%------------------------------------------------------------------------------ % File : Otter---3.3 % Problem : SWV585-1 : TPTP v8.1.0. Released v4.1.0. % Transfm : none % Format : tptp:raw % Command : otter-tptp-script %s % Computer : n016.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Wed Jul 27 13:21:15 EDT 2022 % Result : Unknown 179.77s 179.89s % Output : None % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWV585-1 : TPTP v8.1.0. Released v4.1.0. % 0.06/0.12 % Command : otter-tptp-script %s % 0.13/0.33 % Computer : n016.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Wed Jul 27 06:43:07 EDT 2022 % 0.13/0.33 % CPUTime : % 177.74/177.79 ----- Otter 3.3f, August 2004 ----- % 177.74/177.79 The process was started by sandbox2 on n016.cluster.edu, % 177.74/177.79 Wed Jul 27 06:43:07 2022 % 177.74/177.79 The command was "./otter". The process ID is 832. % 177.74/177.79 % 177.74/177.79 set(prolog_style_variables). % 177.74/177.79 set(auto). % 177.74/177.79 dependent: set(auto1). % 177.74/177.79 dependent: set(process_input). % 177.74/177.79 dependent: clear(print_kept). % 177.74/177.79 dependent: clear(print_new_demod). % 177.74/177.79 dependent: clear(print_back_demod). % 177.74/177.79 dependent: clear(print_back_sub). % 177.74/177.79 dependent: set(control_memory). % 177.74/177.79 dependent: assign(max_mem, 12000). % 177.74/177.79 dependent: assign(pick_given_ratio, 4). % 177.74/177.79 dependent: assign(stats_level, 1). % 177.74/177.79 dependent: assign(max_seconds, 10800). % 177.74/177.79 clear(print_given). % 177.74/177.79 % 177.74/177.79 list(usable). % 177.74/177.79 0 [] A=A. % 177.74/177.79 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)|V_y=V_z|V_w=V_x. % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)|c_Divides_Odiv__class_Omod(V_a,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a_H,V_b_H,T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_y,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Omult__zero(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Omult__zero(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_c,c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),V_d,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Opordered__ring(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,V_d,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a). % 177.74/177.79 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(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_c,V_a,T_a),c_HOL_Oplus__class_Oplus(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a). % 177.74/177.79 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(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_n,tc_nat)=V_m. % 177.74/177.79 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),V_n,tc_nat)=V_m. % 177.74/177.79 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a)=V_a. % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=V_a. % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a. % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=V_n. % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m. % 177.74/177.79 0 [] V_x=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). % 177.74/177.79 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=V_a. % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)=V_x. % 177.74/177.79 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a. % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=V_a. % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a. % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat),V_n,tc_nat)=c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=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)). % 177.74/177.79 0 [] c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))!=V_n|c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat). % 177.74/177.79 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). % 177.74/177.79 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_d,T_a),T_a)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)|V_c=V_d|V_a=V_b. % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a)=c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_m,T_a),c_HOL_Otimes__class_Otimes(V_b,V_m,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_m,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_a_H,T_a),V_b,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_ya,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Oplus__class_Oplus(V_b,V_b_H,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Ocomm__monoid__mult(T_a)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_n,T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Power_Opower__class_Opower(V_b,V_n,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_q,T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),c_Power_Opower__class_Opower(V_y,V_q,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oring__no__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ono__zero__divisors(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,T_a),c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,T_a),c_HOL_Otimes__class_Otimes(V_x,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Osemiring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_c,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_e,T_a),V_c,T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_xa,c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),T_a)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_xa,V_x,T_a),c_HOL_Otimes__class_Otimes(V_xa,V_y,T_a),T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_b,V_b_H,T_a),T_a)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b_H,T_a),T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_a_H,T_a),V_b,T_a)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(V_a_H,V_b,T_a),T_a). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),V_ya,T_a)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_ya,T_a),c_HOL_Otimes__class_Otimes(V_y,V_ya,T_a),T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(c_Int_OBit0(V_w),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a). % 177.74/177.79 0 [] c_Int_OBit1(c_Int_OMin)=c_Int_OMin. % 177.74/177.79 0 [] c_Int_OBit1(V_k)!=c_Int_OMin|V_k=c_Int_OMin. % 177.74/177.79 0 [] c_Int_OMin!=c_Int_OBit1(V_l)|c_Int_OMin=V_l. % 177.74/177.79 0 [] c_Int_OMin=c_Int_OBit1(c_Int_OMin). % 177.74/177.79 0 [] c_Int_OPls!=c_Int_OMin. % 177.74/177.79 0 [] c_Int_OMin!=c_Int_OPls. % 177.74/177.79 0 [] c_Int_OMin!=c_Int_OBit0(V_l). % 177.74/177.79 0 [] c_Int_OBit0(V_k)!=c_Int_OMin. % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat). % 177.74/177.79 0 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_i,tc_nat). % 177.74/177.79 0 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_j,V_i,tc_nat),V_i,tc_nat). % 177.74/177.79 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). % 177.74/177.79 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). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_j,V_l,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,V_l,tc_nat)!=c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)| -c_HOL_Oord__class_Oless(V_k,V_l,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat). % 177.74/177.79 0 [] -c_HOL_Oord__class_Oless(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). % 177.74/177.79 0 [] -c_HOL_Oord__class_Oless(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)=V_m| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_y,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_x,V_z,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_i,V_k,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_k,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_j,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_i,c_HOL_Oplus__class_Oplus(V_m,V_j,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)),V_n,tc_nat). % 177.74/177.79 0 [] c_Suc(V_nat_H)!=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_Suc(V_m)!=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 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). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat)=c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat)=c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_Suc(V_m),V_n,tc_nat)=c_HOL_Oplus__class_Oplus(V_m,c_Suc(V_n),tc_nat). % 177.74/177.79 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). % 177.74/177.79 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_nat_H). % 177.74/177.79 0 [] c_HOL_Ozero__class_Ozero(tc_nat)!=c_Suc(V_m). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat)=c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))|c_Suc(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat))=V_n. % 177.74/177.79 0 [] -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_Suc(V_x),tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_Suc(V_x),tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),V_n,tc_nat)=V_m| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_n,tc_nat)=V_m| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),V_m,tc_nat)),V_n,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(V_m),V_n,tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_xa,tc_nat),tc_nat). % 177.74/177.79 0 [] -c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),V_xa,tc_nat)),tc_nat). % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),T_a)=c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_m,T_a),V_n,T_a). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_w,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat)|V_y=V_z|V_w=V_x. % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_d,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)|V_c=V_d|V_a=V_b. % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)|V_m=V_n|V_k=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n. % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat)!=c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=V_n. % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_k,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)=c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Otimes__class_Otimes(V_n,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_z,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_y,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_d,tc_nat),c_HOL_Otimes__class_Otimes(V_x,V_c,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_x,V_p,T_a),V_q,T_a)=c_Power_Opower__class_Opower(V_x,c_HOL_Otimes__class_Otimes(V_p,V_q,tc_nat),T_a). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_i,V_u,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_j,V_u,tc_nat),V_k,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_i,V_j,tc_nat),V_u,tc_nat),V_k,tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_k,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_k,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_k,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_HOL_Ominus__class_Ominus(V_c,V_d,T_a),T_a). % 177.74/177.79 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. % 177.74/177.79 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. % 177.74/177.79 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. % 177.74/177.79 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_nat),tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] -class_RealVector_Oreal__normed__algebra(T_a)|c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_x,V_a,T_a),V_b,T_a),T_a),c_HOL_Otimes__class_Otimes(V_a,c_HOL_Ominus__class_Ominus(V_y,V_b,T_a),T_a),T_a). % 177.74/177.79 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 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. % 177.74/177.79 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. % 177.74/177.79 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,c_HOL_Oplus__class_Oplus(V_j,V_k,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Ominus__class_Ominus(V_n,c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Ozero__class_Ozero(tc_nat),T_a)!=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_m,T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a). % 177.74/177.79 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),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(V_c,c_HOL_Oplus__class_Oplus(V_a,V_d,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_b,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),V_d,T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Oab__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,T_a),T_a). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(V_y,c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),V_k,tc_nat)=c_HOL_Oplus__class_Oplus(V_m,c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),V_z,T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)=c_HOL_Oplus__class_Oplus(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_OrderedGroup_Ogroup__add(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_b,T_a)=V_a. % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)|c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Suc(V_n),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)| -c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat)=V_x| -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=V_m|V_n=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] V_x!=c_HOL_Oplus__class_Oplus(V_x,V_a,tc_nat)|V_a=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|V_x!=c_HOL_Oplus__class_Oplus(V_x,V_a,T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=V_m. % 177.74/177.79 0 [] c_HOL_Ominus__class_Ominus(V_m,V_m,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 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. % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_p,T_a),c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a)=c_Power_Opower__class_Opower(V_x,c_HOL_Oplus__class_Oplus(V_p,V_q,tc_nat),T_a). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)=c_Suc(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat))|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_a,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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). % 177.74/177.79 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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 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(c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_a,V_a,T_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). % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),V_x,T_a)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a)|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a)!=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a)=V_a|V_b=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a)=V_a|V_b=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 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. % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_b,tc_nat),V_c,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(T_a)|c_Power_Opower__class_Opower(V_a,V_n,T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a)=c_HOL_Ozero__class_Ozero(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_b,V_a,T_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(V_b,c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),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). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(V_a,V_b,tc_nat),V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(V_a,V_b,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Omod(V_q,V_c,tc_nat),tc_nat),V_r,tc_nat),c_HOL_Otimes__class_Otimes(V_b,V_c,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_r,V_b,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_c,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),V_n,tc_nat)|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,tc_nat),tc_nat)|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_c,T_a),T_a)!=c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_r,V_d,T_a),T_a)|V_c=V_d|V_r=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_x,V_x,T_a),c_HOL_Otimes__class_Otimes(V_y,V_y,T_a),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_x,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=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). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|V_a=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a)=V_a. % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a)=V_a. % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_k,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)|c_HOL_Oord__class_Oless(V_m,c_HOL_Otimes__class_Otimes(V_n,c_Suc(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)),tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a)|V_y=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__semiring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(V_c,c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Osemiring(T_a)| -class_Int_Onumber(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oring(T_a)| -class_Int_Onumber(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a),c_HOL_Otimes__class_Otimes(V_b,c_Int_Onumber__class_Onumber__of(V_v,T_a),T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oring(T_a)| -class_Int_Onumber(T_a)|c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_HOL_Ominus__class_Ominus(V_b,V_c,T_a),T_a)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),V_b,T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Osemiring(T_a)| -class_Int_Onumber(T_a)|c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),c_HOL_Oplus__class_Oplus(V_b,V_c,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),V_b,T_a),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_v,T_a),V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_HOL_Ozero__class_Ozero(T_a)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a). % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a),V_a,T_a)=V_a. % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OPls,T_a),T_a)=V_a. % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_Power_Opower__class_Opower(c_HOL_Ominus__class_Ominus(V_x,V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)=c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),V_x,T_a),V_y,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_q,T_a),V_x,T_a)=c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a)=c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_Suc(V_n),T_a)=c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_a,V_n,T_a),V_a,T_a). % 177.74/177.79 0 [] -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(V_n),T_a)=c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_Suc(V_q),T_a)=c_HOL_Otimes__class_Otimes(V_x,c_Power_Opower__class_Opower(V_x,V_q,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Osemiring__1(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)!