick-wt=31): 191 [] A=B| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,C),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),E,tc_Lambda_OdB,tc_Lambda_OdB)),B))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,C),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(D),E,tc_Lambda_OdB,tc_Lambda_OdB)),A)).
% 37.07/37.21 ** KEPT (pick-wt=28): 192 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),B),hAPP(hAPP(c_Type_Otype_OFun,c_Type_Osko__Type__Xtyping__elims__2__1(C,A,B,D)),C)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),hAPP(hAPP(c_Lambda_OdB_OApp,B),D)),C)).
% 37.07/37.21 ** KEPT (pick-wt=14): 193 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=14): 194 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Nat_Osemiring__1__class_Oof__nat(B,A),A).
% 37.07/37.21 ** KEPT (pick-wt=34): 195 [] 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))).
% 37.07/37.21 ** KEPT (pick-wt=20): 196 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB)| -c_List_Olistsp(c_InductTermi_OIT,A,tc_Lambda_OdB).
% 37.07/37.21 ** KEPT (pick-wt=8): 197 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 37.07/37.21 ** KEPT (pick-wt=14): 198 [] hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OAbs(A)),c_Lambda_OdB_OAbs(B)))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,A),B)).
% 37.07/37.21 ** KEPT (pick-wt=13): 199 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_OdB_OApp,A),c_Lambda_OdB_OVar(B))))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 37.07/37.21 ** KEPT (pick-wt=20): 200 [] 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)).
% 37.07/37.21 ** KEPT (pick-wt=13): 201 [] 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).
% 37.07/37.21 ** KEPT (pick-wt=26): 202 [] c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),A),B),C),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),B),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(A,D,E).
% 37.07/37.21 ** KEPT (pick-wt=20): 203 [] 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)).
% 37.07/37.21 ** KEPT (pick-wt=20): 204 [] 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)).
% 37.07/37.21 ** KEPT (pick-wt=23): 205 [] c_Fun_Ocomp(A,B,C,D,E)!=c_Fun_Ocomp(c_Fun_Oid(D),F,D,D,E)|hAPP(A,hAPP(B,G))=hAPP(F,G).
% 37.07/37.21 ** KEPT (pick-wt=5): 206 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 37.07/37.21 Following clause subsumed by 206 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=14): 207 [] -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).
% 37.07/37.21 ** KEPT (pick-wt=14): 208 [] -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).
% 37.07/37.21 ** KEPT (pick-wt=5): 209 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 37.07/37.21 ** KEPT (pick-wt=8): 210 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OAbs(B)|A=B.
% 37.07/37.21 ** KEPT (pick-wt=8): 211 [] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 37.07/37.21 ** KEPT (pick-wt=4): 212 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 37.07/37.21 Following clause subsumed by 212 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=6): 213 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 37.07/37.21 ** KEPT (pick-wt=6): 214 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 37.07/37.21 ** KEPT (pick-wt=6): 215 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A).
% 37.07/37.21 ** KEPT (pick-wt=13): 216 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 37.07/37.21 ** KEPT (pick-wt=13): 217 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A).
% 37.07/37.21 Following clause subsumed by 217 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)|C=B.
% 37.07/37.21 Following clause subsumed by 217 during input processing: 0 [] -class_Orderings_Olinorder(A)|c_HOL_Oord__class_Oless(B,C,A)|C=B|c_HOL_Oord__class_Oless(C,B,A).
% 37.07/37.21 Following clause subsumed by 217 during input processing: 0 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A).
% 37.07/37.21 ** KEPT (pick-wt=14): 218 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|B=D.
% 37.07/37.21 ** KEPT (pick-wt=14): 219 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=hAPP(hAPP(c_Lambda_OdB_OApp,C),D)|A=C.
% 37.07/37.21 ** KEPT (pick-wt=32): 220 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),hAPP(hAPP(c_Lambda_OdB_OApp,B),C)),D))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),C),E))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),B),hAPP(hAPP(c_Type_Otype_OFun,E),D))).
% 37.07/37.21 ** KEPT (pick-wt=7): 221 [] -hBOOL(hAPP(hAPP(c_Lambda_Obeta,c_Lambda_OdB_OVar(A)),B)).
% 37.07/37.21 Following clause subsumed by 212 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).
% 37.07/37.21 ** KEPT (pick-wt=15): 222 [] 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).
% 37.07/37.21 ** KEPT (pick-wt=14): 223 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|B=D.
% 37.07/37.21 ** KEPT (pick-wt=14): 224 [] hAPP(hAPP(c_Type_Otype_OFun,A),B)!=hAPP(hAPP(c_Type_Otype_OFun,C),D)|A=C.
% 37.07/37.21 ** KEPT (pick-wt=8): 225 [] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 37.07/37.21 ** KEPT (pick-wt=8): 226 [] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OVar(B)|A=B.
% 37.07/37.21 ** KEPT (pick-wt=8): 227 [] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 37.07/37.21 ** KEPT (pick-wt=5): 228 [] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 37.07/37.21 ** KEPT (pick-wt=24): 229 [] c_Fun_Ocomp(A,B,C,D,E)!=c_Fun_Ocomp(F,G,H,D,E)|hAPP(A,hAPP(B,I))=hAPP(F,hAPP(G,I)).
% 37.07/37.21 ** KEPT (pick-wt=28): 230 [] hAPP(A,hAPP(B,C))!=hAPP(D,hAPP(E,F))|hAPP(c_Fun_Ocomp(A,B,G,H,I),C)=hAPP(c_Fun_Ocomp(D,E,J,H,K),F).
% 37.07/37.21 ** KEPT (pick-wt=10): 231 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 37.07/37.21 ** KEPT (pick-wt=10): 232 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 37.07/37.21 ** KEPT (pick-wt=10): 233 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 37.07/37.21 Following clause subsumed by 233 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A).
% 37.07/37.21 ** KEPT (pick-wt=27): 234 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),A),B),C)),hAPP(hAPP(c_Lambda_Olift,D),B)),E))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),D),E)).
% 37.07/37.21 ** KEPT (pick-wt=37): 235 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),A),B)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,C),A),v_T____))| -hBOOL(hAPP(c_InductTermi_OIT,A))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),C),B),v_T____)),v_b____),D)).
% 37.07/37.21 ** KEPT (pick-wt=22): 236 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),B),C))| -hBOOL(hAPP(hAPP(c_Lambda_Obeta,D),B))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),D),C)).
% 37.07/37.21 ** KEPT (pick-wt=15): 237 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),c_Lambda_OdB_OVar(B)),C)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 37.07/37.21 ** KEPT (pick-wt=18): 238 [] hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(A),B),C),D),E)=hAPP(B,E)| -c_HOL_Oord__class_Oless(E,C,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=12): 239 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(c_Lambda_Olift,A),B)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 37.07/37.21 ** KEPT (pick-wt=48): 241 [copy,240,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)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,F),D),B))| -hBOOL(hAPP(c_InductTermi_OIT,D))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),F),E),B)),C),G))| -hBOOL(hAPP(c_InductTermi_OIT,C)).