=c_HOL_Ozero__class_Ozero(T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_m,V_m,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=V_m. % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Ozero__class_Ozero(tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat). % 177.74/177.79 0 [] c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(V_m))),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(c_Suc(V_m))),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),c_Int_Onumber__class_Onumber__of(V_v,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(V_m,c_Suc(c_Suc(c_Suc(V_n))),tc_nat)=c_Divides_Odiv__class_Omod(V_m,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(V_m))),V_n,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_Suc(c_Suc(V_n))),tc_nat)=c_Divides_Odiv__class_Odiv(V_m,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(c_Suc(V_m))),V_n,tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_m,tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),c_Suc(V_m),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_i,V_m,tc_nat)),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_i,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_i,tc_nat)),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_m,c_Suc(c_HOL_Oplus__class_Oplus(V_m,V_x,tc_nat)),tc_nat). % 177.74/177.79 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). % 177.74/177.79 0 [] V_x=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_x=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_x),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(V_n),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)|V_m=V_n. % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_i,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_j,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_i,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_j,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat)| -c_HOL_Oord__class_Oless(V_i,V_j,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_k,tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_m,c_Suc(V_n),tc_nat)=c_HOL_Oplus__class_Oplus(V_m,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_Suc(V_m),V_n,tc_nat)=c_HOL_Oplus__class_Oplus(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a)|V_a=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_Power_Opower__class_Opower(c_HOL_Oplus__class_Oplus(V_x,V_y,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),c_Power_Opower__class_Opower(V_y,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),V_x,T_a),V_y,T_a),T_a). % 177.74/177.79 0 [] c_Suc(c_Suc(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)))=c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_Suc(c_Suc(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),V_n,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)))=c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),V_n,tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_n,c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_m,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_n,tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),V_n,T_a),T_a)| -c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_m,tc_nat). % 177.74/177.79 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),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Olordered__ab__group__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_a,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=V_m. % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_HOL_Ozero__class_Ozero(tc_nat),T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)|c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a)=c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a)=c_Divides_Odiv__class_Odiv(V_a,V_b,T_a)|V_c=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat)|V_k=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,V_b,tc_nat),V_c,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat),c_Divides_Odiv__class_Odiv(V_b,V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat),c_Divides_Odiv__class_Omod(V_b,V_c,tc_nat),tc_nat),V_c,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat). % 177.74/177.79 0 [] -c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat). % 177.74/177.79 0 [] -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)|c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] -c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_m,tc_nat)|c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_Suc(V_x),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Suc(c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat))|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))| -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),c_HOL_Oplus__class_Oplus(V_c,V_d,T_a),T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(V_a,V_c,T_a),c_HOL_Oplus__class_Oplus(V_b,V_d,T_a),T_a). % 177.74/177.79 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat)!=c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat)|V_m=V_n. % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat)!=c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat)|V_m=V_n. % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_x,V_y,tc_nat)!=c_HOL_Oplus__class_Oplus(V_x,V_z,tc_nat)|V_y=V_z. % 177.74/177.79 0 [] -class_Ring__and__Field_Oidom(T_a)| -class_Int_Onumber__ring(T_a)|c_HOL_Oplus__class_Oplus(V_x,V_y,T_a)!=c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)|V_y=V_z. % 177.74/177.79 0 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)!=c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)|V_b=V_c. % 177.74/177.79 0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)!=c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)|V_b=V_c. % 177.74/177.79 0 [] -class_OrderedGroup_Ocancel__semigroup__add(T_a)|c_HOL_Oplus__class_Oplus(V_b,V_a,T_a)!=c_HOL_Oplus__class_Oplus(V_c,V_a,T_a)|V_b=V_c. % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a)| -c_Parity_Oeven__odd__class_Oeven(V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_m,V_k,tc_nat),c_HOL_Oplus__class_Oplus(V_n,V_k,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat). % 177.74/177.79 0 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(V_k,V_m,tc_nat),c_HOL_Oplus__class_Oplus(V_k,V_n,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat). % 177.74/177.79 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.74/177.79 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(V_a,V_c,T_a),V_b,T_a),V_c,T_a). % 177.74/177.79 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,c_Divides_Odiv__class_Omod(V_b,V_c,T_a),T_a),V_c,T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Oab__group__add(T_a)|c_HOL_Oplus__class_Oplus(V_x,c_HOL_Oplus__class_Oplus(V_y,V_z,T_a),T_a)!=c_HOL_Oplus__class_Oplus(V_y,V_u,T_a)|c_HOL_Oplus__class_Oplus(V_x,V_z,T_a)=V_u. % 177.74/177.79 0 [] c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat))=V_x|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 0 [] c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_Suc(V_a),V_c,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(V_a,V_c,tc_nat),c_Divides_Odiv__class_Odiv(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_c,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_c,tc_nat),c_Divides_Odiv__class_Omod(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),V_c,tc_nat),tc_nat),V_c,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a)=c_Divides_Odiv__class_Omod(V_a,V_b,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_e,T_a),V_c,T_a)=V_d. % 177.74/177.79 0 [] -class_Ring__and__Field_Oring(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_a,V_e,T_a),V_c,T_a)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,V_e,T_a),V_d,T_a)|V_c=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(V_b,V_a,T_a),V_e,T_a),V_d,T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,V_c,T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(V_b,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a),c_Divides_Odiv__class_Omod(V_a,V_b,T_a),T_a),V_c,T_a)=c_HOL_Oplus__class_Oplus(V_a,V_c,T_a). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat)=c_HOL_Ominus__class_Ominus(V_m,c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,c_HOL_Ozero__class_Ozero(T_a),T_a)=V_a. % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_a,V_a,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_c,T_a)=c_HOL_Oplus__class_Oplus(V_c,V_a,T_a). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)=c_HOL_Oplus__class_Oplus(V_n,V_m,tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Oplus__class_Oplus(V_x,V_y,T_a)=c_HOL_Oplus__class_Oplus(V_y,V_x,T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Ocomm__monoid__add(T_a)|c_HOL_Oplus__class_Oplus(V_a,V_b,T_a)=c_HOL_Oplus__class_Oplus(V_b,V_a,T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a),V_b,T_a)=c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a),V_b,T_a)=c_HOL_Oplus__class_Oplus(V_c,c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),T_a)|V_b=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)|c_Divides_Odiv__class_Omod(V_a,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(V_a_H,V_b_H,T_a),V_c,T_a). % 177.74/177.79 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_m=c_HOL_Ozero__class_Ozero(tc_nat)|V_n=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(V_m,V_n,tc_nat)|V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_m=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__semidom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_a,V_n,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Osemiring__0(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ozero__ne_q__one(T_a)| -class_Ring__and__Field_Ono__zero__divisors(T_a)| -class_Ring__and__Field_Omult__zero(T_a)| -class_Power_Opower(T_a)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a)=c_HOL_Ozero__class_Ozero(T_a)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),V_n,tc_nat)=c_HOL_Ominus__class_Ominus(V_m,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_n,c_Divides_Odiv__class_Odiv(V_m,V_n,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(V_m,c_Divides_Odiv__class_Omod(V_m,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(V_m,c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_HOL_Oplus__class_Oplus(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). % 177.74/177.79 0 [] -class_OrderedGroup_Opordered__comm__monoid__add(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Oplus__class_Oplus(V_a,V_b,T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_a,T_a). % 177.74/177.79 0 [] -class_Divides_Oring__div(T_a)|c_Divides_Odiv__class_Omod(V_b,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_b_H,V_c,T_a)|c_Divides_Odiv__class_Omod(V_a,V_c,T_a)!=c_Divides_Odiv__class_Omod(V_a_H,V_c,T_a)|c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a,V_b,T_a),V_c,T_a)=c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(V_a_H,V_b_H,T_a),V_c,T_a). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)|c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_x,c_HOL_Otimes__class_Otimes(V_n,V_xa,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(V_y,c_HOL_Otimes__class_Otimes(V_n,V_xb,tc_nat),tc_nat)|c_Divides_Odiv__class_Omod(V_x,V_n,tc_nat)=c_Divides_Odiv__class_Omod(V_y,V_n,tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),V_x,T_a)|c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_Suc(V_x),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Divides_Odiv__class_Odiv(V_x,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat). % 177.74/177.79 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(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(V_i,V_k,tc_nat),V_j,tc_nat)| -c_HOL_Oord__class_Oless(V_i,c_HOL_Ominus__class_Ominus(V_j,V_k,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_d,V_x,tc_nat),V_d,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_b,V_a,T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_b,T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_nat),tc_nat). % 177.74/177.79 0 [] -c_Parity_Oeven__odd__class_Oeven(V_x,tc_nat)|c_Parity_Oeven__odd__class_Oeven(V_y,tc_nat)|c_HOL_Oord__class_Oless(V_x,V_y,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(V_x,V_y,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Divides_Osemiring__div(T_a)|c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(V_a,V_b,T_a),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(V_a,V_b,T_a),V_b,T_a),T_a)=V_a. % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(T_a),c_HOL_Ozero__class_Ozero(T_a),T_a),T_a)=c_HOL_Ozero__class_Ozero(T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a)|V_x=c_HOL_Ozero__class_Ozero(T_a)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_Int_Onumber__class_Onumber__of(V_w,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(T_a),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(T_a),c_Int_Onumber__class_Onumber__of(V_w,tc_nat),T_a),T_a)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(V_w,tc_nat),tc_nat). % 177.74/177.79 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). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_n,c_HOL_Ominus__class_Ominus(V_m,V_n,tc_nat),tc_nat)=V_m|c_HOL_Oord__class_Oless(V_m,V_n,tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__idom(T_a)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(V_a,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_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). % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_a,T_a),V_a,T_a). % 177.74/177.79 0 [] c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.74/177.79 0 [] c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat)=c_Suc(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))). % 177.74/177.79 0 [] c_Suc(c_Suc(c_Suc(V_n)))=c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),V_z,T_a)=c_HOL_Oplus__class_Oplus(V_z,V_z,T_a). % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),T_a),T_a)=c_HOL_Oplus__class_Oplus(V_z,V_z,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)=c_Power_Opower__class_Opower(V_x,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)=c_HOL_Otimes__class_Otimes(V_a,V_a,T_a). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat). % 177.74/177.79 0 [] c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)=c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))). % 177.74/177.79 0 [] c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(V_m)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_Suc(c_Divides_Odiv__class_Odiv(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)=c_Suc(c_Suc(V_n)). % 177.74/177.79 0 [] c_HOL_Oplus__class_Oplus(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_Suc(c_Suc(V_n)). % 177.74/177.79 0 [] c_Divides_Odiv__class_Omod(c_Suc(c_Suc(V_m)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(V_m,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat). % 177.74/177.79 0 [] c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat). % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a)=c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a). % 177.74/177.79 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_x,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_z,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_z,tc_nat)=c_HOL_Oplus__class_Oplus(V_z,V_z,tc_nat). % 177.74/177.79 0 [] c_HOL_Ominus__class_Ominus(c_Suc(V_m),V_n,tc_nat)=c_HOL_Ominus__class_Ominus(V_m,c_HOL_Ominus__class_Ominus(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),V_n,tc_nat). % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__mult(T_a)| -class_Int_Onumber(T_a)|c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a)=c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(V_w,T_a),c_Int_Onumber__class_Onumber__of(V_w,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat),T_a)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a). % 177.74/177.79 0 [] V_n=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|V_n=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(V_n,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat). % 177.74/177.79 0 [] -c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_x,tc_nat)),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_Power_Opower__class_Opower(V_x,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a)=c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(V_x,V_n,T_a),c_Power_Opower__class_Opower(V_x,V_n,T_a),T_a),T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Omonoid__mult(T_a)|c_Power_Opower__class_Opower(V_a,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_n,tc_nat)),T_a)=c_HOL_Otimes__class_Otimes(V_a,c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(V_a,V_n,T_a),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),T_a),T_a). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] c_Int_OBit0(c_Int_OPls)=c_Int_OPls. % 177.74/177.79 0 [] -class_Orderings_Opreorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a). % 177.74/177.79 0 [] -c_HOL_Oord__class_Oless(V_x,V_x,tc_nat). % 177.74/177.79 0 [] -c_HOL_Oord__class_Oless(V_n,V_n,tc_nat). % 177.74/177.79 0 [] -class_Orderings_Oorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a). % 177.74/177.79 0 [] -class_Orderings_Olinorder(T_a)| -c_HOL_Oord__class_Oless(V_x,V_x,T_a). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] c_Suc(V_x)!=c_Suc(V_y)|V_x=V_y. % 177.74/177.79 0 [] c_Suc(V_nat)!=c_Suc(V_nat_H)|V_nat=V_nat_H. % 177.74/177.79 0 [] c_Int_OPls!=c_Int_OBit1(V_l). % 177.74/177.79 0 [] c_Int_OBit1(V_k)!=c_Int_OPls. % 177.74/177.79 0 [] c_Int_OBit0(V_k)!=c_Int_OPls|V_k=c_Int_OPls. % 177.74/177.79 0 [] c_Int_OBit0(V_k)!=c_Int_OBit0(V_l)|V_k=V_l. % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_a,V_c,T_a),c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Oordered__ring__strict(T_a)|c_HOL_Oord__class_Oless(V_b,V_a,T_a)|c_HOL_Oord__class_Oless(V_a,V_b,T_a)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_c,V_a,T_a),c_HOL_Otimes__class_Otimes(V_c,V_b,T_a),T_a). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] c_Int_OBit1(V_k)!=c_Int_OBit0(V_l). % 177.74/177.79 0 [] c_Int_OPls=c_Int_OBit0(c_Int_OPls). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_y,V_z,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),V_z,T_a). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat),V_k,tc_nat)=c_HOL_Otimes__class_Otimes(V_m,c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(V_lx,V_ry,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ry,T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a)=c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,V_rx,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_rx,T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),V_ly,T_a). % 177.74/177.79 0 [] -class_OrderedGroup_Oab__semigroup__mult(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_a,V_b,T_a),V_c,T_a)=c_HOL_Otimes__class_Otimes(V_a,c_HOL_Otimes__class_Otimes(V_b,V_c,T_a),T_a). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat)!=c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat)|V_m=V_n. % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_x,T_a)=V_x. % 177.74/177.79 0 [] c_Suc(V_n)!=V_n. % 177.74/177.79 0 [] V_n!=c_Suc(V_n). % 177.74/177.79 0 [] -class_OrderedGroup_Oab__semigroup__idem__mult(T_a)|c_HOL_Otimes__class_Otimes(V_x,c_HOL_Otimes__class_Otimes(V_x,V_y,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_x,V_y,T_a). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_k,V_m,tc_nat),c_HOL_Otimes__class_Otimes(V_k,V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(V_m,V_k,tc_nat),c_HOL_Otimes__class_Otimes(V_n,V_k,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_n,c_Suc(V_n),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_x,c_Suc(V_x),tc_nat). % 177.74/177.79 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). % 177.74/177.79 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. % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 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. % 177.74/177.79 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. % 177.74/177.79 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. % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_rx,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),V_ry,T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(V_lx,c_HOL_Otimes__class_Otimes(V_ly,c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a),T_a). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_ly,T_a),c_HOL_Otimes__class_Otimes(V_rx,V_ry,T_a),T_a)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(V_lx,V_rx,T_a),c_HOL_Otimes__class_Otimes(V_ly,V_ry,T_a),T_a). % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),V_a,T_a)=V_a. % 177.74/177.79 0 [] -class_Int_Onumber__ring(T_a)|c_HOL_Otimes__class_Otimes(V_a,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),T_a),T_a)=V_a. % 177.74/177.79 0 [] c_Int_OPls!=c_Int_OBit0(V_l)|c_Int_OPls=V_l. % 177.74/177.79 0 [] c_Int_OBit1(V_k)!=c_Int_OBit1(V_l)|V_k=V_l. % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_x,V_y,T_a)=c_HOL_Otimes__class_Otimes(V_y,V_x,T_a). % 177.74/177.79 0 [] c_HOL_Otimes__class_Otimes(V_m,V_n,tc_nat)=c_HOL_Otimes__class_Otimes(V_n,V_m,tc_nat). % 177.74/177.79 0 [] -class_Ring__and__Field_Ocomm__semiring__1(T_a)|c_HOL_Otimes__class_Otimes(V_a,V_b,T_a)=c_HOL_Otimes__class_Otimes(V_b,V_a,T_a). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] -class_Int_Oring__char__0(T_a)| -class_Int_Onumber__ring(T_a)|c_Int_Onumber__class_Onumber__of(V_x,T_a)!=c_Int_Onumber__class_Onumber__of(V_y,T_a)|V_x=V_y. % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(V_m,V_n,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_m,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(V_k),V_n,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(V_m,V_n,tc_nat). % 177.74/177.79 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). % 177.74/177.79 0 [] c_Int_OBit0(V_k)!=c_Int_OBit1(V_l). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 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). % 177.74/177.79 0 [] c_HOL_Oord__class_Oless(v_x,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),v_n,tc_nat),tc_nat). % 177.74/177.79 0 [] v_x!=c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_xa,tc_nat))| -c_HOL_Oord__class_Oless(V_xa,v_n,tc_nat). % 177.74/177.79 0 [] v_x!=c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),V_xa,tc_nat)| -c_HOL_Oord__class_Oless(V_xa,v_n,tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Oordered__semidom(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Oab__semigroup__add(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Ocomm__semiring(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Osemiring__1(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Osemiring__0(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Omult__zero(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Omonoid__mult(tc_nat). % 177.74/177.79 0 [] class_Ring__and__Field_Osemiring(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Omonoid__add(tc_nat). % 177.74/177.79 0 [] class_Divides_Osemiring__div(tc_nat). % 177.74/177.79 0 [] class_Orderings_Opreorder(tc_nat). % 177.74/177.79 0 [] class_Orderings_Olinorder(tc_nat). % 177.74/177.79 0 [] class_Orderings_Oorder(tc_nat). % 177.74/177.79 0 [] class_Power_Opower(tc_nat). % 177.74/177.79 0 [] class_Int_Onumber(tc_nat). % 177.74/177.79 0 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Oordered__semidom(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Opordered__ring(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Ozero__ne_q__one(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Oordered__idom(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Osemiring__1(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Osemiring__0(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Oab__group__add(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Omult__zero(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Omonoid__mult(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Osemiring(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Omonoid__add(tc_Int_Oint). % 177.74/177.79 0 [] class_OrderedGroup_Ogroup__add(tc_Int_Oint). % 177.74/177.79 0 [] class_Divides_Osemiring__div(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Oring(tc_Int_Oint). % 177.74/177.79 0 [] class_Ring__and__Field_Oidom(tc_Int_Oint). % 177.74/177.79 0 [] class_Orderings_Opreorder(tc_Int_Oint). % 177.74/177.79 0 [] class_Orderings_Olinorder(tc_Int_Oint). % 177.74/177.79 0 [] class_Divides_Oring__div(tc_Int_Oint). % 177.74/177.79 0 [] class_Orderings_Oorder(tc_Int_Oint). % 177.74/177.79 0 [] class_Int_Oring__char__0(tc_Int_Oint). % 177.74/177.79 0 [] class_Int_Onumber__ring(tc_Int_Oint). % 177.74/177.79 0 [] class_Power_Opower(tc_Int_Oint). % 177.74/177.79 0 [] class_Int_Onumber(tc_Int_Oint). % 177.74/177.79 end_of_list. % 177.74/177.79 % 177.74/177.79 SCAN INPUT: prop=0, horn=0, equality=1, symmetry=0, max_lits=6. % 177.74/177.79 % 177.74/177.79 This ia a non-Horn set with equality. The strategy will be % 177.74/177.79 Knuth-Bendix, ordered hyper_res, factoring, and unit % 177.74/177.79 deletion, with positive clauses in sos and nonpositive % 177.74/177.79 clauses in usable. % 177.74/177.79 % 177.74/177.79 dependent: set(knuth_bendix). % 177.74/177.79 dependent: set(anl_eq). % 177.74/177.79 dependent: set(para_from). % 177.74/177.79 dependent: set(para_into). % 177.74/177.79 dependent: clear(para_from_right). % 177.74/177.79 dependent: clear(para_into_right). % 177.74/177.79 dependent: set(para_from_vars). % 177.74/177.79 dependent: set(eq_units_both_ways). % 177.74/177.79 dependent: set(dynamic_demod_all). % 177.74/177.79 dependent: set(dynamic_demod). % 177.74/177.79 dependent: set(order_eq). % 177.74/177.79 dependent: set(back_demod). % 177.74/177.79 dependent: set(lrpo). % 177.74/177.79 dependent: set(hyper_res). % 177.74/177.79 dependent: set(unit_deletion). % 177.74/177.79 dependent: set(factor). % 177.74/177.79 % 177.74/177.79 ------------> process usable: % 177.74/177.79 ** KEPT (pick-wt=31): 1 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A)|C=E|B=D. % 177.74/177.79 ** KEPT (pick-wt=35): 2 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_Divides_Odiv__class_Omod(D,C,A)|c_Divides_Odiv__class_Omod(E,C,A)!=c_Divides_Odiv__class_Omod(F,C,A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(E,B,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(F,D,A),C,A). % 177.74/177.79 ** KEPT (pick-wt=10): 3 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.79 ** KEPT (pick-wt=10): 4 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.79 ** KEPT (pick-wt=10): 5 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.79 Following clause subsumed by 5 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.79 ** KEPT (pick-wt=10): 6 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.79 Following clause subsumed by 6 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.79 Following clause subsumed by 3 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.79 ** KEPT (pick-wt=10): 7 [] -class_Ring__and__Field_Omult__zero(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.80 ** KEPT (pick-wt=10): 8 [] -class_Ring__and__Field_Omult__zero(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.80 ** KEPT (pick-wt=10): 9 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.80 ** KEPT (pick-wt=10): 10 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A). % 177.74/177.80 ** KEPT (pick-wt=20): 12 [copy,11,flip.2] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,A),A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.74/177.80 ** KEPT (pick-wt=20): 14 [copy,13,flip.2] -class_Divides_Osemiring__div(A)|c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.74/177.80 ** KEPT (pick-wt=20): 15 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A)|B=c_HOL_Ozero__class_Ozero(A). % 177.74/177.80 ** KEPT (pick-wt=20): 16 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),A)|C=c_HOL_Ozero__class_Ozero(A). % 177.74/177.80 ** KEPT (pick-wt=16): 17 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A),c_HOL_Ozero__class_Ozero(A),A). % 177.74/177.80 ** KEPT (pick-wt=20): 18 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A),A). % 177.74/177.80 ** KEPT (pick-wt=31): 19 [] -class_Ring__and__Field_Opordered__ring(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A),E,A),F,A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),E,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,A),F,A),A). % 177.74/177.80 ** KEPT (pick-wt=31): 20 [] -class_Ring__and__Field_Opordered__ring(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),F,A). % 177.74/177.80 ** KEPT (pick-wt=31): 21 [] -class_Ring__and__Field_Opordered__ring(A)|c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(C,D,A),E,A),F,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,E,A),B,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,E,A),F,A),A). % 177.74/177.80 ** KEPT (pick-wt=31): 22 [] -class_Ring__and__Field_Opordered__ring(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A),A). % 177.74/177.80 ** KEPT (pick-wt=19): 23 [] -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). % 177.74/177.80 ** KEPT (pick-wt=19): 24 [] -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). % 177.74/177.80 ** KEPT (pick-wt=20): 25 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A)| -c_HOL_Oord__class_Oless(C,E,A)| -c_HOL_Oord__class_Oless(B,D,A). % 177.77/177.80 ** KEPT (pick-wt=16): 26 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(D,B,A),c_HOL_Oplus__class_Oplus(D,C,A),A). % 177.77/177.80 ** KEPT (pick-wt=16): 27 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A). % 177.77/177.80 ** KEPT (pick-wt=16): 28 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A). % 177.77/177.80 ** KEPT (pick-wt=16): 29 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=16): 30 [] -class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A)| -c_HOL_Oord__class_Oless(B,D,A). % 177.77/177.80 ** KEPT (pick-wt=16): 31 [] -class_OrderedGroup_Opordered__cancel__ab__semigroup__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,C,A),A)| -c_HOL_Oord__class_Oless(B,D,A). % 177.77/177.80 ** KEPT (pick-wt=21): 32 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=11): 33 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,C,A),C,A)=B. % 177.77/177.80 ** KEPT (pick-wt=9): 34 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B. % 177.77/177.80 ** KEPT (pick-wt=9): 35 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B. % 177.77/177.80 ** KEPT (pick-wt=9): 36 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B. % 177.77/177.80 Following clause subsumed by 34 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B. % 177.77/177.80 ** KEPT (pick-wt=11): 38 [copy,37,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B. % 177.77/177.80 ** KEPT (pick-wt=9): 39 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B. % 177.77/177.80 ** KEPT (pick-wt=9): 40 [] -class_OrderedGroup_Omonoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),B,A)=B. % 177.77/177.80 ** KEPT (pick-wt=9): 41 [] -class_OrderedGroup_Omonoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Ozero__class_Ozero(A),A)=B. % 177.77/177.80 ** KEPT (pick-wt=17): 42 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),D,A)=c_Divides_Odiv__class_Omod(B,D,A). % 177.77/177.80 ** KEPT (pick-wt=17): 43 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),C,A)=c_Divides_Odiv__class_Omod(B,C,A). % 177.77/177.80 ** KEPT (pick-wt=10): 44 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=11): 45 [] c_Divides_Odiv__class_Odiv(A,B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=17): 46 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=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). % 177.77/177.80 ** KEPT (pick-wt=17): 47 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=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)). % 177.77/177.80 ** KEPT (pick-wt=15): 48 [] c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat))!=B|c_Divides_Odiv__class_Omod(c_Suc(A),B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 Following clause subsumed by 1 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,E,A),c_HOL_Otimes__class_Otimes(D,C,A),A)|C=E|B=D. % 177.77/177.80 ** KEPT (pick-wt=17): 49 [] -class_OrderedGroup_Omonoid__mult(A)|c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A). % 177.77/177.80 ** KEPT (pick-wt=23): 51 [copy,50,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),c_Divides_Odiv__class_Omod(D,C,A),A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),C,A). % 177.77/177.80 ** KEPT (pick-wt=20): 53 [copy,52,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=20): 54 [] -class_Ring__and__Field_Ocomm__semiring(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=20): 55 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=20): 56 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.80 Following clause subsumed by 56 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=20): 57 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.77/177.80 Following clause subsumed by 57 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.77/177.80 Following clause subsumed by 53 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=20): 58 [] -class_OrderedGroup_Ocomm__monoid__mult(A)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=20): 59 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,D,A),c_Power_Opower__class_Opower(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=17): 60 [] -class_Ring__and__Field_Oring__no__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=17): 61 [] -class_Ring__and__Field_Ono__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 Following clause subsumed by 61 during input processing: 0 [] -class_Ring__and__Field_Ono__zero__divisors(A)|c_HOL_Otimes__class_Otimes(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=20): 62 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,D,A),C,A). % 177.77/177.80 ** KEPT (pick-wt=25): 63 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A). % 177.77/177.80 Following clause subsumed by 63 during input processing: 0 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(B,C,A),A). % 177.77/177.80 ** KEPT (pick-wt=26): 65 [copy,64,flip.2] -class_Ring__and__Field_Osemiring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),D,A),E,A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,D,A),E,A),A). % 177.77/177.80 ** KEPT (pick-wt=20): 66 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ominus__class_Ominus(C,D,A),A)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.77/177.80 Following clause subsumed by 66 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Ominus__class_Ominus(C,D,A),A)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=20): 67 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.80 Following clause subsumed by 67 during input processing: 0 [] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),D,A)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=20): 69 [copy,68,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A). % 177.77/177.80 Following clause subsumed by 62 during input processing: 0 [flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(B,D,A),C,A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),D,A). % 177.77/177.80 ** KEPT (pick-wt=17): 70 [] -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(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.80 ** KEPT (pick-wt=19): 71 [] -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(c_Int_OBit0(B),A)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,A),A),c_Int_Onumber__class_Onumber__of(B,A),A). % 177.77/177.80 ** KEPT (pick-wt=7): 72 [] c_Int_OBit1(A)!=c_Int_OMin|A=c_Int_OMin. % 177.77/177.80 ** KEPT (pick-wt=7): 74 [copy,73,flip.1] c_Int_OBit1(A)!=c_Int_OMin|c_Int_OMin=A. % 177.77/177.80 ** KEPT (pick-wt=3): 75 [] c_Int_OPls!=c_Int_OMin. % 177.77/177.80 Following clause subsumed by 75 during input processing: 0 [flip.1] c_Int_OPls!=c_Int_OMin. % 177.77/177.80 ** KEPT (pick-wt=4): 77 [copy,76,flip.1] c_Int_OBit0(A)!=c_Int_OMin. % 177.77/177.80 Following clause subsumed by 77 during input processing: 0 [] c_Int_OBit0(A)!=c_Int_OMin. % 177.77/177.80 ** KEPT (pick-wt=14): 78 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=14): 79 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(C,A,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat). % 177.77/177.80 ** KEPT (pick-wt=14): 80 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=7): 81 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=7): 82 [] -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=6): 83 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). % 177.77/177.80 ** KEPT (pick-wt=18): 84 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,D,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,D,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=11): 85 [] 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). % 177.77/177.80 ** KEPT (pick-wt=18): 86 [] 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). % 177.77/177.80 ** KEPT (pick-wt=17): 87 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(C,D,tc_nat)| -c_HOL_Oord__class_Oless(C,B,tc_nat)|c_HOL_Oord__class_Oless(A,D,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=5): 88 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). % 177.77/177.80 Following clause subsumed by 88 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat). % 177.77/177.80 ** KEPT (pick-wt=10): 89 [] c_Divides_Odiv__class_Omod(A,B,tc_nat)=A| -c_HOL_Oord__class_Oless(A,B,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=11): 90 [] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=11): 91 [] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=11): 92 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). % 177.77/177.80 Following clause subsumed by 90 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat). % 177.77/177.80 Following clause subsumed by 91 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=13): 93 [] 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). % 177.77/177.80 ** KEPT (pick-wt=14): 94 [] 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). % 177.77/177.80 ** KEPT (pick-wt=5): 95 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 Following clause subsumed by 95 during input processing: 0 [] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 Following clause subsumed by 95 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 Following clause subsumed by 95 during input processing: 0 [flip.1] c_Suc(A)!