% 37.07/37.21 ** KEPT (pick-wt=48): 243 [copy,242,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)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,F),D),A))| -hBOOL(hAPP(c_InductTermi_OIT,D))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),F),E),A)),C),G))| -hBOOL(hAPP(c_InductTermi_OIT,C)).
% 37.07/37.21 ** KEPT (pick-wt=29): 244 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_Lambda_OdB_OAbs(B)),hAPP(hAPP(c_Type_Otype_OFun,C),D)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),A),c_HOL_Ozero__class_Ozero(tc_nat)),C)),B),D)).
% 37.07/37.21 ** KEPT (pick-wt=14): 245 [] hAPP(A,B)=C| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_Lambda_OdB_OVar(B)),C)).
% 37.07/37.21 ** KEPT (pick-wt=24): 246 [] 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)).
% 37.07/37.21 ** KEPT (pick-wt=43): 247 [] c_Type_Otypings(A,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),B)),C),D,tc_Lambda_OdB,tc_Lambda_OdB),E)| -c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),A),C),F),D,E)| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),B),F)).
% 37.07/37.21 ** KEPT (pick-wt=9): 248 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OAbs(A)))| -hBOOL(hAPP(c_InductTermi_OIT,A)).
% 37.07/37.21 ** KEPT (pick-wt=37): 249 [] -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),B),C))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),A),D),C)),E),F))|hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),hAPP(hAPP(hAPP(c_Lambda_Osubst,E),B),D)),F)).
% 37.07/37.21 Following clause subsumed by 235 during input processing: 0 [] hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),A),B)))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,C),A),v_T____))| -hBOOL(hAPP(c_InductTermi_OIT,A))| -hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),C),B),v_T____)),v_b____),D)).
% 37.07/37.21 ** KEPT (pick-wt=10): 250 [] -hBOOL(hAPP(c_InductTermi_OIT,hAPP(hAPP(hAPP(c_Lambda_Osubst,v_b____),v_xb),v_xc))).
% 37.07/37.21 ** KEPT (pick-wt=6): 251 [] class_Orderings_Opreorder(tc_fun(A,B))| -class_Orderings_Opreorder(B).
% 37.07/37.21 ** KEPT (pick-wt=6): 252 [] class_Orderings_Oorder(tc_fun(A,B))| -class_Orderings_Oorder(B).
% 37.07/37.21 ** KEPT (pick-wt=7): 253 [] A=B| -c_fe_qual(A,B,C).
% 37.07/37.21 129 back subsumes 102.
% 37.07/37.21 130 back subsumes 101.
% 37.07/37.21 ** KEPT (pick-wt=14): 268 [copy,189,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).
% 37.07/37.21 ** KEPT (pick-wt=15): 269 [copy,190,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).
% 37.07/37.21 Following clause subsumed by 211 during input processing: 0 [copy,197,flip.1] c_Lambda_OdB_OVar(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 37.07/37.21 Following clause subsumed by 228 during input processing: 0 [copy,209,flip.1] c_Lambda_OdB_OAbs(A)!=c_Lambda_OdB_OVar(B).
% 37.07/37.21 Following clause subsumed by 197 during input processing: 0 [copy,211,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OVar(C).
% 37.07/37.21 Following clause subsumed by 227 during input processing: 0 [copy,225,flip.1] hAPP(hAPP(c_Lambda_OdB_OApp,A),B)!=c_Lambda_OdB_OAbs(C).
% 37.07/37.21 Following clause subsumed by 225 during input processing: 0 [copy,227,flip.1] c_Lambda_OdB_OAbs(A)!=hAPP(hAPP(c_Lambda_OdB_OApp,B),C).
% 37.07/37.21 Following clause subsumed by 209 during input processing: 0 [copy,228,flip.1] c_Lambda_OdB_OVar(A)!=c_Lambda_OdB_OAbs(B).
% 37.07/37.21 Following clause subsumed by 189 during input processing: 0 [copy,268,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).
% 37.07/37.21 Following clause subsumed by 190 during input processing: 0 [copy,269,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).
% 37.07/37.21
% 37.07/37.21 ------------> process sos:
% 37.07/37.21 ** KEPT (pick-wt=3): 275 [] A=A.
% 37.07/37.21 ** KEPT (pick-wt=15): 276 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ominus__class_Ominus(B,A,tc_nat))=B|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=11): 277 [] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 37.07/37.21 ---> New Demodulator: 278 [new_demod,277] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=7): 279 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 37.07/37.21 ---> New Demodulator: 280 [new_demod,279] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A.
% 37.07/37.21 ** KEPT (pick-wt=7): 281 [] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=8): 282 [] c_HOL_Ominus__class_Ominus(c_Suc(A),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 37.07/37.21 ---> New Demodulator: 283 [new_demod,282] c_HOL_Ominus__class_Ominus(c_Suc(A),c_HOL_Oone__class_Oone(tc_nat),tc_nat)=A.
% 37.07/37.21 ** KEPT (pick-wt=8): 284 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_Suc(A),tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=12): 285 [] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=17): 286 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=8): 287 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.21 ---> New Demodulator: 288 [new_demod,287] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=19): 289 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat).
% 37.07/37.21 ---> New Demodulator: 290 [new_demod,289] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),B),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=19): 291 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat).
% 37.07/37.21 ---> New Demodulator: 292 [new_demod,291] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=15): 293 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=17): 294 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(A),B,tc_nat),c_Suc(C),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 37.07/37.21 ---> New Demodulator: 295 [new_demod,294] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Suc(A),B,tc_nat),c_Suc(C),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=14): 296 [] c_HOL_Ominus__class_Ominus(A,c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),B,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=11): 297 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat)=A.
% 37.07/37.21 ---> New Demodulator: 298 [new_demod,297] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),B,tc_nat)=A.
% 37.07/37.21 ** KEPT (pick-wt=11): 299 [] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat)=B.
% 37.07/37.21 ---> New Demodulator: 300 [new_demod,299] c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),A,tc_nat)=B.
% 37.07/37.21 ** KEPT (pick-wt=22): 302 [copy,301,flip.1] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat)),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=22): 303 [] c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(A)),c_Type_Otype_Otype__size(B))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 37.07/37.21 ---> New Demodulator: 304 [new_demod,303] c_Type_Otype_Otype__size(hAPP(hAPP(c_Type_Otype_OFun,A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Type_Otype_Otype__size(A)),c_Type_Otype_Otype__size(B))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 37.07/37.21 ** KEPT (pick-wt=25): 306 [copy,305,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Type_Otype)),c_Nat_Osize__class_Osize(B,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,A),B),tc_Type_Otype).
% 37.07/37.21 ---> New Demodulator: 307 [new_demod,306] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Nat_Osize__class_Osize(A,tc_Type_Otype)),c_Nat_Osize__class_Osize(B,tc_Type_Otype))),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Nat_Osize__class_Osize(hAPP(hAPP(c_Type_Otype_OFun,A),B),tc_Type_Otype).
% 37.07/37.21 ** KEPT (pick-wt=21): 308 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_ea______),v_ia______),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_n____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_Ha______)).
% 37.07/37.21 ** KEPT (pick-wt=17): 309 [] c_Nat_Ocompow(c_Suc(A),B,C,C)=c_Fun_Ocomp(B,c_Nat_Ocompow(A,B,C,C),C,C,C).
% 37.07/37.21 ---> New Demodulator: 310 [new_demod,309] c_Nat_Ocompow(c_Suc(A),B,C,C)=c_Fun_Ocomp(B,c_Nat_Ocompow(A,B,C,C),C,C,C).
% 37.07/37.21 ** KEPT (pick-wt=13): 312 [copy,311,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.21 ---> New Demodulator: 313 [new_demod,312] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.21 ** KEPT (pick-wt=17): 314 [] c_Lambda_Oliftn(A,c_Lambda_OdB_OVar(B),C)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A))|c_HOL_Oord__class_Oless(B,C,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=17): 316 [copy,315,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Oliftn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Oliftn(A,c_Lambda_OdB_OAbs(B),C).
% 37.07/37.21 ---> New Demodulator: 317 [new_demod,316] c_Lambda_OdB_OAbs(c_Lambda_Oliftn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Oliftn(A,c_Lambda_OdB_OAbs(B),C).
% 37.07/37.21 ** KEPT (pick-wt=5): 318 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 37.07/37.21 Following clause subsumed by 318 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=7): 319 [] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 37.07/37.21 ---> New Demodulator: 320 [new_demod,319] c_Lambda_Oliftn(c_HOL_Ozero__class_Ozero(tc_nat),A,B)=A.
% 37.07/37.21 ** KEPT (pick-wt=13): 321 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.21 ---> New Demodulator: 322 [new_demod,321] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.21 ** KEPT (pick-wt=19): 324 [copy,323,flip.1] c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(A)),B).
% 37.07/37.21 ---> New Demodulator: 325 [new_demod,324] c_Lambda_OdB_OAbs(hAPP(hAPP(c_Lambda_Olift,A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OAbs(A)),B).
% 37.07/37.21 ** KEPT (pick-wt=11): 327 [copy,326,unit_del,212] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.21 ---> New Demodulator: 328 [new_demod,327] c_Lambda_Osubstn(c_Lambda_OdB_OVar(A),B,A)=c_Lambda_Oliftn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)).
% 37.07/37.21 ** KEPT (pick-wt=19): 329 [] hAPP(hAPP(c_Lambda_Olift,c_Lambda_OdB_OVar(A)),B)=c_Lambda_OdB_OVar(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)))|c_HOL_Oord__class_Oless(A,B,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=6): 330 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 37.07/37.21 Following clause subsumed by 330 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(A),tc_nat).
% 37.07/37.21 Following clause subsumed by 318 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=14): 332 [copy,331,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)).
% 37.07/37.21 ---> New Demodulator: 333 [new_demod,332] 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)).
% 37.07/37.21 ** KEPT (pick-wt=3): 334 [] v_n____=v_i____.
% 37.07/37.21 ---> New Demodulator: 335 [new_demod,334] v_n____=v_i____.
% 37.07/37.21 ** KEPT (pick-wt=6): 337 [copy,336,flip.1] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 37.07/37.21 ---> New Demodulator: 338 [new_demod,337] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=14): 339 [] c_Lambda_Oliftn(c_Suc(A),B,C)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C).
% 37.07/37.21 ** KEPT (pick-wt=13): 340 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 37.07/37.21 ** KEPT (pick-wt=17): 342 [copy,341,flip.1] c_Lambda_OdB_OAbs(c_Lambda_Osubstn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Osubstn(c_Lambda_OdB_OAbs(A),B,C).
% 37.07/37.21 ---> New Demodulator: 343 [new_demod,342] c_Lambda_OdB_OAbs(c_Lambda_Osubstn(A,B,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=c_Lambda_Osubstn(c_Lambda_OdB_OAbs(A),B,C).
% 37.07/37.21 ** KEPT (pick-wt=10): 344 [] c_HOL_Oord__class_Oless(A,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=10): 345 [] c_HOL_Oord__class_Oless(A,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A)),tc_nat).
% 37.07/37.21 Following clause subsumed by 344 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=15): 347 [copy,346,flip.1] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B).
% 37.07/37.21 ---> New Demodulator: 348 [new_demod,347] c_Suc(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B).
% 37.07/37.21 ** KEPT (pick-wt=15): 350 [copy,349,demod,348] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_Suc(B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_Suc(A)),B).
% 37.07/37.21 ** KEPT (pick-wt=8): 351 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 37.07/37.21 Following clause subsumed by 351 during input processing: 0 [] hBOOL(hAPP(hAPP(c_Transitive__Closure_Ortranclp(A,B),C),C)).
% 37.07/37.21 ** KEPT (pick-wt=25): 352 [] c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,D,D)=c_Fun_Ocomp(c_Nat_Ocompow(A,C,D,D),c_Nat_Ocompow(B,C,D,D),D,D,D).
% 37.07/37.21 ---> New Demodulator: 353 [new_demod,352] c_Nat_Ocompow(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),C,D,D)=c_Fun_Ocomp(c_Nat_Ocompow(A,C,D,D),c_Nat_Ocompow(B,C,D,D),D,D,D).
% 37.07/37.21 ** KEPT (pick-wt=11): 355 [copy,354,demod,338,338] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 37.07/37.21 ---> New Demodulator: 356 [new_demod,355] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=10): 357 [] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A).
% 37.07/37.21 ---> New Demodulator: 358 [new_demod,357] c_Suc(A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A).
% 37.07/37.21 Following clause subsumed by 340 during input processing: 0 [demod,358] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Oone__class_Oone(tc_nat)).
% 37.07/37.21 ** KEPT (pick-wt=16): 360 [copy,359,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).
% 37.07/37.21 ---> New Demodulator: 361 [new_demod,360] 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).
% 37.07/37.21 ** KEPT (pick-wt=11): 362 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.21 ---> New Demodulator: 363 [new_demod,362] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=23): 364 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).
% 37.07/37.21 ** KEPT (pick-wt=23): 365 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 37.07/37.21 ---> New Demodulator: 366 [new_demod,365] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)),C)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C)).
% 37.07/37.21 ** KEPT (pick-wt=8): 367 [] hAPP(c_COMBK(A,B,C),D)=A.