=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 ** KEPT (pick-wt=7): 96 [] -c_Parity_Oeven__odd__class_Oeven(A,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_Suc(A),tc_nat). % 177.77/177.80 ** KEPT (pick-wt=14): 97 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat)=B| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=14): 98 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),B,tc_nat)=A| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=20): 99 [] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=10): 100 [] -c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),A,tc_nat)),tc_nat). % 177.77/177.80 ** KEPT (pick-wt=17): 102 [copy,101,flip.2] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A)=c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),A). % 177.77/177.80 ** KEPT (pick-wt=12): 103 [] c_Parity_Oeven__odd__class_Oeven(A,tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat). % 177.77/177.80 ** KEPT (pick-wt=27): 104 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)|B=D|A=C. % 177.77/177.80 Following clause subsumed by 104 during input processing: 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,D,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,D,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)|B=D|A=C. % 177.77/177.80 ** KEPT (pick-wt=16): 105 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)|B=C|A=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 Following clause subsumed by 105 during input processing: 0 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=C. % 177.77/177.80 ** KEPT (pick-wt=16): 106 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(C,B,tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)|A=C. % 177.77/177.80 ** KEPT (pick-wt=9): 107 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=9): 108 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=15): 109 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 ** KEPT (pick-wt=17): 110 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),D,A)=c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(C,D,tc_nat),A). % 177.77/177.80 ** KEPT (pick-wt=23): 112 [copy,111,flip.2] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ominus__class_Ominus(D,E,A),A)=c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,E,A),A). % 177.77/177.80 ** KEPT (pick-wt=14): 113 [] -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. % 177.77/177.80 ** KEPT (pick-wt=12): 114 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C. % 177.77/177.80 ** KEPT (pick-wt=12): 115 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=C. % 177.77/177.80 ** KEPT (pick-wt=20): 116 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.80 ** KEPT (pick-wt=12): 117 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=41): 119 [copy,118,flip.2] -class_RealVector_Oreal__normed__algebra(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),c_HOL_Ominus__class_Ominus(D,E,A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),E,A),A),c_HOL_Otimes__class_Otimes(C,c_HOL_Ominus__class_Ominus(D,E,A),A),A)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A). % 177.77/177.80 ** KEPT (pick-wt=15): 120 [] -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(c_Power_Opower__class_Opower(B,C,A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.80 ** KEPT (pick-wt=14): 121 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,C,A)!=c_HOL_Ominus__class_Ominus(D,D,A)|B=C. % 177.77/177.80 ** KEPT (pick-wt=14): 122 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)!=c_HOL_Ominus__class_Ominus(C,D,A)|C=D. % 177.77/177.80 ** KEPT (pick-wt=20): 124 [copy,123,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,D,A),C,A). % 177.77/177.80 ** KEPT (pick-wt=20): 126 [copy,125,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A). % 177.77/177.80 ** KEPT (pick-wt=16): 127 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A)!=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=20): 128 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_HOL_Oplus__class_Oplus(C,D,tc_nat),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=18): 129 [] 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),c_HOL_Oplus__class_Oplus(B,A,tc_nat),tc_nat). % 177.77/177.80 ** KEPT (pick-wt=17): 130 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=17): 131 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=17): 132 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),C,A). % 177.77/177.80 Following clause subsumed by 130 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=17): 133 [] -class_OrderedGroup_Oab__semigroup__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=17): 134 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A). % 177.77/177.80 Following clause subsumed by 130 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=17): 135 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),D,A)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=17): 136 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(C,c_HOL_Oplus__class_Oplus(B,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=22): 137 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat). % 177.77/177.80 ** KEPT (pick-wt=21): 138 [] -class_Ring__and__Field_Oordered__idom(A)|B=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.80 ** KEPT (pick-wt=23): 140 [copy,139,flip.2] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,A),c_Divides_Odiv__class_Omod(D,C,A),A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,D,A),C,A). % 177.77/177.80 ** KEPT (pick-wt=11): 141 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=11): 142 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Oplus__class_Oplus(c_HOL_Ominus__class_Ominus(B,C,A),C,A)=B. % 177.77/177.80 ** KEPT (pick-wt=10): 143 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=22): 144 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(C,tc_nat)|C=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A). % 177.77/177.80 ** KEPT (pick-wt=13): 145 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Suc(B),A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=26): 146 [] -class_Ring__and__Field_Oring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(D,B,A),C,A),E,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(D,C,A),E,A). % 177.77/177.80 ** KEPT (pick-wt=13): 147 [] -class_Ring__and__Field_Oordered__idom(A)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,B,A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.80 ** KEPT (pick-wt=18): 148 [] c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),c_Divides_Odiv__class_Odiv(A,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat),tc_nat)=A| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=10): 149 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 Following clause subsumed by 149 during input processing: 0 [flip.1] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=A|B=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 ** KEPT (pick-wt=14): 151 [copy,150,flip.3] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=B|C=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 Following clause subsumed by 45 during input processing: 0 [] c_Divides_Odiv__class_Odiv(A,B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=11): 152 [] -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). % 177.77/177.80 ** KEPT (pick-wt=9): 153 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=9): 154 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,c_HOL_Ozero__class_Ozero(A),A)=B. % 177.77/177.80 Following clause subsumed by 153 during input processing: 0 [] -class_OrderedGroup_Ogroup__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=9): 155 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Ominus__class_Ominus(B,B,A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=20): 157 [copy,156,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Oplus__class_Oplus(C,D,tc_nat),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,D,A),A). % 177.77/177.80 ** KEPT (pick-wt=22): 159 [copy,158,flip.1] c_Suc(c_Divides_Odiv__class_Odiv(c_HOL_Ominus__class_Ominus(A,B,tc_nat),B,tc_nat))=c_Divides_Odiv__class_Odiv(A,B,tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=13): 160 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oplus__class_Oplus(B,B,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=11): 161 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 ** KEPT (pick-wt=11): 162 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 ** KEPT (pick-wt=10): 163 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=10): 164 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(B,c_HOL_Ozero__class_Ozero(A),A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=15): 165 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.80 ** KEPT (pick-wt=15): 166 [] -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(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.80 ** KEPT (pick-wt=15): 167 [] -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(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.80 ** KEPT (pick-wt=15): 168 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(B,B,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.80 ** KEPT (pick-wt=15): 169 [] -class_Int_Onumber__ring(A)|c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,A),B,A)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,A)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=23): 170 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A)!=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=15): 171 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),B,A)=C|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=15): 172 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),C,A)=B|C=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=17): 173 [] 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. % 177.77/177.80 ** KEPT (pick-wt=19): 174 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=13): 175 [] -class_Ring__and__Field_Oring__1__no__zero__divisors(A)|c_Power_Opower__class_Opower(B,C,A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=20): 176 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 ** KEPT (pick-wt=16): 177 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A)=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 ** KEPT (pick-wt=13): 178 [] c_Divides_Odiv__class_Omod(A,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=13): 179 [] c_Divides_Odiv__class_Omod(A,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=17): 180 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),B,A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),C,A),A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=14): 181 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),B,A)=c_Divides_Odiv__class_Omod(C,B,A). % 177.77/177.80 ** KEPT (pick-wt=14): 182 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),C,A)=c_Divides_Odiv__class_Omod(B,C,A). % 177.77/177.80 ** KEPT (pick-wt=18): 183 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(B,c_HOL_Oplus__class_Oplus(C,D,A),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A). % 177.77/177.80 ** KEPT (pick-wt=25): 184 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),D,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(D,A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=22): 185 [] c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,D,tc_nat),tc_nat)|C=D|B=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.80 ** KEPT (pick-wt=26): 186 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A)!=c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,E,A),A)|D=E|C=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=19): 187 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=19): 188 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Otimes__class_Otimes(C,C,A),A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=18): 189 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_Parity_Oeven__odd__class_Oeven(C,tc_nat). % 177.77/177.80 ** KEPT (pick-wt=12): 190 [] 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). % 177.77/177.80 ** KEPT (pick-wt=12): 191 [] 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). % 177.77/177.80 ** KEPT (pick-wt=18): 192 [] -class_Ring__and__Field_Oordered__idom(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)!=c_HOL_Ozero__class_Ozero(tc_nat)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A),A). % 177.77/177.80 Following clause subsumed by 126 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,C,A),D,A). % 177.77/177.80 Following clause subsumed by 124 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(B,D,A),C,A). % 177.77/177.80 ** KEPT (pick-wt=16): 193 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=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). % 177.77/177.80 ** KEPT (pick-wt=18): 194 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=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)). % 177.77/177.80 ** KEPT (pick-wt=17): 196 [copy,195,flip.2] -class_Divides_Osemiring__div(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A)=B. % 177.77/177.80 Following clause subsumed by 196 during input processing: 0 [] -class_Divides_Osemiring__div(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A)=B. % 177.77/177.80 ** KEPT (pick-wt=17): 197 [] -class_Divides_Osemiring__div(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A),c_Divides_Odiv__class_Omod(C,B,A),A)=C. % 177.77/177.80 ** KEPT (pick-wt=25): 198 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=27): 199 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A)!=c_HOL_Ozero__class_Ozero(A)|C=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=27): 200 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.80 ** KEPT (pick-wt=16): 201 [] -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_HOL_Oord__class_Oless(B,c_HOL_Otimes__class_Otimes(A,c_Suc(c_Divides_Odiv__class_Odiv(B,A,tc_nat)),tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=26): 202 [] -class_Ring__and__Field_Oordered__idom(A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A),A). % 177.77/177.81 ** KEPT (pick-wt=28): 203 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A),A)|C=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=28): 204 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A),A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=24): 205 [] -class_Ring__and__Field_Oordered__idom(A)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=21): 206 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A). % 177.77/177.81 ** KEPT (pick-wt=21): 207 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.77/177.81 ** KEPT (pick-wt=21): 208 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.77/177.81 ** KEPT (pick-wt=21): 209 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A). % 177.77/177.81 ** KEPT (pick-wt=10): 210 [] -class_Ring__and__Field_Oordered__ring__strict(A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,B,A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=22): 211 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,B,A),c_HOL_Otimes__class_Otimes(D,B,A),A). % 177.77/177.81 ** KEPT (pick-wt=22): 212 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.77/177.81 ** KEPT (pick-wt=20): 213 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A). % 177.77/177.81 ** KEPT (pick-wt=20): 214 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A). % 177.77/177.81 Following clause subsumed by 213 during input processing: 0 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=20): 215 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A). % 177.77/177.81 ** KEPT (pick-wt=20): 216 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(C,B,A),A). % 177.77/177.81 ** KEPT (pick-wt=20): 217 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A). % 177.77/177.81 ** KEPT (pick-wt=20): 218 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Otimes__class_Otimes(B,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=21): 219 [] -class_Ring__and__Field_Oordered__comm__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(C,D,A). % 177.77/177.81 ** KEPT (pick-wt=21): 220 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(D,B,A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=21): 221 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(B,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A). % 177.77/177.81 ** KEPT (pick-wt=21): 222 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(B,D,A). % 177.77/177.81 Following clause subsumed by 220 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(C,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,B,A). % 177.77/177.81 ** KEPT (pick-wt=21): 223 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=21): 224 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A). % 177.77/177.81 ** KEPT (pick-wt=21): 225 [] -class_Ring__and__Field_Oordered__semiring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)| -c_HOL_Oord__class_Oless(C,D,A). % 177.77/177.81 Following clause subsumed by 223 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(D,C,A). % 177.77/177.81 Following clause subsumed by 224 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(C,D,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A). % 177.77/177.81 ** KEPT (pick-wt=21): 226 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,B,A),c_HOL_Otimes__class_Otimes(D,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),D,A). % 177.77/177.81 Following clause subsumed by 223 during input processing: 0 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)| -c_HOL_Oord__class_Oless(D,C,A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=21): 227 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A)| -c_HOL_Oord__class_Oless(D,c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=28): 228 [] -class_Ring__and__Field_Osemiring(A)| -class_Int_Onumber(A)|c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,A),A),A). % 177.77/177.81 ** KEPT (pick-wt=28): 229 [] -class_Ring__and__Field_Oring(A)| -class_Int_Onumber(A)|c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,C,A),c_Int_Onumber__class_Onumber__of(D,A),A)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(D,A),A),c_HOL_Otimes__class_Otimes(C,c_Int_Onumber__class_Onumber__of(D,A),A),A). % 177.77/177.81 ** KEPT (pick-wt=28): 230 [] -class_Ring__and__Field_Oring(A)| -class_Int_Onumber(A)|c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Ominus__class_Ominus(C,D,A),A)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A). % 177.77/177.81 ** KEPT (pick-wt=28): 231 [] -class_Ring__and__Field_Osemiring(A)| -class_Int_Onumber(A)|c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),c_HOL_Oplus__class_Oplus(C,D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),C,A),c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),D,A),A). % 177.77/177.81 ** KEPT (pick-wt=8): 232 [] -class_Int_Onumber__ring(A)|c_HOL_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,A). % 177.77/177.81 Following clause subsumed by 232 during input processing: 0 [flip.2] -class_Int_Onumber__ring(A)|c_HOL_Ozero__class_Ozero(A)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,A). % 177.77/177.81 ** KEPT (pick-wt=10): 233 [] -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,A),B,A)=B. % 177.77/177.81 ** KEPT (pick-wt=10): 234 [] -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,c_Int_Onumber__class_Onumber__of(c_Int_OPls,A),A)=B. % 177.77/177.81 ** KEPT (pick-wt=45): 235 [] -class_Int_Onumber__ring(A)|c_Power_Opower__class_Opower(c_HOL_Ominus__class_Ominus(B,C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A)=c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A),B,A),C,A),A). % 177.77/177.81 ** KEPT (pick-wt=15): 237 [copy,236,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A). % 177.77/177.81 ** KEPT (pick-wt=15): 239 [copy,238,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A). % 177.77/177.81 Following clause subsumed by 239 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A). % 177.77/177.81 ** KEPT (pick-wt=15): 240 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),B,A). % 177.77/177.81 ** KEPT (pick-wt=15): 241 [] -class_Power_Opower(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A). % 177.77/177.81 Following clause subsumed by 239 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(C),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(B,C,A),A). % 177.77/177.81 ** KEPT (pick-wt=14): 242 [] -class_Ring__and__Field_Oordered__idom(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=14): 243 [] -class_Ring__and__Field_Osemiring__1(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=17): 244 [] -class_Ring__and__Field_Oordered__idom(A)|c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A)!=c_HOL_Ozero__class_Ozero(A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=14): 245 [] c_Parity_Oeven__odd__class_Oeven(A,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=14): 246 [] c_Parity_Oeven__odd__class_Oeven(c_Divides_Odiv__class_Omod(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=10): 247 [] 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). % 177.77/177.81 ** KEPT (pick-wt=16): 248 [] A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=18): 249 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=17): 250 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_HOL_Otimes__class_Otimes(A,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|B=C. % 177.77/177.81 ** KEPT (pick-wt=15): 251 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=15): 252 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(B,A,tc_nat),c_HOL_Otimes__class_Otimes(C,A,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=13): 253 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=13): 254 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=19): 255 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=19): 256 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),C,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=19): 257 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat). % 177.77/177.81 Following clause subsumed by 255 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat). % 177.77/177.81 Following clause subsumed by 255 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). % 177.77/177.81 Following clause subsumed by 257 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(A,C,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=13): 258 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.77/177.81 ** KEPT (pick-wt=13): 259 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.77/177.81 ** KEPT (pick-wt=14): 260 [] -class_Ring__and__Field_Oordered__idom(A)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=15): 261 [] -class_Ring__and__Field_Oordered__idom(A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A). % 177.77/177.81 ** KEPT (pick-wt=18): 262 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=45): 263 [] -class_Int_Onumber__ring(A)|c_Power_Opower__class_Opower(c_HOL_Oplus__class_Oplus(B,C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A),c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A),B,A),C,A),A). % 177.77/177.81 ** KEPT (pick-wt=19): 264 [] c_HOL_Oord__class_Oless(A,c_HOL_Otimes__class_Otimes(B,A,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=19): 265 [] c_HOL_Oord__class_Oless(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=21): 266 [] c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),A,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)),B,tc_nat). % 177.77/177.81 Following clause subsumed by 147 during input processing: 0 [] -class_Ring__and__Field_Oordered__idom(A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(C,c_Int_Onumber__class_Onumber__of(B,tc_nat),A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=18): 267 [] -class_Ring__and__Field_Oordered__idom(A)|B=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),B,A),A)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat). % 177.77/177.81 Following clause subsumed by 91 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). % 177.77/177.81 Following clause subsumed by 90 during input processing: 0 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=15): 268 [] -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),c_HOL_Oplus__class_Oplus(B,B,A),A). % 177.77/177.81 ** KEPT (pick-wt=15): 269 [] -class_OrderedGroup_Olordered__ab__group__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,B,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A). % 177.77/177.81 ** KEPT (pick-wt=11): 270 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_HOL_Ozero__class_Ozero(tc_nat),A),A). % 177.77/177.81 ** KEPT (pick-wt=18): 271 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(C,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=21): 272 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(B,D,A),A)=c_Divides_Odiv__class_Odiv(C,D,A)|B=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=21): 273 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,C,A),A)=c_Divides_Odiv__class_Odiv(B,D,A)|C=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=12): 274 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=12): 275 [] -c_Parity_Oeven__odd__class_Oeven(A,tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=12): 276 [] -c_Parity_Oeven__odd__class_Oeven(A,tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(B,A,tc_nat),tc_nat). % 177.77/177.81 Following clause subsumed by 274 during input processing: 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.81 Following clause subsumed by 276 during input processing: 0 [] c_Parity_Oeven__odd__class_Oeven(A,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat). % 177.77/177.81 Following clause subsumed by 275 during input processing: 0 [] c_Parity_Oeven__odd__class_Oeven(A,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(B,A,tc_nat),tc_nat). % 177.77/177.81 Following clause subsumed by 275 during input processing: 0 [] -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.81 Following clause subsumed by 276 during input processing: 0 [] -c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.81 Following clause subsumed by 274 during input processing: 0 [] -c_Parity_Oeven__odd__class_Oeven(A,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(B,A,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=14): 277 [] c_Divides_Odiv__class_Omod(A,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)!=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=23): 278 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,C,A),c_HOL_Oplus__class_Oplus(D,E,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(B,D,A),c_HOL_Oplus__class_Oplus(C,E,A),A). % 177.77/177.81 ** KEPT (pick-wt=23): 280 [copy,279,flip.2] -class_Divides_Oring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(B,C,A),c_Divides_Odiv__class_Omod(D,C,A),A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,D,A),C,A). % 177.77/177.81 ** KEPT (pick-wt=12): 281 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(C,B,tc_nat)|A=C. % 177.77/177.81 ** KEPT (pick-wt=12): 282 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(A,C,tc_nat)|B=C. % 177.77/177.81 Following clause subsumed by 282 during input processing: 0 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)!=c_HOL_Oplus__class_Oplus(A,C,tc_nat)|B=C. % 177.77/177.81 ** KEPT (pick-wt=16): 283 [] -class_Ring__and__Field_Oidom(A)| -class_Int_Onumber__ring(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(B,D,A)|C=D. % 177.77/177.81 ** KEPT (pick-wt=14): 284 [] -class_OrderedGroup_Ocancel__ab__semigroup__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(B,D,A)|C=D. % 177.77/177.81 ** KEPT (pick-wt=14): 285 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(B,D,A)|C=D. % 177.77/177.81 ** KEPT (pick-wt=14): 286 [] -class_OrderedGroup_Ocancel__semigroup__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)!=c_HOL_Oplus__class_Oplus(D,C,A)|B=D. % 177.77/177.81 ** KEPT (pick-wt=17): 287 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)|B=c_HOL_Ozero__class_Ozero(A)| -c_Parity_Oeven__odd__class_Oeven(C,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=17): 288 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(A,B,tc_nat)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|B=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.81 ** KEPT (pick-wt=17): 289 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(A,B,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat)|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.77/177.81 ** KEPT (pick-wt=12): 290 [] c_HOL_Oord__class_Oless(c_Divides_Odiv__class_Omod(A,B,tc_nat),B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),B,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=20): 292 [copy,291,flip.2] -class_Divides_Oring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(c_Divides_Odiv__class_Omod(B,C,A),D,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,D,A),C,A). % 177.77/177.81 ** KEPT (pick-wt=20): 294 [copy,293,flip.2] -class_Divides_Oring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,c_Divides_Odiv__class_Omod(C,D,A),A),D,A)=c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(B,C,A),D,A). % 177.77/177.81 ** KEPT (pick-wt=20): 295 [] -class_OrderedGroup_Oab__group__add(A)|c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(C,D,A),A)!=c_HOL_Oplus__class_Oplus(C,E,A)|c_HOL_Oplus__class_Oplus(B,D,A)=E. % 177.77/177.81 ** KEPT (pick-wt=14): 296 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Omod(B,C,A),C,A)=c_Divides_Odiv__class_Omod(B,C,A). % 177.77/177.81 Following clause subsumed by 146 during input processing: 0 [flip.2] -class_Ring__and__Field_Oring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A),A)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A). % 177.77/177.81 ** KEPT (pick-wt=29): 297 [] -class_Ring__and__Field_Oring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(B,E,A),C,A),D,A)=F. % 177.77/177.81 ** KEPT (pick-wt=29): 298 [] -class_Ring__and__Field_Oring(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,A),D,A)!=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(E,C,A),F,A)|D=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(E,B,A),C,A),F,A). % 177.77/177.81 ** KEPT (pick-wt=23): 299 [] -class_Divides_Osemiring__div(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),c_Divides_Odiv__class_Omod(B,C,A),A),D,A)=c_HOL_Oplus__class_Oplus(B,D,A). % 177.77/177.81 ** KEPT (pick-wt=23): 300 [] -class_Divides_Osemiring__div(A)|c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,c_Divides_Odiv__class_Odiv(C,B,A),A),c_Divides_Odiv__class_Omod(C,B,A),A),D,A)=c_HOL_Oplus__class_Oplus(C,D,A). % 177.77/177.81 ** KEPT (pick-wt=9): 301 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,c_HOL_Ozero__class_Ozero(A),A)=B. % 177.77/177.81 ** KEPT (pick-wt=9): 302 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,B,A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=11): 303 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A). % 177.77/177.81 Following clause subsumed by 303 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A). % 177.77/177.81 ** KEPT (pick-wt=11): 304 [] -class_OrderedGroup_Ocomm__monoid__add(A)|c_HOL_Oplus__class_Oplus(B,C,A)=c_HOL_Oplus__class_Oplus(C,B,A). % 177.77/177.81 ** KEPT (pick-wt=12): 305 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Omod(B,C,A),C,A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=24): 306 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),D,A)=c_HOL_Oplus__class_Oplus(C,c_Divides_Odiv__class_Odiv(B,D,A),A)|D=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=24): 307 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(C,D,A),A),C,A)=c_HOL_Oplus__class_Oplus(D,c_Divides_Odiv__class_Odiv(B,C,A),A)|C=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=35): 308 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_Divides_Odiv__class_Omod(D,C,A)|c_Divides_Odiv__class_Omod(E,C,A)!=c_Divides_Odiv__class_Omod(F,C,A)|c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(E,B,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(F,D,A),C,A). % 177.77/177.81 ** KEPT (pick-wt=16): 309 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(A,B,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat)|B=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.81 ** KEPT (pick-wt=18): 310 [] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))!=c_HOL_Oplus__class_Oplus(A,B,tc_nat)|B=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.77/177.81 ** KEPT (pick-wt=15): 311 [] -class_Ring__and__Field_Oordered__semidom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A). % 177.77/177.81 Following clause subsumed by 177 during input processing: 0 [] -class_Ring__and__Field_Osemiring__0(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A)=c_HOL_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.81 Following clause subsumed by 176 during input processing: 0 [] -class_Ring__and__Field_Ozero__ne_q__one(A)| -class_Ring__and__Field_Ono__zero__divisors(A)| -class_Ring__and__Field_Omult__zero(A)| -class_Power_Opower(A)|c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A)=c_HOL_Ozero__class_Ozero(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.81 Following clause subsumed by 138 during input processing: 0 [] -class_Ring__and__Field_Oordered__idom(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A),A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=20): 312 [] -class_OrderedGroup_Opordered__comm__monoid__add(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_HOL_Oplus__class_Oplus(B,C,A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),C,A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A). % 177.77/177.81 ** KEPT (pick-wt=35): 313 [] -class_Divides_Oring__div(A)|c_Divides_Odiv__class_Omod(B,C,A)!=c_Divides_Odiv__class_Omod(D,C,A)|c_Divides_Odiv__class_Omod(E,C,A)!=c_Divides_Odiv__class_Omod(F,C,A)|c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(E,B,A),C,A)=c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(F,D,A),C,A). % 177.77/177.81 ** KEPT (pick-wt=14): 314 [] -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). % 177.77/177.81 ** KEPT (pick-wt=14): 315 [] -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). % 177.77/177.81 Following clause subsumed by 144 during input processing: 0 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat)|c_Int_Onumber__class_Onumber__of(C,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A). % 177.77/177.81 ** KEPT (pick-wt=24): 316 [] c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)!=c_HOL_Oplus__class_Oplus(D,c_HOL_Otimes__class_Otimes(B,E,tc_nat),tc_nat)|c_Divides_Odiv__class_Omod(A,B,tc_nat)=c_Divides_Odiv__class_Omod(D,B,tc_nat). % 177.77/177.81 Following clause subsumed by 271 during input processing: 0 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),B,A)|c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=19): 317 [] c_Divides_Odiv__class_Odiv(c_Suc(A),c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)=c_Divides_Odiv__class_Odiv(A,c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),tc_nat)| -c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=14): 318 [] c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=14): 319 [] c_HOL_Oord__class_Oless(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat)| -c_HOL_Oord__class_Oless(A,c_HOL_Ominus__class_Ominus(C,B,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=12): 320 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),B,A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=12): 321 [] -class_Divides_Osemiring__div(A)|c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(B,C,A),C,A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 ** KEPT (pick-wt=16): 322 [] -c_Parity_Oeven__odd__class_Oeven(A,tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(B,A,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=16): 323 [] -c_Parity_Oeven__odd__class_Oeven(A,tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=17): 324 [] -class_Divides_Osemiring__div(A)|c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(B,C,A),c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(B,C,A),C,A),A)=B. % 177.77/177.81 ** KEPT (pick-wt=19): 325 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(A),c_HOL_Ozero__class_Ozero(A),A),A)=c_HOL_Ozero__class_Ozero(A). % 177.77/177.81 Following clause subsumed by 287 during input processing: 0 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(C,tc_nat),A),A)|B=c_HOL_Ozero__class_Ozero(A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(C,tc_nat),tc_nat). % 177.77/177.81 Following clause subsumed by 267 during input processing: 0 [] -class_Ring__and__Field_Oordered__idom(A)|c_Int_Onumber__class_Onumber__of(B,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(A),c_Power_Opower__class_Opower(c_HOL_Ozero__class_Ozero(A),c_Int_Onumber__class_Onumber__of(B,tc_nat),A),A)| -c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=17): 326 [] 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). % 177.77/177.81 ** KEPT (pick-wt=23): 327 [] -class_Ring__and__Field_Oordered__idom(A)|c_HOL_Oord__class_Oless(c_Power_Opower__class_Opower(B,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),C,tc_nat)),A),c_HOL_Ozero__class_Ozero(A),A)| -c_HOL_Oord__class_Oless(B,c_HOL_Ozero__class_Ozero(A),A). % 177.77/177.81 ** KEPT (pick-wt=20): 328 [] -class_Int_Onumber__ring(A)|c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(c_Int_OMin,A),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),B,tc_nat)),A)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,A). % 177.77/177.81 ** KEPT (pick-wt=18): 329 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,B,A),B,A). % 177.77/177.81 ** KEPT (pick-wt=15): 330 [] -class_Int_Onumber__ring(A)|c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A),B,A)=c_HOL_Oplus__class_Oplus(B,B,A). % 177.77/177.81 ** KEPT (pick-wt=15): 331 [] -class_Int_Onumber__ring(A)|c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),A),A)=c_HOL_Oplus__class_Oplus(B,B,A). % 177.77/177.81 ** KEPT (pick-wt=15): 333 [copy,332,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A)=c_HOL_Otimes__class_Otimes(B,B,A). % 177.77/177.81 ** KEPT (pick-wt=15): 334 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A)=c_HOL_Otimes__class_Otimes(B,B,A). % 177.77/177.81 ** KEPT (pick-wt=25): 336 [copy,335,flip.2] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A)=c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),C,tc_nat),A). % 177.77/177.81 ** KEPT (pick-wt=22): 337 [] c_HOL_Ominus__class_Ominus(c_Suc(A),B,tc_nat)=c_HOL_Ominus__class_Ominus(A,c_HOL_Ominus__class_Ominus(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),B,tc_nat). % 177.77/177.81 Following clause subsumed by 334 during input processing: 0 [] -class_OrderedGroup_Omonoid__mult(A)| -class_Int_Onumber(A)|c_Power_Opower__class_Opower(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A)=c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(B,A),c_Int_Onumber__class_Onumber__of(B,A),A). % 177.77/177.81 ** KEPT (pick-wt=24): 338 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),C,tc_nat),A)=c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,C,A),A). % 177.77/177.81 ** KEPT (pick-wt=17): 339 [] A=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))|A=c_HOL_Ozero__class_Ozero(tc_nat)| -c_HOL_Oord__class_Oless(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=11): 340 [] -c_Parity_Oeven__odd__class_Oeven(c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat)),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=28): 341 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_Power_Opower__class_Opower(B,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),C,tc_nat)),A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(c_Power_Opower__class_Opower(B,C,A),c_Power_Opower__class_Opower(B,C,A),A),A). % 177.77/177.81 ** KEPT (pick-wt=29): 342 [] -class_OrderedGroup_Omonoid__mult(A)|c_Power_Opower__class_Opower(B,c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),C,tc_nat)),A)=c_HOL_Otimes__class_Otimes(B,c_Power_Opower__class_Opower(c_Power_Opower__class_Opower(B,C,A),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A),A). % 177.77/177.81 ** KEPT (pick-wt=10): 343 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A). % 177.77/177.81 ** KEPT (pick-wt=10): 344 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A). % 177.77/177.81 ** KEPT (pick-wt=10): 345 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A). % 177.77/177.81 Following clause subsumed by 345 during input processing: 0 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,C,A)| -c_HOL_Oord__class_Oless(C,B,A). % 177.77/177.81 ** KEPT (pick-wt=6): 346 [] -class_Orderings_Opreorder(A)| -c_HOL_Oord__class_Oless(B,B,A). % 177.77/177.81 ** KEPT (pick-wt=4): 347 [] -c_HOL_Oord__class_Oless(A,A,tc_nat). % 177.77/177.81 Following clause subsumed by 347 during input processing: 0 [] -c_HOL_Oord__class_Oless(A,A,tc_nat). % 177.77/177.81 ** KEPT (pick-wt=6): 348 [] -class_Orderings_Oorder(A)| -c_HOL_Oord__class_Oless(B,B,A). % 177.77/177.81 ** KEPT (pick-wt=6): 349 [] -class_Orderings_Olinorder(A)| -c_HOL_Oord__class_Oless(B,B,A). % 177.77/177.81 ** KEPT (pick-wt=12): 350 [] A=B|c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat). % 177.77/177.81 ** KEPT (pick-wt=12): 351 [] A=B| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat). % 177.77/177.81 Following clause subsumed by 350 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). % 177.77/177.81 ** KEPT (pick-wt=8): 352 [] c_Suc(A)!