% 37.07/37.21 ---> New Demodulator: 368 [new_demod,367] hAPP(c_COMBK(A,B,C),D)=A.
% 37.07/37.21 ** KEPT (pick-wt=11): 370 [copy,369,demod,358,356,358,356,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 37.07/37.21 ---> New Demodulator: 371 [new_demod,370] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Oone__class_Oone(tc_nat))=c_HOL_Oone__class_Oone(tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=19): 373 [copy,372,flip.1] hAPP(c_Nat_Ocompow(A,B,C,C),hAPP(B,D))=hAPP(B,hAPP(c_Nat_Ocompow(A,B,C,C),D)).
% 37.07/37.21 ---> New Demodulator: 374 [new_demod,373] hAPP(c_Nat_Ocompow(A,B,C,C),hAPP(B,D))=hAPP(B,hAPP(c_Nat_Ocompow(A,B,C,C),D)).
% 37.07/37.21 Following clause subsumed by 364 during input processing: 0 [demod,358,366,358] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B)).
% 37.07/37.21 ** KEPT (pick-wt=12): 376 [copy,375,flip.1] hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))=v_T____.
% 37.07/37.21 ---> New Demodulator: 377 [new_demod,376] hAPP(hAPP(c_Type_Otype_OFun,v_T_H_H____),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))=v_T____.
% 37.07/37.21 ** KEPT (pick-wt=20): 379 [copy,378,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).
% 37.07/37.21 ---> New Demodulator: 380 [new_demod,379] 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).
% 37.07/37.21 ** KEPT (pick-wt=10): 382 [copy,381,demod,358,unit_del,212] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=14): 384 [copy,383,demod,358] c_HOL_Oord__class_Oless(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat).
% 37.07/37.21 ** KEPT (pick-wt=9): 385 [] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 37.07/37.21 ---> New Demodulator: 386 [new_demod,385] c_Transitive__Closure_Ortranclp(c_Transitive__Closure_Ortranclp(A,B),B)=c_Transitive__Closure_Ortranclp(A,B).
% 37.07/37.21 ** KEPT (pick-wt=9): 388 [copy,387,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 37.07/37.21 ---> New Demodulator: 389 [new_demod,388] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),c_HOL_Ozero__class_Ozero(tc_nat))=A.
% 37.07/37.21 ** KEPT (pick-wt=9): 390 [] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 37.07/37.21 ---> New Demodulator: 391 [new_demod,390] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat)),A)=A.
% 37.07/37.21 Following clause subsumed by 275 during input processing: 0 [demod,389] A=A.
% 37.07/37.21 ** KEPT (pick-wt=20): 393 [copy,392,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).
% 37.07/37.21 ---> New Demodulator: 394 [new_demod,393] 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).
% 37.07/37.21 ** KEPT (pick-wt=15): 395 [] 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).
% 37.07/37.21 ** KEPT (pick-wt=13): 396 [] hAPP(c_Fun_Ocomp(c_COMBK(A,B,C),D,C,B,t_a),v_x)=A.
% 37.07/37.21 ---> New Demodulator: 397 [new_demod,396] hAPP(c_Fun_Ocomp(c_COMBK(A,B,C),D,C,B,t_a),v_x)=A.
% 37.07/37.21 ** KEPT (pick-wt=21): 399 [copy,398,demod,335] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_List_Ofoldl(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____),v_rs____,tc_Lambda_OdB,tc_Lambda_OdB)),v_T_H____)).
% 37.07/37.21 ** KEPT (pick-wt=9): 400 [] c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),A,B,B)=c_Fun_Oid(B).
% 37.07/37.21 ** KEPT (pick-wt=28): 402 [copy,401,flip.1] c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(A)),B),C).
% 37.07/37.21 ---> New Demodulator: 403 [new_demod,402] c_Lambda_OdB_OAbs(hAPP(hAPP(hAPP(c_Lambda_Osubst,A),hAPP(hAPP(c_Lambda_Olift,B),c_HOL_Ozero__class_Ozero(tc_nat))),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),C),c_HOL_Oone__class_Oone(tc_nat))))=hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OAbs(A)),B),C).
% 37.07/37.21 ** KEPT (pick-wt=39): 405 [copy,404,demod,358] hAPP(hAPP(hAPP(c_Type_Oshift(A),hAPP(hAPP(hAPP(c_Type_Oshift(A),B),C),D)),c_HOL_Ozero__class_Ozero(tc_nat)),E)=hAPP(hAPP(hAPP(c_Type_Oshift(A),hAPP(hAPP(hAPP(c_Type_Oshift(A),B),c_HOL_Ozero__class_Ozero(tc_nat)),E)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C)),D).
% 37.07/37.21 ** KEPT (pick-wt=8): 407 [copy,406,demod,377] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)).
% 37.07/37.21 ** KEPT (pick-wt=16): 409 [copy,408,demod,335,377] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),c_Lambda_OdB_OVar(v_i____)),v_T____)).
% 37.07/37.21 ** KEPT (pick-wt=25): 411 [copy,410,demod,335] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OVar(v_i____)),v_a____)),c_List_Ofoldr(c_Type_Otype_OFun,v_Ts____,v_T_H____,tc_Type_Otype,tc_Type_Otype))).
% 37.07/37.21 ** KEPT (pick-wt=11): 412 [] c_Type_Otypings(hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____),v_as____,v_Ts____).
% 37.07/37.21 ** KEPT (pick-wt=32): 413 [] 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(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),C),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 37.07/37.21 ** KEPT (pick-wt=36): 414 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB).
% 37.07/37.22 ** KEPT (pick-wt=45): 415 [] 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(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),C)),D),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 37.07/37.22 ** KEPT (pick-wt=6): 416 [] hAPP(c_Fun_Oid(A),B)=B.
% 37.07/37.22 ---> New Demodulator: 417 [new_demod,416] hAPP(c_Fun_Oid(A),B)=B.
% 37.07/37.22 ** KEPT (pick-wt=20): 419 [copy,418,flip.1] c_List_Omap(c_Fun_Ocomp(A,B,C,D,E),F,E,D)=c_List_Omap(A,c_List_Omap(B,F,E,C),C,D).
% 37.07/37.22 ---> New Demodulator: 420 [new_demod,419] c_List_Omap(c_Fun_Ocomp(A,B,C,D,E),F,E,D)=c_List_Omap(A,c_List_Omap(B,F,E,C),C,D).
% 37.07/37.22 ** KEPT (pick-wt=10): 422 [copy,421,unit_del,212] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 37.07/37.22 ---> New Demodulator: 423 [new_demod,422] hAPP(hAPP(hAPP(c_Lambda_Osubst,c_Lambda_OdB_OVar(A)),B),A)=B.
% 37.07/37.22 ** KEPT (pick-wt=16): 424 [] hAPP(hAPP(hAPP(c_COMBC(A,B,C),D),E),F)=hAPP(hAPP(D,F),E).