=c_Suc(B)|A=B. % 177.77/177.81 Following clause subsumed by 352 during input processing: 0 [] c_Suc(A)!=c_Suc(B)|A=B. % 177.77/177.81 ** KEPT (pick-wt=4): 354 [copy,353,flip.1] c_Int_OBit1(A)!=c_Int_OPls. % 177.77/177.81 Following clause subsumed by 354 during input processing: 0 [] c_Int_OBit1(A)!=c_Int_OPls. % 177.77/177.81 ** KEPT (pick-wt=7): 355 [] c_Int_OBit0(A)!=c_Int_OPls|A=c_Int_OPls. % 177.77/177.81 ** KEPT (pick-wt=8): 356 [] c_Int_OBit0(A)!=c_Int_OBit0(B)|A=B. % 177.77/177.81 ** KEPT (pick-wt=20): 357 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,D,A),c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.77/177.82 ** KEPT (pick-wt=20): 358 [] -class_Ring__and__Field_Oordered__ring__strict(A)|c_HOL_Oord__class_Oless(B,C,A)|c_HOL_Oord__class_Oless(C,B,A)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(D,C,A),c_HOL_Otimes__class_Otimes(D,B,A),A). % 177.77/177.82 ** KEPT (pick-wt=9): 359 [] -c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(B,c_Suc(A),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=5): 360 [] c_Int_OBit1(A)!=c_Int_OBit0(B). % 177.77/177.82 ** KEPT (pick-wt=17): 362 [copy,361,flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.82 ** KEPT (pick-wt=17): 363 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A)=c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(B,D,A),A). % 177.77/177.82 Following clause subsumed by 362 during input processing: 0 [flip.2] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.82 Following clause subsumed by 362 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.82 ** KEPT (pick-wt=17): 364 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),C,A). % 177.77/177.82 ** KEPT (pick-wt=17): 365 [] -class_OrderedGroup_Oab__semigroup__mult(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),D,A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,D,A),A). % 177.77/177.82 ** KEPT (pick-wt=14): 366 [] c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat)!=c_HOL_Otimes__class_Otimes(c_Suc(A),C,tc_nat)|B=C. % 177.77/177.82 ** KEPT (pick-wt=9): 367 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=9): 368 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=8): 369 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,B,A)=B. % 177.77/177.82 ** KEPT (pick-wt=4): 370 [] c_Suc(A)!=A. % 177.77/177.82 Following clause subsumed by 370 during input processing: 0 [flip.1] c_Suc(A)!=A. % 177.77/177.82 ** KEPT (pick-wt=14): 371 [] -class_OrderedGroup_Oab__semigroup__idem__mult(A)|c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(B,C,A),A)=c_HOL_Otimes__class_Otimes(B,C,A). % 177.77/177.82 ** KEPT (pick-wt=14): 372 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(C,A,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=14): 373 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=13): 374 [] 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). % 177.77/177.82 ** KEPT (pick-wt=13): 375 [] -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. % 177.77/177.82 ** KEPT (pick-wt=13): 376 [] -class_Orderings_Olinorder(A)|B=C|c_HOL_Oord__class_Oless(C,B,A)|c_HOL_Oord__class_Oless(B,C,A). % 177.77/177.82 Following clause subsumed by 376 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). % 177.77/177.82 Following clause subsumed by 376 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). % 177.77/177.82 Following clause subsumed by 376 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. % 177.77/177.82 Following clause subsumed by 363 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(D,c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),E,A),A). % 177.77/177.82 Following clause subsumed by 362 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(B,c_HOL_Otimes__class_Otimes(C,c_HOL_Otimes__class_Otimes(D,E,A),A),A). % 177.77/177.82 ** KEPT (pick-wt=23): 377 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,C,A),c_HOL_Otimes__class_Otimes(D,E,A),A)=c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(B,D,A),c_HOL_Otimes__class_Otimes(C,E,A),A). % 177.77/177.82 ** KEPT (pick-wt=11): 378 [] -class_Int_Onumber__ring(A)|c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A),B,A)=B. % 177.77/177.82 ** KEPT (pick-wt=11): 379 [] -class_Int_Onumber__ring(A)|c_HOL_Otimes__class_Otimes(B,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),A),A)=B. % 177.77/177.82 ** KEPT (pick-wt=7): 381 [copy,380,flip.1] c_Int_OBit0(A)!=c_Int_OPls|c_Int_OPls=A. % 177.77/177.82 ** KEPT (pick-wt=8): 382 [] c_Int_OBit1(A)!=c_Int_OBit1(B)|A=B. % 177.77/177.82 ** KEPT (pick-wt=11): 383 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A). % 177.77/177.82 Following clause subsumed by 383 during input processing: 0 [] -class_Ring__and__Field_Ocomm__semiring__1(A)|c_HOL_Otimes__class_Otimes(B,C,A)=c_HOL_Otimes__class_Otimes(C,B,A). % 177.77/177.82 ** KEPT (pick-wt=14): 384 [] -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). % 177.77/177.82 ** KEPT (pick-wt=14): 385 [] -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). % 177.77/177.82 ** KEPT (pick-wt=14): 386 [] -class_Int_Oring__char__0(A)| -class_Int_Onumber__ring(A)|c_Int_Onumber__class_Onumber__of(B,A)!=c_Int_Onumber__class_Onumber__of(C,A)|B=C. % 177.77/177.82 Following clause subsumed by 372 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(C),A,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(C),B,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=16): 387 [] c_HOL_Oord__class_Oless(c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat),c_HOL_Otimes__class_Otimes(c_Suc(A),C,tc_nat),tc_nat)| -c_HOL_Oord__class_Oless(B,C,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=13): 388 [] c_HOL_Oord__class_Oless(c_Suc(A),B,tc_nat)|c_Suc(A)=B| -c_HOL_Oord__class_Oless(A,B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=5): 389 [] c_Int_OBit0(A)!=c_Int_OBit1(B). % 177.77/177.82 ** KEPT (pick-wt=10): 390 [] c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat)| -c_HOL_Oord__class_Oless(A,B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=10): 391 [] c_HOL_Oord__class_Oless(A,B,tc_nat)| -c_HOL_Oord__class_Oless(c_Suc(A),c_Suc(B),tc_nat). % 177.77/177.82 Following clause subsumed by 390 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). % 177.77/177.82 ** KEPT (pick-wt=15): 393 [copy,392,flip.1] c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat))!=v_x| -c_HOL_Oord__class_Oless(A,v_n,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=14): 395 [copy,394,flip.1] c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat)!=v_x| -c_HOL_Oord__class_Oless(A,v_n,tc_nat). % 177.77/177.82 88 back subsumes 83. % 177.77/177.82 120 back subsumes 70. % 177.77/177.82 174 back subsumes 32. % 177.77/177.82 189 back subsumes 137. % 177.77/177.82 Following clause subsumed by 389 during input processing: 0 [copy,360,flip.1] c_Int_OBit0(A)!=c_Int_OBit1(B). % 177.77/177.82 372 back subsumes 256. % 177.77/177.82 Following clause subsumed by 360 during input processing: 0 [copy,389,flip.1] c_Int_OBit1(A)!=c_Int_OBit0(B). % 177.77/177.82 % 177.77/177.82 ------------> process sos: % 177.77/177.82 ** KEPT (pick-wt=3): 450 [] A=A. % 177.77/177.82 ** KEPT (pick-wt=9): 451 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat)=A. % 177.77/177.82 ---> New Demodulator: 452 [new_demod,451] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),B,tc_nat)=A. % 177.77/177.82 ** KEPT (pick-wt=9): 453 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat)=B. % 177.77/177.82 ---> New Demodulator: 454 [new_demod,453] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),A,tc_nat)=B. % 177.77/177.82 ** KEPT (pick-wt=7): 455 [] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A. % 177.77/177.82 ---> New Demodulator: 456 [new_demod,455] c_HOL_Oplus__class_Oplus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=A. % 177.77/177.82 ** KEPT (pick-wt=7): 457 [] c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A. % 177.77/177.82 ---> New Demodulator: 458 [new_demod,457] c_HOL_Oplus__class_Oplus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A. % 177.77/177.82 Following clause subsumed by 450 during input processing: 0 [demod,458] A=A. % 177.77/177.82 ** KEPT (pick-wt=15): 459 [] c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat),B,tc_nat)=c_Divides_Odiv__class_Omod(C,B,tc_nat). % 177.77/177.82 ---> New Demodulator: 460 [new_demod,459] c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat),B,tc_nat)=c_Divides_Odiv__class_Omod(C,B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=8): 461 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=15): 462 [] 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). % 177.77/177.82 ** KEPT (pick-wt=4): 463 [] c_Int_OBit1(c_Int_OMin)=c_Int_OMin. % 177.77/177.82 ---> New Demodulator: 464 [new_demod,463] c_Int_OBit1(c_Int_OMin)=c_Int_OMin. % 177.77/177.82 Following clause subsumed by 450 during input processing: 0 [demod,464] c_Int_OMin=c_Int_OMin. % 177.77/177.82 ** KEPT (pick-wt=9): 465 [] c_HOL_Oord__class_Oless(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)|A=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ** KEPT (pick-wt=14): 467 [copy,466,flip.1] c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat)),B,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(A),B,tc_nat). % 177.77/177.82 ---> New Demodulator: 468 [new_demod,467] c_Divides_Odiv__class_Omod(c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat)),B,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(A),B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=11): 469 [] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat). % 177.77/177.82 ---> New Demodulator: 470 [new_demod,469] c_HOL_Ominus__class_Ominus(c_Suc(A),c_Suc(B),tc_nat)=c_HOL_Ominus__class_Ominus(A,B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=11): 472 [copy,471,flip.1] c_Suc(c_HOL_Oplus__class_Oplus(A,B,tc_nat))=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat). % 177.77/177.82 ---> New Demodulator: 473 [new_demod,472] c_Suc(c_HOL_Oplus__class_Oplus(A,B,tc_nat))=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=11): 475 [copy,474,demod,473] c_HOL_Oplus__class_Oplus(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat). % 177.77/177.82 Following clause subsumed by 475 during input processing: 0 [] c_HOL_Oplus__class_Oplus(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=17): 476 [] 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). % 177.77/177.82 ---> New Demodulator: 477 [new_demod,476] 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). % 177.77/177.82 ** KEPT (pick-wt=18): 479 [copy,478,flip.1] c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat))=c_Divides_Odiv__class_Omod(c_Suc(A),B,tc_nat)|c_Suc(c_Divides_Odiv__class_Omod(A,B,tc_nat))=B. % 177.77/177.82 ** KEPT (pick-wt=7): 480 [] c_Parity_Oeven__odd__class_Oeven(c_Suc(A),tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.82 Following clause subsumed by 450 during input processing: 0 [demod,473,460] c_Divides_Odiv__class_Omod(c_Suc(C),B,tc_nat)=c_Divides_Odiv__class_Omod(c_Suc(C),B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=9): 481 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Suc(c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))),A,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=15): 482 [] c_Divides_Odiv__class_Odiv(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=8): 483 [] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ---> New Demodulator: 484 [new_demod,483] c_HOL_Otimes__class_Otimes(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ** KEPT (pick-wt=8): 485 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ---> New Demodulator: 486 [new_demod,485] c_HOL_Otimes__class_Otimes(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ** KEPT (pick-wt=18): 487 [] c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 488 [new_demod,487] c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=18): 489 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 490 [new_demod,489] c_HOL_Otimes__class_Otimes(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). % 177.77/177.82 Following clause subsumed by 450 during input processing: 0 [demod,484,484] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 Following clause subsumed by 450 during input processing: 0 [demod,486,486] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ** KEPT (pick-wt=21): 491 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). % 177.77/177.82 Following clause subsumed by 491 during input processing: 0 [] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=27): 493 [copy,492,demod,488,flip.1] c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat),D,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_nat),D,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 494 [new_demod,493] c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(C,B,tc_nat),tc_nat),D,tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(C,B,tc_nat),D,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=18): 495 [] c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 496 [new_demod,495] c_HOL_Otimes__class_Otimes(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=18): 497 [] c_HOL_Otimes__class_Otimes(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 498 [new_demod,497] c_HOL_Otimes__class_Otimes(A,c_HOL_Ominus__class_Ominus(B,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=18): 499 [] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 500 [new_demod,499] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Omod(A,B,tc_nat),C,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=12): 501 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Ominus__class_Ominus(A,B,tc_nat),tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=8): 502 [] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ---> New Demodulator: 503 [new_demod,502] c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(tc_nat),A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ** KEPT (pick-wt=15): 504 [] c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat)=c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=10): 505 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ** KEPT (pick-wt=15): 506 [] c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=15): 507 [] c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 508 [new_demod,507] c_HOL_Oplus__class_Oplus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),C,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). % 177.77/177.82 Following clause subsumed by 450 during input processing: 0 [demod,458] c_HOL_Ozero__class_Ozero(tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 Following clause subsumed by 450 during input processing: 0 [demod,458] c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))=c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)). % 177.77/177.82 ** KEPT (pick-wt=7): 509 [] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A. % 177.77/177.82 ---> New Demodulator: 510 [new_demod,509] c_HOL_Ominus__class_Ominus(A,c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=A. % 177.77/177.82 ** KEPT (pick-wt=7): 511 [] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ** KEPT (pick-wt=27): 513 [copy,512,flip.1] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat). % 177.77/177.82 ---> New Demodulator: 514 [new_demod,513] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,C,tc_nat),tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat),C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=9): 516 [copy,515,demod,484,484] c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ---> New Demodulator: 517 [new_demod,516] c_Divides_Odiv__class_Odiv(c_HOL_Ozero__class_Ozero(tc_nat),c_HOL_Ozero__class_Ozero(tc_nat),tc_nat)=c_HOL_Ozero__class_Ozero(tc_nat). % 177.77/177.82 ** KEPT (pick-wt=24): 519 [copy,518,flip.1] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(B,A,tc_nat),C,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(B,A,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(B,c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 520 [new_demod,519] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(c_Divides_Odiv__class_Odiv(B,A,tc_nat),C,tc_nat),tc_nat),c_Divides_Odiv__class_Omod(B,A,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(B,c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=16): 522 [copy,521,flip.1] c_Divides_Odiv__class_Omod(c_HOL_Ominus__class_Ominus(A,B,tc_nat),B,tc_nat)=c_Divides_Odiv__class_Omod(A,B,tc_nat)|c_HOL_Oord__class_Oless(A,B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=18): 523 [] c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 524 [new_demod,523] c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Omod(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=13): 525 [] c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,A,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=A. % 177.77/177.82 ---> New Demodulator: 526 [new_demod,525] c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,A,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=A. % 177.77/177.82 ** KEPT (pick-wt=6): 527 [] c_HOL_Ozero__class_Ozero(tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat). % 177.77/177.82 ---> New Demodulator: 528 [new_demod,527] c_HOL_Ozero__class_Ozero(tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat). % 177.77/177.82 Following clause subsumed by 450 during input processing: 0 [demod,528] c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=23): 529 [] c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(A))),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 530 [new_demod,529] c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(A))),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=23): 531 [] c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(c_Suc(A))),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 532 [new_demod,531] c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(c_Suc(A))),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),c_Int_Onumber__class_Onumber__of(B,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=19): 533 [] c_Divides_Odiv__class_Omod(A,c_Suc(c_Suc(c_Suc(B))),tc_nat)=c_Divides_Odiv__class_Omod(A,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),B,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 534 [new_demod,533] c_Divides_Odiv__class_Omod(A,c_Suc(c_Suc(c_Suc(B))),tc_nat)=c_Divides_Odiv__class_Omod(A,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),B,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=19): 535 [] c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(A))),B,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),B,tc_nat). % 177.77/177.82 ---> New Demodulator: 536 [new_demod,535] c_Divides_Odiv__class_Omod(c_Suc(c_Suc(c_Suc(A))),B,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=19): 537 [] c_Divides_Odiv__class_Odiv(A,c_Suc(c_Suc(c_Suc(B))),tc_nat)=c_Divides_Odiv__class_Odiv(A,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),B,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 538 [new_demod,537] c_Divides_Odiv__class_Odiv(A,c_Suc(c_Suc(c_Suc(B))),tc_nat)=c_Divides_Odiv__class_Odiv(A,c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),B,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=19): 539 [] c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(c_Suc(A))),B,tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),B,tc_nat). % 177.77/177.82 ---> New Demodulator: 540 [new_demod,539] c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(c_Suc(A))),B,tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=9): 542 [copy,541,demod,528,528] c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=8): 543 [] c_HOL_Oord__class_Oless(c_HOL_Ominus__class_Ominus(A,B,tc_nat),c_Suc(A),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=8): 545 [copy,544,demod,473] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=8): 547 [copy,546,demod,473] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(B,c_Suc(A),tc_nat),tc_nat). % 177.77/177.82 Following clause subsumed by 545 during input processing: 0 [demod,473] c_HOL_Oord__class_Oless(A,c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=7): 549 [copy,548,demod,528] c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),c_Suc(A),tc_nat). % 177.77/177.82 Following clause subsumed by 549 during input processing: 0 [demod,528] c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),c_Suc(A),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=15): 551 [copy,550,demod,528,528,528] c_HOL_Otimes__class_Otimes(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),tc_nat)=c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)). % 177.77/177.82 ---> New Demodulator: 552 [new_demod,551] c_HOL_Otimes__class_Otimes(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),tc_nat)=c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)). % 177.77/177.82 ** KEPT (pick-wt=13): 553 [] c_HOL_Otimes__class_Otimes(A,c_Suc(B),tc_nat)=c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 554 [new_demod,553] c_HOL_Otimes__class_Otimes(A,c_Suc(B),tc_nat)=c_HOL_Oplus__class_Oplus(A,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=13): 555 [] c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). % 177.77/177.82 ---> New Demodulator: 556 [new_demod,555] c_HOL_Otimes__class_Otimes(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(B,c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=31): 558 [copy,557,demod,528] c_Suc(c_Suc(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)))=c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat)|A=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=33): 560 [copy,559,demod,528] c_Suc(c_Suc(c_HOL_Ominus__class_Ominus(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),A,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)))=c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),tc_nat),A,tc_nat)|A=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=9): 562 [copy,561,demod,528] c_Divides_Odiv__class_Odiv(A,c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),tc_nat)=A. % 177.77/177.82 ---> New Demodulator: 563 [new_demod,562] c_Divides_Odiv__class_Odiv(A,c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),tc_nat)=A. % 177.77/177.82 ** KEPT (pick-wt=20): 565 [copy,564,demod,528] c_Divides_Odiv__class_Odiv(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(B,C,tc_nat)|A=c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=33): 567 [copy,566,demod,508,flip.1] c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(C,B,tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_nat),c_Divides_Odiv__class_Omod(C,B,tc_nat),tc_nat),B,tc_nat),tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). % 177.77/177.82 ---> New Demodulator: 568 [new_demod,567] c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,B,tc_nat),c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(C,B,tc_nat),c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Omod(A,B,tc_nat),c_Divides_Odiv__class_Omod(C,B,tc_nat),tc_nat),B,tc_nat),tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,C,tc_nat),B,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=12): 569 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.82 Following clause subsumed by 569 during input processing: 0 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.82 Following clause subsumed by 569 during input processing: 0 [] c_Parity_Oeven__odd__class_Oeven(A,tc_nat)|c_Parity_Oeven__odd__class_Oeven(B,tc_nat)|c_Parity_Oeven__odd__class_Oeven(c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat). % 177.77/177.82 ** KEPT (pick-wt=22): 571 [copy,570,demod,528,528,flip.1] c_Suc(c_Divides_Odiv__class_Odiv(A,c_Suc(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))),tc_nat))=c_Divides_Odiv__class_Odiv(c_Suc(A),c_Suc(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))),tc_nat)|c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=16): 573 [copy,572,demod,528,528] c_Divides_Odiv__class_Omod(A,c_Suc(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))),tc_nat)=c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))|c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=15): 574 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat). % 177.77/177.82 ---> New Demodulator: 575 [new_demod,574] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(C,B,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(A,C,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=15): 576 [] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat). % 177.77/177.82 ---> New Demodulator: 577 [new_demod,576] c_HOL_Ominus__class_Ominus(c_HOL_Oplus__class_Oplus(A,B,tc_nat),c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(B,C,tc_nat). % 177.77/177.82 ** KEPT (pick-wt=14): 579 [copy,578,demod,528,528,528,flip.1] c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),tc_nat)=c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)). % 177.77/177.82 ---> New Demodulator: 580 [new_demod,579] c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)),tc_nat)=c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)). % 177.77/177.82 ** KEPT (pick-wt=39): 582 [copy,581,demod,528,528,556,556,473,473] c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,c_Suc(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))),tc_nat),c_HOL_Oplus__class_Oplus(c_Divides_Odiv__class_Odiv(A,c_Suc(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))),tc_nat),c_Suc(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat),c_Divides_Odiv__class_Odiv(A,c_Suc(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat))),tc_nat),tc_nat)),tc_nat),tc_nat)=A|c_Parity_Oeven__odd__class_Oeven(A,tc_nat). % 177.80/177.82 ** KEPT (pick-wt=7): 584 [copy,583,demod,528,flip.1] c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat). % 177.80/177.82 ---> New Demodulator: 585 [new_demod,584] c_Int_Onumber__class_Onumber__of(c_Int_OPls,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat). % 177.80/177.82 ** KEPT (pick-wt=16): 587 [copy,586,demod,528,585,528,585,508,568] c_Divides_Odiv__class_Odiv(c_Suc(A),B,tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),tc_nat),B,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=15): 589 [copy,588,flip.1] c_HOL_Ominus__class_Ominus(A,c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(A,B,tc_nat). % 177.80/177.83 ---> New Demodulator: 590 [new_demod,589] c_HOL_Ominus__class_Ominus(A,c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(A,B,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=9): 591 [] c_HOL_Oplus__class_Oplus(A,B,tc_nat)=c_HOL_Oplus__class_Oplus(B,A,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=5): 593 [copy,592,demod,528,585] c_Parity_Oeven__odd__class_Oeven(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=15): 594 [] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat)=c_HOL_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(A,B,tc_nat),tc_nat). % 177.80/177.83 ---> New Demodulator: 595 [new_demod,594] c_HOL_Otimes__class_Otimes(c_Divides_Odiv__class_Odiv(A,B,tc_nat),B,tc_nat)=c_HOL_Ominus__class_Ominus(A,c_Divides_Odiv__class_Omod(A,B,tc_nat),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=15): 596 [] c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(B,c_Divides_Odiv__class_Omod(B,A,tc_nat),tc_nat). % 177.80/177.83 ---> New Demodulator: 597 [new_demod,596] c_HOL_Otimes__class_Otimes(A,c_Divides_Odiv__class_Odiv(B,A,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(B,c_Divides_Odiv__class_Omod(B,A,tc_nat),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=11): 599 [copy,598,demod,528,585,528,585] c_Divides_Odiv__class_Omod(A,c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat). % 177.80/177.83 ---> New Demodulator: 600 [new_demod,599] c_Divides_Odiv__class_Omod(A,c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=14): 602 [copy,601,demod,528,585,528,585,528,585,flip.1] c_HOL_Oplus__class_Oplus(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),tc_nat)=c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)). % 177.80/177.83 ---> New Demodulator: 603 [new_demod,602] c_HOL_Oplus__class_Oplus(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),tc_nat)=c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)). % 177.80/177.83 ** KEPT (pick-wt=14): 605 [copy,604,demod,528,585,528,585,528,585] c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),tc_nat)=c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)). % 177.80/177.83 ---> New Demodulator: 606 [new_demod,605] c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)),tc_nat)=c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)). % 177.80/177.83 ** KEPT (pick-wt=11): 608 [copy,607,demod,528,585] c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=13): 609 [] c_HOL_Oplus__class_Oplus(A,c_HOL_Ominus__class_Ominus(B,A,tc_nat),tc_nat)=B|c_HOL_Oord__class_Oless(B,A,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=9): 611 [copy,610,demod,528,585,flip.1] c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat). % 177.80/177.83 ---> New Demodulator: 612 [new_demod,611] c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat))=c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=12): 614 [copy,613,demod,528,585,612,flip.1] c_Suc(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)))=c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat). % 177.80/177.83 ---> New Demodulator: 615 [new_demod,614] c_Suc(c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat)))=c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=13): 616 [] c_Suc(c_Suc(c_Suc(A)))=c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat). % 177.80/177.83 ---> New Demodulator: 617 [new_demod,616] c_Suc(c_Suc(c_Suc(A)))=c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=10): 619 [copy,618,demod,528,585] c_HOL_Oord__class_Oless(c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=11): 621 [copy,620,demod,528,585,612,flip.1] c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat))=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat). % 177.80/177.83 ---> New Demodulator: 622 [new_demod,621] c_Suc(c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat))=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=20): 623 [] c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_Suc(c_Divides_Odiv__class_Odiv(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)). % 177.80/177.83 ---> New Demodulator: 624 [new_demod,623] c_Divides_Odiv__class_Odiv(c_Suc(c_Suc(A)),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_Suc(c_Divides_Odiv__class_Odiv(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)). % 177.80/177.83 ** KEPT (pick-wt=12): 626 [copy,625,flip.1] c_Suc(c_Suc(A))=c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat). % 177.80/177.83 ---> New Demodulator: 627 [new_demod,626] c_Suc(c_Suc(A))=c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat). % 177.80/177.83 Following clause subsumed by 591 during input processing: 0 [demod,627] c_HOL_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=24): 629 [copy,628,demod,627] c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat). % 177.80/177.83 ---> New Demodulator: 630 [new_demod,629] c_Divides_Odiv__class_Omod(c_HOL_Oplus__class_Oplus(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_Divides_Odiv__class_Omod(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat). % 177.80/177.83 Following clause subsumed by 450 during input processing: 0 [demod,528,585,612,622] c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=10): 631 [] c_Parity_Oeven__odd__class_Oeven(c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=13): 632 [] c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(A,A,tc_nat). % 177.80/177.83 ---> New Demodulator: 633 [new_demod,632] c_HOL_Otimes__class_Otimes(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(A,A,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=13): 634 [] c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat)=c_HOL_Oplus__class_Oplus(A,A,tc_nat). % 177.80/177.83 ---> New Demodulator: 635 [new_demod,634] c_HOL_Otimes__class_Otimes(c_Int_Onumber__class_Onumber__of(c_Int_OBit0(c_Int_OBit1(c_Int_OPls)),tc_nat),A,tc_nat)=c_HOL_Oplus__class_Oplus(A,A,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=4): 636 [] c_Int_OBit0(c_Int_OPls)=c_Int_OPls. % 177.80/177.83 ---> New Demodulator: 637 [new_demod,636] c_Int_OBit0(c_Int_OPls)=c_Int_OPls. % 177.80/177.83 ** KEPT (pick-wt=9): 638 [] c_HOL_Oord__class_Oless(A,c_Suc(B),tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=5): 640 [copy,639,unit_del,347] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat). % 177.80/177.83 Following clause subsumed by 450 during input processing: 0 [demod,637] c_Int_OPls=c_Int_OPls. % 177.80/177.83 ** KEPT (pick-wt=15): 641 [] c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat)=c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). % 177.80/177.83 ---> New Demodulator: 642 [new_demod,641] c_HOL_Otimes__class_Otimes(c_HOL_Otimes__class_Otimes(A,B,tc_nat),C,tc_nat)=c_HOL_Otimes__class_Otimes(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). % 177.80/177.83 Following clause subsumed by 640 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat). % 177.80/177.83 Following clause subsumed by 640 during input processing: 0 [] c_HOL_Oord__class_Oless(A,c_Suc(A),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=11): 643 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A. % 177.80/177.83 Following clause subsumed by 643 during input processing: 0 [] c_HOL_Oord__class_Oless(A,B,tc_nat)|c_HOL_Oord__class_Oless(B,A,tc_nat)|B=A. % 177.80/177.83 ** KEPT (pick-wt=9): 644 [] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=7): 646 [copy,645,demod,635] c_HOL_Oord__class_Oless(v_x,c_HOL_Oplus__class_Oplus(v_n,v_n,tc_nat),tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 647 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 648 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 649 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 650 [] class_Ring__and__Field_Oordered__semiring__strict(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 651 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 652 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 653 [] class_OrderedGroup_Ocancel__semigroup__add(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 654 [] class_Ring__and__Field_Ono__zero__divisors(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 655 [] class_Ring__and__Field_Oordered__semidom(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 656 [] class_Ring__and__Field_Ocomm__semiring__1(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 657 [] class_OrderedGroup_Oab__semigroup__mult(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 658 [] class_OrderedGroup_Ocomm__monoid__mult(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 659 [] class_OrderedGroup_Oab__semigroup__add(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 660 [] class_Ring__and__Field_Ocomm__semiring(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 661 [] class_OrderedGroup_Ocomm__monoid__add(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 662 [] class_Ring__and__Field_Ozero__ne_q__one(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 663 [] class_Ring__and__Field_Osemiring__1(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 664 [] class_Ring__and__Field_Osemiring__0(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 665 [] class_Ring__and__Field_Omult__zero(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 666 [] class_OrderedGroup_Omonoid__mult(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 667 [] class_Ring__and__Field_Osemiring(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 668 [] class_OrderedGroup_Omonoid__add(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 669 [] class_Divides_Osemiring__div(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 670 [] class_Orderings_Opreorder(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 671 [] class_Orderings_Olinorder(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 672 [] class_Orderings_Oorder(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 673 [] class_Power_Opower(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 674 [] class_Int_Onumber(tc_nat). % 177.80/177.83 ** KEPT (pick-wt=2): 675 [] class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 676 [] class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 677 [] class_Ring__and__Field_Oordered__comm__semiring__strict(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 678 [] class_Ring__and__Field_Oring__1__no__zero__divisors(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 679 [] class_Ring__and__Field_Oordered__semiring__strict(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 680 [] class_OrderedGroup_Opordered__comm__monoid__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 681 [] class_Ring__and__Field_Oring__no__zero__divisors(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 682 [] class_OrderedGroup_Ocancel__ab__semigroup__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 683 [] class_Ring__and__Field_Oordered__ring__strict(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 684 [] class_OrderedGroup_Opordered__ab__group__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 685 [] class_OrderedGroup_Olordered__ab__group__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 686 [] class_OrderedGroup_Ocancel__semigroup__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 687 [] class_Ring__and__Field_Ono__zero__divisors(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 688 [] class_Ring__and__Field_Oordered__semidom(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 689 [] class_Ring__and__Field_Ocomm__semiring__1(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 690 [] class_OrderedGroup_Oab__semigroup__mult(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 691 [] class_OrderedGroup_Ocomm__monoid__mult(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 692 [] class_OrderedGroup_Oab__semigroup__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 693 [] class_Ring__and__Field_Opordered__ring(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 694 [] class_Ring__and__Field_Ocomm__semiring(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 695 [] class_OrderedGroup_Ocomm__monoid__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 696 [] class_Ring__and__Field_Ozero__ne_q__one(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 