% 37.07/37.22 ** KEPT (pick-wt=9): 425 [] c_Fun_Ocomp(c_Fun_Oid(A),B,A,A,C)=B.
% 37.07/37.22 ---> New Demodulator: 426 [new_demod,425] c_Fun_Ocomp(c_Fun_Oid(A),B,A,A,C)=B.
% 37.07/37.22 ** KEPT (pick-wt=9): 427 [] c_Fun_Ocomp(A,c_Fun_Oid(B),B,C,B)=A.
% 37.07/37.22 ---> New Demodulator: 428 [new_demod,427] c_Fun_Ocomp(A,c_Fun_Oid(B),B,C,B)=A.
% 37.07/37.22 ** KEPT (pick-wt=18): 429 [] 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).
% 37.07/37.22 ** KEPT (pick-wt=23): 430 [] 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)).
% 37.07/37.22 ** KEPT (pick-wt=14): 431 [] hAPP(c_Fun_Ocomp(A,B,C,D,E),F)=hAPP(A,hAPP(B,F)).
% 37.07/37.22 ---> New Demodulator: 432 [new_demod,431] hAPP(c_Fun_Ocomp(A,B,C,D,E),F)=hAPP(A,hAPP(B,F)).
% 37.07/37.22 Following clause subsumed by 275 during input processing: 0 [demod,432] hAPP(A,hAPP(B,C))=hAPP(A,hAPP(B,C)).
% 37.07/37.22 ** KEPT (pick-wt=15): 434 [copy,433,demod,333] hBOOL(hAPP(hAPP(c_Lambda_Obeta,hAPP(hAPP(c_Lambda_OdB_OApp,c_Lambda_OdB_OAbs(A)),B)),c_Lambda_Osubstn(A,B,c_HOL_Ozero__class_Ozero(tc_nat)))).
% 37.07/37.22 ** KEPT (pick-wt=11): 435 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 37.07/37.22 Following clause subsumed by 435 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).
% 37.07/37.22 Following clause subsumed by 435 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A.
% 37.07/37.22 ** KEPT (pick-wt=14): 436 [] hAPP(c_Fun_Ofcomp(A,B,C,D,E),F)=hAPP(B,hAPP(A,F)).
% 37.07/37.22 ---> New Demodulator: 437 [new_demod,436] hAPP(c_Fun_Ofcomp(A,B,C,D,E),F)=hAPP(B,hAPP(A,F)).
% 37.07/37.22 ** KEPT (pick-wt=9): 438 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=23): 440 [copy,439,flip.1] c_Fun_Ocomp(c_Fun_Ocomp(A,B,C,D,E),F,E,D,G)=c_Fun_Ocomp(A,c_Fun_Ocomp(B,F,E,C,G),C,D,G).
% 37.07/37.22 ---> New Demodulator: 441 [new_demod,440] c_Fun_Ocomp(c_Fun_Ocomp(A,B,C,D,E),F,E,D,G)=c_Fun_Ocomp(A,c_Fun_Ocomp(B,F,E,C,G),C,D,G).
% 37.07/37.22 ** KEPT (pick-wt=9): 442 [] c_Fun_Ofcomp(A,c_Fun_Oid(B),C,B,B)=A.
% 37.07/37.22 ---> New Demodulator: 443 [new_demod,442] c_Fun_Ofcomp(A,c_Fun_Oid(B),C,B,B)=A.
% 37.07/37.22 ** KEPT (pick-wt=9): 444 [] c_Fun_Ofcomp(c_Fun_Oid(A),B,A,A,C)=B.
% 37.07/37.22 ---> New Demodulator: 445 [new_demod,444] c_Fun_Ofcomp(c_Fun_Oid(A),B,A,A,C)=B.
% 37.07/37.22 ** KEPT (pick-wt=23): 446 [] c_Fun_Ofcomp(c_Fun_Ofcomp(A,B,C,D,E),F,C,E,G)=c_Fun_Ofcomp(A,c_Fun_Ofcomp(B,F,D,E,G),C,D,G).
% 37.07/37.22 ---> New Demodulator: 447 [new_demod,446] c_Fun_Ofcomp(c_Fun_Ofcomp(A,B,C,D,E),F,C,E,G)=c_Fun_Ofcomp(A,c_Fun_Ofcomp(B,F,D,E,G),C,D,G).
% 37.07/37.22 Following clause subsumed by 407 during input processing: 0 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_e____),v_u____),v_T____)).
% 37.07/37.22 ** KEPT (pick-wt=29): 448 [] 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)).
% 37.07/37.22 Following clause subsumed by 275 during input processing: 0 [demod,423] B=B.
% 37.07/37.22 Following clause subsumed by 275 during input processing: 0 [demod,432] hAPP(A,hAPP(B,v_x))=hAPP(A,hAPP(B,v_x)).
% 37.07/37.22 ** KEPT (pick-wt=15): 449 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_a____),v_T_H_H____)).
% 37.07/37.22 Following clause subsumed by 275 during input processing: 0 [demod,417] v_x=v_x.
% 37.07/37.22 ** KEPT (pick-wt=12): 450 [] hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(A),B),C),D),C)=D.
% 37.07/37.22 ---> New Demodulator: 451 [new_demod,450] hAPP(hAPP(hAPP(hAPP(c_Type_Oshift(A),B),C),D),C)=D.
% 37.07/37.22 ** KEPT (pick-wt=5): 452 [] hBOOL(hAPP(c_InductTermi_OIT,c_Lambda_OdB_OVar(A))).
% 37.07/37.22 ** KEPT (pick-wt=19): 453 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__Xhyps__1__1(v_T____,v_b____,v_e____,v_i____))).
% 37.07/37.22 ** KEPT (pick-wt=8): 454 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_ea______),v_ua______),v_T____)).
% 37.07/37.22 ** KEPT (pick-wt=4): 455 [] hBOOL(hAPP(c_InductTermi_OIT,v_ua______)).
% 37.07/37.22 ** KEPT (pick-wt=19): 456 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__local__XCons__1__1(v_T____,v_b____,v_e____,v_i____))).
% 37.07/37.22 ** KEPT (pick-wt=11): 457 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,A),c_Lambda_OdB_OVar(B)),hAPP(A,B))).
% 37.07/37.22 Following clause subsumed by 275 during input processing: 0 [demod,437] hAPP(B,hAPP(A,v_x))=hAPP(B,hAPP(A,v_x)).
% 37.07/37.22 ** KEPT (pick-wt=4): 458 [] hBOOL(hAPP(c_InductTermi_OIT,v_u____)).
% 37.07/37.22 ** KEPT (pick-wt=13): 459 [] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 37.07/37.22 ---> New Demodulator: 460 [new_demod,459] hAPP(hAPP(hAPP(c_Lambda_Osubst,hAPP(hAPP(c_Lambda_Olift,A),B)),C),B)=A.
% 37.07/37.22 Following clause subsumed by 414 during input processing: 0 [] c_List_Olistsp(c_InductTermi_OIT,c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),c_HOL_Ozero__class_Ozero(tc_nat)),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),v_u____)),v_i____),v_bs____,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB).
% 37.07/37.22 ** KEPT (pick-wt=974): 461 [] c_List_Olistsp(hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_bool,tc_bool),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_and),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_fun(tc_nat,tc_Type_Otype)),c_All(tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_Type_Otype,tc_bool),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_bool,tc_Type_Otype),c_All(tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_bool),tc_Type_Otype),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_bool,tc_Lambda_OdB),c_All(tc_nat))))),hAPP(hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),c_COMBS(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Type_Otype),c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_Type_Otype,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Type_Otype),c_COMBS(tc_nat,tc_bool,tc_bool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_bool,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_fun(tc_bool,tc_bool)),tc_Type_Otype),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_nat),c_implies)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_bool))),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype)),tc_fun(tc_nat,tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_nat),c_Type_Otyping)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),hAPP(hAPP(c_COMBB(tc_fun(tc_nat,tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_Type_Otype,tc_fun(tc_nat,tc_fun(tc_nat,tc_Type_Otype))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_nat,tc_Type_Otype,tc_fun(tc_nat,tc_Type_Otype))),c_Type_Oshift(tc_Type_Otype))),v_T____))))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat)),hAPP(hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies),c_InductTermi_OIT))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_Lambda_OdB),hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),c_COMBS(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_Lambda_OdB,tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool))),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_fun(tc_bool,tc_bool),tc_fun(tc_fun(tc_nat,tc_bool),tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),c_COMBB(tc_bool,tc_bool,tc_nat))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_bool),tc_fun(tc_Lambda_OdB,tc_fun(tc_bool,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),hAPP(c_COMBB(tc_bool,tc_fun(tc_bool,tc_bool),tc_Lambda_OdB),c_implies)),hAPP(hAPP(c_COMBC(tc_fun(tc_nat,tc_Type_Otype),tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_Type_Otype,tc_bool)),tc_fun(tc_Type_Otype,tc_fun(tc_Lambda_OdB,tc_bool)),tc_fun(tc_nat,tc_Type_Otype)),c_COMBC(tc_Lambda_OdB,tc_Type_Otype,tc_bool)),c_Type_Otyping)),v_T____)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),tc_fun(tc_Lambda_OdB,tc_fun(tc_nat,tc_bool)),tc_Lambda_OdB),hAPP(c_COMBB(tc_fun(tc_nat,tc_Lambda_OdB),tc_fun(tc_nat,tc_bool),tc_Lambda_OdB),hAPP(c_COMBB(tc_Lambda_OdB,tc_bool,tc_nat),c_InductTermi_OIT))),c_Lambda_Osubst)))))))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Type_Otype,tc_bool),tc_bool,tc_Lambda_OdB),c_Ex(tc_Type_Otype)),hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)))),v_bs____,tc_Lambda_OdB).
% 37.07/37.22 ** KEPT (pick-wt=19): 462 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_e____),v_i____),v_T____)),v_b____),v_sko__CHAINED__1(v_T____,v_b____,v_e____,v_i____))).
% 37.07/37.22 ** KEPT (pick-wt=15): 463 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,hAPP(hAPP(hAPP(c_Type_Oshift(tc_Type_Otype),v_x),v_xc),v_T____)),v_b____),v_xa)).
% 37.07/37.22 ** KEPT (pick-wt=4): 464 [] hBOOL(hAPP(c_InductTermi_OIT,v_xb)).
% 37.07/37.22 ** KEPT (pick-wt=8): 465 [] hBOOL(hAPP(hAPP(hAPP(c_Type_Otyping,v_x),v_xb),v_T____)).
% 37.07/37.22 ** KEPT (pick-wt=2): 466 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 467 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 468 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 469 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 470 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 471 [] class_Ring__and__Field_Oordered__semidom(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 472 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 473 [] class_OrderedGroup_Oab__semigroup__add(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 474 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 475 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 476 [] class_OrderedGroup_Osemigroup__add(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 477 [] class_Ring__and__Field_Osemiring__1(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 478 [] class_OrderedGroup_Omonoid__add(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 479 [] class_Nat_Osemiring__char__0(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 480 [] class_Orderings_Opreorder(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 481 [] class_Orderings_Olinorder(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 482 [] class_Orderings_Oorder(tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=2): 483 [] class_Orderings_Opreorder(tc_bool).
% 37.07/37.22 ** KEPT (pick-wt=2): 484 [] class_Orderings_Oorder(tc_bool).
% 37.07/37.22 ** KEPT (pick-wt=4): 485 [] c_fe_qual(A,A,B).
% 37.07/37.22 Following clause subsumed by 275 during input processing: 0 [copy,275,flip.1] A=A.
% 37.07/37.22 275 back subsumes 272.
% 37.07/37.22 275 back subsumes 271.
% 37.07/37.22 275 back subsumes 270.
% 37.07/37.22 275 back subsumes 255.
% 37.07/37.22 >>>> Starting back demodulation with 278.
% 37.07/37.22 >>>> Starting back demodulation with 280.
% 37.07/37.22 ** KEPT (pick-wt=7): 486 [copy,281,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,A,tc_nat).
% 37.07/37.22 >>>> Starting back demodulation with 283.
% 37.07/37.22 ** KEPT (pick-wt=12): 487 [copy,285,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat).
% 37.07/37.22 ** KEPT (pick-wt=17): 488 [copy,286,flip.1] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat).
% 37.07/37.22 >>>> Starting back demodulation with 288.
% 37.07/37.22 >>>> Starting back demodulation with 290.
% 37.07/37.22 >>>> Starting back demodulation with 292.
% 37.07/37.22 Following clause subsumed by 293 during input processing: 0 [copy,293,flip.1] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,C,tc_nat),B,tc_nat).
% 37.07/37.22 >>>> Starting back demodulation with 295.
% 37.07/37.22 Following clause subsumed by 286 during input processing: 0 [copy,296,flip.1,demod,358] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,c_HOL_Oone__class_Oone(tc_nat),tc_nat),B,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B),tc_nat).
% 37.07/37.22 >>>> Starting back demodulation with 298.
% 37.07/37.22 >>>> Starting back demodulation with 300.
% 37.07/37.22 >> back demodulating 21 with 300.
% 37.07/37.22 >>>> Starting back demodulation with 304.
% 37.07/37.22 >>>> Starting back demodulation with 307.
% 37.07/37.22 >>>> Starting back demodulation with 310.
% 37.07/37.22 >>>> Starting back demodulation with 313.