697 [] class_Ring__and__Field_Oordered__idom(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 698 [] class_Ring__and__Field_Osemiring__1(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 699 [] class_Ring__and__Field_Osemiring__0(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 700 [] class_OrderedGroup_Oab__group__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 701 [] class_Ring__and__Field_Omult__zero(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 702 [] class_OrderedGroup_Omonoid__mult(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 703 [] class_Ring__and__Field_Osemiring(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 704 [] class_OrderedGroup_Omonoid__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 705 [] class_OrderedGroup_Ogroup__add(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 706 [] class_Divides_Osemiring__div(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 707 [] class_Ring__and__Field_Oring(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 708 [] class_Ring__and__Field_Oidom(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 709 [] class_Orderings_Opreorder(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 710 [] class_Orderings_Olinorder(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 711 [] class_Divides_Oring__div(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 712 [] class_Orderings_Oorder(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 713 [] class_Int_Oring__char__0(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 714 [] class_Int_Onumber__ring(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 715 [] class_Power_Opower(tc_Int_Oint). % 177.80/177.83 ** KEPT (pick-wt=2): 716 [] class_Int_Onumber(tc_Int_Oint). % 177.80/177.83 Following clause subsumed by 450 during input processing: 0 [copy,450,flip.1] A=A. % 177.80/177.83 450 back subsumes 449. % 177.80/177.83 450 back subsumes 448. % 177.80/177.83 450 back subsumes 411. % 177.80/177.83 >>>> Starting back demodulation with 452. % 177.80/177.83 >>>> Starting back demodulation with 454. % 177.80/177.83 >>>> Starting back demodulation with 456. % 177.80/177.83 >>>> Starting back demodulation with 458. % 177.80/177.83 >> back demodulating 413 with 458. % 177.80/177.83 >>>> Starting back demodulation with 460. % 177.80/177.83 Following clause subsumed by 462 during input processing: 0 [copy,462,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). % 177.80/177.83 >>>> Starting back demodulation with 464. % 177.80/177.83 >>>> Starting back demodulation with 468. % 177.80/177.83 >>>> Starting back demodulation with 470. % 177.80/177.83 >>>> Starting back demodulation with 473. % 177.80/177.83 ** KEPT (pick-wt=11): 718 [copy,475,flip.1] c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat)=c_HOL_Oplus__class_Oplus(c_Suc(A),B,tc_nat). % 177.80/177.83 >>>> Starting back demodulation with 477. % 177.80/177.83 ** KEPT (pick-wt=15): 719 [copy,482,flip.1] c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat)=c_Divides_Odiv__class_Odiv(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat). % 177.80/177.83 >>>> Starting back demodulation with 484. % 177.80/177.83 >> back demodulating 436 with 484. % 177.80/177.83 >> back demodulating 406 with 484. % 177.80/177.83 >>>> Starting back demodulation with 486. % 177.80/177.83 >> back demodulating 435 with 486. % 177.80/177.83 >> back demodulating 414 with 486. % 177.80/177.83 >> back demodulating 405 with 486. % 177.80/177.83 >>>> Starting back demodulation with 488. % 177.80/177.83 >>>> Starting back demodulation with 490. % 177.80/177.83 Following clause subsumed by 591 during input processing: 0 [copy,491,flip.1] c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,B,tc_nat),c_HOL_Otimes__class_Otimes(A,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(A,C,tc_nat),c_HOL_Otimes__class_Otimes(A,B,tc_nat),tc_nat). % 177.80/177.83 >>>> Starting back demodulation with 494. % 177.80/177.83 >>>> Starting back demodulation with 496. % 177.80/177.83 >>>> Starting back demodulation with 498. % 177.80/177.83 >>>> Starting back demodulation with 500. % 177.80/177.83 >>>> Starting back demodulation with 503. % 177.80/177.83 ** KEPT (pick-wt=15): 726 [copy,504,flip.1] c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(A,B,tc_nat),C,tc_nat). % 177.80/177.83 ** KEPT (pick-wt=11): 727 [copy,505,flip.1,demod,528,585] c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat). % 177.80/177.83 Following clause subsumed by 506 during input processing: 0 [copy,506,flip.1] c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat)=c_HOL_Oplus__class_Oplus(B,c_HOL_Oplus__class_Oplus(A,C,tc_nat),tc_nat). % 177.80/177.83 >>>> Starting back demodulation with 508. % 177.80/177.83 >> back demodulating 493 with 508. % 177.80/177.83 >>>> Starting back demodulation with 510. % 177.80/177.83 ** KEPT (pick-wt=8): 728 [copy,511,flip.1,demod,528,585] c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_HOL_Ominus__class_Ominus(A,A,tc_nat). % 177.80/177.83 >>>> Starting back demodulation with 514. % 177.80/177.83 >>>> Starting back demodulation with 517. % 177.80/177.83 >>>> Starting back demodulation with 520. % 177.80/177.83 >>>> Starting back demodulation with 524. % 177.80/177.83 >> back demodulating 519 with 524. % 177.80/177.83 >> back demodulating 513 with 524. % 177.80/177.83 >> back demodulating 184 with 524. % 177.80/177.83 >>>> Starting back demodulation with 526. % 177.80/177.83 >>>> Starting back demodulation with 528. % 177.80/177.83 >> back demodulating 516 with 528. % 177.80/177.83 >> back demodulating 511 with 528. % 177.80/177.83 >> back demodulating 509 with 528. % 177.80/177.83 >> back demodulating 505 with 528. % 177.80/177.83 >> back demodulating 502 with 528. % 177.80/177.83 >> back demodulating 485 with 528. % 177.80/177.83 >> back demodulating 483 with 528. % 177.80/177.83 >> back demodulating 481 with 528. % 177.80/177.83 >> back demodulating 465 with 528. % 177.80/177.83 >> back demodulating 461 with 528. % 177.80/177.83 >> back demodulating 457 with 528. % 177.80/177.83 >> back demodulating 455 with 528. % 177.80/177.83 >> back demodulating 445 with 528. % 177.80/177.83 >> back demodulating 442 with 528. % 177.80/177.83 >> back demodulating 441 with 528. % 177.80/177.83 >> back demodulating 438 with 528. % 177.80/177.83 >> back demodulating 437 with 528. % 177.80/177.83 >> back demodulating 434 with 528. % 177.80/177.83 >> back demodulating 417 with 528. % 177.80/177.83 >> back demodulating 416 with 528. % 177.80/177.83 >> back demodulating 410 with 528. % 177.80/177.83 >> back demodulating 407 with 528. % 177.80/177.83 >> back demodulating 339 with 528. % 177.80/177.83 >> back demodulating 326 with 528. % 177.80/177.83 >> back demodulating 317 with 528. % 177.80/177.83 >> back demodulating 310 with 528. % 177.80/177.83 >> back demodulating 309 with 528. % 177.80/177.83 >> back demodulating 290 with 528. % 177.80/177.83 >> back demodulating 289 with 528. % 177.80/177.83 >> back demodulating 288 with 528. % 177.80/177.83 >> back demodulating 277 with 528. % 177.80/177.83 >> back demodulating 270 with 528. % 177.80/177.83 >> back demodulating 267 with 528. % 177.80/177.83 >> back demodulating 266 with 528. % 177.80/177.83 >> back demodulating 265 with 528. % 177.80/177.83 >> back demodulating 264 with 528. % 177.80/177.83 >> back demodulating 259 with 528. % 177.80/177.83 >> back demodulating 258 with 528. % 177.80/177.83 >> back demodulating 257 with 528. % 177.80/177.83 >> back demodulating 255 with 528. % 177.80/177.83 >> back demodulating 254 with 528. % 177.80/177.83 >> back demodulating 253 with 528. % 177.80/177.83 >> back demodulating 252 with 528. % 177.80/177.83 >> back demodulating 251 with 528. % 177.80/177.83 >> back demodulating 250 with 528. % 177.80/177.83 >> back demodulating 249 with 528. % 177.80/177.83 >> back demodulating 248 with 528. % 177.80/177.83 >> back demodulating 247 with 528. % 177.80/177.83 >> back demodulating 201 with 528. % 177.80/177.83 >> back demodulating 194 with 528. % 177.80/177.83 >> back demodulating 193 with 528. % 177.80/177.83 >> back demodulating 192 with 528. % 177.80/177.83 >> back demodulating 191 with 528. % 177.80/177.83 >> back demodulating 190 with 528. % 177.80/177.84 >> back demodulating 185 with 528. % 177.80/177.84 >> back demodulating 179 with 528. % 177.80/177.84 >> back demodulating 178 with 528. % 177.80/177.84 >> back demodulating 177 with 528. % 177.80/177.84 >> back demodulating 176 with 528. % 177.80/177.84 >> back demodulating 173 with 528. % 177.80/177.84 >> back demodulating 170 with 528. % 177.80/177.84 >> back demodulating 162 with 528. % 177.80/177.84 >> back demodulating 161 with 528. % 177.80/177.84 >> back demodulating 159 with 528. % 177.80/177.84 >> back demodulating 149 with 528. % 177.80/177.84 >> back demodulating 148 with 528. % 177.80/177.84 >> back demodulating 144 with 528. % 177.80/177.84 >> back demodulating 138 with 528. % 177.80/177.84 >> back demodulating 129 with 528. % 177.80/177.84 >> back demodulating 127 with 528. % 177.80/177.84 >> back demodulating 109 with 528. % 177.80/177.84 >> back demodulating 106 with 528. % 177.80/177.84 >> back demodulating 105 with 528. % 177.80/177.84 >> back demodulating 100 with 528. % 177.80/177.84 >> back demodulating 99 with 528. % 177.80/177.84 >> back demodulating 98 with 528. % 177.80/177.84 >> back demodulating 97 with 528. % 177.80/177.84 >> back demodulating 95 with 528. % 177.80/177.84 >> back demodulating 94 with 528. % 177.80/177.84 >> back demodulating 93 with 528. % 177.80/177.84 >> back demodulating 88 with 528. % 177.80/177.84 >> back demodulating 48 with 528. % 177.80/177.84 >> back demodulating 47 with 528. % 177.80/177.84 >> back demodulating 46 with 528. % 177.80/177.84 >> back demodulating 45 with 528. % 177.80/177.84 >>>> Starting back demodulation with 530. % 177.80/177.84 >>>> Starting back demodulation with 532. % 177.80/177.84 >>>> Starting back demodulation with 534. % 177.80/177.84 >>>> Starting back demodulation with 536. % 177.80/177.84 >> back demodulating 529 with 536. % 177.80/177.84 >>>> Starting back demodulation with 538. % 177.80/177.84 >>>> Starting back demodulation with 540. % 177.80/177.84 >> back demodulating 531 with 540. % 177.80/177.84 549 back subsumes 542. % 177.80/177.84 >>>> Starting back demodulation with 552. % 177.80/177.84 >>>> Starting back demodulation with 554. % 177.80/177.84 >> back demodulating 551 with 554. % 177.80/177.84 >>>> Starting back demodulation with 556. % 177.80/177.84 >> back demodulating 387 with 556. % 177.80/177.84 >> back demodulating 366 with 556. % 177.80/177.84 >>>> Starting back demodulation with 563. % 177.80/177.84 >>>> Starting back demodulation with 568. % 177.80/177.84 >>>> Starting back demodulation with 575. % 177.80/177.84 >>>> Starting back demodulation with 577. % 177.80/177.84 >>>> Starting back demodulation with 580. % 177.80/177.84 >>>> Starting back demodulation with 585. % 177.80/177.84 >> back demodulating 582 with 585. % 177.80/177.84 >> back demodulating 579 with 585. % 177.80/177.84 >> back demodulating 573 with 585. % 177.80/177.84 >> back demodulating 571 with 585. % 177.80/177.84 >> back demodulating 565 with 585. % 177.80/177.84 >> back demodulating 562 with 585. % 177.80/177.84 >> back demodulating 560 with 585. % 177.80/177.84 >> back demodulating 558 with 585. % 177.80/177.84 >> back demodulating 549 with 585. % 177.80/177.84 >> back demodulating 527 with 585. % 177.80/177.84 >> back demodulating 337 with 585. % 177.80/177.84 ** KEPT (pick-wt=16): 845 [copy,587,flip.1,demod,612,flip.1] c_Divides_Odiv__class_Odiv(c_Suc(A),B,tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat),B,tc_nat). % 177.80/177.84 ---> New Demodulator: 846 [new_demod,845] c_Divides_Odiv__class_Odiv(c_Suc(A),B,tc_nat)=c_Divides_Odiv__class_Odiv(c_HOL_Oplus__class_Oplus(A,c_Int_Onumber__class_Onumber__of(c_Int_OBit1(c_Int_OPls),tc_nat),tc_nat),B,tc_nat). % 177.80/177.84 >>>> Starting back demodulation with 590. % 177.80/177.84 Following clause subsumed by 591 during input processing: 0 [copy,591,flip.1] c_HOL_Oplus__class_Oplus(A,B,tc_nat)=c_HOL_Oplus__class_Oplus(B,A,tc_nat). % 177.80/177.84 591 back subsumes 491. % 177.80/177.84 >>>> Starting back demodulation with 595. % 177.80/177.84 >> back demodulating 589 with 595. % 177.80/177.84 >>>> Starting back demodulation with 597. % 177.80/177.84 >>>> Starting back demodulation with 600. % 177.80/177.84 >>>> Starting back demodulation with 603. % 177.80/177.84 >>>> Starting back demodulation with 606. % 177.80/177.84 ** KEPT (pick-wt=11): 849 [copy,608,flip.1] c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat). % 177.80/177.84 >>>> Starting back demodulation with 612. % 177.80/177.84 >> back demodulating 605 with 612. % 177.80/177.84 >> back demodulating 602 with 612. % 177.80/177.84 >> back demodulating 599 with 612. % 177.80/177.84 >> back demodulating 587 with 612. % 177.80/177.84 >>>> Starting back demodulation with 615. % 177.80/177.84 >>>> Starting back demodulation with 617. % 177.80/177.84 >> back demodulating 539 with 617. % 177.80/177.84 >> back demodulating 537 with 617. % 177.80/177.84 >> back demodulating 535 with 617. % 177.80/177.84 >> back demodulating 533 with 617. % 177.80/177.84 >>>> Starting back demodulation with 622. % 177.80/177.84 >> back demodulating 614 with 622. % 177.80/177.84 >>>> Starting back demodulation with 624. % 177.80/177.84 >>>> Starting back demodulation with 627. % 177.80/177.84 >> back demodulating 623 with 627. % 177.80/177.84 >> back demodulating 616 with 627. % 177.80/177.84 >>>> Starting back demodulation with 630. % 177.80/177.84 >>>> Starting back demodulation with 633. % 177.80/177.84 >>>> Starting back demodulation with 635. % 177.80/177.84 >> back demodulating 631 with 635. % 177.80/177.84 >> back demodulating 395 with 635. % 177.80/177.84 >> back demodulating 393 with 635. % 177.80/177.84 >> back demodulating 342 with 635. % 177.80/177.84 >> back demodulating 341 with 635. % 177.80/177.84 >> back demodulating 340 with 635. % 177.80/177.84 >> back demodulating 338 with 635. % 177.80/177.84 >> back demodulating 336 with 635. % 177.80/177.84 >> back demodulating 328 with 635. % 177.80/177.84 >> back demodulating 327 with 635. % 177.80/177.84 >>>> Starting back demodulation with 637. % 177.80/177.84 >>>> Starting back demodulation with 642. % 177.80/177.84 Following clause subsumed by 644 during input processing: 0 [copy,644,flip.1] c_HOL_Otimes__class_Otimes(A,B,tc_nat)=c_HOL_Otimes__class_Otimes(B,A,tc_nat). % 177.80/177.84 Following clause subsumed by 475 during input processing: 0 [copy,718,flip.1] c_HOL_Oplus__class_Oplus(c_Suc(A),B,tc_nat)=c_HOL_Oplus__class_Oplus(A,c_Suc(B),tc_nat). % 177.80/177.84 Following clause subsumed by 482 during input processing: 0 [copy,719,flip.1] c_Divides_Odiv__class_Odiv(A,c_HOL_Otimes__class_Otimes(B,C,tc_nat),tc_nat)=c_Divides_Odiv__class_Odiv(c_Divides_Odiv__class_Odiv(A,B,tc_nat),C,tc_nat). % 177.80/177.84 Following clause subsumed by 504 during input processing: 0 [copy,726,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,c_HOL_Oplus__class_Oplus(B,C,tc_nat),tc_nat). % 177.80/177.84 Following clause subsumed by 739 during input processing: 0 [copy,727,flip.1] c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat). % 177.80/177.84 Following clause subsumed by 736 during input processing: 0 [copy,728,flip.1] c_HOL_Ominus__class_Ominus(A,A,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat). % 177.80/177.84 >>>> Starting back demodulation with 730. % 177.80/177.84 >>>> Starting back demodulation with 732. % 177.80/177.84 >>>> Starting back demodulation with 735. % 177.80/177.84 Following clause subsumed by 728 during input processing: 0 [copy,736,flip.1] c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_HOL_Ominus__class_Ominus(A,A,tc_nat). % 177.80/177.84 >>>> Starting back demodulation with 738. % 177.80/177.84 Following clause subsumed by 727 during input processing: 0 [copy,739,flip.1] c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat)=c_HOL_Ominus__class_Ominus(A,c_HOL_Oplus__class_Oplus(A,B,tc_nat),tc_nat). % 177.80/177.84 >>>> Starting back demodulation with 741. % 177.80/177.84 >>>> Starting back demodulation with 743. % 177.80/177.84 >> back demodulating 724 with 743. % 177.80/177.84 >> back demodulating 723 with 743. % 177.80/177.84 >> back demodulating 722 with 743. % 177.80/177.84 >>>> Starting back demodulation with 745. % 177.80/177.84 >> back demodulating 721 with 745. % 177.80/177.84 >> back demodulating 720 with 745. % 177.80/177.84 746 back subsumes 439. % 177.80/177.84 >>>> Starting back demodulation with 750. % 177.80/177.84 >> back demodulating 717 with 750. % 177.80/177.84 >>>> Starting back demodulation with 752. % 177.80/177.84 >>>> Starting back demodulation with 826. % 177.80/177.84 >>>> Starting back demodulation with 828. % 177.80/177.84 >>>> Starting back demodulation with 830. % 177.80/177.84 >>>> Starting back demodulation with 838. % 177.80/177.84 >>>> Starting back demodulation with 843. % 177.80/177.84 >>>> Starting back demodulation with 846. % 177.80/177.84 >> back demodulating 835 with 846. % 177.80/177.84 >> back demodulating 765 with 846. % 177.80/177.84 >>>> Starting back demodulation with 848. % 177.80/177.84 Following clause subsumed by 608 during input processing: 0 [copy,849,flip.1] c_Divides_Odiv__class_Omod(c_HOL_Otimes__class_Otimes(A,B,tc_nat),A,tc_nat)=c_Int_Onumber__class_Onumber__of(c_Int_OMin,tc_nat). % 177.80/177.84 >>>> Starting back demodulation with 851. % 177.80/177.84 >>>> Starting back demodulation with 853. % 177.80/177.84 >> back demodulating 827 with 853. % 177.80/177.84 >>>> Starting back demodulation with 855. % 177.80/177.84 >>>> Starting back demodulation with 857. % 177.80/177.84 >> back demodulating 825 with 857. % 177.80/177.84 >>>> Starting back demodulation with 859. % 177.80/177.84 >>>> Starting back demodulation with 861. % 177.80/177.84 >>>> Starting back demodulation with 863. % 177.80/177.84 >>>> Starting back demodulation with 865. % 177.80/177.84 >> back demodulating 858 with 865. % 177.80/177.84 >> back demodulating 856 with 865. % 177.80/177.84 >> back demodulating 854 with 865. % 179.77/179.89 >> back demodulating 852 with 865. % 179.77/179.89 % 179.77/179.89 ======= end of input processing ======= % 179.77/179.89 % 179.77/179.89 =========== start of search =========== % 179.77/179.89 % 179.77/179.89 % 179.77/179.89 Resetting weight limit to 2. % 179.77/179.89 % 179.77/179.89 % 179.77/179.89 Resetting weight limit to 2. % 179.77/179.89 % 179.77/179.89 sos_size=247 % 179.77/179.89 % 179.77/179.89 Search stopped because sos empty. % 179.77/179.89 % 179.77/179.89 % 179.77/179.89 Search stopped because sos empty. % 179.77/179.89 % 179.77/179.89 ============ end of search ============ % 179.77/179.89 % 179.77/179.89 -------------- statistics ------------- % 179.77/179.89 clauses given 248 % 179.77/179.89 clauses generated 194434 % 179.77/179.89 clauses kept 723 % 179.77/179.89 clauses forward subsumed 159 % 179.77/179.89 clauses back subsumed 11 % 179.77/179.89 Kbytes malloced 10742 % 179.77/179.89 % 179.77/179.89 ----------- times (seconds) ----------- % 179.77/179.89 user CPU time 2.13 (0 hr, 0 min, 2 sec) % 179.77/179.89 system CPU time 0.01 (0 hr, 0 min, 0 sec) % 179.77/179.89 wall-clock time 179 (0 hr, 2 min, 59 sec) % 179.77/179.89 % 179.77/179.89 Process 832 finished Wed Jul 27 06:46:06 2022 % 179.77/179.89 Otter interrupted % 179.77/179.89 PROOF NOT FOUND %------------------------------------------------------------------------------