% 37.07/37.22 >>>> Starting back demodulation with 317.
% 37.07/37.22 >>>> Starting back demodulation with 320.
% 37.07/37.22 >>>> Starting back demodulation with 322.
% 37.07/37.22 >>>> Starting back demodulation with 325.
% 37.07/37.22 >>>> Starting back demodulation with 328.
% 37.07/37.22 >>>> Starting back demodulation with 333.
% 37.07/37.22 >> back demodulating 195 with 333.
% 37.07/37.22 >>>> Starting back demodulation with 335.
% 37.07/37.22 >> back demodulating 308 with 335.
% 37.07/37.22 >>>> Starting back demodulation with 338.
% 37.07/37.22 >> back demodulating 321 with 338.
% 37.07/37.22 >> back demodulating 312 with 338.
% 37.07/37.22 >> back demodulating 306 with 338.
% 37.07/37.22 >> back demodulating 303 with 338.
% 37.07/37.22 >> back demodulating 262 with 338.
% 37.07/37.22 >> back demodulating 261 with 338.
% 37.07/37.22 >> back demodulating 258 with 338.
% 37.07/37.22 >> back demodulating 257 with 338.
% 37.07/37.22 >> back demodulating 159 with 338.
% 37.07/37.22 >> back demodulating 158 with 338.
% 37.07/37.22 >> back demodulating 145 with 338.
% 37.07/37.22 >> back demodulating 144 with 338.
% 37.07/37.22 >> back demodulating 104 with 338.
% 37.07/37.22 >> back demodulating 75 with 338.
% 37.07/37.22 >> back demodulating 74 with 338.
% 37.07/37.22 >> back demodulating 45 with 338.
% 37.07/37.22 >> back demodulating 44 with 338.
% 37.07/37.22 >> back demodulating 31 with 338.
% 37.07/37.22 ** KEPT (pick-wt=19): 503 [copy,339,flip.1,demod,358] hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C)=c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),B,C).
% 37.07/37.22 Following clause subsumed by 340 during input processing: 0 [copy,340,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B)=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),A).
% 37.07/37.23 >>>> Starting back demodulation with 343.
% 37.07/37.23 >>>> Starting back demodulation with 348.
% 37.07/37.23 >> back demodulating 345 with 348.
% 37.07/37.23 >> back demodulating 344 with 348.
% 37.07/37.23 >> back demodulating 302 with 348.
% 37.07/37.23 Following clause subsumed by 364 during input processing: 0 [copy,350,flip.1,demod,358,366,358] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),B)).
% 37.07/37.23 >>>> Starting back demodulation with 353.
% 37.07/37.23 >>>> Starting back demodulation with 356.
% 37.07/37.23 >>>> Starting back demodulation with 358.
% 37.07/37.23 >> back demodulating 350 with 358.
% 37.07/37.23 >> back demodulating 347 with 358.
% 37.07/37.23 >> back demodulating 339 with 358.
% 37.07/37.23 >> back demodulating 337 with 358.
% 37.07/37.23 >> back demodulating 330 with 358.
% 37.07/37.23 >> back demodulating 318 with 358.
% 37.07/37.23 >> back demodulating 309 with 358.
% 37.07/37.23 >> back demodulating 296 with 358.
% 37.07/37.23 >> back demodulating 294 with 358.
% 37.07/37.23 >> back demodulating 284 with 358.
% 37.07/37.23 >> back demodulating 282 with 358.
% 37.07/37.23 >> back demodulating 277 with 358.
% 37.07/37.23 >> back demodulating 173 with 358.
% 37.07/37.23 >> back demodulating 172 with 358.
% 37.07/37.23 >> back demodulating 162 with 358.
% 37.07/37.23 >> back demodulating 161 with 358.
% 37.07/37.23 >> back demodulating 156 with 358.
% 37.07/37.23 >> back demodulating 149 with 358.
% 37.07/37.23 >> back demodulating 146 with 358.
% 37.07/37.23 >> back demodulating 115 with 358.
% 37.07/37.23 >> back demodulating 72 with 358.
% 37.07/37.23 >> back demodulating 71 with 358.
% 37.07/37.23 >> back demodulating 61 with 358.
% 37.07/37.23 >> back demodulating 54 with 358.
% 37.07/37.23 >> back demodulating 53 with 358.
% 37.07/37.23 >> back demodulating 50 with 358.
% 37.07/37.23 >> back demodulating 49 with 358.
% 37.07/37.23 >> back demodulating 33 with 358.
% 37.07/37.23 >> back demodulating 30 with 358.
% 37.07/37.23 >> back demodulating 22 with 358.
% 37.07/37.23 >>>> Starting back demodulation with 361.
% 37.07/37.23 >>>> Starting back demodulation with 363.
% 37.07/37.23 Following clause subsumed by 364 during input processing: 0 [copy,364,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C))=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),C)).
% 37.07/37.23 >>>> Starting back demodulation with 366.
% 37.07/37.23 >>>> Starting back demodulation with 368.
% 37.07/37.23 >>>> Starting back demodulation with 371.
% 37.07/37.23 >>>> Starting back demodulation with 374.
% 37.07/37.23 >>>> Starting back demodulation with 377.
% 37.07/37.23 >>>> Starting back demodulation with 380.
% 37.07/37.23 >>>> Starting back demodulation with 386.
% 37.07/37.23 >>>> Starting back demodulation with 389.
% 37.07/37.23 >> back demodulating 362 with 389.
% 37.07/37.23 >> back demodulating 355 with 389.
% 37.07/37.23 >>>> Starting back demodulation with 391.
% 37.07/37.23 >> back demodulating 370 with 391.
% 37.07/37.23 >>>> Starting back demodulation with 394.
% 37.07/37.23 >>>> Starting back demodulation with 397.
% 37.07/37.23 ** KEPT (pick-wt=9): 527 [copy,400,flip.1] c_Fun_Oid(A)=c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),B,A,A).
% 37.07/37.23 >>>> Starting back demodulation with 403.
% 37.07/37.23 ** KEPT (pick-wt=39): 528 [copy,405,flip.1] hAPP(hAPP(hAPP(c_Type_Oshift(A),hAPP(hAPP(hAPP(c_Type_Oshift(A),B),c_HOL_Ozero__class_Ozero(tc_nat)),C)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),D)),E)=hAPP(hAPP(hAPP(c_Type_Oshift(A),hAPP(hAPP(hAPP(c_Type_Oshift(A),B),D),E)),c_HOL_Ozero__class_Ozero(tc_nat)),C).
% 37.07/37.23 ** KEPT (pick-wt=32): 529 [copy,413,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(c_Lambda_Olift,A),B),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),B),C,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB)=hAPP(hAPP(c_Lambda_Olift,c_List_Ofoldl(c_Lambda_OdB_OApp,A,C,tc_Lambda_OdB,tc_Lambda_OdB)),B).
% 37.07/37.23 ** KEPT (pick-wt=45): 530 [copy,415,flip.1] c_List_Ofoldl(c_Lambda_OdB_OApp,hAPP(hAPP(hAPP(c_Lambda_Osubst,A),B),C),c_List_Omap(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),B)),C),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).
% 37.07/37.23 >>>> Starting back demodulation with 417.
% 37.07/37.23 >>>> Starting back demodulation with 420.
% 37.07/37.23 >>>> Starting back demodulation with 423.
% 37.07/37.23 ** KEPT (pick-wt=16): 531 [copy,424,flip.1] hAPP(hAPP(A,B),C)=hAPP(hAPP(hAPP(c_COMBC(D,E,F),A),C),B).
% 37.07/37.23 >>>> Starting back demodulation with 426.
% 37.07/37.23 >> back demodulating 205 with 426.
% 37.07/37.23 >>>> Starting back demodulation with 428.
% 37.07/37.23 ** KEPT (pick-wt=23): 533 [copy,430,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).
% 37.07/37.23 >>>> Starting back demodulation with 432.
% 37.07/37.23 >> back demodulating 396 with 432.
% 37.07/37.23 >> back demodulating 230 with 432.
% 37.07/37.23 >>>> Starting back demodulation with 437.
% 37.07/37.23 >>>> Starting back demodulation with 441.
% 37.07/37.23 >>>> Starting back demodulation with 443.
% 37.07/37.23 >>>> Starting back demodulation with 445.
% 37.07/37.23 >>>> Starting back demodulation with 447.
% 37.07/37.23 ** KEPT (pick-wt=29): 534 [copy,448,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).
% 37.07/37.23 >>>> Starting back demodulation with 451.
% 37.07/37.23 >>>> Starting back demodulation with 460.
% 37.07/37.23 Following clause subsumed by 281 during input processing: 0 [copy,486,flip.1] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.23 Following clause subsumed by 285 during input processing: 0 [copy,487,flip.1] c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),A),B),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.07/37.23 Following clause subsumed by 286 during input processing: 0 [copy,488,flip.1] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),B),C),tc_nat).
% 37.07/37.23 >>>> Starting back demodulation with 492.
% 37.07/37.23 >>>> Starting back demodulation with 494.
% 37.07/37.23 Following clause subsumed by 507 during input processing: 0 [copy,503,flip.1] c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),B,C)=hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C).
% 37.07/37.23 Following clause subsumed by 503 during input processing: 0 [copy,507,flip.1] hAPP(hAPP(c_Lambda_Olift,c_Lambda_Oliftn(A,B,C)),C)=c_Lambda_Oliftn(hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A),B,C).
% 37.07/37.23 >>>> Starting back demodulation with 510.
% 37.07/37.23 >>>> Starting back demodulation with 512.
% 37.07/37.23 ** KEPT (pick-wt=10): 535 [copy,522,flip.1] c_HOL_Ozero__class_Ozero(tc_nat)!=hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A).
% 37.07/37.23 Following clause subsumed by 400 during input processing: 0 [copy,527,flip.1] c_Nat_Ocompow(c_HOL_Ozero__class_Ozero(tc_nat),A,B,B)=c_Fun_Oid(B).
% 37.07/37.23 Following clause subsumed by 405 during input processing: 0 [copy,528,flip.1] hAPP(hAPP(hAPP(c_Type_Oshift(A),hAPP(hAPP(hAPP(c_Type_Oshift(A),B),C),D)),c_HOL_Ozero__class_Ozero(tc_nat)),E)=hAPP(hAPP(hAPP(c_Type_Oshift(A),hAPP(hAPP(hAPP(c_Type_Oshift(A),B),c_HOL_Ozero__class_Ozero(tc_nat)),E)),hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),C)),D).
% 37.07/37.23 Following clause subsumed by 413 during input processing: 0 [copy,529,flip.1] 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(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),c_Lambda_Olift),C),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 37.07/37.23 Following clause subsumed by 415 during input processing: 0 [copy,530,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(hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_nat,tc_Lambda_OdB),hAPP(hAPP(c_COMBC(tc_Lambda_OdB,tc_Lambda_OdB,tc_fun(tc_nat,tc_Lambda_OdB)),c_Lambda_Osubst),C)),D),B,tc_Lambda_OdB,tc_Lambda_OdB),tc_Lambda_OdB,tc_Lambda_OdB).
% 37.28/37.36 Following clause subsumed by 424 during input processing: 0 [copy,531,flip.1] hAPP(hAPP(hAPP(c_COMBC(A,B,C),D),E),F)=hAPP(hAPP(D,F),E).
% 37.28/37.36 Following clause subsumed by 430 during input processing: 0 [copy,533,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)).
% 37.28/37.36 Following clause subsumed by 448 during input processing: 0 [copy,534,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)).
% 37.28/37.36 Following clause subsumed by 522 during input processing: 0 [copy,535,flip.1] hAPP(hAPP(c_HOL_Oplus__class_Oplus(tc_nat),c_HOL_Oone__class_Oone(tc_nat)),A)!=c_HOL_Ozero__class_Ozero(tc_nat).
% 37.28/37.36
% 37.28/37.36 ======= end of input processing =======
% 37.28/37.36
% 37.28/37.36 =========== start of search ===========
% 37.28/37.36
% 37.28/37.36
% 37.28/37.36 Resetting weight limit to 2.
% 37.28/37.36
% 37.28/37.36
% 37.28/37.36 Resetting weight limit to 2.
% 37.28/37.36
% 37.28/37.36 sos_size=148
% 37.28/37.36
% 37.28/37.36 Search stopped in tp_alloc by max_mem option.
% 37.28/37.36
% 37.28/37.36 Search stopped in tp_alloc by max_mem option.
% 37.28/37.36
% 37.28/37.36 ============ end of search ============
% 37.28/37.36
% 37.28/37.36 -------------- statistics -------------
% 37.28/37.36 clauses given 58
% 37.28/37.36 clauses generated 10395
% 37.28/37.36 clauses kept 434
% 37.28/37.36 clauses forward subsumed 104
% 37.28/37.36 clauses back subsumed 6
% 37.28/37.36 Kbytes malloced 11718
% 37.28/37.36
% 37.28/37.36 ----------- times (seconds) -----------
% 37.28/37.36 user CPU time 0.19 (0 hr, 0 min, 0 sec)
% 37.28/37.36 system CPU time 0.01 (0 hr, 0 min, 0 sec)
% 37.28/37.36 wall-clock time 37 (0 hr, 0 min, 37 sec)
% 37.28/37.36
% 37.28/37.36 Process 20382 finished Wed Jul 27 09:31:53 2022
% 37.28/37.36 Otter interrupted
% 37.28/37.36 PROOF NOT FOUND
%------------------------------------------------------------------------------